q, 04 _...un.&.m+..i. .8. _ ,1... . [6‘3 V 4%. 3mm. . v n .- . . $31.1. 5.: a... 5...qu .. x12: . an... .. VH‘Q‘, i. o . . kiwi} , 1 . ihummwrafi U 1 .) v .5: .l..v 1?}..4‘5 .1. I l .d . A! ..4. Avoid“: .. . .2 5.. gfiflwfi . J . ,. . . .fimaazwnfi \Jcflgv a. .2 \ LIBRARIES \ 7 , MICHIGAN STATE UNIVERSITY ff 'N‘f“ EAST LANSING, MICH 48824-1048 baQQOQWE This is to certify that the thesis entitled COMPUTATIONAL INVESTIGATON OF THE VANELSEE DIFFUSER FLOW FIELD presented by TOSHIYUKI SATO has been accepted towards fulfillment of the requirements for the MS. degree in Mechanical Engineering Alas” Major Proféglsor’s Signature 08199‘ o (4‘ Date MSU is an Affirmative Action/Equal Opportunity Institution PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 6/01 c:/C|RC/Date0ue.p65-p.15 COMPUTATIONAL INVESTIGATION OF THE VANELESS DIFFUSER FLOW FIELD BY Toshiyuki Sato A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Mechanical Engineering 2004 ABSTRACT COMPUTATIONAL INVESTIGATION OF THE VANELESS DIFFUSER FLOW FIELD BY Toshiyuki Sato The fluid leaving a centrifugal compressor impeller contains a high amount of kinetic energy to a diffuser. Downstream of the impeller, in the diffuser, part of this energy is diffused and transformed to static pressure. In this present work, the Vaneless Diffuser is used. An existing experimental data of a vaneless diffuser was numerically verified, using Computational Fluid Dynamics (CFD). In order to improve the compressor performance, it is necessary to understand the detailed flow pattern in the diffuser. The flow in the vanless diffuser was numerically analyzed and the result compared with the experimental data. The computation was carried out by applying the experimental data as an initial input just after the impeller and corresponding boundary conditions. The main objective of this study was to verify the numerical accuracy and contribute knowledge towards predicting the performance of the compressor theoretically, which is very essential for the compressor designer and user. This thesis is dedicated to my parents, Toshimasa and Michiko Sato. TABLE OF CONTENTS page LIST OF FIGURES .................................................................................. v LIST OF SYMBOLS ................................................................................ ix CHAPTER 1 INTRODUCTION OF CENTRIFUGAL COMPRESSORS AND DIFFUSERS ........ 1 1-1. Introduction ........................................................................... 1 1-2. Geometrical Effects ................................................................ 6 CHAPTER 2 PROCEDURES ...................................................................................... 9 2-1. Introduction ..................................................................................... 9 2-2. Geometry and Grid ............................................................................ 9 2-3. Boundary Conditions ........................................................................ 10 2-3-1. Inlet Boundary Conditions .................................................... 10 2-3-2. Axisymmetric Swirl Flows ................................................... 13 2-3-3. The Turbulent Model: Spalart—Allmaras Model ........................ 13 CHAPTER 3 RESULTS AND DISCUSSION ................................................................. 16 3-1. Comparative Analysis ............................................................ 16 3-1-1. Flow Velocities ........................................................ 17 3-1-2. Contours ............................................................... 19 3-2. Predictive Analysis ................................................................ 20 CHAPTER4 CONCLUSIONS AND FUTURE WORK ..................................................... 22 4. Conclusions and Future Work .................................................... 22 BIBLIOGRAPHY ................................. . .................................................. 24 FIGURES ............................................................................................ 27 LIST OF FIGURES Page Figure 1-1 Vaneless Diffuser ..................................................................... 4 Figure 1-2 Centrifugal Compressor ............................................................. 5 Figure 2 (A) Schematic Layout of Vaneless Diffuser - Geometry &Grid (mm) ...... 8 Figure 2 (B) Computational Grid - Geometry &Grid (mm) ................................ 8 Figure 3 (A) Swirl Velocity Cu (mls) — Inlet Velocity Profiles ............................ 12 Figure 3 (B) Radial Velocity Cr (mls) — Inlet Velocity Profiles ........................ 