CALIFORNIA STATE UNIVERSITY NORTHRIDGE. Evaluation of Ground Effect on the Drag on an HPV Fairing Using CFD

Transcription

1 CALIFORNIA STATE UNIVERSITY NORTHRIDGE Evaluation of Ground Effect on the Drag on an HPV Fairing Using CFD A thesis submitted in partial fulfillment of the requirements For the degree of Master of Science in Engineering, Mechanical Engineering By Dimitry Tsybulevsky May 2012

2 The Thesis of Dimitry Tsybulevsky is approved: Susan Beatty, Eng. Date Mike Kabo, Ph.D. Date Robert G Ryan, Ph.D., Chair Date California State University, Northridge ii

3 Acknowledgements I would like to thank Dr. Robert Ryan for being my graduate advisor and supporting me throughout this thesis. My thesis never would have been completed without his help. I would also like to thank Professor Susan Beatty for helping me during my time in California State University Northridge (CSUN) and being on my thesis committee. Additionally, special thanks goes to Dr Mike Kabo for assisting me with the application process for the graduate program in CSUN and being on my thesis committee. Lastly, I would like to thank the Department of Mechanical Engineering at CSUN for the encouragement and help to complete my Master s Degree in Mechanical Engineering. iii

4 Table of Contents Signature page.ii Acknowledgements....iii List of Tables...vii List of Figures...viii Abstract......xi Chapter 1: Introduction Problem Statement Purpose of the Thesis Background Information Definition of Drag Definition of Ground Effect Definition of CFD and CFD History Drag Measurement Techniques Using CFD Approach Theoretical Values of Drag on the Ellipsoid body Drag Values on Variation With Ground Clearance HPV Fairing Geometry Description Organization of the Thesis Chapter 2: Importation of Solid Model into ANSYS and Mesh Definition Meshing and Preprocessing Modeling of the HPV Fairing and Ellipsoid Geometries in SolidWorks Importing the Model into ANSYS WORKBENCH from SolidWorks Extracting A Fluid Volume for the Models iv

5 Opening the Models in ANSYS ICEM CFD Preparing the Geometry for Meshing Generating the Initial Mesh Using Octree Mesh Approach and Applying the Correct Mesh Size Generating the Tetra/Prism Mesh Using Delaunay Mesh Approach Smoothing the Mesh to Improve Quality Exporting the Mesh into ANSYS FLUENT Chapter 3: FLUENT Setup and Application of Spalart-Allmaras Turbulence Model Background Information in Computational Software and Methodology Turbulence Model Spalart Allmaras Turbulence Model Application of FLUENT Setup Initial Setup Boundary Condition Solution Setup and Mesh Adaption Solution to the Problem Graphical and Numerical solutions Drag Calculation Chapter 4: Baseline Solution and Calibration of FLUENT FLUENT Calibration Using Flat Plate FLUENT Calibration Using Oblate Ellipsoids Results for Oblate Ellipsoids Comparison between Hoerner s data and CFD data v

6 Chapter 5: HPV Fairing Results HPV CFD Test Results HPV Fairing Benchmark Results HPV Fairing at Different Ground Proximities Results Ground Clearance Effect on Pressure and Skin Frication Ground Clearance Effect on Drag and Lift Estimation of Discretization Error Discretization Error Calculation Tradeoff Study Between Ground Clearances Drag and Stability for a Typical HPV Chapter 6: Conclusion..133 References Appendix A Appendix B Appendix C vi

7 List of Tables Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table C Table C Table C Table C Table C Table C Table C Table C Table C Table C vii

8 List of Figures Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure viii

9 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure A Figure A Figure A ix

10 Figure A Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B Figure B x

11 Abstract Evaluation of Ground Effect on the Drag on an HPV Fairing Using CFD By Dimitry Tsybulevsky Master of Science in Mechanical Engineering The purpose of this study was to evaluate the ground effect on the Human Powered Vehicle (HPV) Fairing with different ground clearances, and its effect on drag using Computational Fluids Dynamics (CFD) software. The short term goal of this thesis was to use the CFD software package ANSYS FLUENT, to find how the ground clearance of the 2010 version of the HPV fairing affects the overall drag and to an optimal ground clearance for the vehicle. The long term goal was to create a guide to help future students use ANSYS FLUENT and other ANSYS software to create mesh and CFD studies to find external forces such as drag and lift coefficients on objects moving through a fluid. In order to create a good computational mesh for the HPV fairing flow field, the mesh was first created for standard geometries, i.e. flat plate and oblate ellipsoids. Drag values computed for various meshes were compared to known drag values for those geometries. The results for the flat plate matched within 3.5% of the theoretical results, and for the oblate ellipsoids the difference was less than 5.6% from experimental values. This process helped to optimize the final mesh settings for the HPV fairing and find acceptable results for the drag coefficient with the fairing at different ground clearances. xi

