CFD STUDY OF FORCED AIR COOLING AND WINDAGE LOSSES IN SMALL
GAP REGION OF HIGH SPEED ELECTRIC MOTORS
A Thesis
Presented to the
Faculty of
California State Polytechnic University, Pomona
In Partial Fulfillment
Of the Requirements for the Degree
Master of Science
In
Mechanical Engineering
By
Alexander J. Wong
2017
SIGNATURE PAGE
THESIS: CFD STUDY OF FORCED AIR COOLING AND WINDAGE LOSSES IN SMALL GAP REGION OF HIGH SPEED ELECTRIC MOTORS
AUTHOR: Alexander J. Wong
DATE SUBMITTED: Summer 2017
Mechanical Engineering Department
Kevin R. Anderson, Ph.D., P.E. Thesis Committee Chair Mechanical Engineering
Henry Xue, Ph.D., Thesis Committee Member Associate Chair and Professor Mechanical Engineering
Angela Shih, Ph.D., Thesis Committee Member Professor and Chair Mechanical Engineering
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ACKNOWLEDGEMENTS
I would like to thank Dr. Kevin R. Anderson for providing both academic and professional insight and guidance throughout my Thesis research and Graduate coursework. I would also like to thank the Dr. Angela Shih and Dr. Henry Xue for taking part of the review committee of the Thesis as well.
Lastly, I would like to acknowledge my father, William W. Wong, who constantly gave me encouragement throughout the last four years to keep pushing through the
Master’s Program, despite his battle with terminal Cancer. Even though I will not be able to thank you in-person, please know that I am forever grateful for your love and support;
May you rest in peace.
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ABSTRACT
A numerical analysis method for characterizing heat generation and windage losses within small gaps of high-speed electric motors was conducted using computational fluid dynamics (CFD) software. The study of these windage losses
(frictional forces and heating of the air flow between the small gaps) is critical for designing for high efficiency at high rotational speeds due to cooling requirements. A total of 13 case studies of varied rotational speeds with a constant inlet flow rate are presented, with the results being compared directly with physical experiment test data. A discussion on the underlying theory, governing equations of motion and turbulence models and software configuration for the ANSYS CFD Simulations are presented.
Results from these simulations were used to both confirm the CFD model relevance in predicting actual measured windage losses and heat generated as well as validate the mechanical and thermal feasibility/limitations of a high-speed electric motor with a small gap between its rotor and stator.
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TABLE OF CONTENTS
SIGNATURE PAGE ...... ii
ACKNOWLEDGEMENTS ...... iii
ABSTRACT ...... iv
LIST OF FIGURES ...... vi
LIST OF TABLES ...... xiii
INTRODUCTION ...... 1
3D MODELS ...... 6
PHYSICS ...... 10
BOUNDARY CONDITIONS ...... 19
MESH ...... 28
STUDY ...... 32
EXPERIMENT SETUP ...... 36
CFD RESULTS ...... 38
CONCLUSION ...... 71
REFERENCES ...... 75
APPENDIX A – EXPERIMENT TEST DATA & PICTURES ...... 76
APPENDIX B – SUPPLEMENTAL CFD CASE STUDIES...... 78
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LIST OF FIGURES
Figure 1: Taylor-Couette Flow Patterns from Rotating Cylinders ...... 4
Figure 2: ANSYS Meshing Techniques: Tetra, Pyramid, Tri Prism, & Hexa...... 5
Figure 3:3d model Of Internal Flow Volume of High Speed Motor (Siemens NX 10) ..... 8
Figure 4:3D Flow Volume with Modified Outlet Geometry (Siemens NX 10) ...... 8
Figure 5: Section View (XY-Plane) of Modified Internal Flow Volume ...... 9
Figure 6: Imported CAD Model of Modified Geometry in ANSYS ...... 9
Figure 7: Physics Models Selection Menu, ANSYS FLUENT, Energy Equation ...... 11
Figure 8: Physics Models, ANSYS FLUENT, Viscous k- 휔 SST Model ...... 12
Figure 9: Continuity Equations, ANSYS, Inc Theory Guide ...... 13
Figure 10: Navier Stokes Equations (ANSYS Fluent Theory Guide) ...... 14
Figure 11: Energy Equation formulation (ANSYS Fluent Theory Guide) ...... 14
Figure 12: Transport Equations used for solving k and 휔 terms in standard model...... 16
Figure 13: ANSYS Fluent k-휔SST Model Equations ...... 17
Figure 14: Boundary Condition Setup Menu, ANSYS Fluent ...... 21
Figure 15: Boundary Conditions for Rotor Surface (RPM input) ...... 22
Figure 16: Inlet Boundary Surface (ANSYS Fluent) ...... 25
Figure 17: Outlet Boundary Surface (ANSYS FLUENT) ...... 25
Figure 18: Wall Surface/Back Face (Outlet Side), ANSYS Fluent ...... 26
Figure 19: Wall Surface, Front Face (Inlet side), ANSYS Fluent ...... 26
Figure 20: Housing Surface (Non-Rotating), ANSYS Fluent ...... 27
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Figure 21: Rotor Surface (Rotating), ANSYS Fluent ...... 27
Figure 22: 3D Mesh of Internal Flow Volume, ANSYS Mesh Module ...... 29
Figure 23: Section Cut View (XZ Plane) showing internal mesh structures ...... 30
Figure 24: Close-Up View of Mesh at the Small Gap Region ...... 30
Figure 25: Inlet Side of 3D Mesh, ANSYS Mesh Module ...... 31
Figure 26: Calculation Residuals Plot, ANSYS Fluent Solver ...... 34
Figure 27: Drag Force Monitors for 3 Surfaces, ANSYS Fluent ...... 34
Figure 28: Moment (Torque) Force Monitor for 3 Surfaces, ANSYS Fluent ...... 35
Figure 29: Force Reports for Drag Force, and Torque after Calculations are Completed 35
Figure 30: Diagram of Experiment Setup ...... 37
Figure 31: Internal Section View of Experiment Setup ...... 37
Figure 32: Total Windage – Experimental vs. CFD Results ...... 38
Figure 33: Heat Generated Comparison (CFD Data vs. Experimental Data) ...... 39
Figure 34: Rotor Torque Comparison, CFD Results vs. Experimental Data...... 42
Figure 35: Temperature Contour Plot, Case Study 1, 3846 RPM, Flow Time = 90s ...... 43
Figure 36: Velocity Contour Plot, Case Study 1, 3846 RPM, Flow Time = 90s ...... 43
Figure 37: Isosurface for Velocity at 10m/s, Case 1, t=90s ...... 44
Figure 38: Velocity Contour Plot, Case Study 2, 6000 RPM, Flow Time = 90s ...... 44
Figure 39: Temperature Contour Plot, Case Study 2, 6000 RPM, Flow Time = 90s ...... 45
Figure 40: Velocity Contour (Case Study 3, 8820 RPM, Flow Time = 90s) ...... 45
Figure 41: Isosurface for Velocity at 10m/s, Case 2, t=90s ...... 46
Figure 42: Temperature Contour (Case Study 3, 8820 RPM, Flow Time = 90s) ...... 46
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Figure 43: Isosurface for Velocity at 10m/s, Case 3, t=90s ...... 47
Figure 44: Velocity Contour (Case Study 4, 11520 RPM, Flow Time = 90s) ...... 47
Figure 45: Temperature Contour (Case Study 4, 11520 RPM, Flow Time = 90s) ...... 48
Figure 46: Isosurface for Velocity at 22 m/s, Case 4, t=90s ...... 48
Figure 47: Temperature Contour (Case Study 5, 14640 RPM, Flow Time = 90s) ...... 49
Figure 48: Velocity Contour (Case Study 5, 14640 RPM, Flow Time = 90s) ...... 49
Figure 49: Isosurface for Velocity at 30m/s, Case 5, t=90s ...... 50
Figure 50: Temperature Contour (Case Study 6, 17640 RPM, Flow Time = 90s) ...... 50
Figure 51: Velocity Contour (Case Study 6, 17640 RPM, Flow Time = 90s) ...... 51
Figure 52: Isosurface for Velocity at 32m/s, Case 6, t=90s ...... 51
Figure 53: Temperature Contour (Case Study 7, 19980 RPM, Flow Time = 90s) ...... 52
Figure 54: Velocity Contour (Case Study 7, 19980 RPM, Flow Time = 90s) ...... 52
Figure 55: Isosurface for Velocity at 40m/s, Case 7, t=90s ...... 53
Figure 56: Temperature Contour (Case Study 8, 21420 RPM, Flow Time = 90s) ...... 54
Figure 57: Velocity Contour (Case Study 8, 21420 RPM, Flow Time = 90s) ...... 54
Figure 58: Isosurface for Velocity at 45m/s, Case 8, t=90s ...... 55
Figure 59: Temperature Contour (Case Study 9, 23100 RPM, Flow Time = 90s) ...... 56
Figure 60: Velocity Contour (Case Study 9, 23100 RPM, Flow Time = 90s) ...... 56
Figure 61: Velocity Profile Development in Small Gap Region (Case Study 9, 23100
RPM, Flow Time = 30s, 60s, 90s) ...... 57
Figure 62: Temperature Contour (Case Study 9, 23100 RPM, Flow Time = 90s) ...... 57
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Figure 63: Velocity Streamlines in Gap Region (Case Study 9, 23100 RPM, Flow Time
=90s) ...... 57
Figure 64: Isosurface for Velocity at 50m/s, Case 9, t=90s ...... 58
Figure 65: Velocity Contour (Case Study 10, 26760 RPM, Flow Time = 90s) ...... 59