12 Figure 4-1 Absolute Radial and Swirl Velocity (Cr/U2, Cule) - C.F.D vs. Experiment, n=13000 rpm ........................................... 28 Figure 4-2 Total Pressure and Total Temperature (7:, t) — C.F.D vs. Experiment, n=13000 rpm ............................................. 30 Figure 4-3 Flow Angle (a) — C.F.D vs. Experiment, n=13000 rpm .................... 32 Figure 5-1 Absolute Radial and Swirl Velocity (Cr/U2, Cule) — C.F.D vs. Experiment, n=15500 rpm ........................................... 34 Figure 5-2 Total Pressure and Total Temperature (7t, r) — C.F.D vs. Experiment, n=15500 rpm ............................................. 36 Figure 5-3 Flow Angle (a) — C.F.D vs. Experiment, n=15500 rpm .................. 38 Figure 6-1 Absolute Radial and Swirl Velocity (Cr/U2, Cule) - C.F.D vs. Experiment, n=18000 rpm ........................................... 40 Figure 6-2 Total Pressure and Total Temperature (7r, 1:) — C.F.D vs. Experiment, n=18000 rpm ............................................. 42 Figure 6-3 Flow Angle (a) - C.F.D vs. Experiment, n=18000 rpm .................. 44 Figure 7-1 Absolute Radial and Swirl Velocity (Cr/U2, Cu/Uz) — C.F.D vs. Experiment, n=20500 rpm ........................................... 46 Figure 7-2 Total Pressure and Total Temperature (It, I) - C.F.D vs. Experiment, n=20500 rpm ......... ' .................................... 48 Figure 7-3 Flow Angle (a) - C.F.D vs. Experiment, n=20500 rpm .................. 49 Figure 8-1 Contours of Flow Angle (a, 13000 rpm) ....................................... 52 Figure 8-2 Contours of Absolute Radial Velocity (Cr/U2, 13000 rpm) ................. 52 Figure 8-3 Contours of Total Pressure (7t, 13000 rpm) ................................ 53 Figure 8-4 Contours of Absolute Swirl Velocity (Cu/U2, 13000 rpm) ................. 53 Figure 8—5 Contours of Velocity Magnitude (mls), 13000 rpm .......................... 54 Figure 8-6 Velocity Vectors Colored by Velocity Magnitude, 13000 rpm ............. 54 Figure 8-7 Contours of Total Temperature (K), 13000 rpm .............................. 55 Figure 9-1 Contours of Flow Angle (a, 15500 rpm) ....................................... 56 Figure 9-2 Contours of Absolute Radial Velocity (Cr/U2, 15500 rpm) ................. 56 Figure 9—3 Contours of Total Pressure (7!, 15500 rpm) ................................ 57 Figure 9-4 Contours of Absolute Swirl Velocity (Cu/U2, 15500 rpm) ................. 57 Figure 9-5 Contours of Velocity Magnitude (mls), 15500 rpm .......................... 58 Figure 9-6 Velocity Vectors Colored by Velocity Magnitude, 15500 rpm ............. 58 vi Figure 9-7 Contours of Total Temperature (K), 15500 rpm .............................. 59 Figure 10-1 Contours of Flow Angle (a, 18000 rpm) ..................................... 60 Figure 10—2 Contours of Absolute Radial Velocity (Cr/U2, 18000 rpm) ............... 60 Figure 10-3 Contours of Total Pressure(n, 18000 rpm) ................................ 61 Figure 10-4 Contours of Absolute Swirl Velocity (Cu/U2, 18000 rpm) ............... 61 Figure 10-5 Contours of Velocity Magnitude (mls), 18000 rpm ......................... 62 Figure 10-6 Velocity Vectors Colored by Velocity Magnitude, 18000 rpm .......... 62 Figure 10-7 Contours of Total Temperature (K), 18000 rpm ........................... 63 Figure 11-1 Contours of Flow Angle (a, 20500 rpm) ..................................... 64 Figure 11-2 Contours of Absolute Radial Velocity (Cr/U2, 20500 rpm) ............... 64 Figure 11-3 Contours of Total Pressure( 7t, 20500 rpm) ................................ 65 Figure 11-4 Contours of Absolute Swirl Velocity (Cu/U2, 20500 rpm) ............... 65 Figure 11-5 Contours of Velocity Magnitude (mls), 20500 rpm ....................... 66 Figure 11-6 Velocity Vectors Colored by Velocity Magnitude, 20500 rpm .......... 66 Figure 11-7 Contours of Total Temperature (K), 20500 rpm ........................... 67 Figure 12 Inlet Velocity Prediction (Cr & Cu) ................................................ 68 Figure 13 Prediction of Boundary Conditions, Flow Angle (a) ......................... 69 Figure 14 Prediction of Boundary Conditions, Total Pressure (Pa) ................... 70 vii Figure 15 Prediction of Boundary Conditions, Radial Velocity Cr (mls) ............... 71 Figure 16 Prediction of Boundary Conditions, Swirl Velocity Cu (mls) ................ 72 Figure 17 Prediction of Boundary Conditions, Velocity Magnitude (mls) ............. 73 Figure 15 Prediction of Boundary Conditions, Path Line ................................. 