title of work · msc computational fluid dynamics msc thesis academic year : 2012 - 13 supervisor :...

CRANFIELD UNIVERSITY

Daniel Bence Ivady

Aerodynamic Force Modificationvia Base Roughness

SCHOOL OF ENGINEERINGMSc Computational Fluid Dynamics

MSc THESISAcademic Year : 2012 - 13

Supervisor : Dr. Panagiotis TsoutsanisAugust, 2013

CRANFIELD UNIVERSITY

SCHOOL OF ENGINEERINGMSc Computational Fluid Dynamics

MSc THESISAcademic Year : 2012 - 13

Daniel Bence Ivady

Aerodynamic Force Modificationvia Base Roughness

Supervisor : Dr. Panagiotis TsoutsanisAugust, 2013

A Thesis submitted in partial fulfilment ofthe requirements for the award ofthe degree of Master of Science.

©Cranfield University, 2013. All rights reserved.No part of this publication may be reproduced

without the written permission of the copyright holder.

Except where acknowledged in the customary manner, the material pre-sented in this thesis is, to the best of my knowledge, original and has not beensubmitted in whole or part for a degree in any university.

Daniel Bence Ivady

Abstract

This thesis report focuses on a numerical simulation done on a simplifiedquarter scale car model called Windsor body. The study is based on an experimen-tal investigation of drag reduction with passive flow control by Rob Littlewood.Measurement consist a baseline configuration and additional roughness elementtest cases. The results showed drag and lift reduction via the roughness. This hasbeen numerically investigated by former Cranfield University students and mytask was to further improve the model. Drag reduction is the main interest of theautomotive flow and this roughness study approach present promising results.

The report includes two study investigating the drag mechanism. TheRoughness Study is a project on investigating the FLUENT solver roughnessoptions capabilities. The k-ε Realizable and k-ω SST turbulence models havebeen tested with the result that the k-ε is not suitable for such an investigation,while the k-ω SST performs reasonably. The other study is based on the differentvertically mounted roughness element cases flow analysis. The conclusion ofthe investigation is that the numerical simulation with the applied assumptionsand conditions it is able to estimate the drag mechanism and reproduce a real-istic wake structure behind the body but only with the k-ω SST turbulence model .

Keywords

Windsor, drag, roughness, wake

v

Acknowledgements

I am deeply grateful to my parents who were supporting me from thebeginning of my life and gave me the opportunity to accomplish my goals tobecoming an engineer. I would like to show my appreciation to Dr Ben Thornberwho established the option to work on an industrial problem and granted myapplication to the Master Course. Special thanks to Adrian Gaylard from JaguarLand Rover who were motivating me and gave useful advices to the project workduring the summer meetings. I would like to express my very great appreciationto Dr Nick Asproulis who gave me the last push to succeed.

Advices and comments given by my supervisor Dr. Panagiotis Tsoutsanishas been a great help in order to do my best. I want to thank to Dr Laszlo Konozsy,who was always available to could discuss my problems with him on my nativelanguage.I have to mention the full staff of the Master Course who were in thefront line to teach me the art of Computational Fluid Dynamics and force me todeepening my knowledge in this field of engineering.

Beside the official crew, I would like to thank to the other students whowere always up to fun but when it comes the time everybody helped each otherin all the situation. And last but not least all those nights in the labs made anunbreakable bond between us. Special thanks to my neighbour and course mateJebin Elias who guided me in the world of LateX.