Figure 66: Velocity Profile Development in Small Gap Region (Case Study 10, 26760
RPM, Flow Time = 60s, 90s) ...... 59
Figure 67: Velocity Streamline Development in Small Gap Region (Case Study 10,
26760 RPM, Flow Time = 60s, 90s) ...... 59
Figure 68: Isosurface for Velocity at 60m/s, Case 10, t=90s ...... 60
Figure 69: Temperature Contours (Case Study 11, 30600 RPM, Flow Time = 90s) ...... 61
Figure 70: Velocity Contours (Case Study 11, 30600 RPM, Flow Time = 90s) ...... 61
Figure 71: Velocity Profile Development in Small Gap Region (Case Study 11, 30600
RPM, Flow Time = 30s, 60s, 90s) ...... 62
Figure 72: Velocity Streamline Development in Small Gap Region (Case Study 11,
30600 RPM, Flow Time = 30s, 60s, 90s) ...... 62
Figure 73: Temperature Profile Development (Case Study 11, 30600 RPM, Flow Time =
30s, 60s, 90s)...... 62
Figure 74: Isosurface for Velocity at 62m/s, Case 11, t=90s ...... 63
Figure 75: Temperature Contour (Case Study 12, 32580 RPM, Flow Time = 90s) ...... 64
Figure 76: Velocity Contour (Case Study 12, 32580 RPM, Flow Time = 90s) ...... 64
Figure 77: Temperature Profile Development in Small Gap Region (Case Study 12,
32580 RPM, Flow Time =30s, 60s, 90s) ...... 65
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Figure 78: Velocity Profile Development in Small Gap Region (Case Study 12, 32580
RPM, Flow Time =30s, 60s, 90s) ...... 65
Figure 79: Velocity Streamline Development in Small Gap Region (Case Study 12,
32580 RPM, Flow Time =30s, 60s, 90s) ...... 65
Figure 80: Isosurface for Velocity at 70m/s, Case 12, t=90s ...... 66
Figure 81: Temperature Contour (Case Study 13, 36600 RPM, Time = 90s) ...... 67
Figure 82: Velocity Contour (Case Study 13, 36600 RPM, Time = 90s) ...... 67
Figure 83: Temperature Profile Development in Small Gap Region (Case Study 13,
36600 RPM, Time = 90s) ...... 68
Figure 84: Velocity Profile Development in Small Gap Region (Case Study 13, 36600
RPM, Time = 90s) ...... 68
Figure 85: Streamline Development in Small Gap Region (Case Study 13, 36600 RPM,
Time = 90s) ...... 68
Figure 86:Isosurface Velocity Plot for airflow at 70 m/s, Case 13, 36600 RPM, t=30s .. 69
Figure 87: Isosurface Velocity Plot for airflow at 70 m/s, Case 13, 36600 RPM, t=60s . 69
Figure 88: Isosurface Velocity Plot for airflow at 70 m/s, Case 13, 36600 RPM, t=90s . 70
Figure 89: Volume Rendering, Velocity, Case 13, t=90s ...... 70
Figure 90: CFD Friction Loss/Viscous Heating Ratio ...... 73
Figure 91: CFD Taylor-Couette Flow vs. Published Flow Structure Forms ...... 73
Figure 92: Physical Test Experiment Setup (Jun T. Lin)...... 76
Figure 93: Heat Fluxes at Rotor Surfaces (100W, 200W, 300W) ...... 78
Figure 94: Velocity Isosurfaces (Heat Flux Study, t=30s, 60s, 90s) ...... 79
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Figure 95: Velocity Streamlines (Heat Flux Study, t=30s, 60s, 90s) ...... 79
Figure 96: Velocity Contours (Heat Flux Study, t=30s, 60s, 90s) ...... 79
Figure 97: Case B1 - Rotor Surface Temperatures (100W at Rotor, 36600 RPM, t=30s,
60s, 90s) ...... 80
Figure 98: Case B1 - Temperature Profiles in Gap Region, 100W, t=30s, 60s, 90s) ...... 80
Figure 99: Case B2 - Rotor Surface Temperatures (200W at Rotor, 36600 RPM, t=30s,
60s, 90s) ...... 80
Figure 100: Case B2 - Temperature Profiles in Gap Region (200W, 36600 RPM, t=30s,
60s, 90s) ...... 80
Figure 101: Case B3 - Rotor Surface Temperatures (300W at Rotor, 36600 RPM, t=30s,
60s, 90s) ...... 81
Figure 102: Case B3 - Temperature Profiles in Gap Region, 300W, 36600 RPM, t=30s,
60s, 90s) ...... 81
Figure 103: Case B4 – 50 LPM inlet, Velocity Isosurfaces, 83m/s (t=30s, 60s, 90s) ...... 82
Figure 104: Case B4 – 50 LPM Inlet, Velocity Profiles in Gap Region, t=30s, 60s, 90s 82
Figure 105: Case B4 – 50 LPM Inlet, Velocity Streamlines in Gap Region, t=30s, 60s,
90s ...... 83
Figure 106: Case B4 – 50 LPM Inlet, Temperature Profiles in Gap Region, t=30s, 60s,
90s ...... 83
Figure 107: Case B5 – 100 LPM Inlet, Velocity Isosurfaces, 83m/s, t=30s, 60s, 90s ..... 83
Figure 108: Case B5 – 100 LPM Inlet, Velocity Profiles in Gap Region, t=30s, 60s, 90s
...... 83
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Figure 109: Case B5 – 100 LPM Inlet, Velocity Streamlines in Gap Region, t=30s, 60s,
90s ...... 83
Figure 110: Case B5 – 100 LPM Inlet, Temperature Profiles in Gap Region, t=30s, 60s,
90s ...... 83
Figure 111: Case B6 – 150 LPM Inlet, Velocity Isosurfaces, 83m/s, t=30s, 60s, 90s ..... 84
Figure 112: Case B6 – 150 LPM Inlet, Velocity Profiles in Gap Region, t=30s, 60s, 90s
...... 84
Figure 113: Case B6 – 150 LPM Inlet, Velocity Streamlines in Gap Region, t=30s, 60s,
90s ...... 84
Figure 114: Case B6 – 150 LPM Inlet, Temperature Profiles in Gap Region, t=30s, 60s,
90s ...... 84
Figure 115: Case B7 – 200 LPM Inlet, Velocity Isosurfaces, 83m/s, t=30s, 60s, 90s ..... 85
Figure 116: Case B7 – 200 LPM Inlet, Velocity Profiles in Gap Region, t=30s, 60s, 90s
...... 85
Figure 117: Case B7 – 200 LPM Inlet, Velocity Streamlines in Gap Region, t=30s, 60s,
90s ...... 85
Figure 118: Case B7 – 200 LPM Inlet, Temperature Profiles in Gap Region, t=30s, 60s,
90s ...... 85
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LIST OF TABLES
Table 1: List of Boundary Conditions ...... 23
Table 2: List of 13 Rotor Speed (RPM) Case Studies ...... 24
Table 3: CFD Heat Generation Results for RPM Study ...... 41
Table 4: CFD Torque vs. Measured Torque ...... 41
Table 5: Final Results – CFD Windage vs. Experiment Windage ...... 42
Table 6: CFD Windage Results – Friction Loss vs. Heat Generated ...... 72
Table 7: Experiment Test Data – Measured Torque ...... 76
Table 8: Experiment Test Data – Heat Generated & Total Windage ...... 77
Table 9: Appendix B - CFD Heat Generation Results from Varied Heat Flux at Rotor .. 78
Table 10: Appendix B - CFD Total Windage Results from Varied Heat Flux at Rotor ... 79
Table 11: Appendix B - Mass Flow Rate Boundary Condition Inputs for Fluent ...... 81
Table 12: Appendix B - CFD Results from Varied Mass Flow Rate Study ...... 82
Table 13: Appendix B - CFD Windage Losses from Varied Mass Flow Rate Study ...... 82
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INTRODUCTION
This culminating report will present a discussion on developing a Computational
Fluid Dynamics (CFD) software model to predict specific performance characteristics of high-speed electric motors. As with any mechanical or electrical system, certain losses in performance or power can be expected. For example, in a rear wheel drive vehicle, typically 20% - 30% loss in power output between the engine crankshaft and the driven wheels can be expected. These losses can be attributed to friction, heat, & play between the bearings, couplers, transmission gearing, clutch, and driveshaft as power is transferred and absorbed from the engine to the wheels. Similarly, a high speed electric motor also experiences mechanical, electrical, thermal and aerodynamic losses. Thermal and aerodynamic losses, which are the basic components of “Windage” losses, will be the main focus of this study. Although the mechanical and electrical losses are equally important for design, these areas will not be covered.
Windage losses are attributed to the drag forces and heat generated within the small gap region between the rotor and stator. At higher rotor speeds, the losses become exponentially greater and have a significant impact on efficiency since additional heat is produced, thus requiring more cooling to maintain optimal operating temperatures. For many applications, forced induction air is used as the cooling fluid. The relationship between the amounts of cooling airflow required, windage generation, and maximum rotor temperature are the three main parameters in high speed electric motor design and integration. To properly study this relationship, CFD simulation analysis must be
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performed because of the complex and dynamic flow profiles coupled with heat and mass transfer as air flows through the system at high rotational speeds. Thus, optimizing for high efficiency will require regulating proper system cooling along with designing ways to reduce windage losses. Other sources of common losses from copper winding, hysteresis, bearing friction, or electrical dependency will not be a part of this study.