12 As mentioned previously, a long term goal for this thesis was to create a tutorial on how to use ANSYS and FLUENT to create good CFD studies. The tutorial can be used with future California State University, Northridge (CSUN) senior design teams to create body geometries and effectively to accurate results for drag and lift on various bodies. This tutorial can also help with regard to importing the geometry from CAD software and performing the correct model setup in ANSYS. The study for the HPV was conducted as a function of h/l, where h is the ground clearance and L is the length of the HPV fairing. (L= 99 inches and was constant). The ground clearance ranged from 3 to 18 inches including two baseline tests, at 30 and 297 inches away from the ground. All of the results are provided in terms of the streamlines, pressure and velocity magnitude fields, and vorticity contours. The goal was to see how high the body had to be off the ground to eliminate the drag ground effect. It was found that the fairing had to be at least 18 inches of from ground in order to see a significant reduction in ground effect. Additionally a trade off analysis was conducted on the HPV fairing to balance the speed benefit from high ground clearance with vehicle stability during cornering. However, the height required to minimize the ground effect was impractical for the HPV competition due the Center of Gravity (CG) considerations. xii

13 Chapter 1: Introduction 1.1. Problem statement The aerodynamics of human powered vehicles (HPV s) is greatly influenced by the shape of the body and the proximity of the ground to the surface of the HPV bodywork. In most cases the airflow between the ground and HPV bodywork results in a drag increase known as the ground effect. Approaches to lessen this effect fall into two categories: a) creating a specialized fairing skirt which helps to direct the airflow away from the underside of the vehicle; or b) increasing the height of the vehicle from the ground. Neither of those strategies is perfect; each strategy has its upside and its downside with respect to vehicle performance Scope of the Thesis The main goal of this thesis is to conduct a computational fluid dynamics (CFD) study on an HPV fairing by using ANSYS 12.1 and FLUENT in the Mechanical Engineering Design center at California State University Northridge (CSUN). This study analyzes airflow around a typical HPV fairing geometry and assesses the impact of the ground effect at typical HPV speeds. In addition, this study is designed to use the oblate ellipsoid and the flat plate as a calibration tool for the HPV s fairing mesh, boundary conditions and FLUENT setup. Then the experimental results found in Fluid Dynamics of Drag by Hoerner [11] are compared to the CFD results from FLUENT for the oblate ellipsoid to make sure that the software computationally precise. To accomplish these objectives the SolidWorks model created by 2010 CSUN s HPV design team was imported into ANSYS 12.1 and modified to be used within ANSYS-FLUENT. The geometry was cleaned within ANSYS 12.1 WORKBENCH 1

14 Geometry Design-Modeler; then the model was imported into ANSYS ICEM to create the mesh that was used by FLUENT. The mesh incorporates an estimation of boundary layer thickness to insure that sufficient points were used near the HPV s fairing surface to accurately predict velocity gradients in this region. Initially a study was performed on an ellipsoid geometry, which is somewhat similar to the shape of an HPV, and for which published drag data is available. In addition, velocities were chosen to match Reynolds numbers with available data. Using the ellipsoid geometry, a strategy was developed to optimize the program settings to get an effective convergence and solution accuracy in terms of drag force. This included running inviscid flow cases, using coarser mesh for the preliminary calculations, and then using FLUENT mesh refinement capabilities. In addition, different turbulence models such as the Spalart-Allmaras turbulence (SA) model and k-ε model within FLUENT were tried to assess the turbulence model s effect on solution convergence and drag calculations. This study was conducted using several different flow conditions and mesh configurations to determine their effect on the calculated drag values. The analysis was conducted on the 2010 HPV geometry at several different flow velocities with a maximum flow velocity of approximately 40 mph (58.67 ft ). These speeds corresponded to a Reynolds number range of approximately to That means the majority of the flow over the HPV fairing after the expected boundary layer transition point was in the turbulent region. Finally, a study was conducted to assess the impact of geometry changes on computed drag, i.e. changing the proximity of the HPV fairing to the ground surface. sec 2

15 Analyses were run for ground clearance of 3, 6, 9, 12, 15, 18, 30 inches and a freestream case of 297 inches above the ground Background Information Definition of Drag Drag refers to the forces that oppose the relative motion of an object through a fluid, either gas or liquid. Drag forces only act in the direction opposite to velocities not the oncoming flow velocity (or upstream velocity U). For a 3-D object moving through a fluid, the drag is the sum of forces due to pressure differences in the flow field (pressure drag) and shear forces on the object s surface (friction drag). Drag force has been found to be dependent on a fluid s density (ρ), object area (A), flow velocity (U) and a dimensionless drag coefficient (C D ), expressed by the following drag equation: D = 1 2 ρu2 AC D (1-1) The drag coefficient is a function of object shape and Reynolds number, and is usually determined experimentally or by CFD analysis. The area can either be the surface or wetted area, or the projected frontal area depending on the source of the drag coefficient values. Generally the wetted area is used if the total drag is dominated by friction drag. 3

16 Figure 1-1 a shows basic example of drag generated by a solid body moving through a fluid. Figure 1-1: Example of drag generated by solid object (Adapted from ) Definition of Ground Effect Ground effect is a term applied to a series of aerodynamic effects that are important in the automotive and aerospace industries. These effects usually cause an increase in drag force and a decrease in lift force (i.e. increase down force). Ground effects relevant to the automotive industry are due to the proximity of the underside of the moving vehicle to the stationary road surface. The ground effect is easily visualized by taking a canvas tarp out on a windy day and holding it close to the ground; when the canvas gets close enough to the ground it will suddenly be sucked downward due to the lowered pressure in the flow between the tarp and the ground. Some vehicle body components, such as a splitter and a diffuser, can be found under the vehicle s body to help increase the ground effect and improve the downforce of the vehicle. This helps it travel faster through the corners by increasing the vertical force on the tires. 4

