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Measurements of heat capacity and heat transfer coefficient of water-oxygen mixtures at near critical… Boskovic, Sanja 2001

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MEASUREMENTS OF HEA T CAPACITY AND HE A T TRANSFER COEFFICIENT OF WA TER-OXYGEN MIXTURES A T NEAR CRITICAL CONDITIONS By Sanja Boskovic B.Sc. (Mechanical Eng.) University of Sarajevo, 1985 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF MECHANICAL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November, 2001 (g) Copyright S a n j a Boskovic, 2001 ABSTRACT: The constant-pressure heat capacity, C p , and local forced convection heat transfer coefficient, h, for water-oxygen mixtures flowing inside horizontal smooth tubes were obtained experimentally. Data were obtained for pressures of 24 to 26 M P a ; f low rates 0.636 to 1.27 1/min, average heat fluxes 34 to 160 kW/m 2 , mass velocities 351 to 701 kg/m 2s and temperatures from 330 to 430 °C. Oxygen flow was 2 to 8 weight percentage of the total mixture flow. For a given flow and heat supplied to the mixture, Cp is determined from the bulk temperature in a heated tube. The heat transfer coefficient, h is determined from the difference in bulk and wall temperatures. The temperature at which the maximum heat capacity occurs (Tpc) is lower for water-oxygen mixtures than for pure water. Another effect o f oxygen addition is a reduction in magnitude of the maximum Cp and h. The enhancement near the critical point appears to be less at high heat flux. i i TABLE OF CONTENTS A B S T R A C T i i L IST OF F I G U R E S vi L IST O F T A B L E S ix N O M E N C L A T U R E x A C K N O W L E D G M E N T x i i D E D I C A T I O N x i i i 1. I N T R O D U C T I O N 1 1.1 Supercritical Water Oxidation 1 1.2 Heat transfer to supercritical fluids 2 1.3 Enhanced heat transfer 3 1.4 Deteriorated heat transfer 4 1.5 Thermodynamic and transport properties 4 1.6 Nusselt number correlation 5 2. E X P E R I M E N T A L S Y S T E M 10 2.1 The U B C / N O R A M pilot plant 10 2.2 Temperature measurement 11 2.3 Pressure measurement 12 2.4 F low rate measurement 12 iii 3. M E A S U R E M E N T S OF C O N S T A N T P R E S S U R E H E A T C A P A C I T Y A N D H E A T T R A N S F E R C O E F F I C I E N T F O R W A T E R - O X Y G E N M I X T U R E S 18 3.1 Constant heat capacity measurement 18 3.2 Heat transfer coefficient measurement 19 3.3 Data processing 22 3.4 Evaluation of the error of the measurements 22 4. R E S U L T S 25 4.1 Constant pressure heat capacity for water-oxygen mixtures 25 4.2 Heat transfer coefficient to supercritical water-oxygen mixtures 25 5. C O N C L U S I O N S 40 6. R E C O M M E N D A T I O N S 41 R E F E R E N C E S 42 A P P E N D I X A Test Section 1-D Transient Heat Loss Mode l in Cyl indrical Polar Coordinates 48 A P P E N D I X B Thermodynamics and transport properties 67 A P P E N D I X C Oxygen flow calibration 77 IV A P P E N D I X D Test summaries 80 A P P E N D I X E Data files for experimental runs 85 A P P E N D I X E l Results of experiments 88 A P P E N D I X F MatLab program outline 142 V L I S T O F F I G U R E S 1.1 S C W O process flow diagram 8 1.2 Phase equilibrium of binary mixtures (P = 25 M P a , calculated from R K S EOS) , (Wang, 2001) 8 1.3 Variation of heat transfer coefficient with temperature for supercritical water, (Bazargan, 2001) : 9 2.1 U B C / N O R A M Pilot Plant 15 2.2 Electrical heating system (Teshima, 1997) 16 2.3 Test section (Teshima, 1997) 16 2.4 Thermocouple setting for the test section (before the venture was installed) 17 2.5 Thermocouple setting for the test section (after the venture was installed) ,,.17 3.1 Heat capacity for pure water Run #11 (P=24.4 M P a , m=1.01 1/min, Q=93 kW/m 2 ) 25 4. l a Heat capacity for Run #11 (P=24.4 M P a , m=l .01 1/min, Q=93 kW/m 2 , 02 = 0), Run #12 (P=24.5 M P a , m=1.01 1/min, 0=97 k W / m 2 , 02 = 2%), Run #15 (P=26.4 M P a , m=l .01 1/min, 0=95 kW/m 2 , 02 = 2.1%) 28 4.1b Heat transfer coefficient (bottom) for Run #11 (P=24.4 M P a , m=1.01 1/min, Q=93 kW/m 2 , 02 = 0), Run #12 (P=24.5 M P a , m=1.01 1/min, 0=97 kW/m 2 , 02 = 2%), Run #15 (P=26.4 M P a , m=1.01 1/min, Q=95 kW/m 2 02= 2.1%) 29 v i 4.1c Heat transfer coefficient (top) for Run #11 (P=24.4 M P a , m=l .01 1/min, Q=93 . k W / m 2 , 0 2 = 0), Run #12 (P=24.5 M P a , m=1.01 1/min, 0=97 kW/m 2 , 0 2 = 2%), Run #15 (P=26.4 M P a , m=1.01 1/min, Q=95 kW/m 2 , 0 2 = 2.1%) 30 4.2a Heat capacity for Run #11 (P=24.4 M P a , m=1.01 1/min, Q=93 kW/m 2 , 0 2 = 0), Run #12 (P=24.5 M P a , m=1.01 1/min, Q=97 kW/m 2 , 0 2 = 2%), Run #13 (P=24.2 M P a , m=1.01 1/min, Q=95 kW/m 2 , 0 2 = 4.9%) 31 4.2b Heat transfer coefficient (bottom) for Run #11 (P=24.4 M P a , m=1.01 1/min, Q=93 k W / m 2 , 0 2 = 0), Run #12 (P=24.5 M P a , m=1.01 1/min, Q=97 kW/m 2 , 0 2 = 2%), Run #13 (P=24.2 M P a , m=1.01 Vmin, Q=95 kW/m 2 , 0 2 = 4.9%) 32 4.2c Heat transfer coefficient (top) for Run #11 (P=24.4 M P a , m=1.01 1/min, Q=93 k W / m 2 , 0 2 = 0), Run #12 (P=24.5 M P a , m=1.01 1/min, Q=97 kW/m 2 , 0 2 = 2%), Run #13 (P=24.2 M P a , m=1.01 1/min, Q=95 kW/m 2 , 0 2 = 4.9%) 33 4.3a Heat transfer coefficient (bottom) for Run #31 (P=25.3 M P a , m=1.01 1/min, Q=98 k W / m 2 , 0 2 = 7.9%), Run #32 (P=25.2 M P a , m=1.01 1/min, Q=160 kW/m 2 , 0 2 = 8%), Run #33 (P=25.3 M P a , m=1.011/min, Q=37 kW/m 2 , 0 2 = 47.6%) ... .34 4.3b Heat transfer coefficient (top) for Run #31 (P=25.3 M P a , m=1.01 1/min, Q=98 k W / m 2 , 0 2 = 7.9%), Run #32 (P=25.2 M P a , m=1.01 1/min, Q=160 kW/m 2 , 0 2 = 8%), Run #33 (P=25.3 M P a , m=1.01 1/min, Q=37 k W / m 2 , 0 2 = 47.6%) 35 4.4a Heat transfer coefficient (bottom) for Run #29 (P=25.1 M P a , m=1.27 1/min, Q=96 kW/m 2 , 0 2 = 3%), Run #30 (P=25.2 M P a , m=1.01 1/min, Q=96 k W / m 2 , 0 2 = 3%) 36 4.4b Heat transfer coefficient (bottom) for Run #29 (P=25.1 M P a , m=1.27 1/min, Q=96 k W / m 2 , 0 2 = 3%), Run #30 (P=25.2 M P a , m=1.01 1/min, Q=96 kW/m 2 , vii 0 2 = 3%) 37 4.5 (Tpwo - Tpw) vs oxygen% 38 4.6 Cpwo(P)/Cpw(P) vs oxygen% 39 vi i i LIST OF TABLES 4.1 Summary for Runs #11- #34 N O M E N C L A T U R E A - area, m2 Cp - heat capacity, kJ/kgK E - temperature ratio Fc - coefficient, Eqs. (3 a) and (3b) h - heat transfer coefficient, W/m2K i - enthalpy, kJ/kg k - thermal conductivity, W/mK L - test section length, m m - mass flow rate, kg/h n i - coefficient, Eq. 3b. ri2 - coefficient, Eq. 3b. Nu - Nuselt number P - pressure, MPa Pr - Prandtl number q - heat fliix, kJ7 m2 Q - heat power supplied to water-oxygen mixtures, kW R - tube radius, m Re - Reynolds number T - temperature, °C Tout - temperature, K V - voltage reading, V V 0 - zero offset, V wc P - error for heat capacity measutrement w m - error for oxygen mass f low rate measurement WT - error for temperature measurement Wh - error for heat transfer coefficient measurement Greek: p - density, kg/m 3 Ax - axial distance between thermocouples, m Subscript: b - b u l k c - critical f - f l u i d i - inlet o - outlet r - reduced temperature w - wall m - pseudocritical condition ACKNOWLEDGMENT First and foremost I would like to thank Dr. Steven Rogak, my supervisor, whose insight and support was never ending. His support kept me motivated throughout the whole course of this study. I wish to thank Dr. Richard Branion for his support, kindness, and time he spent to correct my mistakes. I also would like to thank Dr. Cl ive Brereton for serving in my examination board and for his invaluable comments. I was lucky to meet and be with a number of wonderful fellow graduate students during my stay at U B C . I should thank Tazim Rehmat as well as Maj id Bazargan, Mohamed Khan and Ivette Vera-Perez . M y specially thanks go to Wang Shuo who was my office-mate as well as a very good friend. M y appreciate also goes to the technical support stuff in mechanical shop and electronic shop, secretaries in the department. Loving gratitude is extended to my husband and son. I thank my brother, his family, my relatives from Slovenia and friends, who kept me going and kept me smiling. I thank my parents who taught me the most important lessons, showed me the path, and shaped my life. Finally, the financial support provided by N S E R C of Canada are gratefully acknowledged. xii Dedicated to my husband and son and my very best friends Davor and Andrej. Thank you. 1. INTRODUCTION 1.1 Supercritical Water Oxidation Supercritical Water Oxidation (SCWO) , sometimes referred to as Hydrothermal Oxidation (HTO), is a thermal process capable of destroying a wide variety of hazardous organic wastes. S C W O exploits the ability o f supercritical water to dissolve both oxygen and nonpolar organic compounds thereby allowing wastewater containing organic wastes such as oils and sewage to be completely oxidized to carbon dioxide and water. In a typical S C W O waste treatment system (Fig. 1.1), dilute aqueous organic waste is combined with an oxidizer at elevated pressure and temperature (P> 22.1 M P a , T>550 °C) in a reactor for residence times on the order of 30 - 90 seconds depending on the reaction temperature. Since supercritical water is an excellent solvent as well as an ideal media for heat transfer, the reaction occurs quickly within the reactor. The products o f the reaction are cooled and separated. This feature is very useful when treating highly toxic wastes. Research is ongoing to assist in developing the utilization of S C W O technology on an industrial scale. The high temperature environment within S C W O reactors and processing systems can present significant reliability and performance problems. Unl ike most organic materials, inorganic compounds tend to be highly soluble in liquid water at ambient conditions but have extremely low solubility under supercritical conditions. The resulting inorganic salts can precipitate causing sticky deposits on the reactor wall and can even plug the reactor tube through high local deposition rates. Even i f plugging does 1 not occur, salt deposition significantly affects the pressure drop and flow characteristics as wel l as the heat transfer rate. One very important aspect o f the design of a S C W O facility is having knowledge of the heat transfer rates. Maximiz ing the heat transfer rate is a major task for the design process of any heat transfer equipment. 1.2 Heat transfer to supercritical fluids There are no available data for heat transfer coefficients for water-oxygen mixtures and there are limited heat transfer data for supercritical water covering various ranges of geometry, pressure, mass f low and heat flux (Bazargan, 2001). Such information might provide the necessary knowledge for the optimal design of a S C W O system. To accomplish this goal, the present study focuses on thermodynamic properties and heat transfer to supercritical water-oxygen mixtures f lowing in a pipe. Experimental results to date (Swenson et al., 1965: Yamagata et al., 1972: Kondratev, 1967) have shown different heat transfer behavior for supercritical fluids compared to that observed during single-phase forced convection under subcritical conditions including different features like enhanced and deteriorated heat transfer. 2 1.3 Enhanced heat transfer Suppose the temperature of a fluid f lowing in a heated tube at supercritical pressure was raised until the wall temperature was slightly above the "pseudocritical temperature". Sabaresky et al. (1967) describe the pseudocritical temperature as follows: "The temperature at which the thermodynamic and transport properties have their maximum rate o f change with temperature at constant pressure. Its significance is that below the pseudocritical temperature, the fluid has liquid-like properties while above, it closely resembles a vapor". Under such conditions many investigators have reported a significant enhancement o f the heat transfer rate at low heat fluxes. Swenson et al. (1965) demonstrated a correlation between the heat transfer enhancement and pressure for supercritical water flowing in a smooth, vertical tube. Pitla et al. (1998) in their review article pointed out that Shitsman (1963) and Krasnoshchekov et al. (1970) observed an improvement in heat transfer when the wall temperature was less than the critical temperature and the fluid bulk temperature was greater than the critical temperature. The improvement o f heat transfer during cooling occurs because of the formation of a lower temperature, liquid l ike layer near the wall o f the tube. This layer has higher thermal conductivity than the bulk fluid. Perhaps the most important factor affecting heat transfer is high heat capacity near the pseudocritical point. 