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Physical flow modelling of a kraft recovery boiler Ketler, Stephen Paul 1993

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PHYSICAL FLOW MODELLING OFA KRAFT RECOVERY BOILERbySTEPHEN PAUL KETLERB.A.Sc., The University of British Columbia, 1988A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDepartment of Mechanical EngineeringWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIANovember 1993© Stephen Paul Ketler, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)________________________________Department of Mechanical EngineeringThe University of British ColumbiaVancouver, CanadaDate December 15, 1993DE-6 (2/88)11ABSTRACTMeasurements of the vertical, and one horizontal, components of velocity have been made inan isothermal scale model of a kraft black liquor recovery boiler. The model used water as theworking fluid, and was a 1:28 scale representation of an operating recovery boiler in Plymouth,North Carolina. All of the air ports were represented in the model; however, the char bed shape,mass flow from the bed, and liquor flow were not. Laser-Doppler velocimetry was used to measurevelocities and power spectral densities in the model on a 6x6 grid of points on three horizontalplanes. Quantitative flow visualization was performed using laser sheet illumination of particles inthe flow, with subsequent analysis of the particle images.Flow conditions simulating industrial arrangements and special configurations were run inthe model. Industrial configurations employed flows from primary, starting burner, secondary, andeither concentric load-burner or interlaced tertiary ports. Special configurations using only primaryand secondary port flows were tested to investigate the sensitivity of the flowfield to variations in thelower furnace port flows. Orifice-plate flowmeters and valves were used to set the flowrates throughmanifolds connected to groups of ports. The error between the set and actual model total flowratewas shown to be dependent on the choice of flowmeters, and on the drift of valve settings with time.Considering both sources of error, for a typical model flowrate of 150 US gallons per minute, theexpected difference between the set and actual total flowrate was —6.5 percent. Differences betweenthe set mass flows, and the values calculated from the vertical velocities measured by the laserDoppler velocimeter, were less than ten percent on average. Larger variances between measured andpredicted mass flows were explained on the basis of observed low frequency oscillations.Computer software was created for the computation of velocity power spectral densitiesusing the output of the laser-Doppler velocimeter. A system of digital particle image velocimetry wasalso created for quantitative two-dimensional flow visualization. Laser light was spread into a planarsheet, and the motion of small polystyrene particles added to the flow was recorded on videotape at30 frames per second. The information on the videotape was digitized, and cross-correlation analysis111of successive image pairs yielded a grid of velocity vectors for each 1/30 second interval which couldbe animated.It was found that the flow in the model was extremely sensitive to any asymmetries in thesecondary level port flows. An increase in secondary flow velocity of 10% on one wall, and acorresponding decrease on the opposite wall, caused the core region of vertical upflow at the liquorgun level to occupy half of the model cross section near the wali with the lower velocity. It was verydifficult to balance the flows accurately enough to have the core region of vertical upflow in themodel centre. In the upper regions of the furnace, the majority of the upflow was near the walls,with down or stagnant flow in the model centre. The flow exhibited low frequency unsteadiness inaddition to a high level of turbulence throughout. Periods on an order of 10-20 seconds wereobserved in the velocity power spectral densities, and in the particle image velocimetry results.The use of concentric load-burner port flows on the tertiary level, as opposed to a 2x2interlaced arrangement of high velocity tertiary ports, was found to provide a somewhat moreuniform distribution of turbulence kinetic energy in the upper furnace. Implications for design andoperation of industrial recovery boilers are discussed.ivTABLE OF CONTENTSABSTRACT iiTABLE OF CONTENTS ivLIST OF TABLES viLIST OF FIGURES viiLIST OF SYMBOLS ixACKNOWLEDGMENTS xiiINTRODUCTION 11. MODELLING OF KRAFT RECOVERY BOILER FLOW FIELDS 31.1 Review of Methods 31.2 Non-Dimensional Parameters for Isothermal Modelling 51.2.1 Velocities 51.2.2 Frequencies 72. APPARATUS 82.1 Plymouth Recovery Boiler Model 82.2 Water Flow Systems 132.3 Argon-Ion Laser 132.4 Laser-Doppler Velocimeter 142.5 Particle Image Velocimetry 183. EXPERIMENTAL PROCEDURES 193.1 Water Flow System Calibration 193.1.1 Meter Error 213.1.2 Drift Error 243.1.3 Error Calculation for Typical Experimental Run 263.2 Laser Doppler Velocimetry 293.2.1 Experimental Arrangements 293.3 Laser Sheet Illumination 323.3.1 Experimental Arrangements 323.3.2 Recording Methods 333.4 Particle Tracking Accuracy 334. ANALYSIS METHODS 354.1 Laser Doppler Velocimetry 354.1.1 Velocities 354.1.2 Turbulence Kinetic Energy 364.2 Power Spectral Density 374.2.1 Direct Transform Method 374.2.2 Computational Implementation 39V4.2.3 Validation.394.2.3.1 Simulated Data 394.2.3.2 Fan Blade Experiment 394.3 Particle Image Velocimetry 414.3.1 Review of Techniques 414.3.2 Digital Particle Image Velocimetry 434.3.3 Computational Implementation 434.3.4 Temporal Smoothing 464.3.5 Animation 464.3.6 Validation 465. RESULTS 505.1 Laser Doppler Velocimetry 505.1.1 EarlyRuns 545.1.2 Load Burner Port Flow Case 585.1.3 Tertiary Port Flow Case 625.1.4 Balanced Primary and Secondary Port Flow Case 665.1.5 Balanced Primaries; Biased Secondaries Port Flow Case 705.2 Power Spectral Densities 795.3 Particle Image Velocimetry 825.3.1 Builnose Side View 825.3.2 Lower Boiler Side View 856. DISCUSSION OF RESULTS 876.1 Velocities 876.1.1 Air System Objectives 876.1.2 Velocity Effects in Full-Scale Furnaces 886.1.3 Upper Furnace Flow Configurations 896.2 Transient Behaviour 906.2.1 Data Qualification 906.2.2 Turbulence 936.2.3 Mixing 946.3 Experimental Limitations 956.3.1 Physical Variation 956.3.2 Input Information 966.3.3 Two-Phase Flow 976.3.4 Buoyancy Force Effects 977. CONCLUSIONS AND RECOMMENDATIONS 99REFERENCES 101APPENDIX A ORIFICE-PLATE CALIBRATION STATISTICS 104APPENDIX B POWER SPECTRAL DENSITY CALCULATIONS 110APPENDIX C SUMMARY OF COMPUTER PROGRAMS DEVELOPED 116viLIST OF TABLESTable 1.2.1Table 2.1.1Table 2.1.2Table 2.2.1Table 2.3.1Table 2.4.1Table 2.4.2Table 2.5.1Table 3.1.1Table 5.1.1Table 5.1.2Table 5.1.3Table 5.1.4Typical Port Velocities in Plymouth Recovery Boiler Model 6Plymouth Recovery Boiler Model Ports 11Plymouth Recovery Boiler Feature Locations 12Water Flow System Apparatus 13Argon-Ion Laser Apparatus 14Laser-Doppler Velocimeter Apparatus 15Measurement Volume Parameters 16Particle Image Velocimetry Apparatus 18Example Flow Condition 20Orifice-Plate Meter Error- B9 23Orifice-Plate Meter Error- D7 23Orifice-Plate Drift Error- B9 (3.5 US gpm Set) 25Orifice-Plate Drift Error- D7 (2.5 US gpm Set) 26Meter Errors for Typical Run - No Drift 26Meter Errors for Typical Run - After Drift 27Summary of Flowrates for Typical Run (150 US gpm) 28Plymouth Model Laser-Doppler Velocimetry Conditions 50Plymouth Model Laser-Doppler Velocimetry Results 52Measured Flowrate Errors 53Mean Non-Dimensionalized Vertical Velocities 55viiLIST OF FIGURESFigure 2.1.1Figure 2.1.2Figure 2.1.3Figure 2.4.1Figure Boiler Water Model Experimental Facility 9Plymouth Recovery Boiler Arrangement 10Plymouth Recovery Boiler Ports 12Beam Focal Point Location 16Measured versus Set Flowrates- B9 Orifice—Plates 21Measured versus Set Flowrates- D7 Orifice-Plates 22Flowmeter Reading versus Time - B9 Orifice-Plates 24Flowmeter Reading versus Time- D7 Orifice-Plates 25Laser Doppler Velocimetry Experimental Arrangement 29Tertiary Port Arrangement 31Particle Image Velocimetry Experimental Arrangement 32Power Spectral Density versus Frequency- Fan Experiment 40Digital Particle Image Velocimetry Analysis Procedure 44Simulated Vortex Flow Images 47Results of Cross-Correlation Analysis for Simulated Data 48Velocity Error for Simulated Data 49Two Components of Mean and RMS Velocities - Run 3 56Two Components of Mean and RMS Velocities- Run 4 57Two Components of Mean and RMS Velocities - Run 21 59Contours of Non-dimensionalized Vertical Velocity- Run 21 60Contours of Non-dimensionalized K½- Run 21 61Two Components of Mean and RMS Velocities - Run 26 63Contours of Non-dimensionalized Vertical Velocity- Run 26 64Contours of Non-dimensionalized K½- Run 26 65Two Components of Mean and RMS Velocities- Run 25 67Figure 5.2.1Figure 5.2.2Figure 5.2.3Figure 5.2.4Figure of Non-dimensionalized Vertical Velocity - Run 25 68Contours of Non-dimensionalized K½- Run 25 69Two Components of Mean and RMS Velocities - Run 23 71Contours of Non-dimensionalized Vertical Velocity - Run 23 72Contours of Non-dimensionalized K½- Run 23 73Flow Schematic Front View - Run 23 74Two Components of Mean and RMS Velocities - Run 24 76Contours of Non-dimensionalized Vertical Velocity - Run 24 77Contours of Non-dimensionalized K½- Run 24 78Velocity Trace - Run 25, Level 1, u Component 80Velocity Trace- Run 25, Level 1, w Component 80Power Spectral Density- Run 25, Level 1, a Component 81Power Spectral Density- Run 25, Level 1, w Component 81Builnose Side View 30 Second Average 83Bulinose Side View Consecutive 5 Second Averages 84Lower Boiler Side View 30 Second Average 85Lower Boiler Side View Consecutive 5 Second Averages 86Sequence of Mean Square Measurements, Level 1, w Component 92Extended Power Spectral Density, Run 25, Level 1, w Component 93ixLIST OF SYMBOLSA area, or amplitudeC degrees Celsiusd horizontal distance, or particle diameterd-2 Gaussian beam widthefocal length in air4 fringe spacingdm measurement volume diameterD smoothing window functionE expectation operatorf frequencyFr Froude numberg gray-scale function, or acceleration due to gravityh vertical distancehf ½ beam separation distancek wavenumberK turbulence kinetic energyL lengthmeasurement volume lengthm metren index of refraction, or general integerN number of samplesfr maximum number of fringesq flowraterate of heat transfer per unit massr radiusR correlation coefficientxRe Reynolds numbers seconds vector displacementS power spectral densityS, sample standard deviation of quantity xSt Strouhal numbert timeT general dependent variable, or record durationAt residence time of particle in LDV measurement volumeu instantaneous velocity in x, or general, directionU mean velocity in x, or general, directionu’ fluctuating component of velocity in x, or general, directionAu velocity difference between particles and fluidv instantaneous velocity in y directionV mean velocity in y directionfluctuating component of velocity in y directionw instantaneous velocity in z directionW mean velocity in z directionw’ fluctuating component of velocity in z directionx random variablex vector coordinatesz standard normal random variablez standard normal quantile of order aa significance level, probability of type I errorweighting value6 error• phase angley coefficient of dispersionK half angle between laser beams of same frequencyA wavelength, or shape parameterlocation parameterp densityAp density difference between particles and fluidstandard deviation, or scale parameterO general independent variableV kinematic viscosity, or mean sampling rateangular velocity, or frequencyxiXIIACKNOWLEDGMENTSI would like to thank Dr. I.S. Gartshore for his encouragement and advice throughout thecourse of this research. The assistance of Mr. Michael Savage with the construction of the watermodel facility, and in performing countless hours of experimental runs, was greatly appreciated.Gerry Rohling developed image digitization software crucial to the particle image velocimetrytechnique developed in this work.Financial assistance was provided to myself by the Natural Sciences and EngineeringResearch Council and the British Columbia Science Council. Financial assistance and equipmentwere provided to this project by the Weyerhaeuser Paper Company, the Natural Sciences andEngineering Research Council, Energy Mines and Resources, the United States Department ofEnergy, and H.A. Simons through the GREAT program.Finally, I would like to acknowledge the contribution of Dr. J. Peter Gorog to the genesis ofrecovery boiler physical modelling at the University of British Columbia.1INTRODUCTIONAn integral process in the manufacture of kraft pulp involves recovery of the inorganicchemicals used during pulping in the digester. Pulp mills use a complex system called a black liquorkraft recovery boiler for this chemical recovery, and for additional power generation. The blackliquor is a liquid containing the cooking chemkals along with the lignin from the wood, which hasbeen concentrated to approximately 70% solids prior to firing. The capital cost of such a boiler is onthe order of 100 million dollars. A typical recovery boiler will process approximately 1-3 millionkilograms of dry liquor solids per day. Any improvement in the combustion rate, reductionefficiency, and reduction in fouling or shutdown times of such a boiler would provide a substantialeconomic benefit to the industry. Such economic arguments form the rationak for the presentexperimental investigations into the fluid mechanics of recovery boilers since these units are verycomplex and difficult to model analytically or computationally. Such experiments also provide datafor validation of computational methods currently under development.A kraft recovery boiler is a tube-wall cavity typically 10 metres square by 40 metres high.Black liquor is fired into the boiler though liquor guns placed on either two or all four walls,approximately 10 metres above the boiler floor. These guns use either a conical spray nozzle or asplash plate design. Combustion air is provided through various combinations of ports on the boilerwalls both below and above the liquor gun level. The lowest level of air, typically referred to asprimary, uses many small ports of low velocity on all four walls, and controls and shapes the bed ofsmelt and char which forms on the boiler floor. The secondary level consists of fewer, higher velocityports on all four walls, just above the primaries. Secondary air limits the height of the bed, and isused to burn gases coming off of the bed. Tertiary level ports are placed above the liquor guns,either on two or four walls. They are the largest ports in the boiler, and may be configured toprovide an interlaced, directly opposed, or tangentially oriented flow pattern. The tertiary portsprovide the excess air used to complete the combustion and mixing of the gases. Spouts placed onthe rear wall of the boiler near the base allow molten smelt to flow out of the boiler to be causticized2and re-used in the pulping process. The floor of the boiler may either be flat, or sloped downtowards the smelt spouts.Mass flow ratios between the three levels of combustion air vary according to boilermanufacturer, owner, and operator preferences and objectives. A typical arrangement might have asplit between primaries,, secondaries, and tertiaries of 30, 45, and 25 percent respectively.Combustion air is usually heated to approximately 150°C prior to introduction into the boiler.Temperatures in the boiler centre can reach 1100°C, and the flow is full of entrained smelt, fume,and particulate, creating an extremely inhospitable environment for velocity measurements.The Weyerhaeuser Technical Center (WTC) in Tacoma, Washington originally constructeda Plexiglas water model of a company boiler located in Plymouth, North Carolina. After thetermination of their experimental program with the model, it was donated, along with associatedplumbing hardware, to the University of British Columbia (UBC). Subsequently, a water model ofthe Weyerhaeuser boiler in Kamloops, British Columbia, was also constructed by WTC and donatedto UBC. An argon-ion laser and laser-Doppler velocimetry system were acquired, and installed alongwith the models into a new experimental laboratory located at the UBC Pulp and Paper Centre.The objectives of this research are to develop experimental methods for quantitative velocitymeasurement in water models, and to apply these methods in investigating the flow patterns in thePlymouth recovery boiler model.31. MODELLING OF KRAFT RECOVERY BOILER FLOW FIELDS1.1 Review of MethodsModelling of physical phenomena may be undertaken using one or more of threeapproaches: analytical, computational, or experimental. Due to the complexity of the flow in a kraftrecovery boiler, analytical solutions of the complete or simplified Navier-Stokes equations of fluidflow are not possible. Computation of the flow inside such a boiler may be attempted, providingcertain assumptions are made in order to model the turbulent properties of the flow. This work doesnot concern itself with computational flow simulations, although the results found here may be usedfor validation of computational algorithms.Experimental studies of boiler flows may be conducted either on real boilers or on someform of scale model. Flow studies are extremely difficult to conduct on operating boilers firing blackliquor. The inhospitable thermal environment of up to 1100°C, the fume and char present in theflow, and the necessity of co-existing with operational requirements such as soot-blowing, make thetaking of flow-field measurements extremely difficult. Some qualitative studies of flow patterns usinginfra-red cameras tracking char particles, or added materials such as coke, have been attempted.Some researchers are attempting to develop velocity probes which will tolerate the thermalenvironment of a recovery boiler, but none are past the prototype stage. The use of acoustic Dopplertechniques has been attempted by some researchers, but this has been applied to mapping thethermal field rather than the more difficult task of velocity field estimation in the presence of suchthermal gradients.Measurements may be made in a full-scale recovery boiler which is operating isothermallywithout combustion. ‘While such measurements neglect the effects of buoyancy, liquor and smeltflow, and the gas flow off of the bed, they can provide insight into flow patterns and characteristics.Such studies are typically conducted using hot-wire or hot-film velocity probes which arecantilevered into the furnace cavity through maintenance or liquor-gun openings. These4investigations are hampered by the lack of conclusive velocity direction information, and the low-frequency sampling rates usually employed, and so provide results of limited use (Blackwell 1992).A full-scale boiler is usually only available for isothermal flow studies a few days a yearduring shutdowns, and the effort required to conduct even a minor