17 Ground effects in aerospace applications are due to the proximity of the flying body to the ground. The most important of these effects is the wing in ground (WIG). This is due to the reduction in lift experienced by an aircraft as it approaches a height of roughly the aircraft s wingspan above the ground. Those effects increase as the aircraft approaches the surface, which can lead to loss of control and crashes Definition of CFD and CFD History Computational Fluid Dynamics (sometimes referred to as CFD) is a branch of fluid mechanics which uses complex algorithms in conjunction with numerical methods to solve the partial differential equations describing fluid flow. Advances in CFD software make it possible to perform complex calculations to simulate the interaction of gases and liquids with each other and geometric surfaces defined by Computer Aided Design (CAD) software. Yet even with modern high speed computers, only approximate solutions can be achieved in most cases, particularly for flows involving turbulence and flow separation around blunt bodies because CFD solution is a numerically based. CFD originated in the early part of the 20th century, marked by initial attempts to solve differential equations found in physics and engineering. The main equations governing fluid flow behavior are the Navier-Stokes equations, developed in the early part of the 19th century by George Stokes and Claude Navier. Although the Navier- Stokes equations were a significant development, the analytical mathematical solution of those equations proved untenable at that time period. This led to the development of a large number of simplified equations derived from the Navier-Stokes equation for special cases, which can be tackled analytically using pen and paper or a simple calculator. 5

18 However, these special cases were very limited in terms of describing practical applications. [36] The invention of digital computers led to many changes in solving the complicated Navier Stokes equations. In the late 1940 s, John von Neumann led a group of scientists and engineers to develop modern CFD. The digital computing machines have the analytical solutions of simplified flow equations with numerical solutions of full nonlinear flow equations for arbitrary geometries. Modern day CFD uses high-speed computers to achieve better solutions and improve accuracy of known exact and nonexact solutions to the Navier-Stokes equations such as nonlinear partial differential equations and turbulence analysis. [36] Common CFD codes have a specific structure that revolves around a numerical method or numerical algorithm able to undertake complex fluid flow studies. Most of the CFD codes currently on the market have only three basic elements, which divides the complete simulation to be performed on the specific domain or geometry. The basic three elements are the following: 1. Pre Processor, where the solution domain is defined and the mesh is generated; 2.Solver where the flow equations are solved for the previously defined mesh and domain; and 3. The Post-Processor, where the numerical results are displayed and analyzed Drag Estimation Techniques Using CFD Approach There are several approaches to calculate the drag on a 3-D geometry using the CFD approach. Perhaps the most common and widely used approach to finding drag using CFD is solving the Reynolds Averaged Navier-Stokes (RANS) equations, or the surface integration of stresses, i.e. near field methods. There are several problems with 6

19 this approach to solving CFD problems. For the near field method the problem is usually insufficiently accurate results, for example even if the flow solution is locally accurate in terms of pressure and velocity profile. As for RANS, the problem is mainly related to the numerical solution that generates the drag coefficient. A second problem for the RANS is near field drag computation; it only allows for distinction between pressure and friction drag. [26] Due to the mentioned problems above with the RANS methods, the following approach is used in this thesis to find the drag coefficient of the HPV fairing. This approach is to use the oblate ellipsoid to determine computational precision of FLUENT by finding the proper mesh parameters and turbulence model to provide accurate drag estimates. This approach establishes how fine the mesh should be in order to acquire proper results for drag forces over the HPV fairing. This mesh incorporates estimation of the boundary layer thickness to ensure that there are enough points used near the body surface to accurately predict the velocity gradient within the boundary layer, and the related friction drag. Using the ellipsoid body geometry, a strategy is developed to optimize the program settings within the FLUENT solver for effective convergence and solution accuracy Experimental Values of Drag on the Ellipsoid Bodies An oblate ellipsoid is a disk shaped spheroid where a=b>c, and prolate ellipsoid is a rugby ball shaped spheroid where a=b<c. Drag research on oblate ellipsoids and other similar shapes is very limited. There are only a few real-world examples of such types of bodies. The HPV fairing is being assumed as a streamlined geometry and the oblate ellipsoid is used to help with the initial 7

20 setup of the CFD approach. However, there is a lot of literature that discusses drag information on similar types of bodies, such as prolate ellipsoids and spheroids. This may be used as a baseline reference for the work being performed in this study. The information in Figure 1-2 comes from a well-known drag expert, Dr. S.F Hoerner. In his book Fluid-Dynamic Drag (1965), Hoerner presents the drag coefficient of numerous shapes such as oblate ellipsoids, prolate ellipsoids, and spheroids in both 2-D and 3-D flow fields. Figure 1-2 presents the wetted area drag coefficient of an oblate ellipsoid with different fineness ratios of body of revolution l d over a range of Reynolds number (R e ). The d is the diameter of the ellipsoid at its widest part, and l is the length of the ellipsoid. The points that are shown in Figure 1-2 are the experimental data that were found for those bodies, and the dashed lines represent the theoretical drag for fineness [6, 11, 12] ratio and is given with the following equation. C DWET = C f,lam 1 + d l d l 2 (1-2) 8