3 1.4 Deteriorated heat transfer Yamagata et al. (1972) and Kondratev (1967) studied the effect of heat flux on heat transfer to supercritical fluids. They showed that when the heat flux increased, the heat transfer coefficient decreased in the pseudocritical region. At very high heat fluxes, heat transfer deterioration is a very serious problem and can cause tube failure. Sabaresky and Hauptmann (1967) measured forced convective heat transfer from a flat plate to carbon dioxide near the critical point and showed that at larger heat-transfer rates, the heat transfer coefficient exhibited a sharp drop when the free stream (bulk) temperature slightly exceeded the pseudocritical temperature. Jackson and Hal l (1979) derived an expression for the onset of impaired heat transfer at high heat flux during forced convection. They suggested that the validity o f the expression needed to be investigated experimentally. 1.5 Thermodynamic and transport properties A complete set of thermodynamic properties of supercritical water-oxygen mixture is not available in the literature. From data provided by Christoforakos and Franck (1986), phase equilibria were calculated and P-V-T-x relations for water-oxygen developed. With this Equation of State (EOS) density and mixture heat capacity were calculated (Saur et al, 1993). Viscosity and thermal conductivity were obtained as deviations from values for low density gases. Van der Waals "one fluid theory" was used 4 for mixture rules. Wang (2001) calculated the phase boundary, constant pressure heat capacity and density using the Hard Sphere equation of state and Redlich-Kwong-Soave equation of state. Oh et al. (1997) calculated thermodynamic and transport properties for S C W O fluids (water, ethanol, isopropyl alcohol, nitrogen, oxygen, and carbon dioxide) using the Redlich-Kwong-Soave cubic equation of state. Details are presented in Appendix B. It is difficult to predict the phase equilibrium of two-component or multi-component systems because changes of the fractions of the each component in the liquid and vapor phases need to be considered. A T - x phase diagram for water-oxygen mixtures at pressure 25 M P a was obtained (Wang 2001) Figure 1.2. The phase curve ( A B C D E ) divided liquid, vapor and liquid-vapor regions from each other. Point C is the critical point. Curve A C represents the fraction in the vapor phase, and curve C E represents in the liquid phase. For example, at 580K (line B-D) , the vapor is approximately 55% H 2 0 while the liquid is over 98% H 2 0 . 1.6 Nusselt number correlation Non-dimensional relations are usually developed to make experimental results more general. Nusselt number correlations are used for forced convection heat transfer in pipe flows. They have the following form. A r« = a R e 6 P r c (1) 5 where a,b,c are constants to be determined from the experimental data. Near the critical region, the fluid properties are changing significantly with temperature. Because of that behaviour, the simple Nusselt number correlation, which assumes constant property values and fully developed flow, is not generally applicable for supercritical conditions. To account for the effect of property variations some correction factors have been introduced to the Nusselt number correlation. The ratio of the specific heat, density or viscosity at the wall and bulk temperature, or combinations of these are usually employed. The following are some examples of correlations presented in the literature. Swenson et al. (1965) developed the following correlatio from their experiments with heated turbulent flow: /• \ 0.612 s x 0.231 Nuw = 0.00459(Re6)°9 2 3 \Cp — — (2) V K) \pbJ where the integrated heat capacity is given by P~KTK-Tb) The subscripts w and b refer to conditions at the wall and bulk respectively. Yamagata et al. (1972) examined data from horizontal and vertical test sections to develop the following more complicated correlation: ( \0 .85 / \0.8 Re 6) (PrJ Fc (3a) where the correction factor Fc depends on the temperature T -T Fc=l for E = J " * > 1 T -T 6 0.05 f Cp / \-0.05 L-» ^ = 0 . 6 7 ( P r J for 0<E<\ (3b) the exponents ni and «2 are for E < 0 n l = -0.77 ! 1 ril = 1.44 , 1 + -^ + 1.49 1 1 + — -0 .53 and Prm is the Prandtl number at the pseudocritcal point. The subscript m refers to conditions at the pseudocritical temperature. Shown in Figure 1.3 is a comparision of some available correlations with experimental data P=25.2 M P a , Q = 307 k W / m 2 and G = 965 kg/m 2s (Bazargan, 2001). The sources of disagreement between the results are due to: (a) differences in the test conditions, mainly in terms of the heat flux and buoyancy effects, which can not be fully reflected in a typical Nusselt number correlation and, (b) differences in values of the thermophysical properties used in various correlations either because of different sources of information or difficulty in applying the proper values (as a result of their large variation with small changes in pressure and temperature in the critical region). To apply such Nusselt number correlations to supercritical water-oxygen mixtures, reliable thermodynamic properties in the supercritical region are needed. 7 Oxygen H - i Water & Organics Heating Single Phase Reaction Cooling Separation Figure 1.1 S C W O process f low diagram COj Water Ash Liquid 0 .2 0 .3 0 .4 0 . 5 0.6 0 .7 Water mole fraction 0 .8 0.9 Figure 1.2 Phase equilibrium of binary mixtures for P= 25 M P a , calculated from R K S E O S , (Wang, 2001) 8 Bulk Enthalpy, kJ/kg Figure 1.3 Variation of heat transfer coefficient with temperature for supercritical water, P = 25.2 MPa ,Q = 307 k W / m 2 and G = 965 kg/m 2s (Bazargan, 2001) 9 2. EXPERIMENTAL SYSTEM 2.1 The U B C / N O R A M pilot plant The U B C / N O R A M S C W O facility (Figure 2.1) was constructed for research and development of a tubular-type reactor, for the destruction o f wet organic wastes. A range of pressures, heat fluxes temperatures and mass flows can be achieved. Two 550 L cylindrical storage tanks supply the system with water and waste. Water is pressurized with a triplex plunger pump while oxygen is pressurized using an air-operated booster. Water f low is measured with a graduated cylinder and stop watch, at the system outlet when it is cold (without oxygen). Oxygen flow is measured using a differential pressure transmitter installed across an orifice plate downstream of the booster. Details about transmitter calibration are given in Appendix C. The main heat transfer elements of the S C W O system are the regenerative heat exchanger, two preheaters, the test section, the reactor, and the process cooler. The process cooler is 6.1 m of 9.5 mm stainless steel tube. A l l other tubing is made of A l loy 625 high pressure tubing (6.2 mm ED and 9.5 mm OD). A n electrical current through the tube wall provides the heat supplied to the system (Fig. 2.2). The power is supplied from silicon controlled rectifiers (SCR). The power goes from the S C R panel through two step-down transformers to each preheater. The preheaters are controlled separately from the S C R panel. The power to Preheater 1 is adjusted manually on the S C R panel. The power to Preheater 2 can be adjusted with a feedback temperature controller. The heating for the test section is achieved in the same way as for the preheaters, but power control is always manual. The test section is made from four tube sections (Fig. 2.3). Two shorter 10 sections (0.3 m), placed at the inlet and the outlet of the test section are not heated. The other two (1.52 m each) are electrically heated. The regenerative heat exchanger is designed to recover approximately 30 k W of power from the test section outlet. The tubing is insulated in 15.25 cm x 15.25 cm boxes of ceramic board (Kaowool). There is one absolute pressure transducer located at the beginning of the test section and a differential pressure transducer which measures the pressure drop along the test section. The last one is also used for pressure drop measurement through the venturi, which is placed at the end of the test section. The venturi was used for preliminary density measurements as described in Wang (2001). The temperature measurements are made using 29 surface thermocouples (high temperature thermocouple wire with ceramic fiber insulation) and three bulk temperature thermocouples. 2.2 Temperature measurement A l l thermocouples are K - type (Chromel Alumel) with twisted shielded extension wire. Three thermocouples were placed in the test section (Fig. 2.4). Previously all o f them were used for heat capacity and heat transfer measurements. Runs #28-35 had only two bulk thermocouples working in the test section (Fig.2.5). The test section has 20 top surface thermocouples and 10 bottom ones. A l l of them were spot-welded. Thermocouple error is in range 2 - 3 °C, but it was possible to measure difference of less than 0.5 °C, by cross calibrating thermocouples against each other. 11 2.3 Pressure measurement The absolute pressure transducer is used for the system pressure control. The pressure range of the transducer is 0 - 34.5 M P a and output signal is in range 0-10 volts. The calibration was done with a digital calibrator ( 0 - 5 1 . 7 MPa) with water as a working fluid. A correlation between the absolute pressure and the voltage was linear: P = 6.8119V + 0.0444 (4) Where P is the system pressure (MPa), V is voltage reading (V). This relation gives an error o f 0.04-0.1% ( 0.01 M P a - 0.028 M P a on interval o f 21.9 M P a - 26.9 MPa) . 2.4 F low rate measurement Water flow rate is measured by using a graduated cylinder and a stopwatch after the system is pressurized, and before oxygen is introduced and heat is supplied. For Runs #1-22 and #36-38 oxygen flow rate was measured with Validyne variable reluctance pressure transducer - DP3 03. The differential pressure transducer cell was capable o f detecting pressure differences up to 5.5 M P a . The calibration was performed by supplying nitrogen to the booster and measuring the low pressure outlet flow with a dry gas meter. The correlation between oxygen mass flow rate and voltage signal is as follows: 12 m = (V*p/44.4) 1/2 (5) where: m - mass flow rate, kg/h V- voltage reading, V p - oxygen density at 27.4 M P a More details about calibration are available in Gairns and Rogak (1999). Oxygen flow is measured with a transmitter (Foxboro E 1 3 D H I S A M 2 ) for Runs # 23-35. The diameter o f the orifice is 0.86 mm. The pressure drop is measured by a transmitter. The output signal is in the range 4 - 2 0 mA. To provide an acceptable output signal for the data acquisition (0 - 10 V ) a 500 Ohm resistor was connected in the line. The orifice was calibrated using oxygen at the 27.2 M P a (Appendix C). The correlation between oxygen mass flow rate and voltage signal is as follows: m = 4.16(V-V0)1/2 (6) where: m - mass f low rate, kg/h V- voltage reading, V V0 - zero offset, V 13 The error of measurement is around 16% considering calibration error and zero-offset drift (the major factor). The transmitter maximum flow rate measurement is 12 kg/h. Zero offset varies with the working pressure and it is depends on the possible overloading of the transmitter. A ball valve is used as a bypass to protect the transmitter. 