The term “windage,” is a friction force that is applied to an object which has relative motion between itself and the surrounding air, and produces a significant effect on the object. This force can either be created by a moving object being slowed down by air resistance or by airflow/wind producing drag forces on an object. For example, a cross wind on a projectile can produce a force which can alter its course and require guidance correction, or drag forces on a car can inhibit its top speed and handling characteristics.
Results of the simulation model will be compared and validated with actual experiment test data. To collect physical data on windage losses, the internal components of an electric motor were simplified by using two concentric cylinders (rotor and stator) with an inlet and outlet for forced cooling air flow. This setup would provide a more controlled environment to study the thermal and aerodynamic effects of an electric motor, as air passes through the gaps between the rotating cylinders. Ultimately, the results will lay the groundwork for future case studies and help Engineers in turbomachinery industries gain insight on incorporating high-speed electric motor into designs while compensating for windage and heat. Details on how the model was prepared as well as
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the underlying theory and software configuration will be discussed in subsequent sections.
ANSYS Fluent CFD software will be used to process the fluid model inputs and solve the complex mathematical equations required to study how air will flow within the motor internal cooling cavities. Fluent is capable of solving for incompressible and compressible fluids as well as laminar and turbulent flow from either a steady-state or transient time frame. Furthermore, the tools available in the software make it extremely useful for handling flows with complex geometries with all modes of heat transfer, combustion, and aerodynamic flows and trade studies for turbomachinery applications
(high-speed electric motors, compressors, pumps, fans). Based on the work previously presented by K.R. Anderson et al., with research by Haddadi and Poncet, Taylor-Couette-
Poiseuille flow can be expected to develop between the two concentric cylinders (rotor and stator) with a rotational Reynolds number falling within105 < 푅푒 < 107.
In Figure 1below, five patterns of dynamic motion between rotating cylinders with thin annular gaps are displayed. Most notably, each case represents a flow pattern resulting from a rotating inner cylinder and stationary outer cylinder. Images (a) through
(d) depict fluid motion for varying angular frequencies, with case (a) representing a steady state or time-independent formation. The experimental data will be directly applicable to these specific flow patterns and will help validate the CFD results presented in this study.
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Figure 1: Taylor-Couette Flow Patterns from Rotating Cylinders In addition to having the computational power to handle complex CFD simulations, ANSYS offers numerous techniques and options for fluid domain meshing.
There are four basic types of 3D mesh cells the engineer can choose from: Tetrahedral,
Hexahedral, Prismatic/Wedge, and Pyramidal elements. Selection of mesh cell type as well as applying particular mesh methods for part/body meshing will ultimately determine the quality of the simulation results and impact the efficiency of solving the flow field. Further tactics of meshing the flow domain for a high speed motor model is discussed later in the Mesh section.
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Figure 2: ANSYS Meshing Techniques: Tetra, Pyramid, Tri Prism, & Hexa. ANSYS Fluent allows for both Steady State and Transient (Time Dependent) physics studies. While other studies are available, they will not be discussed in this paper. A Steady State solution implies that the simulation results will no longer vary with time. From an equation stand-point, it simplifies the calculations because it equates all
퐷 푑 time-dependent terms & to zero. By cancelling out transient activity, the Fluent 퐷푡 푑푡 solver ignore what happens to the flow before reaching a steady state condition or how long it takes to reach that point. On the other hand, Transient or Time-Dependent solutions will account for all of the initial flow behavior as well as tracking the amount of time it takes to reach a steady state condition. For the following analysis, a Transient study is most appropriate as we are concerned with the initial conditions and heat generated in the events leading up to a steady state condition.
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3D MODELS
All 3D models of the flow volume were initially created in Solidworks, exported as .step files, and were further manipulated in Siemens NX 10. The original geometry was imported into NX to model various outlet extensions to facilitate the relevance of the
CFD solution and minimize the effects of “Backflow,” at the outlet surface.
Backflow or “Reversed Flow” is typically associated with a pressure-outlet type of boundary condition, in which calculation fluid re-enters or crosses into the outlet surface rather than flowing outwards. Further details on handling the backflow boundary conditions are discussed in subsequent sections. Backflow can affect the overall outlet temperature and velocity, as well as producing erroneous flow behaviors at the outlet if not compensated against.
There are some general tactics with CFD modeling to minimize backflow behavior. One of the most common solutions is to move the outlet further away from the original location. This can be achieved by modeling in an additional length of outlet surface to shift the backflow behavior. After several simulation trials with various outlet lengths and observing the resulting flows, it became apparent to create a pseudo volume at the exit that would be large enough to simulate the airflow flowing outwards into the environment. This new outlet volume was modeled as a cylinder which was 5 times the outlet diameter and 10 times longer. A larger radius was applied to the cylinder to allow the outlet flow to exit the volume in a more natural manner.
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These modified models were then exported as parasolid (.x_t) files, and imported into ANSYS for CFD processing and meshing. The complete flow volume of the motor consists of the inlet, gaps between rotor and stator, and outlet. The diameter of the outer cylinder (stator) is 91 mm and the inner (rotor) cylinder is 87 mm. This provided an annular gap of 2 mm between the two cylinders. The outer cylinder is 85 mm in length, and the inner cylinder is 60 mm, leaving a 12.5 mm gap at the ends between both cylinders. Both inlet and outlets have a diameter of 12.5 mm, which results in an area of
126.68 mm2.
For the modified flow domain in Figure 4, a larger cylinder with large radii at both ends was modeled to the end of the original outlet face. The new outlet would extend the original outlet by 80 mm and have a larger diameter of 55 mm to mimic the air exiting the motor’s flow volume into the environment. The dimensions of the extended outlet were modeled and adjusted accordingly after several trial and error attempts at studying how flow was behaving at the outlet boundary. The final geometry was then imported into the ANSYS Geometry modeler module and initialized as an internal flow volume instead of solid geometry.
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Figure 3:3d model Of Internal Flow Volume of High Speed Motor (Siemens NX 10)
Figure 4:3D Flow Volume with Modified Outlet Geometry (Siemens NX 10)
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Figure 5: Section View (XY-Plane) of Modified Internal Flow Volume
Figure 6: Imported CAD Model of Modified Geometry in ANSYS
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PHYSICS
Once the 3D model has been imported into the ANSYS Geometry, and processed through ANSYS Mesher modules, the Fluent Solver must be configured. Parallel calculations would be enabled for this study to reduce computation time, utilizing 10 processing cores simultaneously. Double-Precision was also selected, which allows the solver to run calculate values to up to the order of 1E-6, instead of 1E-3.
Next, parameters for the Physics models to solve an appropriate form of the
Navier Stokes continuity and momentum equations must be configured. Based on previous research presented by K.R.Anderson, the 풌 − 흎 SST (Shear Stress Transport) turbulence model of Wilcox (1998) and Menter (1993,1996) was selected for its accepted robustness at handling high-swirl and cross-flow behaviors within a narrow gap annulus.
For this formulation, “k” represents the turbulent kinetic energy and 흎 represents the turbulence frequency (1/sec). This model is also used particularly for its performance close to walls in boundary layer flows in addition to flows subjected to strong adverse pressure gradients (Jiyuan, 2013).
The viscous heating term for the 풌 − 흎 SST model was enabled to account for the heat generated within the small gap region. Viscous heating or viscous dissipation will allow the solver to track the amount of turbulent kinetic energy of the airflow that gets transferred into internal energy, or heat, which will increase the airflow temperature.
Lastly, the energy model was enabled to allow input and control of heat transfer terms, as
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well being able to specify initial temperatures at the boundary conditions. Further details on the Boundary Conditions applied to this study will be outlined in subsequent sections.
Figure 7: Physics Models Selection Menu, ANSYS FLUENT, Energy Equation
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Figure 8: Physics Models, ANSYS FLUENT, Viscous k- 휔 SST Model ANSYS Fluent will solve for both mass and momentum conservation equations for all flow problems. When solving for heat transfer or compressible fluid flows, Fluent adds the solving of the energy conservation (Fluent Theory Guide) to the mix. By that same token, for turbulent flows, additional transport formulations are added in. The turbulence models in ANSYS Fluent are useful for solving complex geometry and physics in turbomachinery flow cases.
The basic governing equations behind all flow calculations in ANSYS Fluent are the continuity and momentum equations. The equations shown below are the general forms of the mass conservation or continuity equation, which is used for both incompressible and compressible fluids. Here, 푺풎represents any mass added to the continuous phase from the dispersed second phase as well as any user-defined mass sources. For this study, there will be no additional mass added (injections) to or removed
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(vaporization) from the fluid, which sets the 푺풎term of the 2D incompressible continuity
(conservation of mass) equation to zero. Using the ANSYS Theory manual as a notation reference, “x” represents the axial coordinate, “r” represents the radial coordinate, and
“w” represents the tangential coordinate.
Figure 9: Continuity Equations, ANSYS, Inc Theory Guide In ANSYS, the model geometry will automatically define if 3D or 2D set of equations will be required. The axial, radial, and tangential momentum conservation (Navier
Stokes) equations for incompressible swirling and rotating flows are defined in the figure below.
