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An investigation of squish generated turbulence in. I.C. engines Cameron, Cecilia Dianne 1985

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AN INVESTIGATION OF SQUISH GENERATED TURBULENCE IN. I.C. ENGINES By CECILIA DIANNE CAMERON B.A.Sc, The University of British Columbia, 1981 B.Sc, The University of British Columbia, 1977 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of Mechanical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1985 © CECILIA DIANNE CAMERON» 1985 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date ( O r . T n ^ U l Wj T DE-6(3/81) ABSTRACT Experiments were performed with a single cylinder C.F.R. engine to provide data for the evaluation of the squish designs. Several reference squish chambers were manufactured for the C.F.R. engine. Flow f i e l d data was obtained via hot wire anemometer measurements taken in the cylinder during motored operation of the engine. Pressure data recorded while the engine was operated on natural gas yielded mass burn rate information. Mass burn rate analysis of cylinder pressure data shows the squish design to have greatest impact on the main combustion period (2% to 85% mass burned). A comparison of the reference squish design i n these experiments to the disc chamber shows a 32% reduction in the combustion duration and a 30% increase i n peak pressure occuring 5 crank angle degrees earlier. The squish-jet design provided the additional effect of a reduction i n the ignition delay time (spark to 2% mass burned). The squish-jet design resulted in a reduction of the ignition delay time by 3 crank angle degrees and i n a 4% increase i n peak pressure occuring 3 crank angle degrees earlier compared to the reference squish chamber. The total combustion duration was 5% less with the squish-jet design. - i i -TABLE OF CONTENTS Page ABSTRACT i i LIST OF TABLES v i LIST OF FIGURES v i i NOMENCLATURE x ACKNOWLEDGEMENT x i i 1. INTRODUCTION 1 1.1 General Discussion 1 1.2 The Turbulent Flow Field i n an Engine 2 1.3 Objectives and Scope of Work 6 2. LITERATURE REVIEW 7 2.1 Introduction 7 2.2 Turbulence Measurements i n Engines 7 2.3 Combustion Experiments in Engines 11 3. THE SQUISH COMBUSTION CHAMBER 13 3.1 Introduction 13 3.2 Squish Velocity Calculations 13 3.3 The Squish Chamber Experiments 16 4. APPARATUS AND INSTRUMENTATION 17 4.1 Introduction 17 4.2 Engine and Test Bed 17 4.3 Squish Piston Inserts 18 4.4 Air Supply 19 4.5 Gas Supply 19 4.6 Instrumentation 19 4.7 Data Acquisition System 21 5. EXPERIMENTAL METHOD 23 5.1 Introduction 23 5.2 Motored Engine Tests 23 5.2.1 Hot Wire Preparation 24 5.2.2 Routine Experimental Procedure 25 5.2.3 Flow Measurement Locations 26 5.3 Combustion Tests 26 6. DATA ANALYSIS 27 6.1 Introduction 27 6.2 Pressure Signal Processing 27 6.3 Anemometer Signal Processing 27 6.4 Flow Field Data 32 - i i i -TABLE OF CONTENTS (Continued) Page 6.4.1 Ensemble Averaged Mean Velocity and Turbulence Intensity 33 6.4.2 Cycle by Cycle Time Averaged Means and RMS Velocity 35 6.4.3 Time Scale Analysis 38 6.5 Combustion Data 39 7. DISCUSSION OF RESULTS 40 7.1 Introduction 40 7.2 Flow Field Results 40 7.2.1 Ensemble Averaging vs. Time Averaging 40 7.2.2 Standard Squish Piston (Piston A) Results 42 7.2.3 Squish-Jet Piston (Piston B) Results 44 7.2.4 Comparison of Geometries 46 7.3 Combustion Results 48 8. CONCLUSIONS AND RECOMMENDATIONS 51 BIBLIOGRAPHY 53 APPENDIX A - CALIBRATION CURVES 56 APPENDIX B - HOT WIRE ANEMOMETER CALIBRATION 59 1. Welding and Preparation 59 2. Calibration 59 3. Analytical Procedure for Correlation 60 4. Hot Wire Calibration Computer Program HWCAL 62 APPENDIX C - DATA ACQUISITION PROGRAMS 67 1. Data Acquisition from C.F.R. (CDAQ) 67 2. Transfer of Digital Data to MTS (BYTRD) 72 APPENDIX D - HOT WIRE ANEMOMETER DATA PROCESSING PROGRAMS 75 1. Instantaneous Velocity Evaluation and Ensemble Averaging (ANEM) 75 2. Cycle by Cycle Time Averaged Mean and RMS Velocity (TRAP) 83 3. Nonstationary Analysis (NOTIME) 91 4. Time Scale Analysis (PEAK) 97 APPENDIX E - COMBUSTION DATA PROCESSING 104 1. Pressure Evaluation and Ensemble Averaging from Digital Data (PENH) 104 2. Geometric Analysis of Spherical Flame Front (DFLAME) 108 3. Burning Rate Analysis (MASBRN) 120 APPENDIX F - PROPERTIES OF B.C. NATURAL GAS 150 - iv -LIST OF TABLES Page I. Engine Specifications 153 II. Hot Wire Probe and Anemometer Specifications 154 / - v -LIST OF FIGURES Page 1.1 The squish combustion chamber 155 3.1 The standard squish chamber 156 3.2 The squish-jet chamber 157 3.3 The effect of clearance height on squish velocity 158 3.4 The effect of the squish-jet design on squish velocity 159 4.1 Schematic of experimental setup and instrumentation 160 4.2 The C.F.R. engine 161 4.3 The squish piston inserts 162 4.4 Photograph of squish piston inserts 163 4.5 Top and side view of C.F.R. combustion chamber 164 4.6 Fitting for hot wire probe 165 4.7 Schematic of data acquisition 166 4.8 Photograph of data acquisition system 167 4.9 Photograph of optical trigger system 168 5.1 Hot wire probe locations 169 5.2 Hot wire probe orientation 170 7.1 Three consecutive instantaneous velocity records 171 7.2 Comparison of time averaged and ensemble averaged mean velocity 172 7.3 Cyclic variation of the mean velocity 173 7.4 Comparison of time and ensemble averaging techniques for the evaluation of turbulence intensity 174 7.5 Turbulence intensity evaluated with Lancaster's nonstationary technique 175 - v i -LIST OF FIGURES (Continued) Page 7.6 Mean velocity and turbulence intensity for Piston A; h Q = 3.5 mm; probe at cup edge 176 7.7 Mean velocity and turbulence intensity for Piston A; h £ = 1.5 mm; probe at cup edge 177 7.8 Mean velocity and turbulence intensity for Piston A; h c = 1.5 mm; probe at chamber center 178 7.9 Mean velocity and turbulence intensity for Piston A; h c = 1.5 mm; probe at cup edge; 9 = 90° 179 7.10 Mean velocity and turbulence intensity for Piston A; h c = 1.5 mm; probe at chamber center; 6 = 90° 180 7.11 Comparison of mean velocity traces for Piston A; h c = 3.5 and 1.5 mm; probe at cup edge 181 7.12 Comparison of relative turbulence intensities for Piston A; h c = 3.5 and 1.5 mm; probe at cup edge 182 7.13 Mean velocity and turbulence intensity for Piston B; h c - 3.5 mm; probe at cup edge 183 7.14 Mean velocity and turbulence intensity for Piston B; h c = 1.5 mm; probe at cup edge 184 7.15 Mean velocity and turbulence intensity for Piston B; h c = 1.5 mm; probe at chamber center 185 7.16 Mean velocity and turbulence intensity for Piston B; h £ = 1.5 mm; probe inside cup 186 7.17 Comparison of relative turbulence intensities for Piston B; h c = 3.5 and 1.5 mm; probe at cup edge 187 7.18 Comparison of mean velocity traces for Pistons A and B; h £ = 1.5 mm; probe at cup edge 188 7.19 Comparison of relative turbulence intensities for Pistons A and B; h c = 1.5 mm; probe at cup edge 189 7.20 Comparison of the relative probability distributions of small scale turbulence structure for Piston A at the chamber center and at the cup edge 190 7.21 Comparison of relative probability distributions of small scale turbulence structure at the chamber center for Piston A and the fl a t piston 191 - v i i -LIST OF FIGURES (Continued) Page 7.22 Comparison of relative probability distributions of small scale turbulence structure at the cup edge for Pistons A and B 192 7.23 Comparison of relative probability distributions of small scale turbulence structure at the chamber center for Pistons A and B 193 7.24 Comparison of pressure history for Pistons A and B and the f l a t piston for a spark timing of 30° BTDC 194 7.25 Comparison of mass fraction burn curves for the fl a t piston and for Piston A at a spark timing of 30° BTDC 195 7.26 Comparison of mass fr i c t i o n burn curves for Pistons A and B at a spark timing of 30° BTDC 196 7.27 Comparison of mass fraction burn curves for a l l three pistons at a spark timing of 30° BTDC 197 7.28 Comparison of mass fraction burn curves for Pistons A and B at a spark timing of 25° BTDC 198 A.l Calibration curve for laminar flow element 57 A.2 Calibration curve for orifice metre 58 E.l Flame geometry for a section through a flame above piston bowl (flame section 1) 109 E.2 Flame geometry for a section through a flame in a piston bowl (flame section 2) 110 - v i i i -NOMENCLATURE A area, m2 a,b calibration constants for hot wire correlation C constant pressure specific heat, J/k K P 8 D engine bore, m d wire diameter, m H depth of bowl in squish piston, m h heat transfer coefficient, W/m2 K h^ clearance height, m I electric current, amps k thermal conductivity, W/m K L t integral time scale, s 1 wire length, m N number of engine cycles Nu Nusselt number P pressure, Pa R resistance, ohms R resistance of wire at operating condition, ohms op R autocorrelation coefficient T S distance of piston from TDC, m T temperature, K U velocity, m/s U(i ,8 ) instantaneous velocity at crank angel 6 in cycle i , m/s U mean velocity with respect to time, m/s U(6) true ensemble averaged mean velocity, m/s - ix -U„(i) average (time) velocity i n window 9 for record i , m/s o Ufl U(i) ensemble averaged over N cycles, m/s o U cyclic variation i n mean velocity, m/s rms u'(0) true ensemble averaged turbulence intensity, m/s u'(i) time averaged turbulence intensity i n cycle i , m/s 6 ul u(i) ensemble averaged over N cycles o V volume, m^  a temperature coefficient B orientation angle Y specific heat ratio X micro time scale, s t e crank angle T correlation time, s U viscosity, N.s/m2 subscripts 0 reference condition B squish piston bowl g gas P piston Ref reference condition SA squish piston A SB squish piston B SC squish piston B channel t time, s w wire X length, m - x -ACKNOWLEDGEMENTS The author would like to acknowledge the guidance and support of Professor Evans during the course of the thesi s work* Professors H i l l and Hauptmann are also acknowledged for numerous enlightening discussions and contributions. Special thanks go to Mr. Allan Jones for the development and construction of the data acquisition system. John Hoar, John Wiebe, and Bruce Hansen machined the parts required for the experimental apparatus. P h i l l i p Hurren and John Richards helped in the design of the data acquisition system. - x i -1. INTRODUCTION 1. 1.1 General Discussion The combustion rate i n an internal combustion (I.C.) engine plays a key role in engine performance. Fast burning in engines produces a greater resistance to knock which allows operation at higher compression ratios and thus leads to increased engine efficiency. Fast burning also permits the use of leaner air-fuel mixtures [1]. Furthermore, fast combustion rates have been shown to reduce NO emissions and the cyclic variation of engine x performance [1,2]. Combustion rate i s thought to depend primarily upon flame front area, turbulence and the chemical kinetics of the mixture. To increase the combustion rate i n engines engineers must address two questions; how to increase the flame front area, and how to increase the propagation rate of the flame front into the unburned region. Combustion chamber geometry and turbulence enhancement during the combustion period are the major design variables investigators have focussed on to answer these questions. The effects of chamber geometry and the flow f i e l d are directly linked since chamber configuration does affect turbulence generation. Modern combustion chambers are designed with a large volume to surface area ratio (compact chambers) minimizing contact between the flame and the cylinder walls. With central ignition i n these chambers designers achieve a large flame front area and a reduction in heat transfer (due to minimal contact between flame and walls). Both are factors which contribute to an increase in burn rate. The turbulent flow f i e l d i n an engine i s the more dominant factor i n determining the combustion rate. The mechanism responsible for increased 2. burn rate i s s t i l l a subject of debate among researchers. The two most widely accepted theories of turbulent combustion in engines are the wrinkled flame front and turbulent entrainment theories. The wrinkled flame front model, f i r s t proposed by Damkohler [3], states that the turbulence distorts (wrinkles) the flame front thereby increasing the area available for molecular transport. Entrainment models have been developed by Tabaczynski [4] and Blizzard and Keck [5]. These models propose that a turbulent entrainment process is responsible for increased flame propagation. It i s assumed that laminar burning takes place in cells of size characterized by the Taylor micro-scale and rapid burning takes place along vortex tubes of size characterized by the Kolmogorov scale. The entrainment velocity i s assumed to be proportional to the turbulence intensity. Irrespective of these theories, the link between increased flame speed and turbulence has been firmly established through experiment. The work of Andrews et a l . [6] demonstrates that turbulence can be used to increase flame speeds. 1.2 The Turbulent Flow Field i n an Engine The flow f i e l d i n an engine i s primarily governed by the valve events and the piston motion. The shear flow past the intake valve is a major source of turbulence generation prior to the combustion period. After the intake valve closes this turbulence decays rapidly during the compression stroke. In conventional disc chambers very l i t t l e additional turbulence i s generated during the compression stroke as a result of the piston movement. This i s the c r i t i c a l period for the combustion process. Designers have taken two approaches towards the enhancement of 3. turbulence during compression. Modifications to the inlet port which produce high swirl in the intake jet have proven to increase turbulence levels prior to the combustion period. Also the combustion chamber can be designed so that turbulence is generated on the compression stroke as a result of the piston motion. This type of design i s called a squish chamber. A bowl i n piston type of squish chamber design i s shown schematically in Figure 1.1. As the piston approaches TDC on the compression stroke a pressure differential between the outside annualar area (squish area) and the inner area drives a radial jet inward. Thus an additional source of turbulence i s generated by the strong shear flow i n the jet motion during the latter phase of compression. The flow f i e l d quantities of interest i n an engine are the mean velocity, turbulence intensity, and the macro and micro scales of turbulence. The mean velocity characterizes the gas motion due to the valve events and the piston travel. The mean velocity i s defined to be the time average over a specific interval of the instantaneous velocity. The mean velocity U, i s : 1 T U = i / U dt (1.1) 1 0 where U i s the instantaneous velocity and T is the time interval. In an engine where the mean velocity i s periodic this type of definition can cause problems since the calculated mean w i l l be dependent upon the time interval chosen. This problem i s discussed i n detail i n the data analysis chapter. The turbulence intensity, u*, i s the root mean square of the velocity 4. f l u c t u a t i o n s about the mean. If the instantaneous v e l o c i t y i s wr i t t e n as: U = U + u (1.2) where u represents the f l u c t u a t i o n from the mean, then the turbulence i n t e n s i t y u', may be expressed as: r l r T - o , 1 / 2 u' = ft J [U - U ] 2 dt} (1.3) • 0 The scales of length and time describe the structure of the flow f i e l d . Length scale measurements are very d i f f i c u l t to obtain since they require measurements at two points simultaneously and c o r r e l a t i o n of vast amounts of data. Because of t h i s , i n engine research time scales are used to characterize the eddy siz e d i s t r i b u t i o n . The i n t e g r a l scale L^, i s evaluated from the i n t e g r a l of the autocorrelation c o e f f i c i e n t of the f l u c t u a t i n g v e l o c i t y at a s i n g l e point. The autocorrelation c o e f f i c i e n t R^, Is expressed by: = 1 J T u(T)u(t +T) ^ 0 u^ where T i s the c o r r e l a t i o n time. The i n t e g r a l time scale i s then given as: T L t = / R x d T (1.5) The i n t e g r a l scale characterizes the larger eddies of the flow f i e l d and 5. can be thought of as the mixing time scale. The Taylor micro scale is also obtained from the autocorrelation coefficient. For small values of the correlation time T the Taylor series expansion of the autocorrelation function describes a parabola. The microscale i s defined to be the point at which this parabola intersects the time correlation (T) axis: intersects the time correlation axis (x axis): A 2 = -2 O 2 R t / 8 T 2 ) | t = 0 (1.6) The micro scale describes the small scale structure of the flow. In the model proposed by Tennekes [7] i n which a turbulence structure can be thought of as consisting of tangled vortex tubes (much like spaghetti) the micro scale can be viewed as the typical time between vortex tubes as they are convected past a stationary observer. The turbulence intensity i s thought to be primarily responsible for the increased flame speed observed for turbulent conditions. This view i s supported by the results of Andrews et a l . [6] i n which a strong correlation between the intensity and turbulent burning velocity i s demonstrated. The role of turbulence scale i s thought to be important only in the i n i t i a l stages of combustion. There is l i t t l e evidence that scale affects the flame speed i n a fu l l y developed turbulent flame, although there is some indication that the micro scales are important to the Ignition delay process.. The ignition delay time is arbitrarily defined here to be the time required to burn two percent of the charge mass. Variation i n the ignition delay time i s usually considered to be responsible for the cyclic variation observed in cylinder pressure [5]. 6. 1.3 Objectives and Scope of Work The objective of this thesis was to investigate the effects of the squish chamber design on the flow f i e l d and combustion process in an I.C. engine. The specific focus of the investigation was the comparison of a reference squish chamber design to a new squish-jet chamber design proposed by Evans [8]. The squish-jet i s intended to be an improvement over the conventional design by providing enhanced turbulence production and mixing in the combustion region. It was the purpose of this study to provide experimental data for an i n i t i a l evaluation of the basic squish-jet design. A comparison of mass burn rate, combustion duration and pressure history was made for the two chamber designs; as well as flow f i e l d charateristics mean velocity and turbulence intensity. A series of experiments were designed to meet the objectives of the investigation. Several variations of the two squish designs were manufactured for a single cylinder C.F.R. engine. For each design flow f i e l d data were obtained with a hot wire anemometer for motored conditions, and pressure data was recorded while the engine was operated on natural gas. The experiments were also conducted for the standard C.F.R. disc chamber design as a basis of comparison. The data were processed to yield mass burn rate, combustion duration and the turbulence parameters of interest. The designs were then analyzed on a comparative basis. 7. 2. LITERATURE REVIEW 2.1 Introduction This chapter reviews the literature i n two areas relevant to the investigation. The f i r s t section reviews fundamental turbulence measure-ments i n engines. The second section i s concerned with combustion experi-ments made in engines of different types of geometry, and the correlation of combustion data with turbulence data. 2.2 Turbulence Measurements in Engines Semenov [9] was one of the pioneers i n engine turbulence studies. He investigated the intake and compression process in a C.F.R. engine with a shrouded intake valve and disc combustion chamber. By traversing a hot wire probe across the bore of the chamber he obtained spatial velocity gradients as well as the mean velocity and turbulence intensity. Evidence of large velocity gradients during the intake process confirmed the jet nature of the incoming flow. In comparison velocity gradients near TDC on the compression stroke were insignificant. He also found very l i t t l e spatial variation of the turbulence intensity near TDC. Semenov observed a strong correlation between the turbulence intensity during compression and the velocity gradient during intake. From this he concluded the shear flow through the intake valve was the primary source for turbulence during the compression stroke. Increased engine speed resulted in increased mean velocity and turbulence intensity; however, compression ratio increases yielded relatively small decreases in the two quantities. 8. Dent and Salama [10] were among the f i r s t investigators to measure turbulent time scales in engines. A fast Fourier Transform analyzer was used to obtain the correlation coefficient and spectral density function. The macro and micro time scales were computed from the correlation c o e f f i -cient. The measurements were performed i n two engines of different geometry; a disc chamber design, and a wedge (squish) design. In the disc chamber they found a general decrease i n the mean velocity and turbulence intensity during the compression stroke. In the squish chamber however, they found an increase i n the mean velocity during compression, although a correspond-ing increase in the turbulence intensity was not observed. The micro time scale was found to be virtually independent of geometry and the mean velocity during compression. Calculated values of the micro length scale ranged from 0.2 to 0.6 mm. The macro length scales were three to four times larger than this. Lancaster [11] studied the effects of engine speed, volumetric e f f i -ciency, and compression ratio on the flow f i e l d of an engine. The tests were performed i n a C.F.R. engine with a disc chamber and two intake configurations; shrouded valve (swirl), and a standard valve. A hot wire anemometer probe was used to obtain measurements of mean velocity, turbu-lence intensity, and turbulence time scales. Regardless of intake configuration, Lancaster found increased engine speed resulted in increased mean velocity and turbulence intensity. Throttling or decreased volumetric efficiency yielded similar trends. However, the values near TDC attained with the standard valve were approxi-mately half of those achieved with the shrouded valve. This was attributed to the high swirl velocity generated by the shrouded valve. The micro 9. time scale decreased with increased engine speed but was otherwise inde-pendent of operating conditions. The micro-time scale ranged from 0.05 to 0.25 milliseconds. Compression ratio had a relatively insignificant effect on mean velocity and turbulence intensity. The spectral distribution of the turbulent energy near TDC was also studied for the shrouded valve configuration. Most of the energy was contained in frequencies below 1 kHz . Lancaster used single point measurements with a t r i a x i a l probe. Close agreement between the intensities measured by the three sensors near TDC led him to conclude that the turbulence was isotropic. Witze [12] did a similar set of measurements in an engine with a squish combustion chamber. His major conclusions were that the mean velo-city and turbulence intensity are proportional to engine speed, and that the time scale i s inversely proportional to the engine speed. He also measured the spatial variation of the turbulence intensity near TDC and concluded the structure was not homogeneous. Witze's results for the mean velocity and turbulence intensity show an increase of both quantities during the compression stroke. The increase can be attributed to the bulk gas motion caused by the squish chamber. However, Witze argued that this i s not the production of new turbulence; but simply a magnification of the intake turbulence due to compression. James and Lucas [13] studied flow conditions within several frequency ranges. They used both a squish chamber and a disc chamber in their investigation. They found most of the turbulence energy was i n the frequency range below 700 Hz. They reported that the major effect of the squish chamber was the enhancement of the magnitude of the fluctuating velocities in the frequency range below 1600 Hz. Higher frequency 10. fluctuations appeared to be unaffected by combustion chamber geometry. They also found that the effectiveness of the squish chamber was a strong inverse function of the squish or clearance height. Haghgooie et a l . [14] took a somewhat different approach than other investigators by using uncalibrated hot wire signals to determine micro time scales in an engine. Their work was based on the assumption that there i s a definable small scale structure of the turbulence i n an engine similar to that postulated by Tennekes [7]. They analyzed the anemometer data to obtain the s t a t i s t i c a l distribution of the peak to peak time separation. They then interpreted the most probable time of this distribu-tion as the characteristic time of the small scale structure. This time scale was in the range of 0.1 to 0.25 milliseconds. They reported a shift to higher frequencies as engine speed increased. In summary then, fundamental turbulence measurements in engines established the following: i ) shear flow past the intake valve i s a major source of turbulence, i i ) turbulence intensity and mean velocity are proportional to engine speed, i i i ) turbulence length and time scales are inversely proportional to engine speed, iv) turbulence micro time scales are on the order of tenths of milliseconds, v) turbulence micro length scales are on the order of tenths of millimeters, vi) turbulence i s isotropic near TDC compression however i t i s not homogeneous, and v i i ) turbulence energy i s concentrated i n the low frequencies, below 1000 Hz. 11. 2.3 Combustion Experiments in Engines Studies i n which turbulence and combustion data are correlated for engines of different geometry are rare. Lancaster et a l . [15] correlated turbulence and combustion data for a disc chamber with and without "swirl". A modified Kreiger-Borman [16] heat release model was used to obtain the turbulent flame speed from cylinder pressure history. To separate thermal effects from those of turbulence the turbulent flame speed was normalized by the laminar flame speed. Operating conditions were identical to those for which turbulence measurements were obtained [11]. Turbulence intensity was varied by using shrouded and standard intake valves, as well as by changing engine speed. Lancaster et a l . concluded that the normalized flame speed was a linear function of turbulence intensity. The effect of turbulence scale on flame speed was found to be insignificant. However these tests were conducted for a limited range of turbulent micro scale, 1 to 2 mm. Nagayama et a l . [17] examined the effect of swirl and squish geo-metries on combustion duration. No flow measurements were taken in these experiments. They had four chamber configurations; disc, swirl, squish, and squish plus swirl. They found that squish and swirl both reduced combustion duration and that furthermore, they had distinctly separate effects on the combustion interval. Swirl was effective in the i n i t i a l stage of combustion; whereas, squish was most effective during the main stage of combustion. The two effects were additive and thus the combina-tion squish plus swirl chamber yielded the best results. More recently investigators have used engine simulation models to predict the effect of chamber geometry on combustion duration [18-21]. In general these models predict that squish type chambers give better 12. performance than disc chambers. In addition, the importance of central spark plug location is established by these models. Although there i s an abundance of engine performance data for a variety of chamber designs available in the literature [2,15,18,19,21-25], very few attempts have been made to isolate the effects which result i n one design's superiority over another. Thus progress towards defining the c r i t e r i a for optimal chamber design has been slow. 3. THE SQUISH COMBUSTION CHAMBER 13. 