velocity study in such a facilityis significant in terms of both personnel and expense. It would be advantageous to conductisothermal studies of the velocity flow field inside a small-scale representation of a kraft recoveryboiler. Such experimental studies have been conducted in the past using a model with air as theworking fluid, and a five-hole pitot tube or hot-wire anemometer for velocity measurements(Chapman and Jones 1990, Jones, Grace, and Monacelli 1989). Due to the expected highturbulence level of the flow, a non-intrusive measurement technique capable of recording theinstantaneous velocity direction and magnitude in multiple components would be preferable. Multi-hole pitot-static tubes cannot resolve highly turbulent flows, are disruptive to the flow, and have lowtemporal resolution (Pankhurst and Holder 1968). Measurement devices such as the pulsed hot-wireanemometer (Lomas 1986) are capable of distinguishing instantaneous velocity vectors, but are stilldisruptive to a highly turbulent flow of this nature and are rather fragile.A method capable of accurate measurement of unsteady velocities, while not physicallyaltering the flow, is the laser-Doppler velocimeter (LDV) (Fingerson et al. 1991). The LDV is ableto simultaneously measure multiple components of velocity at a single point, with both hightemporal and spatial resolutions. The technique requires that light be scattered from small particleswhich accurately follow the flow. ‘While an air model is economical in terms of construction andoperation, it is not conducive to accurate flow visualization or LDV measurements in turbulentflow, due to the difficulty in generating small particles with a specific gravity very close to that of thefluid. For this reason the working fluid in the model was chosen to be water, as opposed to air. Theuse of a water analog to simulate a gaseous internal flow has been shown to be a valid representationfor a wide range of applications (Sacher 1987).51.2 Non-Dimensional Parameters for Isothermal ModellingThe use of a scale model of a boiler for experiments requires that the parameters measured inthe model may be scaled, via some method, to equivalent values in the full-scale boiler. Theparameters considered here will be velocity and frequency.1.2.1 VelocitiesFor experimental modelling of fluid flows, a customary dimensionless parameter used is theReynolds numberULRe=—- ( is a measure of the ratio of inertial to viscous forces. At high enough Reynolds number,provided wall shear is not an important parameter, the large scale motions become independent ofviscosity, and therefore of Reynolds number.There is no possibility of equating the Reynolds number of a small water model to that of anoperating furnace: the model will have a Reynolds number, defined in any convenient way, at leastan order of magnitude smaller than that of an actual furnace. However, provided that both flows arefully turbulent, and viscous effects at walls are not important, the Reynolds number should not be asignificant parameter, and the velocity at which the model is run can be set for the convenience ofthe test apparatus and not to satisfy any similarity requirement.Jets become turbulent at quite iow Reynolds numbers so there is no concern over the initialstate of the jets entering the cavity of the model. Round, simple turbulent jets have an effectiveturbulent viscosity which decreases in the streamwise direction so that the ratio of effective tomolecular viscosity decreases along the length of the jet, and reverse transition to laminar flow willultimately occur. For a jet in a surrounding stream which is itself turbulent, the point at whichmolecular viscosity, and hence Reynolds number, becomes important, is difficult to estimate. At6some point in the boiler flow near the outlet, the flow may re-laminarize, but there have been noindications in this experimental study that the flow is anything but turbulent for locations at orbelow the builnose. Tests were completed with identical flow percentages between port levels, butdifferent Reynolds numbers. Results of the test, which will be discussed in §5.1.1, showedcomparable non-dimensional velocities, within experimental accuracy, for the two Reynoldsnumbers.In the actual furnace, the combustion air enters at a temperature of approximately 15OC,while the temperature in the furnace is about 1OOOC. The density change which the combustion airin the full-scale furnace undergoes cannot be simulated in an isothermal water model. The modelports in the Plymouth model are scaled using the same size ratio as the boiler itselE With subscripts“p” and “v’1 denoting port flow and vertical cross-flow respectively, if the mass flux ratio betweenvertical and port flow is maintained between the full-scale and model, the ratio of velocities betweenmodel and full-scale is:(Ui i I’. vJ full-scale p) full-scale v modelBecause this relationship uses ratios rather than absolute velocities, at least one velocity in thefull-scale boiler must be known before the model results may be scaled. For a typical experimentalrun in the model, the expected bulk vertical velocity is approximately 5 cm/s. Typical port velocitiesin the experimental model are shown in Table 1.2.1.Table 1.2.1 Typical Port Velocities in Plymouth Recovery Boiler ModelPort Name Typical Velocity [mis]Primary 2.2Starting Burner 0.8Secondary 3.4Tertiary 6.8Load Burner 2.07This scaling arrangement used does not permit the ratio of momentum between port andvertical flows to be preserved between model and full-scale. When momentum flux is preserved byappropriate enlargement of the ports, jet trajectories should scale between model and full-scale.Experiments have been successfully conducted using such scaling criteria (Perchanok, Bruce, andGartshore 1991); however, the present geometric port scaling arrangement was a legacy from theconstruction of the Plymouth model and could not be changed.1.2.2 FrequenciesThe velocity frequencies observed in the model may also be translated to full-scaleequivalents. The non-dimensional frequency may be defined as the Strouhal numberfL( this non-dimensional number between model and full-scale.ñ,ll-scale 1JfulIscaJe Lmodel= 11 r ( “model Lfullsca1eEquations and may be combined to form.ñxll-sc2le Lmodel (UfUllSCe”1 1’”1model ull-scale model }p pvJ full-scaleFor a typical total flowrate in the Plymouth boiler model of 150 Us gallons per minute, assumingflu-scale boiler air temperatures of 1000°C and 150°C for interior and port flows respectively, full-scale total air flow of 1012 pounds per hour, and secondary port velocities, this ratio may beestimated ashsi1-scaie (1 (68.2(0.837odel i28)3.4 )1\O.277,) 2.16 ( APPARATUS2.1 Plymouth Recovery Boiler ModelAn experimental flow facility has been constructed at the UBC Pulp and Paper Centre inwhich water models of kraft recovery boilers may be tested. Up to two models may be tested in thefacility at a given time. The focus of the present experimental study is a 1:28 scale model of a boilerlocated in Plymouth, North Carolina, originally commissioned by Combustion Engineering (flowAsea Brown Boveri). The second model is of a recovery boiler in Kamloops, British Columbia whichwill not be considered here.A centrifugal pump draws water from a 5600 litre reservoir, sending it vertically into threeheader pipes feeding the primary, secondary, and load-burner or tertiary model ports respectively.Gross flow control is achieved by adjusting four gate valves which control the bypass line and theflow into each of the three headers. A total of 59 lines of 1.6 cm diameter flexible hose eachtransport water from the header pipes through a valve and an orifice-plate flowmeter. The hosesthen lead to manifolds feeding between four and nine ports each, with the exception of the loadburner ports which are connected direcdy to the headers. To set a given flow condition, a portabledifferential pressure meter is ‘attached to each orifice-plate in turn and the corresponding valveadjusted to achieve the desired flowrates. A plan view of the experimental facility is shown in Figure2.1.1.9Figure 2.1.1 Recovery Boiler Water Model Experimental FacilityThe arrangement of the Plymouth recovery boiler model is shown in Figure 2.1.2, which isdrawn to scale. The full-scale boiler is approximately 43 metres high, has a square cross-section of 11metres per side, and employs one liquor gun at the centre of each wall. The model is constructed of4.8 mm thick Plexiglas, and all ports present in the full-scale boiler are modelled. The floor of themodel is flat, as in the full-scale furnace. Liquor flow into, and smelt flow out of, the boiler are notmodelled. It is assumed that the mass flux of each is approximately equal, and any influence of theliquor droplets or their combustion products on the flow patterns or velocities is neglected. Arepresentation of the char bed is not included in the model. The three horizontal levels showndesignate the planes on which laser velocimetry measurements are made.10The arrangement of the Plymouth recovery boiler model is shown in Figure 2.1.2, which isdrawn to scale. The full—scale boiler is approximately 43 metres high, has a square cross-section of 11metres per side, and employs one liquor gun at the centre of each wall. The model is constructed of4.8 mm thick Plexiglas, and all ports present in the full-scale boiler are modelled. The floor of themodel is flat, as in the full-scale furnace. Liquor flow into, and smelt flow out of, the boiler are notmodelled. It is assumed that the mass flux of each is approximately equal, and any influence of theliquor droplets or their combustion products on the flow patterns or velocities is neglected. AFigure 2.1.2 Plymouth Recovery Boiler Arrangement11representation of the smelt bed is not included in the model. The three horizontal levels showndesignate the planes on which laser velocimetry measurements are made.A total of four starting burners are located at the corners of the front and rear faces at theprimary air port level, angled in a horizontal plane towards the centre at 25° from the perpendicular.Primary air ports on all four walls are angled down 100 from the horizontal while secondary air portson all four walls are directed straight into the boiler. The third level of flow may use one of two portsets: load-burner (sometimes referred to as high-secondary) air ports which are directed along thetangent of an imaginary horizontal circle located above the liquor gun level, or directly opposedtertiary air ports on the front and rear walls. The model ports are summarized in Table 2.1.1, andillustrated in Figure 2.1.3. The model primary ports were constructed larger than required for theoverall scale, so two strips of 1/32” stainless steel was bolted to the inner wall of the model,symmetrically above and below the primary ports. The plates were separated by a vertical gap of0.23” inch, changing the primary port shape to a rectangle, and maintaining the proper scale.Table 2.1.1 Plymouth Recovery Boiler Model PortsPort Name Number Area (in2) CommentsPrimary 156 0.0 144* Vertical rectangle angled down 10°Starting Burner 4 0.066 1 Vertical oval angled to centre at 25°Secondary 66 0.0262 Vertical ovalTertiary 28 0.0262 Vertical ovalLoad Burner 10 0.3526 Circular*-After accounting for adjustable plate opening12CR5SECONDARY & TERTIARY PORTSH 25 (TYP)CR5__0Figure 2.1.3 Plymouth Recovery Boiler PortsHeights above the boiler floor of the measurement levels, port centres, and liquor guns areshown in Table 2.1.2 for both model and flu-scale.Table 2.1.2FeaturePrimariesStarting BurnersSecondariesLiquor GunsTertiariesLoad Burners*Level 1Level 2Level 3Plymouth Recovery Boiler Feature ElevationsHeight Above Boiler Floor [mlModel Full-Scale0.042 1.190.051 1.430.108 3.020.242 6.780.316 8.860.383 10.720.256 7.160.546 15.290.705 19.74•O.O78 ± O.005LOAD BURNER PORTS± O.005.—lSIDE VIEWPRIMARY PORTSFRONT VIEW± O.OO5 CR5PLAN VIEW FRONT VIEWSTARTING BURNER PORtS*- N.B. Top load-burner; for each lower port subtract O.0295m (model scale)132.2 Water Flow SystemsEquipment necessary for running, and measuring the flowrates into, the model flow systemare summarized in Table 2.2.1. The measurement range of the D7 orifice-pLate is from 1.0 to 7.5US gallons per minute, while the B9 models are capable of measuring from 2.0 to 12.5 US gallonsper minute.Table 2.2.1 Water Flow System ApparatusQuant. Name Description Manufacturer Model1 Motor 30 kW AC Electric Motor U.S. Electrical RC-1Motors1 Pump Centrifugal Pump Bingham22 Orifice-Plate Orifice-plate flowmeter Gerand D723 Orifice-Plate Orifice-plate flowmeter Gerand B91 Meter Differential pressure meter Gerand M- 125calibrated for B9 and D7orifice-plates2.3 Argon-Ion LaserThe apparatus used in the operation of the argon-ion laser, either for laser-Doppler orparticle image velocimetry measurements, is detailed in Table 2.3.1 The laser is configured formultiline operation, and is rated for five watts total output, but has typically produced up to 6.8watts. With the laser at full power, the three wavelengths available for LDV use are respectively ratedat: 476.5 nm - 0.60 W, 488.0 nm- 1.5 W, 514.5 nm - 2.0 W. Beam diameter is specified as 1.5mm with a divergence of 0.5 mrad.14Table 2.3.1 Argon-Ion Laser ApparatusQuant. Name Description Manufacturer Model1 Laser 5-Watt Argon-Ion Coherent Innova 70-5Continuous-Wave Laser1 Power Meter Broadband Power/Energy Melles Griot 1 3PEMOO 1Meter2 Mirror 4)25mm mirror wI Maxbrite Melles Griot 02-MPG-coating 007/0012 Mirror Holder 4)25mm kinematic type Melles Griot 07-MHT-0012 Mounting Post 4)12 mm, L=6Omm Melles Griot 07-RMH-0022 Post Holder 4)12 mm, L=5Omm Melles Griot 07-PHS-0132 Base square, ¼-20 thds Melles Griot 07-RPC-0121 Optical Table 2’x6½’ optical mounting Newport CS-26-4bench1 Collimator 1.1:1 Collimator TSI Inc. 91081 Water Filter 5-tim Water filter Envirogard Prod. FC-1002.4 Laser-Doppler VelocimeterThe main pieces of equipment needed for acquisition of velocity measurements using laser-Doppler velocimetry, in addition to the laser apparatus listed in Table 2.3.1, are shown in Table2.4.1. The LDV is capable of measuring two components of velocity simultaneously, and is capableof being expanded to measure three components with the addition of a second probe. The beamfrom the laser enters the Colorburst and is split into two laser lines of 514.5 and 488.0 nm. Eachline is split again, and one is shifted by a user-selected frequency. The four beams then are directedinto single-mode polarization-preserving optical fibres via appropriate fibre-optic couplers. Thefibre-optic cable is connected to the portable barrel probe. This probe focuses the beams to a waist atthe measurement volume, and receives light scattered by the particles passing though themeasurement volume. The separation of the beams and focal length of the probe are 50 and 350mm respectively.15Table 2.4.1 Laser-Doppler Velocimeter ApparatusQuant. Name Description Manufacturer Model1 Colorburst Multicolour beam separator TSI Inc. 92014 Coupler Polarization-preserving fibre TSI Inc. 9271optic coupler1 FIND Software for controlling TSI Inc. Ver. 3.5.3processors and Colorlink2 Processor Burst-correlator processor TSI Inc. IFA 5501 Computer Intel 486DX compatible V-Com 486-331 Probe 2-component backscatter TSI Inc. 9832transmitting & receivingprobe1 Colorlink Photomultiplier tubes & TSI Inc. 9230bandpass filtersThe back-scattered light received by the probe is transmitted by another fibre-optic cable tothe Colorlink device. Here each laser line is separated and sent to a high voltage photomultipliertube for amplification. The signal is bandpass filtered and the shift frequency removed, leaving theDoppler signal. The signal from each channel is sent to a separate processor unit. An autocorrelationis performed on the signal, and if 8 successive zero-crossings of the signal correlate, it is considered atrue Doppler frequency. If not, no measurement is considered to have been made. The Dopplerfrequency, and the time between measurements points, are sent to the computer via the FINDsoftware program.The measurement volume of a laser-Doppler velocimeter is ellipsoidal in shape, thedimensions of which may be found as (Fingerson et al 1991)4f)dmd (2.4.1)dm (2.4.2)m42sinsc (2.4.3)d(2.4.4)16where d_2 = laser beam diameter4 fringe spacingdm = measurement volume diameterf = frequency= measurement volume length= maximum number of fringesIc = half angle between laser beams of same frequencyA = wavelengthFor the two laser velocimeter components used, parameters of the measurement volume aresummarized in Table 2.4.2, which assumes that the collimator is not in use.Table 2.4.2 Measurement Volume Parameters488.0 nm 514.5 nmdm 145.0 pm 152.9 pm2.03mm 2.14mm4 3.4pm 3.61 pmfr 42 42n3 n2 niIdFigure 2.4.1 Beam Focal Point Location17The measurement location of the focused laser beams within the water model is shown inFigure 2.4.1. Only one beam is shown; the probe is located to the right with the beam pointingtowards the left. The dotted line shows where the beam would cross the probe centre-Line ifmeasurements were made in air only. The location of the measurement volume depends on theprobe focal length in air, the separation of the beams, the indices of refraction of the mediums thebeams pass through, the wall thickness of the model, and the distance the probe is placed from themodel outside wall. The distance the probe should be located from the model wall, as a function ofthe measurement volume distance inside the model may calculated by application of SnelUs law ash=€4 tan K1 +4tanK2t4ta3-1 (n. -1IC1 = I — I K2 = Sifl I — Sin K1 K = Sin I — Sin K) 3 2— tan K2— d3 tafl K3so€4 = (2.4.5)tan icwhere 4 = horizontal distance beam travels in medium i4 = probe focal length in airhf = ½ beam separation distance= vertical distance beam travels in medium i= refractive index for medium i= beam half-angle in medium iThe following values apply to the apparatus used in the measurements:n1 = 1.00 (air) 4 9.525 mm (3/8”)= 1.50 (Plexiglas) hf= 25 mm= 1.33 (water) 4= 350 mmFor example, if€4 is to be 60 mm,€4 should be made equal to 298.6 mm.182.5 Particle Image VelocimetryVelocity measurements made by particle image velocimetry require the apparatus listed inTable 2.5.1, in addition to the laser equipment shown in Table 2.3.1. The core diameter of thefibre-optic cable is 2O04m, and the doped silica cladding has a diameter of 25Ojim. The glass/glassconstruction makes this fibre more suitable for high-power handling than plastic-clad silica fibres. Atargon-ion laser wavelengths, the attenuation of the fibre is approximately 18 dB per kilometre. Themicroscope objectives focus the beams to a waist of size roughly equal to the transmitting fibrediameter. Using a higher magnification objective could cause the laser beam to exceed the energydensity limitation of the fibre. A concave cylindrical lens was used to eliminate the hazard caused bythe focal point created by a similar convex lens. The fibre-optic positioner used has only twotranslational degrees of freedom, limiting