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Figure 10: Navier Stokes Equations (ANSYS Fluent Theory Guide) Since it is also known that viscous heating will attribute to temperature rise in the system, the energy model must be enabled. The energy equation in Fluent would be formulated as shown, in Figure 11.
Figure 11: Energy Equation formulation (ANSYS Fluent Theory Guide) The RHS of the ANSYS Energy Equation for convective and conductive heat transfer has three components. The first term covers the conductive component, with the term 푘푒푓푓 representing the effective conductivity defined as 푘 + 푘푡.Within this term, 푘푡 is the turbulent thermal conductivity of the current turbulence model. The second component, containing the term 퐽푗 , identifies the energy transfer due to diffusion of species in the flow field. The third component covers energy transfer from viscous dissipation. The viscous dissipation term, defined as the Brinkman number, is responsible for characterizing the heating of the air flow due to friction forces. The last term, 푆푕 incorporates the heat from chemical reaction as well as any user-defined volumetric heat sources, but will not be used in this simulation. On the LHS of the
Energy Equation, 퐸 is defined as: 14
푝 푣2 퐸 = 푕 − + 휌 2
For the LHS, 푕 is the sensible enthalpy defined for ideal gasses. This enthalpy is defined as the sum of all the mass fraction of species 푗and the heat equation. In equation forms, 푕 is written as the following for ideal gas and incompressible flow:
푝 푕 = 푌 푕 + 푗 푗 휌 푗
Within the sensible enthalpy term, 푕푗 is defined as the following integral, bounded
푇 by 푇푟푒푓 =298.15 퐾: 푕푗 = 푐푝,푗 푑푇. 푇푟푒푓
As mentioned previously, the governing Energy Equation must also account for
Viscous Dissipation terms, in order to capture any thermal energy generated by viscous shear of the moving fluid, such as windage forces on the rotor surface. Viscous
Dissipation is defined in ANSYS by the Brinkman number, 퐵푟 . The Brinkman number is has components of dynamic viscosity 휇, flow velocity 푢, and thermal conductivity 푘. It strongly influenced by the temperature difference, ∆푇 of the system, and is defined as:
휇푈2 퐵 = 푒 . 푟 푘∆푇
By default, when a pressure-based solver is used, ANSYS views the effects of viscous heating as negligible, and ignores the viscous dissipation form of the Energy
Equation. However, these terms can be manually selected by enabling the Energy
Equation and selecting the viscous heating option in Fluent.
To handle turbulent flows, the 푘-휔 SST Model is used. The Standard 푘-휔 model in ANSYS Fluent is derived from the standard푘-휔model (Wilcox), which is an empirical
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model based on transport equations involving turbulence kinetic energy, 푘 and the frequency of specific dissipation, 휔.This model has particularly good performance for solving flows within a narrow gap annulus and high swirl. Fluent implements modifications for low-Reynolds numbers, compressibility, and shear flow spreading.
This model sets up two transport equations to solve for 푘 and 휔, shown below.
Figure 12: Transport Equations used for solving k and 휔 terms in standard model.
The terms 퐺푘, 퐺휔 , 훤푘 , 훤휔 represent respectively: the generation of turbulent kinetic energy due to mean velocity gradients, generation of specific dissipation rate, and the effective diffusivity of both 푘 and 휔.The Y and S terms are user-defined source terms.
Additionally, the Shear-Stress Transport (SST) 푘-휔model is designed to augment the standard 푘-휔formulation, in which the accuracy and robustness in the near-wall region is increased while keeping all of the benefits of the far-field free-stream independence of the 푘-휀 model. Since the gaps between the motor’s rotor and stator are small, it is imperative to have accuracy close to the boundary surfaces.
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Figure 13: ANSYS Fluent k-휔SST Model Equations
In the above SST equations for k-휔, ~퐺푘 defines the turbulence kinietic energy generated from the mean velocity gradients, which are obtained from 퐺푘of the Standard equation. The generation of 휔 from the standard equation also defines 퐺휔 .
Similarly,훤푘 , 훤휔 , represent the effective diffusivities of k and 휔. 푌푘 , 퐾휔 are defined as the dissipation from turbulence from their respective terms. The 퐷휔 term sets up a cross- diffusion variable while the S terms are all user-defined. Although further derivation of these terms will not be covered in this paper, it should be noted that the remaining terms and constants involving the푘-휔 SST model were left at their default values for all CFD simulation case studies.
Once the Energy, Viscous, and Turbulence Transport models of the governing continuity and momentum equations are configured, Fluent solution controls must be configured next. Fluent provides the user with several options for numerically solving the flow field and heat transfer equations. The SIMPLE method, developed by Patankar and
Spalding (1972) was selected for this analysis.
The SIMPLE Scheme is a commonly used algorithm for many CFD applications, in which an initial guess for the pressure field is used to solve the momentum equations. 17
This algorithm enforces a relationship between pressure and velocity through correction values, which regulate the mass conservation and pressure fields in the model. Terms involving u, v, w, and pressure fields are solved independently, then coupled together these pressure and velocity corrections. Initial values for pressure and velocity gradients are then iteratively refined as the momentum, pressure correction, pressure and velocity, and transport equations are solved for. With each calculation loop, the algorithm determines if the solution has converged and adjusts the guessed values from the previous iteration accordingly until convergence is obtained.
Overall, the SIMPLE scheme provides a robust method for calculating the pressure and velocities for an incompressible flow field. When coupled with other governing variables, such as temperature and turbulent quantities, the calculation needs to be performed sequentially, since the SIMPLE algorithm is an iterative process. The calculation loop is also user controlled, where the number of calculations per iteration, time step, and length of time can be specified for each solution.
Convergence is then monitored by calculating normalized scalars for each flow field term, which are called residuals. As residual values gradually become smaller, this indicates the solution values for each term are no longer changing after the prior iteration.
A solution is considered converged when the residuals of each equation are calculated below a tolerance value, typically on the order of 1E-3 to 1E-6. In ANSYS Fluent, convergence tolerance is configured by enabling single or double precision or manually configured in Fluent’s Solution Monitoring menus.
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BOUNDARY CONDITIONS
Boundary Conditions are critical for solving all CFD simulations, as they assign any initial assumptions that characterize the flow at a bounding surface, such as an inlet, outlet, or wall. For example, an inlet must contain information as to how the air will enter into the fluid volume, as well as flow properties and behavior at the walls and other surfaces in the domain. For this study, it is necessary to specify which surfaces will be stationary and which walls need to rotate at a to simulate the electric motor’s rotor movement for the case of two concentric cylinders.
For the primary case studies, all surfaces are assumed adiabatic, meaning no external heat transfer entering the system and heat will not be lost from the system. The purpose of simplifying external & internal heat transfer out of the analysis is to determine how much heat can be generated from just windage losses alone. A supplementary study, discussed in Appendix B was performed to consider both the effects of heat flux at the rotor and the cooling impact of supplying different inlet mass flow rates.
To solve the proceeding flow field, the governing Navier-Stokes’ equations must be defined by surface conditions to control how the flow enters, exits, and behaves at the bounding walls of the flow domain. In ANSYS Fluent, boundary conditions are applied to surface identifies or named surfaces. Prior to loading the Fluent module, a surface or group of surfaces can be given a specific name, such as “housing wall, rotor surface, or environment air,” to simplify the process of applying the right boundary condition to the desired surface.
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By default, ANSYS treats all surfaces with a “wall” boundary condition.
However, if a surface is labeled with a specific name containing the words “inlet” or
“outlet,” ANSYS automatically initializes that surface with an inlet or outlet boundary condition, respectively, with the defaults as velocity-inlet and pressure-outlet. Therefore, it is important to plan ahead of time, the names or identifiers for all surfaces in a model.
This not only makes the boundary condition assignment process much more efficient, but also provides additional control over the boundary behavior. For instance, the total rotor surface contains 8 surfaces total, and all surfaces within that group can be assigned the same rotational boundary condition.
The inlet surface was re-configured as a mass-flow inlet, using air for its fluid material, with a flow rate of 0.003961 kg/s at 294.55°퐾 (21.4℃) to match the experiment test setup. This flow rate was converted from Standard LPM (Liters per Minute) units since ANSYS Fluent requires kg/s as the units for all mass-flow rates. Outlet surfaces were treated with a backflow gauge pressure and backflow temperature. For the rotor surfaces, a frame of rotational motion, in units of Revolutions per Minute, with rotation along the positive X-Axis was specified. A total of 13 constant RPM values would be used for each case study. For the remaining housing surfaces (gap region and at both ends), a stationary and adiabatic non-slip wall condition was selected.
To reduce computation time and minimize computer resources, a popular strategy is to divide the flow geometry along symmetry planes. However, even though the majority of the flow domain in this study involves symmetric cylinders, the entire model must be analyzed in one piece for two reasons: 1) the location of the inlets and outlets in
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the model do not share the same planes of symmetry; and 2) the rotational motion of the fluid must be captured for the entire domain to study the windage.
It is also possible to specify heat transfer rates as a boundary condition. For example, a heat flux, in units of 푊 could be applied at any surface. Although this study 푚 2 is primarily focused on adiabatic conditions, a heat flux could be applied to the rotor surface (See Appendix B).Additional heating to the system would effectively simulate how the heat from the electric motor contributes to the overall heat generation of the system, in addition to potentially affecting the air flow in the small gap region.