3.1 Introduction An i l l u s t r a t i o n of the conventional bowl in piston squish design i s shown in Figure 1.1. Although the chamber shown is in the piston i t is also possible to achieve the same effect with a f l a t piston and a recessed chamber in the head. The squish design i s intended to provide an additional source of tur-bulence on the compression stroke. In Figure 3.1 a schematic of the squish process i s shown. As the piston approaches TDC (compression) the relative compression in volume Vj in the figure Is higher than that in volume V 2« Thus, there i s a 'squish' velocity, U , as a i r moves from V across the DA. boundary A 3 into V 2« In this investigation a variation of the squish design, the squish-jet design proposed by Evans [8] w i l l be studied as well. A schematic of this design i s illustrated i n Figure 3.2. The concept here i s similar to that discussed above except that the channels (see Figure 3.2) provide an addi-tional route for the squished a i r . The desired results are an increase i n the relative turbulence intensity and enhanced mixture turbulence at the center of the chamber where the jets collide. Several embodiments of this design have been described by Evans [8]. In Figure 3.1 the conventional squish design is labelled Piston A and the squish-jet design in Figure 3.2 is labelled Piston B. This convention w i l l be used throughout the thesis. 3.2 Squish Velocity Calculations In this section a very simplified model w i l l be used to predict the squish velocity during the f i n a l stage of the compression stroke for each of the two designs. 14. To predict the squish v e l o c i t y f o r the conventional design the basic assumption i s that the density i s uniform throughout the chamber. The squish v e l o c i t y i s c a l c u l a t e d f o r the piston movement over one crank angle degree. From mass conservation the following equation can be written, U A- U A, U A-v 2 v 2 V, Vi The quantities U , U , A,, A-, A,, V,, and V, are defined i n Figure IT 3.1. Equation (3.1) can then be solved f o r the squish v e l o c i t y U , O n u USA = A f ^ ( A 1 V 2 " A2 V1>/( V1 + V2>} ( 3- 2) From Equation (3.2) i t can be seen that squish v e l o c i t y i s propor-t i o n a l to the piston speed (or engine speed) and that I t i s inversely proportional to area A 3. The area A 3 i s a function of the bowl diameter Dfi, the clearance height h c > and the distance of the piston from TDC, S. The p r e d i c t i o n of the squish v e l o c i t y f o r the squish-jet design i s s i m i l a r to that above except that now there i s an a d d i t i o n a l route for the gas. The design i s P i s t o n B i n Figure 3.2. Equation (3.1) i s rewritten as: U A 9 U A. II A k U A, U A 9 U A. P 2 SB 3 SC *• = P I SB 3 _ SC *» v 2 v 2 v 2 v x "• vl v x ^ ; In t h i s equation Ug B i s the squish v e l o c i t y normal to the area A 3 and U i s the squish v e l o c i t y (hereafter c a l l e d squish-jet v e l o c i t y ) normal to A^. The other terms i n the equation are defined i n Figure 3.2. An addi-t i o n a l equation i s required to solve for the new v e l o c i t y term U . This 15. is obtained by treating the problem with a parallel pipe flow method. The assumption is that the pressure drop of the flow across the boundary A3 is equal to that of the flow through the channels and across the boundary A^. The pressure drop w i l l be a function of the hydraulic radius and the velo-cit y head. Simultaneous solution of the equations for conservation of mass and head loss yields expressions for the squish velocity U , and the SB squish-jet velocity U . The squish velocity U c o i s : SC SB U {A2 - (Aj + A 2)[A 2(h + S)]/(V 1 + V 2)} U__ = - i - (3.4) A 3 + [2D (S + h )/(D (D + S + h ) ] 1 / 2 and the squish-jet velocity U i s : USB U 55 (3.5) S C {2D (S + h )/D (D + S + h )>1/2 It can be seen from both Equations (3.2) and (3.4) that the squish velocity across the piston face (U and U ) w i l l be a strong function of SA SB the clearance height. In Figure 3.3, the squish velocity calculated from Equation (3.2) is shown for two clearance heights, 3.5 and 1.5 mm. The geometric parameters for the C.F.R. engine were used in the calculations. From the graph i t can be seen that the squish velocity reaches a maximum at approximately 10° BTDC and decays rapidly to zero at TDC. It i s clear from this figure that clearance height is very important. The peak mean velo-city calculated for a clearance height of 1.5 mm i s almost twice that for a clearance height of 3.5 mm. In Figure 3.4 the effect of adding the squish-jet channels i s shown. The squish velocity across the face of the 16. piston i s reduced by about 30%. The squish-jet velocity i s consistently lower than U__ except near the peak which occurs at approximately 10° BTDC. D O 3.3 The Squish Chamber Experiments The method of predicting squish velocities outlined above was very simplified and not intended to yield quantitative results. Rather i t was employed as an aid i n designing the experiments. As a result of the calculations i t was decided to vary the clearance height and observe the effect. Three heights were selected 1.5, 2.5, and 3.5 mm. Both chamber designs were tested at these heights. The clearance height of 1.5 mm was the minimum that could be attained due to the clear-ance between the valves and the piston. The piston wall thickness and the placement of the channels for Piston B were the constraints governing the selection of bowl diameter. A bowl diameter of 1.5 inches resulted i n a 78% squish area expressed here as a percent and is defined to be the ratio of the area Aj (see Figure 3.1) to the total area (Aj^  + A 2 ) . Because i t was desirable to compare both flow and combustion data from case to case the compression ratio was kept constant. The bowl depth was varied to accommodate the various clearance heights. Hot wire anemometer measurements were made at the edge of the bowl and at the center of the chamber for each configuration. In addition, for Piston B a measurement was made with the probe inside the bowl opposite a channel at TDC. In summary, the experiments were designed to observe the effects of clearance height, and squish-jet channels on the flow f i e l d and combustion process. Tests were also conducted with a disc chamber operating at the same compression ratio as a standard for comparison. 4. APPARATUS AND INSTRUMENTATION 1 7 . 4.1 Introduction This investigation required test results operating with several combustion chamber designs. To f a c i l i t a t e changes of configuration for each test, a C.F.R. engine with a f l a t head was used i n conjunction with a squish piston design. Thus a change in combustion geometry required only a change of pistons. The engine was then instrumented to obtain pressure and flow f i e l d information. The instrumentation and engine are described in detail i n the following sections. 4.2 Engine and Test Bed A schematic of the experimental apparatus i s shown i n Figure 4.1 The engine used for the tests was a single cylinder C.F.R. coupled to a synchronous reluctance type motor by twin v-belts. Specifications for the engine are presented in Table I. The C.F.R. cylinder and head i s cast in one piece which has an adjustable height above the TDC postion of the piston to allow for variable compression ratio. For these experiments the following changes were necessary to the basic C.F.R. configuration: i) the pulley set was replaced to obtain a higher operating speed than the standard 900 RPM. The speed achieved was 1140 RPM, i i ) the shrouded intake valve was replaced by a standard intake valve to reduce the effects of inlet swirl, i i i ) the gasoline carburetor was removed and replaced with a venturi element so that the engine could be operated with natural gas, and 18. iv) the C.F.R. ignition system was replaced with a capacitive discharge ignition c i r c u i t . The synchronous motor was used to start the engine, to maintain constant speed, and to absorb the power developed by the engine when fired . The engine and motor are shown in Figure 4.2. 4.3 Squish Piston Inserts Seven pistons were required for the tests. Rather than manufacture a piston for each test, the original C.F.R. piston was bored through the crown and the inside wall threaded. Threaded Inserts were then manufactured for each experiment. The piston material was cast iron so steel was used i n the production of the inserts. Three basic designs were manufactured; the basic squish design (Piston A), the squish-jet design (Piston B), and the f l a t disc chamber design. The design drawings of these piston inserts are in Figure 4.3 and a photograph i s i n Figure 4.4. In Figure 4.3 case 1 corresponds to a clearance height of 1.5 mm; case 2 corresponds to a clearance height 3.5 mm. The two squish designs were altered to accommodate the three clearance heights used. The bowl diameter was held constant at 1.5 inches. Because the bottom of the Insert had to clear the top of the o i l ring the maximum depth of the bowl that could be achieved was 1.4 inches. This maximum depth was used for the test of minimum clearance height (1.5 mm). The bowl depth was decreased for the other tests so that a constant compression ratio was maintained throughout the experiments. The center line of the access port for the hot wire anemometer probe was 9 mm below the head. Because of this and the small clearance heights used a slot was milled i n the inserts to accommodate the probe. 19. 4.4 Air Supply The intake a i r for the engine was drawn into a 2.5 inch pipe through an orifice plate and into a surge tank. The air was then filtered as i t l e f t the surge tank and passed into the venturi. The intake a i r was not throttled at anytime. 4.5 Gas Supply The natural gas used as fuel was supplied from the building mains at a pressure of 5 psig to a pressure regulator where the pressure was reduced to 3 inches of water above atmospheric pressure. From the regulator the gas flowed f i r s t through a laminar flow element then through a control valve which was used to adjust the air/fuel ratio. From the control valve the gas flowed through 1/2 inch tubing to the venturi. 4.6 Instrumentation A schematic of the instrumentation layout Is shown i n Figure 4.1. Pressure measurements were made for combustion and motored operation. The location of the transducer for each of the operational modes Is shown in Figure 4.5. The pressure transducer installed in the cylinder was a Kistler 609C piezo electric transducer mounted in a steel sleeve. The transducer was recessed 2 mm to eliminate thermal shock effects as recommended by Benson [26]. The transducer signal was transmitted via low noise cable to a Kistler 5004 charge amplifier. The amplified signal was sent to an analogue to d i g i t a l converter which was interfaced to an I.B.M. personal computer. The digitized pressure signals for 120 engine cycles were then stored on floppy discs. The air flowrate was monitored with an o r i f i c e plate mounted on top of 20. the surge tank. The pressure drop across the plate was measured on an inclined manometer. Volumetric flowrate was calculated from the calibra-tion curve for the o r i f i c e plate. The or i f i c e plate was calibrated against a Meriam Laminar Flow Element Model 50MW-1.5. The calibration curves for both instruments are i n Appendix A. The natural gas flowrate was metered with a Meriam Laminar Flow Element Model 50MW-1.5 positioned in the gas line between the pressure regulator and control valve. The pressure drop was recorded on an inclined manometer. Volumetric flowrate was determined from the calibration supplied by the manufacturer with appropriate correction factors applied for the effects of natural gas viscosity (see Appendix F). Air movement within the cylinder during motored operation was measured with a hot wire anemometer probe. The probe used was a TSI Model 1226 which i s designed for high temperature environments. The sensor, Platinum-Iridium wire of 6.3 micrometer diameter, was mounted on the support needles by spot welding. The probe was Installed i n the side port of the cylinder through an airtight f i t t i n g . The f i t t i n g is shown in Figure 4.6. The access port for the probe i s shown in Figure 4.5. A Disa Model 50D anemo-meter bridge unit, operated in the constant temperature mode, was used in conjunction with the probe. The specifications for the probe and the anemometer are listed in Table II. The anemometer voltage signal was sent to a Hewlett Packard Model 3968A tape recorder where i t was recorded on analogue tape. This was necessary because high resolution was required for the hot wire data. A sample rate of every 0.2 crank angle degrees was selected. However the data acquisition system could not perform analogue to d i g i t a l conversions this fast, so the anemometer signal was f i r s t recorded on tape and then 21. played back to the data acquisition system at a slower speed. This procedure is described in more detail in the following section. The anemo-meter signal was recorded on two channels; one with a passband of 70 to 64,000 Hz, and the other with a passband of DC to 5,000 Hz. The data stored on the channel with the broad passband was processed to obtain frequency distribution information. The data recorded in the narrow band was used to obtain mean velocity and turbulence intensity information. 4.7 Data Acquisition System The basic data acqusition system consisted of an optical crank angle trigger, a trigger and clock circ u i t , an analogue to d i g i t a l converter, and an I.B.M. PC. In addition, for turbulence measurements a Hewlett Packard Model 3968A tape recorder was used for data acquisiton. A schematic of the system is shown in Figure 4.7. A photograph of the system is shown in Figure 4.8. Optical pickups mounted on a slotted wheel coupled to the engine crankshaft provided pulses every two crank angle degrees and at BDC. The optical pickup system i s shown i n Figure 4.9. These pulses were fed to the trigger and clock circuit simultaneously with the pressure and the signal being sampled. The two degree signal was passed through a phase lock loop which multiplied the frequency by ten. The BDC input pulse and pressure signal were used to start the A/D process. The analogue pressure signal was input to a comparator whose output was sent to a f l i p flop. The output of the f l i p flop and the BDC pulse were fed to a NOR gate. The f l i p flop went low when a preset pressure threshold was reached at the start of compression and thus when the next BDC pulse arrived at the NOR gate a trigger pulse was sent out. This pulse served two functions; i t signaled the computer to i n i t i a t e data acquisition, and i t enabled an AND gate which 22. allowed the 0.2 degree pulses to flow to a counter. If a slower sample rate was desired (0.4, 1.0, and 2.0 degrees), this could be set at the counter and the frequency of the pulses reduced by 2, 5, or 10. The output of this counter was then fed to a clock counter where pulses were counted u n t i l 16,000 pulses had been detected. After this threshold was reached the clock counter shut off the pulses until the whole process was started again. For each pulse leaving the clock counter the signal of interest was sampled and an analogue to d i g i t a l conversion performed. When 16,000 points were collected the data was transferred to a floppy disc for further processing off - l i n e . The analogue-to-digital converter had an upper frequency limit of 27 kHz. The pressure signal from combustion experiments was sampled every degree and posed no problem. High resolution was required, however, for the hot wire data and hence a sample rate of every 0.2 degrees was selec-ted. At a speed of 1140 rpm the 0.2 degree pulses arrive at the clock counter at a frequency of 34.2 kHz. To overcome this problem a tape recorder was used to record the two degree and BDC pulses, pressure, and anemometer signals at a tape speed of 15 inches per second. The signals were then played back to the trigger and clock circuit at a speed of 7.5 inches per second. Thus the clock counter saw pulses with a frequency of 17.1 kHz but because the anemometer signal was "stretched" the same amount as the original 2 degree pulses the effective sample rate was 34.2 kHz as desired. Data acquisition was performed with the aid of the program CDAQ which was loaded into the I.B.M. microcomputer. This program was interactive and allowed the user to issue commands to the analogue-to-digital conversion system. This program is described in Appendix C. 5. EXPERIMENTAL METHOD 23 . 5.1 Introduction The goal of the experiments was to provide combustion and turbulence data for the combustion chambers under study. For each combustion chamber geometry two types of experiments were performed; combustion tests i n which the pressure trace was recorded, and motored tests in which the air move-ments were monitored. A l l of the tests were conducted at a constant engine speed of 1140 rpm, a compression ratio of 11.3, and with a wide open throttle. The combustion tests were performed with a stoichiometric a i r - f u e l ratio. 5.2 Motored Engine Tests These tests yielded flow f i e l d data for each of the configurations. The quantities of primary interest were the mean velocity and turbulence intensity for several locations i n the chamber: at the edge of the bowl (i.e. a measurement of squish velocity as It l e f t the squish region); at the center of the chamber. For configurations with channels (Piston B) the probe was positioned so that i t would be directly opposite a channel exit at TDC in an attempt to measure the jet entering the bowl via the channels. These positions are shown schematically in Figure 5.1. The majority of these tests were performed with the wire axis oriented perpendicular to the cylinder axis (parallel to the piston face). This position i s shown i n Figure 5.2 as a = 0. This orientation was selected since the radial (or squish) velocity was of primary interest. However, in one set of tests the sensor was rotated 90° (see Figure 5.2) to obtain an indication of the tangential velocity. 24. 5.2.1 Hot Wire Preparation Wire breakage was a frequent occurrence during the course of the experiments and thus i t became necessary to establish a routine procedure for repair and calibration. Sensors were repaired by spot welding Platinum-Iridium wire onto the support needles. The welding was done with the aid of a microscope and a Disa welding unit. Each wire was inspected to ensure that the weld was of acceptable quality and that the wire was free of any di r t or defects. The sensor was calibrated i n a wind tunnel against a pitot tube. The operating temperature of the wire was 600°C. The probe was calibrated for air speeds of 0.5 to 20 meters per second. From the velocity obtained from the pitot tube a Reynolds number was formed based on the wire diameter and the ambient conditions. From the corresponding anemometer voltage a Nusselt number was calculated based on the free stream gas properties. The method used to determine the Nusselt number from the anemometer voltage i s that proposed by Witze [27]. This involves solving the one-dimensional heat balance equation for the hot wire (neglecting radiation) to obtain an expression for the mean wire temperature in which the heat transfer c o e f f i -cient i s the only unknown. The heat transfer coefficient i s determined through iteration and the Nusselt number formed. This technique i s discussed more f u l l y i n the following chapter and i n Appendix B. From the calibration data set a correlation of the form Nu = a + b Re" was found using a non-linear curve f i t t i n g procedure [27]. (5.1) 25. After calibration the probe was placed into the three-piece f i t t i n g shown in Figure 4.6. This assembly was then positioned i n a measurement test r i g . There the probe orientation was set (0° or 90°) with s p i r i t levels and by lining up sight lines on the probe and test r i g . In addition the length of the probe to extend into the chamber was set. The pressure f i t t i n g was then tightened to secure the probe position within the f i t t i n g . 5.2.2 Routine Experimental Procedure At the start of each experiment the one-piece cylinder head and cylinder were l i f t e d off the engine block and the appropriate piston inserted. After careful cleaning of a l l parts the head was replaced. To adjust the clearance height the flywheel was rotated until the piston was at TDC. A plug gauge was inserted between the head and the piston crown in the top access port shown in Figure 4.5 and the cylinder was cranked up (via a worm gear) to the proper position. A d i a l micrometer mounted between the stationary crankcase and the cylinder was set to a reference point. The cylinder was then clamped into position, the flywheel rotated beyond TDC and the plug gauge removed. The pressure transducer was then installed. Next the valve rocker arm linkage was l i f t e d over the cylinder and the pushrods removed to allow for insertion of the probe. The threaded portion of the probe f i t t i n g assembly (part A i n Figure 4.6) was f i r s t tightened into the side access port. The remainder of the assembly with probe tight-ened into position was pressed into the threaded sleeve. The f i t t i n g was then rotated in the sleeve until the probe was properly oriented. This was done by lining up sight lines on the f i t t i n g and on the engine. Finally a nut was threaded onto the sleeve to secure the entire assembly. 2 6 . The pushrods were replaced, the rocker arm linkage brought down into position, tightened, and the valve clearances set. The engine was started and allowed to come to 6peed before data acquisition was initiated. 5.2.3 Flow Measurement Locations For each of the squish chambers tested the probe was positioned 10 mm from the bowl edge for one set of measurements, and then at the chamber center for another set. In addition, measurements were taken i n the bowl for the squish-jet chamber. For the disc chamber one measurement was made at the center of the chamber. These positions are shown i n Figure 5.1 and labelled Rl, R2 nd R3, respectively. For each of the clearance heights tested the probe was positioned so that the sensor was 2 mm below the chamber head. These positions are also shown in Figure 5.1 and labelled Z l , Z2, and Z3, respectively. 5.3 Combustion Tests These combution tests provided the pressure history of the combustion process for each of the configurations. Combustion tests were performed after the motored tests as the configuration was already i n place. For these tests the hot wire probe was removed from the side port and the pres-sure transducer mounted. The spark plug was installed i n the top access port. These positions are shown in Figure 4.5. After the instrumentation was i n place the valve clearance and TDC clearance height were checked. The engine was started with the motor. Once speed was achieved the ignition was switched on and the gas flow started. The a i r - f u e l mixture was maintained at the stoichiometric point by adjusting the gas control valve. Spark timing was varied from 20 to 40 degrees BTDC in 5 degree increments. For each setting 120 cycles of data was collected. 6. DATA ANALYSIS 27. 6.1 Introduction The techniques employed for data reduction and analysis are described in this chapter. Two types of signals were processed, hot-wire anemometer and pressure data. The f i r s t part of this chapter briefly describes the method of processing the analogue signals to obtain meaningful data. The second part describes i n detail the methods used to interpret this data. 6.2 Pressure Signal Processing The raw d i g i t a l data was f i r s t ensemble-averaged over 120 engine cycles. The di g i t a l data was then transformed to pressures with the appro-priate conversion factor. This conversion factor was a function of the system gain and the charge amplifier setting. The pressures obtained from this conversion were relative pressures and had to be shifted by the appro-priate value to obtain the absolute cylinder pressure. The method of Lancaster et a l . [29] was used to determined the reference condition. This involves assuming that the pressure in the cylinder at BDC after intake is equal to the average intake manifold pressure. The intake manifold pressure was estimated by subtracting the measured losses through the intake system from the ambient pressure. After the absolute cylinder pressures were evaluated the pressure trace was smoothed using cubic spline interpolation. 6.3 Anemometer Signal Processing The hot wire anemometer registers the change in resistance ( e l e c t r i -cal) which results from the heat transfer from the sensor due to the 28. cooling effect of the flow. Because the heat transfer process i s a function of the driving temperature differential and fluid properties such as viscosity, density, and conductivity the sensor response i s highly sensitive to changes in temperature and pressure in the flow. Ideally a probe should be calibrated over the range of temperatures and pressures encountered in the engine cylinder. However, this time-consuming procedure i s not practical i n light of the frequent occurrence of wire breakage. Thus i t becomes necessary to rely on analytical models to correct for variations from the calibrated conditions. The two most widely used models of heat transfer from a hot-wire are those of C o l l i s and Williams [30] and Davies and Fisher [31]. Both models are modifications to the theory developed by King [32], known as King's Law which gives the Nusselt number as a function of the Reynolds number: Nu = a + b Re 1 / 2 (6.1) where a and b are determined by calibration. Collis and Williams [30] developed a heat transfer correlation i n which convection was the only significant form of heat transfer considered. They were able to justify this by using wires with a length to diameter ratio greater than 2000. In the work of Davies and Fisher conduction to the wire supports was considered to be significant. Their theory involves solving the one dimensional heat balance equation along the wire to obtain an expression for the mean wire temperature i n which the heat transfer coefficient i s the only unknown. The heat transfer coefficient is determined through iteration. 2 9 . In this study neither of these universal correlations was used; however, an approach similar to that of Davies and Fisher as proposed by Witze [27] was taken. In this method the one-dimensional energy equation for the wire is solved to obtain an expression for the temperature d i s t r i -bution along the wire. This temperature distribution i s integrated along the wire to yield a mean wire temperature: T M 2(T -C ) P -1 tanh [/C7 l/l] + C, (6.2) /~c7 A 2 1 where and hT + I 2R (1 - anTn)/(ird£) = — § — (6.3) h - l 2 R a 0/(irdA) C 2 = 4[h - I 2R 0a 0/(Trd*)]/k wd (6.4) where h is the heat transfer coefficient, T p is the sensor support tempera-ture, T i s the gas temperaure, k is the mean thermal conductivity of the g w wire, RQ i s the resistance of the wire at the reference temperature T^, a Q i s the temperature coefficient of resistance for the wire, and I i s the current through the wire. The mean wire temperature can be calculated from the probe resistance and the wire temperature coefficient of resistance. A l l other quantities except the heat transfer coefficient h are known. The heat transfer coefficient is determined from iteration. Thus for a given flow condition the heat transfer coefficient can be determined from the measured probe current, and a Nusselt number formed. Then a Reynolds number may be found from Equation (5.1). The f l u i d velocity i s then determined from the Reynolds number. 