21 Figure 1-2: Drag Data on 3-D Bodies of Revolution Aligned Straight-and-Level (Adapted from Hoerner Fluid Dynamics of Drag, 1965, 6-16) Figure 1-2 represents the effect of Reynolds number on the drag of the ellipsoid with different fineness ratios of l d. In the laminar region where the Reynolds number is less than 10 5 the drag coefficients tend to be higher. When the Reynolds number reaches between 10 5 and 10 6, the boundary layer flow begins to transition from laminar to turbulent, and a significant drop is seen in the drag coefficient. After the drag reaches its minimum value, the drag begins to rise slightly as the boundary layer transition point continues to move forward. Finally, when the Reynolds number reaches 10 7, the flow is fully turbulent and the drag starts to decrease again. In reference to Figure 1-2 the higher the Reynolds numbers, the lower the drag at the fineness ratios. Additionally, the higher the fineness ratio the lower the drag coefficient will be. 9

22 To define the fineness ratio that is used in Figure 1-3 and its relationship to the friction drag coefficient C f the following equation is employed. C DWET C f = d l d l 3 (1-3) To find the correct ratio of wetted area to frontal area S wet S f for streamline bodies, the wetted area can be approximated as S wet = (0.7 to 0.8) l perimeter, where the perimeter is equal to π d, and the frontal area is equal to πd2. The ratio of wetted area to frontal area is equal to: 4 S wet S f = 0.75 l d π d 2π 4 = l d = 3 l d This expression is then substituted into equation 1-3 to find the C D C f for the frontal area coefficient and curve fit for Figure 1-3 as derived by Hoerner. C D = 3 l C f d d d + 21 l l 2 (1-4) Figure 1-3: Drag coefficient of streamlined bodies as a function of their thickness ratio (Adapted from Hoerner Fluid Dynamics of Drag, 1965, 6-19) 10

23 Figure 1-3 illustrates the drag coefficients based on frontal area of streamline bodies as a function of their fineness ratio, the points in Figure 1-3 are the experimental data and the dashed lines are evaluated from equation 1-4. When the fineness ratio increases, the drag coefficient also increases expect for low fineness ratios. The drag coefficient for the HPV fairing based on its frontal fineness ratio of 3.53 is between 0.02 and for Reynolds numbers This was found using Figure 1-3 and equation 1-4. It is difficult to isolate the critical Reynolds number on the oblate ellipsoid where the transition will occur from laminar to turbulent flow with estimated Reynolds numbers from 500 to 600 thousand for that geometry. Figure 1-4 [8] shows the wetted area drag coefficient for the x l = 0. 5 prolate spheroid for several different surface roughnesses. The roughness has an enormous effect on the drag coefficient in the low Reynolds numbers. This is because the flow is not fully developed and this adds to the total skin friction coefficient as illustrated in figure 1-4. During Dr. Dress s study the critical Reynolds number reached about 800 thousand where the transition from laminar to turbulent region occurs, and the minimum drag coefficient happened at a Reynolds number of almost 1.2 million for a fine grit of 80. The different types of runs show the effect of skin roughness from laminar to turbulent flow, and the effect on the wetted drag. 11

24 Figure 1-4: Drag Data from a x = 0. 5 Prolate Spheroid Aligned Straight-and-Level free transition l is the base run, 80 is the fine grit, and 40 is the rough grit (Adapted from Dress, NASA Technical Paper , 29) Drag Values on Variation With Ground Clearance Once the potential of using aerodynamic downforce in automotive racing applications was realized, many teams started to experiment with other methods to increase aerodynamic downforce other than simply attaching inverted wings. It was found that with a larger underbody area of the vehicle, significant levels of downforce could be generated. This kind of effect was first seen in 1935 in the racing circuit with early wing prototypes used in ground effect models. [13] 12

25 Figure 1-5 illustrates a basic principle of ground effect on typical car shapes represented by an oblate ellipsoid and half streamlined body. However, to understand ground effect the nature of the flow under the vehicle must be considered. The top part of the Figure, shows an oblate ellipsoid that is approaching the ground. The flow under the oblate ellipsoid and the downforce ( C L ) are increasing as distance to the ground reduces and creates low pressure. If one looks at the bottom part of the Figure and closely examines the half streamlined body, the drag coefficient is seen to be nearly the same as the oblate ellipsoid. The lift force is opposite due to the reduced flow under the body, with the result of increased lift due the reduced ground clearance. In both Figures the transition to significant ground effect starts to occur at h l < However, this only applies to these specific geometries. The transition point can shift to either left or right depending on the fineness ration and overall shape of the geometry. There are several options for the car body shape to generate lower pressure under the body. Option one is to streamline the underbody to create low pressure. Option two is to create a seal between the underbody of the car and the ground and only leave the rear portion of the car open. Then the low pressure behind the car would dictate the pressure [14, 15] under the car. 13