Figure 14: Boundary Condition Setup Menu, ANSYS Fluent
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Figure 15: Boundary Conditions for Rotor Surface (RPM input)
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Table 1: List of Boundary Conditions
Surface Boundary Condition Type Value Units
Mass-Flow Inlet Mass Flow Rate 0.003916 kg/s Inlet Inlet Temperature Temperature 294.55 k Pressure Outlet Gauge Pressure 0 Pa Outlet Backflow Temperature Temperature 294.55 k Backflow Direction Normal to Boundary
Moving Wall Rotation, +X axis RPM Table 2 Wall- Roughness Height 0 m Wall Roughness Rotor Roughness Constant 0.5
Shear Condition No Slip
Thermal Conditions - Heat Flux 0 W/m2 Adiabatic Stationary Wall
Shear Condition No Slip
Wall- Roughness height 0 m Wall Roughness Housing Roughness Constant 0.5
Thermal Conditions - Heat Flux 0 W/m2 Adiabatic Stationary Wall - - - Shear Condition No Slip - - Wall- Roughness Height 0 m Wall Roughness Back Roughness Constant 0.5
Thermal Conditions – Heat Flux 0 W/m2 Adiabatic
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Stationary Wall - - - Shear Condition No Slip - - Wall- Roughness Height 0 m Wall Roughness Front Roughness Constant 0.5
Thermal Conditions – Heat Flux 0 W/m2 Adiabatic Stationary Wall - - - Shear Condition No Slip - - Wall- Roughness Height 0 m Wall Roughness Inflow Roughness Constant 0.5
Thermal Conditions – Heat Flux 0 W/m2 Adiabatic Stationary Wall - - - Shear Condition No Slip - - Wall- Roughness Height 0 m Wall Roughness Outflow Roughness Constant 0.5
Thermal Conditions – Heat Flux 0 W/m2 Adiabatic
Table 2: List of 13 Rotor Speed (RPM) Case Studies
Case 휴 (rad/s) RPM 1 402.75 3846 2 628.32 6000 3 923.63 8820 4 1206.37 11520 5 1533.10 14640 6 1847.26 17640 7 2092.30 19980 8 2243.10 21420 9 2419.03 23100 10 2802.30 26760 11 3204.42 30600 12 3411.77 32580 13 3832.74 36600
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Figure 16: Inlet Boundary Surface (ANSYS Fluent)
Figure 17: Outlet Boundary Surface (ANSYS FLUENT)
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Figure 18: Wall Surface/Back Face (Outlet Side), ANSYS Fluent
Figure 19: Wall Surface, Front Face (Inlet side), ANSYS Fluent
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Figure 20: Housing Surface (Non-Rotating), ANSYS Fluent
Figure 21: Rotor Surface (Rotating), ANSYS Fluent
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MESH
Unstructured 3D Tetrahedral elements were selected to mesh the fluid flow domain geometry. The unstructured mesh allows for random connectivity between neighboring nodes and cells, and is capable of conforming to complex geometry and shapes more easily and organically than a structured grid mesh. The final mesh model was refined by creating a stronger bias and growth rate around the rotor surfaces as well as a higher density of mesh cells within the small gap region. Inflation layers were also added within the small gap region and along the rotating rotor surfaces to increase the likelihood of capturing any boundary layer effects for this transient study. The motivation for adding these inflation layers was influenced from earlier research presented by K.R. Anderson, where Taylor-Couette-Poiseuille flow vortices within the small annular gap region between the cylinders were expected.
To ensure satisfactory grid independence and calculation efficiency, several mesh attempts were made to test the accuracy and results with different mesh methods and number of elements. For the initial attempt, over 2 million elements were used for a simulation with rotor speeds at 36600 RPM. A second attempt with a course mesh, containing fewer than 750,000 elements was then made. This course mesh revealed a similar temperature profile as the higher quality mesh, but lacked the formation of most of the vortices in the small gap region, and required several adjustments to the under- relaxation factors to avoid divergence, and temperature limited cells. Based on the previous test simulations, the model was then meshed with 1.2 million cells which
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yielded comparable results as the 2 million cell mesh, but with a significantly shorter computation time (average time of 45 minutes instead of 1.5 hours).
After iterating an ideal grid size and quality, attention was then shifted to the small gap region. Since Taylor-Couette vortices and flow structures were known to develop in those areas specifically, several attempts at boundary layer inflation settings were made to capture those patterns. Initial simulation trials with the inflation layer settings at a max layer height of 1mm and growth rate ratio of 1.2 were too course, and unable to show any vortex formations in the small gap region along the rotor surface. To resolve this, the inflation layer options were then set to first aspect ratio, with a layer height of 1mm, 10 division layers, and a growth rate ratio of 1.1. The refined mesh produced some reasonable vortices, and brought the final mesh element count to fewer than 1.5 million cells. This refined mesh would then be used for subsequent case studies.
Figure 22: 3D Mesh of Internal Flow Volume, ANSYS Mesh Module
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Figure 23: Section Cut View (XZ Plane) showing internal mesh structures
Figure 24: Close-Up View of Mesh at the Small Gap Region
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Figure 25: Inlet Side of 3D Mesh, ANSYS Mesh Module
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STUDY
ANSYS Fluent provides various methods for carrying out a particular CFD study.
To model the fluid flow behavior within the high-speed motor’s air volume, a transient analysis will be performed. Using a time-dependent model will allow the observation of pre-steady-state behavior, as well as when the system will reach a steady-state condition.
Furthermore, it will make possible to visually “track” how the flow changes and where the expected vortices develop and progress within the small gap region for a particular rotor speed.
As mentioned earlier in the Physics section, the k-ω SST Turbulence model was used to solve the internal flow field. Introduced by Menter in 1993, this is a two-equation velocity model with a shear stress transport formulation. It is similar to the popular k-휀 viscous model in terms of computational efficiency and solution robustness, but with the additional benefit of improved boundary layer behavior.
The following Fluent solver settings were influenced from previous studies presented by K.R. Anderson et al., with regards to the Pressure-Velocity coupling and
Spatial Discretization. For the Pressure-Velocity Coupling, the SIMPLE (Semi-Implicit
Method for Pressure Linked Equations) algorithm was chosen to iteratively solve the flow field. For the most part, “second order” formulations were used for the Pressure,
Momentum, Turbulence Kinetic Energy, Specific Dissipation Rates, and Energy solvers.
To solve the flow gradients, the Least Squares Cell Based method was selected. Under-
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Relaxation Factors were left unchanged, at the ANSYS Fluent Defaults, as divergence was not observed during the simulations.
Several monitors were established to visualize the calculation progress for each time-step as well as verify solution convergence. In addition to calculation residuals,
Drag and Moment vectors in the X, Y, and Z directions were monitored at the housing, rotor, and end-walls. In addition, the mass flow rate exiting the flow volume was monitored to verify that the same amount of air was exiting at the same rate as the inlet.
Initially, the time step was set to 1 second iterations per time step. After observing the convergence and steady-state behavior for a few trial simulations, the time step was reduced to 0.5 seconds with 180 time-steps for a total flow time of 90 seconds. Towards the 90 second mark, force and temperature monitors along the housing and rotor surfaces were showing minimal fluctuations, indicating a near steady-state condition had been achieved.
To maintain consistency in each calculation, each rotor RPM was set up as a separate case with all other boundary conditions held constant. Obtaining force and torque data would then be extrapolated from ANSYS Fluent after each simulation, by selecting the force vectors (1,0,0; 0,1,0; 0,0,1) for each respective surface of interest. For this study, forces at the rotor, housing, and back-wall surfaces would be compared.
Moment-forces about the positive X-direction (1,0,0) vector would also be used to evaluate the Torque (N-m) at those surfaces as well. Finally, each test case was post- processed individually to generate the respective contour and streamline plots shown in the CFD Results section.
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Figure 26: Calculation Residuals Plot, ANSYS Fluent Solver
Figure 27: Drag Force Monitors for 3 Surfaces, ANSYS Fluent
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Figure 28: Moment (Torque) Force Monitor for 3 Surfaces, ANSYS Fluent
Figure 29: Force Reports for Drag Force, and Torque after Calculations are Completed
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EXPERIMENT SETUP
A series of experiments were carried out by Jun T. Lin, a fellow Cal Poly Pomona
Master’s Student, which focused on measuring real-world windage losses and heat generated of a high speed electric motor. The internal components of a high-speed electric motor were simplified by constructing two smooth concentric cylinders as the rotor and stator. The “rotor” would be driven by a variable frequency controlled electric motor and a gearbox to achieve high RPM speeds. This setup closely resembles actual electric motors without copper windings, in which the stator grooves are filled with epoxy to produce a smooth and uniform cylinder surface. All experiment test data was collected with the same rotor dimensions as the CFD model (87 mm in diameter, and
60mm long) with a 2 mm air gap annular region between the rotor and stator surfaces.
Two parameters of data were collected: windage torque at the housing and temperatures at the inlet and outlet areas. The test results and calculations for spin-down torque, rotor windage torque, and heat generation were used as a basis for the building each case-study in the ANSYS CFD model. To experimentally measure the windage, a moment arm was placed at the rotor’s housing to measure the resultant torque produced at each RPM test point. Rotor RPM was then measured with a hall-effect sensor. To ensure the collected data was only influenced by windage, a calibration to compensate for bearing losses was performed, in which the torque produced by a much smaller 25 mm
OD rotor was used to offset the data.