30. There are several important points to make about this procedure. First in the correlation both the Reynolds number and the Nusselt number are based on the free stream gas temperature. In an extensive study i n which hot wire anemometer results were compared to LDV results Witze [27] found that this choice of reference temperature gave the best agreement between the two results. The support temperature T p in Equation (6.2) was taken as room temperature and invariant. The support needles are much larger than the wire and are not appreciably heated by the electric current. Their temperature can be assumed to follow the instantaneous gas temperature somewhat. However, unless a direct measurement of the needle temperature i s made, as Lancaster [10] did, there i s no straight forward method to estimate the temperature. Again using LDV results as a standard for comparison Witze found that the choice of invarient room temperature for the supports gave adequate results. Determination of the gas temperature i n the cylinder i s very important to the results. In this study the air temperature was calculated from: <V± = ^ W W i * y-T (6-5) where y i s the temperature dependent specific heat ratio evaluated at <Vi-i-The i n i t i a l reference condition was taken at the point of intake valve closing, where the pressure and temperature were taken as ambient condi-tions. The temperature dependent specific heat ratio was calculated by assuing the air was 21% 0 2 and 79% N 2. The constant pressure specific heats of N 2 and 0 2 were evaluated from expressions given i n Van Wylen and Sontag [33]: and 31. (C )„ - 39.060 - 512.798"1*5 + 1072.76~2 - 820.406~3 (6.6) p 1*2 ( C B ) n = 37.432 + 0.02010261*5 - 178.576" 1 , 5 + 236.889~2 (6.6) r u 2 where 8 = T(kelvin)/100. Witze [27] compared mean velociites obtained using measured and calculated temperatures. His results show that the adiabatic computation gives good results during the compression process but tends to perform poorly beyond approximately 50 degrees after TDC. Since the region of interest in this study was the combustion period (from 60 degrees before TDC to 40 degrees after TDC) the adiabatic calculation was deemed adequate for temperature evaluation. The thermal conductivity and viscosity of the a i r were calculated from the expressions used by Collis and Williams [30]: J - - J * - ) 0 " 8 0 (6.8) Tlef Ref and W£- - J * - ) 0 * 7 6 (6.9) PRef TRef Details of the calculation procedure for the determination of the instantaneous velocity from the anemometer are presented i n Appendix B. From the foregoing discussion i t can be seen that there are many sources for uncertainties i n the evaluation of the instantaneous velocity from the anemometer signal. The main uncertainties are: wire physical properties such as uniformity of diameter, sensing length, and temperature coefficient of resistance; imperfections of the weld at the supports; and fouling of the wire during measurement. Uncertainty i n the experimental 32. value of pressure, the reference temperature, the computed gas temperature, and the selected sensor support temperature lead to uncertainty In the heat transfer coefficient and thus the computed velocity. For these experiments the uncertainty in the reference temperature is estimated to be 5% and in the reference pressure 5%. Sensitivity analysis shows this leads to uncertainty on the order of 35% in the calculated instantaneous velocity. In addition to uncertainty arising from the analytical procedure the effects of probe interference and the probe's insensitivity to flow direction also contribute to error i n the interpreted results. In light of the high uncertainty associated with hot wire measurements caution should be exercised when they are interpreted, especially when absolute magnitudes of mean velocity or turbulence intensity are to be applied to empirical models. However, hot wire measurements do provide a qualitative indication of the flow f i e l d in an engine and are valuable in studies such as this one where evaluation i s based on a relative comparison rather than the absolute magnitudes of the flow f i e l d characteristics. 6.4 Flow Field Data Interpretation of hot wire measurements i n engines poses several dilemmas. Because of the complex nature of the flow f i e l d generated by the valve events and piston motion the directional characteristics are d i f f i -cult to determine since the sensor cannot distinguish between forward and reverse flow conditions. Although analytical models can be used to predict the sensor response to conditions different from the calibration, there are many assumptions and variables involved In the computation of the instan-taneous velocity, and thus many sources of error exist. The major obstacle to data interpretation and processing arises from the periodic and thus nonstationary nature of the flow f i e l d in the engine. Because of this, most investigators have resorted to ensemble averaging techniques. There are two problems with this approach. The f i r s t is that 33. the fundamental equations which define turbulence characteristics use time averages. For most stationary processes time averages of the s t a t i s t i c a l properties are equal to ensemble averages. These are called ergodic processes. Since many turbulent flows may be considered as stationary and ergodic the substitution of ensemble averages for time averages poses no problem. However the flow f i e l d in an engine is unsteady and non-stationary. This means that the time averaged mean w i l l be dependent upon the length of the averaging interval and furthermore ensemble averages w i l l not equal time averages. The second objection to ensemble averaging i s that not only i s the "mean" velocity periodic but there is also a cycle to cycle variation i n the mean velocity i t s e l f . This cyclic variation in the mean velocity i s included in the computed turbulence intensity when ensemble averaging i s used. Time averaging methods also present d i f f i c u l t i e s . The main problem arises in the selection of a window size for averaging. The calculated mean velocity w i l l be highly dependent upon the length of the averaging interval. Ideally the window size should be as small as possible since the mean velocity can change quite rapidly. If the window size i s made too large then information is lost. The. same problem arises in calculation of the turbulence intensity; i f the window size i s too small then low frequency turbulence data is lost. Thus a compromise must be made. In this investigation both techniques (time and ensemble averaging) were employed to interpret the data and the results were compared. 6.4.1 Ensemble Averaged Mean and RMS Velocity An ensemble average i s performed on a series of records each consist-ing of a sequence of equally spaced samples in time. If the instantaneous 34. velocity i s written as U(i,6) where i denotes the engine cycle (record) and 8 the crank position (time) within the cycle then the ensemble averaged mean velocity for the position 0 obtained from an ensemble of N cycles i s : 1 N U(0) = i E U(i,0) (6.10) i=l The turbulence intensity i s defined as the rms of the velocity fluctuations about the mean and i s : i N u'(0) = { i E (U(i,0) - U ( 0 ) ) 2 } 1 / 2 (6.11) i=l There are several variations on this method. Rask [34] compared two methods; a window ensemble and a smoothed ensemble. In the window ensemble a crank angle interval was selected and data points within averaged to obtain a single point. The window averages were then ensembled as described above. In the smoothed ensemble a curve was fitted to the window averages for each cycle using cubic spline interpolation. The smoothed curves were then ensembled to obtain mean and rms velocities. He also performed a cycle by cycle analysis on the smoothed mean velocity curves. This involved evaluating the rms velocity from the smoothed curves for each cycle. The respective mean and rms velocity curves were then ensembled. He found that the turbulence intensity obtained by a cycle by cycle analysis was lower than that obtained from the other methods. This confirmed the fact that conventional ensemble averaging includes the cyclic variation of the mean flow i n computed intensity. In this study conventional ensemble averaging was compared to a cycle by cycle time averaging technique. The ensemble averaging was taken over 100 engine cycles. Each cycle consisted of samples for every 1/5 of a 35. crank angle degree. The mean velocity was obtained from Equation (6.10) and the turbulence intensity in Equation (6.11) was obtained by: 1 N u'(0) = {i- I U 2(i,6) - U 2 ( 6 ) } 1 / 2 (6.12) i=l Details of the calculation and the computer program used are i n Appendix D. 6.4.2 Cycle by Cycle Time Averaged Mean and RMS Velocity Two approaches for evaluating the mean and rms velocities on a cycle by cycle time averaged basis were studied. The majority of data was processed with a method similar to that of Catania and Mittica [35]. This technique is similar to the cycle-by-cycle smoothed ensemble proposed by Rask [34] except that time averages were performed i n the windows rather than arithmetic averages. In their study Catania and Mittica evaluated a mean velocity curve for each cycle. This was done by finding the time average of the instantaneous velocity for specific time intervals (crank angles) within the engine cycle. The average values, taken at the center of the window, were then used with cubic spline interpolation to generate a smoothed mean velocity curve. The turbulence intensity was then obtained in a similar fashion from the instantaneous velocity and smoothed mean velocity for each cycle. The mean and rms velocity curves for each cycle were then ensembled. They investigated the effect of different averaging intervals on computed mean and rms velocities. They found that window sizes ranging from 4 to 12 crank angle degrees had no significant effect on the mean velocity. For turbulence intensity calculations they varied the windows 36. from 1 to 20 crank angle degrees. They found that for intervals less than 8° the intensity values decreased. Between 8° and 20° however, there was relatively l i t t l e difference. This interval (8° to 20°) corresponded to a time interval of between 0.83 and 2.08 milliseconds which corresponds to the range of macro time scales that can be expected i n an engine. The fact that the turbulence intensity decreased for averaging intervals less than 8° indicates that low frequency turbulence information was being lost. In the present study the same type of technique was employed. The mean velocity within specified time intervals for each cycle I was calculated by: 1 A U (i) jl U(i,6) d9 (6.13) 0 Window sizes ranging from 2 to 8 crank angle degrees were examined. Since these window sizes had relatively l i t t l e effect on the resulting mean velocity curve a 4 degree window was selected for computational ease. Mean velocity curves were then obtained using cubic spline interpolation [28] between the evaluated points for each cycle. The turbulence was then computed for each cycle by: u 6 ( i ) = l / {[U(i,6) - U e ( i ) ] 2 de} 1'* (6.14) where the averaging window 6 was 12 crank angle degrees. Window sizes ranging from 2 to 14 degrees were studied. There was a decrease i n the turbulence Intensity for windows smaller than 6 crank angle degrees, however there was relatively l i t t l e difference for windows larger than this. Based on these results, an averaging interval of 12° was used throughout for evaluating the turbulence intensity from Equation (6.14). 37. The mean velocity and turbulence intensity curves were then ensembled over 40 cycles to obtain one representative curve for each of the two properties, the ensemble averaged mean velocity: - 1 4 0 -u e - To ±lx V 1 * ( 6 ' 1 5 ) and the ensemble averaged turbulence intensity without the cyclic variation of the mean velocity: 40 A u e = m 1 (ud.e) - u ( i ) ) 2 de]}i/2 ( 6 . 1 6 ) i=l 0 The cyclic dispersion of the mean velocity was determined from the difference between the ensembled mean velocity of Equation (6.15) and the individual mean velocity curves for each cycle: i 40 U R M S - fe±z=1 [ V 4 > - ° e W l / 2 ( 6 - 1 7 ) Also the nonstationary analysis proposed by Lancaster [10] was studied for comparative purposes. Lancaster redefined the instantaneous velocity to be the sum of a stationary mean velocity U(i), a time varying mean velocity U(0), and a turbulent fluctuation u(i,8): U(i,6) = U(i) + U(6) + u(i,6) (6.18) In the present study the mean velocity obtained from ensemble averaging was f i r s t evaluated. Then the stationary mean velocity U(i) was calculated from: , A U(i) = i j [U(i,6) - U(0)] d6 (6.19) fl 0 for each engine cycle (record). The window size 6 was varied from 40 to 100 crank angle degrees about TDC. The intensity was then computed from: 38. i A M {T I [U(i,6) - U(6) - U(i)]2 de}1'* (6.20) 0 The intensity records were then ensembled. Details of the calculation and the computer program used are in Appendix D. 6.4.3 Time Scale Analysis An analysis similar to that of Haghgooie et a l . [13] was performed on uncalibrated hot wire anemometer signals to obtain relative probability distributions of the peak-to-peak time separation. This analysis depends on the assumption of a definable small scale structure of turbulence in an engine similar to that proposed by Tennekes [7]. The technique involves the determination of an amplitude threshold for peak discrimination. This i s obtained by operating the probe in quiescent ambient a i r . The problem with this technique is that the "noise" level sampled in quiescent air w i l l be a turbulence signal resulting from natural convection. This "noise" w i l l be insigificant in forced convection flow. Thus by setting a discrimination level for peak Identification some of the high frequency turbulence information is lost. After the amplitude thres-hold i s set the signal i s sampled and a relative probability distribution is formed for the peak-to-peak time separation. Haghgooie et a l . [13] concluded that the most probable frequency obtained i n this fashion appears to be related to the small scale structure of the turbulence. Based on the assumption that there i s a definable small scale struc-ture of turbulence in an engine similar to that proposed by Tennekes and that the method of Haghgooie et a l . can be used to detect differences i n the turbulent frequency distribution in engines a peak-to-peak time separa-tion analysis was performed on the anemometer data obtained for the chambers studied. The noise amplitude threshold was obtained by evaluating the probability distribution from data collected while operating he probe 3 9 . i n quiescent ambient ai r . The relative distrtibution of the peak-to-peak, time separation was then formed. It was found that this distribution was relatively insensitive to variations of up to 30% i n the amplitude thres-hold. This could mean that high frequency turbulence data was lost. A window of 60° around TDC compression was used i n the evaluation of the relative probability distribution. Details of the procedure and a l i s t i n g of the computer program are i n Appendix D. 6.5 Combustion Data The pressure recorded during combustion tests was processed to yield mass burn rate curves for the configurations under study. The raw d i g i t a l data was processed as detailed earlier i n the chapter. The computer program used to process the data was developed by Jones [36]. The thermo-dynamic model i n the program i s based on the two zone approach and is similar to that of Keck [37] and Lavoie et a l . [38]. The basic assumptions are that a thin spherical flame front separates the charge into two zones; the unburned region containing the reactants, and the burned region containing the products. Properties are assumed to be spatially uniform throughout each region. Furthermore both products and reactants have varying specific heats and obey the equation of state for an ideal gas. The unburned gas is assumed to be isentropically compressed due to the expansion of the burned region. The heat transfer i s calculated using the Annand [39] equation. Six dissociation reactions are accounted for. With the assumptions above and the application of the f i r s t law and conservation of mass an iterative procedure is followed from which the mass fraction burned i s obtained at each crank angle degree. Minor changes to the program were necessary to accommodate the C.F.R. combustion chamber geometries. A complete discussion of these changes and a program l i s t i n g is in Appendix E. A detailed discussion of the calculation procedure i s given i n [36]. 40. 7. DISCUSSION OF RESULTS 7.1 Introduction In this chapter the results obtained from the experiments conducted on the C.F.R. engine are presented and discussed. In the f i r s t section results from flow f i e l d measurements are presented, while i n the second section results from the combustion tests are presented and discussed. 7.2 Flow Field Results This section Is divided into four parts. In part one the different methods of processing the data (discussed in Chapter 6) are examined and compared. In part two results obtained for the standard squish chamber, Piston A, are presented. In the following section results for Piston B the squish chamber with channels are given. The f i n a l section deals with a comparison of the geometries investigated. In the following sections flow velocities are presented plotted against crank angle degrees. The convention used is that 0° is BDC and 180° i s TDC compression. Most of the plots are shown from 60 to 220 degrees. This is the portion of the engine cycle important to the combustion process. At 60° the intake generated flow has decayed and i n a disc chamber would continue to decrease through TDC. The combustion period ranges from 30° BTDC to approximately 30° ATDC. At 220° the combustion period Is finished. 7.2.1 Ensemble Averaging vs. Time Averaging In this section the averaging techniques discussed i n the previous chapter are compared. The results shown in this section were obtained with the standard squish chamber (Piston A) at a clearance height of 1.5 mm. Three consecutive instantaneous velocity traces are shown in Figure 7.1. The basic mean velocity trend i s evident and repeatable although there i s considerable variation in the individual traces from cycle to cycle. In Figure 7.2 the mean velocity trace obtained from conventional ensemble averaging techniques (Equation (6.10)) is shown with the mean velocity evaluated from Equation (6.15) using a window of 4 crank angle degrees as the time averaging window. From the figure i t i s clear that the two techniques yield almost indistinguishable results for the mean velocity trace. The cyclic variation of the mean velocity is shown in Figure 7.3. This curve was formulated from Equation (6.17). The cyclic variation can be seen to be f a i r l y consistent throughout the compression stroke with a slight increase near TDC. In Figure 7.4 the turbulence intensities obtained from conventional ensemble averaging using Equation (6.12) and from the time averaged window, cycle-by-cycle analysis of Equation (6.16) are shown. The window size used in Equation (6.16) was 12 degrees for the reasons discussed in the previous chapter. It i s evident that the ensembled intensity has included in i t some of the cyclic variation of the mean velocity. This is shown even more by comparing Figures 7.3 and 7.4. The turbulence intensity obtained from Equation (6.11) using the non-stationary analysis proposed by Lancaster [10] is shown in Figure 7.5 for averaging windows of 40, 60, 80, and 100 degrees around TDC. Comparison of Figures 7.4 and 7.5 shows that the computed values l i e between the ensembled and time averaged results. The problem with this formulation i s the assumption that the difference between the ensembled mean and the instantaneous mean i s constant during an individual cycle; that i s , that 42. the curves are i n phase and simply shifted up or down with respect to one another. However inspection of Figures 7.1 and 7.3 shows that this is not the case. In the following sections the mean velocity was evaluated using the method described in Chapter 6 from Equation (6.15). A four degree window was used for the averaging interval. Turbulence intensities were computed from Equation (6.16) with an averaging interval of 12 crank angle degrees. The basis for the selection of these windows was discussed i n Chapter 6. 7.2.2 Standard Squish Piston (Piston A) Results In Figure 7.6 the mean velocity and turbulence intensity traces for a clearance height of 3.5 mm are shown. This data was taken at the edge of the bowl. The mean velocity decays steadily as TDC i s approached. At approximately 10° BTDC there is a slightly increase in the mean velocity. After the small peak the mean velocity decreases u n t i l 10° ATDC. Another peak is then reached at 20° ATDC. A comparison of these results with the calculations i n Chapter 3 (see Figure 3.2) shows that although the magni-tude of the velocities do not agree the timing of the velocity peaks i n Figure 7.6 corresponds to the trend predicted for the squish velocity. The turbulence intensity remains relatively constant throughout. The effect of squish for a clearance height of 1.5 mm i s clearly evident in Figure 7.7. The mean velocity is steady throughout the compres-sion stroke u n t i l about 20° BTDC where there i s a sharp increase which comes to a peak near TDC and then decays. The interesting effect here i s that the previous case (h £ =3.5 mm) showed the effect of squish on both sides of TDC (as the model presented i n Chapter 3 predicts); however, i n this case (h = 1.5 mm) only one peak centered approximately around TDC i s shown. The results of James [25] showed a similar trend to the previous case (h^ = 3.5 mm); that i s , squish effects before TDC and reverse squish on the expansion stroke. However he used large clearance heights and did not achieve pronounced squish effects. The results of both Witze [12] and Dent and Salama [10] show only one velo-city peak near TDC similar to the trend exhibited i n the data for h^ = 1.5 mm. The calculations in Chapter 3 predict the trend of two velocity peaks as shown in the data for h £ = 3.5 mm. However this model was very simpli-fied and did not account for effects such as momentum and viscosity. It is possible that there is another flow regime at work (such as a piston gener-ated vortex) with the squish; however, without flow visualization i t i s d i f f i c u l t to determine exactly what is happening. At 10° BTDC a comparison of Figures 7.6 and 7.7 shows that the mean velocity achieved for a clearance height of 1.5 mm is approximately four times that for the lower clearance height. This i s i n agreement with the trend predicted by the calculations in Chapter 3 and demonstrates the c r i t i c a l effect of clearance height. In Figure 7.8 the velocity trace obtained with the probe postioned at the center of the chamber (h =1.5 mm) is shown. Again there is a large c velocity peak at TDC. However careful examination of the figure shows that the point at which the mean velocity starts to increase comes approximately 5° later than i t did for the measurement taken at the cup edge. This trend is to be expected since the arrival time of the squish-jet should be later as the probe i s moved away from the cup edge. To get an indication of how much swirling motion was present the probe was rotated 90° (see Figure 5.4) so that the probe axis was perpendicular to the piston face. Results obtained at the cup edge and at the chamber 44. center are shown i n Figures 7.9 and 7.10. Both mean velocity and turbu-lence intensity are slightly higher indicating the presence of a tangential velocity component. However because only single sensor measurements were made i t was not possible to resolve this component. The later arrival time of the squish-jet to the center can be seen more clearly from these two figures. In Figure 7.11 the mean velocity curves obtain at clearance heights of 3.5 and 1.5 mm are compared. Although the two curves are similar in the early part of the compression stroke the effect of the squish can be seen as they begin to deviate from one another at approximately 30° BTDC. Measurements were also made for the clearance height of 2.5 mm. The resulting velocity traces were not that different from the 3.5 mm case and are not presented. From these results i t can be seen that the clearance height is important in the observed squish effect as predicted by the calculations i n Ghapter 3. A comparison of the relative turbulence intensities for the two heights is shown in Figure 7.12. It is evident that although the magni-tudes of the velocity traces vary considerably, the relative quantities show only a maximum increase of about 25% for the clearance height of 1.5 mm during the squish period. 7.2.3 Squish-Jet Combustion Chamber (Piston B) Results Measurements were made at the same locations and conditions as for Piston A. The mean velocity and turbulence intensity profiles for a clear-ance height of 3.5 mm are shown i n Figure 7.13. In this case i t i s d i f f i -cult to detect any effect of squish at a l l prior to TDC and only a small peak occurs after TDC. However from calculations i n Chapter 3 this trend 45. could be expected i f the gas i s now using the additional routes provided by the channels. At the smaller clearance height shown i n Figure 7.14 the squish effect can be seen again. In this case the peak effect at TDC is not as pro-nounced as i t was for Piston A although the same general trend for both mean velocity and turbulence intensity is exhibited. Examination of the figure shows that the mean velocity trace i s consistently lower for Piston B. The most probable explanation for this is that there was leakage past the piston rings for the previous measurements. A l l hot wire measurements except those for Piston B at a clearance height of 1.5 mm were obtained before a failure i n the C.F.R. engine required that the cylinder be honed out and the piston rings replaced. If there was considerable blow-by past the piston rings then the velocity measurements would be a r t i f i c i a l l y inflated. This could explain the observed differences in the velocity traces before the squish could start affecting the flow. In Figure 7.15 the mean velocity trace and turbulence intensity traces are shown for Piston B at the center of the chamber (h = 1.5 mm). The c interesting effect here is the character of the mean velocity trace after top dead center. After the peak starts to decay the velocity i s relatively f l a t for a few degrees and then there is a small peak. This could be the separate effects of squish, and another flow regime. In Figure 7.16 the velocity and intensity traces for the measurement taken inside the cup are shown. This was an attempt to get an idea of the jet velocity leaving the channel as It entered the bowl. Unfortunately geometric constraints would only permit the probe to be aligned with the channel centerline right at TDC. Although calculations in Chapter 3 indi-cate the velocity of the channel jet should be zero at TDC i t was hoped 46. that the probe would detect the f i n a l part of the jet as the top of the channel passed the probe. As can be seen from Figure 7.15 the jet was not detected at a l l . However this i s most probably due to the i n a b i l i t y to position the probe properly rather than the lack of a jet velocity. In Figure 7.17 the relative turbulence intensities for the clearance heights of 3.5 and 1.5 mm are shown. The maximum difference between the two i s approximately 10 percentage points, on the same order as the difference between relative intensities for Piston A at the same height. 