the practical coupling efficiency to about 40 percent. Thismight be improved through the addition of a tilt-stage to the positioner, adding two angular degreesof freedom.Table 2.5.1 Particle Image Velocimetry ApparatusQuant. Name Description Manufacturer Model2 Fibre-Optic Fibre-optic positioner with Newport F9 1 5T-DJPositioner Delrin jaws2 Microscopic 5:1 Microscopic objective Newport M-5XObjective for fibre-optic coupler1 Optical Fibre Multi-mode enhanced Newport FC-2UV-10transmission fibre [lOm]1 Cylindrical Lens Piano-concave optical glass Newport CKVOO6AR. 14with anti-reflection coatingF.L. =—6 mm, L=25 mm1 Lens Mount Cylindrical lens mounting Newport LM-1ring1 Bracket 900 angle bracket Newport 360-901 Video Recorder S-VHS Video Recorder Sony SVO-9500MD1 Digitizer Imaging Board Sharp GPB-11 Video Camera S-VHS Movie Camera Panasonic AG-455P1 Tripod Heavy-duty tripod & head Hercules 5302/522 11 Optical Rail lOOxSOOmm Newport 07-ORP-0031 Rail Carrier lOOx65mm Newport 07-OCP-003193. EXPERIMENTAL PROCEDURES3.1 Water Flow System CalibrationEarly experimental results recorded in the Plymouth boiler model displayed a tendency forthe core region of vertical flow to be near the front-left corner of the boiler (Ketler, Savage, andGartshore 1993), and will be discussed further in 5.l.1. A manifold feeding secondary ports in therear-right corner was subsequently found to be permitting an additional 10% of the total secondarymass flow into the boiler due to a faulty orifice-plate flowmeter. This finding emphasized thesensitivity of the model to any secondary flow imbalance, and the importance of being able to set theport flowrates accurately. A statistical test of the flow errors was therefore initiated for each of the 59orifice-plate/valve packages used in the facility.During an experimental run, flowrates are measured by connecting a portable differentialpressure meter across each orifice-plate in turn. The meter measures pressure differential, but has adial calibrated by the manufacturer which reads in US gallons per minute. The error in a portflowrate is=fi ( time) or 8toral fi2 (6meter’ 6drift) (3.1.1)where 8meter refers to the error between the meter reading and the true flowrate, which may be afunction of time, and 8drjft measures the change in the meter reading, which may be a function oftime and the flowrate set. The expected values and variances of each error may be separatelydetermined through experimentation and statistical analysis. Where E is the expectation operator,the variance of a function Tof k random variables°l••’0kmay be found as (Bury 1986, 159)var(T) or or (3.1.2)i=i oE{O } oE{O }If k= 2, then20(aT 2 (OT”2var(T){ ] var01 oE{o}J var02+I or ( or2{}JoE{o2}]. COV(o, O) (3.1.3)To demonstrate the effects of the two types of orifice-plate error, an example scenario is shown inTable 3.1.1.Table 3.1.1 Example Flow ConditionTime Meter Reading [US gpm] True Flowrate [US gpmj0 5.00 = 4.851-8jftlO%1-1 4.50 = —2.22% 4.40In this example, the flowrate is set at five gallons per minute at time 0, when the meter erroris —3%. After some interval, time 1 is reached, when the drift error is —10%. However, the metererror has now changed to —2.22%. The overall error at time index 1 is therefore(1 — .10)(1 — .0222) — 1 = —0.12. Note that the errors cannot be simply added; rather the twosources of error compound. ThereforeE{8 }=E{e }+E{s }E{c. }+E{8. } (3.1.4)total meter meter drift driftIf we assume that coy = 0, from Equation 3.1.2meter drift jvar(e0al) (i + 6drifr)2. var() + (i + 8meter )2 . var (Sd f) (3.1.5)where Emeter is taken at the meter reading to which the flow has drifted to after the specified time,and 8drjft is taken at the original meter reading. The total error may increase or decrease as timeprogresses following the setting of the flow. Assuming that the absolute value of the drift errorincreases with time, and assuming nothing about the sign of the error218tot Lax = £meter 8meter + EmererEdrift + Ejfwhere liii indicates that the maximum of the contents should be taken.3.1.111109E. 8C)0D 760LL0a) 40a)a) 320Meter Error(3.1.6)The meter error of each orifice-plate used with the Plymouth boiler model was measured inthe experimental facility. The model was modified so that the model flow oudet to the reservoir wasremoved and replaced with a hose emptying into a closed cylindrical column which had beenaccurately calibrated to a capacity of 12.0 US gallons. All valves except for the bypass were fullyclosed, the pump was turned on, and the system was purged of air. After confirming that theflowrate into the calibrated column was zero, one valve was turned on. The differential pressuremeter was attached across the orifice-plate meter connected to the opened valve. The valve was thenset to a number of flowrates as measured by the meter, and the times to fill the column wererecorded and converted to flowrates. Figures and show the mean values, and themeans plus or minus 3 standard deviations, of the measured flowrates for each set value..:z:.. z.:::z .:2z II0 1 2 3 4 5 6 7 8 9 10Set Flowrate [US gpm]11229876E4A number of statistical distributions were postulated to model the data, and preliminaryprobability analysis revealed that the Weibull distribution would be a suitable choice. The B9orifice-plate flowmeters were well represented by the two-parameter model, while the three-parameter model was required to adequately represent the data from the D7 flowmeters. The three-parameter model employs a location parameter which gives a lower bound to the model. This maybe required due to the fact that many measurements on the D7 scale were very close to theminimum measurable flowrate of the orifice-plate.Weibull parameters were estimated using maximum likelihood equations, and are detailed inAppendix A. Expected values and standard errors (square root of the variance of the expected value)of the Weibull models, for each set flowrate, are shown in Tables and Values havebeen converted to percentages of the set flowrates.ECoDI....-:z:zzzzz::.EEfE32100 1 2 3 4 5 6 7 8 9Set Flowrate [US gpmlFigure Measured versus Set Flowrates- D7 Orifice-Plates23Table Orifice-Plate Meter Error- B9Set Flow [US gpm] E{Meter Error} [%] SE(Meter Error) [%]2.5—4.608 4.7323.5—1.676 4.2054.5 2.130 3.2166.0 5.033 2.4427.5 6.164 2.2119.0 7.125 2.413Table Orifice-Plate Meter Error- D7Set Flow [US gpm] E{Meter Error} [%] SE(Meter Error) [%]1.5—0.962 2.1172.0 0.404 2.0482.5 4.881 2.0723.0 6.076 1.8144.5 8.972 2.1476.0 9.613 2.2737.5 10.435 2.096Expected values and standard errors of the meter error for any set flowrate may beinterpolated from the above tables. For the meter error of an entire boiler model flowrate, theexpected value may be geometrically averaged. The standard error of the meter error of the entireflow may found through geometric averaging of the variances, again assuming that the covariancesare zero.From the expected error values and the measured versus predicted figures, it is seen that themeter error is negative for low flowrates, and positive for higher flows. It appears that the factorycalibration as shown on the meter scale is incorrect in both intercept and slope. This deviationbetween the manufacturer’s calibration and the data presented here may be related to the particularinstallation in the experimental facility.243.1.2 Drift ErrorThe drift error was measured using the same experimental arrangement as described in§3.1.1. A flowrate typical used in a LDV run of the Plymouth model was chosen for each orifice-plate type. All of the valves connected to B9 orifice-plates were set to 3.5 US gpm as read by thedifferential pressure meter, while those valves attached to D7 orifice-plates were set to 2.5 US gpm.This arrangement provided a uniform starting point for each flowmeter, at approximately the samepercentage of the full-scale reading. However, any dependence of the drift error on the set flowratewas assumed to be insignificant. The flowrate as displayed on the differential pressure meter, foreach orifice-plate, was recorded at discrete time intervals over approximately 7.5 hours, whichapproximated the length of an experimental run. Flowmeter readings as a functions of time for theB9 and D7 orifice-plates are shown in Figures and 60 120 180 240 300 360Time Since Flowrate Set [mm.]420 480Figure Flowmeter Reading versus Time - B9 Orifice-Plates25E(I)DD)Ca)a)ELLProbability analysis revealed that the Weibull distribution would adequately represent thedrift error. Weibull model parameters for the drift error data were estimated using maximumlikelihood equations, a scale parameter again being necessary for the D7 data. Expected values andstandard errors of the drift error for the B9 and D7 orifice-plates are shown as percentages in Tables3.1.2.1 and Orifice-Plate Drift Error- B9 (3.5 US gpm Set)Time Since Set [mm] E{Drift Error) [%] SE(Drift Error) [%]73.0—5.538 6.077147.5—6.377 6.566221.5—6.834 6.589299.0—8.062 8.386372.5—9.528 8.203447.5—8.867 7.711432I0. Ill,. llli ll l Ill il• trill li• Ill illl0 60 120 180 240 300 360 420Time Since Flowrate Set [mm.]Figure Flowmeter Reading versus Time- D7 Orifice-Plates48026Table Orifice-Plate Drift Error- D7 (2.5 US gpm Set)Time Since Set [mini E{Drift Error} [%] SE(Drift Error) [%J73.0—12.258 8.900147.5—14.253 9.188221.5—14.712 9.922299.0—17.511 12.118372.5—21.690 16.604447.5—24.703 19.855It is seen that the drift error increases with time, and that the D7 drift errors are substantiallyhigher than those for the B9 orifice-plates. The expected values are all negative, and increase themost shortly after the flows are set, reaching an approximately asymptotic value as time increases.The variance of the drift error increases with time, particularly for the D7 orifice-plates.3.1.3 Error Calculation for Typical Experimental RunTo estimate the total meter flowrate error in a real experimental run, consider Table number and type of orifice-plates set to each flowrate are shown, along with the expected valueand standard errors of the flowrates assuming only meter error to be present. This corresponds to thecase immediately after setting the flows for an experimental run, before enough time has passed forany of the valves to drift from their set values.Table Meter Errors for Typical Run - No DriftOrifice Number of Set Flowrate E{Flowrate} SE(Flowrate)Type Orifices-Plates [US gpm] [US gpmj [US gpm]6 2.73 2.628 0.1249B9 12 3.64 3.603 0.14681 6.00 6.302 0.14654 8.62 9.216 0.204210 1.82 1.820 0.03764D7 4 2.12 2.155 0.043564 2.65 2.790 0.052594 3.05 3.240 0.0558227The tabulated data corresponds to the flow condition of Run 21, which had a total flowrateset to 150 US gallons per minute, and used primary, starting burner, secondary, and load burnerports. Considering meter error only, the expected value of the total flowrate is 153.11 US gallons perminute, or 2.07%. From Equation 3.1.2, the standard error of the total flowrate is then 2.15 USgallons per minute, or 1.43%.Table Meter Errors for Typical Run - After DriftOrifice Number of Set Flowrate Meter Reading E{Flowrate} SE(Flowrate)Type Orifice-Plates [US gpml after 73 mm [US gpm] [US gpm][US gpm]6 2.73 2.58 2.469 0.1206B9 12 3.64 3.44 3.378 0.14541 6.00 5.67 5.927 -0.14614 8.62 8.14 8.679 0.187710 1.82 1.60 1.590 0.03360D7 4 2.12 1.86 1.862 0.038384 2.65 2.33 2.413 0.048124 3.05 2.68 2.824 0.05275The addition of drift error to the equation requires that the meter errors be calculated at themeter reading drifted to, not the value set to. Assuming that the flow was reset at least every 73minutes, the values in Table show the resulting flowrates from meter error only, but afterhaving drifted. Percentages are based on the meter reading at the given time.After the valves have been allowed to drift for 73 minutes, the cumulative meter readingstotal to 138.47 US gpm, or —7.69%, with standard error of 2.81%. The expected value andstandard error of the true total flowrate are 140.29 and 2.09 US gpm respectively. This translates toexpected value and standard deviation of the meter error after drift, based on the “drifted” meterreadings, of 1.3 14% and 1.5 10% respectively.Using the above total meter and total drift errors along with Equation 3.1.4, the expectedvalue of the total error is —6.48%. From Equation 3.1.5, the standard error of the combination is3.17%. This is a larger error than the meter error alone before drift is accounted for, and should be28taken as an upper bound on the port flowrate error during an experimental run. Meter and drifterrors for the typical run of 150 US gpm set total flowrate are summarized in Table Summary of Flowrates for Typical Run (150 US gpm)Errors Expected Value Standard ErrorConsidered [US gpm] [%] [US gpm] [%]Meter Only 153.1 2.07 2.15 1.43Meter & Drift 140.2—j48 4.75 3.17Using the central limit theorem for large samples, confidence bounds my be found on thetotal error using the standard normal distribution z = (x — u)Icr where the parameters p and a aregiven by Efe0}and \Jvar(ç,) respectively. Considering meter error only, for a typical run of 150US gpm set total flowrate, a 95% confidence interval for the expected value of the total flowrate isgiven by (148.9, 157.3) US gpm or (—0.9%, +4.9%) error. If both meter and drift error areconsidered, for a typical run of 150 US gpm set total flowrate, a 95% confidence interval for theexpected value of the total flowrate is given by (130.9, 149.5) US gpm or (—12.7%, —0.3%) error.293.2 Laser Doppler Velocimetry3.2.1 Experimental ArrangementsThe laser-Doppler velocimeter used for making measurements was a two-componentdifferential beam system using a burst-correlator processor as detailed in 2.4. A continuous-waveargon-ion laser was used as the coherent light source. Vertical and horizontal velocities, includingnegative and near-zero velocities, may be measured simultaneously at any point within the model.The experimental arrangement is shown in Figure Compatible486 ComputerArgon-IonLaserFibre OpticCouplersFibresColorlinkIFA 550 #11FA550#2Transmitting andReceiving ProbeRecovery BoilerWater ModelFigure Laser Doppler Velocimetry Experimental Arrangement30The flow was not seeded with artificial particles to enhance data rates. It was found thatunfiltered tap water possessed suitable scattering particles of approximately 10-50 jim in diameter.With natural seeding, data rates of between 50 and 5000 samples per second were attained,depending on the laser power, optical efficiency, and measurement location within the model. Tomaintain adequate laser power at the model, it was necessary to realign the fibre-optic couplers usingthe laser power meter prior to, and during, every run. The software which controlled the processorsdid not permit selection of measurement times, but only the total number of Doppler burstsbetween the two processors. This required that the approximate data rate be observed at eachlocation, and the sample size adjusted to approximate the desired record length.The measurement duration was desired to be approximately two and one-half minutes,which was chosen to obtain a suitable mean value in the presence of very low frequency oscillationsin the velocity. However, as the software was written for the DOS operating system, the maximumnumber of data points per measurement was limited to about 30,000. In order to stay within thislimit, the laser power often had to be reduced, sometimes to minimum levels, to lower the data rates.Data rates could also be modified by selecting different bandpass filters in the Colorlink processor ofvarying gains, but which still bracketed the expected Doppler frequencies. This procedure did notaffect the actual velocities measured but only the signal to noise ratio of the Doppler signal.Simultaneous measurements were made of the instantaneous velocity components in the xand z directions, as defined in Figure 2.1.1. Mean and root-mean-square velocities were found byaveraging the data over the entire length of the data record. Nominal port exit velocities wereapproximately 0.8 mIs for the starting burners, 2.2 m/s for the primaries, and 3.4 m/s for thesecondaries. ‘When in use, nominal port velocities were 2.0 m/s for the load burners, and 6.8 m/s forthe tertiaries. To permit comparison of results to those from computational fluid dynamics, all runsfollowing Run 6 were made with the Plexiglas plates which model the screen tubes and boiler tubebanks removed.31Two-dimensional velocity information was obtained on three different horizontal planes of36 points each, as shown in Figure 2.1.1. Horizontal planes were divided into 6x6 grids of equalarea, the centre of each being the measurement location. These levels are seen to be near the liquorguns, above the load burners, and below the builnose. It was necessary to interrogate the model fromtwo sides in order to obtain sufficient data rates at all points. Cleaning the model walls and tuningthe optics was helpful in increasing data rates, but measuring 6 rows deep into the model from oneside was never possible in the Plymouth boiler.x000Xxx0000XxxFor those runs in which thetertiary ports were used, thearrangement shown in Figure3.2.1.2 was used. This grouping ofports effectively generates a 2x2interlaced arrangement, with a slightX — PORT CLOSED.clockwise swirl component, asO — PORT OPENviewed from above.xx xxooo ox xoooxFRONTFigure Tertiary Port Arrangement323.3 Laser Sheet Illumination3.3.1 Experimental ArrangementsUsing the same laser as for the LDV, a separate fibre-optic cable brought laser power to theboiler model to be spread into a sheet of approximately 3 mm thickness by a cylindrical lens, asshown in Figure This laser sheet was used to illuminate sections of the model to permitobservation and recording of the flow patterns. For this purpose, the water was seeded withpolystyrene latex spheres of approximately 300 jim diameter, and specific gravity of 1.05. The sheetcould either be oriented to enter the boiler model though one of the side walls, or through the clearmodel bottom. The coupling efficiency between the laser itself and the output of the cylindrical lenswas approximately 40 percent, so nearly three watts of laser light could be presented to the modelwith this system.Recovery BoilerWater ModelArgon-IonLaserFibre OpticCouplerCollimatorCylindricalLensOptical Fibre S-VHS Video Camera LightSheetFigure Particle Image Velocimetry Experimental Arrangement333.3.2 Recording MethodsThe movement of the polystyrene spheres in the flow was recorded using a Super-VHS (SVHS) camcorder which had a lens system optimized for low-light situations. A tripod was requiredto stabilize the camera at slow shutter speeds. Through trial and error, the optimum shutter speedwas found to be either 1/00 or 1/60 second, with the aperture fully open. Laser powers of 0.5, 1.0,and 3.0 watts were used.The entire system was checked for distortion error by photographing a square 8.5” on a sidewith the camera, and then digitized. The number of pixels in the x and y direction were 353 and361 pixels respectively, for a distortion error of 2.22 percent. This distortion error was consideredsmall enough to