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To calculate any heat generated from the axial air-flow in and out of the system, the temperature at two points and mass-flow rate must be known. Therefore, temperatures were recorded by placing thermocouple probes within the inlet and outlet tubes. A vortex flow meter was installed upstream of the inlet to measure the air mass flow rate. Provided with the properties of air, the test setup contained measurement of all necessary variables to calculate the heat generated by the windage losses.
Figure 30: Diagram of Experiment Setup
Figure 31: Internal Section View of Experiment Setup 37
CFD RESULTS
The ANSYS Fluent CFD model was able to closely approximate the experimental data. On average, the total windage losses predicted by the CFD model were in agreement within 17% from the experimental data. From a heat generation standpoint, the
CFD model was on average 21% higher from 15000 to 36000 RPM. Below this RPM range, the CFD model would under-predict the experimental heat-generation data.
Total Windage (W): Experiment vs. CFD
200
150
100 ExperimentalTotal CFDTotal 50 Poly. (CFDTotal) Windage Loss Loss (W) Windage 0 0 10000 20000 30000 40000
Rotor Speed (RPM)
Figure 32: Total Windage – Experimental vs. CFD Results
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Heat Gen: Experiment vs ANSYS CFD 60.0 50.0 40.0
30.0 Experimental 20.0 CFD 10.0 Poly. (CFD) Heat Generated (W) Generated Heat 0.0 0 10000 20000 30000 40000 Rotor Speed (RPM)
Figure 33: Heat Generated Comparison (CFD Data vs. Experimental Data) The over-prediction of windage losses from the CFD model, in its current setup and configuration, yields an acceptable approximation to the physical real-world conditions. Based on prior research by K.R. Anderson et al., in which a similar CFD study was done with STAR CCM+ analysis software, a 20% over-prediction from experimental data was reported. Tabulated results of the Heat Generated between
ANSYS CFD and experiment test data are shown in Table 3.
Visualizations of the temperature profiles and velocity characteristics generated by the ANSYS Fluent models are displayed in Figure 35 through Figure 85. The total amount of windage losses requires calculation for both the heat generated due to viscous heating of the air flow and the frictional torque from drag forces on the rotor. Results of these two calculations are then combined to yield the total power lost from the system.
Frictional torque along the rotational axis was measured through the Fluent Force Output
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Report options menu. Heat Generation within the system was calculated from the fundamental heat transfer rate equation: 푄 = 푚푐푝 ∆푇 , where:
푄 = 푇표푡푎푙퐻푒푎푡푇푟푎푛푠푓푒푟푅푎푡푒 (푊푎푡푡푠)
푘푔 푚 = 푀푎푠푠퐹푙표푤푅푎푡푒표푓푎푖푟 푠
퐽 푐 = 푆푝푒푐푖푓푖푐퐻푒푎푡표푓푎푖푟 푝 푘푔℃
∆푇 = 푇푖푛푙푒푡 − 푇표푢푡푙푒푡 ℃
In order to gain insight on how windage losses relate to heat generation, the variables 푚 &푐푝 were held constantas specified by the inlet boundary conditions.
Temperature at the inlet was also held constant at 21.4℃ (294.55 °퐾), which was also part of the initial boundary condition. As a result, only the temperature probed at a specific point in the outlet plane would control the overall heat transfer rate from the windage losses.
Frictional Torque, outlined in Table 4 was monitored along 3 surfaces of interest:
The Outer Housing, Rear Wall (on the outlet side), and Rotor. It should be noted that although the experimental torque was measured at a point on the end plate of the housing,
CFD data shows that torque measured along the rotating surfaces of the rotor provide the most reasonable set of data. For rotor speeds below 19,000 RPM (Cases 1 – 6), formation of Taylor-Couette vortices did not occur. Coincidentally, CFD data shows a lower amount of total windage for these cases, as opposed to speeds above 19000 RPM. For these higher RPMs, the amount of windage increases exponentially as more Taylor-
Couette-Poiseuille flow formations and friction forces develop in the narrow gap region. 40
Table 3: CFD Heat Generation Results for RPM Study
CFD Temperatures CFD Experiment Rotor Heat Inlet Outlet ∆푻 Heat Gen Speed Gen RPM °퐾 ℃ °퐾 ℃ ℃ W W 3846 294.55 21.4 295.173 22.023 0.623 2.501 6.633 6000 294.55 21.4 295.425 22.275 0.875 3.513 5.768 8820 294.55 21.4 295.912 22.762 1.362 5.468 6.973 11520 294.55 21.4 296.642 23.492 2.092 8.398 8.220 14640 294.55 21.4 297.19 24.04 2.64 10.598 8.572 17640 294.55 21.4 297.891 24.741 3.341 13.412 10.165 19980 294.55 21.4 298.844 25.694 4.294 17.238 12.648 21420 294.55 21.4 299.384 26.234 4.834 19.405 15.021 23100 294.55 21.4 300.002 26.852 5.452 21.886 17.018 26760 294.55 21.4 301.482 28.332 6.932 27.827 23.100 30600 294.55 21.4 303.775 30.625 9.225 37.032 28.590 32580 294.55 21.4 304.511 31.361 9.961 39.987 33.144 36600 294.55 21.4 306.909 33.759 12.359 49.613 39.696
Table 4: CFD Torque vs. Measured Torque Note: Negative values indicate torque acting along the –X axis direction. Rotor motion was initialized as rotation along the +X axis.
Rotor Speed CFD Torque Measured Torque RPM N-m N-m 3846 -0.00180 0.002 6000 -0.00284 0.002 8820 -0.00425 0.011 11520 -0.00589 0.013 14640 -0.00850 0.018 17640 -0.01091 0.020 19980 -0.01299 0.022 21420 -0.01440 0.027 23100 -0.01630 0.025 26760 -0.02067 0.025 30600 -0.02559 0.031 32580 -0.02859 0.036 36600 -0.03421 0.038
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Windage Torque: CFD vs. Experiment 0.045 0.04 0.035 0.03 0.025 CFD Torque, Rotor (abs) 0.02 0.015 CFD Torque, Housing
Torque, N-m Torque, 0.01 CFD Torque, Back Wall 0.005 Experiment Torque 0 -0.005 0 10000 20000 30000 40000 Rotor RPM
Figure 34: Rotor Torque Comparison, CFD Results vs. Experimental Data. Table 5: Final Results – CFD Windage vs. Experiment Windage
Rotor CFD Experiment Speed Windage Windage Percent Difference RPM W W 3846 3.226 7.106 54.61% 6000 5.297 5.024 -5.44% 8820 9.390 12.927 27.36% 11520 15.501 17.894 13.37% 14640 23.633 27.031 12.57% 17640 33.558 36.009 6.81% 19980 44.422 46.265 3.98% 21420 51.716 60.939 15.14% 23100 61.314 60.900 -0.68% 26760 85.762 73.516 -16.67% 30600 119.022 107.435 -10.78% 32580 137.517 132.233 -4.00% 36600 180.724 159.286 -13.46%
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Figure 35: Temperature Contour Plot, Case Study 1, 3846 RPM, Flow Time = 90s
Figure 36: Velocity Contour Plot, Case Study 1, 3846 RPM, Flow Time = 90s
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Figure 37: Isosurface for Velocity at 10m/s, Case 1, t=90s
Figure 38: Velocity Contour Plot, Case Study 2, 6000 RPM, Flow Time = 90s
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Figure 39: Temperature Contour Plot, Case Study 2, 6000 RPM, Flow Time = 90s
Figure 40: Velocity Contour (Case Study 2, 8820 RPM, Flow Time = 90s)
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Figure 41: Isosurface for Velocity at 10m/s, Case 2, t=90s
Figure 42: Temperature Contour (Case Study 3, 8820 RPM, Flow Time = 90s)
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Figure 43: Isosurface for Velocity at 10m/s, Case 3, t=90s
Figure 44: Velocity Contour (Case Study 4, 11520 RPM, Flow Time = 90s)
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Figure 45: Temperature Contour (Case Study 4, 11520 RPM, Flow Time = 90s)
Figure 46: Isosurface for Velocity at 22 m/s, Case 4, t=90s
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Figure 47: Temperature Contour (Case Study 5, 14640 RPM, Flow Time = 90s)
Figure 48: Velocity Contour (Case Study 5, 14640 RPM, Flow Time = 90s)
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Figure 49: Isosurface for Velocity at 30m/s, Case 5, t=90s
Figure 50: Temperature Contour (Case Study 6, 17640 RPM, Flow Time = 90s) 50
Figure 51: Velocity Contour (Case Study 6, 17640 RPM, Flow Time = 90s)
Figure 52: Isosurface for Velocity at 32m/s, Case 6, t=90s
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Figure 53: Temperature Contour (Case Study 7, 19980 RPM, Flow Time = 90s)
Figure 54: Velocity Contour (Case Study 7, 19980 RPM, Flow Time = 90s)
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Figure 55: Isosurface for Velocity at 40m/s, Case 7, t=90s
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Figure 56: Temperature Contour (Case Study 8, 21420 RPM, Flow Time = 90s)
Figure 57: Velocity Contour (Case Study 8, 21420 RPM, Flow Time = 90s)
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Figure 58: Isosurface for Velocity at 45m/s, Case 8, t=90s
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Figure 59: Temperature Contour (Case Study 9, 23100 RPM, Flow Time = 90s)
Figure 60: Velocity Contour (Case Study 9, 23100 RPM, Flow Time = 90s)
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Figure 61: Velocity Profile Development in Small Gap Region (Case Study 9, 23100 RPM, Flow Time = 30s, 60s, 90s)
Figure 62: Temperature Contour (Case Study 9, 23100 RPM, Flow Time = 90s)
Figure 63: Velocity Streamlines in Gap Region (Case Study 9, 23100 RPM, Flow Time =90s) 57
Figure 64: Isosurface for Velocity at 50m/s, Case 9, t=90s
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Figure 65: Velocity Contour (Case Study 10, 26760 RPM, Flow Time = 90s)