7.2.4 Comparison of Geometries In this section a comparison between the two geometries is made. The two mean velocity traces (h £ = 1.5 mm) are compared in Figure 7.18. As was mentioned earlier i t i s believed that the mean velocity trace of Piston A is a r t i f i c i a l l y inflated due to leakage past the piston rings. There is no other explanation for the difference between the two curves between 60 and 140 degrees. The points to notice from this figure are that the trends are basically similar; the mean velocity begins to increase about 20° BTDC, the peak occurs near TDC, and about 20° ATDC there is a slight secondary peak. In Figure 7.19 the relative intensities are compared for the probe located at the cup edge (h c = 1.5 mm). The relative intensity of Piston B i s consistently higher than for Piston A. The maximum difference between the two is 11 percentage points; that i s , Piston B shows a 29% improvement. However i t i s d i f f i c u l t to say how much of this i s due to increased turbulence generation by Piston B design. This is because although flow induced by leakage past the rings would create a higher mean velocity i t might not generate new turbulence. Thus the relative intensity for Piston A might be a r t i f i c i a l l y low. However a comparison of Figures 7.12 and 7.17 shows that even at the clearance height of 3.5 mm the relative turbulence intensity was higher from Piston design B. In this case the relative turbulence intensities of the two designs were approximately equal un t i l 30° BTDC through 20° ATDC. In this region the maximum difference between the two curves was approximately 6 percentage points. This trend indicates that the squish-jet piston design i s more effective at generating turbu-lence during the compression stroke (or squish period). This would be important to combustion since i t i s the level of turbulence and not the mean velocity that enhances combustion. The relative probability distributions of the peak-to-peak time separation are shown in Figures 7.20 to 7.23. These measurements were performed for the clearance heights of 1.5 mm and for the disc chamber for comparison. The distributions presented are for a crank angle window of 60° around TDC. The distributions were obtained using the peak to peak time separation technique described in Chapter 6. In Figure 7.20 the distributions for Piston A at the bowl edge and at the chamber center are shown. From the graph i t can be seen that there i s a slight broadening of the distribution towards the center of the chamber. In Figure 7.21 the distribution for the flat piston is compared to that of Piston A at the center of the chamber. From this graph i t i s evident that there is some clustering of frequency bands for the flat piston chamber. In general the relative probability for Piston A i s higher i n the high frequency range than i t is for the f l a t piston; however the differences are minor. In Figure 7.22 the distributions of Pistons A and B are compared for the probe position at the cup edge. Although the most probable frequency for the two designs i s the same, approximately 1 millisecond, the distribu-tion for B shows less skew to the l e f t (higher frequencies) than that of 48 . Piston A. In Figure 7.23 the distributions for the two designs are shown for the center probe location. Here there has been a definite shift in Piston B's distribution to the right and lower frequencies; whereas for Piston A, although there has been some broadening of the distribution, the most probable time has not changed. Although there are differences in the distributions they are minor and the results indicate that the squish chamber has a small effect on the turbulent frequency distribution i n the chamber. However i n view of the limitations of the analytical method the reults are somewhat inconclusive since i t i s possible that high frequency information was lost. 7.3 Combustion Results In this section results from the combustion tests are presented. The pressure traces for each of the pistons A and B as well as the f l a t piston were analyzed for mass fraction burned history. The fi n a l mass fraction burned for the tests was about 93%. There are a number of reasons 100% burned was not achieved; blow by could not be adequately accounted for i n the calculations, combustion may have been incomplete, and there could have been an error in the heat transfer calculations. The uncertainty in the i n i t i a l reference pressure i s estimated to be 5%. However this gives an insignificant percentage error (<.1%) in peak pressure. The major source of uncertainty i n the mass burn rate analysis arises i n the evaluation of the i n i t i a l energy of the charge in the cylinder. The uncertainty in the i n i t i a l energy i s a function of uncertainty i n pressure, temperature, and charge mass. The uncertainty in the charge mass arises from measurement of air and fuel rates, and estimation of the residual fraction. The total uncertainty in the mass Is estimated to be 5%. This leads to an uncertainty of 15% i n the mass fraction burned. 49. In Figure 7.24 the pressure histories for Pistons A and B (h =1.5 c mm) and the flat piston are shown for a spark timing of 30° BTDC. The maximum cylinder pressure of 63.3 Bar was achieved with Piston B at 8° ATDC. The maximum pressure obtained with Piston A was 61.1 Bar at a crank position of 11° ATDC. The f l a t piston yielded the poorest results with a maximum pressure of 46.0 Bar occuring 16° ATDC. In Figure 7.25 the mass fraction burned curves for the f l a t piston and Piston A are shown (spark timing 30° BTDC). It can be seen that the basic squish design appears to have very l i t t l e effect on the ignition delay time. The ignition delay time here is defined to be the time taken to burn 2% of the charge mass. The effect of squish i s seen i n the main stage of combustion, defined here to be the period for 2 to 85% mass burned. The burn time for the fl a t piston was 38 crank angle degrees whereas for Piston A this time was reduced by 26% to 28 crank angle degrees. These results are in agreement with Nagayama et a l . [17] who found that squish increased burning rate i n the main combustion stage and resulted in higher maximum pressures. In Figure 7.26 the mass fraction burned curves are compared for Pistons A and B. The spark timing was again in both cases 30° BTDC. It can be seen from this figure that the main effect of the squish jet channels i s a reduction in the ignition delay time. The ignition delay time i s 3° less for Piston B; a 17% reduction. However the main stage of combustion does not appear to have been affected. The burn time for both designs i s approximately 28 crank angle degrees. In.Figure 7.27 the three curves are plotted together and the separate effects of faster burn rate during the main combustion period due to the squish, and reduced ignition delay due to the channels can be clearly seen. The total combustion duration is defined here to be the time from spark to 85% mass burned. The total combustion durations for 5 0 . the f l a t piston and Pistons A and B were 58, 44 and 42 crank angle degrees respectively. In Figure 7.28 the mass fraction burned curves for the two squish designs are compared for a spark timing of 25° BTDC. Again the only real effect appears to be a reduction i n ignition delay time i n the case of Piston B. However the effect is not as pronounced in this case. This i s to be expected since ignition delay effects w i l l be enhanced for earlier spark timing (as in the 30° BTDC case) since the i n i t i a l pressure and temperature of the mixture i s lower. In this case (25° BTDC) there i s only 2° difference in the ignition delay period for the two designs. 51. 8. CONCLUSIONS AND RECOMMENDATIONS The objective of this thesis was to investigate the effects of the squish chamber design on the combustion process and flow f i e l d of an I.C. engine and particularly to compare the reference squish design to the squish-jet design [8]. A number of conclusions may be drawn on the basis of the experimental data. Cylinder pressure data shows the squish design to be effective i n increasing the mass burn rate during the main combusion period. For a spark timing of 30° BTDC the combustion duration for the disc chamber was 58° compared to 45° for Piston A at h = 1.5 mm. The peak pressure achieved with Piston A was 30% higher and occurred 5° earlier. Comparisons of cylinder pressure data for Pistons A and B show the squish-jet chamber design to give superior performance. For a spark timing of 30° BTDC the maximum pressure attained with Piston B was 4% higher and occurred 3° earlier. The major effect of the squish-jet chamber design was the reduction i n ignition delay time by 3° for a 17% improvement. The main stage of combustion does not appear to have been affected. The combustion duration for Piston B was 42°; 3° less than for Piston A. Although the uncertainty in the computed flow f i e l d parameters i s high, because the experiments were performed from case to case with conditions as identical as possible some of the uncertainty is systematic. From the flow f i e l d data i t appears that the clearance height has a significant effect on the mean velocity. The mean velocity computed for Piston B was less than that for Piston A for identical clearance heights. The peak-to-peak time separation analysis results indicated no significant difference i n the turbulence frequency distributions for the two designs. 52. Further work i s recommended for the combustion experiments i n this study i t was not possible to vary the operating conditions nor to obtain adequate performance data. Pressure history was the only obtainable data. Therefore, i t is recommended that extensive performance tests be carried out with the two squish chamber designs. Also i n this study the engine used had a side point ignition. It is recommended that further experiments be performed i n an engine with a central ignition to study the f u l l benefit of the mixing in the combustion chamber due to the squish-jet channels. Further flow f i e l d experiments are also recommended. Flow visualization would be valuable. Measurement of length scales in the squish-jet chamber could provide valuable Insight Into the link between ignition delay and small scale turbulence structure. 53. BIBLIOGRAPHY 1. MATTAVI, J.N., "The Attributes of Fast Burning Rates in Engines", SAE 800920, 1980. 2. MAYO, J., "The Effect of Engine Design Parameters on Combustion Rate in Spark-Ignited Engines", SAE 750355, 1975. 3. DAMKOHLER, G., "The Effects of Turbulence on the Flame Velocities i n Gas Mixtures", NACA TM 1112, 1947. 4. TABACZYNSKI, R.J., FERGUSON, CR. and RADNAKRISHNAN, K., "A Turbulent Entrainment Model for Spark Ignition Engine Combustion", SAE 770 , 1975. 5. BLIZARD, N.C. and KECK, J.C., "Experimental and Theoretical Investigation of Turbulent Burning Model for Internal Combustion Engines", SAE 740191, 1974. 6. ANDREWS, G.E., BRADLEY, D. and LWAKABAMBA, S.B., "Turbulence and Turbulent Flame Propagation - A C r i t i c a l Appraisal", Combustion and Flame, Vol. 24, pp. 285-304, 1975. 7. TENNEKES, H., "Simple Model for the Small-Scale Structure of Turbulence", Physics of Fluids, Vol. 11, No. 3, 1968. 8. EVANS, R.L., Patent Applications. 9. SEMENOV, E.S., "Studies of Turbulent Gas Flow in Piston Engines", Otedelenle Technicheskikh Navk, No. 8, 1958 (English Translation: NASA Technical Translation, F97). 10. DENT, J.C. and SALAMA, N.S., "The Measurement of the Turbulence Characteristics i n an Internal Combustion Engine Cylinder", SAE 750886, 1975. 11. LANCASTER, D.R., "Effects of Engine Variables on Turbulence i n a Spark-Ignition Engine", SAE 760159, 1975. 12. WITZE, P.O., "Measurements of the Spatial Distribution and Engine Speed Dependence of Turbulent Air Motion i n an I.C. Engine", SAE 770220, 1977. 13. JAMES, E.H. and LUCAS, G.G., "Turbulent Flow in Spark Ignition Engine Combustion Chambers", SAE 750885, 1975. 14. HAGHGOOIE, M., KENT, J.C. and TABACZYNSKI, R.J., "Turbulent Time Scale Measurements in a Spark-Ignition Engine Using Hot Wire Anemometry and Fast Response Ion Probes", Symposium on Flows in I.C. Engines, ASME WAM, 1982. 54. 15. LANCASTER, D.R., KRIEGER, R.B., SORENSON, S.C. and HULL, W.L., "Effects of Turbulence on Spark-Ignition Engine Combustion", SAE 760160, 1976. 16. KRIEGER, R.B. and BORMAN, G.L., "The Computation of Apparent Heat Release for Internal Combustion Engines", ASCE 66-WA/DGP-4, 1966. 17. NAGAYAMA, I., ARAKI, Y. and IOKA, Y., "Effects of Swirl and Squish on S.I. Engine Combustion and Emission", SAE 770217, 1977. 18. LUCAS, G.G. and BRUNT, M.F., "The Effect of Combustion Chamber Shape on the Rate of Combustion In a Spark Ignition Engine", SAE 820165, 1982. 19. DAVIS, G.C., TABACZYNSKI, R.J. and BELAIRE, R.C., "The Effect of Intake Valve L i f t on Turbulence Intensity and Burnrate i n S.I. Engines-Model Versus Experiment", SAE 240030, 1984. 20. P0UL0S, S.G. and HEYW00D, J.B., "The Effect of Geometry on Spark-Ignition Engine Combustion", SAE 830334, 1983. 21. WITZE, P.O., MARTIN, J.K. and BORGNAKKE, C , "Measurements and Predictions of the Precombustion Fluid Motion and Combustion Rates i n a Spark Ignition Engine", SAE 831697, 1983. 22. GROFF, E.G. and MATEKUNAS, F.A., "The Nature of Turbulent Flame Propagation i n a Homogeneous Spark-Ignited Engine", SAE 800133, 1980. 23. BRANDL, F., REVERENCIC, I., CARTELLIERI, W. and DERT, J.C., "Turbulent Air Flow in the Combustion Bowl of a D.I. Diesel Engine and i t s Effect on Engine Performance", SAE 790040, 1979. 24. CHARBONGSAI, S., KAD0TA, T. and HENEIN, N.A., "The Burning Velocity i n a C.F.R. Engine with Different Turbulent Flow Fields Generated by Intake Valve", SAE 800860, 1980. 25. JAMES, E.H., "Investigations of Combustion in 'Squish' Chamber Spark Ignition Engines", ASME 84-i>GP-10, 1984. 26. BENSON, R.S. and PICK, R., "Recent Advances in Internal Combustion Instrumentation with Particular Reference to High Speed Data Acquisition and Automated Test Bed", SAE 740695, 1974. 27. WITZE, P.O., "A C r i t i c a l Comparison of Hot-Wire Anemometry and Laser Doppler Velocimetry for I.C. Engine Applications", SAE 800132, 1980. 28. MOORE, C , "UBC Curve, Curve Fitting Routines", Computing Centre, University of British Columbia, 1984. 29. LANCASTER, D.R., KRIEGER, R.B. and LIENESCH, J.H., "Measurement and Analysis of Engine Pressure Data", SAE 750026, 1975. 55. 30. COLLIS, D.C. and WILLIAMS, M.J., "Two Dimensional Convection From Heated Wires at Low Reynold's Numbers", Journal of Fluid Mechanics, Vol. 6, 1959, pp. 357-384. 31. DAVIES, P.O.A.L. and FISHER, M.J., "Heat Transfer From Ele c t r i c a l l y Heated Cylinders", Proc. Roy. Soc. A., Vol. 280, 1964, pp. 32. KING, L.V., "On Convection of Heat From Small Cylinders in a Stream of Fluid i n Determination of the Convective Constants of Small Platinum Wires with Application to Hot Wire Aneraometry", Proc. Roy. Soc, Vol. 214A, No. 14, 1974. 33. VAN WYLEN, G.J. and SONNTAG, R.E., "Fundamentals of Classical Thermo-dynamics", John Wiley & Sons, 1978. 34. RASK, R.B., "Comparison of Window, Smoothed-Ensemble, and Cycle-by-Cycle Data Reduction Techniques for Laser Doppler Anemometer Measure-ments of In-Cylinder Velocity", Symposium on Fluid Mechanics of Combustion Systems, ASME FED, Spring Meeting, 1981. 35. CATANIA, A.E. and MITTICA, A., "A Contribution to the Definition and Measurement of Turbulence i n a Reciprocating I.C. Engine", ASME 85-DGP-12, 1985. 36. JONES, A.L., "The Performance of a Turbocharged Spark-Ignition Engine Fuelled with Natural Gas and Gasoline", M.A.Sc. Thesis, University of British Columbia, 1985. 37. KECK, J.C., "Turbulent Flame Structure and Speed in Spark Ignition Engines", Nineteenth Symposium {International} on Combustion, The Combustion Institute, 1982, p. 1451-1466. 38. LAVOIE, G., HEYW00D, J.B. and KECK, J.C, "Experimental and Theoretical Study of Nit r i c Oxide Formation i n Internal Combustion Engines", Combustion, Science & Technology 1, 313, 1970. 39. ANNAND, W.J.D., "Heat Transfer in the Cylinders of Reciprocating Internal Combustion Engines", Proc. I. Mech. E., Vol. 177, No. 36, 1963. 40. VINES, R.F., "The Platinum Metals and Their Alloys", The International Nickel Company, Inc., New York, New York, 1941. 41. NICOL, T., "Integration (Quadrature) Routines", Computing Centre, University of British Columbia, 1982. 56. APPENDIX A ~ CALIBRATION CURVES In this appendix the calibration curves for the Meriam laminar flow element, used to monitor natural gas flow, and the o r i f i c e plate used to monitor air intake flow to the C.F.R., are presented. The calibration for the laminar flow element was supplied by the manufacturer. The laminar flow element was used to calibrate the orifice plate. 57. — i 1 r CALIBRATION CURVE MERIAM LAMINAR FLOT'7 ELEMENT MODEL 50MH10-1.25NT 0 1 2 3 4 DIFFERENTIAL PRESSURE IN INCHES OF WATER Figure A . l . Calibration curve for laminar flow element. Figure A.2. Calibration curve for o r i f i c metre. 59. APPENDIX B - HOT WIRE CALIBRATION PROCEDURE In this appendix the preparation and calibration of hot wire probes for measurement of a i r movement within the C.F.R. cylinder are described. 1. Welding and Preparation Wire breakage was a frequent occurence during the course of experi-ments and thus i t became necessary to establish a routine repair procedure. Platinum Iridium wire (diameter =6.3 micrometers) obtained from TSI Incorporated was spot welded onto the support needles. The welding was performed with the aid of a microscope and a Disa welding unit model 55A12. Each welded wire was inspected visually for any defects or contamination after welding. The resistance of the sensor was measured by placing i t into the ane-mometer bridge circuit and adjusting the variable load resistance until bridge balance was achieved. The resistance of the cable and the internal resistance of the probe were accounted for in this procedure. The internal resistance of the probe varied from weld to weld but was generally between 0.58 and 0.80 ohms. Some sensors were found to have a high weld resistance after repair. These wires were maintained at a high overheat ratio u n t i l the resistance dropped and stabilized. If the weld resistance remained high the wires were discarded. 2. Calibration The probes were calibrated in an open wind tunnel with a pitot tube at ambient conditions for air speeds ranging from 0.5 to 20 m/s. The wire was operated at a temperature of 600°C. The operating temperature of 600°C ws 60. selected because Vines [40] has reported that above this temperature platinum-iridium wire undergoes a phase transformation and thus i t s resist-ance characteristics are altered. The operating resistance of the wire was determined from: R O P = Ro + V o ( T O P - V ^ where a^, RQ , TQ were supplied by the manufacturer. From the pitot tube data a Reynolds number was formed based on the wire diameter and the ambient air conditions. From the corresponding ane-mometer voltage a Nusselt number was calculated again based on the a i r conditions. From the calibration data a correlation was formed. The analytical method i s described i n the next section. 3. Analytical Procedure for Correlation The hot wire anemometer registers the change i n resistance (electrical) which results from the heat transfer from the sensor. Heat i s transferred by radiation, buoyant convection, forced convection by the flow, and conduction along the wire to the supports. The radiation portion i s small and can be neglected. Also for a l l applications except those involving very small velocities buoyancy may be neglected. Thus forced convection induced by the flow and conduction to the supports are the main modes of heat transfer. Because the convection heat transfer process i s a function of the driving temperature differential and fluid properties such as viscosity, density, and conductivity the sensor response i s sensitive to changes in temperature and pressure in the flow. Ideally a probe should be calibrated 61. over the range of temperatures and pressures encountered i n the engine cylinder. However this is not a practical solution in light of the frequent occurence of wire breakage. Thus i t becomes necessary to rely on analytical models to correct for variations from the calibrated conditions. Most of the universal calibrations developed are modifications to the theory of King [32] and express the Nusselt number as a function of the Reynolds number i n the form: where a, b, and n are determined from calibration. The Nusselt number i s also a function of the Prandtl number; however, since the Prandtl number i s almost constant In air (about 0.7) i t is not considered explicitly in the correlation. In this study an approach similar to that of Davies and Fisher as proposed by Witze [27] was taken. In this method the one dimensional energy equation for the wire i s solved to obtain an expression for the temperature distribution along the wire. This temperature distribution i s integrated along the wire to yield a mean wire temperature: Nu . <• — h = a + b Re (A.2) T. M tanh [/cT £/2] + C (A.3) where c c n T n ) / ( T u U ) (A.4) h - I2Rnan/(TTd£) and C, 2 4[h - I 2R 0a 0/(TrdJD]/k wd (A.5) 62. where h i s the heat transfer coefficient, i s the sensor support tempera-ture, T is the gas temperature, k is the mean thermal conductivity of the g w wire, RQ i s the resistance of the wire at the reference temperature T^, i s the temperature coefficient of resistance for the wire, and I i s the current through the wire. Since the mean wire temperature is fixed at 6006C, the only unknown i n the above equations i s h, the heat transfer coefficient. Iteration can be used to find h. The Nusselt number i s then formed. 4. Hot Wire Calibration Computer Program HWCAL This program uses the data obtained to f i t a correlation of the form of Equation (A.2). The program uses a nonlinear least squares method [28] to f i t the data. Inputs to the program are the ambient conditions temperature and pressure, operating resistance of the wire, and the calibration data pressure differential and anemometer bridge voltage. The data is processed within the subroutine ANEM to obtain Nusselt number, as described i n the previous section, and Reynolds numbers from the pitot tube data. The arrays of Reynold and Nusselt numbers are then passed to the curve f i t t i n g program NL2S0L from the U.B.C. curve f i t t i n g library [20]. The outputs of the program are the calibration constants a,b,n and the residuals. A program l i s t i n g and flow chart follows. 63. DEFINITION OF PROGRAM SYMBOLS A Constant ALFAO Temperature coefficient of wire resistance B Constant C2 Constant C2 i n Equation A.5 D Diameter of wire EV Anemometer bridge voltage corresponding to flow measurement H Heat transfer coefficient IV Working array of curve f i t routine KG Thermal conductivity of gas KW Thermal conductivity of wire L Length of wire NV Nusselt number P Coefficient array RE Reynolds number RHO Density of gas RO Ice point resistance of wire RW Operating resistance of wire V Pressure differential corresponding to pitot tube measurement v i s e Kinematic viscosity of gas HWCAL FLOWCHART CALL SUBROUTINE ANEM INPUTS RW, TO, TG, KG, KW, L, D, RHO, ALFAO, RO, RT, V, EV, VISC INITIAL CALCULATION A = EV2(1-ALFA0*T0)R0 PI*D*L*RTZ B = EV2*ALFA0*R0 PI*D*L*RT2 H I = EV2*RW . KG*RT2*PI*D*L(AT) VELOCITY CALCULATION V = 2*V/RHO HEAT TRANSFER COEFFICIENT C2 E H TOL HI = 4*(HI-B)/(KW*D) = TANH(C2 L/2) C2 L = (A (1-2 *E )+B (TW-2 *TO *E ) ) TW - TG + 2*E(TG-TO) = (H-HI)/HI = H TOL<0.OOOl? H YES NUSSELT NUMBER NU = H*D/KG REYNOLDS NUMBER RE = V*D/VISC CALL NL2S0L a, b, n 65. HWCAL at 10:25:13 on JUN 27, 1985 f o r CC1d=CILL Page 1 1 IMPLICIT REAL*8 (A-H.O-Z) 2 DIMENSION P(3),IV(65).V(350) 3 EXTERNAL CALCR.CALCJ 3.5 COMMON X(20).Y(20) 4 M=3 5 CALL ANEM(N) 8 P(1)=0.25DO 9 P(2)=0.25DO 10 P(3)=0.45D0 10.5 FIND (7'10O0) 11 DO 88 JJ=1,N 11.5 READ(7,89) X(UJ),Y(JJ) 11.7 89 FORMAT(2F20.2) 11.8 88 CONTINUE 12 IV(1)=0 17 CALL NL2S0L(N,M,P,CALCR,CALCJ.IV1V,IPARM,RPARM,FPARM) 18 WRITE(6,30O) IV( 1 ) 19 3O0 FORMAT(' RETURN CODE - ',12) 20 WRITE(6,301) (P(I),I•1.3),V(10) 21 301 FORMATC SOLUTION: '.1P3G16.8/ 22 1 ' SUM OF SQUARES/2 -'.1PG16.8) 31 STOP 32 END 33 SUBROUTINE CALCRf N,M,P,NF,R,IPARM,RPARM,FPARM) 34 IMPLICIT REAL*8(A-H.0-Z) 35 DIMENSION P(M),R(N) 36 COMMON X(20).Y(20) 37 DO 100 I-I.N 38 R(I)« P(1) + P(2)*X(I)**P(3) - Y(I) 40 100 CONTINUE 43 RETURN 44 END 45 SUBROUTINE CALCd(N,M,P,NF,D,IPARM,RPARM,FPARM) 46 IMPLICIT REAL*8(A-H,0-Z) 47 DIMENSION P(M),D(N.M) 47.2 COMMON X(20).Y(20) 47.7 DO 10O 1-1,N 47.8 D(I.1)=1.D0 47.9 D(I,2)=X(I)**P(3) 47.95 D(I,3)=P(2)*(X(I)**P(3))*DL0G(X(D) 47.97 ICO CONTINUE 48 RETURN 49 END 50 SUBROUTINE ANEM(NDAT) 51 REAL*8 KW,KG,L.D.RO.ALFAO.TO.TG,RW,TW,A.B.HI.C2.E.H 52 REAL'S RE(18),NU(18),EV(18),V(18),VO 53 KW-18.D0 54 KG-0.025100 55 L-1.5E-03 56 D-6.30E-06 57 ALFA0-0.O009 58 T0=293.15 59 WRITECS, 1 ) 60 1 FORMATC AMBIENT TEMPERATURE - ?') 61 CALL FREAD('GUSER','R:'.TO) 62 WRITE(6,2) 63 2 FORMATC GAS TEMPERATURE - 7') 64 CALL FREADCGUSER','R: ' ,TG) 66. HWCAL at 10:25:13 on JUN 27, 1985 f o r CC1d=CILL Page 2 65 WRITE(6.3) 66 3 FORMAT(' AMBIENT RESISTENCE OF WIRE =7') 67 CALL FREAD('GUSER','R:'.RAMB) 68 WRITE(6.4) 69 4 FORMATC OPERATING RESISTANCE OF WIRE =7') 70 CALL FREAO('GUSER'.'R:',RW) 71 WRITE(6.5) 72 5 FORMATC NUMBER OF DATA POINTS « ?') 73 CALL FREAD('GUSER','I:'.NDAT) 74 DO 999 «J=1.N0AT 75 WRITE(6,6) 76 6 FORMATC PRESSURE DIFFERENTIAL =• 7') 77 CALL FREAD('GUSER'.'R:',V(J)) 78 WRITE(6.7) 79 7 FORMAT(' ANEMOMETER VOLTAGE =7') 80 CALL FREADC GUSER','R :'. EV( J ) ) 81 999 CONTINUE 82 WRITE(6.8) 83 8 FORMATCICE POINT RESISTANCE OF WIRE 7 ') 84 CALL FREAD('GUSER'.'R:',R0) 85 TW»(RW-RO)/(ALFAO*RO) 86 TG=TG+273.15 86. 5 RA=RAMB 87 T0=T0+273.15 87. 5 TL-T0-273.15 88 RT=RW+50.214 89 TW=TW+273. 15 90 ALFA0=O.OOO9 91 DO 10 Ja1,NDAT 92 NCOUNT-0 93 V(J)=DS0RT(2.0*V(J)/1.144) 94 A=EV(d)**2*( 1 .-ALFA0*(273.15))/(3.141593*0*L*RT«*2)*RC 95 B=EV(0)**2*ALFA0/(3.141593*D*L"RT**2)*R0 96 HI=EV(d)**2/(KG*(RT**2)*3. 141593*0*L*(TW-TG))*RW 97 22 C2=4*(HI-B)/(KW*D) 98 NC0UNT=NC0UNT+1 99 IF (NCOUNT .GT. 100) GO TO 100 lOO E=DTANH(DSQRT(C2)*L/2)/(0SQRT(C2)*L) 101 H-(A*(1.-2*E)+ B*(TW-2*T0*E))/(TW-TG+2*(TG-TO)*E) 102 TOL= DABS((H-HI)/HI) 103 HI=H 104 IF (TOL .GT. 0.001) GO TO 22 105 NU(d)=H*D/KG 106 RE(J)« V(J)*D/15.7E-06 111 10 CONTINUE 111, .2 DO 102 J=1,NDAT 111. .5 WRITE(7.101) RECJ).NU(d) 111. .7 101 F0RMAT(2F20.2) 111 .8 102 CONTINUE 112 GO TO 98 113 100 WRITE(6,99) 114 99 FORMAT(' '.'ERROR. TOO MANY ITERATIONS N=100!') 1 15 98 CONTINUE 116 RETURN 117 END 67. APPENDIX C ~ DATA ACQUISITION PROGRAMS In this appendix the computer programs used for data acquisition are presented. The f i r s t program CDAQ, was used to collect data directly from the experiments. The second program BYTRD was used to transfer the d i g i t a l data from floppy discs to the MTS system. 1. Data Acquisition from C.F.R. CDAQ This program was used to acquire pressure and anemometer data from the C.F.R. engine. The program CDAQ was loaded into the I.B.M. microcomputer which was interfaced with an ananlogue to d i g i t a l conversion board. The program CDAQ was linked with PCLAB software [41] so that commands for analogue to d i g i t a l conversions could be issued from the terminal. CDAQ is an interactive program which allows the user to select sample rate, gain, and amount of data to be taken. The user may also view stored data d i g i t a l l y or graphically. CDAQ acquires data i n blocks of 32K bytes. Each analogue data point is converted to a half word (2 byte) integer. Thus each block contains 16K data points. Once data acquisition i s initiated CDAQ allows 16K analogue to d i g i t a l conversions to occur. Each data point is stored in a 16K array. Once a block i s complete CDAQ transfers the block to a f i l e on a diskette. If more than one block was requested CDAQ then goes back for more. A flow chart and the program l i s t i n g follows. CDAQ FLOWCHART MANUAL SWITCH INITIALIZATION PROCEDURES FOR DATA ACQUISITION SYSTEM INPUT DESIRED GAIN FACTOR INPUT DESIRED SAMPLE RATE AND NUMBER OF DATA BLOCKS START DATA ACQUISITION PERFORM A/D CONVERSION, PUT RESULT IN THE INTEGER ARRAY ANALOG. DATA% NO REM = REM - 1 REM 50? WRITE DATA BLOCK TO RAMDRIVE NBLCK = NBLK - 1 NO NBLK =0? VIEW THE DATA? NO WHICH BLOCK AND CYCLE? YES VIEW MORE? WRITE DATA TO FLOPPY DISC 69. 