Daniel Bence Ivady

vi

Table of Contents

Abstract v

Keywords v

Acknowledgements vi

List of Figures ix

List of Tables xii

List of Symbols xiiiAbbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiNotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

1 Introduction 11.1 Aims and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Literature Review 32.1 Aerodynamic Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1.2 Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Bluff Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Simplified models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.1 Ahmed Body . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.2 Windsor Model . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Drag Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4.1 Passive Control . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4.2 Active Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.5 Related Aeordynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 162.5.1 SUV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.5.2 Heavy Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3 Theoretical Background 203.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.2 Numerical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.3 Turbulence Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3.1 k-ε Realizable . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3.2 k-ω SST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4 Methodology 274.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2 Grid Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

vii

4.3 Solver Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.4 Simulation Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5 Results and Discussion I. 395.1 Roughness Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.1.1 Grid Convergence . . . . . . . . . . . . . . . . . . . . . . . . . 425.1.2 Roughness on Roof and Back . . . . . . . . . . . . . . . . . . 485.1.3 Boundary Layer Evolution . . . . . . . . . . . . . . . . . . . . 555.1.4 Flow Features . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

6 Results and Discussion II. 636.1 Vertical Element Study . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.1.1 Drag and Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.1.2 Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.1.3 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686.1.4 Wake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706.1.5 Moving Ground Study . . . . . . . . . . . . . . . . . . . . . . 78

7 Conclusions and Recommendations 837.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837.2 Recommendations for Future work . . . . . . . . . . . . . . . . . . . 84

References 84

Appendix 88A. Bookmark A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88B. Bookmark B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

viii

List of Figures

2.1 Acting Moments and Forces on a Car . . . . . . . . . . . . . . . . . . 32.2 Streamlined and Bluff body . . . . . . . . . . . . . . . . . . . . . . . 62.3 Boundary layer separation . . . . . . . . . . . . . . . . . . . . . . . . 72.4 Simplified Model Geometry . . . . . . . . . . . . . . . . . . . . . . . 92.5 Ahmed body baseline configuration . . . . . . . . . . . . . . . . . . 102.6 Ahmed body flow structure[1] . . . . . . . . . . . . . . . . . . . . . . 102.7 Ahmed body LDA mesurement layout . . . . . . . . . . . . . . . . . 112.8 Windsor model different concepts . . . . . . . . . . . . . . . . . . . . 122.9 Drag and Lift Coefficient evolution of the measurement . . . . . . . 122.10 Ahmed body with added elements . . . . . . . . . . . . . . . . . . . 142.11 Ahmed body with drag reduction element . . . . . . . . . . . . . . . 142.12 Ahmed body with applied Active Control . . . . . . . . . . . . . . . 152.13 Full Scale tested SUV horizontal slat configuration . . . . . . . . . . 162.14 SUV Drag Coefficient Evolution . . . . . . . . . . . . . . . . . . . . . 172.15 SUV Drag Reduction Techniques . . . . . . . . . . . . . . . . . . . . 172.16 Heavy Vehicle Drag Distribution . . . . . . . . . . . . . . . . . . . . 182.17 Truck Boat Tailing Examples . . . . . . . . . . . . . . . . . . . . . . . 192.18 Truck Rotating Element Design . . . . . . . . . . . . . . . . . . . . . 19

3.1 SIMPLE Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2 Staggered Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3 Turbulent Energy Spectrum . . . . . . . . . . . . . . . . . . . . . . . 253.4 Wall Treatment of Turbulence Models . . . . . . . . . . . . . . . . . 26

4.1 Baseline Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2 Configuration C1 with 3 total slats . . . . . . . . . . . . . . . . . . . 294.3 Configuration C2 with 3 short slats . . . . . . . . . . . . . . . . . . . 294.4 Configuration C3 with 5 total slats . . . . . . . . . . . . . . . . . . . 294.5 Configuration C4 with 5 short slats . . . . . . . . . . . . . . . . . . . 294.6 Computational Domain . . . . . . . . . . . . . . . . . . . . . . . . . 304.7 Meshing problem at the support . . . . . . . . . . . . . . . . . . . . 314.8 Meshing problem at the slats . . . . . . . . . . . . . . . . . . . . . . . 324.9 Mesh Densities Positions . . . . . . . . . . . . . . . . . . . . . . . . . 324.10 Applied Meshes for C0 baseline configuration . . . . . . . . . . . . 334.11 Velocity and Kinetic Energy Profiles . . . . . . . . . . . . . . . . . . 354.12 Turbulence dissipation ε and ω Profiles . . . . . . . . . . . . . . . . 354.13 Inlet Turbulence Intensity . . . . . . . . . . . . . . . . . . . . . . . . 35