14 Figure 2.1 UBC/NORAM Pilot Plant Note that all preheaters and test section are horizontal SCR SCR SCR Figure 2.2 Electrical heating system (Teshima, 1997) Union I Union 2 Heated Sections / Union 3 \ Union 4 Union 5 Barrel Connectors Figure 2.3 Test section (Teshima, 1997) B2 SI S10 B3 Sll S20 B4 - ^ ^ P — i i r~\ i I I— i i mB(i SB 1 SB 9 SB20 Figure 2.4 Thermocouple setting for the test section (before the venturi was installed) B2 SI SIG B3 S l l S20 B5 SB1 SB9 SB20 Figure 2.5 Thermocouple setting for the test section (after the venturi was installed) 17 3. MEASUREMENTS OF CONSTANT PRESSURE HEAT CAPACITY AND HEAT TRANSFER COEFFICIENT FOR WATER-OXYGEN MIXTURE: 3.1 Constant heat capacity measurement For a given system pressure, measurements were done by slowly increasing the temperature of the system. The power supplied to the working fluid was calculated using a heat loss model (Appendix A) . Power supplied to the fluid was calibrated in pure-water (known Cp) measurements at temperature far from T c . In order to quantify the small transient thermal effect and non-constant heat losses, a 1-D transient thermal model was developed (Appendix A) . This model was used to correct the supplied power for all experiments. The difference between the correct supplied power and the adiabatic case was 20%, which represents total heat loss. The transient effect is only 20% o f the total heat loss. Heat capacity was calculated as: Cp = Qflm(Tbout-Thin) (7) where Qf is the power supplied to the working fluid, Tou( is the temperature at the test section outlet and Tin is the temperature at the test section inlet. The mean value o f inlet and outlet temperature was used as the nominal temperature for reporting Cp values. Figure 3.1 gives the comparison between the measurements, exact values from IAPWS-95 (International Association o f Properties o f Water and Steam) and values from 18 I A P W S - 95 averaged over the AT of the test section for the actual experiments for pure water at 24.4 M P a . From the location o f the peak in Cp, it appears that the measured temperature is 2 degrees too high. A discrepancy of 2°C appeared, which could be related to errors in the thermocouple readings (the thermocouples were not calibrated at high temperature and all other tests done on this facility gave a similar offset). 3.2 Heat transfer coefficient measurement As written before, the thermocouples are welded to the outer surface of the tube. Technically it is very difficult to measure the inner wall temperature in a small bore tube without violating the f low pattern. Thus the inside wall temperature was calculated from measured outside temperatures. The differential equation for the temperature distribution is given by: where r is distance measured from the center o f the tube, k is the thermal conductivity o f the tube wall (Al loy 625) and assumed to be constant across the tube, Rt is the inside tube radius, Ro is the outside tube radius and q is heat flux. The boundary conditions at the outer tube surface (r = Ro) are: T=T0 (9) dT/dr = - qioSJk The solution of the equation for the temperature distribution across the wall to get the inside wall temperature Th at r = R, is: qA(R2 - R2) R (qRA \ s T i = T ' + 4k +~tl 2 - ^ J ( l n ^ -lnJ0 (10) This correction results in heat transfer coefficients about 10% higher than those based on the raw outside temperature. To calculate the local heat transfer coefficient, the local bulk temperature needs to be known. The bulk temperature o f the fluid as a function o f the axial position, x, can be estimated from an energy balance Q =• mAi, where Ai = Cp(Tb(j+i) - Tbj), Cp is heat capacity for water-oxygen mixtures and Tbi and Tb(i+i) are bulk temperatures at axial position j and j+1 respectively, i is enthalpy. Those bulk temperatures are calculated as follows (assuming that the pressure drop along the test section is small and that the enthalpy of the fluid is only a function of the bulk temperature): Tb = ^ + Th (11) mCp "' where q L = Q/L Qf- heat power supplied to water-oxygen mixtures, k W L - test section length, m 20 m - f low rate, kg/s Cp - heat capacity, kJ /kgK Ax - axial distance between thermocouples, m Knowing the inside wall and bulk temperatures, the local heat transfer coefficient can be obtained by: h=, V x (12) where: q = Q/A and Qf- heat power supplied to water-oxygen mixture, k W A - area, m 2 Tw - inlet wal l temperature, K Tb - bulk temperature, K Heat loss model The heat power supplied to the working fluid is primarily a function of applied voltage, but also depends on steady and transient heat losses to the tubing, fitting, insulation, and surroundings. Appendix A describes the methods used to determine these heat losses. The first component of the thermal model is a one-dimensional transient heat loss model, which uses measured tube wall temperatures as a boundary condition. This model is shown to reproduce transient heat fluxes quite well. 21 The second component is a model to predict the electrical power dissipated in the tube and transferred to the flow and the losses mentioned above. Finally, a method for using these models in the heat capacity measurements is described. Details of the model are given in Appendix A . 3.3 Data processing A MatLab program (heatdata.m) was developed for the data processing. The outline of the program is given in Appendix F. Raw data are used as input in the program. The program consists o f filtering data (running median calculation), heat loss, heat capacity, electrical power and heat transfer coefficient calculations. For all runs, the number o f 5 seconds measurements averaged was nav = 20. Final results are heat capacity and heat transfer coefficient data, which can be, used for graphical presentation either using a MatLab program or any other program. 3.4 Evaluation of the error of the measurements The major errors for the heat capacity and heat transfer coefficient measurements are the errors in the oxygen flow rate measurements and the temperature measurements. The estimated error for the transmitter is 16% and for thermocouple (AT) is 20%. The estimated error for heat flux is 4%. Since heat capacity is function of flow rate, heat flux and temperature, the total error of heat capacity measurements is obtained by differentially Eq . 7: 22 wc = sc cm \ 2 s c ^ 1 f SAT) + w, SCp^ V u SQ (13) where: wcp - error for heat capacity measutrement wm - error for oxygen mass flow rate measurement wT - error for temperature measurement WQ - error for heat flux measurement The estimated error for heat capacity measurement is 26%. Heat capacity error for pure water far from the critical point is less than 4% (Figure 3.1). The heat transfer coefficient measurement error is estimated using the same expression considering that the heat transfer coefficient is function of heat capacity, bulk temperature and oxygen flow rate. ch cm ch ~c7T + ch (14) The estimated error for the heat transfer coefficient is 36 % 23 x10 Figure 3.1 Heat capacity for pure water, Run #11 (P = 24.4 MPa, m = 1.01 l/min, Q = 93 kW/m2) 0 — IAPWS95(averaged over delT) IAPWS95 (exact) O Run#11 300 320 340 360 380 400 420 tempertaure, °C 440 460 480 500 Student Version of MATLAB 4. RESULTS 4.1 Constant pressure heat capacity for water-oxygen mixtures Figure 4.1a shows measurements at system pressures of 24 M P a (Run#12) and 26MP (Run #15) with 2% oxygen by weight. The peaks are clearly smaller and appear at a lower temperature than for pure water (Run #11), but have the same trends as for pure water. Figure 4.2a gives the oxygen concentration effect on values and positions o f the peaks of heat capacity. It is clear that with an increase of the oxygen concentration, the peak value of heat capacity is lower and the position of the peak occurs at a lower temperature. Complete results, which include 3% and 8% of oxygen concentrations, are presented in Appendix E l . 4.2 Heat transfer coefficient to supercritical water-oxygen mixtures Figures 4.1b,c show measurements of the heat transfer coefficient at system pressures o f 24 (Run #12) and 26 (Run #15) M P a with a 2% oxygen weight concentration. Figures 4.2b,c give the oxygen concentration effect on the values and positions o f the peaks in the heat transfer coefficient. It is clear that with an increase in the oxygen concentration, the peak values of the heat transfer coefficient are lower and the positions of the peaks are occurring at lower temperatures. The effect of heat flux on heat transfer coefficient was also explored. With an increase of heat flux, the peak of heat transfer coefficient is lower, but it is not dramatically lower as it is for pure water 25 (Figs. 4.3a,b). Figures 4.4a,b show the flow rate effect on the heat transfer coefficient. With an increase in flow rate the heat transfer coefficient peak is higher. For all cases heat transfer coefficient is higher for the top surfaces than for bottom surfaces (Figures 4.1b,c, 4.2b,c, 4.3a,b, 4.4a,b). These plots also include predictions of heat transfer coefficient for pure water. The heat transfer coefficient was calculated using Swenson et al. correlation (Eq. 2) for Nusselt number for supercritical water. In each case, the correlation was evaluated at the same values of the reported pressures, flows, and heat fluxes. The mass flow used in the correlation was the water f low without oxygen flow. It can be seen that in all cases Swenson correlation over predicts the heat transfer coefficient. Figure 4.5 shows a difference between temperature at the peaks of heat capacity for water-oxygen mixtures and for pure water as a function o f oxygen concentrations. Figure 4.6 shows a ratio between heat capacity for water-oxygen mixtures and for pure water as a function o f oxygen concentrations. Table 4.1 summary results for the Run #11 to # 34. A n average heat transfer coefficient was calculated based on a Cp weighted average +/- 15 °C of the temperature at Cp peak. 26 CD CO CO CO i n CO 1^ 00 oo CO CM 00 CD CO Lri CM CO CO o CO co o co CD CM CO CD CM CM CO CM O Q. CD CN CO CO o oo CO CU X CM CD ^ ° -3 o co co a . co £ 5 co r--,CD CO CO CD CD co m CO o CO o 1^ co CD , CO 0) CO — g a . co ® ro " | co co co CD co co co oo CO CO CO M l 1^ -co CM o CD co 0 o o CM CO CN CD oo iri co CO oo CD 1^ OO I J c 5 - -m o CD CO co co co o CM CO § CD 9= CO i m iri CM CM CM i n CM CM I iri CM CM CM CO oo CO CM CM CO CM CO CO 27 4.5, x 10 Figure 4.1a Heat capacity for Run #11 (P = 24.4 MPa, m = 1.01 l/min, Q = 93 kW/m ), Run #12 (P = 24.5 MPa, m = 1.01 l/min, Q = 97 kW/m 2, 02 = 2%), Run #15(P = 26.4 MPa, m = 1.01 l/min, Q = 95 kW/m 2, 02 = 2.1%) T 3.5 Run#12 Run#15 Run#11 12.51 o ro o. ro o •*-» ro <D x : 1.5 0.5 0 ' 150 200 250 300 350 temperature, °C 400 450 Student Version ofMATLAB 2$ 2.2 Figure 4.1 b Heat transfer coefficient (bottom) Run #12 (P=24.5 MPa, m=1.01 l/min, 0=97 kW/m 2 , 02=2%), x 1 0 Run #15 (P=26.4 MPa, m=1.01 |/min, Q=95 kW/m 2 , 02=2.1%) Run#12 Run#15 Swenson correlation - 24.5MPa, 96kW/m 2 ,1.01 l/min Swenson correlation - 26.4 MPa, 96kW/m 2 ,1 .01 l/min 1.8 1.6 C N E •*11.4| *-» c CD o o as co 0.8 0.6 0.4 1 280 300 320 340 360 380 400 420 temperature, ° C Student Version ofMATLAB 29 x10 Figure 4.1c Heat transfer coefficient (top) for Run #12 (P=24.5 MPa, m=1.01 l/min, Q=97 kW/m 2 , 02=2%), Run #15 (P=26.4 MPa, m=1.01 l/min, Q=95 kW/m 2 , 02=2.1%) 2 2 1 Kun#12 Run#15 _ Swenson correlation - 24.5MPa, 96kW/m 2,1.01 l/min Swenson correlation - 26.4 MPa, 96kW/m 2 1.01 l/min 1.8 1.6 E 1.4 c CD O u c C0 CO CD 0.8 0.6 0.41 _L 280 300 320 340 360 380 temperature, °C 400 420 440 Student Version of MATLAB 3 0 4.5 r x10 Figure 4.2a Heat capacity for Run #11 (P=24.2MPa, m=1.01 l/min, 0=93 kW/m 2 , 02=0), Run #12 (P=24.5 MPa, m=1.01 l/min, Q=97 kW/m 2 , 02=2%), Run #13 (P=24.2 MPa, m=1.01 l/min, Q=96 kW/m 2 , 02=4.9%) Run#11 Run#12 Run#13 3.5 h 1*2.51 o CO Q -co o "ro 2 | CD 1.5 0.5 150 200 250 300 temperature, °C 350 400 450 Student Version ofMATLAB 5 1 Figure 4.2b Heat transfer coefficient (bottom) for Run #11 (P=24.2 MPa, m=1.01 l/min, 0=93 kW/m 2, 02=0), Run #12 (P=24.5 MPa, m=1.01 l/min, Q=97 kW/m 2, 02=2%), x1Q Run #13 (P=24.2 MPa, m=1.01 l/min, Q=96 kW/m 2, 02=4.9%) | _ K u n # l J ' 1 ^ Run#12 Run#13 i| Swenson correlation - I • 24.5MPa,96 kW/m 2,1.01 l/min ; | 0 4 ' 1 1 I I J 150 200 250 300 350 400 450 temperature, °C Student Version of MATLAB 1S>Z 2.2, x10 Figure 4.2c Heat transfer coefficient (top) for, Run #11 (P=24.2 MPa, m=1.01 l/min, Q=93 kW/m 2, O2=0), Run #12 (P=24.5 MPa, m=1.01 l/min, Q=97 kW/m 2, 02=2%), Run #13 (P=24.2 MPa, m=1.01 l/min, Q=96 kW/m 2, 02=4.9%) — . . i — 1 r 1.8 1.6 ~ 1.4 +-* c o 'o !E a> o o L 1 1.21 (0 CO cu J Z 0.8 Run#11 Run#12 Run#13 Swenson correlation -24.5MPa,96 kW/m 2,1.01 l/min 0.6 0.4' 150 200 250 300 350 temperature, °C 400 450 Student Version ofMATLAB *>2> 3.5 r x10 Figure 4.3a Heat transfer coefficient (bottom) for Run #31 (P=25.3 MPa, m=1.01 l/min, 0=98 kW/m 2, 02=7.9%), Run #32 (P=25.2 MPa, m=1.01 l/min, Q=160kW7m2 02=8%), Run #33 (P=^5 3 MPa, m=1 0 1 l/min, p=37 kW/m 2 Q?