74 viii LIST OF SYMBOLS NOTATION b Diffuser inlet height (mm) D Diameter (mm) h Height (mm) n Rotational speed (rpm) 7t Total pressure I Total temperature 0 Flow angle (degree) C Velocity (mls) U Impeller speed (mls) Subscripts 2 Inlet of diffuser 3 Outlet of diffuser r Radial Swirl/Rotational ix CHAPTER 1 INTRODUCTION OF CETRIFUGAL COMPRESSORS AND DIFFUSERS 1-1. INTRODUCTION Figure 1.2 shows that a centrifugal compressor consists of two parts, which are an impeller and a diffuser. The diffuser may lead pressurized fluid to the exit pipe system. The energy is transferred to the fluid in the impeller, and then the fluid leaves the impeller with a high amount of kinetic energy. To achieve a good efficiency, it is necessary to convert the kinetic energy to static pressure rise smoothly. To change the kinetic energy to static pressure rise, two different methods can be used: > Increasing the flow area, which reduces the velocity and increases the static pressure > Changing the mean flow path radius, which decreases the tangential velocity and increases the static pressure The diffusers of centrifugal compressor can be of two different types, which are vaneless and vaned. Vaneless diffusers are used when large operation range and inexpensive design are primary goals. On the other hand, the vaned diffuser has a more limited operation range and more complex geometry, which means more expensive design. In this study, all of experimental data was supplied by Turbomachinery Laboratory, Michigan State University. On the other hand, the computational fluid dynamics (CFD) is used to investigate the flow field of the diffuser, numerically. And the experimental data was used as the input boundary condition for this computation. The goals of this study are: > To study steady phenomena in the vaneless diffuser with CF D > To study the effect of input conditions change with CFD > To compare with the experimental data and the numerical data > To predict inlet boundary conditions and make sure the effects and accuracy The diffusers of centrifugal compressors have been studied for many 2 decades, and comprehensive literature on the design and construction of different kinds of diffusers is available. s7? CROSS SCTION Figure 1-1: VANELESS DIFFUSER Figure 1-2: CENTRIFUGAL COMPRESSOR 5 1-2. GEOMETRICAL EFFECTS The geometry of the vaneless diffuser is very simple. It consists of parallel or almost parallel walls which form a radial annular passage from the impeller outlet radius to some outlet radius of the diffuser. The diffuser is usually followed by a volute or a collecting chamber which leads the flow to one single exit. Ludtke (1983) has tested four types of vaneless diffusers: > parallel walls > highly tapered > constant area > parallel walls but reduced width (reduced 52.7% from the original width) The diffuser with the parallel walls showed best efficiency. The diffuser with the constant area diffuser has a slightly lower efficiency but the operation range was larger. The narrowed diffuser decreased the efficiency. The highly tapered diffuser showed improvement in surge margin but the efficiency was decreased. Yingkang and Sjolander (1987) have tested vaneless diffusers with various taper angles. They found that small amount of wall convergence was beneficial and yielded better static pressure recovery at the intermediate flow rate than parallel wall diffuser. The parallel wall diffuser showed better static pressure recovery at the high flow rate. Liberti et al. (1996) have tested two vaneless diffusers with different widths. They found that a narrower diffuser showed better efficiency and total-total pressure ratio than a wider diffuser. Japikse and Baines (1998) have found that the aspect ratio, AS=b/W1, was strongly coupled with aerodynamic blockage, Mack number, and Reynolds number. Small aspect ratios invariably penalize the pressure recovery substantially. Large area ratios are usually less deleterious, but the variations must be carefully considered. The walls of the vaneless diffuser are usually straight. Lee et al. (2001) have optimized the vaneless diffuser of the centrifugal compress using the Direct Method of Optimization (DMO). In their optimization method the height of the diffuser was altered by moving the shroud wall. They optimized the new geometry which had a minimum height at the middle of the diffuser passage. it showed 2-3% increase of efficiency at the design point and 1-5% increase of efficiency at the off-design point. EEG 9mm 8 E5280 ”N 2:9“. pro .mcozmSano Amy .6955 mmo_ocm> ho 59:3 oszmzom A3 '(IIIIEI' 00. r 'MIHWOBS' no. r nu. —. O.N u « (“II") CHAPTER 2 PROCEDURES 2-1. INTRODUCTION In this study, performance of a vaneless diffuser was investigated using a computational fluid dynamics (CFD) analysis. Also numerical simulations were done to analyze further details. All of the experimental data was supplied by Turbomachinary Laboratory Michigan State University. The flow solver Fluent