5.1 Wall Roughness Modelling . . . . . . . . . . . . . . . . . . . . . . . . 41

ix

5.2 Grid Convergence Drag Force R50 . . . . . . . . . . . . . . . . . . . 425.3 Grid Convergence Drag Lift R50 . . . . . . . . . . . . . . . . . . . . 435.4 Grid Convergence Drag Coefficient R50 Turbulence . . . . . . . . . 435.5 Grid Convergence Lift Coefficient R50 Turbulence . . . . . . . . . . 445.6 Grid Convergence Drag Difference R50 Turbulence . . . . . . . . . . 445.7 Grid Convergence Lift Difference R50 Turbulence . . . . . . . . . . 445.8 General Car Pressure Distribution . . . . . . . . . . . . . . . . . . . . 465.9 Grid Convergence Pressure Coefficient Centerline R50 . . . . . . . . 475.10 Grid Convergence Pressure Coefficient Centerline ZOOM R50 Tur-

bulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.11 Grid Covergence Skin Friction Coefficient R50 . . . . . . . . . . . . 485.12 Roughness Study Drag Coefficient R50 H10 ROOF . . . . . . . . . . 495.13 Roughness Study Drag Coefficient Difference R50 H10 ROOF . . . 495.14 Roughness Study Drag Coefficient R50 H10 BACK . . . . . . . . . . 505.15 Roughness Study Drag Difference R50 H10 BACK . . . . . . . . . . 505.16 Roughness Study Drag Coefficient R50 H20 ROOF and BACK . . . 515.17 Roughness Study Drag Difference R50 H20 ROOF and BACK . . . 515.18 Roughness Study Viscous Forces on the roof ROOF . . . . . . . . . 535.19 Roughness Study Viscous Forces on the roof BACK . . . . . . . . . 535.20 Roughness Study Pressure Coefficients on Coarse Mesh Heights . . 545.21 Roughness Study Skin Friction Coefficient on Coarse Mesh Heights 545.22 Boundary Layer Description . . . . . . . . . . . . . . . . . . . . . . . 555.23 Boundary Layer Monitoring . . . . . . . . . . . . . . . . . . . . . . . 555.24 Boundary Layer Velocity Isosurface . . . . . . . . . . . . . . . . . . . 565.25 Boundary Layer Evolution Grid Convergence R50 . . . . . . . . . . 575.26 Boundary Layer Evolution Roughness Height ROOF . . . . . . . . 575.27 Boundary Layer Evolution KEPS . . . . . . . . . . . . . . . . . . . . 575.28 General Pressure Coefficient Distribution . . . . . . . . . . . . . . . 585.29 Pressure Coefficient Back Coarse-Fine SST (left) KEPS (right) . . . . 595.30 Pressure Coefficient Back Coarse-Coarse (left) Fine-Fine (right) . . . 595.31 General Symmetry Pressure Distribution . . . . . . . . . . . . . . . . 605.32 General Symmetry Velocity Distribution . . . . . . . . . . . . . . . . 605.33 General Symmetry Turbulent Kinetic Energy . . . . . . . . . . . . . 615.34 General Symmetry Streamline SST (left) and KEPS (right) . . . . . . 615.35 General Wake Streamline SST (left) and KEPS (right) . . . . . . . . . 625.36 General Vortex Structure SST (left) and KEPS (right) . . . . . . . . . 62