neglect when calculating the u and v velocities.3.4 Particle Tracking AccuracyThe accuracy of both laser-Doppler and particle-image velocimetry depend on the ability ofparticles to accurately follow the motion of the fluid. Ideally this means that they should be as smallas possible and neutrally buoyant. As the detectability of a particle is proportional to its size,extremely small particles are not practical. If the motion of the fluid near a particle is expressed as asuperposition of harmonics, AguI and Jimenez (1987) have shown that341Lu) p) 56v (..)where u = instantaneous fluid velocitytXu = velocity difference between particles and fluidp = fluid densityiXp = density difference between particles and fluidd = particle diameter= typical fluctuation frequencyV = kinematic viscosity34In LDV experiments, the sediment in the water is estimated to have diameters of up to5Opm, and specific gravity of approximately 4. Assuming an arbitrary maximum frequency of 10Hz, the error in the velocity would be 0.4 percent. In PIV experiments, the polystyrene latex spheresused have diameters of approximately 300pm, and specific gravity of 1.05. Again assuming a typicalfrequency of 10 Hz, the particle tracking error would be 0.6 percent. This analysis shows that theparticle tracking error may be neglected unless regions of high frequency flow motion areencountered.354. ANALYSIS METHODS4.1 Laser Doppler VelocimetryData taken using the laser-Doppler velocimeter was stored as binary data files (TSI FINDVersion 3.5.3) containing the times required for eight Doppler cycles, and the times betweensuccessive data points. Each raw data file corresponding to one measurement location was analyzedusing the FIND software to create an ASCII file of statistics and a binary file of velocities. Theprogram CONCAT13 was written to perform concatenation of the ASCII statistics files from all ofthe measurement locations from one run into a single file, and is summarize in Appendix C.4.1.1 VelocitiesThe FIND program was run to estimate velocity moments such as the mean, standarddeviation, skewness, and flatness coefficients, excluding data points lying outside U± 3 .S from allvelocity statistics. Bias in the estimates of velocity moments arises due to faster particles havinghigher probabilities of traversing the measurement volume than do slower particles. Methods havebeen proposed for correction of bias in the measured u1 values, using various weighting functions asuin 13i( u = estimator of the n-th statistical moment of the flow‘3j = weighting value for the i-th measurementFor cases of low data rates, such as in the experimental facility used in this research, the mostappropriate choice for the weighting function j3. is the residence time of the i-th particle in themeasurement volume (Edwards 1987). While the IFA 550 processors used are unable to recordresidence times, they do record multiple measurements per particle as a result of the use of frequencyshifting. The number of measurements recorded per particle is inversely correlated with velocity,36reducing somewhat the effects of velocity bias. Ensemble averaging, where j3. = 1 for all i, was usedfor estimation of all velocity statistics in this work. This approach was felt to be acceptable in light ofthe agreement shown in §5.1 between bulk flowrates measured by the orifice-plate flowmeters andthe laser-Doppler velocimeter.For plotting velocity vectors, the program BOILER1 3 was written in the AutoLisp languagefor use with Autodesk Autocad Version 11 or higher. This program takes the concatenated data filesas input, and plots vectors of length proportional to velocity inside a three-dimensional wireframedrawing of the Plymouth boiler. This wireframe drawing is used as a template on which the resultsof each run are plotted. The standard deviation of each velocity component is represented by a crossemanating from the root of each velocity vector. Contour plots of the vertical velocity component,non-dimensionalized by the expected bulk upwards velocity at level three, were generated usingstandard surface-plotting programs, missing points being interpolated from the neighbours. Themeasured bulk upward velocity was calculated as the geometric mean of all recorded verticalvelocities on each plane. This could be compared to the expected bulk velocity ofuIkA ( q accounts only for the flowrate contributed by ports located below the measurement level.Full-scale velocities may be found from model measurements through Equation Turbulence Kinetic EnergyThe kinetic energy in all fluctuating components of velocity may be used as a tool forevaluating the potential for mixing and combustion at a particular location. Although only twocomponents of velocity were recorded at each location, the turbulence kinetic energy may beestimated by assuming that the fluctuating velocity in the y direction is approximately equal to thatin the x direction. With superscript ““ denoting an estimator of the quantity underneath, thestandard representation (White 1991, 405) of turbulence kinetic energy may be modified as37K=(2.uu’+ w’) ( was calculated by the program CONCAT13 from the individual statistics files. Contour plotsof K½ were generated, again non-dimensionalized by the expected vertical velocity at level three, foreach horizontal measurement plane.4.2 Power Spectral DensityOscillations in the flow field may be roughly noted by examining velocity traces. However, aquantitative method of determining the relative energy in the velocity fluctuations as a function offrequency would be preferable. Traditional methods of determining power spectral density requirethat the data be equi-spaced in time, a requirement not met by laser-Doppler velocimetry. Particlesarrive at the measurement volume randomly, and data approximates a continuous signal only incases of extremely high seeding, a condition not possible in the boiler flow apparatus.A number of methods have been advocated for the generation of spectral estimates fromrandomly sampled signals. These include the discretized lag product (Gaster and Roberts 1975), thedirect transform (Gaster and Roberts 1977, Srikantaiah and Coleman 1985), correlation (Mayo1978, Roberts and Ajmani 1986), and fractal reconstruction methods (Chao and Leu 1991). Onereview (Bell 198 1.) of some of these techniques indicates that a variation of the correlation techniquewhich resolves the random times into equidistant time intervals shows the best compromise betweenspeed and accuracy.4.2.1 Direct Transform MethodThe method chosen for computation of power spectral densities for these experiments wasthe direct transform method. ‘While the correlation method may be faster, the direct transform ismore easily implemented computationally, does not suffer from aliasing, and is robust with respectto data dropouts.. With the superscript ““ indicating an estimator of the quantity underneath, thepower spectral density function S(f) of the process is given by Gaster and Roberts (1977)38=)D( )ej22 )D2()]. i=J ( S = power spectral densityf = frequencyV = mean sampling rateT = record duration= fluctuating component of velocity= time at index jD = smoothing window functionThe Hanning function was used as a smoothing windowD() =1— cosjJ ( the record length increases, the variance of the spectral estimate becomes (Gaster and Roberts1977)as T ( coefficient of dispersion of the spectral estimate is therefore of order unity, which is fairly high.Because the laser velocimeter measures the flow velocity at random intervals correspondingto the arrival of particles, the Nyquist criteria is not applicable. Power spectral densities may becomputed at frequencies above the mean sampling rate. The minimum frequency at which spectramay be computed should be related to the length of the record. Generating simulated data records ofa Poisson-sampled normal process, and using the direct transform method, power spectral densitiescomputed at frequencies greater than SIT were found to represent both the height and width ofpeaks accurately. Calculations on the minimum frequency for computation of power spectral densityusing the direct transform method are shown in Appendix B.394.2.2 Computational ImplementationThe computer program SPECTRA21 was written by this author to evaluate the spectralestimator of Equation, and is described in the summary of programs given in Appendix C.The program computes power spectral densities at a user-specified number of frequencies betweenan upper and lower frequency bound. The user inputs the frequency range of interest, number ofspectral estimates, choice of data window (Hanning or none), and the axis style (linear or log forboth abscissa and ordinate). A coarse smoothing algorithm was included which calculates averagepower spectra over a number of frequencies which increase by one for each subsequent logfrequency decade. Computations typically take ten to fifteen minutes to determine the spectraldensities at 500 frequencies from a record of about 20,000 data points from each of two processors.4.2.3 ValidationWhile investigators have reported validation of the direct transform method using simulatedand experimental data, some brief validation of the technique as implemented in the water modelfacility was desired. Two methods were devised for validation; the first being a computationalsimulation of a data record, and the second a physical test using a known frequency. Simulated DataSimulated data records were created in order to test the algorithm as implemented. Thesewere generated by adding three out of phase sine waves and random noise. The resulting functionwas randomly sampled according to a Poisson waiting interval, simulating a real LDV data record.Results of power spectral density analysis of simulated data records are shown in Appendix B. Fan Blade ExperimentTo test the spectral estimate using the actual laser velocimetry apparatus in the laboratory,some sort of reference frequency was needed. A small, alternating-current cooling fan was chosen.‘While not an ideal constant-frequency source, it is a source of a relatively constant velocity whichcan be observed intermittently. This ‘square-wav& signal of zero and non-zero velocity should40provide a frequency close to that of the blade. One shortcoming of this approach is that the signal isnot randomly sampled.A small square of reflective tape was placed on one of the fan blades where there was zerotwist and the radius was 7.0 cm. The fan speed was measured with a digital stroboscope, and foundto be 1800 revolutions per minute, or 30 Hertz. The laser velocimeter apparatus was set up for onevelocity component, the measurement volume being oriented parallel to the blade path. Theresulting data file was analyzed using the FIND and SPECTRA21 programs for velocity statisticsand power spectral density respectively. The plot of computed power spectral density versuslogarithmic frequency is shown in Figure The data record used spanned 6.25 secondswith a mean sampling rate of 648 samples per second. Power spectral densities were computed for atotal of 500 frequencies using a Hanning spectral window, and the resulting data was thensmoothed. The 30 Hertz frequency is clearly visible above the background noise. Harmonics of themain frequency are also seen at 60 and 90 Hertz, but this may be due to the quasi even-timesampling, rather than the power spectral density estimator itself.0.0100.0090.0080.0070.0060.0050.0040.0030.0020.0010.00010 1000100f [Hz]Figure Power Spectral Density versus Frequency - Fan Experiment414.3 Particle Image VelocimetryA limitation of studies made using laser-Doppler velocimetry is that velocities may only beresolved at single point in time. If the flow is steady, averaging over some appropriate durationallows measurements to be made at different places at different times. The flow must also be ergodicif experiments are stopped and then resumed. A method capable of resolving velocities on a grid ofpoints in a plane or volume at an instant of time would be a valuable tool as an addition to LDV.Such a method has been developed for planar velocity measurements by analysis of video recordingsmade using the apparatus described in §2.5 and the arrangements of § Review of Techniques-Many methods and variations of are described in the literature (Adrian 1986) forquantitative measurement of planar fluid flow velocities using optical means. These methods includelaser speckle, streak photography, marker image tracking using photography or holography, andparticle image velocimetry. In general, four things are needed for quantitative flow visualization:illumination, markers, recording, and analysis.Light illumination is typically provided by some sort of laser source. Incandescent sourcescan be used, but suffer disadvantages in their incoherence, large power consumption, and heatgeneration. Very fast pulsed Nd:Yag (Nyodium:Yttrium-garnet) lasers can provide extremely highpowers over short durations (i.e. 13MW over 15 ns). Pulsed lasers may also be made from addingQ-switching apparatus to standard continuous-wave lasers, or by using mechanical beam chopping.Regardless of the laser source used, some form of cylindrical lens is used to turn the laser beam into atwo-dimensional sheet. A spherical lens used downstream of the cylindrical lens may be used to haltthe spreading induced by the angle of the cylindrical lens. Power may be transferred from the lasersource to the measurement volume either through free-air beams via mirrors, or by fibre-opticmeans capable of handling high power levels.42Recording methods may use either film or electronic means to capture the particle motions.Standard reflex cameras are limited to the frame rates capable of high-speed winders. Rotatingmirror or other film motion picture cameras offer high temporal and spatial resolution (>3000 linesper inch), but suffer from drawbacks such as film shrinkage, expense, and the need to transfer theinformation to an electronic media for analysis. Digital video camera recording of the flow isgenerally a preferable alternative. Video camera-recorders such as the Kodak Ektapro system offerlimited resolution (230x 192) but high frame rates of up to 10,000 per second. Low light levels canbe a problem for some charge-coupled-device (CCD) digital cameras, unless they are equipped withan intensifier lens. Cameras which record on S-VHS format tape offer a fairly high resolution (>400lines) but are limited to 30 frames per second. Analog cameras employ interlacing where first theeven, and then the odd, horizontal lines are eachrecorded at 60 frames per second, for an overallrate of 30 frames per second. Combining data from such cameras into a digital format is difficult.The exposure time of any camera must be carefully selected to ensure that blurring of the particles isnot significant, unless the streak method is being employed.Some form of particles must typically be added to the flow in order to reflect light from theillumination source onto the recording media. These particles must have a density which permitsthem to follow the flow with sufficient accuracy and still generate a high signal to noise ratio. Inwater, titanium dioxide and other heavy particles offer good optical properties, but tend to come outof suspension and cover surfaces, undesirable in a complex Plexiglas apparatus. Polystyrene latex(PSL) beads having a specific gravity of 1.05 are often used in water experimental apparatus. Theoptimum seeding density of particles in the fluid is usually determined empirically. As the particledensity is increased, the light attenuated by the water between the camera and the light plane alsoincreases, indicating that an optimum seeding density may exist.Analysis methods must first deal with any directional ambiguity present on the images.Double exposure images offer no indication of the particle direction, and some form of imageshifting may have to be employed between frames. Laser pulses or encoding may be used to show43direction of particle streaks. Analysis methods are typically based on some sort of particle tracking orcorrelation method. The particle tracking method becomes complicated when the particle density,and amount of out of plane movement, increases. The correlation process may be performedthrough optical interrogation of double-exposure images to create Young’s fringes, orcomputationally using digitized single or double-exposure images. The optical Fourier transformrequires the least analysis time per vector, but requires a second laser to generate the fringe patternfrom the film, and an automatic traversing mechanism to make the method practical.4.3.2 Digital Particle Image VelocimetryDigital particle image velocimetry uses sequential, single-exposure images that are capturedusing a digital video camera (Cho and Park 1990). Some of the advantages of this technique includethe lack of any directional ambiguity, and the ability to dispense with particle identification andtracking algorithms. Such images may be analyzed using the digital Fourier transform or cross-correlation method, which are equivalent in principle. On a digital video tape, the brightness of eachelement, or pixel, is recorded as an integer between 0 and 255. If the gray-scale functions of twosuccessive images are represented by g1 (x ) and g2 ( x) thens)=ffg1(x).g2+ s)dx ( identical grid of cells are superimposed on each image, and the integration is carried out for thelocal area enclosed by each sampling cell, in which the velocity is assumed to be uniform. Thisuniform velocity in the cell is defined by the vector s, divided by the image separation time, at whichthe cross-correlation function R is maximized.4.3.3 Computational ImplementationA series of programs have been written by the present author to compute cross-correlationsfor successive image pairs, all of which are summarized in Appendix C. The steps involved in thedigital particle image velocimetry analysis procedure are shown in Figure images have been recorded on a S-VHS tape, sections of interest are digitized using avideo frame grabber unit. The program BUBBLE was developed specifically for this hardware, andaliows the user to define a region of interest on the tape of the fluid motion. The program requeststhe number of successive frames that are to be digitized, and the threshold integer gray-scale value.Within the region of interest on each frame, those pixels with a brightness value greater than thethreshold value are noted, and the coordinates of each pixel are written to a file. The software is ableto automatically advance the tape and scan each frame until the total number is reached. Themaximum resolution of the digitizer is 51 2x5 12 pixels in any frame. The actual pixel gray-scalevalues returned were not used for simplicity of analysis, but could be added in order to increase thesophistication of the technique. This would require the addition of a routine to eliminate biasFigure Digital Particle Image Velocimetry Analysis Procedure45towards the cross-correlation of bright over dim points. Geometric overlapping of cells