10 ' C F R D A Q . B A S T h i s p r o g r a m a c q u i r e s p r e s s u r e c r a n e i n m o r . e t e r d s t e f r o m 2 0 ' "========== t h e C . F . R . e n g i n e . 3 0 , ' 4 0 ' P R I N T " T H I S P R O G R A M A C Q U I R E S C Y L I N D E R P R E S S U R E OR HOT WIRE A N E M O M E T E R " 5 0 P R I N T " D A T A F R O M T H E C F R E N G I N E AND S T O R E S T H E V A L U E S ON D I S K . " 6 0 P R I N T 7 0 ' BO T I M E O U T - / . « 2 0 9 0 C A L L S E T . T I M E O U T ( T I M E O U T X ) JOO ' 1 1 0 P O R T . S E L E C T - / . «= 2 1 2 0 C A L L E N A B L E . F O R . O U T P U T ( P O R T . S E L E C T - / . ) ' E n a b l e b o t h o u t p u t p o r t s 1 3 0 -1 4 0 NCHAN7.=0 1 4 B P R I N T 1 4 9 I N P U T ; " I N P U T D E S I R E D B A I N ( 1 , 2 , 4 , OR B ) " ; B A I N 7 . 1 6 0 T I M I N G . S O U R C E - / . "= 3 1 9 0 S I ART . CHAN - / . = NCHAN7. 2 0 0 E N D . CHAN - / . = NCHAN7. 2 1 0 ' 2 2 0 C A L L S E T U P . A D C ( T I M I N G . S O U R C E - / . , S T A R T . C H A N - / . , E N D . C H A N - / . , GAIN - / . ) 2 3 0 ' 2 4 0 D E F I N T V , X , Y , N , I , M , Z 2 5 0 D I M DUMMY -/. ( 1 4 0 0 0 ) . A N A L O G . DATA - / . ( 1 6 1 0 0 ) 2 6 0 INC7.=0 2 7 0 P R I N T 2 B 0 I N P U T ; " T A K E NEW D A T A ( 1 ) OR V I E W D A T A I N R A M D R I V E ( 2 ) " ; D7. 2 9 0 R A T E = 1 3 0 0 I F D7.= l GOTO 3 2 0 3 1 0 I F Q7.=2 GOTO 1 1 1 0 3 2 0 P R I N T 3 3 0 P R I N T " T O S E T T H E S A M P L E R A T E , A D J U S T THE THUMBWHEEL Sl-J1TCH£S DM THE' FRONT 3 4 0 P R I N T " O F T H E C I R C U I T BOX T O : 0 1 , 0 2 , 0 5 , OR 1 0 , C O R R E S P O N D ING TO S A M P L I N G 3 5 0 P R I N T " A T E V E R Y 0 . 2 , 0 . 4 , 1 , OR 2 D E G R E E S C R A N K A N G L E R E S P E C T I V E L Y , A ^ B O , " 3 6 0 P R I N T " I N P U T T H E R A T E S E L E C T E D ( 0 . 2 , 0 . 4 , 1 . 0 OR 2 . 0 ) " 37C> I N P U T ; R A T E 3 8 0 P R I N T 3 9 0 I N P U T ; "HOW MANY B L O C K S OF D A T A DO YOU WANT ( M A X . 10 ) " ; N B L O C K 4 0 0 P R I N T 4 1 0 P R I N T 4 2 0 N = 1 6 0 0 0 ' S e t s t h e n u m b e r d a t a p o i n t s t a k e n i n e a c h b l o c k 4 3 0 K 7 . = R A T E * 4 3 0 0 ' S e t s t h e d e l a y t i m e f o r d a t a a c q u i s i t i o n 4 4 0 N U M B E R . O F . E L E M E N T S - / . «= N 4 5 0 . M = N * 2 ' S e t s t h e n u m b e r o-f b y t e s o-f m e m o r y - f o r d a t a 4 6 0 ' 4 7 0 I N P U T ; " P R E S S R E T U R N K E Y TO S T A R T " ; A S 4 8 0 P R I N T 4 9 0 P R I N T " D A T A B E I N G A C Q U I R E D " 5 0 0 P R I N T 5 1 0 INC7.= I N C X + 1 ' C o u n t s n u m b e r o-f b l o c k s o-f d a t a a c q u i r e d 5 2 0 ' 5 2 5 P R I N T " F L I P T O G G L E O N " 5 2 6 P R I N T 5 3 0 ' T h e - f o l l o w i n g s e c t i o n s e n d s t h e n u m b e r o-f d a t a p o i n t s t o b e t a k e n p e r 5 4 0 ' b l o c k t o t h e c i r c u i t b o a r d s . O n l y t h i s n u m b e r o f c l o c k p u l s e s w i l l b e 5 5 0 ' a l l o w e d t h r o u g h t o t h e d a t a a c q u i s i t i o n b o a r d . 5 6 0 ' 5 7 0 D . M A S K 7 . = & H B 0 0 0 ' M a s k a l l t h e l i n e s e x c e p t 1 5 ( l o a d l i n e ) 5 8 0 D . V A L U E / ! = & H 0 ' S e t l o a d l i n e l o w 5 9 0 C A L L O U T F ' U T . D I G I T A L . V A L U E ( P O R T . S E L E C T ' / . , D . M A S K 7 . , D . V A L U E - / . ) 6 0 0 ' 6 1 0 D . M A S K 7 . = & H 7 F F F ' M a s k l i n e n u m b e r 1 5 6 2 0 D . V A L U E - / . = N+2 ' S e t t h e o t h e r l i n e s t o t h e n u m b e r o-f s a i r . o l e s 70. 6 3 0 C A L L O U T P U T . D I G 1 T A L . V A L U E ( P O R T . S E L E C T * , D . M A S K ' / . , D . VALUE ' / . ) 6 4 0 -6 5 0 F O R I = I T D B O ' D e l a y f o r s u f f i c i e n t l o a d t i m e 6 6 0 N E X T I 6 7 0 ' 6 8 0 D . M A S K V . •= & H 8 0 0 0 ' M a s k e v e r y l i n e e x c e p t 1 5 6 9 0 D . V A L U E ' / . = J . H B 0 0 0 ' S e t l i n e 1 5 h i g h ( l o a d l i n e ) 7 0 0 C A L L O U T P U T . D I G I T A L . V A L U E ( P O R T . S E L E C T 5 S , D . MASK ' / . , D . VALUE ' / . ) 7 1 0 ' 7 2 0 ' S t a r t d a t a a c q u i s i t i o n . . . . 7 3 0 ' 7 4 0 C A L L C O N T I N U O U S . A D C . DMA <NUMBER. O F . E L E M E N T S ' / . , A N A L D S . DATA' / . ( 1 ) ) 7 5 0 C A L L T E S T . A D C . DMA (COUNT.REM' / .> 7 6 0 I F C O U N T . R E M ' / . > 5 0 6 0 T O 7 5 0 7 7 0 ' 7 B 0 ' 7 9 0 C A L L S T O P . A D C . DMA 8 0 0 P R I N T " C O U N T . R E M •= " , C O U N T . REM'.'. B I O N E G % = - I N C 7 . B 2 0 A * = 5 T R * (NEG'/.> 8 3 0 B * = " C i D A T A . " + A * 8 4 0 ' 8 5 0 Z«=0 8 6 0 Z = V A R P T R ( A N A L O E . D A T AV. <1) ) ' F i n d s t h e m e m o r y l o c a t i o n o f s t a r t o f s r r e y 8 7 0 B S A V E B * , Z , M ' S a v e s t h e 16k d a t a b l o c k t o R a m d r i v e C : B B O ' 8 8 5 P R I N T B B 6 P R I N T " F L I F T O G G L E O F F " 9 0 0 I F INC' / . < N B L O C K GOTO 5 1 0 9 1 0 P R I N T 9 2 0 P R I N T • ' « < < < < < D A T A A C Q U I S I T I O N C O M P L E T E > > > » > > " 9 3 0 P R I N T 9 4 0 I N P U T ; " D O YOU WANT TO V I E W T H E D A T A <Y/N) A N S * 9 5 0 I F A N S * = " Y " T H E N 1 1 1 0 9 6 0 I F A N S * « = " y " T H E N 1 1 1 0 9 7 0 P R I N T 9 8 0 P R I N T " D A T A R E S I D E S I N R A M D R I V E C : A N D C A N NOW B E T R A N S F E R E D TO D I S K B : 9 9 0 P R I N T 1 0 0 0 I N P U T j " D O Y O U WANT TO S T O R E T H E D A T A "5 A N S * 1 0 1 0 I F A N S * = " Y " GOTO 1 0 7 0 1 0 2 0 I F A N S * - " y " GOTO 1 0 7 0 1 0 3 0 P R I N T 1 0 4 0 I N P U T ; " D O Y O U W I S H TO T A K E MORE D A T A ? " j A N S * 1 0 5 0 I F A N S * = " Y " GOTO 2 6 0 1 0 6 0 I F A N S * = " y " GOTO 2 6 0 1 0 7 0 E N D 1 0 B 0 ' 1 0 9 0 ' 1 1 0 0 ' 1 1 1 0 P R I N T 1 1 2 0 I N P U T ; " W H I C H D A T A B L O C K DO VDU W I S H TO V I E W " ; NVIEW7. 1 1 3 0 P R I N T 1 1 4 0 I N P U T ; " I N P U T N TO V I E W C Y C L E S 1 , 1 + N , 1 + 2 N E T C " ; V / . 1 1 5 0 P R I N T 1 1 6 0 ' 1 1 7 0 S'/.= l 1 1 8 0 N E G = - N V I E W X 1 1 9 0 A * = S T R * ( N E G > 1 2 0 0 B * = " C : D A T A . " + A * 1 2 1 0 P R I N T B * 1 2 2 0 Z = V A R P T R ( A N A L O G . D A T A X ( 1 ) ) 1 2 3 0 B L O A D B * , Z 1 2 3 5 S ' / .=S ' / . - l 1 2 4 0 I N P U T j " D O YOU W I S H TO L I S T T H E D A T A " ; A N S * 1 2 5 0 I F A N S * = " N " GOTO 1 3 4 0 " 7 1 . '.110 L l = 5 4 0 / R A T E - 5 0 1 2 8 0 L 2 = 5 4 0 / R A T E + 5 0 1 2 9 0 P P C 7 . = 7 2 0 / R A T E 1 3 0 0 F O R I = L I TO L 2 1 3 1 0 P R I N T I . A N A L O G . DAT A7. ( I + S 7 . * P P C 7 . > 1 3 2 0 N E X T I 1 3 3 0 I N P U T ; U7. 1 3 4 0 K E Y O F F 1 3 5 0 S C R E E N 2 , , 0 , 0 1 3 6 0 L I N E ( 1 0 0 , 9 0 ) - ( 4 6 0 , 9 0 ) 1 3 7 0 L I N E ( 1 0 0 , 1 > - ( 4 6 0 , 1 > 1 3 B 0 L I N E ( 1 0 0 , 1 B O ) - ( 4 6 0 , 1 B O ) 1 3 9 0 L I N E ( 1 0 0 , 1 ) - ( 1 0 0 , 1 B 0 ) 1 4 0 0 L I N E ( 4 6 0 , 1 > - < 4 6 0 , 1 B 0 > 1 4 1 0 L I N E ( 1 0 0 , 4 5 ) - ( 1 0 5 , 4 5 > 1 4 2 0 L I N E ( 4 6 0 , 4 5 ) - ( 4 5 5 , 4 5 ) 1 4 3 0 L I N E ( 4 6 0 , 1 3 5 ) - ( 4 5 5 , 1 3 5 ) 1 4 4 0 L I N E ( 1 0 0 , 1 3 5 > - ( 1 0 E , 1 3 5 ) 1 4 S 0 L I N E ( 2 8 0 , 1 8 0 > - ( 2 B 0 , 1 7 6 ) 1 4 6 0 L O C A T E 1 2 , 7 , 0 : P R I N T " 0 . 0 0 " ; 1 4 7 0 L O C A T E 1 , 7 , 0 i P R I N T " 1 0 . 0 " ; 1 4 8 0 L O C A T E 6 , 7 , 0 i P R I N T " 5 . 0 " ; 1 4 9 0 L O C A T E 2 3 , 6 , 0 : P R I N T " - 1 0 . 0 " ; 1 5 0 0 L O C A T E i e , 7 , 0 : P R I N T " - 5 . 0 " ; 1 5 1 0 L O C A T E 2 5 , 4 0 , 0 t P R I NT " D E G R E E S C . A . " ; 1 5 2 0 L O C A T E 9 , 1 , 0 i P R I N T " V O L T S " ; 1 5 3 0 L O C A T E 1 , 2 0 , 0 r P R I N T " E N G I N E P R E S S U R E T R A C E " ; 1 5 4 0 L O C A T E 2 4 , 1 3 , 0 s P R I N T " 0 " ; 1 5 5 0 L O C A T E 2 4 , 3 5 , 0 i P R I N T " 3 6 0 " ; 1 5 6 0 L O C A T E 2 4 , 5 7 , 0 : P R I N T " 7 2 0 " ; 1 5 7 0 L O C A T E 1 , 1 , 0 1 5 0 0 F O R X = 1 0 0 TO 4 6 0 1 5 9 0 Y = I B O - A N A L O G . DATA7. ( < ( X - 9 9 ) * 2 / R A T E ) + < S 7 . * F P C 7 . ) ) ,'2Z 1 6 0 0 P S E T ( X , Y ) 1 6 0 9 N E X T X 1 6 1 0 I N P U T ; S T * 1 6 1 1 S C R E E N O 1 6 1 2 S7.=S7.+V7.+ 1 1 6 1 5 IF S 7 . < = ( 2 2 * R A T E > GOTO 1 2 3 5 1 6 4 0 ' 1 6 5 0 I N P U T ; " D O YOU WANT TO V I E W A N O T H E R B L O C K ? " ; A N S * 1 6 6 0 I F A N S * = " Y " GOTO 1 1 1 0 1 6 7 0 I F A N S * = " y " T H E N 1 1 1 0 E L S E 9 6 0 1 6 8 0 ' 1 6 9 0 ' P R D G R A M E N D . 72. 2. Conversion of Digital Data to MTS (BYTRD) This program was used to convert integer data from CDAQ into a form which could be read by the MTS system. This was necessary because the IBM microcomputer stored half word integers with the low order byte f i r s t , high order byte second and MTS uses the opposite order. The program reads the integer data as logical variables, in array form. The array indexes are interchanged and then the logical array i s read into an integer array. BYTRD also strips off the seven byte label placed before each block of data by CDAQ. A flow chart and program l i s t i n g follow. 73. BYTRD FLOWCHART LOGICAL*l PC(64), MTS(64), SAVE, SAVB INTEGER LNUM, NLINE INTEGER*2 LEN, DAT(32) EQUIVALENCE (DAT,MTS) CALL READ (PC,LEN,0,LNUM,5) WRITE DAT(K), K=l,28 TO FILE INPUT NUMBER OF LINES IN FILE, NLINE NLINE = NLINE - 1 CALL READ (PC,LEN,0,LNUM,5) MTS(l) = PC(1) MTS (2) = SAVE NO NLINE =0? MTS(K) = PC(K) MTS(K+1) = PC(K-l) 1 K < C 63 1 SAVE = > PC(64) 1 WRITE DAT(K), K=l,32 TO FILE J = 8 K = J-7 J = J + 2 | MTS(K) = PC(J+1) NO | MTS(K+1) = PC(J) I J < 62? | SAVE = PC(64) K = K + 2 NO STOP L i s t i n g of BYTRD at 17:46:06 on OUN 26, 1985 f o r CC1d=CILL Page 1 LOGICALM PC(64),MTS(64),SAVB,SAVE 2 INTEGER LNUM.NLINE 3 INTEGER*2 LEN,DAT(32) 4 EOUIVALENCE(DAT.MTS) 5 LEN=2 5.5 dd=1 6 CALL READ(PC,LEN,0,LNUM,5) 7 10 DO 1 0=8,62,2 8 K = d-7 9 MTS(K)=PC(d+1) 10 MTS(K+1)=PC(d) 11 1 CONTINUE 11.5 NFLG S1 12 SAVE=PC(64) 13 WRITE(7,99) (DAT(K),K=1.28) 13.5 IF (dd.GT. 1 ) GO TO 11 14 WRITE(6,100) 15 100 FORMAT(' '.'HOW MANY LINES ARE IN YOUR FILE 7' 16 CALL FREADf'GUSER','I:'.NLINE) 18 11 dd=dd+1 19 NREC=dd*1000 20 FIND(7'NREC) 21 CALL READ(PC.LEN,0,LNUM,5) 21.5 NFLG=NFLG + 1 21.7 IF (NFLG .EO. 503) GO TO 10 22 MTS(1)=PC(1) 23 MTS(2)=SAVE 24 DO 2 K=3,63,2 25 MTS(K)=PC(K) 26 MTS(K+1 )=PC(K-1) 27 2 CONTINUE 28 SAVE=PC(64) 29 WRITE(7,99) (DAT(K ) ,K=1,32) 29.5 99 FORMAT(' ',3215) 30 IF (Jd .LE. NLINE) GO TO 11 31 STOP 32 END 75. APPENDIX D ~ HOT WIRE ANEMOMETER DATA PROCESSING PROGRAMS 1. Instantaneous Velocity Evaluation and Ensemble Averaging (ANEM) In this section the program used to process the digitized anemometer signal to obtain an instantaneous velocity is described. A l l anemometer data for which velocity was required was processed with this program. Included In this program is the ensemble technique described in Chapter 6.4.1. The outputs of this program are the instantaneous velocity every 1/5 of a crank angle degree for 40 or more engine cycles, the ensemble averaged mean velocity, and the ensemble averaged turbulence intensity. The inputs to this program are the digitized anemometer voltage; the calibration constants a,b, and n for the hot wire correlation (Equation (5.1)), and the ensemble averaged pressure trace. The pressure trace contains data points for every crank angle degree In the engine cycle. At each point the temperature of the cylinder air is calculated assuming an adiabatic process (Equation (6.5)); the thermal conductivity i s calculated from Equation (6.8), and the kinematic viscosity is calculated from Equation (6.9). The reference condition was taken at the point of intake valve closing, where the pressure and temperature were taken as the ambient condition. The anemometer data i s f i r s t converted back to a voltage using the appropriate system gain and offset. Then the heat transfer coefficient from Equations 6.2, 6.3, and 6.4 i s solved for using the iteration tech-nique described in Appendix B. Once the heat transfer coefficient has been determined the Nusselt number may be formed and from the correlation (Equation (5.12) the velocity may be solved for. The instantaneous velocity obtained for each point i s stored for later 76. processing by other programs. In addition as the program runs through the data a cumulative sum of the instantaneous velocity as well as the square of the instantaneous velocity i s kept. After a l l the data has been processed the ensemble average mean velocity and turbulence intensity i s obtained from Equation 6.10 and 6.12 respectively. A flow chart and a program l i s t i n g follow. 77. Definition of Program Symbols (ANEM) AA Intercept for Nu-Re Correlation ALFAO Temperature Coefficient of Resistance for Wire BB Slope for Nu-Re Correlation CEV Anemometer Voltage Obtained from Digital Data D Wire Diameter EV Digitized Anemometer Voltage H Heat Transfer Coefficient KG Thermal Conductivity of Gas KW Thermal Conductivity of Wire LN Wire Length NBLK Number of 32K Byte Data Blocks NEW Kinematic Viscosity of Gas NEXP Exponent for Nu-Re Correlation NU Nusselt Number P Pressure PPC Data Points Per Engine Cycle RAMB Ambient Resistance of Wire RATE Data Acquisition Rate RE Reynolds Number RO Ice Point Resistance of Wire RW Operating Resistance of Wire TG Temperature of Gas TO Ambient Temperature VENS Ensemble Averaged Mean Velocity UPRIME Ensemble Averaged RMS Velocity UTOT Instantaneous Velocity 78. INPUTS TO,RAMB,RW,RO,AA,BB,NEXP,NCYC,KW,ALFAO,LN P,TG,KG,NEW,EV NCYC = NCYC -1 I CONVERT DIGITIZED DATA TO VOLTAGE INITIAL CALCULATION A= EV 2(l-ALFAO*TO)RO PI*D*L*RT 2 B^ EV 2*ALFAO*RO PI*D*L*RT 2 HI= EV2*RW KG*RT *PI*D*L (AT) 1 HEAT TRANSFER COEFF C2= 4*(HI - B)/(KW*D) E = TANH( C2 L/2) C2 L H= (A(1-2*E) +B (TW-2*T0*E) )' TW - TG + 2*E(TG - TO) TOL= (H - HI)/HI HI = H NUSSELT NUMBER' CALC" NU =H*D/KG(IND) I REYNOLDS NUMBER CALC RE = ((NU-AA)/BB)**NEXP INSTANTANEOUS VELOCITY CALC UTOT=RE*NEW/D UENS(INC)=UENS(INC) + UTOT U2(INC) = U2(INC) + UTOT**2 NCYC=0 ? NO ENSEMBLE AVERAGE UENS(J)= UENS(J)/NCYC UPRIME(J)=SQRT[U2(J)/NBLK - UENS(J)**2 * STOP 80. ANEM at 10:53:37 on JUN 27, 1985 f o r CC1d=CILL Page 1 1 REAL KW.LN.D.RO,ALFAO,TO,TG(720),RW,TW.A.B,HI,C2,E,H 2 REAL RE,NU,P(720),KG(720),NEW(720),NEXP,AA,B8,RATE,TEMP 2.5 REAL X(1801),Y1(1801),Y2(1801) 3 REAL UT0T(36OO),UENS(1801),VO.NEV,CEV,U2C1801),UPRIME(1801) 4 INTEGER EV(22.360O).PPC.NCYC,NBLK.ULIM,NREC,IND.DD(3600) 5 KW=18. 7 LN=1.5E-03 8 D=6.3E-06 9 ALFAO=9.0E-04 10 DO 11 J-1,1801 10.5 UENS(J)»0. 10.7 UTOT(J)«0. 10.75 U2(d)=0. 10.77 UPRIME(d)=0. 10.8 11 CONTINUE 11 WRITE(6.1) 12 1 FORMAT(' AMBIENT TEMPERATURE - 7') 13 CALL FREADC'GUSER','R:',T0) 14 WRITE(6.2) 15 2 FORMATC AMBIENT RESISTENCE OF WIRE » 7') 16 CALL FREADCGUSER','R:',RAM8) 17 WRITE(6.3) 18 3 FORMATC OPERATING RESISTANCE OF WIRE = ?') 19 CALL FREADCGUSER','R:',RW) 20 WRITE(6.4) 21 4 FORMATC ICE POINT RESISTANCE OF WIRE » ?') 22 CALL FREAD('GUSER','R:',RO) 23 WRITE(6,5) 24 5 FORMATC' INTERCEPT FOR NU-RE CORRELATION =7') 25 CALL FREADC'GUSER','R:'.AA) 26 WRITEC6.6) 27 6 FORMATC SLOPE FOR NU-RE CORRELATION • ?') 28 CALL FREADCGUSER','R: ' ,BB) 29 WRITE(6.7) 30 7 FORMATC' EXPONENT FOR NU-RE CORRELATION • ?') 31 CALL FREADC'GUSER'.'R:'.NEXP) 32 WRITEC6.8) 33 8 FORMATC' WHAT WAS THE DATA ACQUISITION RATE 7') 34 CALL FREADC'GUSER','R:',RATE) 35 WRITE(6 9) 36 9 FORMATC HOW MANY BLOCKS OF DATA WERE TAKEN 7') 37 CALL FREADC'GUSER','I:',NBLK) 38 DO 10 «J»1 ,720 39 READC4.100) Z,PCJ).TGCJ),KGCd),NEW(J) 40 10 CONTINUE 41 100 FORMATC ' , F8.2. 2X. F 12 .2. 2X . F 12 .2, 2X. F 12 .8, 2X , F 14 . 10) 42 PPC=720/RATE 43 NCYC=22*RATE 44 ULIM»713/RATE 47 TW=600. + 273. 15 48 T0=T0+273.15 48.5 C READ IN THE DIGITIZED HOT WIRE DATA 49 DO 50 d-I.NBLK 49.5 WRITEC6.987) J 49.7 987 FORMATC ',14) 50 NREC»C502*Cd-D+1 )*1000 51 FIND(5'NREC) 52 READC5.200) CEVC1.N),N=35.PPC).C(EV(M.N).N=1,PPC).M=2.NCYC). ANEM at 10:53:37 on JUN 27. 1985 f o r CC1d=CILL Page 2 52.2 1 (EV(1,N),N»1,34) 53 200 FORMATC '.3215) 53.8 RT=RW+50.214 53.95 NCT=0 54 DO 40 K-1.NCYC 55 DO 30 L-1800.PPC 56 IND=L*RATE 56.7 NCT=NCT+1 57 NC0UNT=O 57.5 C CONVERT THE DIGITIZED DATA TO A VOLTAGE 58 CEV=0.004883*EV(K.L) - 10. 59 NEV»CEV 59.5 C BEGIN ITERATION FOR HEAT TRANSFER COEFFICIENT 60 A=NEV**2*(1.-ALFA0*(273.15))/(3.141593*D*LN*RT**2)*R0 61 B=NEV**2*ALFA0/(3.141593*D*LN*RT**2)*R0 62 HI=NEV**2/(KG(IND)*3.141593*D*LN*(TW-TG(IND))*RT**2)*RW 63 20 C2=4*(HI-B)/(KW*D) 64 NC0UNT=NC0UNT+1 65 IF (NCOUNT .GT. 100) GO TO 70 66 E-TANH(SQRT(C2)*LN/2)/(S0RT(C2)*LN) 67 H»(A*(1.-2*E)+B*(TW-2*T0*E))/(TW-TG(IND)+(TG(IND)-T0)*2* 68 TOL- ABS((H-HI)/HI) 69 HI=H 70 IF (TOL .GT. .001) GO TO 20 70.5 C ITERATION COMPLETE EVALUATE NUSSELT NUMBER 71 NU=H*0/KG(IND) 71.5 IF (NU-AA .LT. 0.) GO TO 21 72 RE=((NU-AA)/BB)**(1/NEXP) 72.5 C CALCULATE INSTANTANEOUS VELOCITY 73 22 UTOT(L)=RE*NEW(IND)/D 73.5 INC=L-1799 74 UENS(INC)=UENS(INC)+UTOT(L) 74.5 U2(INC)»U2(INC)+UTOT(L)**2 75 30 CONTINUE 76 WRITE(7.31) (UTOT(M).M-1800.3600) 77 31 FORMATC '.10F7.2) 78 40 CONTINUE 79 50 CONTINUE 79.5 C DO ENSEMBLE AVERAGING 80 DO 60 d*1.1801 81 UENS(d)»UENS(d)/(NCYC*NBLK) 81.5 U2( d)"U2(d)/(NCYC*NBLK) 82 60 CONTINUE 83 GO TO 80 84 70 WRITE(6,400) 85 400 FORMATC '.'ERROR, TOO MANY ITERATIONS N-1001') 86 80 CONTINUE 86.2 WRITE(8,500) 86.3 C CALCULATE ENSEMBLED INTENSITY 86.5 DO 90 K=1.1801 86.7 UPRIME(K)=SQRT(U2(K)-UENS(K)**2) 86.77 CA=359.8+ K*RATE 86.8 WRITE(8,600)CA,UENS(K).UPRIME(K) 86.9 500 FORMATC ',' CA ',5X,'UBAR',3X,'UPRIME') 86.95 600 FORMATC ' . F5 . 1 . 3X . F6 . 2. 3X . F6 . 2 ) 86.955 C PLOT OUT THE RESULTS 86.96 X(K)=K/1801. *20. 86.965 Y1(K)= UENS(K)/5. *2. 82. ANEM at 10:53:37 on JUN 27. 1985 f o r CC1d=CILL Page 36.967 Y2(K)=UPRIME(K)/5. *2. 86.968 IF (Y1(K) .GT. 20.)Y1(K)=20. 86.969 IF (Y2(K) .GT. 20.)Y2(K)=20. 86.97 90 CONTINUE 86.98 CALL AXPL0T('CA DEGREES:'.0..20..0.,1.) 86.99 CALL AXPLOT('ENSEMBLES:',90..20.,0..1.) 86.995 CALL LINE(X.Y1,1801,1) 86.997 CALL LINE(X,Y2,1801,1) 86.998 CALL PLOTND 87 STOP 88 END 83. 2. Cycle by Cycle Time Averaged Mean and RMS Velocity (TRAP) This program was used to obtain the mean velocity and turbulence intensity from the instantaneous velocity records processed with program ANEM. The program begins by reading i n the instantaneous velocity U(i,v ) obtained every 1/5 of a crank angle degree over 40 engine cycles. For each velocity U(i,v ), the area under the curve, A(i,v), i s calculated for a grid size of 1/5 of a crank angle degree using the trapezoidal approximation: A(i,v ) - U(i,v ) + U(i,v+l)/2/5 (D.l) The mean velocity is calculated by constructing a 4 degree averaging interval. This i s accomplished by summing the individual areas calculated above in blocks of 20 and averaging: \> +10 U (i) = I A(i,v)/4 (D.2) 6 e- io The average is taken as the mid-point of each interval. The resulting curve i s the mean velocity Ug(d-) for the engine cycle being processed. Next the turbulence intensity i s computed. F i r s t cubic spline interpolation is used to generate points along the mean velocity record at every crank angle degree. The velocity fluctuation u^ i s then calculated as the difference between the mean velocity and the instantaneous velocity at each point: 84. u e = U(i ,9) - U 6 ( i ) (D.3) The average of u2, was then calculated using a 12 degree averaging window i n the same manner as described for the mean velocity evaluation. This procedure was performed for each of the 40 engine cycles evaluated. The ensemble averaged mean velocity was then obtained from: 1 4 0 -u e = 4 0 ^ u e ( i ) <D-4> and the ensemble averaged turbulence intensity from: 40 6 The cyclic dispersion was also evaluated in this program from: i 4 0 A program l i s t i n g and flow chart follow. 8 5 . Definition of Program Symbols (TRAP) A Trapezoidal Area Under Instantaneous Velocity AT Sum of Areas i n Averaging Interval for Mean Velocity AT12 Sum of Areas in Averaging Interval for Intensity P Tension Array for Interpolation SI Working Array of Interpolation Routine S Interpolated Valves Returned 51 First Derivative at End Points 52 Second Derivative at End Points T Crank Angle Degrees for Which Interpolated Velocity Valves are Required U Instantaneous Velocity UE Ensemble Averaged Mean Velocity UP12 Turbulence Intensity Values UPE12 Ensemble Averaged RMS Velocity URMS Cyclic Variation in Mean Velocity UT Interpolated Mean Velocity Values FLOWCHART FOR PROGRAM TRAP INPUTS U(1801,40) I IJK=0 IJK=IJK + 1 X TRAPAZOIDAL AREA CALC J=0 J=J+1 « A (J) = (U (J, UK) +U (J+l, IJK) /2/5 J ^ 1801— NO MEAN VELOCITY CALC FOR 4 WINDOW J=0 , K=0 J=J+1 « • K=K+1* L=(J-1)*20 +20 AT(J)= AT(J)+A(L) K<20 NO Y(J)=AT(J)/4 j <9Q INTERPOLATION CURVE FIT A CUBIC SPLINE TO POINTS GENERATE INTERPOLATION POINTS,S(J) ADJUST TENSION UT (J, UK) =S (J) ,J=1,360 IJK r 40 I ENSEMBLE AVERAGE MEAN VELOCITY CURVES J=0,K=0 J=J+1 « K=K+1 •* : UE(J)=UE(J)+UT(J,K) K ^ 40 NO UE(J)=UE(J)/40 J < 360 NO AREA--CALCULATION FOR INTENSITY IJK=0,KIND=0,IND=1,J=0 IJK=IJK+1 * KIND=KIND+1 , J=J+1 « j k IF (KIND=6) IND=IND+1, & KIND=1 Z1=U(J,IJK)-UT(IND,IJK) Z2=U(J+l,IJK)-UT(IND,IJK) A(J)=(Z1**2 + Z2**2)/2./5 N 0 J< 1800 • T 12 WINDOW AVERAGE J=0,K=0 J=J+1 *• K=K+1 * L=(J-1)*60+K+ll AT(J)=AT(J)+A(L) K <60 N©" UP12(J,IJK)=AT12(J)/12 J <30 IJK 40 ML NO, ENSEMBLE AVERAGE J=0,IJK=0 J=J+1 I JK=I JK+1 -+ UPE12(J)=UPE12(J)+UP12(J,IJK) IJK *40 m-J UPE12(J)=SQRT(UPE12(J)/40) J <30 WRITE DATA TO FILE UPE12(J),J=l,30 UE(J),J=l,360 * STOP 88. TRAP at 10:53:05 on JUN 27. 1985 f o r CC10-CILL Page 1 1 REAL UT(357.40),UE(357),U(1801.40),A(1800).AT(180) 2 REAL X(200).Y(200).P(1400).SI(2).S(357).Z1.Z2.URMS(357) 3 REAL UP12(36,40) 4 REAL UPE12(36) 5 REAL AT12(90) 6 REAL S1(357),S2(357).T(357) 7 DO 13 J=1.357 8 URMS(J)=0. 9 13 UE(J)=0. 10 DO 11 J=1.357 1 1 DO 12 K=1,40 12 UT(J,K)»0. 13 12 CONTINUE 14 11 CONTINUE 15 C READ IN THE INSTANTANEOUS VELOCITY FOR 40 CYCLES 16 DO 10 IJK»1,40 17 READ(5,1) (U(d.IJK).d=1,1801) 18 1 FORMATC '.10F7.2) 19 DO 2 d-1.90 20 AT(d)=0. 21 AT(J+90)-0. 22 AT2(d)=0. 23 AT4(J)«0. 24 AT8(J)=0. 25 AT12(J)-0. 26 2 CONTINUE 27 C EVALUATE TRAPAZOIDAL AREAS UNDER VELOCITY TRACE 28 DO 23 d*1.1800 29 A(J)=(U(J.IdK)+U(d+1,IdK))/2/5. 30 23 CONTINUE 31 C 32 C USE A 4 DEGREE INTERVAL FOR MEAN VELOCITY 33 C ADD UP THE AREAS FOR WINDOW OF 4 DEGREES 34 DO 4 d»1.90 35 DO 3 K-1.20 36 L=(d-1)*20+ K 37 AT(d)*AT(d)+A(L) 38 3 CONTINUE 39 C TAKE THE AVERAGE IN EACH INTERVAL 40 Y(d)«AT(d)/4. 41 . 4 CONTINUE 42 SI( 1 ) — 1 43 SI(2)»1 44 00 40 d«1.1400 45 40 P(d)=0. 46 DO 41 d»1.357 47 41 T(d)»361. + FLOAT(d) 48 DO 42 d=1.180 49 42 X(d)-358.*d»4. 50 C FIT A i CUBIC SPLINE TO THE POINTS 51 CALL SM00TH(X,Y.P,90.SI. 1.8.99) 52 C GENERATE INTERPOLATION POINTS BETWEEN AVERAGES 53 CALL SMTH(T.S.SI ,S2,357,8.99) 54 C ADJUST TENSION 55 CALL SMOOTH(X. Y.P.90.SI .0.8.99) 56 CALL SMTH(T,S.S1 .S2.357.8.99) 57 DO 43 d=1.357 58 43 UT(d,IJK)-S(d) 89. TRAP at 10:53:05 on JUN 27. 1985 f o r CC1d=CILL Page 2 59 10 CONTINUE 60 C CALC ENSEMBLED CURVE FROM INDIVIDUAL TRACES 61 DO 20 J=1,357 62 DO 19 K=1 ,38 63 UE(d)=UE(d)+UT(J.K) 64 19 CONTINUE 65 UE(J)=UE(J)/38. 66 20 CONTINUE 67 WRITE(6,300) 68 300 FORMATC '.'FINISHED MEAN VELOCITY') 69 C CALCULATE CYCLIC VARIATION IN MEAN 70 DO 800 d= 1.357 71 DO 801 K»1,38 72 URMS(d)=URMS(d)+(UT(d,K)-UE(J))**2 73 801 CONTINUE 74 URMS(J)=SQRT(URMS(J)/38.) 75 800 CONTINUE 76 WRITE(6,802) 77 802 FORMATC '.'CYCLIC VARIATION COMPLETE') 78 C CALCULATE INTENSITY NOW USE A WINDOW OF 12 DEGRE 79 DO 1000 IJK=1.40 80 IND=1 81 KIND«0 82 DO 100 J-11.1799 83 KIND-KIND+1 84 IF (KIND .EQ. 6 ) IND=IND+1 85 IF (KIND .EQ. 6 )KIND»1 86 Z1 = U(d.IJK)- UT(IND.IJK) 87 Z2=U(d+1,UK) -UT(IND,IJK) 88 A(J)-(Z1**2 +Z2**2)/2./5. 89 100 CONTINUE 90 C 12 DEG WINDOW 91 DO 401 d-1.30 92 DO 402 K=1.60 93 L=(J-1)*60 +K +11 94 AT12(d)"AT12(d)+A(L) 95 402 CONTINUE 96 UP12( J. UK W A T 12(d)/12. ) 97 AT12(d)=0. 98 401 CONTINUE 99 1000 CONTINUE 100 WRITE(6.502) 101 502 FORMATC '.'INTENSITY CALCS DONE') 102 DO 405 d«1.30 103 405 UPE12(d)»0. 104 DO 407 d»1.30 105 DO 406 IJK=1,40 106 406 UPE 12( J ) =UPE 12 ( J )+UP 12( J , UK ) 107 UPE12(d)=SQRT(UPE12(d)/40.) 108 407 CONTINUE 109 WRITE(6,503) 1 10 503 FORMATC '.'ENSEMBLE AVERAGING COMPLETE') 111 DO 21 d=1,357 112 X(d)=361. + FLOAT(d) 113 WRITE(7.22) X(d).UE(d) 114 21 CONTINUE 115 DO 28 d=1,357 116 WRITE(8.22) X(d).URMS(d) •no r. TRAP at 10:53:05 on JUN 27. 1985 f o r CC1d=CILL Page 1 17 28 CONTINUE 118 DO 410 d»1.30 1 19 X(J)=370. +(J-1)*12. 120 WRITE(7,22) X(J).UPE12(d) 121 410 CONTINUE 122 22 FORMAT(' '.2F20.2) 123 99 STOP 1 124 END 91. 3. Nonstationary Analysis (NOTIME) This program evaluates the turbulence intensity obtained from the type of nonstationary analysis proposed by Lancaster [10]. In this analysis the turbulent fluctuation u(i,9) i s defined to be the difference between a stationary mean velocity U(i), a time varying mean velocity U(6), and the instantaneous velocity U(i,8): u(i,8) = U(i,8) - U(i) - U(8) (D.7) In this program the instantaneous velocity and ensemble averaged mean velocity from the program ANEM are inputs. For each engine cycle the stationary mean is calculated from Equation 6.19 using the trapezoidal rule to evaluate the integral. The averaging window was varied from 40 to 100 degrees about TOC. The average turbulence Intensity i s evaluated for 12 degree intervals from Equation 6.20. The Intensity records were then ensembled to give an ensemble averaged turbulence intensity. A program l i s t i n g and flow chart follow. 9 2 . Definition of Program Symbols (NOTIME) A Trapezoidal Areas UE Ensemble Averaged Mean Velocity Ul Instantaneous Velocity UP40 RMS Velocity for Averaging Window of 40° UP60 RMS Velocity for Averaging Window of 60° UP80 RMS Velocity for Averaging Window of 80° UP100 RMS Velocity for Averaging Window of 100° UT40 Stationary Velocity for Averaging Window of 40° UT60 Stationary Velocity for Averaging Window of 60° UT80 Stationary Velocity for Averaging Window of 80° UT100 Stationary Velocity for Averaging Window of 100° FLOWCHART FOR PROGRAM NOTIME INPUTS UE(500),UI(1800,40) AREA CALCULATION J=0,IJK=0 IJK=IJK+1» J=J+1* < , P1=UI(J,IJK)-UE(J) P2=UI(J+l,IJK)-UE(J+l) A(J)=(Pl+P2)/2/5 N Q J < 500 •» STATIONARY MEAN VELOCITY J=0 J=J+1 "* UT(IJK)=UT(IJK)+A(J) N Q JC 500 UT(IJK)=UT(IJK)/WINDOW UB=UB+UT(IJK) CYCLIC VARIATION OF MEAN VELOCITY RMS=RMS+UT(IJK)* * 2 IJK< 40 UB=UB/4 0 RMS=SQRT(RMS/40) NO INTENSITY CALCULATION IJK=0 I JK=I JK+1 CALL INTENS(Ul,UE,UT,1,UP,IJK) IJK < 40 J=0 J=J+1 * a UP(J)=SQRT(UP(J)/40) J < 5 00/WINDOW • NO I — WRITE RESULTS UP(J),J=1,500/WINDOW J STOP 94. ' c NOTIME at 10:53:49 on JUN 27, 1985 f o r CC1d=CILL Page 1 1 REAL UE(500),UI(1801,40),UT40(40),UT60(40),UT80(40),X(20) 2 REAL UT100(40).A(500),UP40(40),UPS0(40),UP80(40),UP100(40) 2.5 C THIS PROGRAM CALCULATES THE STATIONARY MEAN VELOCITY IN A GIVEN 2.7 C WINDOW FROM THE ENSEMBLED MEAN VELOCITY AND THE INSTANEOUA VELOCITY 2.8 C BY THE METHOD OF LANCASTER. THE TURBULENCE INTENSITY IS THEN 2.9 C CALCULATED FROM THE DIFFERENCE OF THE INSTANTANEOUS VELOCITY 2.95 C AND THE TWO MEANS. ENSEMBLED AND STATIONARY 3 DO 1 0-1,40 4 UT40(d)»0. 5 UT60(J)-0. 6 UT80(0)=0. 7 UT100(0)-0. 7.5 UP40(U)«0. 7.7 UP6O(0)=O. 7.8 UP8O(0)«O. 7.9 UP100(0)-0. 8 1 CONTINUE 9 U40B-0. 10 UGOB-O. 11 U80B-0. 12 U100B-0. 13 RMS40-0. 14 RMS60-0. 15 RMS80-0. 1G RMS100=0. 17 DO 3 0-1,500 17.5 C READ IN THE ENSEMBLED MEAN 18 READ(5,2) D.UE(O) 19 2 FORMATC ' . F5. 1, 3X. F10.2) 20 3 CONTINUE 20.5 C READ IN 40 CYCLES OF THE INSTANTANEOUS MEAN 21 DO lOO IOK-1.40 22 READ(4,4) (Ul(0,IOK),0-1.1801) 23 4 FORMATC '.10F7.2) 23.5 C EVALUATE THE INTEGRAL BT THE TRAPAZOIDAL METHOD 24 DO 5 0-1,499 25 P1»UI(0+649,I0K)-UE(0) 26 P2-UK0+65O. I0K)-UE(0+1) 27 A(0)-(P1+P2)/2./5. 28 5 CONTINUE 28.5 C CALCULATE THE STATIONARY MEAN VELOCITY 29 DO 6 0-1,499 30 UT10O(I0K)«UT1OO(IUK)+A(0) 31 IF ((0.LT.50) .OR. (0 .GE. 450)) GO TO 6 32 UT8O(I0K)-UT8O(I0K) + A(0) 33 IF ((0 .LT.100) .OR. (0 .GE.4CO)) GO TO 6 34 UT60(IOK)=UT60(IOK) + A(0) 35 IF ((0.LT.15O) .OR. (0 .GE. 350)) GO TO 6 36 UT40(IdK)-UT40(IOK) + A(0) 37 6 CONTINUE 37.5 UT4O(I0K)«UT4O(I0K)/4O. 37.7 UT60(I0K)-UT60(I0K)/6O. 37.8 UT8O(I0K)«UT8O(I0K)/8O. 37.9 UT1OO(I0K)=UT1OO(I0K)/1OO. 38 U40B=U40B+UT40(IOK) 39 U60B-U6OB+UT6OU0K) 40 U80B=U80B+UT80(IOK) 41 U100B=U100B+UT100(IOK) 95. WOT IME at 10:53:49 on JUN 27, 1985 f o r CC1d=CILL Page 2 41.5 C EVALUATE THE CYCLIC VARIATION OF THE MEAN VELOCITY 42 RMS40=RMS40 + UT40(IJK)*»2 43 RMS60=RMSG0 + UTG0(IJK)**2 44 RMS80=RMS80 + UT80(IJK)**2 45 RMS100=RMS100 + UT100(IJK)»*2 46 100 CONTINUE 47 U40B=U40B/40. 