Figure 66: Velocity Profile Development in Small Gap Region (Case Study 10, 26760 RPM, Flow Time = 60s, 90s)
Figure 67: Velocity Streamline Development in Small Gap Region (Case Study 10, 26760 RPM, Flow Time = 60s, 90s)
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Figure 68: Isosurface for Velocity at 60m/s, Case 10, t=90s
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Figure 69: Temperature Contours (Case Study 11, 30600 RPM, Flow Time = 90s)
Figure 70: Velocity Contours (Case Study 11, 30600 RPM, Flow Time = 90s)
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Figure 71: Velocity Profile Development in Small Gap Region (Case Study 11, 30600 RPM, Flow Time = 30s, 60s, 90s)
Figure 72: Velocity Streamline Development in Small Gap Region (Case Study 11, 30600 RPM, Flow Time = 30s, 60s, 90s)
Figure 73: Temperature Profile Development (Case Study 11, 30600 RPM, Flow Time = 30s, 60s, 90s)
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Figure 74: Isosurface for Velocity at 62m/s, Case 11, t=90s
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Figure 75: Temperature Contour (Case Study 12, 32580 RPM, Flow Time = 90s)
Figure 76: Velocity Contour (Case Study 12, 32580 RPM, Flow Time = 90s)
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Figure 77: Temperature Profile Development in Small Gap Region (Case Study 12, 32580 RPM, Flow Time =30s, 60s, 90s)
Figure 78: Velocity Profile Development in Small Gap Region (Case Study 12, 32580 RPM, Flow Time =30s, 60s, 90s)
Figure 79: Velocity Streamline Development in Small Gap Region (Case Study 12, 32580 RPM, Flow Time =30s, 60s, 90s)
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Figure 80: Isosurface for Velocity at 70m/s, Case 12, t=90s
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Figure 81: Temperature Contour (Case Study 13, 36600 RPM, Time = 90s)
Figure 82: Velocity Contour (Case Study 13, 36600 RPM, Time = 90s)
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Figure 83: Temperature Profile Development in Small Gap Region (Case Study 13, 36600 RPM, Time = 90s)
Figure 84: Velocity Profile Development in Small Gap Region (Case Study 13, 36600 RPM, Time = 90s)
Figure 85: Streamline Development in Small Gap Region (Case Study 13, 36600 RPM, Time = 90s)
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Figure 86:Isosurface Velocity Plot for airflow at 70 m/s, Case 13, 36600 RPM, t=30s
Figure 87: Isosurface Velocity Plot for airflow at 70 m/s, Case 13, 36600 RPM, t=60s
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Figure 88: Isosurface Velocity Plot for airflow at 70 m/s, Case 13, 36600 RPM, t=90s
Figure 89: Volume Rendering, Velocity, Case 13, t=90s
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CONCLUSION
After comparing the results of the initial adiabatic case study with the experimental data, it can be concluded that the CFD model was viable in predicting the overall windage losses for the system. More specifically, the ANSYS Fluent model and cases can be utilized for future studies to explore how heat transfer/heat-flux at both the rotor and stator surfaces affects these losses. Based on the CFD results, the majority of these losses are generated by the frictional torque of the airflow acting against the rotor.
The streamline plots at the gap region after 90 seconds of flow time also reveal the formation of Taylor-Couette-Poiseuille structures around 20,000 RPM, with vortices forming around 27,000 RPM. As rotor RPM increases, more swirled flow begin to form within the gap region. It is also evident that the vortices and waves become clustered near the outlet as flow time progresses, which could lead to increased drag and heat generation.
Although there is evidence of velocity peaks developing towards the end of the gap as early as 20,000 RPM, there are not enough formations to induce the Taylor-
Couette vortices. It does appear that once the rotor reaches faster speeds to shear and disturb the airflow that the velocity peaks are high enough to cause the vortex behavior to appear. With the exception of the 1st case (3846 RPM), the CFD data seems reasonable when compared to the actual test data. For cases above 10,000 RPM, the percentage error between CFD Windage predictions and Experiment Windage is within ±20%, while the total average of percentage error across all cases is under 7%.In addition,
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polynomial regression trendlines for both 2nd and 3rd order yield 푅2 values of 0.9992 and
0.9999, respectively.
From the CFD data, it can also be concluded that a majority of the windage losses are generated by the frictional torque acting on the rotor. On average, across all 13 cases, the friction torque on the rotor is 2.5 times greater than the heat generated through viscous heating of the air flow (see Table 6 below). Lastly, the CFD results show that the total windage losses are asymptotic in behavior, where the otal windage and heat will also significantly increase with rotor speed. Based on the trendlines for total windage, if the motor were run at higher RPM speeds, a significant amount of cooling would be required to maintain optimal efficiency.
Table 6: CFD Windage Results – Friction Loss vs. Heat Generated
Heat Gen Friction Loss Friction-Heat Case RPM (W) (W) Ratio 1 3846 2.501 3.226 1.290 2 6000 3.513 5.297 1.508 3 8820 5.468 9.390 1.717 4 11520 8.398 15.501 1.846 5 14640 10.598 23.633 2.230 6 17640 13.412 33.558 2.502 7 19980 17.238 44.422 2.577 8 21420 19.405 51.716 2.665 9 23100 21.886 61.314 2.801 10 26760 27.827 85.762 3.082 11 30600 37.032 119.022 3.214 12 32580 39.987 137.517 3.439 13 36600 49.613 180.724 3.643
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Friction Loss/Viscous Heating Ratio
4.0 3.5 3.0 Ratio:Friction/Heat 2.5
2.0 Poly. Ratio 1.5 (Ratio:Friction/Heat) 1.0 0.5 0.0 0 10000 20000 30000 40000 RPM
Figure 90: CFD Friction Loss/Viscous Heating Ratio
Figure 91: CFD Taylor-Couette Flow vs. Published Flow Structure Forms There are some factors which could contribute to the differences between experimental and CFD data. For determining Heat Generation, Probe placement could make a difference in final calculations of both inlet and outlet temperatures. From the
CFD results, the flow tends to swirl and carry more temperature on one side of the outlet.
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Also, from temperature contours at the outlet surface, temperature readings will vary if measured from the physical center to the outer surface. All measurements of temperature were taken near the center line of the outlet surface.
To further improve the simulation results, the mesh methods could be refined further in the small gap region, using smaller boundary inflation layers and cell sizes.
Although the 3D mesh presented in this study was adequate in producing Taylor-Couette formations with axial Poiseuille flow in the small gap region, as early as 20,000 RPM
(see Figure 91), it is possible that the grid may need more refinement to capture any vortices developing in the small gap region at lower rotor rotational speeds.
Overall, the results presented in indicate that the ANSYS CFD model developed for this study achieved agreeable estimations of windage losses to the actual test measurements. In addition, the formation of Taylor-Couette Flow Structures also proves that the CFD model can be viable in studying the physical losses and heat generation due to windage for further studies. However, the results also indicate that the rising asymptotic trend of power losses and heat generated are also concerning from a design standpoint. With the data presented, it is still unclear if high efficiency can still be achieved at faster rotor speeds. For designs implementing a small gap size between rotor and stator, the physical limitations to offset windage loss and provide enough cooling to dissipate excessive heat buildup leave for a very challenging road ahead for further development. Therefore, it would be beneficial to perform additional trade studies at higher RPMs as well as looking into compressible flow models for evaluation.
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REFERENCES
Anderson, K.R., Lin, J., McNamara, C. and Magri, V. (2015) CFD Study of Forced Air Cooling and Windage Losses in a High Speed Electric Motor. Journal of Electronics Cooling and Thermal Control, 5, 27-44. http://dx.doi.org/10.4236/jectc.2015.52003
ANSYS Fluent 6.0 User Manual, 25.4.3 Pressure-Velocity Coupling. Fluent Inc. September 09, 2006. https://www.sharcnet.ca/Software/Fluent6/html/ug/node998.htm
Glenn Research Center, Navier-Stokes Equations: 3 – dimensional – unsteady. NASA. May 05, 2015. https://www.grc.nasa.gov/www/k-12/airplane/nseqs.html
ANSYS, Inc. ANSYS FLUENT Theory Guide. Release 14.0, Southpointe, 2011, Canonsburg, PA
Cross, Greenside. Pattern Formation and Dynamics in Nonequilibrium Systems. Cambridge University Press, 2009, New York.
Tu Jiyuan. Computational Fluid Dynamics, A Practical Approach. 2nd Edition. Elsevier, 2013, Waltham, MA
Vallentine. Applied Hydrodynamics. 1st Edition. Butterworth & Co. Limited, 1959, London and Colchester.
White. Viscous Fluid Flow. 3rd Edition, McGraw Hill Education, 2006, New York.