could also beemployed to increase the number of vector points, at the expense of computational time.The program CCR17 was written to compute the velocity values on a grid of points forsuccessive images, using the binary data file returned by BUBBLE as input. The user supplies thename of the input data file, the recording rate in frames per second, the window width in metres,and the desired number of cells in the x and y directions, which may differ. The program reads intomemory the coordinates of the pixels which are ‘on’ for the first two images. The information fromeach frame is then subdivided into an appropriate grid of cells, and the cross-correlation function Ris computed for each cell. To limit computational times, the maximum displacements within eachcell must be less than half the width or height of the cell. The maximum value of R is then searchedfor within each cell. The displacement in the x and y directions corresponding to the maximumvalue of R within each cell s and Sy, the frame rate, and the window width in metres, are used to findthe actual velocities in metres per second. When the function R has two or more equal peaks withina cell, the maximum is found through linear interpolation.Accuracy of the calculated velocity is limited by the physical size recorded on each pixel, andcould be improved through the use of curve-fitting functions applied to the R function, which is notdone at this time. The number of cells that the measurement window may be subdivided into islimited by the search algorithm for the R maxima. The maximum x and y distance covered by amoving particle between frames must not be more than half the cell width and height respectively.Computational time is proportional to the number of ‘on’ pixels in an image, the number of cells,and the area of each cell. A large number of small cells requires less computation time than do fewvery large cells. For a typical digitization of the full 51 2x5 12 pixel window size, the time to computevelocity vectors on a lOxlO grid is approximately 10 minutes on an Intel-based 486 computer. TheCCR17 program then outputs an ASCII file which contains the location of the centre of each cell,and the velocity for each cell for each image pair. Measures of the cross-correlation signal-to-noiseratio, R value, and the number of peaks are also contained. The entire R function may be includedin the output if requested.464.3.4 Temporal SmoothingThe resulting velocity data computed at every 1/30 of a second may be quite turbulent, andmay need temporal smoothing prior to plotting or animation. The program IMGAVG was writtento average output files from CCR1 7 using a sliding window format of variable length and stepsize.The length of the averaging window is the number of consecutive image pairs to include in theaverage. The stepsize is the number of image pairs to advance before creating a new average. Theentire record of analyzed images may be averaged to find a grid of mean velocity vectors over thattime.4.3.5 AnimationThe averaging program, IMGAVG, provides output for each averaged image frame in anASCII format compatible with the TECPLOT program. Each frame may be viewed on the screen,or plotted on the printer, as vectors of length proportional to velocity. A macro file has been writtenwhich will, running under TECPLOT, automatically create a raster metafile containing informationon each frame. The raster metafile may then be animated with the program FRAMER The framerate at which the raster metafile may be played back depends on the hardware, an R4000 basedSilicon Graphics workstation being capable of approximately 6 frames per second.4.3.6 ValidationIn order to gain confidence in the ability of the cross-correlation technique to provideaccurate velocities, a validation method was devised. A program was written which generated asimulated image of pixels at random locations, corresponding to a given seeding density. Theprogram then generated a second image, which shifted the pixels in the first image as if they were ina forced vortex U= cor. The simulated images of a forced vortex flow are shown in Figure a flow case is a non-trivial test of the analysis algorithm, due to the large range of velocitiescontained in the images.47Image 0 Image 1Figure Simulated Vortex Flow ImagesThe rotational speed of the simulated vortex was chosen as 617 revolutions per minute withan image separation time of 1/30 second. This was calculated to the be the limiting speed to permitanalysis on a lOxlO grid of cells, keeping the maximum particle displacement between images withinthe limit of ½ the cell width or height. The window size was 512x512 pixels, and the number ofilluminated pixels was two percent of the total. Results of the cross-correlation analysis of the twosimulated images are shown in Figure / ,_r—t I, — —- \ \t IL t I i/\ \-.- / / Ie/ / /Figure Results of Cross Correlation Analysis for Simulated DataIt is seen that the velocities calculated by cross-correlation represent the real flow withreasonable accuracy. This is the case even in the image corners, where many of the simulatedparticles in the first image are not present in the second. In this example, each cell is a square 52pixels wide, so the maximum allowable displacement in the x or y directions would be 26 pixels, or37 pixels on a cell diagonal. Therefore the limit on the precision to which the maximum R may befound is 2.7% for this example. Figure shows the error in the calculated mean cell velocity asa function of the predicted velocity for the sample data file. The predicted velocity has been nondimensionalized by the maximum velocity that can be resolved. A least-squares fit line issuperimposed on the data, and shows that the mean error decreases as the cell velocity approachesthe maximum allowable by the cell size. The high error for low-velocity situations is due to the meandisplacement between images being only two to three pixels, and the large velocity variation acrossthe cell area, as a fraction of the mean velocity. Accuracy at resolving near-zero velocities could beimproved by incorporating a smoothing algorithm into the resulting cross-correlation function so49the location of the maximum could be resolved with sub-pixel resolution. Other sources of errorinclude the random location of the particles in an image, and any noise induced by the digitizationprocess. -0.3-0.4C)-0.5-0.6-0.7-0.8-0.9Figure Velocity Error for Simulated DataIt was also intended to find a steady, laminar flow with which to test the actual velocitiesobtained from the cross-correlation method. Unfortunately, a suitable flowfield was not found, andso the flow near the model bullnose was used instead. The flowfield there was found to be stillunsteady and turbulent, so its use for validation is limited. The results of this experiment arediscussed in § 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Vte I Vm505. RESULTS5.1 Laser Doppler VelocimetryA total of 26 experimental runs were conducted using the Plymouth recovery boiler modeland the laser-Doppler velocimetry measurement system. Each run took approximately ten hours fordata acquisition during which time the model was run continuously. The configurations of themodel during the runs are summarized in Table 5.1.1.Table 5.1.1 Plymouth Model Laser-Doppler Velocimetry Conditions5 150.06 150.07 150.08 150.09 150.010 150.011 150.012 55.513 60.014 29.015 62.016 115.517 115.518 115.519 115.520 115.521 150.022 115.523 115.524 115.525 115.526 139.0-- 100-- 100-- 10043 5 5243 5 5243 5 5243 5 5243 5 5233 4 4043 5 5243 5 5243 5 5243 5 5236 4 4323232323231515RunNo.1234Set Mass Flow Ratios [%]Set Flowrate[US gpm]150.0150.075.0150.0CommentsPri. S.B. Sec. L.B. Ter.37 - 40 23 -37 - 40 23 -37 - 40 23 -37 - 40 2337 4033 4 4033 4 4033 4 4033 4 4032 4 4932 4 4989 11 -L.B. -2 ports/wall-L.B. -2 ports/wallL.B. - 2 ports/wall- L.B. -2 ports/wallnew primary plates from now on- L.B. - 1 port/wall now on- screen tubes removed from now onboiler banks removed from now on2x2 interlaced grouping2x2 interlaced grouping-- Four wall secondaries-- Front & rear secondaries only-- Left & right secondaries only-- Secondaries: L+10%, R—10%-- Secondaries: L+10%, R—10%-- Secondaries: L+10%, R—10%-- Secondaries: L+10%, R—10%-- Secondaries: L—10%, R+10%23 - Orifice-plates O.K. from now on-- Secondaries: balanced-- Secondaries: L+10%, R—10%-- Secondaries: L—10%, R+10%-- Secondaries: balanced- 17 2x2 interlaced grouping51Early runs in the load-burner configuration used two load-burner ports per wall, which waslater changed to one port per wall in order to more closely match the full-scale boiler. Primary plateswere re-constructed and adjusted prior to Run 4 in order to minimize differences between the fourwalls. Plexiglas plates which modelled the screen tubes and boiler banks were removed prior to Runs7 and 9 respectively to permit comparison of computational fluid dynamics results with theexperiments:The removal of the plates caused a slight increase in the swirl component on level threeas compared to the flow with the plates.For each of the runs noted above, bulk average vertical velocities were calculated from themeans of the 36 measured vertical velocities on each plane. This comparison between measured andpredicted vertical velocities is given in Table 5.1.2. Runs 1, 14, and 18 were aborted due tomalfunctions with the laser. During the test program, it was decided to calibrate each and everyorifice-plate flowmeter used in conjunction with the Plymouth model, and in the course of thiswork, one orifice-plate flowmeter was found to be incorrectly labelled as to its size. This orifice-platewas attached to a secondary level port at the rear-right of the model. For runs 1 through 20, anadditional 10% of the total predicted secondary flow was passing through this port. While this doesnot invalidate the results from these runs, the asymmetric port flow must be taken into account. Theresults from these runs clearly show that the upflow is predominantly near the front-left corner.From Run 21 on, the offending orifice-plate was replaced. Following the completion of Run 22, onesecondary port was found to be plugged with teflon tape, and so the run was repeated.52Results from laser-Doppler velocimetry investigations of particular flow arrangements in thePlymouth recovery boiler model will be presented in three formats. The two components of meanvelocity (averaged over 2½ minutes) recorded using the LDV system will be shown in vector formsuperimposed on a three-dimensional wireframe representation of the boiler model interior walls.The length, and arrowhead size, of each vector is proportional to the magnitude of the velocity atthat location. These plots also show horizontal projections of the velocity vectors on each levelseparately. Because each arrowhead is drawn as a three-dimensional object, the horizontal projectionmay appear as an odd shape depending on the vector angle. A cross emanates from the base of eachTable 5.1.2 Plymouth Model Laser-Doppler Velocimetry ResultsRun Predicted w [mis] Measured w [mis] CommentsNo.( Level > < Level1 2 3 1 2 31 .0483 .0627 .0627 Laser malfunctioning2 .0483 .0627 .0627 .0541 .0464 .06173 .0241 .0313 .0313 .0279 .0292 .03194 .0483 .0627 .0627 .0393 .0711 .07745 .0483 .0627 .0627 .0529 .0571 .05946 .0483 .0627 .0627 .0482 .0593 .05897 .0483 .0627 .0627 .0627 .0545 .05128 .0483 .0627 .0627 .0601 .0664 .06729 .0483 .0627 .0627 .0498 .0633 .060710 .0530 .0627 .0627 .0778 .0707 .069311 .0530 .0627 .0627 .0889 .0599 .067512 .0232 .0232 .0232 .0354 .0250 .0269 -13 .0251 .0251 .0251 .0267 .0349 .031814 .0121 .0121 .0121 .0268—.0071 - Laser & processor problems15 .0259 .0259 .0259 .0163—.0050 —.0121 Processors malfunctioning16 .0483 .0483 .0483 .02 13 .0258 .0 107 Processors malfunctioning17 .0483 .0483 .0483 .009 1 .0294 .034218 .0483 .0483 .0483 .0212 - - Laser malfunctioning19 .0483 .0483 .0483 .0398 .0520 .041620 .0483 .0483 .0483 .0528 .0534 .053421 .0483 .0627 .0627 .0266 .067 1 .0623 Orifice-plates O.K. now on22 .0483 .0483 .0483 .0523 .0838 .0478 One secondary port plugged23 .0483 .0483 .0483 .0432 .0592 .049624 .0483 .0483 .0483 .0600 .0490 .048825 .0483 .0483 .0483 .0346 .0682 .063626 .0483 .0483 .0579 .0653 .0499 .059853vector, the length of each branch being proportional to the root-mean-square velocity in thatdirection.Vertical velocities on each level were also non-dimensionalized by the predicted bulk velocityfor level three, and used to generate contour plots. Using the same non-dimensionalization value foreach level permits comparisons between contour plots of the three levels. The square root of theturbulence kinetic energies, as defined by equation, measured at each point have been nondimensionalized using the same predicted bulk velocity for level three, and used to generate contourplots.Table 5.1.3 Measured Flowrate ErrorsRun Flowrate Errors [%]No. < Level1 2 32 12.01—26.00 —1.593 15.77—6.71 1.924—18.63 13.40 23.445 9.52—8.93 —5.266—0.21—5.42 —6.067 29.81 13.08—18.348 24.43 5.90 7.189 3.11 0.96—3.1910 46.79 12.76 10.5311 67.74—4.47 7.6612 52.59 7.76 15.9513 6.37 39.04 26.6917—81.16—39.13 —29.1919—17.60 7.66—13.8720 9.32 10.56 10.5621—44.93 7.02 —0.6423—10.56 22.57 2.6924 24.22 1.45 1.0425—28.36 41.20 31.6826 35.20 3.31 3.28Bulk vertical velocity (or flowrate) errors are shown in Table 5.1.3 for all runs where datawas obtained on all levels, and during which there were no equipment malfunctions. The meanerrors for each level are 6.8, 4.8, and 3.2 percent for levels one, two, and three respectively. It is54evident that the variance of this error is substantial. Both the mean and variance of the error decreaseas the level increases. Seldom is the error in the bulk vertical velocity less than ten percent on allthree levels for the same run. Run 25 is an example of how poor Ilowrate agreement can occur on allthree levels even when data is taken for over 2½ minutes at every point. The unsteadiness of thisconfiguration probably contributes to this difficulty in obtaining a good average velocity in theplane, and will be discussed further in §5.2 and §5.3. The large velocity gradients present, especiallyon level one, also increase the difficulty in obtaining a good average on a grid of only 36 points.Port flow arrangements were originally chosen based on consultations with the WeyerhaeuserPaper Company, the operator of the full-scale boiler. Two basic configurations have been used inthe real boiler: primaries, secondaries, and load-burners; and primaries, secondaries, and interlacedtrtiaries. ‘When it became clear that the resulting flow pattern was sensitive to secondary port flows,various configurations of two-level flows without any load-burner or tertiary flow. This allowed theeffect of variations in secondary level flows to be examined without any complicating effects fromhigher level flows.In the following sections, LDV results will be presented for a select number of runs whichare representative of each major port flow arrangement, and for which the flow conditions are not inquestion. Results from other runs listed in Table 5.1.1 may be requested from the Department ofMechanical Engineering, U.B.C. It may not be possible to provide every data plot from every run.5.1.1 Early RunsVector plots of velocity from two early runs are presented in Figures and are both for the load-burner upper flow configuration, and are shown to illustrate the effectsof the secondary flow imbalance, and the mass flowrate independence. Figure shows theresults from Run 3, which was conducted at 75 US gallons per minute, half the standard value.Results from Run 4, which was performed at 150 US gallons per minute, are shown in Figure5.1.1.2. Run 4 also had re-manufactured primary port plates, as described in §2.1. Reynolds55numbers, based on predicted bulk average vertical velocities and the model width, were 12,200 and24,400 for Runs 3 and 4 respectively.It can be seen that both Run 3 and 4 show similar velocity patterns, accounting for thedifference in total flowrates. The tendency for the region of maximum vertical upflow to be near thefront-left corner of the boiler is apparent. A comparison of the mean non-dimensionalized verticalvelocities from the LDV results on each level are shown for the two runs in Table 5.1.4.Table 5.1.4 Mean Non-Dimensionalized Vertical VelocitiesLevel Run 3 Run 41 1.0664 0.89862 1.0639 1.18503 1.0064 1.234456C,’a’C)’420UzoU>U,042U,Li)100U,ft‘ *ft4 I 4•. .. .. .FRONTzZDIF—0>-—J00aU-)0::-JFw00aC40U-’0C”0I’-)0aC>U-J4 1I ‘I4 4 4 I4 6.‘ .FRONTt It t4 4It• tI,. ..‘ oFRONT II?A‘V V V57C)I.—QUcizHIt)0 —0CN0owIt)• III IIt• . •. 7I I Ij III I• ? IFRONT(‘4(.1FRONTzDH0>--J0I C‘4 0-Jbi-JFRONT>b40IDLiI:-JU00585.1.2 Load Burner Port Flow CaseFor the configuration using starting burners, four-wall primaries and secondaries, and thetangentially-firing load burners in Run 21, a plot of two components of velocity is shown in Figure5.1.2.1, and contours of vertical velocity, non-dimensionalized by the expected bulk velocity, areshown in Figure Non-dimensionalized contours of the square root of the turbulence kineticenergy K½ are shown in Figure level one, most of the upflow is near the centre of the cross-section, with downflow nearthe corners. Level two shows upflow in the centre and near the right wall, while on level three, themajority of the upflow is near the back and rear wall, with stagnant flow in the centre. The swirlcomponent imparted by the load burner ports is clearly seen on levels two and three, both above theload burner port level. Some evidence of swirl in the opposite direction is seen on level one. Onlevels one and two, the regions of maximum K ½ correspond to the regions of maximum verticalupflow. On level three, the turbulence kinetic energy distribution is quite even. Upflow coversapproximately 75% of level one, 90% of level two, and all of level three.4I IIiiIII I II IFRONT59Inw1(-)InbJ-JI—wU,zDH0>--JUN00I.,0)In00Inr’4UC)UzE0I II I iiittI III IIitFRONTU-J‘I ••I ‘•, II I• I j IFRONTz0LIIz0lIIz0IYU-60Level 3Level 2Level I(Figure Contours of Non-dimensionalized Vertical Velocity - Run 21Hz0Hz0LiHz0li61Level 3Level 2Level 1Figure Contours of Non-dimensionalized K½- Run 21625.1.3 Tertiary Port Flow CaseThe configuration using starting burners, four-wall primaries and secondaries, and interlacedtertiaries was tested in Run 26. The banks of 14 tertialy level ports on the front and rear wall wereeach ganged into four groups, alternating on and off as shown in Figure This provided aneffective 2x2 interlaced arrangement, which induced some clockwise swirl, as viewed from above.Two components of velocity are shown in vector form in Figure, contours of nondimensionalized vertical velocity in Figure, and contours of non-dimensionalized K ½ inFigure plots show that the upflow is in the centre of the furnace at level one, with two roughlysymmetric, distinct peaks apparent. This may be due to oscillations of the core flow region fromfront to rear, as has been seen in flows with balanced primaries and secondaries, and will bediscussed in 5.3. Such separate peaks of upflow could not be noted when the flow was observedqualitatively during the course of the run. On levels two and three, the upflow is fairly uniformlydistributed about the four walls, with stagnant flow in the central region. The maximum turbulencekinetic energy is seen to be between the two vertical velocity peaks on level one, with secondarypeaks offset clockwise from the velocity peaks. Level two shows the peak K½ at the rear wall, whilethe turbulence is maximum along the front and rear walls on level three. Vertical upflow coversapproximately 60% of level one, 90% of level two, and all of level three.