v.6 was used to solve the flow field. The solver is capable to solve compressible, incompressible, steady, and steady flow fields. Spalart-Allmaras turbulence model was used in this analysis. As the inlet boundary condition, Turbulence Specification Method was used and the value of Modified Turbulent Viscosity was set up as 0.05. Axisymmetric Swirl was applied for the space to simulate the swirl velocity as a symmetry velocity along the x-axis using two-dimensional grid. 2-2. GEOMETRY AND GRID The schematic geometry and the computational grid are shown in Figure 2 respectively. The diffuser is simple vaneless diffuser. The inlet diameter: D2 is 290 (mm) and the exit diameter: D3 is 580 (mm). The heights of each point are shown as above. The passage of the diffuser through the inlet to outlet was divided into nine parts/i = d/Dz; 1.06, 1.15, 1.23, 1.38, 1.60 1.83, and 1.93. “”z/b means the distance toward the shroud from the hub at the diffuser inlet. Figure 2(A) presents the two dimensional computational grid created with the interactive grid generator Gambit, Fluent Inc. The number of cells is 6525. Axisymmetric Swiri was applied to the grid to compute the swirl velocities. 2-3. BOUNDARY CONDITIONS 2-3-1. INLET BOUNDARY CONDITIONS The experimental data was used for the inlet boundary conditions. The radius velocity Cr, and the swirl velocity Cu, which were from the experimental data, were read very carefully, and then put directly into the inlet boundary conditions. Also the temperature data was used as the inlet boundary. Pressure was not applied as inlet boundary conditions, but gage pressure was applied to entire flow filed. Figure 3 shows the radial and swirl velocities of each rotational speed which were used for the inlet boundary conditions. Figure 3(A) shows that the 10 swirl velocities simply become bigger in proportion to the rotational speed. And Figure 3(B) presents that when the rotational speed is getting bigger and bigger, the reverse flow at the inlet shroud side is getting stronger. ll 360 N ‘1 o SVVIRL VELOCITY Cu (mls on o o l J I 0.0 0.2 0.4 0.6 0.8 1.0 z/b (A) Swirl Velocity Cu (mls) 180 $1 20 <3 E 60 o O _J DJ 3 o S o 3‘: -60 0.0 0.2 0.4 0.6 0.8 1.0 z/b -0— 13000 -I- 15500 :t: 18000 “Air’- 20500 (B) Radial Velocity Cr (mls) Figure 3: INLET VELOCITY PROFILES 12 2-3-2. AXISYMMETRIC SWIRL FLOWS Axisymmetric Swirl was applied for the computational grid. In this vaneless diffuser case, axial (tangential) velocities are not important. And with this two dimensional grid, it is impossible to calculate the swirl velocities. But Axisymmetric Swirl may lead to indicate the swirling velocities Cu. The difficulties associated with solving swirling and rotating velocities are a result of the high degree of coupling between the momentum equations, which is introduced when the influence of the rotational terms is large. A high level of rotation introduces a large radial pressure gradient which drives the flow in the axial and radial directions. This determines the distribution of the swirl or rotation in the field. This coupling may lead to instabilities in the solution process. 2-3-3. THE TURBULENT MODEL: Spalart-Allmaras Model The Spalart and Allmaras turbulence model has been implemented in a finite volume code using an implicit finite difference technique. A wide range of turbulent flows have been computed to validate the implementation and numerical results are shown. The Spalart-Allmaras model belongs to the family of eddy viscosity models. This family of the models is based on the assumption that 13 the Reynolds stress tensor (—pu,uj) is related to the mean strain rate through an apparent turbulent viscosity called eddy viscosity v7. 65? 6? —u,uj =v,. -—+———— ay, ay. In the Spalart-Allmaras model, the eddy viscosity is computed through a partial differential equation. In particular the eddy viscosity v, computed by an intermediate variable V through the relation VT = Tful(l) Where 2’ is the ratio Z: <| Absolute radial and swirl velocities: Crle, CU/Uz > Total pressure and Total temperature: 7t, r > FIowAngle: ar(° ) 16 “* " and “e ” indicate the computational and the experimental data respectively. “"z/b means “height! inlet height”, the distance toward the hub from the shroud at the diffuser inlet. And “/1 ” is “diameter! inlet diameter” the distance of the flow direction from inlet to exit. 3-1-1. FLOW VELOCITIES AND THERMODYNAIIIIIC PROPERTIES According to all of figures (Figure 4 to 7), they show that the computational results are quite similar to the experimental results. On the Figure 4-1, the radial and swirl velocities are shown as different from each other at the inlet. But at the outlet, the velocities become almost same values. Figure 4-2 shows that the distributions of total pressure are always flat thought inlet to outlet. And Figure 4-3 shows that there is a difference between the computational and experimental results of flow angle, where z/b is around 0.7 to 1.0. Furthermore the difference becomes bigger around middle section (A =1.23 — 1.6). After that, the difference disappears and experimental and computational results indicate alike values. 