48 U60B=U60B/40. 49 U80B=U80B/40. 50 U100B=U100B/40. 51 RMS40=S0RT(RMS40/40.) 52 RMS60=SQRT(RMS60/40.) 53 RMS80=S0RT(RMS80/40.) 54 RMS100=SQRT(RMS100/40.) 55 DO 200 IJK-1,40 55.5 C EVALUATE THE INTENSITY 56 CALL INTENS(UI.UE.UT40,1.UP40.IJK) 57 CALL INTENS(UI.UE.UT60,2,UP60,IJK) 58 CALL INTENS(UI.UE.UT80,3.UP80,IJK) 59 CALL INTENS(UI,UE.UT100,4.UP100.IJK) 60 200 CONTINUE 61 DO 300 J»1.20 62 UP100(J)=SQRT(UP100(J)/40.) 63 IF ( J .GT. 16) GO TO 300 64 UP80(J)=SQRT(UP80(J)/40.) 65 IF ( J .GT. 12) GO TO 300 66 UP60(J)=S0RT(UP60(J)/40.) 67 IF ( J .GT. 8) GO TO 300 68 UP40(J)»SQRT(UP40(J)/40.) 69 300 CONTINUE 70 WRITE(7,4CO) U40B,U60B.U80B.U100B 71 400 FORMATC '.4F10.2) 72 WRITE(7.400) RMS40.RMS60.RMS80.RMS 100 73 DO 500 J"1,8 74 X(J)=522.5+(J-1)*5. -360. 75 WRITE(7,6O0) X(J).UP40(J) 76 500 CONTINUE 77 DO 501 J=1. 12 78 X(J)=512.5+(J-1)*5. - 360. 79 WRITE(7.600) X(d).UP60(d) 80 501 CONTINUE 81 DO 502 d=1,16 81.5 X(J)=502.5+(J-1)*5. -360. 81.7 WRITE(7,600) X(J).UP80(J) 81.8 502 CONTINUE 81.9 DO 503 J-1,20 81.95 X(J)=492.5+(J-1 )*5. -360. 81.97 WRITE(7,600) X(d),UP100(J) 81.98 503 CONTINUE 81.99 600 FORMAT(' '.2F20.2) 82 STOP 83 END 83.5 C THIS SUBROUTINE EVALUATES THE INTENSITY 84 SUBROUTINE INTENSCUI.UE.UT.IFLG.UP.IJK) 85 REAL UI(1801.40),UE(500).UT(100),UP(100).A(500) 86 INTEGER IFLG,LOW.HI.IJK 87 TEMP=0. 88 NP=(IFLG-1)*20 + 40 96. NOTIME at 10:53:49 on JUN 27. 1985 f o r CC1d=CILL Page 3 89 L0W=(4-IFLG)*50 +1 90 HI=(L0W)+NP*5 -2 91 DO 1 d=L0W.HI 91.5 K=J+649 92 P1=UI(K.IdK)-UE(d)-UT(IdK) 93 P2=UI(K+1,IdK)-UE(d+1)-UT(IdK) 94 A(J)=(P1»«2 +P2**2)/2./5. 95 1 CONTINUE 96 NP1=NP/5 97 DO 3 d=1,NP1 98 DO 2 K«1,25 99 L=LOW + (d-1)*25 • K -1 100 TEMP=TEMP+A(L) 101 2 CONTINUE 102 UP(J)=(TEMP/5.) + UP(d) 103 TEMP=0. 104 3 CONTINUE 105 RETURN 106 ENO 9 7 . 4. Time Scale Analysis (PEAK) This program was used to obtain turbulence time scale information from unprocessed anemometer signals. The basic procedure is to scan the signal for peaks. The time separation between peaks i s recorded and a relative probability distribution is constructed for this variable. An amplitude threshold i s input to the program as a c r i t e r i a for defining a peak. This amplitude threshold was determined by operating the hot wire probe in quiescent ambient a i r and forming a distribution of the noise amplitude for this condition. The mean of this distribution was selected as the amplitude threshold. The program starts by looking at the f i r s t two data points. If the second point is less than the f i r s t the program begins to search for a valley; otherwise i t scans for a peak. The procedure for scanning for a peak or a valley are similar and only one w i l l be described here. The reader should refer to the following flow chart for complete detail. The data is read to the program in array. The program keeps track of the index and as long as the following data point i s greater than or equal to the present one the index is increased by one. When a peak is found the index i s saved u n t i l the next peak i s found. There are many tests to check for the peak validity and the reader i s referred to the flow chart for a clear description of these. Once two peaks have been found with indexes i and j respectively, the difference between the two indexes gives the time separation. This is because the sample rate was set for every 1/5 of a crank angle degree. Thus the time separation t is obtained from: 9 8 . ' 5 RPM ( D ' 8 ) Because the time separation between peaks can only occur in multiples of 1/5 of a crank angle degree the program can easily keep track of the occurences of a given time separation. The array PDF keeps track of the number of occurences of a specific separation; for example, Pdf(l) keeps track of the number of occurences of m/5 of a crank angle degree separation between peaks. The relative probability distribution of the time between peaks can then be easily determined. A program l i s t i n g and flow chart follow. 99. Definition of Program Symbols (PEAK) AMP Signal Amplitude Array D Digital Anemometer Data Array DAT Working Array of Digital Data KCNT Keeps Track of Number of Peaks NOISE Noise Amplitude Threshold PDF Keeps Track of Number of Occurences of Specific Peak Time Separation PK Index of Peak PICIND Array of Peak Indexes RDF Real Probability Distribution Function of Peak Time Separation VALE Valley Value VALE2 Valley Value 100. FLOWCHART FOR PROGRAM PEAK INPUTS DAT(40,300),NOISE INITIALIZE ALL ARRRAYS READ IN THE INTEGER DATA INITIALIZE ALL COUNTERS INITIALIZE ALL FLAGS NCYC = NCYC + 1 J = 1 KCNT=0 PKIND(J)=0,J=1,200 DAT(NCYC,2) < DAT(NCYC, 1)? •4 SEARCH FOR A PEAK -m> FLG=1 C DAT(NCYC,J+1) > DAT(NCYC,J)? J=J+1 NO DAT (NCYC, J ) = F DAT (NCYC, J+1) ? PKj=J DAT(NCYC,J)_- VALE 4 NOISE?—^ DAT (NCYC, J) >. VALE ? ^° NO KCNT = KCNT + 1 *-PKIND(KCNT)=PK JP=J SEARCH FOR A VALLEY FLG = 0 -•DAT (NCYC, J+1 )< DAT (ttCYC, J) ? J = J+ 1 ,J) f NO 1 3 DAT(NCYC,J+1)?• DAT(NCYC, DAT(NCYC,J+1)^DAT(NCYC,J) ? VALE 2-DAT(NCYC,J) TEST=DAT(NCYC,JP) TEST - VALE2> NOISE? JVALEjVALE 2 NO NO DAT (NCYC, J) ^  DAT (NCYC, JP) ?—»pO •KCNT=KCNT -1 J=^J+ 1 JINT=J •« J O O ' O — w e -DAT(NCYC,J+l) = DAT(NCYC,J)?—*NO J=J+ 1 FLG4 0? + PKjJINT + ( -JINT)/2 PDF EVALUATION K=0 K=K+1 "* INDEX=PKIND(K+l)-PKIND(K) PDF(INDEX)=PDF(INDEX)+1 K >y 300 — N O RELATIVE PD KSUM=0,K=0 K=K+1 * KSUM=KSUM + PDF(K) K^200 NO K=0 K=K+1 RDF(K)=PDF(K)/KSUM 200 NO STOP 102. 1 o-< PEAK at 17:47:25 on dUN 2S. 1985 f o r CC1d=CILL Page 1 1 INTEGER DAT(4,300),VALE,VALE2,NOISE,PKIND(200) 2 INTEGER PK.FLG.PDF(200).D(4,3600),AMP(30) 2.02 C THIS PROGRAM COUNTS THE TIME SEPARATION BETWEEN PEAKS AND 2.03 C FORMS A RELATIVE PROBABILITY DISTRIBUTION OF THIS QUANTITY 2. 05 REAL RDF(200) 2. , 1 DO 103 K=> 1,200 2. . 15 RDF(K)=0. 2. 2 PKIND(K)»0 2. 3 PDF(K)=0 2. 4 103 CONTINUE 2. ,5 DO 98 MM-1.20 2. ,7 NREC=((MM-1)*502 + 1)*1000 2. 8 FIND(5'NREC) 3 READ(5.100)(D(1.M).M-35.3600).((D(M.N).N=1,3600) 4 100 FORMATC ',3215) 5 KCNT-0 6 NOISE-7 7 PK=0 8 dP=0 9 JINT-0 10 VALE-0 11 VALE2-0 12 DO 99 K»1,30 13 AMP(K)»0 14 99 CONTINUE 15 DO 102 K-1.4 16 DO 101 L-1.300 17 M-L + 2549 18 DAT(K.L)=D(K,M) 19 101 CONTINUE 20 102 CONTINUE 25 DO 30 NCYC-1,4 26 0=1 27 KCNT-0 28 DO 104 K-1.200 29 PKIND(K)=0 30 104 CONTINUE 31 IF (DAT(NCYC,2) .GT. DAT(NCYC,1)) GO TO 4 32 1 GO TO 9 33 2 GO TO 4 34 3 IF ( J .LE. 300) GO TO 1 35 GO TO 18 36 4 FLG- 1 37 c 38 C ! SEARCH FOR A PEAK 39 c 40 IF (d .GE. 300) GO TO 18 41 5 IF (DAT(NCYC,d+1) .LE. DAT(NCYC.d)) GO TO 6 42 d = d+1 43 GO TO 5 44 6 IF (DAT(NCYC.d) .EQ. DAT(NCYC,d+1)) GO TO 15 45 PK=d 46 IF ((DAT(NCYC.d)-VALE) .GT. NOISE) GO TO 8 47 7 IF (DAT(NCYC.d).LE. VALE) GO TO 9 48 8 KCNT- KCNT + 1 49 PKIND(KCNT)=PK 50 IAMP-OAT(NCYC,d)-VALE 51 IF (IAMP .GT. 30)IAMP=30 103. " PEAK at 17:47:25 on dUN 2S. 1985 f o r CCld=CILL Page 2 52 AMP(IAMP)=AMP(IAMP)+1 53 dP«d 54 GO TO 3 55 9 FLG=0 5G C 57 C SEARCH FOR A VALLEY 58 C 59 IF (d .GE. 300) GO TO 18 60 10 IF <DAT(NCYC.d+1) .GE. DAT(NCYC.d)) GO TO 11 61 d=d+1 62 GO TO 10 63 11 IF (DAT(NCYC,d) .EQ. DAT(NCYC.d+1)) GO TO 15 64 12 IF (DAT(NCYC.d+1) .LT. DAT(NCYC.d)) GO TO 10 65 VALE2=DAT(NCYC,d) 66 TEST=DAT(NCYC,dP) 67 IF (dP .EQ. 0)TEST»10000 68 IF ((TEST -VALE2) .LE. NOISE) GO TO 13 69 VALE=VALE2 70 GO TO 2 71 13 IF (DAT(NCYC.d) .LT. DAT(NCYC.dP)) GO TO 14 72 KCNT=KCNT-1 73 GO TO 4 74 14 d=d+1 75 GO TO 10 76 15 dINT»d 77 IF (d .GE. 300) GO TO 18 78 16 IF (0AT(NCYC.d+1) .NE. DAT(NCYC.d)) GO TO 17 79 d=d+1 80 GO TO 16 81 17 IF (FLG.EQ.O)GO TO 12 82 PK=dINT +(d-dINT)/2 83 GO TO 7 84 18 CONTINUE 85 DO 20 K»1.300 86 INDEX=PKIND(K+1)-PKIND(K) 87 IF (INDEX .LE. 0) GO TO 21 88 PDF(INDEX)=PDF(INDEX) + 1 89 20 CONTINUE 90 21 CONTINUE 91 30 CONTINUE 91.5 98 CONTINUE 92 KSUM=0 93 DO 23 K»1,200 94 KSUM-KSUM + PDF(K) 95 C WRITE(6,22) K.PDF(K).KSUM 96 C22 FORMATC ',3110) 97 23 CONTINUE 101.5 DO 26 L»1.200 101.7 RDF(L)=FLOAT(PDF(L))/FLOAT(KSUM) 101.8 X-L/5.*(60./(1140.*360.))*10O0O0O. 101.9 WRITE(7.27) X.RDF(L) 101.95 27 FORMATC ',F10.2.2X.F10.3) 101.97 26 CONTINUE 102 STOP 103 END 104. APPENDIX E ~ COMBUSTION DATA PROCESSING 1. Pressure Evaluation and Ensemble Averaging from Digital Data (PENH) This program was used to read i n the digitized pressure data, ensemble average i t , convert the integers to a pressure in bars, and then save the data i n a f i l e for later use. A program l i s t i n g and flow chart follow. 105. Definition of Program Symbols (PENH) I Integer Array Used to Ensemble Digital Pressure Data KG Thermal Conductivity of Air NV Kinematic Viscosity of Air P Digital Pressure Data PE Pressure Converted to Bars RHO Density of Air TG Temperature of Air V Voltage Obtained From Digital Data FLOWCHART FOR PROGRAM PENH INPUTS INTEGER PRESSURE DATA P(21,720) I READ IN DATA J=0 J=J+1 * READ P(M,N) N=1,720;M=1,21 ENSEMBLE AVERAGE THE DIGITAL DATA M=0,N=0 M=M+1 "*" N=N+1 I(N)=I(N)+P(M,N) N >, 720 M >,21 NO NO J ->i 5 J=0 J=J+1 * I(J)=I(J)/(105) J >y 7 2 0 • — — N 9 CONVERT INTEGER TO PRESSURE IN PASCALS J=0 J=J+1 PE(J)=(004883*I(J) -10 +0.42185)*10. PE(J)=PE(J)*102.642*1000 J >/720 WRITE DATA TO FILE WRITE PE(J) ,J= 1,720 STOP 102. 1ng of PENH at 10:53:24 on dUN 27, 1985 f o r CC1d=CILL Page 1 \ £»« *» *»»* *»» * * *«« *» *»»»»««»* * * *»» * *»«»• *» *»»* *» *«««»»»•• *» * *»» *• *«» * * 2 C* * 3 C* * 4 C* THIS PROGRAM ENSEMBLES THE DIGITAL DATA FROM THE PRESSURE * 5 C* TRACE. 5-10 GRABS OF 32 K CHUNKS ARE MADE. THIS CORRESPONDS * 6 C* APPROX 22.75 CYCLES PER GRAB. * 9 C* THE INTEGERS ARE READ INTO A MATRIX, 22 CYCLES AT A TIME AND 10 C* ARE THEN ENSEMBLED THEY ARE THEN CONVERTED TO PRESSURE DATA * 11 C* AMBIENT CONDITIONS ARE ASSUMED TO EXIST IN THE CYLINDER FOR * 12 C* THE BDC CRANK POSITION 15 C* * 17 INTEGER P(21,720),D(720).I(720) 18 REAL PE(720),TG(720).U(720),KG(720),RH0(720).NU(720) 19 REAL TO.KO.PO.UO 22 P0=101300 24 DO 101 d-1,720 25 I(d)=0 26 101 CONTINUE 27 C READ IN THE DATA 28 DO 1 d-1.5 29 NREC=( 502*(d-1) + 1)*1000 30 FIND(5'NREC) 31 READ(5,99) K 32 READ(5,99)(D(L).L=1.685),((P(M.N),NM.720),M=1.21) 33 99 FORMATC ',3215) 33.5 C ENSEMBLE AVERAGE THE DATA 34 DO 2 M«1.21 35 DO 3 N=1.720 36 I(N) » I(N) + P(M,N) 37 3 CONTINUE 38 2 CONTINUE 39 NCNT»d 40 1 CONTINUE 41 DO 4 d-1,720 42 I(d)=I(d)/(NCNT*21) 42.5 4 CONTINUE 43 C 44 C THE DATA HAS NOW BEEN READ IN DIGITAL FORM AND ENSEMBLED 45 C FOR DIGITIZATION, -10 TO +10 VOLTS CORRESPONDS TO 0 TO 4096 46 C CONVERT INTEGERS BACK INTO A VOLTAGE 47 C V»(-10 + 0.004883 * I) 48 C FOR PRESSURE TRANSDUCER.10 BAR PER VOLT. REF PRESSURE IS AT BDC 48.5 C AND CORRESPONDS TO THE INTAKE MAINIFOLD PRESSURE 50 C 50.5 DO 10 'd»1.720 51 V= (.004883*1(d) - 10.) 52 PE(d)= (V+0.42185 )*10. 53 PB-PE(d) 54 C 55 C CONVERT TO PASCALS 56 C 57 PE(d)» (PE(d)*102.642)*1000. 61 10 CONTINUE 62 DO 5 d"1.180 63 K= 360 +(d-1)*2 64 WRITE(7,6) PE(K) 65 5 CONTINUE 66 6 FORMAT(' ' ,F12 4) 67 STOP 68 END 108. 2. Geometric Analysis of a Spherical Flame Front (DFLAME) This program was written to produce the flame front geometry figures required by the program MASBRN. The required information was the volume, surface area, and wetted perimeter area for a spherical flame front of radius r i n an engine cylinder with the CFR squish geometry under study. The geometry is shown schematically in Figure E . l . The combustion chamber i s a cylinder of radius RC and variable height H. The spark, is on the side. The flame is assumed to expand spherically into the chamber from the spark location. F i r s t the equations to solve for a geometry without squish w i l l be developed. Then the procedure to incorporate squish in the calculation w i l l be outlined. From Figure E . l i t can be seen that the volume of the flame V may be F expressed as: h = / [Area of flame section] dz (E.2) 0 where the area of the flame section AFS1 is given by: AFS1 = R 2a + Rc 2 (6 - sin6) (E.3) and the flame front area AFF1 i s : H AFF1 = 2R / a dz * 0 (E.4) Similarly the area of the wetted perimeter AWP1 is expressed by: Figure E.l Flame geometry for a section through a flame above the piston bowl (Flame Section 1). Figure E.2 Flame geometry for a section through a flame in the piston bowl (Flame Section 2). 111. H AWP1 = 2RC / 3 dz + AFSl(z=0) + AFSl(z=H) (E.5) 0 If the flame radius is small enough that the flame does not contact the bowl then the above equations are sufficient. However when the flame enters the bowl the geometry of the flame section shown in Figure E.2, AFS2 becomes important. The area AFS2 i s given by: AFS2 = YR2 + 6RB2 - R 2siny - RB 2sin6 (E.6) The expressions for the volume, flame front area, and wetted perimeter are similar to those given previously except that the lower limit of integra-tion is now H and the upper limit H+D (D is the bowl depth). The program DFLAME generates a table of volumes and areas for combina-tions of flame radius and cylinder height. A l l calculations are done in two parts. The f i r s t for a cylinder without a squish bowl and the second adds in the effect of the squish bowl i f required. The integration i s performed with the aid of UBC DCADRE [41]. A program l i s t i n g and flow chart follow. 112. Definition of Program Symbols (DFLAME) AFLAM1 Area of Flame Front 1 AFLAM2 Area of Flame Front 2 AFND Nondimensional Area of Flame Front AFS1 Area Function for Section 1 AFS2 Area Function for Section 2 ALF Function for Angle Alfa APND Nondimensional Area of Wetted Perimeter AWP1 Area of Wetted Perimeter, Section 1 AWP2 Area of Wetted Perimeter, Section 2 BET Function for Angle Beta D Depth of Piston Bowl DEL Function for Angle Delta ERRAF Error in Flame Area ERRAP Error i n Wetted Perimeter Area ERRV Error in Volume GAM Function for Angle Gamma H Piston Distance from Head HND Nondimensional H HU1 Upper Integration Limit for Section 1 HU2 Upper Integration Limit for Section 2 RB Radius of Piston Bowl RC Radius of Cylinder RF Radius of Flame RND Nondimensional Radius VOLF Volume of Flame VND Nondimensional Flame Volume 113. FLOWCHART FOR PROGRAM DFLAME INITIALIZE ALL VARIABLES TO ZERO K=0 K=K+1 •* CA=(K-1)*PI/180. CALC PISTON HEIGHT B=ARCSIN(R/S * SIN(CA)) H=S + R - S*COS(B) - R*COS(CA) + HC HND(K)= H/HC START FLAME-GEOMETRY CALC J=0 J=J+1 * SET FLAME RADIUS RF=J*0.08125/2 RND(J)=RF/RC VOLUME CALC \ » VOLFl=DCADRE(AFS1,0,HUl,DEPS,DREL,ERROR) ft*0-—HU1>,H ? |#-HU1* RF ? NO HU2=RF tRF> H+D? HU2=H+D VOLF2=DCADRE(AFS2,H,HU2,DEPS,DREL,ERROR) 1 f »VOLF=VOLF1+VOLF2 VOLF1=0 VOLF2=0 VND(J)=VOLF/(PI*(RC**2 *H + RB**2 *D)) AREA OF FLAME FRONT CALC AFLAM1=DCADRE(ALF,0,HUl,DEPS,DREL,ERROR) NO HU2 >, H ? AFLAM2=DCADRE(GAM,H,HU2,DEPS,DREL,ERROR) 'AFLAME= (AFLAM1+AFLAM2) *2*RF AFLAM1=0 AFLAM2=0 HU1=RF HU1> H ? HU1=H AFND(J)=AFLAME/(2*PI*RC**2) 1 2 WETTED PERIMETER CALC AWP=(DCADRE(BET,0,HUl,DEPS,DREL,ERROR))*2*RC J J 0 AWP1=AWP+AFS1 (0.0) HU2 >, H ? AWP2=DCADRE(DEL,H,HU2,DEPS,DREL,ERROR)* 2 *RB , 0 AWP2=AWP2'+AFS1(H)-AFS2(H) «—HU2 ...= HT ? AWP2=AWR2 + AFS2(HT) L-*APND(J) =(AWP1 + AWP2)/(2*PI(RC*H + RB*D + RC**2) AWP1=0 AWP2=0 HU1=0 HU2=0 NO ~VND(J) < 1 ? NO J^.1000 ? } WRITE RESULTS TO FILE WRITE RND(J),VND(J),AFND(J),APND(J):J=1,N K ? 45 NO STOP F U N C T I O N A F S l ( Z ) R =SQRT(RF**2 - Z**2) A L F A = A R C O S ( R / ( 2 * R C ) ) B ETA=ARCOS((2*RC**2-R**2)/(2*RC**2)) EB E T A < P I / 2 ? AFS1=R**2*ALFA + R C * * 2 ( B E T A - S I N ( B E T A ) ) AFS1=' R**2 ( A L F A - S I N (ALFA).'!'+ BETA*RC**2 +(R*COS(GAMMA) - R C ) * R * S I N ( A L F A ) L RETURN F U N C T I O N AFS2(Z) E L R=SQRT(RF**2 - Z**2) GAMMA=ARCO S ( R / ( 2 * R B ) ) D E L T A = A R C O S ( (2*RB**1|-R**2) / (2*RB**2) ) D E L T A < P I / 2 ? AFS2=R**2*GAMMA + R B * * 2 * D E L T A - R**2*SIN(GAMMA) - R B * * 2 * S I N ( D E L T A ) AFS2=R**2*(GAMMA-SIN(GAMMA)) + DELTA*RB**2 + (R*COS(GAMMA)-RC)*R*SIN(GAMMA) RETURN F U N C T I O N A L F ( Z ) R=SQRT(RF**2 - Z**2) - A L F = A R C O S ( R / ( 2 *RC) ) RETURN F U N C T I O N GAM(Z) R=SQRT(RF**2-Z**2) GAM=ARCOS(R/(2*RB)) RETURN F U N C T I O N D E L ( Z ) R=SQRT(RF**2-Z**2) DEL=ARCOS((2*RB**2 RETURN - R**2)/(2*RB**2)) F U N C T I O N B E T ( Z ) R =SQRT(RF**2 - Z**2) B E T = A R C O S ( ( 2 * R C * * 2 -RETURN R**2)/(2*RC**2)) 116. ing of DFLAME at 17:47:41 on JUN 26. 1985 for CC1d«CILL Page 1 1 IMPLICIT REAL*8(A-H,0-Z,$) 2 EXTERNAL AFS1.AFS2.ALF,GAM,BET,DEL 3 REAL*8 RND(100).VND(100).AFND(100).APND(100),HND(100) 3, .5 REAL*8 ERRV(100),ERRAF(100),ERRAP(100) 4 C HU1 IS THE UPPER LIMIT OF INTEGRATION FOR SECTION 1 5 C HU2 IS THE UPPER LIMIT OF INTEGRATION FOR SECTION 2 6 c RND IS THE NONDIMENSIONAL RADIUS; RF/RC 7 c VND IS THE NONDIMENSIONAL VOLUME; VOLF/VC 8 c AFND IS THE NONDIMENSIONAL FLAME FRONT AREA; AFLAME/AC 9 c APND IS THE NONDIMENSIONAL WET PERIMETER AREA; AWP/(AC + Al 10 c S IS THE CONNECTING ROD LENGTH 11 c H IS S+HC.(HC IS THE CLEARANCE HEIGHT) 12 c RF IS THE FLAME RADIUS 13 c RC IS THE CYLINDER RADIUS 14 c RB IS THE BOWL RADIUS 15 c VOLF IS THE VOLUME ENCLOSED BY THE SPHERICAL FLAME FRONT 16 c D IS THE DEPTH OF THE BOWL 17 COMMON RF.RC.RB 18 PI=3.141593 18. . 1 VOLF2-0.0 18, .2 AWP-0.0 18 .3 AWP1-0.0 18 .4 AWP2-0.0 18. .5 AFLAM1-0.0 18. .6 AFLAM2-0.0 19 5=10.0 20 R-2.25 21 00 2000 K-1.45 22 CA=(K-1)-PI/180.0 23 B-DARSINCR/S* DSIN(CA)) 24 H= S + R - S*DCOS(B) - R*DC0S(CA) 25 DEPS-0.0 25. .5 DREL-0.OOOOOOO1 26 0*1.337 27 RC-3.25/2 28 RB-O.83 29 HC-.059 30 H-H+HC 31 HU2«0. 32 HT-H+D 35 RF-.00 36 HND(K)-H/HC 37 WRITE(6,20) HND(K) 38 20 FORMATC'1'.' DIMINSIONLESS HEIGHT OF PISTON H/RC - '.F8.I 39 DO 1000 d»1,100 39. .5 DEPS-1.OOE-11 42 N=d 43 RF=d*.08125/2. 44 RNDC d)-RF/RC 45 c FIRST CALC THE VOLUME OF THE FLAME. THE CALC IS DONE IN 46 c TWO PARTS. PART ONE ASSUMES A DISC CHAMBER OF HEIGHT H 47 c PART TWO BRINGS IN THE EXTRA VOLUME OF BOWLS OR DEPRESSIONS 48 c IN THE CYLINDER HEAD OR PISTON 49 HU1-RF 50 c THE UPPER LIMIT OF INTEGRATION IS SET TO THE FLAME RADIUS 51 IF (HU1 .GT. H) HU1-H 52 VOLF1«DCA0RE(AFS1.O.DO.HU1.DEPS.DREL,ERROR) 52. 2 ERRV(d)-ERROR 117. :1ng of DFLAME at 17:47:41 on JUN 26, 1985 f o r CC1d=CILL Page 2 53 IF (HU1 .LT. H) GO TO 98 54 IF (HU1 .EQ. RF) GO TO 98 55 C THIS MEANS THE SPHERE DOES NOT INTERSECT THE PISTON & THEREFORE 56 C NO FURTHER VOLUME CALC IS REQUIRED. 57 HU2=RF 58 IF (RF .GT. H+D)HU2=H+D 59 - VOLF2-DCADRE(AFS2,H,HU2.DEPS,DREL,ERROR) 59. .2 ERRV(d)»ERRV(d)+ERROR 60 98 V0LF-V0LF1 + V0LF2 60. ,5 ERRV(d)-100.000-(VOLF - ERRV(d))/V0LF *100. 61 V0LF1-0. 62 V0LF2-0. 63 VND(d)-V0LF/(3.14*(RC**2»H + RB*»2*0)) 64 C NOW CALCULATE AREA OF FLAME FRONT 65 C THE CALCULATION IS SIMILAR TO THE VOLUME CALC 66 AFLAM 1-DCADRE(ALF,0.,HU1,DEPS,DREL,ERROR) 66. .5 ERRAF(J )-ERROR 67 IF (HU2 .LT. H) GO TO 99 68 AFLAM2=DCADRE(GAM,H.HU2,DEPS,DREL.ERROR) 68. 5 ERRAF(J)=ERRAF(J)+ERROR 69 99 AFLAME"(AFLAM1 + AFLAM2)*2*RF 69. .2 IF ((AFLAM1+AFLAM2).LE. 0.0)GO TO 33 69 .5 ERRAF(d)"100.-((AFLAM1+AFLAM2)-ERRAF(J))/(AFLAM1+AFLAM2)* 100 69. .7 GO TO 34 69. .8 33 ERRAF(d)»100.00- ERRAF(J)* 100.0 70 34 AFLAM1"0. 71 AFLAM2-0. 72 AFND(d)=AFLAME/(2*3.14*RC**2) 73 C NOW CALCULATE AREA OF WETTED PERIMETER 74 C 75 AWP"(DCADRE(BET,0.,HU1.DEPS,DREL.ERROR))*2*RC 75. 2 AWP1"AWP+AFS1(0.DO) 75. .5 ERRAP(U)"ERROR 76 IF (HU2 .LT. H)G0 TO 100 77 AWP2-(DCADRE(DEL.H.HU2.DEPS.DREL.ERROR))*2*RB 77. .2 AWP»AWP+AWP2 77, .5 ERRAP(d)«ERRAP(d)+ERROR 78 AWP2»AWP2+ AFS1(H)-AFS2(H) 79 IF (HU2 .EQ. HT) AWP2»AWP2+AFS2(HT) 80 100 APN0(d)-(AWP1 + AWP2)/(2«3.14*(RC»H + RB*D +RC*»2 )) 80. .5 ERRAP(J)"lOO.OO-(AWP-ERRAP(d))/(AWP)* 100. 80. .7 AWP-O.O 81 AWP1-0. 82 AWP2-0. 83 HU1-0. 84 HU2=0. 85 IF (VND(d).GE. 1.) GO TO 2 86 10OO CONTINUE 87 2 CONTINUE 88 WRITE(6,3) N 89 3 FORMAT('-'.'N - '.13) 90 WRITE(6.30) 91 30 FORMAT('-',4X, 'RF/RC',9X,'VF/VT',9X. 'ERROR%'.7X.'AFF/AFT' , 91 . 5 1 8X,'ERROR%'.7X,'AWP/APT',8X.'ERROR%') 92 DO 10 d»1 ,N 93 WRITE(6, 1) RND(d),VND(d).ERRV(d),AFND(d),ERRAF(d).APND(d), 93. .5 1 ERRAP(d) 94 1 FORMAT!'0',2(F12.10.2X),F12.9,2X,2(F12.10,2X,F12.9.2X)) 118. mg of DFLAME a t 17:47:41 on JUN 26. 1985 f o r CCld=CILL Page 3 95 10 CONTINUE 96 2000 CONTINUE 97 STOP 98 END 99 DOUBLE PRECISION FUNCTION AFS1(Z) 100 IMPLICIT REAL*8(A-H,0-Z,$) 101 COMMON RF.RC.RB 101 . 5 PI=3.141593 102 R=DSQRT(RF**2 - Z*»2) 103 IF (R .GT. 2«RC)R=2»RC 104 ALFA=DARC0S(R/(2*RC)) 105 BETA=DARC0S((2*RC**2 - R«*2 )/(2*RC**2)) 106 IF(BETA .GT. PI/2) GO TO 1 107 AFS1=R*»2 * ALFA +RC»*2*(BETA-DSIN(BETA)) 108 GO TO 2 109 1 AFS1=R**2*(ALFA-DSIN(ALFA) ) + BETA*RC**2 + 110 1 (R*DCOS(GAMMA)- RC)*R*DSIN(ALFA) 1 10. 5 2 CONTINUE 1 1 1 RETURN 112 END 113 DOUBLE PRECISION FUNCTION AFS2(Z) 114 IMPLICIT REAL*8(A-H,0-Z.$) 115 COMMON RF.RC.RB 115. 5 PI=3.141593 1 16 DIFF" RF**2-Z**2 120 R=DSQRT(RF**2 - Z**2) 121 IF (R .GT. 2*RB) R«2*RB 122 GAMMA-DARCOS(R/(2*RB)) 123 DELTA=0ARC0S((2*RB*»2-R**2)/(2*RB**2)) 124 IF (DELTA .GT. PI/2) GO TO 1 125 AFS2=R**2*GAMMA •RB**2*DELTA - R**2*DSIN(GAMMA) 125. 2 1 RB**2*DSIN(DELTA) 126 RETURN 129 1 AFS2«R**2*(GAMMA-DSIN(GAMMA) ) + DELTA*RB**2 130 1 + (R*DCOS(GAMMA)-RC)*R*DSIN(GAMMA) 131 RETURN 132 END 133 DOUBLE PRECISION FUNCTION ALF(Z) 134 IMPLICIT REAL*B(A-H,0-Z.$) 135 COMMON RF.RC.RB 136 R=DS0RT(RF**2-Z**2) 137 IF (R .GT. 2*RC)R»2*RC 138 ALF«DARC0S(R/(2*RC)) 139 RETURN 140 END 141 DOUBLE PRECISION FUNCTION GAM(Z) 142 IMPLICIT REAL*8(A-H.0-Z.$) 143 COMMON RF.RC.RB 144 R=DSQRT(RF**2-Z**2) 145 IF (R .GT. 2*RB)R=2*RB 146 GAM=DARC0S(R/(2*RB)) 147 RETURN 148 END 149 DOUBLE PRECISION FUNCTION DEL(Z) ISO IMPLICIT REAL*8(A-H.0-Z.$) 151 COMMON RF.RC.RB 152 R=0SQRT(RF**2 - Z**2) 153 IF (R .GT. 2*RB)R»2*RB 119. ing of DFLAME at 17:47:41 on JUN 26. 1985 f o r CCfd=CILL Page 4 154 DEL=DARCOS((2*RB**2 - R**2)/(2*RB**2)) 155 RETURN 156 END 157 DOUBLE PRECISION FUNCTION BET(Z) 158 IMPLICIT REAL*8(A-H.O-Z,$) 159 COMMON RF.RC.RB 160 R«DS0RT(RF**2-Z**2) 161 IF (R .GT. 2*RC)R=2*RC 162 BET=DARCOS((2*RC**2 - R**2)/(2*RC**2)) 163 RETURN 164 END 120. 3. Burning Rate Analysis (MASBRN) The program used to perform the mass burn rate analysis was developed by Jones [36] and a complete description and flow chart may be found. Only alterations concerned with the CFR cylinder geometry were made. These occur in statements defining cylinder volume. The other change was in the way the flame front geometry i s evaluated. The old geometry was calculated based on a cylindrical chamber with a hemispherical head. The program DFLAME was used to produce a table of values which MASBRN reads i n when required. No other changes were made. 121. MASBRN at 17:46:21 on JUN 26, 1985 f o r CCid=CILL Page 1 1 C MB THIS PROGRAM CALCULATES MASS BURNING RATE AND 2 C === FLAME SPEED FROM MEASURED PRESSURE DATA TAKEN 3 C FROM THE CFR ENGINE. 4 C 5 IMPLICIT REAL*8(A-H.0-Z) 6 REAL*8 MPV,K,L,M,N,NO,N2,N02,NCH,KK,NUM,NUM1,NMIX,MOLFL, 7 -NM.NM1,NNM1,NNM2.NN2.NN02,MEP,LENG.MTOT.MWMIX,MFX1,NNCH, 8 -MFX2,MW(14),MMFX2,NRN2.NRES.NR02.NRC02,NRH20,NNFUEL 9 -.MF(5.200),IGNDEL.MWBMIX 10 C 11 COMMON /AREA 1/ NCH,N02,K,L,M,N,KFUEL 12 COMMON /AREA2/ MOLFL,NMIX,HF1,NN02,NN2,NNFUEL,KOM 13 COMMON /AREA3/ AREAB.HTEXP,MPV,HTFCN,TWALL.VISC,THCOND 14 COMMON /AREA4/ NDISS,IPRINT 15 C 16 DIMENSION X(10),PP(5.200),VV(5,200).VV2(5,200).VVX(20), 17 -DH(20),CPG(20),PP2(5,200),DI(5,200),TIM(5.200).XX(5,200), 18 -CCA(10),DL(5,200),ZZ(5,200),DC(5,200),YY(5.200),P0UT( 180), 19 -UUU(10),CC(10),PDAT(5,200),CB(5,200),TB(5.200), 20 -FS(5,200),RB(5,200) 21 C 22 INTEGER IPRES(5,200).NREP,NMODE 23 C 24 C STATEMENT FUNCTION USED THROUGHOUT PROGRAM TO CALCULATE CYLINDER 25 C VOLUME (DVOL) AT A GIVEN CRANK ANGLE (DALFA). VOLUME OBTAINED MUST 26 C BE ADDED TO THE CLEARANCE VOLUME TO GIVE TOTAL CYLINDER VOLUME 27 C 29 DVOL(DALFA)=3.14159*((BORE/2.)**2.)*((STR0K/2.)*(1.-DCOS(DALFA* 30 -0.0174532))+LENG*(1.-DSORT(1.-(DSIN(DALFA*0.0174532)*DSIN(DALFA 31 -*0.0174532)*((STROK/2./LENG)**2.))))) 31.5 PI=3.14159 32 NUMBR=1 33 IPRINT=0 33.5 JFLG=0 34 IGRAPH=0 35 DO 222 IL=1,NUMBR 36 C 37 C 38 C READ TYPE OF FUEL (11=CH4. 12=C8H18, 13=C3H8 ): 39 C TEMP. (T1)(K) AT START OF COMBUSTION; 40 C ENGINE SPEED (RPM); COMPRESSION RATIO (COMPR); REL. AIR/FUEL 41 C RATIO, LAMBDA (AF); SPARK ADVANCE (SPKAD) (DEG. B.T.D.C.); 42 C HEAT TRANSFER MULTIPLIER (HTFCN); 43 C HEAT TRANSFER EXPONENT (HTEXP); 44 C RESIDUAL GAS FRACTION (%), ( F ) ; PERCENTAGE CONSTITUENTS IN 45 C RES. FRACTION (PR02,PRC02.PRH20.PRN2); 46 C WHETHER FULL DISSOCIATION (NDISS=0), OR PARTIAL (NDISS=1); 47 C CRANK ANGLE ITERATION INCREMENT (PDCA); CYL. WALL TEMP. (TWALL); 48 C s 49 C THERE IS AN OPTION TO ENTER DATA IN THE INTERACTIVE MODE OR 50 C CONVENTIONALLY THRU A DATA FILE 51 C 52 WRITE(6,1) 53 1 FORMATC ','DO YOU WANT TO READ THE DATA FILE (0) OR ENTER DATA 54 11NTERACTIVELY (1) 7') 55 CALL FREAD('GUSER','I:',NMODE) 55.5 JFLG=0 56 IF (NMODE .EO. 1) GO TO 3 12 2-r MASBRN at 17:46:21 on JUN 26. 1985 f o r CC1d=CILL Page 2 57 READ(5,47 ) KFUEL.T1.SPEED.COMPR.AF.SPKAD.HTFCN,HTEXP 58 47 FORMAT(I3.2F7.1.3F6.2.F6.3.F5.2) 59 READ(5,46) F,PR02.PRC02.PRH20.PRN2,NDISS,PDCA,TWALL 60 46 FORMAT(5F7.3,13.F6.2.F7.1) 61 REA0(5.2) PINLET,AIRFLO,IGNDEL,SCONST,IPRNTS.PAMB 62 READ(5,22) CUPD.CUPH.HC 63 22 F0RMAT(3F8.3) 64 2 F0RMAT(F6.1,3F6.2.13.F6.2) 64. 5 JFLG=1 64. 7 WRITE(6,5) 64 . 8 5 FORMAT(' ','DO YOU WANT TO CHANGE ANY OF THE INPUTS 1=Y,0=N 7' 64 . 9 CALL FREAD('GUSER','I:',NREP) 65 IF ( NREP .EO. 0)GO TO 4 66 3 CALL INPUTS(JFLG,KFUEL.T1.SPEED,COMPR,AF, 67 1 SPKAD.HTFCN,HTEXP,F,PR02,PRH20,PRN2,NDISS,PDCA, 68 1 TWALL.PINLET.AIRFLO.IGNDEL,SCONST.IPRNTS.PAMB,CUPD.CUPH.HC) 69 4 CONTINUE 70 C 71 C READ IN PRESSURE DATA 72 C 73 CALL SMOOTH(POUT.SCONST,IPRNTS) 74 C 75 DO 658 KJ-1,180 76 PDAT(IL.KJ)=POUT(KJ) 77 658 CONTINUE 78 C 79 C DETERMINE FUEL PROPERTIES: MOL.WEIGHT, LOW HEAT VAL., BO C ENTHAL. OF FORMATION 81 C 82 IF(KFUEL.GT.11) GOTO 10 83 CN=1.0 84 HM=4.0 85 MW(11)=16.04 86 QVS=500S0.0 87 HF1--74873.0 88 WRITEO,45) CN.HM 89 45 FORMATdH .'FUEL TYPE:- METHANE C '.F3.1.' H '.F3.1/) 90 GOTO 30 91 C 92 10 IF(KFUEL.GT.12) GOTO 20 93 CN=8.0 94 HM-18.0 95 MW(12)»114. 14 96 0VS-435OO.0 97 HF1=-208447.0 98 WRITEO.43) CN.HM 99 43 FORMATdH ,'FUEL TYPE:- OCTANE C '.F3.1,' H ',F4.1/) 100 GOTO 30 101 C 102 20 IF(KFUEL.GT.13) STOP 103 CN=3.0 104 HM=8.0 105 MW(13)«44.097 106 0VS=46353.O 107 HF1--103847.0 108 WRITEO.44) CN.HM 109 44 FORMATdH .'FUEL TYPE:- PROPANE C '.F3.1.' H '.F3.1/) 110 C • 123. MASBRN at 17:46:21 on JUN 26, 1985 f o r CC)d=CILL Page 3 111 C ENGINE PARAMETERS 112 c 113 30 CONTINUE 114 STROK-4.5*.0254 1 15 B0RE=3.25*.0254 116 LENG=10.0*.0254 117 HTCLRV=HC 118 c CLEARANCE HEIGHT IS SET FOR EACH GEOMETRY 119 CLRV=HTCLRV*3.141593*(B0RE**2)/4.0 +CUPD**2/4.*PI*CUPH+0.0OO0027 120 c 121 c GAS CONSTANT (KJ/KMOL K) 122 c 123 RMOL-8.31434 124 dd»0 125 c 126 c 127 c CALC STOICH A/F RATIO(STAFR) AND AIR/FUEL RATIO(AFR) 128 c 129 STAFR«((CN+HM/4.)*32.+3.762*(CN+HM/4.)*28.01)/((CN*12)+HM) 130 AFR=STAFR*AF 131 c 132 c CALCULATE VOLUMETRIC EFFICIENCY FROM AIR MASS FL0W(g/sec), 133 c INLET TEMP(K) AND PRES(kpa), RPM. AND DENSITY FACTOR 134 c FOR GASEOUS FUELS 135 c VOLEFF=AIRFLOW/(P/RT)*FACTOR*SPEED*(SWEPT V0L./2) 136 c FACTOR-DENSITY CORRECTION FOR FUEL VAPOUR IN CHARGE 137 c PINLET=PAMB-PLOSS(LOSS THRU VENTURI ELEMENT) 137 .5 - PLOSS-1.8 138 FACTOR-1 139 IF(KFUEL.EO.12) GOTO 700 140 FACTOR-1.0+(1.0/AFR)*(29.0/(MW(KFUEL))) 141 c 142 c INLET PRES REDUCED BY PLOSS 143 c 144 700 V0LEFF»45.858*FACT0R*AIRFL0*T1/(SPEED*(PINLET-PL0SS)) 144.5 145 c 146 c CONVERT PRESSURE DATA IN BAR TO KPA, AND CORRECT DATA FOR 147 c VOL. EFF. 148. c 149 P1-V0LEFF*(PINLET-PL0SS) 150 PVEFF-(101.3)-P1 151 WRITE(9,701) PI.VOLEFF,FACTOR,PVEFF 152 701 F0RMAT(1H ,'P1,VOLEFF.FACTOR,PVEFF '.4F10.3/) 153 DO 267 1-1,180 154 PDAT(IL.I)=PDAT(IL.I)/1000.-PVEFF 155 267 CONTINUE 156 c 157 c 158 c CALC. NUMBER OF KMOLS OF REACTANTS AND PRODUCTS BEFORE AND AFTER 159 c COMBUSTION RELATIVE TO ONE KMOL OF FUEL 160 c (NOT INCLUDING DISSOCIATION). NCH-HYDROCARBON 161 c N02-AVAILABLE OXYGEN. N-NITROGEN. K-C02. L-H20, M-UNBURNT OXYGEN 162 c 163 NCH- 1 164 N02=(CN+HM/4)*AF 165 N-3.762*(CN+HM/4 )*AF 166 K-CN 124. MASBRN a t 17:46:21 on JUN 26, 1985 f o r CC1d=ClLL Page 4 167 L=HM/2 168 M=(CN+HM/4)*(AF-1) 169 C 170 WRITEO,655) NCH,N02.N.K.L,M 171 655 FORMATdH , ' NCH, N02 . N. K, L . M= ' . 6F9 . 5/ ) 172 C 173 C CALC. TOTAL NUMBER OF KMOLS OF REACTANTS... 