(0zFD0>--J0634 4 4 fIII I• ...14I.,Li-JI.,CN00044,-)In0LiC-)Pz2.4E-FRONT• . I It‘ft It• . , tttI •44 • I I‘•t 4 4 II -11 - II I• 4 1FRONTLi-J4FRONTmI1w-JI—uJUILi>Li0Li-J00C-)64I—z0Lovol 3IL/Level 2Iz0Lvol 1ILFigure Contours of Non-dimensionalized Vertical Velocity- Run 263 C.) 0 0 C -I C.’, 0 - z 0 C.’, 0 N 0FRONTFRONTFRONTF a aFF C C 1.)665.1.4 Balanced Primary and Secondary Port Flow CaseRun 25 was conducted using starting burners, primaries and secondaries with equal flow oneach wall. The flow showed a tendency to quickly drift away from the balanced condition, and forthe core to move towards one wall or another. Ports were continuously monitored during the run toensure that the flows on each of the walls remained balanced, and that none became plugged. Avector plot of two components of velocity is shown in Figure, non-dimensionalized contoursof vertical velocity in Figure, and contours of K½ in Figure figures show a symmetric core of upflow on level one, with downflow on the perimeter.On level two, the most upflow is near the left wall and the central region, with no downflow. Levelthree shows a fairly even vertical velocity distribution, with slightly more flow on the left wall. Peaksin the turbulence kinetic energy occur slightly to the left and right and right of the central core onlevel one. Levels two and three have clear maximums of K½ very nearly in the boiler centre, wheretheir is no correspondingly pronounced velocity maxima. Vertical upflow covers approximately 50%of the horizontal cross-section on level one, 95% of level two, and all of level three.67¶• . .• . I I• . .I •: :I II II •_ II I IC) 0 0 0 z 0 0 rz 0FRONTFRONTFRONTFFF0000l’)C’ Coc)3 n 0 fr C’, 0 z 0 C., 0 N t)FRONTFRONTFRONTF 0 0F C 0F 0 V705.1.5 Balanced Primaries; Biased Secondaries Port Flow CaseRun 23 was performed using starting burners, four-wall primaries and secondaries. Primaryport flows on each wall are identical, as in Run 25. The mass flow, and hence velocity, of the left-wall secondaries are 10% higher than nominal, while the right-wall secondary mass flows are 10%lower than nominal. Two components of velocity are shown in Figure, and nondimensionalized contours of vertical velocity in Figure Contours of non-dimensionalizedK½ are shown in Figure majority of the upflow is near the right side wall of the boiler on level one, symmetricfrom front to rear. Higher in the boiler on levels two and three, the upflow is still predominantly upon the right side, and stagnant on the left. The peak of the turbulence kinetic energy distribution isalso on the right side of boiler on levels one and two. Level three shows K ½ to be higher near theperimeter of the model, as opposed to the right wall. Vertical upflow occurs for about 60%, 75%,and 80% of the cross-sectional areas at levels one, two, and three respectively.714 t4 1 1 . • I4 • . .4 o:FRONTFRONTFRONTr1 0 8 0 z 0 Fr Cr K 0r 0 C 0 ()ri C-) 0 8 C 0 z 0 (D 0 N CDFRONTFRONTFRONTF CF C I,74BULLNOSELEVEL3 A + fALEVEL 2—LEVEL1SECONDARY / I___+10 % w4 4__-10 %PRIMARY :Figure Flow Schematic Front View - Run 23Figure shows qualitatively the flow pattern as viewed from the front of the boilermodel. A large recirculation region is noted at level one, slightly to the left of the model centreline.Flow beneath the secondary port level was too turbulent to be sketched accurately.The configuration used in Run 24 is the mirror image of that in Run 23. The mass flow ofthe left-wall secondaries are 10% lower than nominal, while the right-wall secondary mass flows are10% higher than nominal. Two components of velocity are shown in Figure, nondimensionalized contours of vertical velocity in Figure Contours of non-dimensionalizedare shown in Figure region of upflow is now towards the left side wall of the boiler on level one, fairlysymmetric from front to rear, with downflow on the right wall. Higher in the boiler on levels twoV 75and three, the upflow is still predominantly up on the left side. The zero velocity line is somewhatangled from front to rear on level two. The contours of turbulence kinetic energy on level one aresteep, coming to a maximum near the centre, where the vertical velocity is near zero. The maximumof the K½ distributions on levels two and three are near the cross-section centre. Upflow occurs onapproximately 60%, 75%, and 90% of the areas on levels one, two, and three respectively. Thus thechange of flow of 10% has effectively switched the flow pattern from side to side on the three planesof measurement.76. 4. I I. t 4-., I t* ‘ I.FRONTLi-J. II 4FRONTzH0>--J(NQII,InaI-)OIIn0mLfl0::bJ-JIIiJUCr;8UIII.-JI-i-JI, ,1 1, •oI •I0 I. I.I • 4FRONTLi>Li0LI-J0I-,CD 0 0 0 - z 0 C., 0FRONTFRONTFRONTFFF000( 00r\)—1n 0 0 0) 0 t) 0 0- S CD C-, 0 0- L%Jrj C CDFRONTFRONTFRONTF 0 0F 0 0 N1-)F 0 0—.400795.2 Power Spectral DensitiesLow frequency oscillations in the velocities were noted on the plots of power spectral densityfor all of the cases run. This unsteadiness could sometimes be observed in the velocity time traceitself, and also from qualitative and quantitative visualization. For flow cases in which the mass flowsfrom each wall of primaries and secondaries were balanced, the distribution of the unsteadinessseemed somewhat more uniform throughout the boiler volume. The observed unsteadiness shouldnot be confused with turbulence, for which the frequencies are at least an order of magnitudehigher. For a single measurement location on level one for Run 25 (starting burners, balancedprimaries and secondaries), plots of velocity are shown in Figures 5.2.1 and 5.2.2, and plots ofpower spectral density are shown in Figures 5.2.3 and 5.2.4.-The data record displayed had a length of 155.2 seconds, and mean sampling rates of 42.3and 56.6 samples per second for u and w components respectively. The PSD values computed atfrequencies lower than the 5/ T boundary described in §4.2.1 are shown as a dotted line. Peaks ofpower spectral density are seen at 0.049 Hertz in the u component and 0.088 Hertz in the wcomponent, corresponding to periods of 20 and 11 seconds respectively. Such plots as those shownare representative of the power spectral density in other runs also. Results varied with the geometriclocation within the boiler, but low frequency peaks in the range of 0.05 and 0.1 Hertz weredominant in all locations and configurations tested.-0.3-0.4-0.5FI11E0 20 40 60 80 100Figure 5.2.1 Velocity Trace - Run 25, Level 1, u Component0. ‘time [s]120 140 160: h Ifi i1 iLh IIL1 I.”’ J IIII0.••••i: II 9i:::.... 1•0 20 40 60 80 100 120time [s]140 160Figure 5.2.2 Velocity Trace - Run 25, Level 1, w Component0.0400.0350.0300.025U,0.0200.0150.0100.0050.0000.01NIU)(0N-.__1’ — . .0.1 1 10f [Hz]f [Hz]Figure 5.2.4 Power Spectral Density- Run 25, Level 1, w Component810. 5.2.3 Power Spectral Density - Run 25, Level 1, u ComponentTh,V0.000.01V V j V V0.1v.*W4VW1 10825.3 Particle Image VelocimetryFor the case of balanced flow from only the primary and secondary ports, equivalent to Run25, two different views of the flow were analyzed using particle image velocimetry. The boiler wasilluminated using the laser sheet system, and the flow pattern recorded using the video technique asdescribed in §3.3. The laser sheet was introduced through the clear bottom of the model toilluminate an x-z plane, using the coordinate system of Figure 2.1.1. The flow was viewed from theside of the model at two levels; near the bulinose, and between the secondary and tertiary levels.About thirty minutes of the flow were recorded at each location, but storage and time requirementslimited the maximum analysis segment to thirty seconds of data.Filming was also conducted from the front of the model, using a laser sheet oriented in the yplane. Unfortunately, the threaded bolt holes holding the model together are in the front and rearwalls. These glowed with an intensity greater than that of most of the particles, reducing the possibleanalysis area to a small region in the centre of the model. To effectively film the flow from the front,the rear and side interior walls of the model would have to be coated with a flat black paint orcoating to eliminate any glow other than that from particles. If laser velocimetry was also to beperformed through these walls, the coating would have to be easily removable.5.3.1 Bullnose Side ViewThe region near the builnose was photographed through the right side wall, and analyzedusing particle image velocimetry, originally for validation of the experimental method. It wasthought that this region of the boiler would have a reasonably steady, uniform upflow which wouldlend itself well to validation of the absolute velocities returned by the particle image velocimetry.However, it was found that, even near the bullnose, the flow was neither uniform nor steady. Theresults are of more use in describing the boiler characteristics than validating the approach.The laser light sheet was placed below the model and aligned vertically in a plane runningfrom the front to rear walls, in the centre of the model. The unsteady characteristics of the flow are83not adequately described by static vector plots, but can be observed using the animation proceduredescribed previously. An average of the velocity vectors over the entire 30 second length of the datarecord is shown in Figure Flow is generally up near the front wall and down off the top ofthe builnose.ft ft \ \t t ttt t \I f f ‘ \ \ \\ \‘-\O.lrn/s,nose\ t\\, -‘I\ t . /•Figure Bullnose Side View 30 Second AverageFor the same 30 seconds of data, averages - over six consecutive five second intervals areshown in Figures (a) through (0. It is clearly evident that the flow pattern is not staticduring the 30 second record duration, rather changing continually over time. The flow pattern doesnot appear to re-occur during the 30 second interval, indicating that any period of the flow may belonger than this. The 30 second average is therefore probably not long enough to provide astationary average. A vortex which appears in (d) is seen to convect up and to the right in (e).841 - \ \ ‘. \ I- -\\\ \\\ \ S -/- t\ \ \ / I\ \ \ \-.5 \-.-.I \ t , 7 \I’ / f 1 1t ft itt, — . /t / //,,____j / / 1 / ,/1_I -/\0.1 rn/S(a)/bulirioseN\7— ‘ S\ t \I /— // I - / /-t\ \ t \ itI \\ I\ \ I \ \\‘S.5 \ \\ I-S-S-S(C)t I ‘I I “j \ I \, /I 7 / I \ I I //7 /\\ t \/ / \\ \ \t f 7- \ \ \/III -\ t._ / / IS- . S/ // —S -0.1 rn/s(b)0.1 ni/S(d)0.1 rn/S(I)/bulinoseNI0.1 rn/S(e)/ I 71 1 /‘S\ / t//- /1 / 7 / — It I ‘ /SI-.t ‘.5/ I.- ‘ ‘/ /I \ / / // / / //builnoseN\ *1\-S.S \ II-S7, /-I / t - —ti ,,.‘ I’ -.-S.\ tN_/Figure Builnose Side View Consecutive 5 Second Averages855.3.2 Lower Boiler Side ViewA 30 second average of the flow pattern for balanced primaries and secondaries only, asviewed from the left side of the model between the secondary and tertiary levels, is shown in Figure5.3.2.1. The laser sheet was introduced from the model bottom, illuminating a x-z plane locatedhalftvay between the side walls. A load burner port which blocked the view of all particles behind itis shown in the lower right region of the frame. The 30 second average of the flow shows a centralcore region of upflow near the secondary level, which shifts towards the boiler front as the tertiarylevel is approached. For the same 30 seconds of data shown in Figure, consecutive fivesecond averages of the flow are shown in Figure (a) through (f). Large vortices approximatelyone third the model width in size may be seen in (b) and (c). Downflow near the rear wall appears,disappears, and reappears with a period of about ten seconds. This is similar to the low frequencyoscillations seen in the power spectral densities discussed in §5.2.f t I t tf tREAR FRONTII / It I’ t tLoad4’ 0.lm/st / I Burner \ii”I I t Port \\, tFigure Lower Boiler Side View 30 Second Average86(a)FRONT REARt0.1 mIsFRONT REARIt0.1 tn/SFRONT REARIt01 rn/sI,’0.1 ntIsIt0.1 Ifl/SIt0_I rn/sREAR FRONT(0)_._-/ 7 71 t \t‘7—‘ t \ / r---‘\ \ I Load/IHI Burner,)_ ‘,‘ POn I‘I‘—___ / \ t t 1-iI -_ — —- /%7/ / / /t,/ / /‘5‘5 ._ /•/ /ILoad \tI Burner i\/P‘5—_- I ‘5Ott I/\lft/‘ ,.n f I ‘i / ,t / / Itt ‘r-’-----I’LoadI I/ I Burner1 ‘ ‘— \\ I P 01 I -— I -FRONTI t / / - \ \ ‘\ \Act I I-\t /I \ \ r—-----’\ ‘S. ‘IS.. \ / I Loadf//II Burner1’’‘Port‘5tI \ /4—FIt / I I-_ /T /1 T1 /// ‘ /‘r-- /,i\ t ?II Load1\ 7/II Burneri//Ac I IRon II IAc t\\\-Ac /-\ f\ ?.- I I r--/ /‘Ac /I —I Load —S “/\tI// / 1 PonII IREAR(c)REAR(e)(d)FRONT(I)Figure Lower Boiler Side View Consecutive 5 Second Averages876. DISCUSSION OF RESULTSOne of the difficulties in modelling a recovery boiler is that an optimum flow condition orgoal is difficult to define. The isothermal flowfield resulting from a particular physical portarrangement and mass flow ratio may be determined with adequate precision, but the implicationfor real boilers is somewhat more subjective. Some of the relationships between the experimentalresults and the full-scale boiler condition will be examined in the following sections. The two mainfindings of the experimental results have been that the core of central upflow does not persist muchhigher than the liquor gun level, and that low frequency unsteadiness is a dominant feature.6.1 Velocities6.1.1 Air System ObjectivesThe optimal air system must maximize the recovery of both chemicals and energy asmeasured by the chemical efficiency ( Na2S/(Na +Na2SO4)), and the thermal efficiency(Isteaml2liiquor)’ and these two requirements may conflict with each other (Lefebure and Burelle 1989).For efficient chemical recovery, the lower part of the furnace must be oxygen deficient to obtainmaximum reduction efficiency defined as the percentage of Na2S which is obtained in the smelt.However, for thermal efficiency and maximum heat release, the combustion of the organics must becompleted higher in the furnace in an oxygen-rich environment. The high temperatures necessary inthe bottom of the boiler are maintained by partial combustion of the organics. The simultaneousoptimization of all of these processes is the goal of a recovery boiler air system.For maximum thermal efficiency, the heat release rates must be maximized with minimumentrainment, or carryover, of liquor droplets and char particles. It has been suggested that one of thefunctions of the tertiaries is to break up the “high velocity central core” which can cause carryover.Adams and Frederick (1988, 160) suggest that a typical flow will have a central core of upflowcovering about 18% of the cross-section. Typical results for level one in Figure show anupflow area of about 50% with downflow elsewhere in the cross-section, and a maximum velocity of88approximately five times the bulk average. Results shown in Figure for arrangements withonly primary and secondary port flows indicate that the high velocity central core dissipates on itsown by the time it reaches the tertiary level. This leaves the main function of the tertiaries to beprovision of oxygen for combustion, hopefully without promotion of carryover.6.1.2 Velocity Effects in Full-Scale FurnacesThe realization that a central core of upflow does not necessarily persist at all levels in arecovery boiler may have consequences for other researchers. Those who model liquor droplet flight,drying, and pyrolysis often use a symmetric core flow profile as an input to their models (Adams andHorton 1992). The effects of using a flowfield without an upper furnace core of vertical upflowshould be used to examine its effects on any model of other phenomena in recovery boilers.Chapman and Jones (1990) have argued that secondary level flows are a critical aspect of theoverall air delivery, affecting the intensity of the flow channel and recirculation zones. Theirexperiments and calculations led to the conclusion that at a plane just above the secondaries, thecentral upward velocities and perimeter recirculation zones can be attenuated by interlacing or theuse of a strong-weak flow arrangement, but not eliminated. This finding is not incompatible withthe results presented in this work.One problem in full-scale boiler operation is entrainment, or carryover, of black liquor andchar particles which can cause plugging of the tubes in the convective heat transfer section. It maybe impossible to eliminate carryover completely, unless the regions of liquor injection, and upflow oforganics into the burning zone, can be separated. A more uniform distribution of liquor dropletsmay be achieved if the flow is weakly up near the walls, permitting the droplets to fall slowly andallowing time for drying and pyrolysis to occur. A fairly even flow distribution is needed at thesuperheater entrance for uniform heat transfer and mechanical and thermal loading. The particleimage velocimetry results show that, at least for an arrangement without tertiary or load-burnerflows, oscillating downflow may occur at the builnose. Although the plates representing the89convective heat transfer were not present for these runs, such results indicate that a uniform flowdistribution may not exist in all situations at the superheater entrance.Regions of higher velocity in the upper furnace may be related to zones of increased tubewear or fouling due to the high mechanical and thermal stresses. Regions of oscillation between highand low velocity may indicate zones of increased tube-wall cracking due to the high cyclic loading ofboth thermal and mechanical stresses.6.1.3 Upper Furnace Flow ConfigurationsOne of the reasons the Weyerhaeuser Paper Company began a research program intorecovery boiler fluid mechanics was to investigate differences between load burner and tertiary upperfurnace arrangements in the Plymouth boiler. Examining Figures and, it may be seenthat there are only subtle differences between the measured velocities in the two cases. At level one,two distinct velocity peaks exist when tertiaries are used, indicating the possibility of oscillation ofthe core between these two places. On level two, there is a more uniform velocity distribution usingtertiaries (Figure By the time level three is reached, the velocities in the load burner case(Figure are more evenly distributed about the cross-section, while the maximum velocitiesusing tertiaries (Figure are on the front and rear walls. Measured turbulence kinetic energiesare slightly higher on Level 1 using tertiaries (Figure, while the regions of maximum K½ arenear the front and rear walls (as opposed to being evenly distributed) using load-burners (Figure5.1.3.1).The swirl component of velocity is of course