=7 fi%) Kun#31 Run#32 Run#33 Swenson correlation ,2 1.01 l/min 25.3MPa,98 kW/m Swenson correlation -25.3 MPa, 160 kW/m2,1.01 l/min Swenson correlation -25.3 MPa, 37 kW/m2,1.01 l/min 2.5 1.5 0.5 " X -330 340 350 360 370 380 390 400 410 temperature, C Student Version of MATLAB =>4 Figure 4.3b Heat transfer coefficient (top) for Run #31 (P=25.3 MPa, m=1.01 l/min, 0=98 kW/m 2 02=7.9%), 10 Run #32 (P=25.2 MPa, m=1.01 l/min, Q=160 kW/m 2, 02=8%), I I Run #33 (H=2S.3 MHa, m=1.01 l/min, 0=3/ kW/m 2, 02=/.6%) I Run#31 Run#32 Run#33 j •_ Swenson correlation - ,\ 25.3MPa,98 kW/m2,1.01 l/min | \ Swenson correlation - ' I ^  ' 25.3 MPa, 160 kW/m2,1.01 l/min I ^ Swenson correlation - ' I 25.3 MPa, 37 kW/m2,1.01 l/min J | 340 350 360 370 380 390 400 410 420 temperature, °C Student Version ofMATLAB 35* Figure 4.4a Heat transfer coefficient (bottom) for Run #29 (P=25.1 MPa, m=1.27 l/min, 0=96 kW/m 2 02=3%), 1 0 Run #30 (P=25.2 MPa, m=1.01 l/min, Q=95 kW/m 2 , 02=3%) 3 | Kun#29 ' " I ' ' : r r " Run#30 Swenson correlation -25.2MPa,96 kW/m 2,1.01 l/min Swenson correlation - \ . 25.2 MPa, 96 kW/m 2 ,1.27 l/min j 2 h • 5 h 1 h •5h 300 320 340 360 380 400 420 440 460 temperature, ° C Student Version of MATLAB 2>6 x10 Figure 4.4b Heat transfer coefficient (top) for Run #29 (P=25.1 MPa, m=1.27 l/min, 0=96 kW/m 2, 02=3%), Run #30 (P=25.2 MPa, m=1.01 l/min, 0=95 kW/m 2 Q2=3%) Ruh#29 Run#30 Swenson correlation -25.2MPa,96 kW/m2,1.01 l/min Swenson correlation -25.2 MPa, 96 kW/m2,1.27 l/min 0 l 280 _L 300 320 340 360 380 temperature, °C 400 420 440 460 Student Version ofMATLAB 5>7 Figure 4.5 (Tpwo - Tpw) vs oxygen% Student Version of MATLAB 2>S 0.65 Figure 4.6 (Cpwo(P)/Cpw(P))max vs oxygen% 4 5 oxygen% Student Version ofMATLAB 5. C O N C L U S I O N S The constant-pressure heat capacity, Cp, and local forced convection heat transfer coefficient, h, for supercritical water-oxygen mixtures flowing inside horizontal smooth tubes were obtained experimentally. Data were obtained for pressures of 24 and 25 M P a ; flow rates o f 0.636 and 1.27 1/min, heat fluxes of 34 to 160 k W / m 2 and temperatures from 330 to 430 °C. Oxygen f low was 2 to 8 weight percentage of the total mixture flow. For a given f low and supplied heat to the mixture, Cp was determined from the bulk temperature in a heated tube. The heat transfer coefficient, h was determined from the difference in bulk and wall temperatures. Based on the measurement data it can be concluded: 1. A s oxygen concentration increases heat capacity as well as heat transfer coefficient has a maximum at a lower bulk temperature 2. Introducing more oxygen reduces the magnitude of the heat capacity as well as for the heat transfer coefficient. 3. Wi th increasing the pressure the maximum in the heat capacity and heat transfer coefficient are reduced and occur at higher temperatures. 4. The enhancement near the critical point appears to be less at high heat flux. 5. To develop any Nusselt number correlations, more accurate density measurements and an equation of state which would be suitable for thermodynamic and transport properties is needed. 40 6. R E C O M M E N D A T I O N S The U B C / N O R A M SCWO facility is capable of measuring the constant pressure heat capacity and heat transfer coefficient near the critical point for water-oxygen mixtures. However, during the course of this study it was shown that many improvements could be made to increase the accuracy of measurements. Accuracy of the thermocouples should be checked for high temperature. Accurate values of density are needed for the Nusselt number correlation. The question of thermal conductivity and viscosity values for water-oxygen mixtures is open. Either a good measurement system or a suitable equation of state which will be able to predict those values with acceptable accuracy is needed. 41 REFERENCES Bazargan, M . , "Forced Convection Heat Transfer to Turbulent F low of Supercritical Water in a Round Horizontal Tube", Ph.D. Thesis, U B C , September 2001. Bourke, P.J., Pull ing, D.J., G i l l , L E . and Denton, W.H . , "Forced Convective Heat Transfer to Turbulent CO2 in Supercritical Region", Int. J. Heat Mass Transfer, Vo l 13, pp. 1339-1348, 1970. Christoforakos, M . and Franck, E .U . , " A n Equation of State for Binary F lu id Mixtures to High Temperatures an High Pressure", Ber. Bunsenges Phys. Chem. V o l 90, pp. 780-788, • 1986. Croft, D.R and Li l ley, D.G. , Heat Transfer Calculations Using Finite Difference Equations, Applied Science Publishers, New York, 1977 . Dusinberre, M .G . , Heat-Transfer Calculations by Finite Differences, The Haddon Craftsmen Inc., New York, 1961. Gairns, S. and Rogak, S., " U B C S C W O System Calibration Report", U B C Report, Feb. 16, 1999. Hagen, D. K., Heat Transfer with Applications, Prentice-Hall Inc, London, 1999. 42 Hal l , W .B . , "Heat Transfer Near the Critical Point" in Advances in Heat Transfer, T.F. Irvine, Jr. and J.P. Hartnett, Eds. Academia Press, 1971. Jackson, J.D. and Hal l , W . B , "Forced Convection Heat Transfer to Fluids at Supercritical Pressure", Turbulent Forced Convection in Channel and Bundles , V o l 2, pp. 563 - 599, Hemisphere, New York, 1979. Japas, M . L. and Franck, E .U . , "H igh Pressure Equil ibria and PVT-Data of the Water-Oxygen System Including Water-Air to 673 K and 250 M P a " Ber. Bunsenges Phys. Chem. Vo l . 89, pp. 1286-1274, Munich, 1985. Kakac, S and Yaman, Y., Heat Conduction , Hemisphere Publishing Corporation, New York, 1985. Kakac, S., "The Effect o f Temperature-Dependent Fluid Properties on Convective Heat Transfer", in Handbook of Single Phase Convective Heat Transfer, S. Kakac, R.K. Shah and W. Aung eds., 1987. Knapp, K . K . and Saberesky, R.H. , "Free Convection Heat Transfer to Carbon Dioxide Near the Critical Point", Int. J. Heat Mass Transfer, Vo l . 9, pp. 41-51, New York, 1966. Kondratev, N.S., "Heat Transfer and Hydraulic Resistance with Supercritical Water Flowing in Tubes", Teploenergetika, Vo l . 16, No . 8, pp. 116-119, Moscow, 1967. 43 McCormick, M.J. and Salvadori, M . G . M . , Numerical Methods in Fortran, Prentice-Hall Inc., London, 1964. Miropolski, L. and Shitsman, M.E. , "Heat Transfer to Water and Steam at Variable Specific Heat (in Near-Critical Region), Soviet Physics, Vol 27, No. 10, pp. 2359 - 2372, Moscow, 1957. Oh, C.H., Kochan, R.J. and Beller, J.M., "Numerical Analysis and Data Comparison of a Supercritical Water Oxidation Reactor", J. AIChE, Vol. 43, pp. 1672-1636, New York, 1997. Oka, Y. , Koshizuka, S. Jevremovic, T. and Okano, Y , "System Design of Direct-Cycle Supercritical Water Cooled Fast Reactors", Nuclear Technology, Vol. 109, pp. 1-10, Jan. 1995. Petukhov, B.S., Polyakov, A.F., Kuleshohov, V .A . and Sheckter, Y . L . , "Turbulent Flow and Heat Transfer in Horizontal Tubes with Substantial Influence of Thermo-Gravitational Forces", in Proc. 5th Int. Heat Transfer Conf, Tokyo, Paper No. NC4.8. A.S.M.E. , 1974. 44 Pitla, S.S., Robinson, D .M. , Groll, E.A. and Ramadhyani, S., "Heat Transfer from Supercritical Carbon Dioxide in Tube Flow: A Critical Review", HVAC&R Research, Vol 4 No. 3,pp281, 1898. Polyakov, A.F., "Heat Transfer under Supercritical pressures", Advances in Heat Transfer, Vol 21, pp. 2-51, 1991. Robert R.C., Prausnitz J. M . and Poling E. B., The Properties of Gases and Liquids, McGraw-Hill, Inc., New York, 1980. Rogak, S.N. and Teshima, P., "Deposition of Sodium Sulfate in Heated Flow of Supercritical Water", AlChe Journal, Vol 45, No. 2, February 1999. Rogak, S., "Measurements of the Constant-Pressure Heat Capacity of Water-Oxygen Mixtures at Near-Critical Conditions" , Proc. Of the 13th International Conference on the Properties of Water and Steam, P R Tremaine, P.G. Hill , D E . Irish and P.V. Balakrishnan, Eds. NRC Research Press, 149-156, 2000. Sabaresky, R.H. and Hauptmann, E.G., "Forced Convection Heat Transfer to Carbon Dioxide Near the Critical Point", Int. J. Heat Mass Transfer, Vol. 10, pp. 1499-1508, 1967. 45 Saur, A M . , Behrendt, F. and Franck, E. TJ., "Calculation of High Pressure Counterflow Diffusion Flames up to 3000 bar", Ber. Bunsenges Phys. Chem., Vol. 97, pp. 900-908, 1993. Shaw, R.W., Brill , T.B., Clifford, A .A. , Eckert, C A . and Franck, E.U, , "Supercritical Water, A Medium for Chemistry" ,C&ENpp. 26-39, December 1991. Swenson, H.S., Carver, JR . and Kakarla, C.R., "Heat Transfer to Supercritical Water in Smooth-Bore Tubes", J. Heat Transfer, pp. 477-484, Nov. 1965. Teshima P., "Fouling Rates from a Sodium Sulphate - Water Solution in Supercritical Water Oxidation Reactors", M.Sc. Thesis, UBC, October 1997. Van Wylen, G., Sonntag, R. and Borgnakke, C , Fundamentals of Classical Thermodynamics, John Wiley & Sons, New York, 1994. Vargaftik, N.B. , Tables on The Thermophysical Properties of Liquids and Gases, Hemisphere Publishing Corporation, Washington, 1975. Wang, S., "Properties of Supercritical Water-Oxygen Mixtures", M.Sc. Thesis, U B C , September 2001. 46 Yamagata, K, Nishikawa, K. , Hasegawa, S., Fyjii, T. and Yoshida, T., "Forced Convective Heat Transfer to Supercritical Water Flowing in Tubes", Int. J. Heat Mass Transfer, Vol. 15, pp. 2575-2593, 1972. 47 APPENDIX A Test Section 1-D Transient Heat Loss Model in Cylindrical Polar Coordinates Introduction The constant pressure heat capacity of a fluid (C p) can be measured in a flow system, knowing the applied heat flux (q), the mass flux (m), and the bulk temperature difference (ATb) of the flow. C = — — (Al ) " mATb The heat flux is primarily a function of applied voltage, but also depends on steady and transient heat losses to the tubing, fittings, insulation and surroundings. This Appendix describes the methods used to determine these heat losses. The first component of the thermal model is a one-dimensional transient heat loss model, which uses measured tube wall temperatures as a boundary condition. This model is shown to reproduce transient heat fluxes quite well. The second component is a model to predict the electrical power dissipated in the tube and transferred to the flow and the losses mentioned above. Finally, a method for using these models in the heat capacity measurements is described. 48 Heat Loss Model The heat losses were calculated applying an unsteady, one-dimensional, heat transfer model. Treating the heat transfer as one-dimensional is reasonable because of the nature of the heat penetration into the insulation and the ratio of the test section and the insulation dimensions. As mentioned above the configuration of the test section and the insulation around it was considered as a 1-D cylindrical polar coordinate problem (shown in Fig. A l b ) in which the heat transfer in the z and 0 direction are insignificant. The insulation width W is 0.07125 m and the tube diameter rin is 0.00475 m. The first law of thermodynamics was applied to control volumes 1 (the insulation) and 2 (the test section pipe and fittings). For control volume 1, Where: dECvi /dt - derivative of energy for the insulation, kJ/s Cp - insulation constant pressure heat capacity, kJ/kgK p - insulation density, kg/m3 V- insulation volume, m 3 qin - inlet heat flux, kJV m 2 49 qout - outlet heat flux, kJV m 2 Ain - insulation inlet area m Aout - insulation outlet area m 2 For control volume 2 for the test section without electrical heating, ^df = $ l t ' p C ' d f r = ~Ai"qi" +mC'»iT»<" ~T»°J ( A 3 ) Where: dEcv2 /dt -derivative of energy for the test section, the fittings and the working fluid, kJ/s Cp - test section, the fittings and working fluid constant pressure heat capacity, kJ/kgK Ain - test section outlet area which is equal to the insulation inlet area, m 2 qin - outlet heat flux which is equal to inlet flux for the insulation, kJ/ m 2 m - working fluid mass flux, kg/s Cpw - working fluid constant pressure heat capacity, kJ/kgK Tun - inlet bulk temperature, °C Tout - outlet bulk temperature, °C From the Eq. A3 the heat losses are calculated as: mCpw{Tbin -Tboul) = Qlosses = $-rCpdV + Ainqin (A4) v2 a t 50 The second part on the right side of the Eq. A3 was evaluated using the experimental data for the input and the output bulk temperature. Assuming that Cp and p for the test section are constant, the integral on the right side of the Eq. A4 is written: The last term in Eq. A5 is neglected in the model, because the mass of the tube is much greater than the mass of the water. C p w from Equation A4 was calculated