26 Figure 1-5: Effect of ground Proximity on the lift and drag of two streamline bodies (Adapted from Race Car Aerodynamics by Joseph Katz 1995) 14

27 1.4. HPV Fairing Geometry Description Figures 1-2 and 1-3 are used as a reference to estimate the expected drag coefficient for the HPV fairing. If one assumes the HPV fairing is a body of revolution then the oblate ellipsoid can be used as a computational precision tool for the mesh setup, turbulent model selection, and optimize FLUENT parameters. To apply Figures 1-2 and 1-3 one needs to estimate an equivalent fineness ratio for the HPV fairing, and a range of drag values can then be estimated for the HPV fairing in freestream flow. This is used as a benchmark for the HPV fairing analysis. Figure 1-6 shows the dimensions of the HPV fairing; this data can then be used to find the fineness ratio based on the height of the HPV fairing which is equal to 3.53 for half of a body of revolution. However, because the HPV fairing is assumed to be a body of revolution the height needs to be doubled to get the correct fineness ratio l = the h resulting wetted area drag coefficient value for Re = is approximately C D,Wetted =0.009 and C D,surface area = Figure 1-6: Dimensions of the HPV fairing from SolidWorks 2010 where l= inches, h=d= inches 15

28 1.5. Organization of the Thesis The remainder of this thesis will be organized as follows. Chapter 2 describes the model design and importation of the model into ANSYS WORKBENCH and fluid volume extraction. It also explains how to import the model in to ANSYS ICEM and the mesh setup and creation. Lastly, it will be explained how to import the mesh from ANSYS ICEM to ANSYS FLUENT. Chapter 3 explains how to operate FLUENT using ANSYS WORKBENCH and apply FLUENT setups as an initial setup, materials for the fluid and geometry, dynamic mesh, and boundary conditions. It will demonstrate how to use FLUENT to generate numerical and graphical solutions for the HPV fairing geometry with different ground clearances ranging from 3 inches to 18 inches away from the ground. Chapter 4 presents the results of the baseline solution of the oblate ellipsoid with l d = 2&4 and results for the flat plate. This chapter also compares the CFD results of the baseline solution to the results found in Chapter 6 in Fluid Dynamics of Drag by Hoerner. [11] Chapter 5 presents the results of the HPV fairing with different ground clearances ranging from 3 inches to 18 inches away from the ground. Then the results from the HPV fairing CFD analysis are compared to the benchmark results (freestream and 30 inch ground clearance). In addition, the results for drag and lift are discussed, and calculations of discretization error are presented. Then the final part of Chapter 5 will include the trade-off study regarding the optimum vehicle height while considering both vehicle stability and aerodynamic drag. 16

29 Chapter 6 is the conclusion and the summarization of the study. It is based on the results shown in Chapters 4 and 5. References and an appendix follow the conclusion. 17

30 Chapter 2: Importation of Solid Model into ANSYS and Mesh Definition 2.1.Meshing and Preprocessing The pre-processing of a CFD procedure consists of several inputs for the flow problem that are done by the user in CFD software. For this study the pre-processing software is ANSYS ICEM CFD, and the solver software is ANSYS FLUENT. The inputs are then transferred into a form made suitable for use by the solver. The pre-processor is the main connection between the CFD solver and the user. The user has to complete several significant steps in the pre-processing stage of the CFD problem. A schematic of the process is shown in Figure 2-1.The following definition, gives a brief explanation of these steps. 1. Define the geometry of interest: This step uses ANSYS DesignModeler CAD software within ANSYS WORKBENCH to help design and model the topology of the fluid flow domain inside or outside the geometry. This domain is defined and optimized for the best CFD results. 2. When the geometry preparation is defined within the pre-processor software, the fluid domain and every surface affected by the fluid is then also defined. Each fluid and surface has its own distinct property; those properties are used in the CFD process and must be defined at this stage. The output of the DesignModeler software is a xxxx.agdb file. 3. Meshing is the third step. Because the CFD process uses a finite volume method, the domain of interest has to be divided into structured and unstructured elements. All the elements are connected to each other through nodes to and from the flow domain. For this study ANSYS ICEM CFD software is used to create the mesh in the form of a 18

31 xxxx.mesh file. The quality of the mesh contributes to the accuracy of the final results. 4. Definition of boundary conditions is the final step at the pre-processing stage. Each CFD domain needs an initial condition to begin calculations, which is defined by the user s input. In addition, the CFD code implements the boundary conditions at a specific locations. The following few sections will explain these four steps in complete detail and explain how to use ANSYS 12.1 for external flow problems. Lastly, Figure 2-1 illustrates how the files from the different software packages move through the overall solution process..agdb ANSYS ICEM CFD.mesh SolidWorks.SLDPRT ANSYS DesignModeler ANSYS FLUENT.wbpj ANSYS WORKBENCH Figure 2-1: Block Diagram illustrates where each file type goes to 19