much stronger using tangentially firing loadburners than the interlaced tertiaries. Compared to the case of a 2x2 interlaced tertiary flow, theswirl component induced by the load-burner upper flow arrangement may be more effective atdiffusion and mixing, and providing an even velocity distribution in the upper furnace region.906.2 Transient Behaviour6.2.1 Data QualificationThe low frequency oscillations observed in the course of this work have not been reportedpreviously for recovery boilers, although similar phenomena has been noted in an isothermal modelof a hog-fuel boiler (Perchanok, Bruce, and Gartshore 1989). To help understand the processesoccurring in recover boiler flow, some classification of the observed “unsteadiness” is warranted.Bendat and Piersol (1986) provide a good starting point for analysis of random data. Theoretically,the fluid velocity inside a kraft recovery boiler is a deterministic process in that mean values could bedescribed by the Reynolds averaged Navier-Stokes equations. The impracticality of specif,ring initialconditions and solving these equations means that the instantaneous fluid velocity at a point inside akraft recovery boiler must be considered a partly random, as opposed to a completely deterministic,process.The goal of any experimental modelling is to obtain statistical moments of parameters whichrepresent the data from a very large number of realizations, or ensemble, of a particular experiment.To avoid having to perform many identical experiments, the assumption is .typically made that theprocess is stationary and ergodic, which implies the equality of ensemble and time averages. ‘Whilesuch an assumption is convenient, and has been implicitly made in this work, its validity should beexamined in light of the transient velocity behaviour observed.A stationary random process is defined as one in which the ensemble, (infinite collection ofidentical experiments) statistical moments are not a function of the instant in time at which they arecalculated. An individual time history record may also be considered stationary if statistical momentscomputed over short time intervals do not vary with more than “normal statistical variation” frominterval to interval. Thus the velocity at a particular location in a turbulent, time-dependent flowsuch as a recovery boiler is stationary only if an appropriate averaging time interval is chosen.91A stationary random process is considered ergodic if statistical moments do not vary whencomputed for different realizations of identical experiments. Note that a non-stationary randomprocess cannot be ergodic, and a stationary process need not be ergodic. Statistical properties of astationary, ergodic, random process may be computed from either ensemble or time averages.The similar results shown for two different runs at two different flowrates in Figures suggest that, for one configuration at least, the flow was both ergodic and stationary ingeneral. However, the transient velocity behaviour documented in §5.2 and §5.3, and the difficultyin obtaining accurate bulk vertical velocities suggest that recovery boiler flow may not be a stationaryprocess, at all locations, at all times. Bendat and Piersol (1986, 437) have shown that the bias errorof a time-averaged mean value estimate of a non-stationary random process is proportional to thesquare of the averaging time T Random error in the estimate should decrease as T becomes larger,so the choice of averaging time T for a non-stationary process must be a compromise betweenrandom and bias errors. The demonstrated difficulty in estimating bulk velocities may result fromthe fact that for a constant averaging time 7 the random and bias errors vary with location in theboiler. If the flow is non-stationary, the only practical way of measuring parameters in a plane is touse simultaneous measurements, as is done in the particle image velocimetry technique.A test for stationarity has been performed using the method describedby Bendat and Piersol(1986, 342-345). The boiler model was configured for the balanced primary and secondary portflow case, and a velocity record was made using the laser-Doppler apparatus. This record was thendivided into 25 equal time intervals of 2½ minutes duration each. This time was chosen asrepresentative of measurement intervals during actual runs, over which the data is consideredindependent. A mean square value was computed for each interval, and the sequence of values isshown in Figure The data were tested for the presence of underlying trends using the runtest, and for stationarity using the reverse arrangements test.920.0240.022c’1U)E 0.020> 0.0180.0160.0140.0120MeasurementFigure Sequence of Mean Square Measurements, Level 1, w ComponentLet it be hypothesized that the observations are independent, and there are no underlyingtrends. At the a=0.02 level of significance, from run distribution tables, the acceptance region forthis hypothesis is [7, 19] runs. This hypothesis is accepted, as the number of runs are 13 and 15 foru and w components respectively. Now let it be hypothesized that the data are stationary. Fromtables of the reverse arrangements distribution, at the a=0.02 level of significance, the acceptanceregion is [106, 206] reverse arrangements. The number of reverse arrangements is 131 and 126 forthe u and w components respectively, and so the hypothesis of stationarity is accepted at the 2%level of significance. Such a statistical test cannot establish truth, but only states whether the datasupports the hypothesis or not, and the term “accepted” should stricdy be replaced by the term “notrejected”. The possibility remains that the flow may still be non-stationary at some locations forsome flow configurations.5 10 15 20 25936.2.2 TurbulenceFor the configuration of balanced primary and secondary flows only, Figure showscomputed power spectral densities (PSD) for the vertical flow component measured on level one.Values were computed for frequencies from the minimum value of 5/7 up to a frequency where thefirst unrealistic negative value was obtained. The data are plotted against the wavenumber,k = 22rf/ U, which has been non-dimensionalized by the boiler half-width, L /2. The results ofLawn (1971) for the power spectral density of the axial component of turbulent pipe flow are shownfor reference. Both the pipe flow data of Lawn and the present spectrum have been nondimensionalized such that_I_ JS(.k)dk)= 1 ( required by the definition of the power spectral density function.100-—/rI!P now ua Qj LawnU)C”1 010.21i o4i ow61 01.::::::...*!!HH1’ : E /LI100 101 102(L12)k1Figure Extended Power Spectral Density, Run 25, Level 1, w Component94Below nondimensional wavenumbers of approximately 1O, a noise type spectrum is seen,where computed PSD values are much below those for pipe flow, and which decay only slightly withincreasing wavenumber. At higher wavenumbers, evidence is seen of a —5/3 region (inertialsubrange), where energy production and viscous dissipation are in balance (Tennekes and Lumley1972, 248-287). The boiler flow power spectra is seen to approach the —5/3 slope at approximatelyone log decade higher wavenumber than does the power spectra of fully developed turbulent pipeflow. The use of the boiler width as the non-dimensionalizing value L may be inappropriate due tothe greater influence from small scales of turbulence than in pipe flow. The scales of turbulence inthe boiler flow may be related to the port sizes, which are nearly two orders of magnitude less thanthe boiler width. The computed PSD values also do not show a clear separation between frequenciescorresponding to unsteadiness and turbulence respectively. Similar results were also seen incomputed spectra from velocities measured on level three.6.2.3 MixingGas mixing dictates the combustion rate and final combustion efficiency. Reaction rates atfurnace temperatures are often fast enough that mixing between fuel and oxidizer becomes thelimiting step in combustion (Adams and Frederick 1988, 150). Incomplete mixing results in highcarbon monoxide and total reduced sulfur (TRS) in the exhaust gases. “While intimate mixing isdependent on very small scale turbulence, gross diffusion of species across the boiler cross sectionrequires regions of fluid shear stress. Such action occurs on the edges of a high velocity jet where theshear stress entrains the surrounding fluid. Large scales of motion provide the power source for theturbulence energy cascade from large to small scales.Low frequency oscillations may be beneficial in the oxidation zone, from approximatelyabove the liquor guns to below the bulinose level. If such low frequency oscillations exist inoperating recovery boilers, they probably persist with varying strength throughout the entire volume.Figures and indicate that large vortices approximately half the boiler width indiameter may be slowly convected up the furnace. Unsteady behaviour has also been reported in95computations of turbulent flow of symmetrical arrays of opposed rectangular jets in a weak crossflow (Quick, Gartshore, and Salcudean 1993).Oscillations which persist down near the bed will bring oxygen down with them, reducingthe reduction efficiency, and possibly disrupting the bed shape or causing plugging of low velocityprimary ports. Should strong oscillations continue up above the bulinose, temperature and flowdistributions may be uneven at the superheater entrance, and flow could go backwards through thesuperheater. However, weak, low frequency oscillations without direction reversals occurring at thesuperheater entrance might be beneficial in distributing mechanical and thermal loading through thetube banks.6.3 Experimental LimitationsModelling, whether mathematical, computational, or physical, is limited as to the accuracywith which any problem may be represented. Certainly modelling a recovery boiler requires anumber of simplifications as to the flow conditions.6.3.1 Physical VariationGeometrically, the only significant divergence between model and full-scale is the absence ofa char bed shape. Effects on the flowfield resulting from the lack of a bed shape are difficult toascertain further without experimental testing. Primary jets which would be deflected upward by thebed in the frill-scale are permitted to oppose each other in the model. However, the low velocityprimary jets probably cannot penetrate far enough across the cross-section to interact with eachother, and may attach to the floor. The higher velocity secondary jets are able to be deflecteddownward in the model, while they would be constrained by the bed in the full-scale. The effects ofgas flow off of the bed are not known.The examination of bed effects is complicated by the fact that bed shape is not constant inan operating furnace. For comparison with computational results, a constant shape would be thesimplest addition. However, a shape that is initially deformable by the flow to a constant shape could96be used. This could be accomplished by placing a layer of ball-bearings on the furnace floor, ofappropriate density so that the forces on the bed scale from model to full-scale. Another methodwould be to place a plastic bladder on the model floor, connected to the drain hose on the modelbottom. Water would be pumped in through the drain line, and the bladder pressurized to maintaina relatively constant shape against the pressure of the primary jets. The shape of the bed during thetest would be noted and input to the computational model. Alternatively, a physical bed shape couldbe machined from Plexiglas or stainless steel and placed in the model. Holes could be placed in thetop surface through which water could be pumped to simulate the gas flow off of the bed.The limited accuracy with which port flows may be set in the model affects the accuracy ofbulk average vertical velocities calculated from laser-Doppler measurements taken at differentlocations and time. Flow setting accuracy could be improved through the use of an electronic flowmonitoring and controlling system. Ideally, the orifice-plates would be replaced with flowmeterswhich output a voltage proportional to flowrate. Possible choices include vortex, paddlewheel,rotameter, and turbine flowmeters as well as differential pressure transducers. The present gate-typevalves could be replaced with a different type such as globe or butterfly valves, which may be morestable over time. The replacement of the centrifugal pump with one of lower capacity may reducethe tendency of the valves to drift from their set values over time.6.3.2 Input InformationOne of the real problems associated with physical and CFD modelling of recovery boilers isthe lack of knowledge of the appropriate full-scale input conditions, even for a purely isothermalcase. In a real recovery boiler, air is typically delivered to the air ports at a given level by a windboxwrapping around the boiler perimeter. Air enters on one side, splits in two directions and travelsaround the boiler to respective sides. The distribution of air to the individual ports is not known, asit is difficult to accurately measure the port velocities in an operating recovery boiler. Generally, thisis attempted by trying to measure static pressure in the windbox around the boiler at differentlocations. Through application of Bernoulli’s equation and some empirical corrections, the average97port velocity is estimated. No attempt is made to find the distribution of velocity within a port.Unfortunately, static pressure cannot be accurately measured without a priori knowledge of the flowdirection. While such windbox measurements can be used by an experienced operator to balance afurnace, it cannot provide accurate input information for a model. In addition, the air ports,particularly the primaries, tend to plug and so vary their effective shape with time.When modelling, one typically assumes equal flows around the model perimeter, and theseare applied separately by different hoses, or to great precision by CFD modelling. Monte Carlosimulation may be necessary if small differences in the inputs cause seemingly random variation inthe computed flowfields. One other variation in flows between model and full-scale is the lack of airinfiltration in the model. Approximately 8.5 percent of the total fan air flow may typically be drawninto by the furnace draft through port and liquor gun openings (Adams and Frederick 1988, 27).6.3.3 Two-Phase FlowThe effect of the liquor droplets on the flow was neglected in this work. Adams and Horton(1992) have shown that the impact of the liquor sprays on the flowfield is modest due to the relativemomentum of the flows and the large droplet size. Any effects should be confined to regions nearthe liquor guns where jet velocities are the highest and the jet is most concentrated.6.3.4 Buoyancy Force EffectsAn isothermal model cannot represent effects on the flowfield from buoyancy forces. Thislimitation was accepted at the start of this study as isothermal results are still valid for comparisonswith full-scale cold flow tests and isothermal computations. Such computation of the isothermalflowfield is generally carried out before attempting to calculate the coupled energy and momentumequations. A brief examination of expected effects of buoyancy forces is in order.The ratio of inertial to buoyant forces is given by the Froude number for a jet in a crossflow(Schetz 1980)98U2Fr= rjet1 ([( P — Pjet) “PiJ ‘4etAssuming typical values from §1.22, full-scale Froude numbers vary from 152,000 to 1019for the tertiary and starting-burner port flows respectively. This indicates that buoyancy forces onthe jets are not significant, although they may become important elsewhere in the flow dependingon the local velocity and thermal environment.997. CONCLUSIONS AND RECOMMENDATIONSIsothermal modelling of a recovery boiler using water as the working fluid has beenaccomplished. Principal sources of experimental error will be summarized prior to discussion ofmajor conclusions and recommendations.The error in the actual model flowrate with respect to the set value was shown to bedependent on the orifice-plate flowmeters, and the tendency of the valves to drift. Consideringmeter error oniy, for a typical run of 150 US gpm total set flowrate, a 95% confidence interval forthe expected value of the total flowrate is given by (148.9, 157.3) US gpm. If both meter and drifterror are considered, for the same typical run, a 95% confidence interval for the expected value ofthe total flowrate is given by (130.9, 149.5) US gpm. The major source of error in setting the modelflowrate is due to the drifting of valves from the set values. Bulk vertical velocities at the threemeasurement planes, found by integration of measured vertical velocities, erred from the set valuesby mean errors of 6.8, 4.8, and 3.2 percent for levels one, two, and three respectively. The error inthe measured bulk velocities may be affected by a sampling grid which is too coarse in light of thelarge velocity gradients, or by non-stationary behaviour of the flow.The central core of vertical upflow thought to dominate boiler flow was, at least for the- physical boiler and flow configurations examined here, found to represent only a portion of the flow.A central core of upflow was observed near the liquor gun level, but disappeared above the tertiaryport level for all flow configurations examined. In the upper regions of the boiler below the bullnose,the upflow was concentrated near the boiler walls, with down or stagnant flow in the central region.It was not possible to balance the port flows so that a stable, central core upflow was present at alllevels.The model was found, in the absence of any tertiary level flow, to be extremely sensitive toasymmetries in secondary level port flows. An increase in secondary port flow velocity of 10% onone wall, and a corresponding decrease by 10% in the velocity of the port flows on the opposite wall,caused the region of maximum vertical upflow to occupy the half of the boiler cross-section near the100wall with the Lower velocity. The port flow setting apparatus was not accurate enough to testimbalances of less than 10%. Strong iow frequency unsteadiness with periods on an order of 10 to20 seconds was observed in the velocity power spectral densities. For the case of balanced flows fromprimary and secondary ports, particle image velocimetry analysis of central, vertical planes, showedgross motions of similar frequencies. At the bulinose level, the location of the region of maximumupflow was seen to oscillate between the boiler front and rear. Such oscillation was also seen at thetertiary level, as was the passage of large vortices on the order of one half the boiler width.The use of concentric load-burner port flows, as opposed to a 2x2 interlaced arrangement ofhigh velocity tertiary ports, was found to provide a more uniform distribution of turbulence kineticenergy in the upper furnace. Configurations employing opposed, high velocity port flows appearedto generate large vortices and regions of unsteadiness. The region of maximum vertical upflowtended to move towards the wall or walls with the lowest port flowrate. This effect has been shownto occur with the secondary ports, and may also occur with high velocity opposed tertiary ports.Swirling or interlaced flow arrangements may be superior for establishing a stable flow conditionwhich is not affected by port plugging or minor changes in port flowrates. The marked tendency forthe flow in the upper levels of the boiler to be up near the walls, and the possibility of downflow,should be accounted for in the design of the convective heat transfer section.Methods for reduction of the errors in setting port flowrates in the model by installation ofhigher quality valves, or a pump of lower capacity, or an electronic flow control system should beinvestigated. The particle image velocimetry technique should be applied to other flowconfigurations and boiler models. Possible sources of the observed unsteadiness should beinvestigated through the testing of other flow configurations and port geometries, and the additionof a char bed shape. Results should be compared against future computational fluid dynamicscalculations of flows in the Plymouth boiler. The applicability of particle image velocimetry methodsfor velocity measurements in cold or hot flows in full-scale boilers should be examined. Finally, toenable an increase in sophistication of recovery boiler modelling, more velocity data on the portflows in full-scale operating recovery boilers should be obtained.101REFERENCESAdams, Terry N., and Wm. James Frederick. 