for a pressure of 25 MPa using the Steam Tables (Van Wylen et al, 1994). Evaluation of q™ in equations (A2) and (A3) require a transient thermal analyses of the insulation. The energy balance for the small control volume (control cell) ( Figure A2.) was obtained by Eq.A2. The relevant partial differential equation for the 1-D Transient heat transfer is: c^T 1 dT a k {a2 r at) = pCp (A6) 51 The appropriate finite differential equation for the computing cell shown on Figure A2 is T2-2Tl+Tw^l(T2-Tw)' (Ar) 2 r 2Ar pCp At (A7) for node 1, and similar expressions for each of the other nodes, except the last node and the node 0. The space step was chosen very small (0.0032m). The last node is obtained by applying the convective boundary condition. In terms of the Fourier number Fo, where Fo = a At k At (Ar) 2 pCp{Arf equation (A7) becomes T, = Fo 1-Ar 2(>-o W 1 + Ar 2(r 0+/Ar), (A8) Over a small time interval At, the energy balance method gives the following equation for the boundary node : (A9) 52 where n is the number of nodes. Eq. A9 can be rearranged and expressed in the explicit form T=Fo T_,+BiTa)+Tm[—-Bi-l (A10) where Fo kist pCp(Ar) and hAr For stability there is a restriction on the value of Fo and from Eqs. (A8) and (A10) the criteria are (Croft et al, 1977): — - - 4 > 0 Fo Fo < 0.5 (interior nodes) ( A l l ) 1 —--1-Bi>0 Fo j (boundary nodes) Fo< 2(1 +Bi) Ambient temperature was 20 °C and the heat transfer coefficient for the surrounding air was assumed to be 7 W/m 2K. The left boundary condition was wall 53 temperature, which was measured. The heat losses were calculated for a 3.00 m long test section. Figure A3 shows the heat loss as a function of the different time steps and the same thermal conductivity coefficient 0.35 W/mK, density 480 kg/m 3 , specific heat 710 J/kgK and radial step 0.0032 m. The losses are almost independent of the time step. The heat losses predicted by the model have the same trend as has the experimental ones (Figures A6, A7 and A8). Figure A4 shows the heat losses for two different insulation densities (480 and 600 kg/m3) and thermal conductivity coefficient 0.5 W/mK. With increasing density, the heat losses increased. Figure A5 shows the effect of different assumed values of insulation thermal conductivity. It is clear that heat losses increased with an increase in the thermal conductivity. The model with thermal conductivity 0.35 W/mK predicts the heat losses fairly well (Fig.A6). The presented experimental data are for the slow heating case with average heating rate of about 0.3 °C/s and a flow rate 0.636 kg/min. The agreement between model and experiment is acceptable in the temperature range below the critical temperature. When T<Tc the difference is about 0.3 kW. An experiment was done also for the cooling case with an average cooling rate of 0.23 °C/s and a flow rate 0.636 kg/min and with cooling rate 0.25 °C/s and flow rate 1.269 kg/min. Figures A7 and A8 present the model prediction and the experimental values. The agreement is acceptable for all of the temperature range including the critical temperature. 54 Electrical Power Dissipation Model The heat flux supplied to the working fluid was calculated by subtracting heat losses from the power supplied to the test section. The power supplied to the test section was calculated using the data from the calibration test (UBC SCWO System Calibration Review, pp 14) and resistivity as a function of wall temperature. Figure A9 shows the resistivity as function of wall temperatures. Figure A10 shows the correlation between the SCR voltages and R.M.S. voltages. The correlations for the resistivity and voltages are: Power was calculated from: QeUc=V2IR R = pl/A where R is resistivity in ohms and A is area: ^ = ^ (^ 2-i?/) = 3.14(0.00482 - 0.0G31372) = 41.486 mm 2 /= 1.473 m Where Ro and Rt are the outside and the inside tube radius respectively. ; O = (l0-9rw3 -KTX 2 +0.00047; + I .288) *10~6, ohms*m (A12) RMS voltage = 0.0491CRvoltage-1.2564, volt (A13) 55 The heat supplied to the working fluid was obtained from: Qf = Qelec - Qlosses (A15) The Evaluation of the Power Dissipation Model: Pure water measurements were used to evaluate the power dissipation model. Heat flux supplied to the working fluid was calculated using: Qf=mCp(Tb0UrTbir) (A 16) For the constant pressure heat capacity values from the steam tables were used (Van Wylen et al., 1994). Figure A l 1 shows the heat supplied to the first part of the test section for the measurements and for the model. The predictions of the model are acceptable. This model was used to predict the heat supplied to the working fluid in the case when the working fluid was a water-oxygen mixture. Figure A12 shows Cp as a function of temperature. The experiment was done for a 2% 02 weight concentration, water flow rate = lkg/min and pressure = 25 MPa (Run#17). Cp was calculated in two different ^ways: • applying the present model and • assuming constant heat flux 56 The constant heat flux assumption is acceptable. This agreement occurred when the heating rate was about 0.1 °C/s. Figure A13 shows Cp for 5% O 2 by weight, water flow rate =1 kg/min and pressure = 23.9 MPa (Run #13). The heating rate was the same as in the previous case 0.1 °C/s. The constant heat flux assumption is acceptable for heating rate in the range 0.1 - 0.3 °C/s. This conclusion was used for the heating strategy in the experiments. Electric power has to be corrected by a factor F. Factor F was found from a low temperature, low flow rate test for pure water. Under these conditions the temperature difference is large, losses are low and the heat capacity is well known. V2 mCpAT = F — mCpATR Table A l shows values for the coefficient F for Runs 36, 37 and 38. For the calculations F equals 0.789 was used. Temperature does not have significant effect on the coefficient F (Figure A14 and A 15). Table A l . Value of coefficient F for Runs 36,37 and 38 Run# mass flow, l/min Heat flux, V bulk temperature interval, C average coefficient F = mCpAT/(VA2/R(T)) TS1 TS2 TS2 TS1 36 1.068 300 162-165 180-183 0.845 0.799 37 1.068 300 185-208 227-246 0.795 0.764 38 1.068 300 223-301 253-331 0.785 0.742 Average value 0.81 0.768 57 58 Figure A2. Computing cell 2000 1500 -K IA o jg 1000 ro 500 • time step ° time step _ »time step =0.05s =5s =0.5 8 ft % f « % ft ft « < S ft 1 1 ¥ ft 100 200 300 temperature, C 400 500 Figure A3. Heat losses as a function of time step for assumed insulation density of 480 kg/m3, conductivity 0.35 W/m, Run #19 2500 100 200 300 temperature, C 400 500 Figure A4. Heat losses as a function of density for assumed insulation conductivity 0.5 W/mK,Run#19 60 0 -I 1 : 1 1 1 1 0 100 200 300 400 500 temperature, C Figure A5. Heat losses as a function of thermal conductivity for assumed density 480 kg/m3, Run #19 Figure A6. Heat losses as a function of a wall temperature, Run #19 61 1500 1000 500 in in o ^ - i ro cu sz -500 -1000 -1500 20D0 time, s Figure A7. Heat losses for assumed insulation density 480 kg/m and conductivity 0.35 W/mK and for the experiment with flow rate 0.636 kg/min, Run #21 1500 1000 500 in 0 cu in in O 13 -500 co .c -1000 -1500 -2000 5D0 time, s Figure A8. Heat losses for assumed insulation density 480 kg/m3 and conductivity 0.35 W/mK and for the experiment with flow rate 1.296 kg/min, Run #21 62 E JC o to < © > W '55 £ Ii u u 0) 1.39 1.38 1.37 1.36 1.35 1.34 1.33 1.32 1.31 resistivity = 1 E-09Tw3 -1 E-OOTw2 + 0.0004Tw + 1.288 100 200 300 400 wall temperature Tw, C 500 600 Figure A9. Resistivity as a function of the wall temperature 63 Figure A l 1. Heat supplied to the working fluid for the model and the experiment, Run #19 (P. = 24.5 MPa, m = 0.636 1/min) 50 45 40 2 30 i " 25 cs a g 20 to I 15 10 5 I o model | • adic abatic %:° 300 320 340 360 380 temperature, C 400 420 Figure A12. Heat capacity for water-oxygen mixture - Run #17 (P = 25.4 MPa, m = 1. 1/min, Q = 95 kW/m 2 , 02 = 4%) 80 320 340 360 380 400 temperature, C Figure A13. Heat capacity for water-oxygen mixture -Run #13 ( P =24.2 MPa, m = 1.01 1/min, Q = 96 kW/m 2, 02 = 4.9%) sr o.8 < a. 0.6 Q. o E 0.4 c a> o « 0.2 o u 100 150 200 250 average bulk temperature, C 300 350 Figure A14 Coefficient F as a function of bulk temperature for part 1 of test section and Run # 36 - 38 65 1 o « Figure A14 Coefficient F as a function of bulk temperature for part 2 of test section and Run #36-38 66 APPENDIX B Thermodynamic and transport properties A complete set of thermodynamic properties for supercritical water-oxygen mixtures is not available in the literature. From data provided by Christoforakos and Franck (1986), phase equilibria were calculated and P-V-T-x relations for water-oxygen developed. They developed an Equation of State (EOS) for mixtures based on a Caranhan-Starling repulsive term with a temperature dependent sphere diameter (a) and square well potential as a basis for the attraction coefficient. RT Vl+V2mP{T,x)+VmP\T,x)-p\T,x) ART m m (Bl) with mixing rules: P(T,x)= Y^x^iT) (B2) fij(T)^TN0alj(T) (B3) where 0, e are temperature dependent parameters defined by: 67 P(T) = t3{TC)(TJT) J3(TC) = 0.04682 (B4) Pc Tc, pc are the critical temperature and pressure, k is the Boltzman constant. The parameter m can take values 9.5 or 10, while X depends on molecular polarity and, for example, for water it is 1.199. As a first aproximation £ and C, can be taken as equal to one. Christoforakos and Franck (1986) applied this equation of state to water-nitrogen, water-methane, water-xenon and water-carbon-dioxide mixtures. With this EOS density and mixture heat capacity were calculated (Saur et al, 1993). Viscosity and thermal conductivity were obtained as deviations from values for low density gases. Van der Waals "one fluid theory" was used for mixture rules. Expressions for viscosity and thermal conductivity with mixture rules are as follow: If a gas consists of polyatomic molecules, the "monatomic" part has to be separated to calculate the high-density collision contribution to the thermal conductivity. n is the density N/V. The hard sphere equation of Caranhan-Starling was used to defined - 1 +—rnicT3z + 0.76l((2/3)7ma3zy K+k(^ma3% + 0.757((2/3)micr3%y (BS) 68 the x, where n is the density (number of mols per cubic meter) and o is the sphere diameter: X = (B6) The mixing rules are defined by combination of the parameters of the pure components according to their relative mole fractions: Wang (2001) in her thesis applied the Redlich-Kwong-Soave equation of state (RKS EOS). This equation was improved for both liquids and gases, polar and non-polar compounds. where: P- pressure, Pa T- temperature, K v - specific volume, mVkg (B7) J 69 a - coefficient depends on the attractive force between molecules b - coefficient depends on the repulsive force between molecules Coefficients a and b are given by: where: TC - critical temperature, K Pc - critical pressure, Pa TR -reduced temperature 77 TC Function/is given with: b = 0.08664 RTC where: The coefficients Cj, C2 and C3 are given below (Dahl et al, 1991): For water, Cj= 1.0873, C2 = -0.6377 and C3 = 0.6345 For oxygen, Ci= 0.8252, C2 = 0.2515 and C3 = -0.7039. Wang (2001) calculated the phase boundary applying both equation of states and compared it with the experimental data from Christoforakos and Franck (1986) . The phase boundary predicted by RKS EOS and Hard Sphere EOS at 25 MPa agreed well with experimental data (Fig. B l ) . Heat capacity values calculated with the Hard Sphere EOS are higher than experimental data in the sub-critical region and lower in the supercritical region (Fig B2, B3). Better prediction is given by the RKS EOS (Fig. B4). To validate the equation of state specific volume experimental data was used, which were obtained, by using a venturi. Density is calculated applying only the RKS EOS. It has shown a significant difference in the subcritical and critical region. Better agreement was seen in the higher temperature region. Oh et al. (1997) calculated thermodynamic and transport properties for SCWO fluids (water, ethanol, isopropyl alcohol, nitrogen, oxygen and carbon dioxide). They applied the Redlich-Kwong cubic equation of state, which is recommended for highly nonideal systems at high pressures and temperatures. The mixture properties were computed based on mass fractions. These are ideal mixing assumptions and may not be strictly accurate at supercritical conditions. 