174 SUMNS=NCH+N02+N 175 C CALC. NO. OF KMOLS OF RESIDUAL GAS GIVEN THE VOLUME FRACTION OF 176 C RESIDUAL GASES 'F' 177 NRES=(F/(1-F))*SUMNS 178 C CALC. NO. OF KMOLS IN CYLINDER PER KMOL OF FUEI 179 NMIX-SUMNS+NRES 180 SUMNS=NMIX 181 C CALC. NO OF KMOLS OF EACH RESIDUAL GAS... 182 NR02=PR02*NRES/100.0 183 NRC02=PRC02*NRES/100.0 184 NRH20=PRH20*NRES/100.0 185 NRN2=PRN2*NRES/100.0 186 C CALC. NEW VALUES FOR THE TOTAL NO. OF KMOLS OF N2. 02, C02.& H20 187 N=N+NRN2 188 N02=N02+NR02 189 K=K+NRC02 190 L*L+NRH20 191 M=M+NR02 192 WRITEO.655) NCH,N02.N,K,L,M 193 C 194 C CALC. ENERGY OF REACTANTS AT INLET TEMP; 5=02. 6=N2. 11= CH4 195 C 12=C8H18, 13=C3H8, 1=C02. 3=H20.... (IN KJ/KMOL OF FUEL) 196 DH(1)=((3.096*T1+0.00273*(T1**2)-7.885E-07*(T1 **3 ) 197 1+8.66E-11*(T1**4))-1t45.0)*RM0L 198 DH(3)=((3.743*T1+5.656E-04*(T1**2)+4.952E-08*(T1**3) 199 1-1 .818E-11*(T1**4))-1167.0)*RM0L 200 DH(5)=((3.253*T1+6.524E-04*(T1**2)-1.495E-07*(T1**3) 201 1+1.539E-11*(T1**4))-1024.0)*RM0L 202 0H(6)=((3.344*T1+2.943E-O4*(T1**2)+1.953E-09*(T1**3) 203 1-6.575E-12*(T1**4))-1023.0)*RM0L 204 DH(11) = ((1.935*T1+4.965E-03*(T1**2. )-1.244E-06*(T1 **3. ) 205 1+1.625E-10*(T1**4.)-8.586E-15*(T1**5.))-985.9)*RMOL 206 DH(12)=((-0.72*T1+4.643E-02*(T1**2.)-1.684E-05*(T1**3. ) 207 1+2.67E-09*(T1**4.))-3484.0)*RMOL 208 DH(13)=((1.137*T1+1.455E-02*(T1**2.)-2.959E-06*(T1**3. ) 209 1)-1552.9)*RM0L 210 UUU(1)=-3.93522E05 211 UUU(3)=-2.41827EOS 212 C CALC. TOTAL ENERGY OF MIXTURE (KJ/KMOL FUEL) 213 ERCT=(NCH*(HF1+DH(KFUEL )-RM0L*T1)+N02*(DH(5)-RMOL*T1) 214 -+N*(DH(6)-RM0L*T1)+NRC02*(UUU(1)+DH(1)-RMOL*T1)+NRH20* 215 -(UUU(3)+DH(3)-RM0L*T1)) 216 C 217 C CALC. SWEPT VOL.(CYLV),CLEARANCE VOL.(CLRV).TOTAL VOL.(VI), 218 C VOLUME CORRESPONDING TO GIVEN SPARK ADVANCE (DVOLM)... 219 CYLV = 3. 1415926*((BORE/2. )**2.)*STROK 220 V1=CYLV + CLRV 221 VT0TAL=V1 222 MPV=SPEED*STR0K/30.0 223 C SUBT. SPK ADV. ANGLE FROM 360'AND ADD IGNITION DELAY... 224 ANG=(360.0-SPKAD+IGNDEL) 125. MASBRN at 17:46:21 on JUN 26. 1985 f o r CC1d=CILL Page 5 225 C INITIALISE CRANK ANGLE COUNTER AT B.D.C. & SET TIME TO ZERO 226 DLF1-180.0 227 TIME=0.0 228 C CALC. VOLUME IN CYLINDER AT SPARK TIME (USED LATER) 229 DVOLM=(CLRV+DVOL(ANG)) 230 TIME=0.0 231 c TOTAL NO. OF MOLS IN CYL."NO. OF MOLS OF FUEL*(1+4.76(CN+HM/4).AF) 232 c WHERE (1+4.76(CN+HM/4).AF)"NMIX. 233 c I.E. NTOT=MOLFL*NMIX 234 c BUT P1.V1=NT0T.RM0L.T1 OR NTOT=P1.V1/RMOL.T1 = MOLFL.NMIX 235 c THEREFORE NO. OF MOLS OF FUEL IN CYL. » P1.V1/NMIX.RMOL.T 1 236 M0LFL=(P1*V1)/(NMIX*RM0L*T1) 237 c ENERGY OF CYLINDER CONTENTS IN KJ 238 ENGY1»ERCT*MOLFL 239 c CALC. STOICH. A/F RATIO (STAFR).AIR/FUEL RATIO (AFR),PERCENTAGE 240 c OXYGEN (NN02), NITROGEN (NN2) AND FUEL (NNCH) IN MIXTURE... 241 STAFR"((CN+HM/4.)*32.+3.762*(CN+HM/4.)*28.01)/((CN*12)+HM) 242 AFR=STAFR*AF 243 NN02=(N02/NMIX)*1OO. 244 NN2=(N/NMIX)*100. 245 NNCH"1OO.-(NN02+NN2) 246 NNFUEL=NNCH 247 c GIVEN MOLECULAR WEIGHTS OF FUELS, CALC. MOLECULAR WEIGHT OF 248 c MIXTURE (MWMIX); TOTAL MASS OF MIXTURE (MTOT); AND SPECIFIC 249 c VOLUME OF MIXTURE 250 MWMIX"(NN02*32.0/100.)+(NN2*28.0/100.)+(NNCH*MW(KFUEL)/1O0.) 251 MTOT"(PDAT(IL,1)*V1 *MWMIX)/(T1*RMOL) 252 VT0T1"V1 253 VSU1=VT0T1/MT0T 254 ETOT1"ERCT/MWMIX/NMIX ' 255 c 256 c 257 WRITE(9,735) MPV,TWALL,HTFCN.HTEXP 258 735 FORMATdH .'MPV.TWALL.HTFCN.HTEXP '.4E12.4/) 259 WRITE(9,734) ERCT,ENGY1.NMIX,MWMIX.MOLFL,MTOT 260 734 FORMAT(1H ,'ERCT,EG1,NMIX,MWMX,MOLFL,MTOT;',6E12.4//) 261 c 262 WRITE(9.652) SPEED.SPKAD 263 652 FORMATdH .'SPEED (RPM) - ' , F7 . 1. 264 -7X.'SPARK ADVANCE (DEG. BTDC) "'.F7.2.3X/) 265 WRITE(9.813) AFR.STAFR,AF,COMPR 266 813 F0RMAT(1H ,15HAIR/FUEL RATIO",F6.2,3X,18HST0ICH. A/F RATIO". 267 -F6.2.3X.7HLAMBDA-.F6.2.3X,12HC0MP. RATIO",F5.1/) 268 WRITE(9,31) 269 31 F0RMAT(1H ,IX.'STEP',IX.'VOL',3X.'PRESS'.3X.'TU'.5X.'TB'.5X 270 -.'MFX',4X,'VFRBNT'.2X,'CBVEL'.3X.'TBVEL'.3X,'FLMSPD',2X. 271 -'FSR'.3X. 'RADF'.2X.'AREAF'.3X,'C.A.'.3X, 'ENERGY'/) 272 DO 106 KI»1.10 273 X(KI)=0.0 274 106 CONTINUE 275 NI-1 276 V1-V1*(1E+06) 277 WRITE(9.893) NI.V1,PDAT(IL.NI).T1.(X(I).I-1,9). 278 -DLF1,ENGY1 279 893 FORMATdH . 13. IX . F6 . 1. 3F7 . 1. F9.4. F7 .2. 2F8. 3. F7 . 2. F7 . 2. F7 . 3. 280 -F7.2.F7.1,F9.5) 281 TU1=T1 282 V1»V1/(1E+06) 126. ASBRN at 17:46:21 on JUN 26. 1985 f o r CC1d=CILL Page 6 283 T2 = T1 284 PP2(IL.1)*PDAT(IL. 1 ) 285 VV2(IL.1)=V1 286 TIM(IL.1)=TIME 287 MF(IL,1)=0.0 288 CB(IL.1)=0.0 289 TB(IL,1)=0.0 290 FS(IL. D-0.0 291 RB(IL,1)«0.0 292 JJJ»1 293 NUT=0 294 DCA-POCA 295 NDCA=(360./DCA) 296 ADCA-0.0 297 C 298 C START COMPRESSION STROKE 299 C B B 3 S B B B B S S B B B B B S 8 B E S B B S B 300 C 301 C THIS SECTION CALCULATES ADIABATIC PRESSURE RISE AT EACH CRANK 302 C ANGLE INTERVAL AND COMPARES THE RESULT WITH THE CORRESPONDING 303 C MEASURED PRESSURE VALUE TO DETERMINE IF COMBUSTION HAS STARTED 304 C 305 DO 40 NI=2,NDCA 306 C 307 C CALC. VOLUME DIVISION (DIV) FOR GIVEN C.A. DIVISION (DCA) 308 DIV=DV0L(DLF1)-DVOL(DLF1+DCA) 309 C CALC. NEW VOLUME IN CYLINDER & RESET C.A. COUNTER TO NEW VALUE 310 V2*V1-DIV 311 DLF1=DLF1+DCA 312 DTIME=0CA/(6.0*SPEED) 313 DIST=(DV0L(DLF1))/(3.14159*((BORE/2.)**2)) 314 C 315 C CALC. NEW MIXTURE TEMPERATURE USING P.V = R.T 316 T2»(MWMIX*PDAT(IL.NI)*V2)/(MTOT*RMOL) 317 CALL C0MP(T2,ENGY2.NRC02.NRH20) 318 C 319 C- IF NEW C.A. < SPK. ADV., CONTINUE WITH COMP. STROKE CALCS. 320 IF(DLF1.GT.ANG) GOTO 610 321 C IF NEW C.A. > SPK. ADV., CALCULATE ADIABATIC PRESSURE RISE 322 C AND COMPARE RESULT WITH MEASURED VALUE.. 323 C 324 C IF(IPRINT.EO.O) GOTO 393 325 CALL GAM(T2.T1,GAMU) 326 PISEN=((V1/V2)**GAMU)*PDAT(IL,(NI-1)) 327 C WRITE(9.257) PDAT(IL.NI),PISEN.T2,GAMU 328 C 257 FORMATdH , ' PDAT, PI SEN, T2. GAMU '.4F10.3) 329 C 330 331 C IF(IDELP.EQ.2) GOTO 217 ) 332 C DELP1=(PDAT(IL.NI)-PISEN) ) 333 C IDELP=2 ) 334 C GOTO 51 ) 335 c ) 336 C217 DELP2=(PDAT(IL.NI)-PISEN) ) 337 C IF((DELP2-DELP1).GT.PTHRES) GOTO 610 ) 338 339 C 340 C CALC. CURRENT TIME: AND PRESS. AT GIVEN VOL. & TEMP. 127. < MASBRN at 17:46:21 on JUN 26. 1985 f o r CC1d*CILL Page 7 341 393 TIME=(DLF1-180.)/(6.0*SPEED) 342 C RECORD PERMANENT VALUES OF PRESS.. -VOL.. TIME, VOL. DIV, AND 343 C C.A. DIV, AT END OF EACH C.A. STEP... 344 PP2(IL.NI)=PDAT(IL.NI) 345 VV2(IL.NI)=V2 346 TIM(IL.NI)=TIME 347 D K I L . (NI-1))=DABS(DIV) 348 DC(IL.(NI-1))=DCA 349 MF(IL,NI)=0.0 350 CB(IL,NI)=0.0 351 TB(IL.NI)=0.0 352 FS(IL.NI)»0.0 353 RB(IL.NI)=0.0 354 C DELP1=DELP2 355 KTDC-0 356 T1=T2 357 V1=V2 358 C ADJUST MAGNITUDE OF VOLUME FOR WRITE STATEMENT... 359 360 V2=V2*(1E+06) 361 WRITE(9.893) NI,V2,PDAT(IL.NI),T2.(X(I).1-1.9). 362 363 -DLF1,ENGY2 364 650 V2-V2/(1E+06) 365 40 CONTINUE 366 610 TU1-T1 367 VSU1-V1/MT0T 368 C CALCULATE ENERGY OF MIXTURE JUST BEFORE START OF COMBUSTION 369 C 370 CALL COMP(T1,ENGY1,NRC02,NRH20) 371 K2Z-2 372 C 373 374 C r% START OF PROGRESSIVE BURNING u 375 c 376 c ITERATION CONTROLS ANO INITIALISATION 377 NG-O 378 KOM-O 379 NED- 1 380 JJJ-1 381 NDC-1 382 IDTM-1 383 IMX-1 384 MFX1-0.0 385 NNN-1 386 IVOL-1 387 KTDC-0 388 SUMXS-NMIX 389 TB2-1900.0 389.5 MWBMIX-MWMIX 390 THCOND-0.1 391 VISC-0.5E-04 392 VSB2-0.5 393 DOSUM-0.0 394 PDVSUM-0.0 395 ESPARK-ENGY1 396 397 c c 128. MASBRN at 17:46:21 on JUN 26. 1985 f o r CC1d=CILL Page 8 398 DO 333 LMN=1,50 399 C B3T3«n»aaao=aa= 400 C 401 C1500LC. TIME TAKEN FOR PISTON TO TRAVEL THROUGH 'DCA' DEGREES C.A. 402 C 403 C IF FIRST TIME THROUGH FROM COMPRESSION STROKE. SKIP VOLUME 404 C CALCULATIONS... 405 C "406 IF(KZZ.E0.2) GOTO 727 407 NI=NI+1 408 508 DTIME=DCA/(6.0*SPEED) 409 C UPDATE TIME AND CRANK ANGLE COUNTER... 410 TIME=TIME+DTIME 411 DLF1=0LF1+0CA 412 C CALC. DISTANCE FROM PISTON TOP TO T.O.C 413 DIST=DV0L(DLF1 )/(3.14159*((BORE/2.)**2)) 414 C CALC. CHANGE IN VOLUME DUE TO PISTON MOTION... 415 DIV=0V0L(DLF1-DCA)-DV0L(DLF1) 416 C CALC. NEW TOTAL VOLUME 417 V2-V1-DIV 418 727 VT0T1-V2 419 C WRITE(9.461) DTIME,TIME,DLF1,DIST,DIV.V2 420 C 461 F0RMAT(1H ,'DTIME,TIME,DLF1,DIST,DIV.V2=',6E11.4) 421 C UPDATE ITERATION COUNTER AND FIND NO. OF ITERATION AT T.D.C. 422 IF(KTDC.GT.O) GOTO 350 423 IF(DLF1.GE.360.0) KTDC-NI 424 C 425 C START BURNING... 426 C *************** 427 C 428 350 IF(NG.EO.O) AREAB-0.0 429 C 430 PDT1=PDAT(IL,(NI-1)) 431 PDT2=PDAT(IL.NI) 432 CALL ENUFLS(PDT2.PDT1.TU1,VSU1,MWMIX.TU2.VSU2, 433 -EU2.TBVEL.AF.T2.NRC02.NRH20) 434 HTCOEF=(THCOND/BORE)*((MPV*B0RE/(VS82*VISC))**HTEXP)/10OO.O 435 DO=HTCOEF *AREAB*(TB2-TWALL)*HTFCN*OTIME 435.5 IF (DCA .GT. 60.) WRITE(6.7777) AREAB.DO.DCA 435.7 7777 FORMATC '.3F20.10) 436 NG«1 437 PDV=((PDAT(IL.NI)+PDAT(IL.(NI-1)))/2.)*DIV 438 ENGY2=ENGY1+PDV-DO 439 PDVSUM=PDVSUM+PDV 440 D0SUM=D0SUM+D0 441 TRT=(MWBMIX*PDAT(IL.NI)*V2)/(MT0T*RM0L) 442 C 443 IF(IPRINT.EO.O) GOTO 971 444 WRITE(9.737) ENGY2.ENGY1.PDV.DO,HTCOEF.TRT 445 737 FORMATdH .'E2 , E1 . PDV,DO.HTCOEF ' . 5E 12 . 4. F8 . 1) 446 C 447 971 ETOT1 =ENGY2/MT0T 448 CALL TEMP(PDT2.TB2.NNN.CC.MFX2.MT0T.EU2.VSU2. 449 -VTOT1.ETOT1,VSB2,MWBMIX) 450 C 451 IF(MFX2.LT.0.5) GOTO 394 452 IF(MFX2.GT.0.98) GOTO 312 453 IF((MFX2-MFX1).GT.0.01) GOTO 394 129. MASBRN at 17:46:21 on JUN 26. 1985 f o r CC1d=CILL Page 9 454 312 KZZ=2 455 GOTO 365 456 394 CALL CALFLS(MFX1.MFX2.VSB2,MTOT,DTIME.VSU2,CBVEL.VSU1. 457 -AREAF1.VOLB2.IVOL.VOLB1,AREAF2,RB1.RB2,DLF1.DIST) 458 KOM=0 459 C 460 970 V0LU2=VT0T1-V0LB2 461 FLMSPD*(RB2-RB1)/(DTIME) 462 VFRBNT=(V0LB2/VT0T1)*100.0 463 FSR=CBVEL/TBVEL 464 V=VT0T1»(1E+06) 465 PRB2=RB2*100.0 466 PAREAF-AREAF2*10000.0 467 C 468 WRITEO.893) NI , V, PDAT( IL.NI), TU2.TB2.MFX2, VFRBNT , CBVEL, 469 -TBVEL.FLMSPD,FSR.PRB2.PAREAF,DLF1,ENGY2 470 C 471 PP2(IL.NI)=PDAT(IL.NI) 472 TIM(IL.NI)»TIME 473 VV2(IL.NI)=V2 474 DI(IL,(NI-1))»DABS(DIV) 475 DC(IL,(NI-1))=0CA 476 MF(IL.NI)=MFX2 477 CB(IL,NI)=CBVEL 478 TB(IL.NI)«TBVEL 479 FS(IL.NI)=FLMSPD 480 RB(IL,NI)«PRB2 481 C 482 V0LB1=V0LB2 483 AREAF1-AREAF2 484 RB1-RB2 485 TU1-TU2 486 MFX1=MFX2 487 VSU1=VSU2 488 V1»V2 489 T1-T2 490 ENGY1-ENGY2 491 KZZ-1 492 IV0L=2 493 333 CONTINUE 494 C 495 365 T1=MFX2*TB2+(1-MFX2)*TU2 496 ECEND=ENGY2 497 C WRITEO,266) MWBMIX , PDAT( IL , NI ) . V2 . MTOT . RMOL 498 C-266 FORMATdH .5E12.4/) 499 TRT=(MWBMIX*PDAT(IL.NI)*V2)/(MTOT*RMOL) 500 CALL ENERGY(TRT.PDAT(IL.NI),EPR0D.SUMXS.NNN.CC,X.EB2.VSB2. 501 -GAMMA,MWBMIX) 502 TENGY=EPROD*MOLFL 503 TDO"(ESPARK-TENGY)-PDVSUM 504 WRITEO.265) E SPARK, EC END. TENGY , PDVSUM, OOSUM, TDO, T1 , TRT 505 265 FORMATdH , ' ESPK , ECND ,TENG,PDVS ,DOS,T1 ,TRT ' .6F 10 .6. 2F7 . 1 / ) 506 DO 249 KKI=1,10 507 249 X(KKI)-0.0 508 NUT-0 509 JJJ=1 510 NNN=1 511 IF(KZZ.EQ.2) GOTO 396 130. MASBRN at 17:46:21 on JUN 26. 1985 f o r CCId=CILL Page 10 512 513 C START EXPANSION STROKE 514 C s s a a a a a B a a s m c s s a a a a s a a 515 C 516 310 DIV«DV0L(DLF1+DCA)-DV0L(DLF1) 517 V2=V1+DIV 518 IF(V2.LT.497.0E-06) GOTO 851 519 DLF1-DLF1+0CA 520 IF(DLF1.GE.538) JJJ=2 521 TIME«(0LF1-180.0)/(6.0*SPEED) 522 NI-NI+1 523 GOTO 718 524 851 DLF1=DLF1+DCA 525 DIST=DV0L(DLF1)/(3.14159*((BDRE/2. )**2)) 526 DTIME=DCA/(6.0*SPEED) 527 TIME=(DLF1-180.0)/(6.0*SPEED) 528 NI-NI+1 529 NUT=NUT+1 530 IF(NUT.GT.80) STOP 531 396 AT0T=3.14159*(2.*B0RE**2/4 +(HC+OIST)*BORE + CUPO'CUPH) 533 CALL EXP(PDAT(IL.(NI-1)),VI,TI,PDAT(IL.NI).V2.T2,NNN,CC, 534 -SUMXS,ENGY1,ENGY2,ATOT,DTIME,MTOT,MWBMIX) 535 718 ENGY1=ENGY2 536 T1-T2 537 V1-V2 538 PP2(IL,NI)»PDAT(IL.NI) 539 VV2(IL.NI)=V2 540 TIM(IL,NI)=TIME 541 DI(IL.(NI-1))=DABS(DIV) 542 DC(IL.(NI-1))=DCA 543 MF(IL.NI)«MFX2 544 - CB(IL,NI)«0.0 545 TB(IL.NI)»0.0 546 FS(IL,NI)=0.0 547 RBdL.NI )«0.0 548 V4«V2 549 T4 = T1 550 V4>V4*(1E+06) 551 C 285 IF(JJJ.E0.2) GOTO 277 552 c IF(NUT.GT.2) GOTO 817 553 554 277 WRITE(9.893) NI.V4,PDAT(IL.NI),X(1),T4.MFX2.VFRBNT,(X(I),I =1.6). 555 -DLF1.ENGY2 556 557 817 IF (JJJ.E0.1) GOTO 310 558 C 559 WRITE(9,818) (CC(I),I=1.8) 560 818 F0RMAT(1H ,'%C02=',F7.3,' %C0"'.F7.3.' %H20='.F7.3.' %H2»' ,F7.3, 561 -' %02=',F7.3,' %N2='.F7.3.' %N0='.F7.3.' %0H='.F7.3/) 562 C 563 C 564 C THIS SECTION CALCULATES INTEGRAL OF PDV (PDV),MEAN EFFECTIVE 565 C PRESSURE (MEP),POWER AND THERMAL EFFICIENCY. 566 C asaaaaasaasaasasssassssaeaaaaaasseesaaaassasaassasaaasaeaasa 567 C 568 304 POV=0.0 569 SUMDI=0.0 570 AREA1=0.0 131. t . MASBRN at 17:46:21 on JUN 26. 1985 f o r CC1d=CILL Page 11 571 AREA3-0.0 572 MTDC=KTDC-1 573 DO 300 J=1,MTDC 574 300 AREA1=AREA1+(PP2(IL.J)+PP2(IL.(J+1)))*DI(IL,J)/2.0 575 NTDC=KTDC+1 576 NID=NI-1 577 DO 302 J=NTDC.NID 578 302 AREA3=AREA3+(PP2(IL.d)+PP2(IL.(J+1)))*DI(IL,J)/2.0 579 DO 303 J=1.MTDC 580 303 SUMDI= SUMDI+DI(IL,J) 581 VA1=CYLV-SUMDI 582 VA2=DI(IL.KTDC)-VA1 583 PPTDC-PP2(IL.KTDC)+((VA1/DI(IL,KTDC))*(PP2(IL.NTDC)-584 -PP2(IL.KTDC))) 585 AREA2*(PPTDC+PP2(IL.KTDC ))*VA1/2.0 586 AREA4*(PPTDC+PP2(IL.NTDC))*VA2/2.0 587 IF(IPRINT.EO.O) GOTO 269 588 WRITEO.486) AREA 1 , AREA2. AREA3, AREA4 . VA 1 . VA2. PPTDC , PDV 589 486 FORMAT(1H ,'A 1,A2.A3.A4.VA1,VA2.PTDC.PDV',8E12.4/) 590 269 PDV=(AREA3+AREA4)-(AREA1+AREA2) 591 MEP=PDV/(CYLV*100.0) 592 P0WER=(PDV*SPEED/120.) 593 EFF«(PDV*100.)/(M0LFL«QVS*(12.»CN+HM)) 594 C — 595 WRITEO,301) POWER , MEP . EFF 596 301 FORMAT(10X,6HP0WER-,F8.3.5X.9HI.M.E.P.«,F7.3.5X,11HEFFICIENCY= . 597 -F10.5///) 598 C 599 C WRITE VALUES OF PRESSURE. MASS FRACTION BURNT, CALC. BURNING 600 C VELOCITY, LAMINAR BURNING VELOCITY. AND FLAME SPEED FOR USE 601 C BY THE PLOTTING PROGRAM 'DP2' 602 C 603 I JUMP 1-0 604 IJUMP2-0 605 IJUMP3-0 606 IJUMP4-1 607 NUMM»1 608 ISPK»IDINT(SPKAD) 609 IF(IL.GT. 1) GOTO 799 610 C WRITEO.933) NUMBR. I JUMP 1.1JUMP2. IJUMP3. IJUMP4 611 C933 F0RMAT(5I3) 612 799 WRITEO.934) NUMM, SPEED , I SPK .KFUEL 613 934 F0RMAT(I4.F8.1,14.13) 614 DO 928 JK-1.180 615 WRITE(9,929) PP2(IL.JK).MF(IL,JK).CB(IL,JK).TB(IL.JK).FS(IL.JK) 616 -.RB(IL.JK) 617 929 F0RMATOF10.4) 618 928 CONTINUE 619 C 620 C 621 C 622 222 CONTINUE 623 C 625 C 626 C 627 C THIS SECTION GENERATES A P-V DIAGRAM AND A 628 C PRESSURE-CRANK ANGLE DIAGRAM. 132. MASBRN a t 17:46:21 on dUN 26. 1985 f o r CC1d=CILL Page 12 629 C 630 C 631 IF(IGRAPH.EO.O) GOTO 599 632 387 DO 605 IL=1.NUMBR 633 DLF-180.0 634 ZZ(IL. 1) = 2.0 635 DO 605 d-1,NID 636 VV(IL.d)«VV2(IL,d)*1000. 637 PP(IL.d)=PP2(IL,d)/10O. 638 DLF=DLF+DC(IL.d) 639 DL(IL.(d+1))»DLF 640 C XX(IL.d)=(5.*VV(IL.d))+2.0 641 YY(IL.d)»(PP(IL,d)/20.)+2.0 642 ZZ(IL.(d+1))=((DL(IL.(d+1))-180.0)/60.0)+2.0 643 605 CONTINUE 644 p 645 c CALL AXIS(2..2..'VOLUME ( L ) ' , - 10.5..0..0..0.2) 646 c CALL AXIS(2..2..'PRESSURE (BAR)'.14.5.,90.,0..20.) 647 c DO 607 IL«1,NUMBR 648 c DO 607 I=1,NID 649 c 607 CALL SYMBOL(XX(IL,I),YY(IL.I).0.05.IL.O..-1) 650 c CALL LINE(XX(1,I).YY(1.I),NID.1) 651 \ * • 652 CALL PLOT(10..0.,-3) 653 CALL AXIS(2.,2.,'CRANK ANGLE',-11,6.0.0.,180..60.) 654 CALL AXIS(2..2..'PRESSURE (BAR)',14,5.,90..0..20.) 655 DO 415 IL=1,NUMBR 656 DO 415 1*1.NID 657 415 CALL SYMB0L(ZZ(IL.I).YY(IL.I).0.05,IL,0..-2) 658 c CALL LINE(ZZ(1.I),YY(1,I),84.1) 659 CALL PLOTND 660 599 STOP 661 END 662 c 663 664 c 665 c SUBROUTINE TEMP CALCULATES TEMP. OF BURNT GAS AND MASS FRACTION 666 c m a: 667 c 668 SUBROUTINE TEMP(P1,TB2,NNN,CC.MFX,MTOT.EU2.VSU2,VTOT1,ETOT.VSB2 669 -MWBMIX) 670 c 671 COMMON /AREA 1/ NCH.N02.K,L,M,N.KFUEL 672 COMMON /AREA2/ MOLFL,NMIX,HF1,NN02,NN2.NNFUEL,KOM 673 COMMON /AREA4/ NDISS.IPRINT 674 c 675 REAL'S XF.DX.EPS.Y1,Y2.Y3,XX2.YY2, 676 -X1,X2.X3,X30LD,P1,P2.P3.CC(10),X(10),K,L,M.N,GAMMA,MFX,MTOT 677 -,EU2,VSU2,VTOT1,VSB2,EB2,TB2,ETOT.VTOTC,NMIX,MFXE.MFXV 678 -,EPROD,SUMXS.NCH,N02,MOLFL.HF1,NN02.NN2.NNFUEL.GA,MWBMIX 679 c 680 NNN* 1 681 K0M=»K0M+1 682 IF(KOM.GT.10) GOTO 93 683 NUT-0 684 dDX«1 685 IDX-1 686 X1=1900.0 133. MASBRN at 17:46:21 on JUN 26. 1985 f o r CC1d=CILL Page 13 687 XF=4000.0 688 DX=100.0 689 EPS=O.0O010 690 5 CALL ENERGY(X1.P1,EPROD,SUMXS,NNN,CC.X.EB2.VSB2.GA,MWBMIX) 691 MFXE=(ETQT-EU2)/(EB2-EU2) 692 C WRITE(9.777) X 1 .ETOT.VTOT1.P1.EB2.MFXE 693 C 777 FORMATdH . ' X1 . ETOT, VTOT 1. P1. EB2.MFXE ' . 6E 12 . 4 ) 694 IF(MFXE.GT.O.O) GOTO 10 695 X1-X1+DX 696 IF(XLGT.XF) GOTO 91 697 JDX=2 698 GOTO 5 699 10 MFXV-(VT0T1/MT0T-VSU2)/(VSB2-VSU2) 700 Y1=MFXV-MFXE 701 IF(JDX.EO.I) GOTO 30 702 IF (Y1.LT.0.0) GOTO 30 703 DX=-DX/2. 704 IDX = 2 705 30 X2=X1+DX 706 IF(X2.GT.XF) GOTO 91 707 20 CALL ENERGY(X2,P1.EPROD,SUMXS.NNN.CC.X.EB2.VSB2.GA.MWBMIX) 708 MFXE=(ET0T-EU2)/(EB2-EU2) 709 C 747 FORMATdH . 'X2. MFXE . MFXV. VSB2. VSU2. EB2. EU2; ' . 7E 10. 3) 710 IF(MFXE.GT.O.O) GOTO 15 711 DX=DX/2. 712 IDX=2 713 X2=X2-DX 714 NUT=NUT+1 715 IF(NUT.GT.SO) GOTO 91 716 GOTO 20 717 15 IF(IDX.EO.I) GOTO 16 718 DX=DX/2. 719 16 MFXV»(VT0T1/MT0T-VSU2)/(VSB2-VSU2) 720 Y2=MFXV-MFXE 721 C WRITE(9.747) X2,MFXE.MFXV,VSB2.VSU2.EB2,EU2 722 IF(Y1*Y2.LE.0.0) GOTO 25 723 X1=X2 724 Y1=Y2 725 NUT-NUT-M 726 IF(NUT.GT.60) GOTO 91 727 GOTO 30 728 25 IF(Y2.EQ.0.0) GOTO 50 729 IF(X2.GT.X1) GOTO 35 730 XX2=X2 731 YY2=Y2 732 X2-X1 733 Y2=Y1 734 X1=XX2 735 Y1=YY2 736 35 IF(MFXE.LT.10.0) GOTO 36 737 DX=DX/10.0 738 X2=X2-DX 739 GOTO 20 740 36 X30LD=X2 741 40 X3=(X1*Y2-X2*Y1)/(Y2-Y1) 742 NUT-NUT*1 743 IF (NUT.LT.150) GOTO 80 744 91 IS»2 134. MASBRN at 17:46:21 on OUN 26. 1985 f o r CC1d=CILL Page 14 745 RETURN 746 93 WRITEO.90) KOM 747 90 FORMATdH .'PROGRAM STOP DUE TO TEMP ITERATIONS EXCEEDING'.14) 748 STOP 749 80 IF(DABS((X3-X30LD)/X3).LT.EPS) GOTO 60 750 X30LD=X3 751 CALL ENERGY(X3,P1,EPROD,SUMXS,NNN,CC,X,EB2.VSB2.GA,MWBMIX) 752 MFXE=(ET0T-EU2)/(EB2-EU2) 753 MFXV=(VTOT1/MTOT-VSU2)/(VSB2-VSU2) 754 Y3=MFXV-MFXE 755 C WRITEO,767) X3 . MFXE , MFXV. Y3 756 C 767 FORMATdH , ' X3 , MFXE . MFXV, Y3 ' , 4E 12 . 4 ) 757 IF(Y1*Y3.LE.0.) GOTO 45 758 X1=X3 759 Y1«Y3 760 GOTO 40 761 45 X2=X3 762 Y2 = Y3 763 GOTO 40 764 50 TB2=X2 765 GOTO 70 766 60 TB2=X3 767 70 MFX=(MFXE+MFXV)/2.0 768 IF(IPRINT.EO.O) GOTO 225 769 C 770 WRITEO, 112) TB2 , MFXE , MFXV, EB2 . VSB2 . GA 771 112 F0RMAT(1H ,'TB2.MFXE,MFXV,EB2,VSB2,GA:',6E12.4) 772 C 773 225 IS«1 774 RETURN 775 END 776 C 777 C SUBROUTINE ENERGY TO CALCULATE ENERGY (EPROD) OF BURNT GAS 778 C -»•»-•««--»=»»-«« AT A GIVEN TEMP. AND PRESS. ( INCLUDES 779 C DISSOCIATION ). 780 C 781 SUBROUTINE ENERGY(T.P,EPROD.SUMXS.NNN,CC.X.EB2.VSB2.GAMMA, 782 -MWBMIX) 783 C 784 COMMON /AREA1/ NCH,N02, K, L,M.N,KFUEL 785 COMMON /AREA2/ MOLFL,NMIX,HF1,NN02,NN2.NNFUEL.KOM 786 COMMON /AREAS/ AREAS,HTEXP,MPV.HTFCN,TWALL,VISC,THCOND 787 COMMON /AREA4/ NDISS.IPRINT 788 C 789 REAL*8 K,L,M,N,X(10),CPG(10).UUU(10),DH(10),KA,KB,KC,KD, 790 -KE,KF,NM.P,T,A1,B1.C1.D1.E1.F1,S.SUMXS,TT.A.B.C.D.E.F,RMOL, 791 -A2.B2.C2.D2.E2.F2.RESA.RESA1 .RESB.RESB1,RESC,RESC1,RESD. 792 -RESD1,RESE.RESE1,RESF,RESF1,KK,CC(10),EPROD.GAMMA,MWBMIX 793 - . MW(10).EB2.VSB2,NMIX,NCH,N02.MOLFL.HF1.NN02,NN2.NNFUEL 794 -.VC02,KC02,VH20.KH20,VN2,KN2,VISC.THCOND.AREAB.ATOT.MPV, 795 -HTFCN.TWALL.HTEXP 796 C 797 IF(T.LT.1750.0) GOTO 17 798 IF(NNN.E0.2) GOTO 15 799 C INITIAL ESTIMATES OF THE NO. OF MOLES OF SPECIES DISSOCIATED 800 C A:- C02=CO+0.502: B:- H20=0H+O.5H2 C:- H20=H2+0.502 801 C D:- N02=.5N2+.502:E:- H2 = 2H F:- 02=20 802 IF(NDISS.EO.1) GOTO 747 135.-MASBRN at 17:46:21 on JUN 26, 1985 fo r CCld=CILL Page 15 803 A=.7 804 B=0.1 805 C=.5 806 D=0.1 807 E=0.0 808 F=0.00 809 GOTO 737 810 747 A=.7 811 B=0.0 812 C=.5 813 0=0.0 814 E=0.0 815 F=0.0 816 737 A2=0 817 B2=0 818 C2=0 819 D2=0 820 E2=0 821 F2=0 822 NNN=2 823 C CALC. OF EQUILIBRIUM CONSTANTS INCLUDING PRESSURE TERM 824 15 KA=DEXP(DL0G(T)**(-7.4721)*(-65549OOO)+10.53) 825 1*DSQRT(101.3/P) 826 KB=DEXP(DL0G(T)**(-7.O457)*(-3O3721OO)+1O.1590) 827 1»DSQRT(101.3/P) 828 KC=DEXP(DLOG(T)•*(-6.8674)*(- 18878550)+8.7095) 829 1*DSQRT(101.3/P) 830 KD=DEXP(DLOG(T)**(-7.3355)*(-16592550)+1.80127) 831 KE=DEXP(DLOG(T)**(-6.81208)*(-30743850)+17.8668) 832 1«(101.3/P) 833 KF=DEXP(DL0G(T)**(-6.93319)*(-43428280)+19.3067) 834 1*(101.3/P) 835 RM0L=8.3143 836 NUT=0 837 C CALC. NO. OF MOLES OF SPECIES DISSOCIATED (A TO F) 838 10 00=1 839 NUT=NUT+1 840 IF (NUT.LT.200) GOTO 400 841 WRITEO,401) NUT 842 401 FORMATC1H , ' PROGRAM STOP DUE TO ENERGY ITERATIONS 843 1EXCEEDING',14) 844 STOP 845 400 IF (KA.LE.1E-10) GOTO 2 846 1 S=(A+B+C)/2+E+F+K+L+M+N 847 A1=A 848 IF C(M+(CA+C-D)/2)-F).LE.0.0) GOTO 2 849 RESA=A/(K-A)*DSQRT((M+((A+C-0)/2)-F)/S)-KA 850 A=A+.001 851 IF ((M+C(A+C-D)/2)-F).LT.O) A=2*CF-M)+0-C 852 RESA1=A/CK-A)*DSQRTC(M+CCA+C-D)/2)-F)/S)-KA 853 A = A+.001*RESA1/(RESA-RESA1 ) 854 IF (A.GT.K) A-K-0.0011 855 IF (A.LT.O) A=1E-12 856 IF (A.EQ.A1) GOTO 2 857 IF CDABS((A-A1)/A1).GT.0.01) GOTO 1 858 IF CDABSCCA-A2)/A1).GT.0.010) QQ=0 859 2 IFCNDISS.EQ.1) GOTO 3 860 S=(A+B+C)/2+E+F+K+L+M+N 136. MASBRN at 17:46:21 on JUN 26. 1985 f o r CC1d=CILL Page 16 861 IF (KB.LE.1E-10) GOTO 3 862 B1-B 863 IF ((B/2+C-E).LE.O.O) GOTO 3 864 RESB=B/(L-B-C)*DSQRT((B/2+C-E)/S)-KB 865 B=B+.001 866 IF ((B/2+C-E).LT.O) B=2*(E-C) 867 RESB1=B/(L-B-C)*DSQRT((B/2+C-E)/S)-KB 868 B=B+.001*RESB1/(RES8-RESB1) 869 IF (B.GT.(L-C)) B=L-C-.0011 870 IF (B.LT.O) B=1E-12 871 IF (B.EQ.BI)GOTO 3 872 IF (DABS((B-B1)/B1).GT.0.01) GOTO 2 873 IF (DABS((B-B2)/B1).GT.0.010) 00=0 874 3 S»(A+B+C)/2+E+F+K+L+M+N 875 IF (KC.LE.1E-10) GOTO 4 876 C1=C 877 IF ((M+((A+C-D)/2)-F).LE.0.0) GOTO 4 878 RESC»(B/2+C-E)/(L-B-C)*DSQRT((M-F+(A+C-D)/2)/S)-KC 879 C-C+.001 880 IF ((M+((A+C-D)/2)-F).LT.0) C«2*(F-M)+D-A 881 RESC1=(B/2+C-E)/(L-B-C)*DS0RT((M-F+(A+C-D)/2)/S)-KC 882 C=C+.001*RESC1/(RESC-RESC1) 883 IF (C.GT.(L-B)) C=L-B-.0011 884 IF (C.LT.O) C-1E-12 885 IF (C.E0.C1) GOTO 39 886 IF (DABS((C-C1)/C1).GT.0.01) GOTO 3 887 IF (DABS((C-C2)/C1).GT.0.010) 00=0 888 39 IF(NDISS.EQ.1) GOTO 67 889 IF (N.LT.0.01) GOTO 5 890 4 S=(A+B+C)/2+E+F+K+L+M+N 891 IF (KD.LE.1E-10) GOTO 5 892 D1-D 893 IF (((N-D/2)*(M-F+(A+C-D)/2)).LE.0.0) GOTO 5 894 RESD=0/DS0RT((N-D/2.)*(M-F+(A+C-D)/2.))-KD 895 D=D+.001 896 IF (((N-D/2)*(M-F+(A+C-D)/2)).LE.O.O) GOTO 5 897 RESD1=D/DSQRT((N-D/2.)*(M-F+(A+C-D)/2.))-KD 898 D=D+.001*RESD1/(RESD-RESD1) 899 IF (D.GT.(2»N)) D=2*N-.0011 900 IF (D.LT.O) D=1E-12 901 IF (D.E0.D1) GOTO 5 902 IF (DABS((D-D1)/D1).GT.0.01) GOTO 4 903 IF (DABS((D-D2)/D1).GT.0.010) 00=0 904 GOTO 413 905 5 GO TO 67 907 E1=E 908 IF ((B/2+C-E).LE.0.001) E=B/2+C-.002 909 RESE=((2*E)**2)/S/(B/2+C-E)-KE 910 E=E+.001 911 RESE1=((2*E)**2)/S/(B/2+C-E)-KE 912 E=E+.001*RESE1/(RESE-RESE1) 913 IF (E.GT.(C+B/2)) E»B/2+C 914 IF(E.LT.O) E=1E-12 915 IF (E.E0.E1) GOTO 6 916 IF (DABS((E-E1)/E1).GT.0.01) GOTO 5 917 IF (DABS((E-E2)/E1).GT.0.010) 00=0 918 6 S=(A+B+C)/2+E+F+K+L+M+N 919 IF (KF.LE.1E-10) GOTO 67 137. MASBRN at 17:46:21 on JUN 26. 1985 f o r CCld=CILL Page 17 920 F1 = F 921 IF ((M-F+(A+C-D)/2).EQ.0) GOTO 67 922 RESF=((2*F)**2)/S/(M-F+(A+C-D)/2)-KF 923 F=F+.001 924 RESF1=((2*F)**2)/S/(M-F+(A+C-0)/2)-KF 925 F=F+.001*RESF1/(RESF-RESF1) 926 IF (F.GT.(M+(A+C-D)/2)) F=M+(A+C-D)/2-.011*F 927 IF (F.LT.O) F*1E-12 928 IF (F.E0.F1) GOTO 67 929 IF (DABS((F-F1)/F1).GT.0.01) GOTO 6 930 IF (DABS((F-F2)/F1).GT.0.010) 00=0 931 413 CONTINUE 932 67 A2=A 933 B2=B 934 C2=C 935 02=D 938 IF(00.E0.O)G0T0 10 939 C CALCULATING CHANGE IN ENTHALPIES FOR SPECIES 1 TO 10 BET. T ANO 289K 940 C C02-1, C0=2, H20=3. H2=4, 02"5, N2»6. N0=7. H=10. 0«9. 0H=8 941 KK=0 942 17 TT=T/100 943 IF (T.GT.3000.0) GOTO 99 944 DH(1)=((3.096*T+0.00273*(T**2)-7.885E-07*(T**3) 945 1+8.66E-1 1*(T**4))-1145.0)*RMOL 946 DH(2)=((3.317*T+3.77E-04*(T**2)-3.22E-08*(T**3) 947 1-2. 195E-12*(T«*4))- 1022.0)*RMOL 948 DH(3)=((3.743*T+5.656E-04*(T**2)+4.952E-08*(T**3) 949 1-1 .818E-11*(T**4))-1167.0)*RMOL 950 DH(4)-((3.433*T-8.18E-06*(T**2)+9.67E-08*(T**3) 951 1-1 . 444E-1 1*(T*»4))-1025.0)*RMOL 952 DH(5) = ((3.253*T+6.524E-04*(T»»2)-1.495E-07* (T**3) 953 1+1.539E-11*(T**4))-1O24.O)*RM0L 954 DH(6)=((3.344»T+2.943E-04*(T**2)+1.953E-09*(T**3) 955 1-6.575E-12*(T*»4))- 1023.0)*RMOL 956 DH(7)»((3.502*T+2.994E-04*(T*«2)-9.59E-09*(T**3) 957 1-4.904E-12*(T«»4))-1070.0)*RMOL 958 DH(10)-((2.5*T)-745.0)*RM0L 959 DH(9)»((2.764*T-2.514E-04*(T*»2)+1.002E-07* ( T»*3) 960 1-1.387E-11»(T**4))-804.0)*RMOL 961. DH(8)«((81.546*TT-47.48»(TT**1.25)+9.902*(TT»*1.75) 962 1-2.133*(TT**2.))* 100-10510) 963 GOTO 91 964 99 DH(1)»((5.208*T+0.00059*(T**2)-5.614E-08*(T**3) 965 1+2.05E-12*(T**4))-1126.0)*RMOL 966 DH(2)=((3.531*T+2.73E-04*(T**2)-3.28E-08*(T**3) 967 1 + 1.565E-12*(T**4))-1042.0)*RMOL 968 0H(3)=((143.05*TT-146.83*(TT**1.25)+55.17*(TT**1.5) 969 1-1.85*(TT**2.))*100-11945.O) 970 DH(4)=((3.213*T+2.87E-04*(T**2)-2.29E-08*(T**3) 971 1+7.666E-13*(T**4))-1018.0)*RM0L 972 DH(5)»((3.551*T+3.203E-04*(T**2)-2.876E-08*(T**3) 973 1+1.005E-12*(T**4))-1044.O)*RMOL 974 0H(6)=((3.514*T+2.583E-O4*(T**2)-2.841E-O8*(T**3) 975 1 + 1 .242E-12*(T**4))-1043.0)*RM0L 976 DH(7)*((3.745*T+1.950E-04*(T**2)-1.88E-08*(T**3) 977 1+7.703E-13*(T**4))-1106.0)*RM0L 978 DH(10)»((2.5*T)-74S.0)*RM0L 979 DH(9)=((2.594*T-3.843E-05*(T**2)+7.514E-09*(T**3) 138. ting of MASBRN at 17:46:21 on JUN 26, 1985 for CC1d=CILL Page 18 980 1-3.209E-13*(T**4))-809.0)*RM0L 981 DH(8)=((81.546*TT-47. 4B*(TT**1.25)+9.902*(TT**1.75) 982 1-2.133*(TT**2.))*100-10560.) 983 C CALCULATE CP VALUES 984 91 CPG(1)--3.7357+30.529*(TT**(0.5))-4.1034*TT+0.024198* (TT**2) 985 CPG(2)=69.145-.70463*(TT**(0.75))-200.77*(TT**(-0.5)) 986 -+176.76*(TT* *(-0.75)) 987 CPG(3) = 143.05-183.54*(TT**(0.25))+82.751 *(TT**(0.5)) 988 --3.69889*TT 989 CPG(4)=56.505-702.74*(TT**(-.75))+1165.0/TT-560.7*(TT** ( - 1.5)) 990 CPG(5) = 37.432+0.020102*(TT**1.5)- 178.57*(TT**(- 1.5)) 991 -+236.88*(TT**(-2)) 992 CPG(6)=39.060-512.79*(TT**(-1.5))+1072.7*(TT**(-2)) 993 —820.4*(TT**(-3)) 994 CPG(7)»59.283-1.7096*(TT**0.5)-70.613*(TT**(-0.5)) 995 -+74.889*(TT**(-1.5)) 996 CPG(8)=81.546-59.35*(TT**0.25)+17.329*(TT**0.75)-4.266*TT 997 C NUMBER OF MOLES OF EACH SPECIES AFTER DISSOCIATION 998 X( 1 )=K-A 999 X(2)=A 1000 X(3)=L-B-C 1001 X(6)=N-D/2 1002 X(7)=D 1003 X(4)=C+B/2-E 1004 X(5)=M-F+(A+C-D)/2 1005 X(10)=2*E 1006 X(9)=2*F 1007 X(8)=B 1008 C CALC. VISCOSITY ft THERMAL CONDUCTIVITY OF PRODUCTS... 1009 VC02 = ((0.019*T+24.2)*X(1)•1E-06)/(X(1)+X(3)+X (6)) 1010 KC02=((0.04 1*T+36.1)*X(1)*1E-03)/(X(1)+X(3)+X(6)) 1011 VH20=((0.025*T+15.8)*X(3)*1E-06)/(X(1)+X(3)+X(6)) 1012 KH20=((0.130*T-0.60)*X(3)*1E-03)/(X(1)+X(3)+X(6)) 1013 VN2 = ((0.019*T+24.1)*X(6)* 1E-06)/(X(1)+X(3)+X(6)) 1014 KN2 = ((0.039*T+35.8)*X(6)*1E-03)/(X(1) + X(3)+X( 6)) 1015 VISC=VC02+VH20+VN2 1016 THC0ND=KC02+KH20+KN2 1017 c HFO FOR EACH SPECIES 1018 UUU(1)=-3.93522E05 1019 UUU(2)=-1.10529E05 1020 UUU(3)=-2.41B27E05 1021 UUU(4)=0.00O00E0O 1022 UUU(5)=O.OOOOOEOO 1023 UUU(6)=0.00000E00 1024 UUU(7)=9.05920E04 1025 UUU(10)=2.17986E05 1026 UUU(9)=2.49195E05 1027 UUU(8)=39463.0 1028 c MOLECULAR WEIGHT FOR EACH SPECIES 1029 MW(1)=44.01 1030 MW(2)=28.01 1031 MW(3)=18.01 1032 MW(4)»2.02 1033 MW(5)=32.00 1034 MW(6)=28.01 1035 MW(7)=30.00 1036 MW(8)=17.00 1037 MW(9)=16.00 139. MASBRN at 17:46:21 on JUN 26, 1985 f o r CC1d=CILL Page 19 1038 MW(10)=1.00 1039 C CALC. ENERGY OF PRODUCTS 1 TO 10 1040 EPROD=0. 1041 DO 109 1 = 1 , 10 1042 EC0MP = X(I)*(UUU(I)+DH(I)-RMOL *T) 1043 EPROD=EPROD+ECOMP 1044 109 CONTINUE 1045 C CALCULATE SUM OF X VALUES 1046 SUMXS=0 1047 DO 231 ILG=1,10 1048 231 SUMXS=SUMXS+X(ILG) 1049 C CALC PERC. OF PRODUCTS AND MOLECULAR WEIGHT OF MIXTURE 1050 MWBMIX=0.0 1051 DO 232 ILH=1,10 1052 CC(ILH)=(X(ILH)/SUMXS)*100. 1053 232 MWBMIX=MWBMIX+(CC(ILH)«MW(ILH)/100.) 1054 EB2=EPR0D/MWBMIX/SUMXS 1055 VSB2=RM0L*T/(MWBMIX-P) 1056 C CALC CP 1057 CP=0 1058 DO 233 ILF=1,8 1059 233 CP=CP+(CC(ILF)»CPG(ILF))/100. 1060 CV=CP-RM0L 1061 GAMMA=CP/CV 1062 C WRITE(9,889) MWBMIX,EB2,VSB2,GAMMA,NNN,NDISS 1063 c 889 FORMATdH . ' MWBMIX , EB2 . VSB2 , GAMMA , N, NDS ' , 4E 12 . 4 , 213 ) 1064 RETURN 1065 END 1066 c 1067 c SUBROUTINE CALFLS THIS IS USED TO OBTAIN THE CALCULATED 1068 c • " = « = = = o = = a»»a»» BURNING VELOCITY 1069 c 1070 SUBROUTINE CALFLS(MFX1,MFX2,VSB2.MTOT.DTIME,VSU2.CBVEL, 1071 -VSU1,AREA1,V0LB2.IV0L.V0LB1.AREA2.RB1,RB2,DLF1.DIST) 1072 c 1073 COMMON /AREA4/ NDISS.IPRINT 1074 COMMON /AREA3/ AREAS.HTEXP,MPV,HTFCN,TWALL,VISC,THCOND 1075 c 1076 INTEGER NREC.CA.NDIM 1077 REAL RCA 1 1078 REAL*8 RF,DR,EPS.Y1,Y2.Y3,BORE.D.XDOT,ARAVG,AREA , 1079 -R1,R2.R3.R30LD.DTIME.RMAX,R,VOLB1.MFX2.AREA 1.AREA2,RB1.RB2, 1080 -FFF,MFX.VSB2.VSU2.MTOT,MFX1,V0LB2,VOLB,CBVEL.VSUAVG.VSU1,RADBMB 1081 -,DLF1.RFT(100).VFT(100).AFF(100).AWP(100).DIST.AREAB 1082 c 1083 IF (IVOL .GE.2) GO TO 546 1084 RB1=O.DO 1085 AREA 1=0.DO 1086 546 RCA 1=SNGL(DLF1) 1087 CA=IFIX(RCA1) 108S IF(CA.LE.360) CA-360-CA 1089 IF (CA .GT. 360)CA=CA-360 1090 CALL BLKRD(CA,RFT,VFT,AFF,AWP,NDIM) 1091 V0LB2=MT0T*MFX2«VSB2 1092 CALL GEOM(NDIM,DIST,V0LB2.RFT.VFT.AFF.AWP.RB2,AREA2,AREAB,CA) 1093 ARAVG=(AREA1+AREA2J/2. 1094 VSUAVG=(VSU1+VSU2)/2. 1095 XD0T=(MFX2-MFX1)/DTIME 140 MASBRN at 17:46:21 on JUN 26. 