1988. Kraft Recovery Boiler Physical and ChemicalProcesses. New York: The American Paper Institute.Adams, Terry N., and Robert R Horton. 1992. The Effects of Black Liquor Sprays on Gas PhaseFlows in a Recovery Boiler, 1992 Engineering Conftrence Proceedings, 81-101. Atlanta:TAPPI Press.Adrian, R.J. 1986. Multi-Point Optical Measurements of Simultaneous Vectors in Unsteady Flow -A Review, InternationalJournal ofHeat d Fluid Flow, 7: 127-145.AguI, Juan C., and J. Jimenez. 1987. On the performance of particle tracking, Journal of FluidMechanics, 185: 447-468.Bell, W.A. 1981. Spectral Analysis Algorithms for the Laser Velocimeter: A Comparative Study,AJAAJourna42l:714-719.Bendat, Julius S., and Allan G. Piersol. 1986. Random Data: Analysis and Measurement Procedures,2nd ed., 1-36. New York: John Wiley & Sons, Inc.Blackwell, Brian. 1992. Validity of physical flow modeling of kraft recovery boilers, Tappi Journai75(9): 122-128.Bury, Karl V. 1986. Statistical Models in Applied Science. New York: John Wiley & Sons, 1975;reprint, Malabar, Florida: Robert E. Kreiger (page references are to reprint edition).Chao, Y.C., and J.H. Leu. 1992. A fractal reconstruction method for LDV spectral analysis.Experiments in Fluids, 13: 9 1-97.Chapman, P.J, and A.K. Jones. 1990. Recovery Boiler Secondary Air System Development UsingExperiments and Computational Fluid Dynamics, 1990 Engineering Conference Proceedings,193-203. Atlanta: TAPPI Press.Cho Y.C., and H. Park. 1990. Instantaneous Velocity Field Measurement of Objects in CoaxialRotation Using Digital Image Velocimetry, SPIE Ultrahih and High-Speed Photography,Videography, Photonics, and Velocimetry, (1346): 160-171.Edwards, R.V., ed. 1987. Report of the Special Panel on Statistical Particle Bias Problems in LaserAnemometry, Journal ofFluids Engineering, 109: 89-93.FIND Manual Ver. 3.5.3. 1991. St. Paul: TSI Inc.Fingerson, L.M., R.J. Adrian, R.K. Menon, and S.L. Kaufman. 1991. Data Analysis, Laser DopplerVelocimetry and Particle Image Velocimetry, TSI Short Course Text, 1-16. St. Paul: TSI Inc.Gaster, M., and J.B. Roberts. 1975. Spectrum analysis of randomly sampled signals, Journal of theInstitute ofMathematics and its Applications, 15: 195-216.102__________1977. The spectral analysis of randomly sampled records by a direct transform,Proceedings ofthe Royal Society, London, A.354: 27-5 8.Jones, A.K., T.M. Grace, and T.E. Monacelli. 1989. A comparison of computational andexperimental methods for determining the gas-flow patterns in the kraft recovery boiler,TappiJournah 72(5): 193-198.Ketler, S.P., M.C. Savage, and I.S. Gartshore. 1993. Physical modeling of flows in black liquorrecovery boilers, Tappi journaL 76(9): 97-106.Lawn, C.J. 1971. The determination of the rate of dissipation in turbulent pipe flow, Journal ofFluid Mechanics, 48: 477-505.Lefebvre, B.E., R Burelle. 1989. The Chemical Recovery Boiler Optimized Air System, 1989 KraftRecovery Operations Seminar Proceedings, 239-246. Adanta: TAPPI Press.Lomas, C.G. 1986. Fundamentals of Hot Wire Anemometry, 190-195. Cambridge: CambridgeUniversity Press.-Mayo, W.T. 1978. Spectrum measurements with laser velocimeters, Proceedings of Dynamic FlowConference, Skoolunder, Denmark, 851-868. Denmark: DISA Electronik S/A.Pankhurst, RC., and D.W. Holder. 1968. Wind Tunnel Technique, 2nd ed., 204-211. London: SirIsaac Pitman & Sons.Perchanok, M.S., D.M. Bruce, and I.S. Gartshore. 1989. Velocity Measurements in an IsothermalScale Model of a Hog Fuel Boiler Furnace, Journal of Pulp and Paper Science, 15(6): 212-219.Quick, J.W., I.S. Gartshore, and M. Salcudean. 1993. The interaction of opposing jets. InProceedings ofthe Ninth Symposium on “Turbulent Shear Flows” held in Kyoto, Japan, August16-18, 1993, 64 1-646.Roberts, J.B., and D.B.S. Ajmani, 1986. Spectral analysis of randomly sampled signals using acorrelation-based slotting technique, lEE Proceedings, F. 133 (April): 153-162.Sacher, P.W. ed. 1987. Aerodynamic and Related Hydrodynamic Studies Using Water Facilities:AGARD Confrence Proceedings No. 413. Neuilly sur Seine, France: North Atlantic TreatyOrganization, Advisory Group for Aerospace Research and Development.Schetz, J.A. 1980. Injection and Mixing in Turbulent Flow. New York: American Institute ofAeronautics and Astronautics.Srikantaiah, D.V., and H.W. Coleman. 1985. Turbulence spectra from individual realization laservelocimetry data, Experiments in Fluids, 3: 3 5-44.Tennekes, H., and J.L. Lumley. 1972. A First Course in Turbulence. Cambridge, Massachusetts: TheMIT Press.White, Frank M. 1991. Viscous Fluid Flow. New York: McGraw.-Hill, Inc.103104APPENDIX A ORIFICE-PLATE CALIBRATION STATISTICSThe suitability of a number of distributions for representing the data was explored usingprobability plotting (Bury 1986, 208). In this technique, the cumulative distribution function of theproposed model is linearized to develop plotting positions. The ordered sample data is plottedagainst these plotting positions; if a relatively linear relationship is observed, the postulated modelcannot be rejected. This technique cannot be used for parameter estimation, but rather forpreliminary examination of the suitability of different models. The Weibull model was chosen torepresent the data from meter and drift errors from both B9 and D7 orifice-plates.A. 1 Weibull Analysis-An example of a Weibull probability plot using meter error from B9 orifice-plates is shownin Figure A. 1.1. Each curve represents one set flowrate tested; the relatively linear relationshipsbetween the data and the plotting positions indicate that the hypothesis that the data is modelled bythe Weibull distribution cannot be rejected.it/f III Set Flowrate [US gpml—B-— 2.5—z—— 3.5—v--— 4.5—-— 6—±-— 7.5—s—— 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4In(measured flowrate) [US gpm]Figure A. 1.1 Weibull Probability Plot- B9 Meter Error Data105The probability distribution function of the three-parameter Weibull model isfw(x; ))=X_lexp{_X_iLJ}where ji<x,—<p<, 0<cr,A (A.1.1)The three-parameter Weibull cumulative distribution function isFw(x; p, , A) = 1 — exp{_x_} (A.1.2)where x = random variable= location parameter-= scale parameterA = shape parameterThe two-parameter Weibull model is a special case of the above when the location parameterj.i is equal to zero. The Weibull distribution requires that realizations of the random variable xalways be greater than the value of the location parameter. Methods for maximum likelihoodestimation and unbiasing of the Weibull parameters by iterative methods are described by Bury(1986, 405 - 439). The first two moments of the measured data were calculated separately from thedata for each set flowrate (meter error) or time after flowrate setting (drift error).(A.1.3)Sq=qIn1l(q;_)2V (A.1.4)where n = number of orifice-plates of each respective type.The sample coefficient of dispersion is a non-dimensional measure of the variance of the measureddata106S(A.1.5)qDuring calibration of the orifice-plates in the recovery boiler water model facility, the backpressure on the orifice-plates was determined by the difference in height of the water free surfaceand the orifice-plates. This back pressure was kept constant at 1.49 metres of water throughout thetrials. When measuring meter errors, times to fill the calibrated cylinder were recorded, andconverted to flowratesq= (A.1.6)While data must be kept in actual units when calculating statistical quantities, the results may beconverted to fractional meter errors as represented by s— q_qset8=(A.1.7)S(A.1.8)Using the Weibull parameters calculated from maximum likelihood methods, the expectedvalue and standard error (square root of the model variance) of the model may be calculated. As thesample size is greater than 15 for both error types and orifice-plate models, large sample methodsmay be used to calculate confidence intervals and perform hypothesis tests using the calculatedexpected values and standard errors. Confidence intervals are found asCIonE’(z2.SE+EVziV)where z41 = a - quantile of standardized normal distribution107A.2 Meter ErrorFor testing the meter error, a number of flowrates were chosen to test each type of orifice-plate at. These completely covered the range of flows set during all experimental runs, and are shownin Table A.2.1.Table A.2.1 Set Flowrates for Meter Errorq, [US gpmj B9 D71.5 No Yes2.0 No Yes2.5 Yes Yes3.0 No Yes3.5 Yes No4.5 Yes Yes6.0 Yes Yes7.5 Yes Yes9.0 Yes NoStatistics of the sampled data from the meter error test forflowmeters are summarized in Table A.2.2.Table A.2.2 Meter Error Means, Standard Deviations, and Coefficients of Dispersionq, B9 6meter D7 6meer[USgpmJ S8 y S81.5--- —0.00900 0.01954 0.019722.0--- —0.00398 0.02002 0.019942.5—0.04346 0.03833 —0.8821 0.04900 0.01960 0.018693.0--- 0.06075 0.01763 0.016623.5—0.01428 0.03446—2.4134 ---4.5 0.02309 0.02636 1.1419 0.08967 0.02086 0.019156.0 0.05174 0.02034 0.3932 0.09636 0.02154 0.019647.5 0.06266 0.01966 0.3138 0.10445 0.01995 0.018069.0 0.07228 0.02103 0.2909---both types of orifice-plateUnbiased parameters, expected values, and standard errors of the Weibull random variablerepresenting meter error are shown in Tables A.2.3 and A.2.4. Because the Weibull model requiresthe use of actual flowrate values, as opposed to errors which may be negative, values shown in thetables are dimensional as opposed to fractional values.108Table A.2.3 Meter Error Weibull Model Parameters and Moments- B9 Orifice-Platesset Model Parameters Model Moments [US gpm][USgpm] A E{q} SE(q)2.5 0.0 2.437 25.16 2.385 0.11833.5 0.0 3.507 29.29 3.441 0.14724.5 0.0 4.660 40.02 4.596 0. 14476.0 0.0 6.367 54.45 6.302 0. 14657.5 0.0 8.036 60.86 7.962 0.16589.0 0.0 9.738 56.22 9.641 0.2172Table A.2.4 Meter Error Weibull Model Parameters and Moments- D7 Orifice-Platesq Model Parameters Model Moments [US gpm][US gpm] A E{q} SE(q)1.5 1.232 0.2676 9.611 1.486 0.031742.0 1.920 0.0995 2.280 2.008 0.040952.5 2.497 0.1408 2.590 2.622 0.051833.0 3.072 0.1251 2.145 3.182 0.054404.5 4.706 0.2237 2.160 4.904 0.096666.0 6.203 0.4191 2.991 6.577 0.136387.5 7.894 0.4375 2.664 8.283 0.15720A.3 Drift ErrorThe drift error was measured for the orifice-plates at six different times following the settingof the entire suite of orifice-plates, simulating a real experimental run. The B9 orifice-plates were allset to a flowrate of 3.5 US gallon per minute, while the D7 models were set to 2.5 US gpm. Themaximum time for checking the meter error roughly corresponded to the duration of a boiler run.Means and standard deviations of the drift error for B9 and D7 orifice-plates in Table A.3. 1.Table A.3. 1 Drift Error Means, Standard Deviations, and Coefficients of Dispersiontsjnce set B9 Emeter D7 Emeter[mm.] y S5 y73.0—0.05280 0.05353 —1.0138 —0.1217 0.09263 —0.7613147.5—0.06250 0.05498 —0.8797 —0.1439 0.10072 —0.6700221.5—0.06522 0.05646 —0.8657 —0.1483 0.10694 —0.7210299.0—0.07702 0.07230 —0.9387 —0.1767 0.13910 —0.7874372.5—0.09130 0.07139 —0.7819 —0.2178 0.18472 —0.8482447.5—0.08634 0.07136 —0.8265 —0.2472 0.21520—0.8705109Parameters and moments of the Weibi.ill model for drift error for the B9 and D7 orifice-plate flowmeters are shown in Tables A.3.2 and A.3.3 respectively.Table A.3.2 Drift Error Weibull Model Parameters and Moments - B9 Orifice-Platesq Model Parameters Model Moments [US gpm][USgpm] 11 u A E{q} SE(q)73.0 0.0 3.399 19.243 3.306 0.2127147.5 0.0 3.377 17.665 3.277 0.2290221.5 0.0 3.362 17.445 3.261 0.2306299.0 0.0 3.346 13.388 3.219 0.2935372.5 0.0 3.291 13.468 3.167 0.2871447.5 0.0 3.307 14.476 3.190 0.2699Table A.3.3 Drift Error Weibull Model Parameters and Moments- D7 Orifice-Platesq, Model Parameters Model Moments [US gpm][US gpm] A E{q } SE(q)73.0 0.0 2.289 11.972 2.1936 0.2225147.5 0.0 2.242 11.301 2.1437 0.2297221.5 0.0 2.238 10.362 2.1322 0.2480299.0 0.0 2.189 8.085 2.0622 0.3030372.5. 0.0 2.122 5.440 1.9578 0.4151447.5 0.0 2.069 4.283 1.8824 0.4964APPENDIX B POWER SPECTRAL DENSITY CALCULATIONS110A simulated laser-Doppler velocimetry signal was generated and used for validation of thedirect transform method of power spectral density calculations, and for exploration of the minimumfrequency detectable using the method. For thçse purposes, consider a function made up of threesinusoidal components of differing frequency and phase.y (t) = A1 Sifl( W1 t+ + A2 Sifl(°2 2) + A3 Sifl( 0)3 t+ 3) (B.1)where A1 1Jr•12C,a)>C)0a)>A2=1 A3=1 0)1=0.6.27r=0)23.0 2ir3,r= 20)320. 22rand A = amplitudet time0) frequency•= phase angleThe simulated signal is shown as a continuous function in Figure B. 0.5 1.0 1.5 2.0 2.5time [sec.]Figure B. 1 Simulated Signal as a Continuous Function111Now the continuous function of Equation B. 1, with a random noise component added, willbe sampled at random time intervals corresponding to the arrival of particles in the laser-Dopplervelocimeter measurement volume. A total of N random numbers between 0 and 1 will be generatedfrom a larger set of 10*N random numbers, wherev = mean sampling rateN = number of samples from the continuous signalIt is known that the inter-arrival times of particles in a measurement volume is a Poissonprocess, and the waiting times to given arrivals may be modelled by the Erlang distribution. Thefinal set of random numbers is thereby used to generate an equal number of realizations of waitingtimes from the Erlang cumulative distribution function (Bury 1986, 323-326)xF(x; o, A)=fjj exp(_ 9 (B.2)where x = waiting time to -th particle(1= mean inter-arrival-time I =VA = particle number (integer)Having chosen a mean sampling rate, the continuous signal of Equation B. 1 is sampled atN= 100 random times as determined by Equation B.2. A random noise component is added to thesimulated signal, where the amplitude signal to noise ratio was arbitrarily set equal to 5, a relativelylow value. The final randomly sampled random signal is shown in Figure B.2.112C,a)>00‘1)> 0.5 1.0 1.5 2.0 2.5time [sec.]Figure B.2 Randomly-Sampled Simulated Laser-Doppler Velocity SignalThe power spectral density of the simulated signal may now be computed using the methodsof §4.2. Holding the number of measurements constant at 100, the mean sampling rate v and totalrecord length Tmay be varied to observe the effects on the output spectra. Plots of computed powerspectral density are shown in Figures B3 through B6. It can be seen that a record of longer durationis required to adequately capture the information in the lowest frequencies. The resolution withwhich each frequency component of the signal is detected could be quantified by peak location andwidth, but would still somewhat subjective. Note that in Figure B.6 the 20 Hertz component is notvisible because the limited number of frequencies at which spectra were computed happen to overlapthe narrow bandwidth of the spectral peak.ii 0 I) ci-‘—•T1 0 CpS(f)[(mis)2/Hz]oppppppooo000-——ot’)4.0)0t30S(f)[(m/s)2/Hz]popoopo0o00000o-.(..0)000 00 00 4 (p C., c—i C,jS(f)[(mis)2/Hz]•00000oC)0 0)S(f)[(m/s)2/Hz]p 0 00o•0o-C,)0CoppoI’3C.)C.)o(7100)Ti (P 0 I. I-I NI>zr*-h N.. zN:.cz0 0 0Table B.1 Number of Periods of Each Frequency in Simulated SignalFigure v T f.TNo. [samples/sec.] [sec.] 0.6 Hz 3.0 Hz 20 HzB.3 500 0.259 0.155 0.78 5.18B.4 250 0.517 0.310 1.80 10.3B.5 100 1.292 0.775 3.88 25.8B.6 50 2.584 1.550 7.75 51.7The number of periods of each of the three frequencies in the simulated signals which arecaptured on each figure are shown in Table B.1. It was concluded that frequencies greater thanapproximately 5/ 7 where T is the record length, could be detected with reasonable resolution usingthe direct transform method of power spectral density estimation.115116APPENDIX C SUMMARY OF COMPUTER PROGRAMS DEVELOPEDA number of computer programs were developed in the course of this work to accomplishanalysis not possible using commercial software. The name and description of each piece of softwareis shown in Table C.1. With the exception of BOILER13, all programs were written in the ANSIstandard C language, and compiled using a Borland compiler for either DOSIWindows or OS/2.They are executable on any personal computer which uses an Intel-compatible 386 or higherprocessor. An i387 math coprocessor is required for execution using an i386 machine.Unless stated otherwise, all programs were developed and written by the present author. Acopy of any of these computer codes may be requested from the Department of MechanicalEngineering, U.B.C.117Concatenation of multiplestatistics files generated fromTSI FIND software intoformat usable byBOILER13 for plottingPlotting three-dimensionalvelocity vectors onto awireframe boilerrepresentationComputation of powerspectral densities fromvelocity data files generatedby TSI FIND software,including graphical displayand plottingBinarization of particle datarecorded on a S-VHS tape,including VCR controlCross-correlation analysis ofsuccessive single-exposureimages using input filesfrom BUBBLETemporal averaging ofcross-correlation results, andgeneration of Tecplotformat files for plotting andanimationWritten in AutoLisplanguage (provided withAutoCad)OS/2 Ver. Flat memory model andix 32-bit speed of OS/2essentialDOS Ver.5.0Flat memory model and32-bit speed of OS/2essentialTable C. 1 Summary of Computer Programs DevelopedTide Description Required CommentsOperatingSystemCONCAT13 DOS Ver.5.0AutocadVer. 11underDOS Ver.5.0BOILER1 3SPECTRA2 1BUBBLECCR17IMGAVGWindowsVer. 3.xwith DOSVer. 5.0OS/2 Ver.2.xWritten by G. Rohling,Dept. of Mech. Eng.,U.B.C. specifically forSFIARP GPB digitizer


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