71 RKSEOS Hard-Sphere EOS + Experimental • • • ; / V . XsA~ . • ^ * •• ^•f.., i^,,; „„- , . . , ,„• i • ••• •  500 S50 600 650 Tomporature (K) Figure B1. The boundary phase for water-oxygen mixtures at 25 MPa 0" — — 1 J—: 1 '~i —I.-600*-' 620 640 660 680 " " 700 ;Temporahjfo(K)i • • • Figure B2. Heat capacity for 2% oxygen at 26 MPa (Run #12) 72 80 "femperalure (K) Figure B3. Heat capacity for 5% oxygen at 24 MPa (Run #13) Figure B4. Heat capacity for 8% oxygen at 25 MPa (Run #31) APPENDIX C Oxygen flow calibrations A Foxboro E13DH-ISAM2 Transmitter was used for oxygen flow rate measurements. It contains a orifice (0.86 mm) and pressure differential measurement across the orifice. The output signal has a range 4 - 2 0 mA. Since the data acquisition system has a 0-10 V signal, a 500 Ohm resistor is used to get 2-10 V output from the transmitter. A 24 V power supplier was used to provide the power for the transmitter. A correlation between mass flow rate and output signal was obtained by applying Bernoulli's equation and a lineer correlation between pressure and output signal: m 2 P P kAP (CI) k\v-v0) where: V- voltage signal, V Vo - zero offget, V k,k'- coefficient m - mass flow rate, kg/h p- density, kg/m3 P - pressure, Pa The transmitter was calibrated at three different pressures 101.3 kPa, 22.06 MPa and 27.23 MPa. 74 At 101.3 kPa and 27.23 MPa, a bubble meter was used to measure the outlet flow rate. Nitrogen was used as the working fluid. Oxygen as the working fluid was used at 27.23MPa. At 22.06 MPa, the mass flow rate was measured by an Omega mass flow meter (range 0-5 V) and nitrogen was used as a working fluid. The calibration data are listed in Tables 1 to 3. At each pressure, the coefficient k was found. It changes from 0.0627 at 101.3 kPa to 0.047 at 22.06 MPa and to 0.048 at 327.23 MPa. The mass flow rate for 27.23 MPa is claculated by: (C2) where: m - mass flow rate, kg/h V- output voltages, V V0 - zero offset of the transmiter 75 Table CI Calibration data for oxygen flow rate at 101.3 kPa Output of the transmitter, V Bubble flow meter, 1/min Flow rate, kg/h v - v 0 m2/p 1.997 0.0 0.0 0.0 0.0 2.0584 0.8384 0.0780 0.0614 0.0039 2.1557 1.261 0.1172 0.1587 0.0089 2.2173 1.531 0.1424 0.2203 0.0131 2.2482 1.638 0.1523 0.2512 0.0150 2.3131 2.833 0.1705 0.3161 0.0187 2.4190 2.100 0.1953 0.4220 0.0246 2.5363 2.415 0.2246 0.5393 0.0325 2.7376 2.852 0.2652 0.7406 0.0454 2.8764 3.122 0.2903 0.8794 0.0544 3.0491 3.408 0.3169 1.0521 0.0648 3.2181 3.696 0.3437 1.2211 0.0762 3.6250 4.227 0.3931 1.6280 0.0997 3.9624 4.701 0.4372 1.9654 0.1233 4.3432 5.160 0.4799 2.3462 0.1486 ,4.9134 5.752 0.5349 2.9164 0.1846 5.0370 5.896 0.5483 3.0400 0.1940 76 Table C2 Calibration data for oxygen flow rate at 22.06 MPa Output of the transmitter, V Bubble flow meter, 1/min Flow rate, kg/h v - v 0 m2/p 2.0600 0.0 0.0 0.0 0.0 2.0756 0.203 0.5891 0.0156 0.0015 2.1277 0.310 0.8996 0.0677 0.0035 2.1827 0.409 1.1869 0.1227 0.0061 2.2660 0.512 1.4858 0.2060 0.0096 2.3122 0.602 1.747 0.2522 0.0132 2.3977 0.701 2.0343 0.3377 0.0179 2.5503 0.805 2.3361 0.4903 0.0236 2.6796 0.912 2.6466 0.6196 0.0303 2.7766 1.010 2.931 0.7166 0.0372 2.9467 1.117 3.2415 0.8867 0.0455 ^ 3.1009 1.215 3.5259 1.0409 0.0538 3.2585 1.297 3.7639 1.1985 0.0613 3.5547 • 1.454 4.2195 1.4947 0.0771 3.9368 1.589 4.6113 1.8768 0.0920 4.4958 1.795 5.2091 2.4358 0.1175 5.0186 1.972 5.7227 2.9586 0.1418 5.8211 2.214 6.425 3.7611 0.1787 6.5829 2.417 7.0141 4.5229 0.213 7.5668 2.695 7.8209 5.5068 0.2648 8.3414 2.823 8.1923 6.2184 0.2905 9.3874 . 3.038 8.8163 7.3274 0.3365 77 Table C3 Calibration data for oxygen flow rate at 27.23 MPa Output of the transmitter, V Bubble flow meter, 1/min Flow rate, kg/h V-Vo m2/p 1.9945 0.0 0.0 0 0 2.0035 6.203 0.4943 0.0009 0.0007 2.0213 8.902 0.7093 0.0268 0.0014 2.0494 12.40 0.9880 0.0549 0.0027 2.0753 14.84 1.1825 0.0808 0.0039 2.0822 15.28 1.2175 0.0877 0.0041 2.0912 15.99 1.2741 0.0967 0.0045 2.1093 16.99 1.3538 0.1148 0.0051 2.1315 18.21 1.4510 0.137 0.0058 2.1346 19.64 1.56498 0.1401 0.0068 2.1461 20.29 1.6167 0.1516 0.0072 2.1709 22.34 1.7801 0.1764 0.0088 2.1958 23.86 1.9012 0.2013 0.0100 2.2229 23.21 2.0087 0.2284 0.0129 2.2638 27.13 2.1617 0.2693 0.0175 78 25 i ^ », , 1 • > 1 8 1 9 2 2 1 2.2 2.3 2.4 3.5 Transmiter output, V Figure C I . Calibration data (kg/hour vs voltage) for oxygen flow rate transmitter •0.3 ' V-V.0 Figure C2. Oxygen flow rate (m2/p) versus output voltage reading ( V - V _ 0 ) 79 APPENDIX D Test summaries 1. Date: September 2, 1998 (Runs 1-6) Objectives: Water -oxygen and ethanol tests Operation: The first run was for pure water. At 12:44 pm., the water oxygen mixture was sampled from the intermediate sample point for 10 minutes. Ethanol was stopped in the period from 13:00 to 13:14, because the pump did not work properly. Observation and comments Surface temperatures for test section and reactors were around 10 °C lower than bulk temperatures. 2. Date: March 10, 1999 (Runs 7-10) Objectives: Pure water and water-oxygen heat capacity test Operation: Different heat fluxes applied to the test section. Observation and comments: Steam leaking was observed. Oxygen pressure was 19.3 MPa.. Booster was running 1 cycle/min. 80 3. Date: June 17, 1999 (Runs 11-16) Objectives: Water-oxygen heat capacity tests. 4. Date: December 8, 1999 (Runs 17-18) Objectives: Water-oxygen heat capacity tests. Operation: Heater voltage for the test section was 300 V. Heater voltage for the preheater 1 was 300V and for the preheater 2 was set on automatic control. Observation and comments: The test was interrupted by oxygen flow rate fluctuation. 5. Date: June 19, 2000 (Runs 19-22) Objectives: Heat losses test - pure water Operation: No heat flux applied to the test section Observation and comments: At 13:03, the surface temperature tripped the alarm. Pump speed was increased to cool down the system. 81 6. Date: May 24, 2001 (Run 23) Objectives: Pure water test for the venturi calibration at 25 MPa and 450 °C. Operation: The flow rate was initially set with the pump speed of 1600 rpm. Power supply to the preheater 2 was broken. Pump speed was reduced to 12000 rpm at 12:53. At 13:02, flow was reduced to 1000 rpm. The experiment was finished at 14:49. The system pressure was set at 27.5 MPa. Full power was supplied to the preheater 1, test section and the reactor. Observation and comments: The offset of the transducer for pressure drop across the venturi was different for low and high pressure. The fluctuation of the flow effected the pressure differential reading. Valve 9 was closed to reduce the fluctuation. The outlet temperature from the test section was lower then desired. Pump speed was decreased from 1200 rpm to 1000 rpm. 7. Date: June 5, 2001 (Runs 24-27) Objectives: Pure water and water-oxygen density and heat capacity test Operation: The pump was set at 800 rpm and 1600 rpm. The power applied on the test section was 300 V. The preheater 2 ternperature was ramped. 82 Observation and comments: File 1600wo.txt uses a constant test section voltage of 289 V. From 13:32:29 (logbook and file time), the pump ran at 1600 R P M . Power slowly decreased in Preheater 2 as the temperature dropped. At 14:05, near the temperature minimum, pump R P M changed to 800 R P M . At 15:00, the oxygen was turned off. The bypass valve of DPT 429 leaked. A thermocouple was attached at the surface of the pressure tap at the inlet of the venturi. It was observed that the temperature increased very slowly. The oxygen flow rates from gas flow meter were also recorded. The zero offset of the transmitter for oxygen flow rate changed from 2 V to 1.9033 V. 8. Date: June 20, 2001 (Run 28-35) Objectives: The test was performed to get heat capacity, heat transfer coefficient and density of pure water and water-oxygen mixtures at different pressures, flow rates and oxygen concentrations. Operation: In the test section, heat flux were kept constant for each run. Different heat (10.184, 6.122 and 2.315 kW) fluxes were applied to observe the heat transfer effect on the heat capacity for a water-oxygen mixture with 8% oxygen. The range of temperature was between 340 and 400 °C. The ramping time was 30 or 40 minutes. Observation and comments: Water feed valve V9 had leakage. This gave a higher oxygen percentage than was expected. The zero offset of the transmitter for oxygen flow rate changed from 2V at the 83 start to 1.8V when it was stopped. The oxygen flow rates from gas flow meter were also recorded. The pressure gauge near VI5 was reading 200 psi higher than the real pressure was. Calibration of the system pressure was done after the experiment. The bulk thermocouple in the middle of the test section was broken. 9. Date: November 25, 1999 (Run 36-38) Objectives: Heat capacity test for pure water Operation: Heat flux was 6.122 kW. Temperature ramping was applied on Preheater 2. There were three data files with temperature set points of 120, 200 and 300 0 C. 84 APPENDIX E Data files for experimental runs s 1 s a E J > s CM n P E 49 8 u 3 .a s a w en o -L <u •** ot T J C c s u u s « 26 553 P » a C S ! Si 5-•8 § x " o 15 R to rs H Eg S t m 8 a a.s 3 a>Ai " H Q s l l I a. S SIS' is ft 1 8 § S 1 H a c<3 O o oo,.. <—i.. c o o •2 o. o a o o § o a 3 P. 3 O U o ft. Table E2. Channel configuration (Wang, 2001) APPENDIX E l Results of Experiments Results of each of the experiments were presented by five different graphs. The first graph shows inlet and outlet temperature, pressure and oxygen distribution in function of time. The second graph presents constant pressure heat capacity and heat loss distribution in function of bulk temperature. The third and fourth graphs show heat transfer coefficient for different thermocouples for top and bottom surfaces in function of bulk temperature. The last graph presents the average values for heat transfer coefficient for top and bottom surfaces in function of bulk temperature. 88 t1june17.csv run#11 Tbin °C Tbout °C - • - oxflow*1000 kg/min pressure*10 MPa 10 15 20 25 Time, minutes 30 35 40 45 x10 4.5 4 3.5 3 2.5 2 1.5 1F-0.5 0 O Cp J/kg/K — ql_oss*10, Watts o O ODO O ' O O O O O o o o o 200 250 300 350 Average Bulk Temperature, C 400 450 Student Version of MATLAB 8^  Student Version of MATLAB <*0> t1june17.csv run#11 14000 12000 10000 O csT" E *r 8000 o O in c CO CO X 6000 4000 h 2000 hp=24.4 MPa H20 flow=1.01 l/min 02=0 wt% Q=93 kW/m 2 Tpc=385°C Cp(Tpc)=45 kJ/kg/°C h(avg)=9.7 kW/m2/°C 200 250 300 Bulk Temperature, C 350 bottom top 400 Student Version of MATLAB 600 500 400 300 200 100 t2jun17.csv run#12 Tbin °C, Tbout°C oxflow*1000 kg/min pressure*! 