32 2.2. Modeling of the HPV Fairing and the Ellipsoid Geometries in SolidWorks All of the solid models that were used in this study were designed and drafted using SolidWorks Computer-Aided Design (CAD) software, using inches for dimensions. The fairing was originally designed and modeled by the California State University Northridge (CSUN) Human Powered Vehicle (HPV) Team for their competition in April An ellipsoid model was also designed to represent a simpler geometry and was used as the baseline for this thesis. The ellipsoid model establishes the mesh fineness requirements to acquire good results for the drag force, based on comparison with published results from Fluid Dynamics Drag by Hoerner data. [11] The modeling of the ellipsoid geometry in SolidWorks was a little challenging, because the ellipsoid had to represent the fairing shape as closely as possible. The ellipsoid was created using the lofted boss/base tool in SolidWorks. However, before that could be done, several planes were created so that a 2-D ellipse could be drawn on each plane with different chord lengths A and B. This is illustrated in Figure 2-2. A B Figure 2-2: Representation of an ellipse geometry B=99in and A=49.5in After all of the 2-D schematic geometries were drawn, the lofted boss/base tool was used to create the 3-D ellipsoid body that can be seen in Figure 2-3. The ellipsoid 20

33 model dimensions are: the chord length (l) is 99 inches; height(x) is 49.5 inches, and the diameter (d) of the ellipsoid is inches. The fineness ratio of l d is then can be found as 99 = 2. This ratio is then used to find the drag of a non-oblate ellipsoid body Additionally, another ellipsoid was created in SolidWorks with a fineness ratio of l d = 4, and was used as a baseline test in FLUENT. Additional comparisons were made with a flat plate geometry which is useful because the drag force on a flat plate is completely due to surface stresses. There are a few reasons why two oblate ellipsoids are used to calibrate FLUENT and set correct mesh parameters for the HPV fairing. The first reason is to match the results from FLUENT runs to the known results from Fluid Dynamics Drag by Hoerner. The second reason is to find the limitation of FLUENT on predicting drag on similar geometries with different fineness ratios, as the flow behaves differently for a Falter shape. Generally, a smaller l d ratio will have a larger contribution of pressure forces to the overall drag, especially if the boundary layer separates on the rear portion of the body. Figure 2-3: 3-d Ellipsoid body from SolidWorks 21

34 After the models were created and saved in SolidWorks, one needed to import those models into ANSYS 12.1 for geometry calibration and model clean up before the models were meshed and used within ANSYS FLUENT Importing Model into ANSYS WORKBENCH from SolidWorks ANSYS WORKBENCH is a Computer Aided Engineering (CAE) software package that is used in engineering simulation and analysis. It is an innovative project organizer that ties together the entire simulation process. It helps the user go through several complex studies at once with drag and drop menus. It also has powerful user controls, automated meshing abilities, project level update mechanisms, and integrated [40, 37] optimization tools, which enable complex simulation and product optimization. The next few Figures show a step by step explanation process to import any SolidWorks model into ANSYS WORKBENCH, and clean up the geometry so it can be properly meshed. Figure 2-4 shows how to load the geometry in ANSYS WORKBENCH. In order to load the SolidWorks model in ANSYS WORKBENCH, the user first has to open ANSYS WORKBENCH, then go to the component systems and select Geometry (A). Then the geometry tab is placed on the main WORKBENCH screen, and it then becomes a cell. In order to load the geometry, the user must right-click the Geometry..? tab, and then scroll down until import geometry has been reached. After left-clicking on this item, a new window will open. Then user must left-click browse tab and load the specific geometry (B) to be modified. After the geometry is loaded into the WORKBENCH, the user must double click with the left mouse button on the geometry cell number 2, and ANSYS DesignModeler 22

35 will load. The user then is able to clean, modify, edit and fix the geometry so a better mesh can be created for future analysis of the model. This is explained in Section A B Figure 2-4: ANSYS WORKBENCH front screen; A- geometry is selected first; B-geometry cell where geometry is going to be imported 23

36 Extracting a Fluid Volume for the Models The next few Figures will show step by step how to extract the fluid volume around the imported geometry. The fluid volume must be extracted because one must correctly define the volume that is being occupied by the fluid around a specific solid model. Figure 2-5: Ellipsoid model with in ANSYS DesignModeler and the selection of the external flow. Figure 2-5 illustrates how once the geometry is loaded into ANSYS DesignModeler the user can then begin to select what kind of fluid volume to apply to the specific model, such as internal or external fluid volume. For this study an external fluid volume is being used. This is because the imported geometry represents a solid body and the air flow is external to the body surface. 24

37 Figure 2-6: Selection of shape and cushion type Figure 2-6 illustrates the shape and the cushion size of the fluid volume enclosure. The cushion size is also known as the domain size. For this study the shape of the fluid volume is the box shape, since it is convenient for generating the mesh around the solid body. Since the CFD process is a numerical approximation approach that uses the finite volume method to solve the Navier Stokes equations, the fluid volume domain is going to be composed of an Octree Mesh, sometimes referred to as an unstructured mesh. In order to create the fluid volume domain, the user must set the cushion size and select either uniform or non uniform size. For this thesis the non-uniform cushion size will be used on all the models. This is done to make a more efficient study that does not require a large quantity of computing power. The ellipsoid model was run in freestream condition without any ground plane representation. The HPV fairing simulation consisted of eight different cases. The first two cases are set as benchmarks, where one is in freestream condition and the other one simulation a ground clearance of 30 inches. The other six cases will simulate the HPV fairing with ground clearances ranging from 3 to