17 The radial velocity of C.F.D results shows lower than the experimental data and the radial velocity make the flow angle of C.F.D results smaller then experimental (Figure 4-1 and 4-3). As well as Figure 4-1, Figure 5-1 also shows smaller radial velocities at the same positions where A =1.23 to 1.6 and zlb=0.7 to 1.0. It is conceivable that the inlet velocity conditions affect this phenomenon. Because there is a huge reverse flow region at inlet-shroud corner, that causes counterclockwise rotation in entire flow field. The counterclockwise rotation leads the radial velocity of hub side smaller and makes the gap between experimental and computational results. In addition, the inlet reverse flow region becomes larger as well as the rotational speed becomes bigger. This makes rather stronger counterclockwise rotation of entire flow field. Thereby, the radial velocities of hub side at the higher rotational speed become smaller. On the other hand, the distributions of total pressure and total temperature show nice results which are those nice flat distributions of total pressure and constant and uniform temperature (Figure 5-2). Figure 5-3 shows good results such as the reverse flow at the corner of inlet and hub and almost uniform flow with 45 degree flow angle around the exit. 18 3-1-2. CONTOURS This section presents the contours of flow angle a, absolute radial velocity Crle, total pressure 11, absolute swirl velocity Cu/Uz, velocity magnitude, velocity vectors, and total temperature 1: (Figure 8 through 11). Absolute radial and swirl velocities are normalized by impeller rotational speed, U2. According to the figures of the absolute radial velocities, the flow tends to lean to the shroud side when the rotational speed becomes higher. The reason is that the reverse flow region at the corner of inlet and shroud side is getting bigger when the rotational speed becomes higher, and this causes to appear the big stagnation region at the comer. In the same way, the figures of the flow angle and the total pressure show the similar phenomenon. Figure 8-4 (B) shows that the distribution of swirl velocity at low rotational speed indicates horizontal. But when the rotational speed becomes higher, the distribution becomes tilted shape (Figure 11-4 (3)). Initial inlet boundary condones can explain this phenomenon. Figure 3 shows that the swirl velocity of hub side (zlb=1.0) is always higher than shroud side (zlb=0). l9 3-2. PREDICTIVE ANALYSIS Figure 12 shows the fifteen cases of inlet conditions of each rotational speed which were predicted from the four experimental data: 13000, 15500, 18000, and 20500 rpm. Those inlet boundary conditions of 0 to 13000 rpm and 20500 to 33000 rpm. were predicted from four conditions of the experimental data. All of these data were computed and flow angle a, total pressure tr, radial velocity Cr, swirl velocity Cu, velocity magnitude, and path line were created and discussed through those rotational speeds (Figure 13 through 18). Figure 13 shows that the distributions of flow angle are different along the passage, but rotational speed is getting higher, the distributions are getting same kind and the differences toward to hub-shroud are appearing clearly. Wide reverse flow region appears at the corner of inlet and shroud on 33,000 rpm When rotational speed is around 18000 and 23,000 rpm, the flow tends to go to shroud side. But the rotational speed becomes higher, the flow becomes uniform again (Figure 14 and 15). Figure 16 shows that horizontal distribution at the lower rotational speed and the distribution of tilted shape at the higher rotational speed. Furthermore, the highest swirl speed region tends to gather at the comer of inlet ant hub, when 20 rotational speed becomes higher. Figures of velocity magnitude show an undiversified phenomenon through all of rotational speeds (Figure 17). There is a huge vortex region at the inlet-shroud corner. And it continues till almost middle of passage at the shroud side (Figure 18). 