0 MPa 10 15 20 25 30 Time, minutes 35 40 45 50 x10 3.5 3 2.5 2 1.5 1 0.5 0 O o O ' o o o o o o o o o o o o o o o o o o o 0 e o 350 360 370 380 390 400 410 420 Average Bulk Temperature, C O Cp J/kg/K qLoss*10, Watts o 430 440 450 Student Version ofMATLAB 92 20001 320 340 360 380 400 420 440 460 Bulk Temperature, C 4000 i 1 1 1 1 1 1 1 1 1 1 330 340 350 360 370 380 390 400 410 420 430 Bulk Temperature, C Student Version of MATLAB 9 3 Student Version ofMATLAB 9 4 500 450 400 350 300 250 200 150 100 50 0 t3jun17.csv run#13 Tbin °C Tbout °C — oxflow*1000 kg/min pressure* 10 MPa 10 15 20 Time, minutes 25 30 35 Student Version ofMATLAB IS Bulk Temperature, C Bulk Temperature, C Student Version ofMATLAB 9€ t3jun17.csv run#13 14000 12000 10000 O CM E § 8000 co o O CO c CO CO X 6000 4000 2000 h P=24.2MPa H20 flow=1.01 l/min 02=4.9 wt% Q=96 kW/m 2 Tpc=372°C Cp(Tpc)=30kJ/kg/°C h(avg)=9.6 kW/m2/°G 340 350 360 370 380 Bulk Temperature, C bottom top 390 400 Student Version of MATLAB x10 i 1 o o o 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 O o o o o o o Cp J/kg/K — qLoss*10, Watts o o o o o o o o o o 340 350 360 370 380 390 400 410 420 430 440 450 Average Bulk Temperature, C Student Version of MATLAB 37 t4jun17.csv run#14 320 340 360 380 400 420 440 460 Bulk Temperature, C 11000 4000 300 320 340 360 380 Bulk Temperature, C 400 420 440 Student Version of MATLAB 98 t4jun17.csv run#14 bottom top 12000 10000 p CO o O CO c CO CO X 8000 6000 4000 2000 P=25.8MPa H20flow=1.01 l/min 02=4.7 wt% Q=97 kW/nT Tpc=381 °C Cp(Tpc)=21 kJ/kg/°C h(avg)=8.9 kW/m 2/°C JL 350 360 370 380 390 400 Bulk Temperature, C 410 420 Student Version of MATLAB 39 x10 320 340 360 380 400 Average Bulk Temperature, C 420 440 Student Version of MATLAB Student Version ofMATLAB (0 | t5jun17.csv run#15 i r ~~1 r i 1 1 r bottom top 12000 10000 O CD O O CO c CO 8000 I— 6000 h co CD X 4000 2000 P=26.4MPa H20 flow=1.01 l/min 02=2.1 wt% Q=95 kW/m" Tpc=386°C Cp(Tpc)=26 kJ/kg/°C h(avg)=9 kW/m2/°C J I I I I L 320 330 340 350 360 370 380 Bulk Temperature, C 390 400 410 Student Version of MATLAB Student Version of MATLAB I 0 5 x 1 04 OITall.csv run#17 1.61 1 1 1 1 1 r 280 300 320 340 360 380 400 420 Bulk Temperature, C 13000 ® 6000 4000 280 300 320 340 360 Bulk Temperature, C 380 400 420 Student Version ofMATLAB tOL, OITall.csv run#17 i r i r 12000 10000 p CD o P C/> c CO CO CD 8000 6000 4000 2000 P=25.4MPa H20 flow=1.05 l/min 02=4 wt% Q=95 kW/m 2 Tpc=373"C Cp(Tpc)=24kJ/kg/°C h(avg)=9.1 kW/m 2/°C J L J I I L bottom top J L 300 310 320 330 340 350 360 370 Bulk Temperature, C 380 390 400 Student Version of MATLAB I OS" Student Version of MATLAB I06 10000 9000 | 6500 5500 280 300 320 340 Bulk Temperature, C 360 380 400 Student Version ofMATLAB 107 02Tall.csv run#18 i ~ r 12000^* i r bottom top 10000 8000 O £ 0) o ° 6000| w c to to (0 4000 2000 P=25.6MPa H20flow=1.05 l/min 02=6.2 wt% Q=96 kW/nrT T p c = 3 6 6 ° C Cp(Tpc )=19kJ /kg / °C h(avg)=8.5 k W / m 2 / ° C _J L _l L 310 320 330 340 350 360 Bulk Temperature, C 370 380 390 Student Version of MATLAB O 1 1 J 1 1 1 1 i i I 0 5 10 15 20 25 30 35 40 45 Time, minutes Student Vqwon of MATLAB ( 0 9 of MATLAB H O jun 19a.csv run#19 4000 3500 3000 2500 O CN E 5 CD O 2000 CO c CO CO CD X hP=24.5MPa H20 flow=0!636 l/minf, O2=0 wt% Q=-15 kW/m'' 1500 1000 Hfpi£=384 500 C Cp(Tpc)=11 kJ/kg/°C h(avg)=-3.5 kW/m 2/°C bottom top 50 100 150 200 250 300 Bulk Temperature, C 350 400 Student Version of MATLAB Student Version of MATLAB X - | Q 5 jun19b.csv run#20 1.51 1 1 1 1 1 r x104 201 1 1 1 1 1 1 1 1 r Bulk Temperature, C Student Version of MATLAB US jun19b.csv run#20 Student Version ofMATLAB 114 jun19c.csv run#21 T b i n ° C Tbout ° C — oxflow*1000 kg/min — pressure* 10 MPa 20 25 Time, minutes x10 2.5 1.5 0.5 150 200 O Cp J/kg/K qLoss*10, Watts o o o 250 300 350 Average Bulk Temperature, C 400 450 Student V i s i o n ofMATLAB StudentiVersion of MATLAB KG jun19c.csv run#21 16000 14000 12000 y 10000 CM E. I **— co o O | 8000 CD CO CD I 6000 h 4000 2000 hp=±24.5 MPa H20 flow=1.3 l/min O2=0 wt% Q=4l2kW/m Tpc=383 °C Cp(Tpc)=29 kJ/kg/ °C h(avg)=-23 kVWm2/ °C 200 250 300 Bulk Temperature, C 350 I • bottom top 400 StuderftYersion ofMATLAB 11? 1600awo.csv run#27 500 450 400 350 300 250 200 150 100 50 0 - - Tbin°C Tbout °C — oxflow*1000 kg/min — pressure*10 MPa 0 10 15 20 25 Time, minutes 30 35 40 45 16000 14000 12000 10000 8000 6000 4000 2000 O o O CpJ/kg/K — qLoss*10, Watts o o o o o o o o o o o o o o o o o o o o 300 350 400 Average Bulk Temperature, C 450 Student Version of MATLAB Student Version of MATLAB 119 Student Version of MATLAB IZO x10 i r i i r O o o o o Cp J/kg/K qLoss*10, Watts 350 360 370 380 390 400 410 420 430 440 450 Average Bulk Temperature, C Student Version of MATLAB 12.1 14water.csv run#28 14000r 12000 -350 360 370 380 390 400 410 420 430 440 Bulk Temperature, C 3000 350 360 370 380 390 400 410 420 430 440 Bulk Temperature, C Student Version of MATLAB 122. •)04 14water.csv run#28 350 360 370 380 390 400 410 420 Bulk Temperature, C Student Version of MATLAB V<Z*> 14wo.csv run#29 0 10 20 30 40 50 60 - 70 80 Time, minutes x10 340 350 360 370 380 390 400 410 420 430 440 450 Average Bulk Temperature, C Student Version of MATLAB 12000 480 Bulk Temperature, C Student Version of MATLAB 1 2 b 14wo.csv run#29 ~r ~ r 14000 bottom top 12000 10000 O <M E | 8000 co o O CO V— I— X 6000 4000 2000 P=25.1 MPa H20flow= 1.27 l/min 02=3 wt% Q=96 kW/m' Tpc=383 °C Cp(Tpc)=28 kJ/kg/ °C h(avg)=9.4 kW/m 2/ °C J I I L 350 360 370 380 390 400 410 420 430 440 Bulk Temperature, C Student Version of MATLAB 12G 12wo.csv run#30 Tbin °C Tbout °C oxflow*1000 kg/min pressure*.10 MPa 10 20 30 Time, minutes 40 50 60 x10 300 350 400 Average Bulk Temperature, C 450 Student Version of MATLAB 127 440 440 Bulk Temperature, C Student Version of MATLAB 12wo.csv run#30 " i 1 1 r T ~ T bottom top 9000 8000 7000 6000 5000 4000 3000 2000 P=25.2MPa H20flow=1.01 l/min 02=3 wt% Q=95 kW/m 2 1000 Tpc=382 °C Cp(Tpc)=34 kJ/kg/ °C h(avg)=10 kW/m 2/ °C (J' L J I L J L 310 320 330 340 350 360 370 380 Bulk Temperature, C 390 400 410 Student Version of MATLAB it'2.9 12wo-5-300.csv run#31 450 400 350 300 250 200 150 100 h Tbin °C Tbout°C oxflow*1000 kg/min pressure*10 MPa 50 I I . I I I : L 0 10 15 20 Time, minutes 25 30 35 x10 2.5 1.5 0.5 o q o o o o o o o o o o o o Cp J/kg/K qLoss*10, Watts 350 360 370 380 390 400 410 420 Average Bulk Temperature, C 430 440 450 Student Version of MATLAB (SO x 10 12wo-5-300.csv run#31 340 350 360 370 380 Bulk Temperature, C 390 400 410 10000 3000 340 350 360 370 380 Bulk Temperature, C 390 400 410 Student Version of MATLAB i-si 12wo-5-300.csv run#31 i r T T 12000 10000 8000 6000 4000 bottom top 2000 P=25.3MPa H20flow= 1.01 l/min 02=7.9 wt% Q=98 kW/nT Tpc=373 °C Cp(Tpc)=27 kJ/kg/ °C h(avg)=8.2 kW/m 2/ °C 355 360 365 370 375 380 Bulk Temperature, C 385 390 395 Student Version of MATLAB 12wo-5-370.csv run#32 450 400 Tbin°C Tbout °C — oxflow*1000 kg/min 350 — pressure*10 MPa 300 250 . - v / - . .^ ^ ^  - . 200 150 100 -50 0 C i i i ) 5 10 15 Time, minutes 20 : Student Version of MATLAB 12wo-5-370.csv run#32 2000 300 320 340 360 380 Bulk Temperature, C 4 0 0 420 440 8000 7000 6000 r 5 0 0 0 o 4000 3000 2000 320 340 360 380 400 Bulk Temperature, C 420 440 Student Version of MATLAB 12wo-5-370.csv run#32 "i r i r 9000 8QQQ bottom top 7000 6000 5000 4000 3000 2000 P=25.2MPa H20flow=1.01 l/min 02=8wt% Q=1.6e+002 kW/m^ 1000 Tpc=374°C Cp(Tpc)=21 kJ/kg/ °C h(avg)=6.1 kW/m 2/°C J I 350 360 370 380 Bulk Temperature, C 390 400 Student Version of MATLAB IBS 450 ( 400 350 300 250 200 150 100 50 12wo-5-200.csv run#33 Tbin °C Tbout°C — oxflow*1000 kg/min — pressure*10 MPa 10 15 20 Time, minutes 25 30 35 x10 2.5. O o o o 1.5 O o 0.5 O o o o o o o o o 0 o o Cp J/kg/K qLoss*10, Watts 360 370 380 390 400 410 420 430 440 450 Average Bulk Temperature, C Student Version of MATLAB xio 4 12wo-5-200.csv run#33 350 360 370 380 390 400 410 420 Bulk Temperature, C x104 350 360 370 380 390 400 410 420 430 Bulk Temperature, C Student Version of MATLAB 12wo-5-200.csv run#33 12000 10000 bottom top 8000 6000 4000 2000 P=25.3MPa H20flow=1.01 l/min 02=7.6 wt% Q=37 kW/m 2 Tpc=372°C Cp(Tpc)=27kJ/kg/°C h(avg)=5.9 kW/m 2/°C 360 370 380 390 Bulk Temperature, C 400 410 Student Version of MATLAB 12wo-534.csv run#34 450 400 350 300 250 200 150 100 50 10 20 30 40 Time, minutes " Tbin °C Tbout °C — oxflow*1000 kg/min pressure*10 MPa 50 60 70 x10 2.5 1.5 0.5. O o o o o o o o o o o o o o o o o o o Cp J/kg/K — qLoss*10, Watts 320 340 360 380 400 Average Bulk Temperature, C 420 440 Student Version of MATLAB Student Version of MATLAB 12wo-534.csv run#34 i i 1 r i r 10000 8000 6000 4000 2000 P=24 MPa H20 flow=1.01 l/min 02=7.8 wt% Q=34 kW/m" Tpc=370°C Cp(Tpc)=29 kJ/kg/°C h(avg)=8.2 kW/m 2/°C _L I I L bottom top 330 , 340 350 360 370 380 Bulk Temperature, C 390 400 410 Student Version of MATLAB APPENDIX F MatLab programs outline Heatdata.m c l e a r %part 1 Channel Setup, %each number indicates the channel for: %bulk i n and out thermcouples Bini=[l,1,3,2,3,3,3,3]; Bouti=[3,3,23,3,5,4,4,5]; % o f f s e t for outlet bulk temperature offsetbout=[-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5] %length between i n , out bulk thermocouples testL=[2.946,2.946,2.946,2.946,2.946,1.473,1.473,3.259]; ^pressure and oxygen channels: PTi=[18,18,18,22,22,22,22,22]; 02i=[20,20,20,24,24,24,24,24]; %number of top and bottom T/C channels for 8 d i f f e r e n t configurations NTOP=[12,10,8,10,8,9,9,9]; NBOT=[0,7,5,5,5,3,3,3]; %make up an array for graphing suface thermocouple data linetype=char('k:','k- 1,'k +',... • b : ' , ' b - ' , ' b + ' , . . . *r:','r-',*r +',... •g-','g +','g:'); i %channel numbers for the top and bottom T/C % each row corresponds to one configuration top=[4,5,6,7,8,9,10,11,12,13,14,15;... 4,5,12,13,14,16,21,22,23,24,0,0;... 10,11,12,13,14,15,21,22,0,0,0,0;... 5, 7, 8,10,12,14,16,17,18,20, 0, 0; .. . 6,8,9,14,15,17,18,20,0,0,0,0;... 7, 8,10,11,12,13,14,15,16, 0, 0, 0; . . . 7,8,10,11,12,13,14,15,16,0,0,0;... 7,8,10,11,12,13,14,15,16,0,0,0]; bot=[0,0,0,0,0,0,0,0,0,0,0,0;... 6,7,8,9,10,11,15,0,0,0,0,0;... 4,5,7,8,9,0,0,0,0,0,0,0;... 6,9,11,13,15,0,0,0,0,0,0,0;... 7,10,11,12,13, 0, 0, 0, 0, 0, 0, 0; .. . 6,9,17,0,0,0,0,0,0,0,0,0;... 6,9,17,0,0,0,0,0,0,0,0,0;... 6,9,17,0,0,0,0,0,0,0,0,0]; % a x i a l l o c a t i o n of the thermocouples, for a given config (row) % and thermocouple number. A l l configs use less than 13 T/Cs. xtop=[0.242,0.447,0.749,0.837,0.969,1.25,1.551,1.721,2.024,2.278,2.414, 2.822;... 0.749,0.969,2.024,0.837,1.123,1.25,2.822,2.414,0.442,1.41,0,0;... 0.247,0.612,0.837,1.123,1.25,1.41,1.551,2.822,0,0,0,0;... 0.612,0.749,0.837,0.969,1.123,1.25,1.41,1.721,2.278,2.822,0,0;... .612,.749,.835, 1.41, 1.721,2.278,2.822,2.874, 0, 0, 0, 0; .. . 1.031, 0.861,.504,.063, 1.551,1.721,2.151,2.551,2.822,0,0,0; .. . 1.031,0.861,.504,.063,1.551,1.721,2.151,2.551,2.822,0,0,0;... 1.031, 0.861, .504, .063,1.551,-1. 721, 2.151, 2. 551, 2. 822, 0,0,0] ; xbot=[0,0,0,0,0,0,0,0,0,0,0,0;... 2.822,0.861, 1.03,1.179,1.329,0.521,0.77 6,0, 0, 0,0,0;.. . 0.148,0.521,1.03,1.179,1.329,0,0,0,0,0,0,0;... 0.691, 0.861, 1.03, 1. 179, 1.329, 0, 0, 0, 0, 0, 0, 0; .. . 143 .691,.861,1.03,1.179,1.329,0,0, 0,0,0,0,0;.. . 1.325, . 612,2. 822, 0, 0, 0, 0, 0, 0, 0, 0, 0; .. . 1.325,.612,2.822,0,0,0,0,0,0,0,0,0;... 1.325,.612,2.822,0,0,0,0,0,0,0,0,0]; %Thermcouple o f f s e t s entered here, assumed to be c o n f i g u r a t i o n - s p e c i f i c offsettop=[0,0,0,0,0,0,0,0,0,0,0,0,;... 0,0,0,0,0,0,0,0,0,0,0,0,;... 0,0,0,0,0,0,0,0,0,0,0,0,;... 0,0,0,0,0,0,0,0,0,0,0,0,;... 0,0,0,0,0,0,0,0,0,0,0,0,;... 0,0,0,0,0,0,0,0,0,0,0,0,;... .0,0,0,0,0,0,0,0,0,0,0,0,;... 0,0,0,0,0,0,0,0,0,0,0,0,]; offsetbot=[0,0,0,0,0,0,0,0,0,0,0,0; . . . 0,0,0,0,0,0,0,0,0,0,0,0;... 0,0,0,0,0,0,0,0,0,0,0,0;... 0,0,0,0,0,0,0,0,0,0,0,0;... 0,0,0,0,0,0,0,0,0,0,0,0;... 0,0,0,0,0,0,0,0,0,0,0,0;... 0,0,0,0,0,0,0,0,0,0,0,0;. . . 0,0,0,0,0,0,0,0,0,0,0,0]; % now enter run-specfic information % f i l e names. The data f i l e should have the f i r s t 2 columns of the raw . txt % f i l e removed, as well as the header row. That, i s the f i l e i s a comma-separated % f i l e with each column corresponding to a p a r t i c u l a r channel. fname=char('sept2a.csv', 1sept2b.csv','sept2c.csv', 1sept2d.csv','sept2e. csv 1,... 'sept2e.csv','qhfmtall.csv 1,'qhfmtal2.csv','qhftall.csv",'marlOcp.csv', 'tljunel7.csv','t2junl7.csv',*t3junl7.csv','t4junl7.csv','t5junl7.csv', 't6junl7.csv','OlTall.csv',... '02Tall.csv','junl9a.csv','junl9b.csv','junl9c.csv','junl9d.csv',... 'may24.csv', '800w.csv",'800w.csv','1600w.csv','1600awo.csv',... '14water.csv','14wo.csv','12wo.csv','12wo-5-300.csv',112wo-5-370.csv',... '12wo-5-200.csv' ,'12wo-534.csv','12water.csv','O0T120.csv','O0T200.csv','O0T300.csv'); cn=[1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,. . . 4,4,5,5,5,5,6,7,7,... 7,7,8,8,8,8,8,8,8,8,4,4,4]; v=[-1,-1,299,299,299,299,-1,-1,-1,-1,... 300,300,300,300,300,300,... 300,300,0,0,0,0,... -1,300, 300,-1, 300, 300, 300, 300,. . . 300,370,200,200,0,300,300,300]; lpm=[1.2,1.2,1.2,1.2,1.2,1.2,-1,-1,0.94,1.2,... 1.01,1.01,1.01,1.01,1.01,1.01,1.05... 1.05,0.636,0.636,1.296,1.296,1.365,1.026,1.026,2.117,2.1168,... 1.269,1.269,1.007,1.007,1.007,1.007,1.007,1.007,1.068,1.068,1.068]; kgps=lpm/60.; timestep=5; 144 %K(1:38)=4.16/60.; %V0(1:38)=2.; K(1:38)=(366.76*3950/3980/44.4)A0.5 % read i n data run=input('run number?') nav=input( 1 averaging window s i z e (-20)?') filename=deblank(fname(run,:)) data=csvread(filename); t i t l e s t r = s t r c a t ( f i l e n a m e , ' runt ',num2str(run)) ic=cn(run); Tbin=data(:,Bini(ic)); Tbout=data(:,Bouti(ic))-offsetbout(ic); L=testL(ic); pres=data(:,PTi(ic)); pres=(992.l*pres-22.353)/145 %oxv=max(data(:,02i(ic))-V0(run) , 0); oxv=data(:,02i(ic)) %voltages less than V0 indi c a t e d zero oxygen flow %oxraw=K(run).*oxv. A.5; oxraw=K(run).