1985 f o r CC1d=CILL Page 20 1096 CBVEL=MTOT*XDOT*VSUAVG/ARAVG 1097 RETURN 1098 END 1099 C 1 100 C 1101 C SUBROUTINE ENUFLS THIS CALCULATES THE PROPERTIES OF THE UNBURNT 1102 C GAS AT THE GIVEN PRESS. BY FIRST CALCULATING 1103 C GAMMA AND THEN ASSUMING ISENTROPIC COMPRESSION 1104 C THE BURNING VELOCITY IS THEN CALCULATED USING THE UNBURNT GAS 1105 C TEMP. AND PRESS. USING PUBLISHED FORMULAE FOR GIVEN FUEL. 1106 C 1107 SUBROUTINE ENUFLS(P2,P1,T1.VSU1,MWMIX.TU2.VSU2.EU2.TBVEL,AF. 1108 -T2.NRC02.NRH20) 1109 C 1110 COMMON /AREA1/ NCH,N02.K.L.M.N.KFUEL 1111 COMMON /AREA2/ MOLFL.NMIX.HF1.NN02.NN2,NNFUEL,KOM 1112 COMMON /AREA4/ NDISS.IPRINT 1113 C 1114 REAL*8 P1,T1,NN02,NN2,NMIX,TU2,VSU2,EU2,TBVEL,TT,NNFUEL,FFF, 1115 -CPG(14),CP.CV.GAMU,DH(14),ENGY.N02,N.RMOL,VSU1.P0W1.P0W2.TT2, 1116 -MWMIX,PU,TU,PBAR2,P2.HF1,T,T2,P0W3,C4,AF,PBAR1,GGAM.B1.B2.B3, 1117 -NCH.K.L.M.MOLFL,FI.SUO(15) .ALPHA(15),BETA(15),NRC02.NRH20,UUU(3) 1118 C 1119 RMOL-8.31434 1120 NUT-0 1121 C 1122 C CALC. GAMMA FOR THE UNBURNT ELEMENTS.... 1123 C 1124 NNFUEL=1OO.-(NN02+NN2) 1125 TT=T1/100. ' 1126 CPG(5)«37.432+0.020102*(TT**1.5)-178.57*(TT**(-1.5)) 1127 -+236.88*(TT**(-2)) 1128 CPG(6)=39.060-512.79*(TT**(-1.5))+1072.7*(TT**(-2)) 1129 --820.4*(TT**(-3)) 1130 CPG(11)=-672.87+439.74*(TT**0.25)-24.875*(TT**0.75)+323.88* 1131 -(TT**(-0.5)) 1132 CPG(13) = -4.042+30.46*TT-1.571 *(TT**2.)+0.03171 *(TT**3 . ) 1133 CPG(12)»8.3143*(-0.72+O.09285*T1-5.O5E-05*(T1**2.)+1.068E-08* 1134 -(T1**3)) 1 135 CP-(NN02*CPG(5)+NN2*CPG(6)+NNFUEL*CPG(KFUEL))/100. 1136 CV=CP-RMOL 1137 GAMU«CP/CV 1 138 C 1139 P0W1=(GAMU-1.)/GAMU 1140 P0W2-1./GAMU 1141 TT2=T1*((P2/P1)**P0W1) 1142 20 CALL GAM(TT2,T1,GAMU) 1143 P0W1=(GAMU-1.0)/GAMU 1144 T2=T1*((P2/P1 )**P0W1) 1145 IF(DABS(TT2-T2).LE.1.0) GOTO 10 1146 NUT=NUT+1 1147 IF(NUT.GT.20) STOP 1148 TT2=T2 1149 GOTO 20 1150 10 P0W2-1.O/GAMU 1151 TU2=T2 1152 VSU2=VSU1*((P1/P2)**POW2) 1 153 C 141. f . . . . cr MASBRN at 17:46:21 on JUN 26, 1985 fo r CC1d=CILL Page 21 1154 C CALC. ENTHALPY OF REACTANTS AT GIVEN TEMP. 1155 DH(1)=((3.096*T2+0.00273*(T2**2)-7.885E-07*(T2**3 ) 1156 1+8.66E-11*(T2**4))-1145.0)*RMOL 1157 DH(3)=((3.743*T2+5.656E-04*(T2**2)+4.952E-08*(T2**3) 1158 1-1.818E-11*(T2**4))-1167.0)*RMOL 1159 0H(5)=((3.253*T2+6.524E-04*(T2**2)-1.495E-07*(T2**3) 1160 1 + 1.539E-11*(T2**4))- 1024.0)*RMOL 1161 DH(6)=((3.344*T2+2.943E-04*(T2**2)+1.953E-09*(T2**3) 1162 1-6.575E-12*(T2**4))-1023.0)*RMOL 1163 DH(11)=((1.935*T2+4.965E-03*(T2**2.)-1.244E-06*(T2**3.) 1164 1+1.625E-10*(T2**4.)-8.586E-15*<T2**5.))-965.9)*RMOL 1165 DH(12)=((-0.72*T2+4.643E-02*(T2**2.)-1.684E-05*(T2**3.) 1 166 1+2.67E-09*(T2**4.))-3484.0)*RMOL 1167 DH(13)=((1.137*T2+1.455E-02*(T2**2.)-2.959E-06*(T2**3.) 1168 1)-1552.9)*RM0L 1169 UUU(1)»-3.93522E05 1170 UUU(3)=-2.41B27E05 1171 C CALC. TOTAL ENERGY OF MIXTURE (KJ/KMOL FUEL).... 1172 ENGY=(NCH*(HF1+DH(KFUEL)-RM0L*T2)+N02*(DH(5)-RM0L*T2) 1 173 -+N*(DH(6)-RM0L*T2)+NRC02*(UUU(1)+DH(1)-RM0L*T2)+NRH20* 1174 -(UUU(3)+DH(3)-RM0L*T2)) 1 175 C CONVERT TO KJ/KMOL MIXTURE... 1 176 ENGY=ENGY/NMIX 1 177 C CONVERT TO KJ/KG MIXTURE... 1178 EU2=ENGY/MWMIX 1179 C CALC. AVERAGE UNBURNT TEMP. AND PRESS. 1180 PU=(P1+P2)/2. 1181 TU=(T1+T2)/2. 1 182 C 1183 C CALCULATE LAMINAR BURNING VELOCITY: 1184 C 1 185 C METGHALCHI & KECK'S EON.S FOR PR0PANE(13). 0CTANE(12), 1 186 C AND IND0LINE(14) 1187 C 1 188 IF(KFUEL.EO.11) GOTO 501 1 189 FI=1./AF 1190 IF(FI.GT.0.95) GOTO 87 1191 C DATA SUO(13),SUO(12),SU0(14)/23.20D0,19.25D0,19.15D0/ 1192 C DATA ALPHA(13).ALPHA(12).ALPHA(14)/2.27D0,2.36D0.2.27DO/ 1193 . C DATA BETA(13),BETA(12).BETA(14)/-0.23DO.-0.22D0.-0.17D0/ 1194 GOTO 89 1195 87 IF(FI.GT.1.05) GOTO 88 1196 DATA SUO( 13) ,SUO(12),SU0(14)/31.90D0.27.OODO.25.21D0/ 1197 DATA ALPHA(13).ALPHA(12),ALPHA(14)/2.13D0,2.26D0,2.19D0/ 1198 DATA BETA(13),BETA(12),BETA(14)/-0.17D0.-0.18D0.-0.1300/ 1199 GOTO 89 1200 88 CONTINUE 1201 C DATA SUO(13),SUO(12),SUO(14)/33.80D0,27.63D0.28.140O/ 1202 c DATA ALPHA(13),ALPHA(12),ALPHA(14)/2.06DO,2.03D0.2.02D0/ 1203 c DATA BETA(13).BETA(12) .BETA(14)/-0.17D0.-O.1100.-O.087DO/ 1204 89 TBVEL»SUO(KFUEL)*((TU/298.)**ALPHA(KFUEL))* 1205 -((PU/100.)**BETA(KFUEL)) 1206 GOTO 510 1207 c 1208 c ANDREWS AND BRADLEYS EOUATION FOR METHANE(11)... 1209 c 1210 c PBAR1=PU/100. 1211 c TBVEL=(10.0+0.000371*(TU**2.)*(PBAR1**(-O.5))) 142. MASBRN at 17:46:21 on JUN 26. 1985 f o r CCId=CILL Page 22 1212 C 1213 C RYAN AND LESTZ'S EON. FOR METHANE(11)... 1214 C 1215 C 501 B1-9655.5 1216 C B2--0.623 1217 C B3--2144.5/TU 1218 C TBVEL=B1*((PU/100.)**B2)*0EXP(B3) 1219 C GOTO 510 1220 C 1221 C AGRAWAL AND GUPTAS EQUATION FOR METHANE... 1222 C 1223 501 PBAR1=PU/100.0 1224 C4 = -418.0+1287.0/AF-1196.0/(AF**2)+360.0/(AF**3)- 15.0*AF* 1225 -DL0G10(PBAR1 ) 1226 P0W3=1.68*DSQRT(AF) 1227 IF(AF.GT.1.) GOTO 65 1228 P0W3 =1.68/DSQRT(AF) 1229 65 TBVEL=C4*((TU/300.0)**P0W3) 1230 C 1231 c DIVIDE BY 100 TO CONVERT FROM CM/S TO M/S... 1232 c 1233 510 TBVEL»TBVEL/100. 1234 c 1235 IF(IPRINT.EQ.O) GOTO 225 1236 1237 WRITEO. 100) TBVEL,VSU2,EU2.PU.TU,P2.T2 1238 100 FORMATdH , ' TBV , VSU2 . EU2 . PU. TU. P2 . T2 «'.7E12.4) 1239 1240 225 RETURN 1241 END 1242 c 1243 c 1244 c SUBROUTINE GAM THIS CALCULATES THE AVERAGE RATIO OF SPECIFIC 1245 c « = • « « HEATS (GAMMA) OF AN UNBURNED GAS MIXTURE 1246 c BETWEEN TWO GIVEN TEMPERATURES. 1247 c 1248 SUBROUTINE GAM(T2.T1,GAMU) 1249 c 1250 COMMON /AREA 1/ NCH.N02.K.L.M.N.KFUEL 1251 COMMON /AREA2/ MOLFL.NMIX,HF1.NN02,NN2.NNFUEL.KOM 1252 c 1253 REAL*8 T2.T1.NN02.NN2,NNFUEL.GAMU.TI,CPA(14),A 1.A2.R1,R2.S1,S2 . 1254 -C1.C2.D1.D2.E1.E2,RMOL.CPAV.TT.NCH,N02.K,L.M.N.MOLFL.NMIX.HF1 1255 c 1256 c CALC. VALUES OF CP FOR THE COMBUSTIBLE MIXTURE; 1257 c 5=02. 6=N2. 11=CH4. 12=C8H18. 13=C3H8. 14-INDOLINE... 1258 c 1259 RM0L=8.31434 1260 TT=T2/100. 1261 TI=T1/100.0 1262 c 1263 A1=(37.432*TT+8.041E-03*(TT**2.5)+357. 14/DSQRT(TT )-236.88/TT ) 1264 A2=(37.432*TI+8.041E-03*(TI**2.5)+357.14/DSQRT(TI)-236.88/TI) 1265 CPA(5)=(NN02/(T2-T1))*(A1-A2) 1266 c 1267 R1 = (39.06*TT+1025.58/DSQRT(TT)- 1072.7/TT+410.2/(TT**2)) 1268 R2=(39.O6*TI+1O25.58/DS0RT(TI)-1O72.7/TI+41O.2/(TI**2)) 1269 CPA(6)=(NN2/(T2-T1))*(R1-R2) 143. MASBRN at 17:46:21 on <JUN 26. 1985 f o r CC1d=CILL Page 23 1270 C 1271 S1 = -672.87*TT+351.8*(TT**1.25)- 14.214*(TT** 1.75)+647.76 1272 -*DSORT(TT) 1273 S2 = -672.87*TI + 351 .8*(TI**1 .25 )-14.2 14*(TI** 1 .75)+647.76 1274 -*DSQRT(TI ) 1275 CPA(11)=(NNFUEL/(T2-T1 ))*(S1-S2) 1276 C 1277 C1=(-4.042*TT+15.23*(TT**2)-0.5237*(TT**3)+7.9275E-03*(TT**4)) 1278 C2=(-4.042*TI+15.23*(TI**2)-0.5237*(TI**3)+7.9275E-03*(TI**4)) 1279 CPA(13) = (NNFUEL/(T2-T1) )*(C1-C2) 1280 C 1281 TT=TT*100. 1282 TI=TI*100. 1283 C 1284 01=RMOL*(-O.72*TT+4.643E-02*(TT**2)-1.684E-05*(TT**3)+2.67E-09* 1285 -(TT**4)) 1286 D2=RM0L*(-0.72*TI+4.643E-02*(TI**2)-1.684E-05*(TI**3)+2.67E-09* 1287 -(TI**4)) 1288 CPA(12)=(NNFUEL*0.01/(T2-T1))*(D1-D2) 1289 C 1290 E1»RM0L*(-O.72*TT+4.643E-O2*(TT**2)-1.684E-05*(TT**3)+2.67E-09* 1291 -(TT**4)) 1292 E2=RMOL*(-0.72*TI+4.643E-02*(TI**2)-1.684E-05*(TI**3)+2.67E-09* 1293 -(TI**4) ) 1294 CPA(14)=(NNFUEL*0.01/(T2-T1))*(E1-E2) 1295 C 1296 c CALC. CP. GAMMA. AND HENCE PRESSURE(P) AT TEMP. T(d) ASSUMING 1297 c ISENTROPIC COMPRESSION 1298 1299 CPAV=CPA(5)+CPA(6)+CPA(KFUEL) 1300 GAMU=CPAV/(CPAV-RMOL) 1301 RETURN 1302 END 1303 c 1304 c 1305 c SUBROUTINE COMP THIS CALCULATES THE SPECIFIC ENERGY OF THE 1306 c a....**.*.*.... UNBURNED MIXTURE. 1307 c 1308 SUBROUTINE COMP(T2,ENGY2,NRC02.NRH20) 1309 c 1310 COMMON /AREA 1/ NCH.N02,K,L,M,N,KFUEL 1311 COMMON /AREA2/ MOLFL.NMIX.HF1,NN02.NN2.NNFUEL.KOM 1312 c 1313 REAL*8 PI,V1,T1,P2.V2.T2.NCH.N02.N,ENGY1,ENGY2,DH(14).RMOL. 1314 -REM.REM1,TT1,REM2,TT2.HF1.MOLFL,DLF1,K.L.M,NMIX.NN02,NN2,NNFUEL 1315 -,UUU(10),T20LD.NRC02.NRH20 1316 c 1317 RMOL=8.31434 1318 c 1319 DH(1)=((3.096*T2+0.00273*(T2**2)-7.885E-07*(T2**3) 1320 1+8.66E-11*(T2**4))-1145.0)*RMOL 1321 DH(3)=((3.743*T2+5.656E-04*(T2**2)+4.952E-08*(T2**3) 1322 1-1.818E-1 1*(T2**4))-1167.0)*RMOL 1323 DH(5) = ((3.253*T2+6.524E-04*(T2**2)-1.495E-07* (T2**3) 1324 1+1.539E-11*(T2**4))-1024.0)*RM0L 1325 DH(6)=((3.344*T2+2.943E-04*(T2**2)+1.953E-09*(T2**3) 1326 1-6.575E-12*(T2**4))-1023.0)*RMOL 1327 DH( 11) = ((1.935*T2+4.965E-03*(T2**2.)- 1.244E-06*(T2**3.) 144. •---Jr., - MASBRN at 17:46:21 on dUN 26, 1985 for CC1d=CILl Page 24 1328 1+1.625E-10*(T2**4.)-B.586E-15*(T2**5.))-985.9) *RMOL 1329 DH(12)«((-0.72*T2+4.643E-02*(T2**2.)-1.684E-05*(T2**3.) 1330 1+2.67E-09*(T2**4.))-3484.0)*RMOL 1331 DH(13) = (( 1 . 137*T2+1.455E-02*(T2**2.)-2.959E-06*(T2**3,) 1332 1)-1552.9)*RM0L 1333 UUU(1)=-3.93522E05 1334 UUU(3)=-2.41827E05 1335 C CALC. TOTAL ENERGY OF MIXTURE ( K J ) . . . . 1336 ENGY2=M0LFL*(NCH*(HF1+DH(KFUEL)-RM0L*T2)+N02*(DH(5)-RM0L*T2) 1337 -+N*(DH(6)-RM0L*T2)+NRC02*(UUU(1)+DH(1)-RM0L*T2)+NRH20* 1338 -(UUU(3)+DH(3)-RM0L*T2)) 1339 c 1340 RETURN 1341 ENO 1342 c 1343 c 1344 c SUBROUTINE EXP THIS CALCULATES THE TEMP. AND CONCENTRATION OF 1345 c S . . » = . > > S 3 . b . B . THE PRODUCTS OF COMBUSTION DURING THE EXPANSION 1346 c STROKE. 1347 c 1348 SUBROUTINE EXP(P1,V1,T1,P2.V2,T2.NNN.CC,SUMXS.ENGY1.ENGY2, 1349 -ATOT.DTIME,MTOT,MWBMIX) 1350 c 1351 COMMON /AREA 1/ NCH,N02,K,L.M,N,KFUEL 1352 COMMON /AREA2/ MOLFL,NMIX,HF1,NN02.NN2,NNFUEL.KOM 1353 COMMON /AREA3/ AREAB,HTEXP,MPV,HTFCN,TWALL.VISC,THCOND 1354 COMMON /AREA4/ NDISS.IPRINT 1355 c 1356 REAL*8 PI,VI,T1,P2,V2.T2.SUMXS.K.L.N,M,NMIX,NM1,TT1,P,EPROD. 1357 -CC(10),X(10).ENGY1.ENGY2.MOLFL.REM1.REM2.TT2,TT3,TT30LD.NNM1. 1358 -NNM3.REM3,NCH,N02,HF1.NN02,NN2.NNFUEL,NNM2.EB2.VSB2.BORE 1359 -,AREAB.ATOT,MPV.HTFCN,TWALL.PDV,DO,HTCOEF,VISC.THCOND,HTEXP 1360 -,DOMEAS.DTIME,GAMMA,MWBMIX.MTOT 1361 c 1362 B0RE»3.25*0.0254 1363 NUT*0 1364 NN=0 1365 c 1366 T2»(MWBMIX*P2*V2)/(MT0T*8.31434> 1367 c 1368 . CALL ENERGY(T2.P2,EPROD.SUMXS,NNN,CC,X,EB2,VSB2,GAMMA,MWBMIX) 1369 c 1370 ENGY2=EPR0D*M0LFL 1371 HTC0EF=(THC0ND/BORE)*((MPV*B0RE/(VSB2*VISC))**HTEXP)/1000.0 1372 D0=HTC0EF *ATOT*(T2-TWALL)*HTFCN*DTIME 1373 PDV»((P1+P2)/2.0)*(V2-V1) 1374 D0MEAS=ENGY2-ENGY1+PDV 1375 c 1376 PISEN=((V1/V2)**GAMMA)*P1 1377 c 1378 IF(IPRINT.EO.O) GOTO 4 1379 c-1380 WRITE(9.409) ENGY1,ENGY2.PDV.DO,DOMEAS,PISEN 1381 409 F0RMAT(1H ,'ENGY1,ENGY2,PDV,DO,DOMEAS '.6E12.4) 1382 c-1383 4 CONTINUE 1384 c 1385 RETURN 145. MASBRN at 17:46:21 on JUN 26. 1985 f o r CC1d=CILL Page 25 1386 END 1387 C 1388 C SUBROUTINE SMOOTH THIS READS IN THE ENSEMBLED PRESSURE VALUES 1389 C 3,can*.* = = = AND SMOOTHS THEM USING MTS LIBRARY ROUTINES 1390 C 1391 SUBROUTINE SMOOTH(POUT.SCONST,IPRNTS) 1392 C 1393 IMPLICIT REAL*8(A-H,0-W) 1394 C 1395 DIMENSION PIN(180). DPDTH(180), T0L(18O). ANGLE( 180), PDK180) 1396 DIMENSION PD2(180). W(2000),XIPIN(200). P0UT(180). D2PDTH(180) 1397 C 1398 C 1399 SVAL-5.0 1400 CONST 1-SCONST 1401 C0NST2-SC0NST 1402 IBEG-60 1403 I END-120 1404 C 1405 C READ IN PRESSURE DATA... 1406 C 1407 READ(4,20)(PIN(K),K»1.180) 1408 20 F0RMAT(F12.4) 1409 C 1410 C DO 600 IJ-1.190 1411 C WRITEO.601) IPIN(IJ) 1412 C 601 FORMATdH .110) 1413 c 600 CONTINUE 1414 c 1415 DO 12 IJ-1.180 1416 ANGLE(IJ)«DFLOAT(IJ) 1417 12 CONTINUE 1418 c 1419 c CALCULATE dP/dTHETA AT EACH DATA POINT... 1420 c 1421 490 DO 5 J-2,179 1422 5 DPDTH(J)-(PIN(J+1)-PIN(d-1))/2.0D0 1423 DPDTH(1)=0.0 1424 DPDTH(180)«DPDTH(179) 1425 C 1426 C 1427 C CALCULATE d2P/d(THETA)**2 AT EACH DATA POINT... 1428 C 1429 491 DO 6 d=2. 179 1430 6 D2PDTH(d) = (DPDTH(J+1)-DPDTH(J-1) )/2.000 1431 D2PDTH(1)=0.0 1432 D2PDTH(180)-D2PDTH(179) 1433 C 1434 C 1435 c CALCULATE STANDARD DEVIATION OF THE SLOPE AT EACH CRANK ANGLE 1436 c BASED ON VARIATION OVER RANGE OF 3 DEGREES EITHER SIDE... 1437 c 1438 492 DO 15 IT-4,177 1439 JS-IT-3 1440 JF-IT+3 1441 AV-0.0 1442 DO 16 J-JS.JF 1443 16 AV-AV+D2PDTH(d) 146. MASBRN at 17:4S:21 on JUN 26. 1985 f o r CCIOCILL Page 26 1444 C 1445 AV-AV/7.0 1446 C 1447 SA=0.0 1448 DO 17 J=JS,JF 1449 17 SA=SA+DABS(D2PDTH(J)-AV)**2 1450 SD=DS0RT(SA/6) 1451 IF(IT.LT.IBEG.OR.IT.GT.IEND) GOTO 431 1452 TOL(IT)=SD*C0NST2+O.OOO1 1453 GOTO 15 1454 431 T0L(IT)«SD*C0NST1+O.OOO1 1455 15 CONTINUE 1456 C 1457 DO 18 IT-1,3 1458 18 T0L(IT)»T0L(4) 1459 C 1460 DO 19 IT-178.180 1461 19 T0L(IT)=T0L(177) 1462 CCCCCCCCCCCCCCCCCCCCCCCCCCCCC 1463 C DO 88 IT-1,180 1464 C WRITEO.87) TOL(IT) 1465 C 87 FORMATdH .F12.5) 1466 C 88 CONTINUE 1467 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 1468 C 1469 C CALL LIBRARY CURVE FITTING ROUTINES... 1470 C 1471 493 CALL DSPLFT(ANGLE.PIN,TOL.SVAL,180.W,&100) 1472 CALL DSPLN(ANGLE,POUT,PD1,PD2.180.&100) 1473 C 1474 GOTO 92 1475 100 WRITEO. 101) 1476 101 FORMATdH .'ERROR IN CURVE FITTING ROUTINE' ) 1477 STOP 1 1478 C 1479 92 IF(IPRNTS.EO.O) GOTO 933 1480 DO 45 JK«1, 180 1481 WRITEO.602) PIN( JK ) , POUT( JK ) 1482 602 FORMATdH .2F12.5) 1483 45 CONTINUE 1484 C 1485 933 RETURN 1486 END 1487 SUBROUTINE BLKRD(CA,RF.VF,AFF,AWP.NDIM) 1488 REAL*8 RF(100),VF(100),AFF(100),AWP(100),01,D2,D3 1489 INTEGER NREC.CA.NDIM 1490 NREC=4 • CA*82 1491 NDIM-79 1492 IF (CA .GE. 3) NDIM=80 1493 IF (CA .GE. 3)NREC=4+246+(CA-3)*83 1493.S IF (CA .GE. 34)NDIM=81 1493.7 IF (CA .GE.34)NREC*4+(CA-34)*84 + 246 +2573 1493.8 IF(CA .EQ. 45) NDIM=82 1493.9 IF (CA .EQ. 45)NREC=3663 1496 NREC=NREC«1000 1497 FIND(7'NREC) 1498 DO 2 J=1.NDIM 1499 READ(7.1) RF(d).VF(J).D1.AFF(J).D2.AWP(J),D3 147 MASBRN at 17:46:21 on JUN 26, 1985 f o r CC1d=CILL Page 27 1500 1 F0RMAT(2(F12.10,2X).F12.9,2X.2(F12.10.2X,F12.9,2X)) 1501 2 CONTINUE 1502 RETURN 1503 END 1504 SUBROUTINE GEOM(NDIM.H,VOLB,RF.VF,AFF.AWP,RAD,AFRNT.APER.CA) 1505 REAL*8 RF(100),VF(lOO),AFF(100),AWP(100),RAO.AFRNT,APER. VOLB 1506 REAL*8 H,VINT,V1.V2.NONDIM 1507 INTEGER CA.NDIM 1508 J=0 1508.5 H-H+0.059 1509 V1=0. 1509.5 V2=0. 1510 J=2 1510.5 FIX=3.14*(.041**2*H +.021**2*.0339) 1511 1 IF (VOLB .LE. VF(J)*FIX) GO TO 2 1512 J=J+1 1513 GO TO 1 1514 2 V1=VF(J-1)*FIX 1514.5 V2=VF(J)*FIX 1515 VINT=(V0LB-V1)/(V2 -VI) 1516 L=J-1 1519 RAD=(RF(L) +VINT*(RF(J)-RF(L)))*3.25/2 *0.0254 1520 AFRNT»(AFF(L)+VINT*(AFF(J)-AFF(L)))*2*3.14 1593*1.625**2 1521 AFRNT=AFRNT*(.0254**2) 1522 N0NDIM=2*3.141593*(1.625*H + 0.83*1.337+1.625**2) 1523 APER=(AWP(L)+VINT*(AWP(J)-AWP(L)))*N0NDIM*0.0254**2 1524 RETURN 1525 END 1526 SUBROUTINE INPUTS(JFLG,KFUEL,T1,SPEED.COMPR,AF . 1527 1 SPKAD.HTFCN,HTEXP.F.PR02,PRH20,PRN2,NDISS,PDCA. 1528 1 TWALL,PINLET,AIRFLO,IGNDEL,SCONST,IPRNTS,PAMB,CUPD,CUPH,HC) 1529 IMPLICIT REAL*8(A-H.O-Z) 1530 INTEGER NCODE,JFLG,NAN,NREP 1530.5 REAL*8 IGNDEL 1531 IF (JFLG .NE. O) GO TO 99 1532 1 WRITE(6.2) 1533 2 FORMATC '.'TYPE OF FUEL; 11-CH4 , 12=C8H18 . 13=C3H8') 1534 CALL FREAD('GUSER'.'I:',KFUEL) 1535 IF (JFLG .NE. O) GO TO 99 1536 . 3 WRITE(6.4) 1537 4 FORMATC ','TEMPERATURE AT START OF COMBUSTION- ?') 1538 CALL FREADCGUSER','R:',T1) 1539 IF (JFLG .NE.O) GO TO 99 1540 5 WRITE(6.6) 1541 6 FORMATC '.'ENGINE SPEED - 7') 1542 CALL FREADCGUSER','R:',RPM) 1543 IF (JFLG .NE. O) GO TO 99 1544 7 WRITE(6,8) 1545 8 FORMATC ','COMPRESSION RATIO » 7') 1546 CALL FREADCGUSER'.'R: ' .COMPR) 1547 IF (JFLG.NE. O) GO TO 99 1548 9 WRITE(6.10) 1549 10 FORMATC '.'AIR TO FUEL RATIO - 7') 1550 CALL FREADCGUSER','R: ' .AF) 1551 IF (JFLG .NE. O) GO TO 99 1552 11 WRITE(6,12) 1553 12 FORMATC ','SPARK ADVANCE (DEG. BTDC) » 7') 1554 CALL FREAD('GUSER'.'R:'.SPKAD) 148. MASBRN at 17:46:21 on JUN 26, 1985 f o r CC1d=CILL Page 28 55 IF (JFLG .NE. 0) GO TO 99 56 13 WRITE(6,14) 57 14 FORMATC ','HEAT TRANSFER MULTIPLIER » ?') 58 CALL FREAO('GUSER'.'R:',HTFCN) 59 IF (JFLG .NE. O) GO TO 99 SO 15 WRITE(6.16) 31 16 FORMATC ','HEAT TRANSFER EXPONENT = 7') 52 CALL FREAD('GUSER','R:',HTEXP) 53 IF (JFLG .NE. 0) GO TO 99 63 . 5 5 7 WRITE(6,58) 63.7 58 FORMATC ','RESIDUAL GAS FRACTION - ?') 63.8 CALL FREAOCGUSER' , 'R: ' ,F) 63.9 IF (JFLG .NE. O) GO TO 99 6 3 . 9 5 5 9 WRITE(6,60) 63.97 60 FORMATC ','RESIDUAL FRACTION C02 (%)= 7') 63.98 CALL FREADCGUSER','R:',PRC02) 63.99 IF (JFLG .NE. 0) GO TO 99 64 17 WRITE(6.18) 65 18 FORMATC '.'RESIDUAL FRACTION 02 (%) =?') 66 CALL FREAD('GUSER','R:',PR02) 67 IF (JFLG .NE. O) GO TO 99 68 19 WRITE(6,20) 169 20 FORMATC '.'RESIDUAL FRACTION H20 (%) « ?') 170 CALL FREADCGUSER','R: ' .PRH20) 171 IF (JFLG .NE. O) GO TO 99 172 21 WRITE(6,22) 173 22 FORMATC ','REDISUAL FRACTION N2 (%) =7') 174 CALL FREADCGUSER','R: ' ,PRN2) 175 IF (JFLG .NE. 0)G0 TO 99 176 23 WRITE(6.24) 177 24 FORMATC '.'FULL DISSOCIATION (0). OR PARTIAL ?') 178 CALL FREADCGUSER','I :'.NDISS) 579 IF (JFLG .NE. 0) GO TO 99 580 25 WRITE(6.26) 581 26 FORMATC '.'CRANK ANGLE ITERATION INCREMENT = ?') 582 CALL FREADCGUSER','R:',PDCA) 583 IF (JFLG .NE. 0) GO TO 99 584 27 WRITE(6,28) 585 28 FORMATC ','CYLINDER WALL TEMPERATURE «?') 586 CALL FREADCGUSER'.'R: ' .TWALL) 587 IF (JFLG .NE. O) GO TO 99 188 29 WRITE(6,30) 189 30 FORMATC '.'INLET PRESSURE (PASCALS) « ?') 190 CALL FREAD('GUSER','R:'.PINLET) 191 IF (JFLG .NE. O) GO TO 99 192 31 WRITE(6.32) 193 32 FORMATC '.'AIR MASS FLOW RATE (G/S) - ?') 194 CALL FREADCGUSER','R: ' .AIRFLO) 195 IF (JFLG .NE. O) GO TO 99 196 33 WRITE(6.34) 197 34 FORMATC ','IGNITION DELAY TIME (CA DEG) =7') 198 CALL FREADCGUSER'.'I :'. IGNDEL) 199 IF (JFLG.NE.O) GO TO 99 .00 3 5 WRITE(6.36) 101 36 FORMATC '.'SMOOTHING ROUTINE CONST, SCONST = ?') !02 CALL FREADCGUSER'.'R: ' .SCONST) 503 IF (JFLG.NE.O) GO TO 99 504 37 WRITE(6.38) MASBRN at 17:4S:21 on JUN 26, 1985 f o r CC)d=CILL Page 29 38 FORMATC ','DO YOU WANT INTERMEDIATE RESULTS Y=1, N=07') CALL FREAD('GUSER'.'I:'.IPRNTS) IF (JFLG.NE.0) GO TO 99 39 WRITE(6,40) 40 FORMATC '.'AMBIENT PRESSURE (KPA) 7') CALL FREAD('GUSER','R:',PAMB) i IF (JFLG.NE. O) GO TO 99 41 WRITE(6,42) I 42 FORMATC '.'PISTON CUP DIAMETER (M) 7') I CALL FREADCGUSER'.'R: ' ,CUPD) 15 IF (JFLG .NE. O) GO TO 99 >7 43 WRITE(6,44) 18 44 FORMATC ','PISTON CUP DEPTH (M)?') J9 CALL FREADCGUSER' . 'R: ' ,CUPH) J95 IF (JFLG .NE. O) GO TO 99 )97 45 WRITE(6,46) )98 46 FORMATC '.'CLEARANCE HEIGHT (M) 7') 399 CALL FREADCGUSER' , 'R: ' .HC) 99 WRITE(6,100) 100 FORMATC '.'DO YOU WISH TO CHANGE ANY INPUTS (1=YES,0=NO) 7' CALL FREADCGUSER','I :', JFLG) IF (JFLG.EO. O) GO TO 104 101 WRITE(6,102) 102 FORMATC '.'ENTER THE NUMBER CODE OF THE INPUT (1,2,3,..)') CALL FREADCGUSER','I:',NCODE) GO TO (1.3,5,7.9,11,13,15,17.19.21.23.25.27.29.31.33.35. 5 137,39,41.43.45.57.59).NCODE 7 104 WRITE(6,103) 3 103 FORMATC '.'DO YOU WANT TO SAVE THIS DATA (0«YES.1"N0) 7') 35 CALL FREADCGUSER','I :',NREP) 9 IF (NREP .EQ. 1 ) RETURN 92 CALL OUTPUT(JFLG,KFUEL,T1,RPM,COMPR,AF , 94 1 SPKAD.HTFCN.HTEXP.F.PRC02.PR02,PRH20.PRN2.NDISS.PDCA. 96 1 TWALL.PINLET.AIRFLO,IGNDEL.SCONST.IPRNTS.PAMB,CUPD.CUPH,HC) RETURN END SUBROUTINE OUTPUT(JFLG.KFUEL,T1,RPM,COMPR.AF . 1 SPKAD,HTFCN.HTEXP,F.PRC02.PR02.PRH20,PRN2,NDISS.PDCA, 1 TWALL.PINLET.AIRFLO.IGNDEL.SCONST.IPRNTS,PAMB,CUPD.CUPH.HC) 5 IMPLICIT REAL*8(A-H,0-Z) 7 REAL*8 IGNDEL WRITE(8,47) KFUEL.TI,RPM.COMPR.AF,SPKAD,HTFCN,HTEXP 47 FORMAT(13,2F7.1,3F6.2.F6.3,F5.2) WRITE(8,46 ) F,PR02,PRC02,PRH20.PRN2.NDISS,PDCA,TWALL 46 F0RMAT(5F7.3,I3.F6.2,F7.1) WRITE(8.2) PINLET.AIRFLO,IGNDEL.SCONST,IPRNTS,PAMB WRITE(8,22) CUPD.CUPH,HC 22 F0RMAT(3F8.3) 2 FORMAT(F6.1,3F6.2,I3,F6.2) RETURN END APPENDIX F - PROPERTIES OF B.C. NATURAL GAS 150. Composition (Volume %) Methane 94.00 Ethane 3.30 Propane 1.00 Iso-butane 0.15 N-butane 0.20 Iso-pentane 0.02 N-pentane 0.02 Nitrogen 1.00 Carbon Dioxide 0.30 Hexane 0.01 Water Content: 3 to lbs/million cubic feet This composition may be conveniently approximated by the following composition: % Volume Volume Molecular Mass Fraction Weight kg/kmo Methane CH4 94.00 0.940 * 16.040 = 15.078 Ethane C2H6 3.30 0.033 * 30.070 = 0.992 Propane C3H8 1.00 0.010 * 44.097 = 0.441 Butane C4H10 0.40 0.004 * 58.124 = 0.232 Nitrogen 1.00 0.010 * 28.013 = 0.280 Carbon Dioxide 0.30 0.003 * 44.010 = 0.132 100 .00 1.000 M= 17.156 It therefore follows that the average molecular weight i s 17.156 and R 8.3143 _ ,„., the gas constant = — = ^ = 0.4846. Hence, density = P/(Z*R*T) = 21.1°C at 1 atm (101.3 kPa) . Generally, density at 1 atm = 209/T(°K) kg/m. Viscosity 151. The viscosity of the natural gas at 0°C may be obtained from the following: given: 1/2 I y± * (M ±) 1/2 where y^ = molecule fraction M. = molecule weight UC 2H 6  C3 H3 Mco2 102.6 micropoise at 0°C. 84.8 micropoise at 0°C. 75.0 micropoise at 0°C. 139.0 micropoise at 0°C. 166.0 micropoise at 0°C. Estimating y as 75.0 for C4H10 as well as C3H8 and including the mole fraction of the former with the latter, the calculation becomes: Viscosity y i m i CH4 102.6 0.940 16.040 C2H6 84.8 0.033 30.070 C3H8 75.0 0.014 48.105 C02 139.0 0.003 44.010 N2 166.0 0.010 28.013 :«±)l/2 y^O^) 1' 2 y i y i ( m i ) 4.005 3.765 386.29 5.484 0.181 15.35 6.936 0.097 7.28 6.634 0.020 2.78 5.293 0.053 8.80 4.116 420.50 with the result u , = t2?,'^ = 102.16 upoise at 0°C. mix 4.116 The viscosity of natural gas at other temperatures can be obtained from, N.G.u = 9.879*T3/2/(T + 163.17) Therefore viscosity of N.G. at 70°F (21.1°C) = 108.96 upoise. 152. Higher and Lower Heating Values mass mass HHV kg/kmol (%) (kJ/kg) CH4 15.078 0.879 55496 48781 C2H6 0.992 0.058 51875 = 3008 C3H8 0.441 0.026 * 50343 = 1309 C4H10 0.232 0.013 * 49500 644 C02+N2 0.412 0.024 * 0 - 0 17.156 1.000 53742 Therefore the Higher Heating Value of B.C. Natural Gas i s 53,742 kJ/kg at 25°C. The Lower Heating Value is given by, mass (%) LHV CH4 0.879 * 50010 43959 C2H6 0.058 * 47484 2754 C3H8 0.026 * 46353 1205 C4H10 0.013 * 45714 640 C02+N2 0.024 * 0 0 1.000 48558 Therefore the Lower Heating Value of B.C. Natural Gas i s 48,558 kJ/kg at 25°C. TABLE I Engine Specifications Engine C.F.R. Displacement 611.7 CC. Bore 82.55 mm Stroke 114.30 mm Compression Ratio 11.3 Con-rod Length 254.00 mm Intake Valves Diam. 35 mm Opening Angle 10 A.T.D.C. Closing Angle 34 A.B.D.C. Exhaust Valve Diam. Opening Angle 40 B.B.D.C Closing Angle 15 A.T.D.C. Spark Plug Champion W18 TABLE II Hot Wire Probe and Anemometer Specifications Probe TSI Model 1226 Wire Material Platimum-Iridium Wire Diameter 6.3 um Wire Length 1.25 mm Wire Temperature Coefficient of Resistance 0.0009 /°C Anemometer Disa Model 55M Top Resistance 50 n Cable Resistance 0.214 n 155. T O P Fig. 1.1 The squish combustion chamber PISTON A ! ! TDC L L 1 1 — I r i Up f s H A x = TT /4 (D 2 - D B 2) A 2 = I T / 4 D f i 2 A 3 = T I D B ( h c + s ) %SQUISH = A 1/(A 1 + A 2) V l A l < h c + S> V 2 = A 2 ( h c + S + H) Fig. 3.1 The standard squish chamber 157. PISTON B — 1 1 r ™ _ j _ _ _ _ _ _ . _ _ _ ( 1 1 r ^ ° s B t/ V l ! 11 \ ^ U S C / < - H » — d . —1 1 1 t ' DB - H . 0 . h1 = IT/4 (D2 - Dfi2) A 2 = IT/4 D B 2 A 3 DB (*c + S ) A 4 = IT/4 d %SQUISH = A-j/fA-j^  + A 2) V l " A l ( h C + S ) V 0 = A 0 (h + S + H) 2 2 C Fig. 3.2 The squish-jet chamber 158. Fig. 3.3 The effect of clearance height on squish velocity 159. Fig. 3.4 The effect of the squish-jet design on squish velocity methane pressure regulator I I filter laminar flow element orifice meter venturi • M -CD rpr fly wheel surge tank CFR induction motor pressure slotted disk anemometer 2'ca data aquisition bdc Fig. 4.1 Schematic of experimental setup and instrumentation 34 mm RADIUS MILL 0.030" 162. 0.390 TYPICAL 0.187 RADIUS .337 Piston A, Case 1 Piston B, Case 1 Piston A, Case 2 Piston B, Case 2 A=0.354 B=0.947 C=1.819 A=0.354 B=0.947 C=1.739 A=0.354 B=0.931 C=1.500 A=0.354 B=0.889 C=1.500 Piston A - exclude the 7 holes Case 2 - do not mill recess for valves Fig. 4.3 The squish piston inserts Fig. 4.4 Photograph of squish piston inserts 164. Fig. 4.5 Top and side view of C.F.R. combustion chamber Fig. 4.6 Fitting for hot wire probe DATA ACQUISITION SYSTEM PRESSURE BDC PULSE 2 PULSE ANEMOMETER HR TAPE RECORDER LPF A/D J CIRCUITt BOARDS «CLOCK TRIGGER S IBM PC IDT2801 CLOCK AND TRIGGER CIRCUIT ESSURE -8! DC PULSE L—KU CLR PULSE MANUAL SWITCH PLL X 10 DEBOUNCEP Q PF2 CK CLR TRIGGER SET N DIVIDE CLOCK BY N COUNTER CLOCK Fig. 4.7 Schematic of data acquisition 1 - Charge Amplifier for Pressure Signal 2 - Anemometer Bridge Unit 3 - Digital Oscilloscope 4 - Hewlett Packard Tape Recorder 5 - I.B.M. Microcomputer 6 - Data Acquisition Circuitry 7 - Bandpass F i l t e r Fig. 4.8 Photograph of data acquisition system 168. 1 - Slotted Wheel 2 - Optical Pickup and Trigger Circuitry Fig. 4 . 9 Photograph of optical trigger system A,B 3.5 2.0 10.0 A,B 3.5 2.0 23.0 B 1.5 16.0 5.0 A,B 1.5 2.0 10.0 A,B 1.5 2.0 23.0 A 2.5 2.0 10.0 A 2.5 2.0 23.0 FLAT 10.7 2.0 10.0 FLAT 10.7 2.0 23.0 A l l dimensions in millimeters Fig. 5.1 Hot wire probe locations ON Fig. 5.2 Hot wire probe orientation 17 b -10 8H z II CRANK ANGLE DEGREES Fig. 7.1 Three consecutive instantaneous velocity records 172. Fig. 7.2 Comparison of time averaged and ensemble averaged mean velocity 173. Fig. 7 . 3 Cyclic variation of the mean velocity 174. 6 Legend A TIME X E N S E M B L E 60 100 140 180 220 CRANK ANGLE DGREES Fig. 7.4 Comparison of time and ensemble averaging techniques for the evaluation of turbulence intensity 175. O O Ld CO OH U l Q_ CO CH U l 100 HO 180 CRANK ANGLE DEGREES 220 Fig. 7.5 Turbulence intensity evaluated with Lancaster's nonstatlonary technique 6 0-r 60 —I 1 •• 1— 100 140 180 CRANK ANGLE DEGREES 220 Fig. 7.6 Mean velocity and turbulence intensity for Piston A h c = 3.5 mm; probe at cup edge 177,. Legend M E A N INTENSITY "1 I 1 ' 1 r 60 100 140 180 220 CRANK ANGLE DEGREES F i g . 7.7 Mean v e l o c i t y and turbulence i n t e n s i t y f o r Piston A; h c = 1.5 mm; probe at cup edge 178. Legend M E A N INTENSITY n i 1 1 r 60 100 140 180 220 CRANK ANGLE DEGREES Fig. 7.8 Mean velocity and turbulence intensity for Piston A; h c = 1.5 mm; probe at chamber center 179. Q Z o o UJ </) Ql UJ D_ 17) 60 100 140 180 CRANK ANGLE DEGREES 220 Fig. 7.9 Mean velocity and turbulence intensity for Piston A; h = 1.5 mm; probe at cup edge; 6 = 90° 180. Legend M E A N INTENSITY , , , f 60 100 140 180 220 CRANK ANGLE DEGREES Fig. 7.10 Mean velocity and turbulence intensity for Piston A; h c = 1.5 mm; probe at chamber center; 6 = 90° 181. Fig. 7.11 Comparison of mean velocity traces for Piston A; h c = 3.5 and 1.5 mm; probe at cup edge 182. 0.8 0.7 -\ >- 0.6H CO U l o UJ 0.5 OA A 0.1 0.0-H 60 Legend 1 1 5 3 . 5 100 140 180 CRANK ANGLE DEGREES 220 Fig. 7.12 Comparison of relative turbulence intensities for Piston A; h c = 3.5 and 1.5 mm; probe at cup edge 183. O U U J to to 01 U J 100 140 180 CRANK ANGLE DEGREES 220 Fig. 7.13 Mean velocity and turbulence intensity for Piston B; h c = 3.5 mm; probe at cup edge 184. Q Z o o CO CH U l CL (/) CH 100 140 180 CRANK ANGLE DEGREES 220 Fig. 7.14 Mean velocity and turbulence intensity for Piston B; h c = 1.5 mm; probe at cup edge 185. 100 140 180 CRANK ANGLE DEGREES 220 Fig. 7.15 Mean velocity and turbulence intensity for Piston B; h c = 1.5 mm; probe at chamber center 186. 6 Legend M E A N INTENSITY CRANK ANGLE DEGREES Fig. 7.16 Mean velocity and turbulence intensity for Piston B; h„ = 1.5 mm; probe inside cup 187. 0.8 0.0-f-60 100 140 180 CRANK ANGLE DEGREES 220 Fig. 7.17 Comparison of relative turbulence intensities for Piston B; h =3.5 and 1.5 mm; probe at cup edge c 188. Fig. 7.28 Comparison of mass fraction burn curves for Pistons A and B at a spark timing of 25° BTDC 189. 0.8 0.7H >- 0.6^  z UJ Z 0.54 U l o z U l =! 0.4H 0.H Legend A B O . O - T -60 100 140 180 CRANK ANGLE DEGREES 220 Fig. 7.19 Comparison of relative turbulence intensities for Pistons A and B; h = 1.5 mm; probe at cup edge >-00 < o on o_ u i > UJ on 0.20-1 0.15-0.10-0 . 0 5 -0.00 Legend Ul EDGE • i CENTER 1 lib H A ammOm* T 200 400 600 800 MICROSECONDS 1000 1200 Fig. 7.20 Comparison of the relative probability distributions of small scale turbulence structure for Piston A at the chamber center and at the cup edge o 0.20 >-OQ < OQ O LY. Q_ LxJ > Ld LY. 0.15-0.10-0 . 0 5 -0.00 J Legend LZ2 FLAT 0 ll ll ll 1 "| •— 1 200 400 600 800 MICROSECONDS 1000 1200 Fig. 7.21 Comparison of relative probability distributions of small scale turbulence structure at the chamber center for Piston A and the fl a t piston i - 1 0 . 2 0-i 0.15-0.10-0.05 0.00 J i 0 - " — ~ 200 400 600 MICROSECONDS 800 1000 1200 Fig. 7.22 Comparison of relative probability distributions of small scale turbulence structure at the cup edge for Pistons A and B 0 5 -00 J 400 600 800 MICROSECONDS Fig. 7.23 Comparison of relative probability distributions of small scale turbulence structure at the chamber center for Pistons A and B 194. 70-1 Fig. 7.24 Comparison of pressure history for Pistons A and B and the f l a t piston for a spark timing of 30° BTDC 195. Fig. 7.25 Comparison of mass fraction burn curves for the fl a t piston and for Piston A at a spark timing of 30° BTDC 196. Fig. 7.26 Comparison of mass f r i c t i o n burn curves for Pistons A and B at a spark timing of 30° BTDC 197. 198. 1 CH m o < OH LL. in in < 180 200 CRANK ANGLE DEGREES 240 Fig. 7.28 Comparison of mass fraction burn curves for Pistons A and B at a spark timing of 25° BTDC 

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