38 Figure 2-7: Generated enclosure for the oblate ellipsoid in freestream Figure 2-8: Editing of the enclosure based on symmetry Figures 2-7 and 2-8 illustrate the generated fluid volume enclosure for the solid model, and the editing process for the fluid enclose based on model symmetry about the XY plane. This makes the computation more efficient because it only has to analyze half 26

39 of the model to achieve the same results. In order to create the symmetric model, the user must right click on the Enclosure tab in the tree outline, and then select the edit selection tab. After the user has selected the previous command, the model enclosure can then be edited to the user s specifications and the correct symmetry plane. The user can then select up to three planes of symmetry. As mentioned earlier this model is only symmetric to one plane, the XY plane. In order to select the symmetry plane, the user must left click on the not selected tab and then the user must select the corresponding plane from the tree outline, then press apply. In order to generate the new model, the user must press the Generate tab to create the symmetric model about the XY plane. This is illustrated in Figure 2-9 where one can see the selection of the total number of planes that can be used at the same time, and the symmetry plane selection. Figure 2-9: Selection of symmetry planes. For this study it is the XY plane. 27

40 Y + =3x X + =3X X - =6x Z=3x Y - =3x Figure 2-10: Fluid volume for the ellipsoid model Figures 2-10 and 2-11 show the final view of the oblate ellipsoid s model and fluid enclosure, and the HPV fairing within the non-uniform fluid volume box. The oblate ellipsoid fluid volume box is X + =Y + =Y - =Z=3 times chord length, and X - =6 times chord length. The fairing fluid volume box is X + =Y + =Z=3 times chord length, X - =6 times chord length, Y - =3 to 18 inches for the test cases, and for the benchmarks it is 30 inches and 297 inches. The domain size was selected to help decrease the total computing power while maintaining accuracy. The optimal domain size for a wing was found by Amir Mohammadi in his thesis and this data is being used as a reference for the domain size used here. [21] Before the mesh can be created, the model needs to be exported as an xxxxxx.agdb file. In order to save the ANSYS DesignModeler file, the user must do the following steps; File>Export > xxxxxx.agdb> then Save. Once the file is saved, it then can be opened by ANSYS ICEM CFD, and a proper mesh can be applied to the solid model and the fluid volume box. 28

41 In addition to creating the fluid volume, naming the surfaces that represent the boundary conditions will help later with ANSYS FLUENT setup and the meshing process in ANSYS ICEM CFD. In order to name the different surfaces, the user must right click on the surface and then click edit to name the surface. For the oblate ellipsoid and the HPV fairing model, the surfaces that are created are the inlet velocity, outlet, boundary volume box, and symmetry plane. The boundary volume box for the oblate ellipsoid is made out of three surfaces that surround the geometry. However, for the fairing the bottom surface is named ground plane and the volume box is made only of two adjacent surfaces. This is illustrated in Figure 2-12 and Table 2-1. Y + =3X X + =3X X - =6X Z=3X Y - =3 to 18 inches Figure 2-11: Fluid volume for the Fairing model 29

42 Plane Name Surface Name For Ellipsoid Surface Name For HPV Right (YZ X+) Velocity Inlet Velocity Inlet Left (YZ X-) Outflow Outflow Top (XZ Y+) Bottom (XZ Far side (XY Z+) Symmetry (XY Fluid Volume Box Fluid Volume Box Fluid Volume Box Symmetry Plane Table 2-1: Surface names for ellipsoid and HPV Fairing Fluid Volume Box Ground plane Fluid Volume Box Symmetry Plane Fluid Volume Box Outflow Velocity Inlet Ground plane Symmetry Figure 2-12: Plane location and names 30

43 Opening the Models in ANSYS ICEM CFD Before the meshing procedure can begin, the file that was saved by DesignModeler must be opened in ANSYS ICEM CFD. In order to do that, the user must do the following steps; File>WORKBENCH Reader>select xxxxxx.agdb file> then Open. Prior to the file being completely loaded into ANSYS ICEM CFD, the user has to go to the scroll down menu below and select the options that are illustrated in Figure Then the user must press apply. A B Figure 2-13: Importing an xxxxxx.agdb file into ANSYS ICEM CFD CFD (A). Opening the xxxxxx.agdb in ANSYS ICEM CFD CFD (B) 31

44 2.3.3.Preparing the Geometry for Meshing Figure 2-14: Extracting the feature curve from the symmetry plane Select those locations for the fluid volume area Figure 2-15: Demonstration the correct location 32

45 Figure 2-14 illustrates how to prepare the geometry that was loaded into ANSYS ICEM CFD so that the correct mesh and grid can be generated. In order to extract the curves from the surface, the user must do the following steps: Geometry tab > Create/ Modify Curve icon> Extract Curves from Surfaces icon, then select the surface on the screen. The user has to click on the glass icon to select all appropriate visible objects, or use the following shortcut key v. The plane that is selected for this study is the symmetry plane. After all the correct surfaces are selected, the user must click apply or OK. Following the Extract Curves procedure, the body for the fluid has to be created. In order to do that, the user must start with the Geometry tab again, and then the user must click the Create Body icon. Following that, name the part as the fluid name; any name can be used to name the region. For this study the name that is used is Fluid Volume. In order to name the fluid region, the user must select Centroid of 2 points for the location and the Material Point icon to select the location of the fluid volume. Then the user must click the two screen locations to select the fluid body region as demonstrated in Figure Following that, the user must click OK to finish creating the fluid volume area and proceed to the meshing setup. In addition, the user must create parts from the Subsets by selecting the inlet velocity, outlet, and the fluid volume boundary, and then right click on the Subsets to create parts. These names, are used when meshing in ANSYS ICEM CFD, and setting the boundary conditions and parameters in ANSYS FLUENT. 33