*(oxv.".5)/60 Ndata=max(size(data)) minutes=timestep/60:timestep/60:timestep*Ndata/60; %now work on the f i l t e r i n g then analyzing data oxflow=cleanup(oxraw,nav,1); short=length(oxflow); Tbinf=cleanup(Tbin,nav,1); Tboutf=cleanup(Tbout,nav,1); Tbavg=(Tbinf+Tboutf)/2; %now c a l l the transient heat trans f e r program for j=l:NTOP(ic) i = t o p ( i c , j ) ; T = d a t a ( : , i ) - o f f s e t t o p ( i c , j ) ; Tt(:,j)=cleanup(T,nav,1); end Ttavg =0. for j=l:NT0P(ic). Ttavg=Ttavg+Tt(: , j) end Ttavg=Ttavg/NTOP(ic) qloss=losses(Ttavg,5*nav,L); i f v(run)==0. Qe=0. else Qe=Qelec(Ttavg,v(run),L); end Q=Qe-qloss; oxraw = 0. figure(1) subplot(2,1,1); plot(minutes,Tbin,'k: 1,minutes,Tbout, 1k-',... minutes,oxraw*1000,'k-.',minutes,abs(pres*10),'k—','LineWidth' , 2) legend('Tbin A o C , 'Tbout AoC','oxflow*1000 kg/min', 'pressure*10 MPa') t i t l e ( t i t l e s t r ) xlabel('Time, minutes') mflow=kgps(run) %mflow=kgps(run)+oxflow/60.; dT=Tboutf-Tbinf; Cp=(Q./(dT))./mflow; %c a l c u l a t e some parameters needed for a quadratic i n t e r p o l a t i o n of temperature %dCpdT=gradient(Cp, Tbavg) ; %a=0.5*dCpdT; %b=Cp-Tbavg.*dCpdT; %cl=0.5*Tbinf.*Tbinf.*dCpdT+Cp.*Tbinf-Tbinf.*Tbavg.*dCpdT; subplot(2,1,2); plot(Tbavg,Cp,'k o',Tbavg,qloss*10,'k-') x l a b e l ('Average Bulk Temperature, C ) axis([min(Tbavg)-5,450,0,max(Cp)+1000]) %notes=strcat(num2str(mean(mflow)),'kg/s , '... % ,num2str(mean(Q)) , ' Watts') %notes2=strcat( 'points averaged(xO.5)=',num2str(nav)) %text([min(Tbavg)+60],[max(Cp)-3500],notes) %text([min(Tbavg)+60],[max(Cp)-9500],notes2) legend('Cp J / kg /K ','qLoss*10, Watts') filename5=strcat('runl6a', '.out')% can construct a filename using the run number M=[Tbavg,Cp]%3 column vectors or more put in t o one matrix dlmwrite(filename5,M)%default formate i s comma delimited %now recover f i l e to see that i t works A=dlmread(filename5, ' , ') % . parse and f i l t e r TOP surface temperatures q=(Q. /Cp)./mflow Ri=0.0031 Ro=0.00475 kin=17 Ariro=2*Ri/(Ro A2-Ri A2) %a=Ri/Ro for j=l:NTOP(ic) i=top(ic, j) ; T = d a t a ( : , i ) - o f f s e t t o p ( i c , j ) ; Tt(:,j)=cleanup(T,nav,1); Tti(:,j)=Tt(:,j)+Qe.*Ariro*(Ro A 2 —Ri A 2)/(4*kin) + (Qe.*Ro*Ariro/2- -qloss)*(log(Ri)-log(Ro))*Ro/kin % T t i ( : , j ) = T t ( : , j ) - Q . * R i * ( a A 2 - 2 * l o g ( a ) - 1 ) / ( 2 * k i n * ( l - a A 2 ) ) x j = x t o p ( i c , j ) ; Ttb(:,j)=q*xj/L+Tbinf; end % parse and f i l t e r BOTTOM surface temperatures for j=l:NB0T(ic)-i = b o t ( i c , j ) ; T = d a t a ( : , i ) - o f f s e t b o t ( i c , j ) ; Tb(:,j)=cleanup(T,nav,1); Tbi(:,j)=Tb(:,j)+Qe.*Ariro*(Ro A 2—Ri A 2)/(4*kin) + (Qe.*Ro*Ariro/2-qloss)*(log(Ri)-log(Ro))*Ro/kin x j = x b o t ( i c , j ) ; 1.46 Tbb(:,j)=q*xj/L+Tbinf; end % TOP surface heat trans f e r c o e f f i c i e n t s T t a l l = [ ] ; h t a l l = [ ] ; A=0.0062*pi*L figure(2) subplot (2,1,1) ; ., for j=l:NTOP(ic) Qa=Q./A ht ( : , j ) = Q a . / ( T t i ( : , j ) - T t b ( : , j ) ) ; T t a l l = [ T t a l l ; T t b ( : , j ) ] h t a l l = [ h t a l l ; h t ( : , j)] p l o t ( T t b ( : , j ) , h t ( : , j ) , l i n e t y p e ( j , : ) , ' L i n e W i d t h ' , j / 2 ) hold on end t i t l e ( t i t l e s t r ) xlabel('Bulk Temperature, C ) ylabel('Heat Trans. Coef., Top,W/mA2/C ') hold o f f % Bottom heat t r a n s f e r c o e f f i c i e n t s Tball=[]; hball=[]; subplot(2,1,2) ; for j=l:NBOT(ic) Qa=Q./A hb(:,j)=Qa./(Tbi(:,j)-Tbb(:,j)); Tball=[Tball;Tbb(:,j)] hball=[hball;hb(:,j)] plot(Tbb(:,j),hb(:,j),linetype(j,:),'LineWidth',2) hold on end xlabel('Bulk Temperature, C') %y l a b e l ( ' A x i a l Position, m') ylabel('Heat Trans. Coef., Bottom, W/mA2/C ') hold o f f % average top and bottom c o e f f i c i e n t s figure(3) [ T t a l l s o r t , s o r t i n d e x ] = s o r t ( T t a l l ) ; h t a l l s o r t = h t a l l ( s o r t i n d e x ) ; [ T b a l l s o r t , s o r t i n d e x ] = s o r t ( T b a l l ) ; hballsort=hball(sortindex); hballclean=cleanup(hballsort, 5, 2000) htallclean=cleanup(htallsort, 5,2000) Tballclean=cleanup(Tballsort, 5, 2000) Ttal l c l e a n = c l e a n u p ( T t a l l s o r t , 5, 2000) filename6=strcat('runl6b','.out')% can construct a filename using the run number N=[Tballclean,hballclean]%3 column vectors or more put in t o one matrix dlmwrite(filename6,N)%default formate i s comma delimited filename7=strcat('runl6c','.out')% can construct a filename using the run number Nl= [ T t a l l c l e a n , h t a l l c l e a n ] % 3 column vectors or more put into one matrix dlmwrite(filename7, Nl) % d e f a u l t formate i s comma delimited 147 %diary ( 1cp and h') % T t i %Tt %Tbi %Tb • %Tbavg %Tbinf %Tboutf %Cp %diary of %Tballclean %hballclean % T t a l l c l e a n % h t a l l c l e a n plot(cleanup(Tballsort,5,2000),cleanup(hballsort,5,2000),*k-') hold on plot(cleanup(Ttallsort,5,2000),cleanup(htallsort,5,2000),'k:') legend('bottom','top') xl a b e l ('Bulk Temperature, C ) ylabel('Heat Trans. Coef.,W/mA2/C') t i t l e ( t i t l e s t r ) hold o f f %post processing/averageing routines %The purpose of these cal c u l a t i o n s i s to generate the run summary information that % i s tabulated i n the thesis % Find the peak Cp and c a l l t h i s the p s e u d o c r i t i c a l point [Cpmax,imax]=max(Cp); Tpc=Tbavg(imax); % The most important range for the averages i s about +/- 15 C of Tpc low=Tpc-15; high=Tpc+15; % create an index that w i l l allow us to calculate averages i n t h i s range of temperatures. % good i s used i n " l o g i c a l subscripting" good=(Tbavg>low)&(Tbavg<high); meanP=mean(pres(good)) meanP=abs(meanP) meanQ=mean(Q(good))/(.0062*pi*L)/1000; %meanOx=mean(oxflow(good))*60. meanOx=0. oxpct=100*meanOx/(meanOx+kgps(run)*3600) %getting average heat t r a n s f e r c o e f f i c i e n t i s more complicated because % we want an average weighted by the heat capacity. In a heat exchanger, % most of the heat trans f e r i s required where the heat capacity i s highest, % so the heat t r a n s f e r c o e f f i c i e n t i s more important near the peak. a l l T = [ T t a l l ; T b a l l ] ; a l l h = [ h t a l l ; h b a l l ] ; [ a l l T s o r t , i s o r t ] = s o r t ( a l l T ) ; a l l h s o r t = a l l h ( i s o r t ) ; %we w i l l need a Cp value for every temperature; use a lookup table here [Tsort,isort]=sort(Tbavg); Cpsort=Cp(isort); C p a l l = i n t e r p l ( T s o r t , C p s o r t , a l l T s o r t ) ; good=(allTsort>low)&(allTsort<high); dT=gradient(allTsort); CpdT=Cpall.*dT; hCpdT=allhsort.*CpdT; Snow the mean value i s the i n t e g r a l of hCpdT divided by the i n t e g r a l of CpdT % but i n Matlab, we use a sumation instead of an i n t e g r a l meanh=sum(hCpdT(good))/sum(CpdT(good))/1000; notes3=strcat( 'P=1,num2str(meanP,3),' MPa H20 flow=',num2str(lpm(run) , 3),' 1/min 02=',... num2str(oxpct,2),' wt% Q=',num2str(meanQ,2),' kW/mA2 ' ); notes4=strcat ( ' Tpc= ' , num2str (Tpc, 3) , ' A'oC Cp(Tpc) = ',num2str(Cpmax/1000, 2) , . .. ' kJ/kg/ AoC h(avg)= ',num2str(meanh,2),' kW/mA2/ A o C ); Preset the axis l i m i t s on the l a s t p l o t of heat trans f e r c o e f f i c i e n t s so that we % can be sure that there i s room for the text. xmin=min(Tbavg) ; xmax=max(Tbavg); ymin=0; %get the y-axis l i m i t ymax=l.3*max(cleanup(allhsort, 5,2000)); axis([xmin,xmax,ymin,ymax]); text([xmin+3],[ymin+2000],notes3); text([xmin+3],[ymin+1000],notes4); %here i s how to put vectors together into a f i l Q dT 149 function ql=losses(Tw,deltime,L) %calculates test section transient heat losses given tube temperature Tw % as a function of time. n=40; W=.15 k=.35; thermalmass=0; rho=480; cp=710; Tambient=20; delr=W/n/2; h=7; Fo=k/rho/cp*deltime/delr/delr; Bi=h*delr/k; desired=.5/{1+Bi); extrasteps=round(0.5+Fo/desired) Fo=Fo/extrasteps; r0=.0095; area=L*2*r0*pi; %make up the " g r i d " Adiag=l-2*Fo; for i=l:n r ( i ) = r 0 + d e l r * i ; A b a c k ( i ) = F o * ( l - d e l r / 2 / r ( i ) ) ; A f o r ( i ) = F o * ( l + d e l r / 2 / r ( i ) ) ; end %make up a matrix f or making the timestep A=zeros(n,n); A(l,l)=Adiag; A(l,l+l)=Afor(1); for i=2:n-l ' • . A ( i , i - l ) = A b a c k ( i ) ; A(i,i)=Adiag; A ( i , i + l ) = A f o r ( i ) ; , end A(n,n)=l-Fo-Fo*Bi; A(n,n-l)=Fo; % Now set i n i t i a l conditions % f o r s i m p l i c i t y , use l i n e a r v a r i a t i o n from inside to outside i=l:n; T=Tw(l)-(Tw(l)-Tambient)*i/n; T=T 1 ; %now march along i n time for as many points as contained i n Tw Ntimes=length(Tw); B=zeros(Ntimes,n+1); ql=Tw*0; for j=l:Ntimes-l for jj=l:extrasteps T=A*T; T(1)=T(1)+Aback(1)*Tw(jj ; T(n)=T(n)+Fo*Bi*Tambient; end B(j,l)=Tw(j) ; B( j,2:n+l)=T'; 150 ql(j)=k*area*(Tw(j)-T(l))/delr+(Tw(j+1) Tw(j))/deltime*thermalmass; end j=l:Ntimes; i=l:n+l; figure ( 5 ) contour(i,j,B) [CS,H]=contour(i,j,B); clabel(CS,H) function q=Qelec(Ttavg,SCRvolts , L) %calculates e l e c t r i c power input using temperature dependent r e s i s i s t i v t y F=0.789 rho=(((Ttavg. A3)/1000000000)-((Ttavg. A2)/1000000)+Ttavg.*0.0004+1.288)./1000000. area=41.486e-6; V=0.0491*SCRvolts-1.2564; R=rho.*1.473/area; q=2*(F*V A2./R); end function y=cleanup(x,nav,cutoff) %y=cleanup(x,nav,cutoff) %takes a vector x and removes o u t l i e r s according to the parameter cut o f f , . . . %and smooths with moving window +/-nav % It returns a shorter vector (roughly nav times shorter) % There i s no r e a l loss of information because we are averaging over a number of points % anyway; the o r i g i n a l longer vector i s more d i f f i c u l t to work with and slower. clean=x; N=length(x); for i=nav+l:N-nav mid=median(x(i-nav:i+nav)); i f abs(x(i)-mid)>cutoff; clean(i)=mid; end end newndata=(N-mod(N,nav))/nav-2; y=(1:newndata) 1; for j=l:newndata i=j*nav+l; y(j)=mean(clean(i-nav:i+nav)); end 153 1 % heat t r a n s f e r c o r r e l a t i o n c l e a r massflow=input('kg/min')/60.; %tube parameters: roughness and conductivity eps=.3048*10A-4; D=.001*input('id mm') area=pi*D A2/4; pressure=25.; %in t e r p o l a t e 2D property tables for the s p e c i f i e d pressure % to get a 1-D table for fast i n t p e r p o l a t i o n of properties [Tp,rhop,Hp,Cpp,visp,Kp,Prp]=tables(pressure); maxtemp=max(Tp); mintemp=min(Tp); %bulk properties Hb=1500000:100000:2500000; Tb=interpl(Hp,Tp,Hb'); visb=interpl(Tp,visp,Tb'); Re=(massflow/area*D)./visb; Db=interpl(Tp,rhop,Tb*); Q=input('heat flux kW/mA2') %guess wall temperature to s t a r t i t e r a t i o n of heat trans f e r c o e f f i c e n t Tw=Tb+10.; % guess i n i t i a l f r i c t i o n factor friction=(-2*logl0(eps/D/3.7+2.51./(Re*.02))). A-2; f i g u r e d ) for i=l:15 %properties at walls and bulks: Dw=interpl(Tp,rhop,Tw'); Hw=interpl(Tp,Hp,Tw*); visw=interpl(Tp,visp,Tw'); kw=interpl(Tp,Kp,Tw*); Pr=(Hb-Hw)./(Tb-Tw)'.*visw./kw; Nu = 0.00459*(Re. A0.923).*(Pr. A0.613).*(Dw./Db). A0.231; friction=(-2*logl0(eps/D/3.7+2.51./(Re.*friction))). A-2; heat=kw.*Nu/D; % generate new estimate of wall temperature Tw=Tb+Q*1000./heat'; end plot(Tb-273.l,heat/1000,Tb-273.1,friction*1000,Tb-273.1,Tw-Tb) legend ('h kW/mA2/C, 'f*1000', 'Tw-Tb') xla b e l ('Tb C ) yla b e l f ' h , f ' ) %here i s how to put vectors together i n t o a f i l e filename=strcat('25.2b','.out')% can construct a filename using the run number M= [Tb,heat',friction']%3 column vectors or more put in t o one matrix dlmwrite(filename,M)%default formate i s comma delimited %now recover f i l e to see that i t works A=dlmread(filename,',') 154 %property loader and p l o t t e r function [T,rhop,Hp,Cpp,visp,Kp,Prp]=tables(Pressure) %load a l l the property tables % a l l must have the same size and the same T,P spacing load dens.txt; load K.txt; load cp.txt; load enth.txt; ' load prand.txt; load v i s . t x t ; % get f i l e sizes from dens, but other f i l e s must have same size [nT,nP]=size(dens); % the f i r s t row contains the pressures i n MPa P=dens(l,2:nP); % the f i r s t column contains the Temperatures i n K T=dens(2:nT,1); % other than the f i r s t rows'and columns, we have actual property values A=dens(2:nT,2:nP); rhop=interp2(P,T,A,Pressure,T); A=K(2:nT,2:nP); Kp=interp2(P,T,A,Pressure,T); A=enth(2:nT,2:nP); Hp=interp2(P,T,A,Pressure,T); A=cp(2:nT,2:nP); Cpp=interp2(P,T,A,Pressure,T); A=vis(2:nT,2:nP); visp=interp2(P,T,A,Pressure,T); A=prand(2:nT,2:nP); Prp=interp2(P,T,A,Pressure,T); figure(2) plot(T,rhop/1000.,'k:',T,Hp/le6, 1k+',T,Cpp/100000,'ko',T,visp*10.0,'k-,T,Kp,'g:',T,Prp/10,'bx') legend('s.g. ','enthalpy MJ 1, 1Cp 10 A5J/kg/K','vis*10*,'conductivity','Prandtl/10') yLABEL('Property') XLABEL('T K') t i t l e ( s t r c a t ( ' p r o p e r t i e s at pressure=',num2str(Pressure),'MPa')) 155 

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