21 CHAPTER 4 CONCLUSIONS AND FUTURE WORK 4. CONCLUSIONS AND FUTURE WORK This paper has presented the results obtained, using computational simulations, on a vaneless diffuser with the experimental results. The following conclusions were made: > The steady phenomena in the vaneless diffuser has been prospected > The experimental and computational data have been compared clearly > The effect of input conditions has been investigated As a future work, three-dimensional simulations are recommended. The effect of the input conditions was very obvious. But the differences between CFD and Experimental results of radial and swirl velocities around A =1.23 were not analyzed clearly. It is estimated that tangential (axial) velocity component might 22 be related to this problem. Therefore, in order to explain about the movement of axial velocity and more detail of inlet boundary conditions, three-dimensional simulation is necessary. 23 BIBLIOGRAPHY 24 LIST OF BIBLIOGRAPHY Rautenberg, M. (1976). Experimental and Theoretical Research of Flow Condition of Diffuser of High Flgw Rate Centrifugal Compressor. Institute of Jet Engine, University of Hannover, Germany Turunen-Saaresti, T. (2004). Computational and Experimental Analggsis of Flow Field in the Diffusers of Centrifugal Compressors. Lappeenranta University of Technology Phillips, D.G, Richards, P.J., Flay, R.GJ. Diffuser Development for a Diffuser Augmented Wind Turbine Using Computational Fluid Dynamics. Department of Mechanical Engineering, University of Auckland, New Zealand Liu, R., Xu, Z. (2004). Numerical Investigation of a High-Sm Centrifugal Compressor with Hub Vane Diffusers. Institute of Fluid Machinery, School of Energy and Power Engineering, Xi’an Jiaotong University, China Chapman, K. Jariwala, J. and Keshavarz, A. Numerical Investigation of a Turbocharger Compressor with Variable Diffuser Vane Setting Angle. National Gas Machinery Laboratory, Kansas State University Hayashi, N, Koyama, M. and Ariga, I. Study of Flow Patterns in Vaneless Diffusers of Centrifugal Compressors Using PlV. Mechanical Engineering Department, Chiba Institute of Technology, Japan Japikse, D. and Baines, NC. (1998). Diffuser Design Technolpgy. Concepts ETI, INC. Fradin, C. (1992). Detailed Measurements of t_he Flow Fieil in Vaneless And Vaned Diffusers of Centrifugal Compressors. ONERA, Direction de I'Energétique, 29 Avenue de la Division Leclerc, 92320 Chatillon, France Niazi, S., Stein, A. and Sankar, L. N. Development and Application of A CFD Solver to the Simulation of Centrifugal Compressors. School of Aerospace Engineering, Georgia Institute of Technology, Atlanta 25 Paciorri, R. and Deconinck, H. et al (1997). Validation of the alart-Allmaras Turbulence Model for Application in Hypersonic Flows. von Karman Institute for Fluid Dynamics, Sint-Genesius-Rode, Belgium Fluent Inc. (1998). Fluent 5 Tutorial Guide. Fluent Incorporated Fluent Inc. (1999). Gambit Tutorial Guide. Fluent Incorporated 26 Figures 27 Crlu2 & Cu/u2 l=1.06 0.8 Cr/u2 8. Cu/u2 .0 .o b O) .0 N 0.0 -0.2 1 =1 .23 Figure 4-1: C.F.D vs. EXPERIMENT Absolute Radial and Swirl Velocity (Cr/U2, Cule), n=13000 rpm Cr/u2 & Cu/u2 -0.2 0.0 0.5 1.0 zlb 1 =1.15 1.0 0.8 Crlu2 8. Culu2 .0 .o h 0) 9 N 0.0 gig 1.0 l=1.38 28 1.0 0.8 Cr/u2 8 Cu/u2 .0 .o $ 0) .0 N 0.0 oz - l=1.60 1.0 0.8 0.6 Crlu2 8. Culu2 0.0 oz 0.0 0.5 1.0 zlb 2. =1.93 Figure 4-1 (cont’d) 29 Cr/uZ 8: Culu2 1.0 0.8 ___m_ _ 0.6 0.4 0.2 0.0 ‘ -0.2 0.0 0.5 1.0 zlb 1 =1.83 +Cr/u2 * -l-Cu/uZ * +Cr/uz e ~H— CuluZ e 0 . _ 1. _ m . _ _ . _ _ n . 5b . ca 0 0. 0. 8. 6. 4. 9. 0 2 1 1 1 1 4| 8322.th .20» a 2:30.... .20» 0 8 6 9. 1. 1. 2328.th .2o... a 2:32.. .2oh 1.15 l: ,1 =1.06 0. 8. 6. A 2 0. 2 1 4| 4| 1 1 236885 .28 w 2...».on .28 0. 8. 6. A 2 . ._ 0. 2 1 1 1 1 1 2322.th .20... a 2:32.". .20... 1.38 A: 1 =1 .23 Figure 4-2: C.F.D vs. EXPERIMENT Total Pressure and Total Temperature (1: , 1.’ ), n=13000 rpm 30 . . . . 0. 8. 6. 2 1 4| 232888 .28 w 238k. _28 o. 5 m 0. z 0 o. o. 8. 6. 4 2 2 1 1 8322.88. .28. a 238k. .20... 2. =1.83 1 =1.60 TI' *- +r +IT gags-nu" 1.0 0.5 zlb 2.0 0.0 8. 6. A 232888 .28 a 2:32.". .28 ,1 =1.93 Figure 4-2 (cont’d) 31 50 50 40 4o 30 ——*—Jfil-‘TEV: 3 3 g E’ 20 .— 3..- - .-_, -_ E E 3’ <9 _ E: 3 “- u. -10 - - -20 1.0 ,1 =1.06 50 50 40 40 -30 30 3 t g 20 §20 9 E 3’ 2 < 10 < 10 *7 7 3 a “' E 0 . 0 , -1o -10 A._ -- - - . -20 -20 0.0 0.5 1.0 0.0 0.5 1.0 z/b z/b 1 =1 .23 l =1_33 Figure 4-3: C.F.D vs. EXPERIMENT Flow Angle a , n=13000 rpm 32 40 20 1o-—— Flow Angle (Degree) 0.0 0.5 z/b l=1.60 Flow Angle (Degree) 0.0 0. 5 z/b l=1.93 Figure 4-3 (cont’d) 33 Flow Angle (Degree) 50 4o 30 2o 10 ———-fi = ~—=== o l -10 - -20 go (zllg 10 l=1.83 memo" 1‘ ~I~ae 0.8 .& Cr/u2 & Cu/u2 ° .0 b a) l l l .i. f - f 0.0 0.5 1.0 z/b 1 =1.06 1.0 0.8 06 . “r, Crlu2 & Cu/u2 O is 0.2 0.0 i. =1 .23 Figure 5-1: C.F.D vs. EXPERIMENT Absolute Radial and Swirl Velocity (Cr/U2, Cule), n=15500 rpm 0.8 Cr/u2 & Cu/u2 ‘3 o '3- a» .0 N 0.0 -0.2 0.0 0.5 1.0 z/b 1 =1.15 1.0 0.8 0.6 Crlu2 & Cu/u2 .0 A .0 N 0.0 l=1.38 34 1 0 1.0 0.8 o 3 0.6 -— 7*— 0.6 N N 3 3 3 3 o 0 ca 0 4 I «50.4 N N s s o o 0.2 _ 7 0.2 0 0 - 0.0 L -0.2 -0 2 0.0 0.5 1.0 0.0 0.5 1.0 zlb zlb 1 =1.60 1. =1.83 1.0 0.8 0.6 Crlu2 & Culu2 .0 .h 0.2 0.0 ‘ -0.2 0.0 0.5 1.0 z/b A =1 .93 Figure 5-1 (cont’d) 35 1.0 2.0 . s e. 4. 