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APPENDIX A – EXPERIMENT TEST DATA & PICTURES
Figure 92: Physical Test Experiment Setup (Jun T. Lin) Table 7: Experiment Test Data – Measured Torque
Total Net Weight Initial Torque Power Hz RPM Force Force (g) F (N) (N-m) (W) (N) (N) 0 0 95 0.931 0.931 0.000 0.000 0.000 64.1 3846 96 0.941 0.931 0.010 0.002 0.904 100 6000 96 0.941 0.931 0.010 0.002 1.410 147 8820 100 0.980 0.931 0.049 0.011 10.364 192 11520 101 0.990 0.931 0.059 0.013 16.244 244 14640 103 1.009 0.931 0.078 0.018 27.525 294 17640 104 1.019 0.931 0.088 0.020 37.311 333 19980 105 1.029 0.931 0.098 0.022 46.955 357 21420 107 1.049 0.931 0.118 0.027 60.408 385 23100 106 1.039 0.931 0.108 0.025 59.717 446 26760 106 1.039 0.931 0.108 0.025 69.178 510 30600 109 1.068 0.931 0.137 0.031 100.679 543 32580 111 1.088 0.931 0.157 0.036 122.507 610 36600 112 1.098 0.931 0.167 0.038 146.225 Constants: Moment Arm Length: 0.229 m
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Table 8: Experiment Test Data – Heat Generated & Total Windage
Heat Small Offset Mass T, T, Adjusted Total Flow Out Rotor Total Flow in out Power Windage (LPM) Rate Power Windage (kg/s) (°C) (°C) (W) (W) (W) (W) (W) 207.7 0.0041 21.4 23.3 7.89 0.00 0.00 7.89 0.00 207.4 0.0040 21.7 23.3 6.63 0.43 0.47 7.11 -0.78 206.1 0.0040 21.8 23.2 5.77 2.15 -0.74 5.02 -2.86 205.2 0.0040 21.7 23.4 6.97 4.41 5.95 12.93 5.04 205.6 0.0040 21.7 23.7 8.22 6.57 9.67 17.89 10.01 204.2 0.0040 21.8 23.9 8.57 9.07 18.46 27.03 19.14 203.4 0.0040 21.8 24.3 10.16 11.47 25.84 36.01 28.12 204.1 0.0040 21.8 24.9 12.65 13.34 33.62 46.27 38.38 203.1 0.0040 21.7 25.4 15.02 14.49 45.92 60.94 53.05 202.7 0.0040 21.8 26 17.02 15.83 43.88 60.90 53.01 192.6 0.0038 21.1 27.1 23.10 18.76 50.42 73.52 65.63 190.7 0.0037 21.1 28.6 28.59 21.83 78.85 107.44 99.55 192.8 0.0038 21.3 29.9 33.14 23.42 99.09 132.23 124.34 192.8 0.0038 21.4 31.7 39.70 26.63 119.59 159.29 151.40
Constant Air Properties:
Density: 1.17 kg/m3
Specific Heat: 1025.1 J/kg°C
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APPENDIX B – SUPPLEMENTAL CFD CASE STUDIES
Heat Flux Study
Case 13 (36600, 200 LPM) was modified with additional heat flux of 100W, 200W, 300W applied to the rotor surfaces. Rotor Surface area measured in CAD: 0.02832741 m2. ANSYS
Fluent requires heat flux in units of W/m2, therefore Rotor Boundary Conditions were configured as follows: B1) 3530.109 W/m2, B2) 7060.217 W/m2, B3) 10590.326 W/m2.
Figure 93: Heat Fluxes at Rotor Surfaces (100W, 200W, 300W) Table 9: Appendix B - CFD Heat Generation Results from Varied Heat Flux at Rotor
Temperatures CFD Heat
Case Study Heat Flux Inlet Outlet ∆T Gen (@ Rotor) W/푚2 °퐾 ℃ °퐾 ℃ ℃ W 0 W 0 294.55 21.4 318.627 45.477 24.077 96.257 100 W 3530.109 294.55 21.4 324.526 51.376 29.976 119.841 200 W 7060.217 294.55 21.4 337.265 64.115 42.715 170.770 300 W 10590.326 294.55 21.4 349.945 76.795 55.395 221.463
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Table 10: Appendix B - CFD Total Windage Results from Varied Heat Flux at Rotor
Case CFD CFD CFD Total Windage Study Torque Power W N-m W W 0 -0.03406 130.55 226.81 100 -0.03406 130.55 250.39 200 -0.03406 130.55 301.32 300 -0.03406 130.55 352.02
Figure 94: Velocity Isosurfaces (Heat Flux Study, t=30s, 60s, 90s)
Figure 95: Velocity Streamlines (Heat Flux Study, t=30s, 60s, 90s)
Figure 96: Velocity Contours (Heat Flux Study, t=30s, 60s, 90s)
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Case 13-B1: 100W at Rotor:
Figure 97: Case B1 - Rotor Surface Temperatures (100W at Rotor, 36600 RPM, t=30s, 60s, 90s)
Figure 98: Case B1 - Temperature Profiles in Gap Region, 100W, t=30s, 60s, 90s)
Case 13-B2: 200W at Rotor:
Figure 99: Case B2 - Rotor Surface Temperatures (200W at Rotor, 36600 RPM, t=30s, 60s, 90s)
Figure 100: Case B2 - Temperature Profiles in Gap Region (200W, 36600 RPM, t=30s, 60s, 90s)
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Case 13-B3: 300W at Rotor:
Figure 101: Case B3 - Rotor Surface Temperatures (300W at Rotor, 36600 RPM, t=30s, 60s, 90s)
Figure 102: Case B3 - Temperature Profiles in Gap Region, 300W, 36600 RPM, t=30s, 60s, 90s) Inlet Mass Flow Study:
Inlet Mass Flow Rates were also varied to observe its effects on windage losses. Cases B4, B5,
B6, and B7 were simulated with the following inlet flow rates: 50 SLPM, 100 SLPM, 150
SLPM, and 200 SLPM at a rotor speed of 36600 RPM with no additional heat input to the rotor.
These inlet rates were converted to units of kg/s, for the ANSYS Fluent Mass Flow Inlet
Boundary Conditions.
Table 11: Appendix B - Mass Flow Rate Boundary Condition Inputs for Fluent
SLPM kg/s 50 0.000975 100 0.00195 150 0.002925 200 0.0039
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Table 12: Appendix B - CFD Results from Varied Mass Flow Rate Study
CFD Temperatures CFD Heat Case Study Inlet Temp Outlet Temp ∆푻 Gen Mass Flow Rate (SLPM) °퐾 ℃ °퐾 ℃ ℃ W 50 294.55 21.4 323.821 50.671 29.271 29.26 100 294.55 21.4 319.188 46.038 24.638 49.25 150 294.55 21.4 318.209 45.059 23.659 70.94 200 294.55 21.4 318.627 45.477 24.077 96.26
Table 13: Appendix B - CFD Windage Losses from Varied Mass Flow Rate Study
Torque Power CFD Windage Case Study Rotor Rotor Mass Flow Rate (SLPM) N-m W W 50 -0.03341 128.0531 157.31 100 -0.0341 130.709 179.96 150 -0.03417 130.9716 201.91 200 -0.03406 130.5529 226.81
Case Study B4 – 50 LPM Inlet Mass Flow Rate, 36600 RPM
Figure 103: Case B4 – 50 LPM inlet, Velocity Isosurfaces, 83m/s (t=30s, 60s, 90s)
Figure 104: Case B4 – 50 LPM Inlet, Velocity Profiles in Gap Region, t=30s, 60s, 90s
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Figure 105: Case B4 – 50 LPM Inlet, Velocity Streamlines in Gap Region, t=30s, 60s, 90s
Figure 106: Case B4 – 50 LPM Inlet, Temperature Profiles in Gap Region, t=30s, 60s, 90s Case B5 – 100 LPM Mass Flow Inlet, 36600 RPM
Figure 107: Case B5 – 100 LPM Inlet, Velocity Isosurfaces, 83m/s, t=30s, 60s, 90s
Figure 108: Case B5 – 100 LPM Inlet, Velocity Profiles in Gap Region, t=30s, 60s, 90s
Figure 109: Case B5 – 100 LPM Inlet, Velocity Streamlines in Gap Region, t=30s, 60s, 90s
Figure 110: Case B5 – 100 LPM Inlet, Temperature Profiles in Gap Region, t=30s, 60s, 90s
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Case B6 – 150 LPM Mass Flow Inlet, 36600 RPM
Figure 111: Case B6 – 150 LPM Inlet, Velocity Isosurfaces, 83m/s, t=30s, 60s, 90s
Figure 112: Case B6 – 150 LPM Inlet, Velocity Profiles in Gap Region, t=30s, 60s, 90s
Figure 113: Case B6 – 150 LPM Inlet, Velocity Streamlines in Gap Region, t=30s, 60s, 90s
Figure 114: Case B6 – 150 LPM Inlet, Temperature Profiles in Gap Region, t=30s, 60s, 90s
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Case B7 – 200 LPM Mass Flow Inlet, 36600 RPM
Figure 115: Case B7 – 200 LPM Inlet, Velocity Isosurfaces, 83m/s, t=30s, 60s, 90s
Figure 116: Case B7 – 200 LPM Inlet, Velocity Profiles in Gap Region, t=30s, 60s, 90s
Figure 117: Case B7 – 200 LPM Inlet, Velocity Streamlines in Gap Region, t=30s, 60s, 90s
Figure 118: Case B7 – 200 LPM Inlet, Temperature Profiles in Gap Region, t=30s, 60s, 90s
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