46 Generating the Initial Mesh Using the Octree Mesh Approach and Applying the Correct Mesh Size The strategy that is used for the mesh process is to have a prismatic or structured mesh around the solid model and then transition to an unstructured mesh. The prismatic mesh represents the boundary layer and is defined as a stair step mesh to decrease the required computing power. The height and the mesh density of the prismatic layer was set to represent the estimated boundary layer thickness around the solid models, i.e. oblate ellipsoids, flat plate and HPV fairing. Then the prismatic mesh transitions to an unstructured mesh to create a hybrid mesh around the solid model and inside the fluid region. Assigning the correct mesh for each model was a trial and error method. The reason behind this is that each model used slightly different mesh parameters, and it also varied from robust to fine mesh. It also depended on the size and shape of the geometry. The Scale Factor multiplies other mesh parameters to globally scale the model, for example if a Max Element Size of a given entity is 64 units and the Scale Factor is 0.3 units, then the actual maximum element size will be = 19.2 units. After countless tries, the correct scale factor was found to be approximately 0.3 for all the models. For that reason, all the models used a proper mesh for balancing accuracy with computed memory requirements. The maximum element size that was selected ranged from This value was selected due to the fact that an Octree Mesh scales by a power of two, and the Octree algorithm is limited to datasets of resolution of power of two. For that reason our values range from (or ). This is very important because all other values that will be input into the maximum scale factor will be rounded off to the closest power of two. In 34

47 order to set the parameters, the user must select Mesh tab> Global Mesh Setup icon > Global Mesh Size. After the correct input is input the user must click apply/ok. This is demonstrated in Figure Lastly, the general grid topology will be talked in chapter 3. Figure 2-16: Meshing sizing with ellipsoid of ratio l/d=2 After the meshing sizing is completed, the user must select the Part Mesh Setup icon. This icon is selected in the Mesh tab area to specify the mesh parameters. In order to create the prism mesh, the user must first select the prism option in the mesh parameter area, only for the solid model and the symmetry plane. The prism height is set to , depending on the model, so it can build the correct boundary layer as learned in ME692. For the ellipsoid and fairing geometry surfaces the maximum size is set in the range of 2.5-3; this creates a proper surface mesh for the solid geometry. Also the user needs to input at least 90 for number of prism layers of to be created, and a height ratio of for the growth factor. This corresponds to the maximum thickness (δ) in the turbulent boundary layer, which is approximately 2 inches. This number was found using the 35

48 calculations that can be seen in appendix A for the boundary layer thickness for the laminar, turbulent, and transition layers on a flat plate with a length equal to that of the ellipsoid and the fairing models. For the fluid volume box (inlet velocity, outlet, symmetry and open domain) the maximum size is set to 64 to allow create an appropriate volume mesh. After the mesh parameter setting are complete, the user must press apply. This is shown in Figure 2-17 for the ellipsoid and HPV fairing models. Figure 2-17: Mesh parameters step for the ellipsoid A B Figure 2-18: Mesh density box setup (a). Shifting of mesh density box to refine wake region (b) The density box is created to represent the wake region of recirculation flow immediately behind the model. The wake region is chaotic due to boundary layer separation on the rear portion of the body. The density box allows local control over the mesh density in the wake region to correctly represent the flow. 36

49 In order to create the density box that represents the wake region, the user must first select the Mesh tab> Create Mesh Density icon, then select the size of the density box. For this study the size was selected at 32, and the ratio and width were left at zero. The user then must select the density location as an entity. After the density box is selected, the user must click OK to generate it. Note that at this point the box surrounds the solid body. In order to shift the density box to the expected wake region location, the user must click Geometry tab> Transform Geometry icon > Translate Geometry icon, then select the density box and keep the translation method as explicit. Before the density can be shifted the model needs to be measured by the Measure Distance feature. Following that the density box is shifted by half of the model length. In this study the model was 99 inches long so the density box was shifted 44.5 inches in the negative X direction to represent the True Wake region. This is illustrated in Figure Following the completion of the creation and shifting of the density box, to generate the mesh, the user must first click the Mesh Tab> Compute Mesh icon, then the user must select the Create a Prism Layers and click Compute, as Figure 2-19 illustrates. Following that another mesh has to be defined to refine the present mesh of the model that can be correctly analyzed within ANSYS FLUENT. This is the Delaunay mesh step, and it will be discussed later in the chapter. The reason why an Octree Mesh was used as opposed to a Delaunay Mesh is to minimize the numerical error as much as possible. This also helps to minimize the total computing power needed to create a solid mesh. [39] 37