2 1.0 gnaw—8E0... _m«o._. .w guinea Each 0. 8. 6. A 2 0. 2 4| 22200Eo... .20 .r a 05008.”. .20 .. 1.15 l: 1 =1.06 232828 _28 a 2:828 28 2.0 23200:..0... .20... a 05822 .20... zilb zlb l=1.38 =1.23 A Figure 5-2: C.F.D vs. EXPERIMENT Total Pressure and Total Temperature (1: , 1:), n=15500 rpm 36 0. 8. 6. 4. 2. 2 1 1 1 4| 2328th .20 8 .w 2:328 .20 x... . m T a... m. 0. 8. 6. 4. 2. 2 4| 1 1 4| 2:20.852... .20... .w 2:39.... .20... 1.0 1.0 1.0 27?. i. =1 .83 0.0 1.0 0.0 l=1.60 +n* +r" +1T .um-r 2.0 232858 .28 0 2:828 .28 1.93 1: Figure 5-2 (cont’d) 37 0| 0 & O 00 O Flow Angle (Degree) . 1.0 zlb l=1.06 50 40 ~ A30 —— S § 20 E 2’ < 3 u. 0.0 0.5 1.0 zlb ,1 =1 .23 Figure 5-3: C.F.D vs. EXPERIMENT Flow Angle a , n=15500 rpm 38 N 00 fi 01 O O O O A o F low Angle (Degree) O z.lb l=1.15 é E 8’ < 5 LL -10 - - -_ -20 00 0.5 10 z/b l=1.38 50 0 0 -10 -20 .858. 292 2.5.“. 0 -10 -20 1.0 0.0 1.0 zlb 0.5 0.0 l=1.83 l=1.60 0 0 0 0 3 2 1 .389 292 so... -10 -20 1.0 0.5 z/b 0.0 l=1.93 Figure 5-3 (cont’d) 39 0.8 0.6 Cr/u2 8. Cu/u2 0.2 0.0 1.0 0.8 0.6 Crlu2 & Cu/u2 o is 0.2 0.0 Figure 0.4 0.0 0.5 1.0 z/b l=1.06 0.0 0.5 1.0 zlb 1 =1 .23 6-1: C.F.D vs. EXPERIMENT Crlu2 & Cu/u2 .0 .o A 03 .0 N 0.0 -0.2 0.0 0.5 1 0 z/b 1 =1.15 1.0 0.8 W ,- 0.6 Crlu2 8: Cu/u2 o is .0 N 0.0 0.0 0.5 1.0 zlb l=1.38 Absolute Radial and Swirl Velocity (Cr/Uz, Cule), n=18000 rpm 1.0 1.0 0.8 0.8 Crlu2 8: Cu/u2 1. =1.60 1 =1 .83 1.0 0.8 ‘E‘: 0.6 +Cr/u2 *‘j 8 +Cu/u2 * 1.: +Cr/u2 e 5 me— Culu2 e 0.0 ‘ -0.2 0.0 0.5 1.0 zlb x =1 .93 Figure 6-1 (cont’d) 41 8. 6. 4. 2 1 1 2.0 1.0 2320050... .20 h a 05320 .20 k 2.0 6 6. 4. 2 1.0 m...3200£0....u.20... a Qfimmen. .23. zlb l=1.15 l=1.06 2.0 2.0 6 6. 4. 2 1.0 232095» .20 .r a 23009.". .20... 8. 6. 4. 2 1.0 9.20080 H. .20 h a Eugen. .2mr 1.0 0.5 zlb 0.0 l=1.38 1 =1 .23 Figure 6-2: C.F.D vs. EXPERIMENT Total Pressure and Total Temperature (7:, 1: ), n=18000 rpm 42 2.0 1.0 2320060... .20 .. a 20002.. .20 .r 1.0 0.0 8. 6. 4. 2220.. E0... .20 .. 0 20002.“. .20 .. 2.0 1.0 1.83 A: 1 =1.60 _._ __J 11' +1T* +1” + -a... T 2.0 reT, 8. 6. 4. 2 O. 1 1 1 1 4| 2220020.. .20 .F a 23020 .20 .r 1.0 0.5 0. O zlb l=1.93 Figure 6-2 (cont’d) 43 so 50 4o _ —— C 40 30 -30 § 20 £20 5 2 °’ 8’ E 10 < 10 E: .3. LL. LL 0 o 40 -10 -20 -20 0.0 0.5 1.0 0.0 0.5 1.0 zlb z/b 1 =1.06 1 =1.15 50 50 4o 30 - g 20 3 E 2 O) U) 2 1o 5 3 5 LL LL 0 -10 -20 -20 0.5 0.0 0.5 1.0 zlb z/b ,1 =1_23 A =1.38 Figure 6-3: C.F.D vs. EXPERIMENT Flow Angle a , n=18000 rpm 44 w m m 0 m m .0208. 0.0.2 26E w m w m m 0 .0... m. .6208. 20.2 32... 1.0 0.0 1.0 0.0 ,1 =1.83 1. =1.60 +a* -I-ae 1.0 0.5 zlb 1 .93 0. o 0 0 2 1 .0280. 0.0.2 so: -1 0 -20 A: Figure 6-3 (cont’d) 45 0.8 .0 m Cr/u2 8. Cu/u2 O A .0 r0 0.0 -O.2 0.0 0.5 1.0 zlb 1 =1 .06 1.0 0.8 Crlu2 & Culu2 .0 .o A a: .0 r0 0.0 -0.2 0.0 0.5 1.0 zlb 1 =1 .23 Figure 7-1: C.F.D vs. EXPERIMENT 0.8 Crlu2 8. Cu/u2 .0 .o # O) .0 N -0.2 i 0.0 0.5 1.0 z/b 1 =1.15 1.0 Crlu2 & Cu/u2 .0 .o s 0: S3 N 0.0 l=1.38 Absolute Radial and Swirl Velocity (Cr/U2, Cule), n=20500 rpm 46 .0 on .0 a: Crlu2 & Cu/u2 0.0 0 5 z'lb l=1.60 1.0 0.3 —;- .- _’-_-_ 0.6 Cr/u2 & Culu2 . .0 .h C N 0.0 . -0.2 0.0 0.5 1.0 z/b ,1 =1.93 Figure 7-1 (cont’d) 47 Cr/u2 & Cu/u2 .0 .§ 0.8 __.,-__. 7 .- . ,- 0.6 - ———————. v, H 0.2 0.0 - 0.2 0.0 07% 1.0 1 =1.83 ‘1 +000? +Cu/u2 * ‘ wk“ Crlu2 e i Ctr/U2 e A 2 2 2 0. 8. 6. 4. 2 1 1 1 2320020.. .20... .0 200020 .20.. A 2 2 2 0. 8. 6. 4. 2320080.. .20 .r .0 230020 .20.. O 5 1.0 0. 0.5 1.0 zlb zlb 1.06 0.0 1.15 l: ,1: A... A 2 2. 0. 8. 6. 2 2 1 1 1 2320080... .20 .. .0 200020 .20.. A 2 2. 0. 8. 6. 4. 2 2 1 1 1 2320080... .20 b .0 230020 .20 h ,1 =1.38 ,1 =1 .23 Figure 7-2: C.F.D vs. EXPERIMENT Total Pressure and Total Temperature (1: , r ), n=20500 rpm 48 .D 3 fl. 8. 1 = «A 4. 2. D 8. 6. 4 2 0 2 2 2 1 1 1. 1. 1. 23200E0... .20.. a 200020 .20 .. m .m 1 .. , x . 4. 2. 0. 8. 6. 4 2 0 4. 2. 0. 8 6 4 2 2 2 1 1 1. 1. 1. 2 2 2 1. 1. 1. 232008.. .20 h .0 230020 .20 k 2320050.. .20 h .0 230020 .20 .. zib 1.93 A: Figure 7-2 (cont’d) 49 5O 50 40 Flow Angle (Degree) Flow Angle (Degree) 1 =1.06 1 =1.15 50 40 30 E 3 § § 20 E E 9 2' < < 10 E» 3 u. u. 0 -10 -20 0.0 0.5 1.0 0.0 0.5 1.0 z/b zlb 1 =1.23 it =1.38 Figure 7-3: C.F.D vs. EXPERIMENT Flow Angle a , n=205000 rpm 50 73 8’ 9, 9 U) E 3 LL 0 I -10 -20 0.0 0.5 1.0 zlb l=1.60 50 40 30 3 § 20 E 2’ < 10 3 LI. 0 1 -10 -20 0.0 0,5 1.0 z/b l=1.93 Figure 7-3 (cont’d) 51 Flow Angle (Degree) 50 0.5 z/b 1. =1.83 0...... 0* ME?- ae 30.0 13.4 7.59 a ‘3'“ I 44.0 (A) Experimental Result (B) Computational Result Figure 8-1: CONTOURS OF FLOW ANGLE (a (DEGREE), 13000 rpm) zlb=1.0 ., 0 Tim" 'm 0.41 1.6 _ g _ 0.21 $044 I-0.15 (A) Experimental Result (8) Computational Result Figure 8-2: CONTOURS OF ABSOLUTE RADIAL VELOCITY (Cr/U2, 13000 rpm) 52 zlhl1.0 1.37 2.0 1 .3 = 1 .31 1 .3 1 .25 1.4 1 .2 1 .14 A =1. .. 1.09 (A) Experimental Result (B) Computational Result Figure 8-3: CONTOURS OF TOTAL PRESSURE (1:, 13000 rpm) zlb=1.9 0 0.95 1.8 ' ' 0.75 1.6 ' ' 0.57 1.4 0.33 1 '2 ' 0.19 A “.0 . I f: o (A) Experimental Result (B) Computational Result Figure 8-4: CONTOURS OF ABSOLUTE SWIRL VELOCITY (Cu/U2, 13000 rpm) 53 215 ‘3172 ‘ ‘ -.; . 130 “ . . l '2 i” .6 o 71': .3 . .1 :Zr‘ .41. f; :1 i % "I! 5 . , . 3.}, P 43.0 ‘0 (a t . . ,. 0 (I!!!) Figure 8-5: CONTOURS OF VELOCITY MAGNITUDE (mls) ~ '. e 1 2} 1 as 54.5 (m) Figure 8-6: VELOCITY VECTORS COLORED BY VELOCITY MAGNITUDE n =13000 rpm 54 aim; a: at 322:1; I 300 (K) Figure 8-7: CONTOURS OF TOTAL TEMPERATURE (K) n =13000 rpm 55 amn1 30.5 zo ' 1.8 26.0 1 .6 15.5 1 '4 " $5.05 1 02 1" 2? Alto ‘ ‘ I IT". -1o.o (A) Experimental Result (B) Computational Result Figure 9-1: CONTOURS OF FLOW ANGLE (a (DEGREE), 15500 rpm) zlb-1.0 0,4 0 0.57 .0? l l 0.4 a. '_'. 1.8 , 0-42 é 1 e6 ‘ ' I 0'2. ‘ I. : ,- ‘ I. L450 ; ;ea in. . . 1 '2 11k j 4.2 -0.05 '1 '1'0 _. . . ._ I .' i 0.4 0.2 -0.2 (A) Experimental Result (8) Computational Result Figure 9-2: CONTOURS OF ABSOLUTE RADIAL VELOCITY (Cr/U2, 15500 rpm) 56 “=1 I 0" 59—1"! 0 1 .6. 2.0 “= ' ’ I 1 ,3 ' 1.55 1.0 1.45 1'2 1.28 A 81.0 I 1.10 (A) Experimental Result (B) Computational Result Figure 9-3: CONTOURS OF TOTAL PRESSURE (1c , 15500 rpm) zlb=1.gh_% 0 1.1 2.. : l 0.00 """" 0'“ 1 0.44 0'22 I 0 (A) Experimental Result (B) Computational Result Figure 9-4: CONTOURS OF ABSOLUTE SWIRL VELOCITY (Cu/U2, 15500 rpm) 57 0 (“118) Figure 9-5: CONTOURS OF VELOCITY MAGNITUDE (mls) 170 ‘0- . .1. .1 s I . . "i . ', /-. 1 I‘ i" o . D . .:k 5. ‘i I l‘ . 50 (INS) Figure 9-6: VELOCITY VECTORS COLORED BY VELOCITY MAGNITUDE n =15500 rpm 58 320 £315 '31 0 (“I Figure 9.7: CONTOURS OF TOTAL TEMPERATURE (K) n =15500 rpm 59 zlb=1.0 35.5 2.0 l 1.0 . 25.0 1 .0 15.0 1 04 4.65 "2 .. 11:31.0 _ I r . . . . . r: '1.-o (A) Experimental Result (B) Computational Result Figure 10-1: CONTOURS OF FLOW ANGLE (a (DEGREE), 18000 rpm) zlb-1.0 9.4, 0 0.05 2.0 l I 0.5 0.0 0.15 o I -0.25 (A) Experimental Result (B) Computational Result Figure 10-2: CONTOURS OF ABSOLUTE RADIAL VELOCITY (CrIUz, 18000 rpm) 60 zlb-1.0 -- 0 .155 1.55 1.45 7 1.35 '11 (A) Experimental Result (B) Computational Result Figure 10-3: CONTOURS OF TOTAL PRESSURE (1: , 18000 rpm) zlb-1.__ 1.5 2.0 ' ! 1.0 - 1.05 1.6 0.75 1.4- ' 0.5 A I1.0 I l’?-. 0 (A) Experimental Result (B) Computational Result Figure 10-4: CONTOURS OF ABSOLUTE SWIRL VELOCITY (CuIUz, 18000 rpm) 61 r I -_i 1 if}. #73: 170 i3. t . 4-55.2125 as. :21". . , V if“ .1 r in: 11 5.". *t". .. I . l '1 , I 0 (W3, Figure 10-5: CONTOURS OF VELOCITY MAGNITUDE (mls) I 2.3 ,. r. .. 5‘1 ,‘1 70 (mls) Figure 10-6: VELOCITY VECTORS COLORED BY VELOCITY MAGNITUDE n =18000 rpm 62 Figure 10-7: CONTOURS OF TOTAL TEMPERATURE (K) n =18000 rpm 63 ”M110 0 55.5 .0 . I 4 . 25.0 1.0 30 1: ’1 1.6 -’ f 14.5 1.4 4.0 1'1-0 i 31 30 20 10 -10.5 (A) Experimental Result (B) Computational Result Figure 11-1: CONTOURS OF FLOW ANGLE (a (DEGREE), 20500 rpm) “-1.0 .7 ‘ _ 0 !o_. ; .4 " if? 1.0 f' , 0.5 1.5 /‘ - . 0.35 /\_I‘ )5 {0.5. , 1-2 '2. ms :1 . \ f7 —— .__ 0 -0.0 (A) Experimental Result (B) Computational Result Figure 11-2: CONTOURS OF ABSOLUTE RADIAL VELOCITY (Cr/U2, 20500 rpm) 64 l 1.05 1 .75 1 .0 1 I5 1.35 I 1 .25 (A) Experimental Result (B) Computational Result Figure 11-3: CONTOURS OF TOTAL PRESSURE (1: , 20500 rpm) zlb=1.0 _ ‘0 1,5 2.0 1 .0 -- 1 .2 1 .6 0.9 1 .2 0.3 A I1.0 ' R 0 (A) Experimental Result (B) Computational Result Figure 11-4: CONTOURS OF ABSOLUTE SWIRL VELOCITY (Cu/U2, 20500 rpm) 65 0 (ml!) Figure 11-5: CONTOURS OF VELOCITY MAGNITUDE (mls) . . . 3 11 M 4 *275 03 (mls) Figure 11-6: VELOCITY VECTORS COLORED BY VELOCITY MAGNITUDE n = 20500 rpm 66 I335 - ‘~‘-‘-I‘E-?.1.- mm- ,ii'vé‘. 1:12? 11.2 .2... 320 (“I Figure 11-7: CONTOURS OF TOTAL TEMPERATURE (K) n = 20500 rpm 67 30 d .0. zO_._.O_Ommm >.—._OOr_m> bur—z. "NF 0.52". 98:5 5.5 .2 E9588 0 , 3 088 A o 88m 0 82m ,, m 2: 88m III, 88w res? com 089 LT 83? III 08% Some IT M 5 83 IT . . . . 8.7 Saw I ... 8... 8% Doom I com 08 IT . \IILo 8R 3_OO_0> .053. As 0.? md 06 com. oo 7 oom oov oom 68 .0039 e m..Oz< 26....- sztono 53:00 042. 00 20.55200 "9 e520 E... 88." .3 E9 e38 .= E9 88" .1. :5. 88a .2 EB 88. .0. 0.0..I 5.0-.I- 0-0PI. 0.0!... 0.0Pl ”VI-OPI— .. _,. m-OPI— . P-PFI_ .. a dV-PPI_ m.OPI_ P0-0| , 00-41) .. M. ., P0-0| ; , .. 00-0l . . . 04.1-0l 41. 0 .__.. .H 041- P 55¢. O a . P05 -Ol. r. . . 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