6.1 Vertical Slats Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.2 Vertical Slats Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.3 Vertical Elements Pressure Coefficient along Centerline . . . . . . . 656.4 Vertical Elements Pressure Coefficient along Centerline ZOOM . . . 656.5 Pressure Coefficient Comparison Experimental (left) and C0 (right) 666.6 Pressure Coefficient Comparison C0 (left) and C1 C2 (right) . . . . . 666.7 Pressure Coefficient Comparison C0 (left) and C3 C4 (right) . . . . . 676.8 Vertical Elements Turbulent Kinetic Energy and Streamline C0 C1 C2 686.9 Vertical Elements Turbulent Kinetic Energy and Streamline C0 C3 C4 69

x

6.10 Vertical Elements Total Pressure (left) and Q criterion (right) FromC0 to C4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.11 Slat Velocity Comparison Y1 (left) Y1 and Y2 (right) for C0 C1 C2 . 746.12 Slat Velocity Comparison Y1 (left) Y1 and Y2 (right) for C0 C3 C4 . 756.13 Slat TKE Comparison Y1 (left) Y1 and Y2 (right) for C0 C1 C2 . . . 766.14 Slat TKE Comparison Y1 (left) Y1 and Y2 (right) for C0 C3 C4 . . . 776.15 Ground Study Drag Coefficients . . . . . . . . . . . . . . . . . . . . . 786.16 Ground Study Lift Coefficient . . . . . . . . . . . . . . . . . . . . . . 796.17 Ground Study Streamlines Ground (left) and original (right) . . . . 806.18 Ground Velocity Comparison Y1 (left) Y1 and Y2 (right) for C0 C1 C2 816.19 Ground Velocity Comparison Y1 (left) Y1 and Y2 (right) for C0 C3 C4 82

xi

List of Tables

4.1 Windsor Model Geometry Dimensions . . . . . . . . . . . . . . . . . 284.2 Applied Mesh Parameters . . . . . . . . . . . . . . . . . . . . . . . . 334.3 Ground Study Inlet Conditions . . . . . . . . . . . . . . . . . . . . . 374.4 Baseline Configuration C0 All cases . . . . . . . . . . . . . . . . . . . 384.5 All Slat configuration cases . . . . . . . . . . . . . . . . . . . . . . . . 38

5.1 Experimental Drag and Lift Coefficients . . . . . . . . . . . . . . . . 395.2 Drag and Lift Coefficients of R50 H0 SST Cases . . . . . . . . . . . . 455.3 Drag and Lift Coefficients of R50 H0 KEPS Cases . . . . . . . . . . . 455.4 Drag and Lift Coefficients of ROOF H10 Cases . . . . . . . . . . . . 515.5 Drag and Lift Coefficients of BACK H10 Cases . . . . . . . . . . . . 525.6 Drag and Lift Coefficients of ROOF H20 Cases . . . . . . . . . . . . 525.7 Drag and Lift Coefficients of ROOF H20 Cases . . . . . . . . . . . . 52

6.1 Vertical Slats Coefficients and Accuracy . . . . . . . . . . . . . . . . 646.2 Extracted data axial position . . . . . . . . . . . . . . . . . . . . . . . 726.3 Plot explanation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

xii

List of Symbols

Abbreviations

CFD Computational Fluid Dynamics

RANS Reynolds Averaged Navier Stokes

URANS Unsteady Reynolds Averaged Navier Stokes

LES Large Eddy Simulation3D 3 Dimension

CAD Computer Aided DesignPIV Particle Image Velocimetry

LDA Laser Doppler AnemometryTKE Turbulent Kinetic Energy

Notations

C0 Configuration 0 - Baseline Geometry

C1 Configuration 1 - 3 full added slat Geometry

C2 Configuration 2 - 3 short added slat Geometry

C3 Configuration 3 - 5 full added slat Geometry

C4 Configuration 4 - 5 short added slat Geometry

ROOF Refers to roof surface in the Roughness Study Case

BACK Refers to back and roof surface in the Roughness Study Case

R H Refers to type of Surface Roughness Study Cases

SST Refers to k-ω Shear Stress Transport Model

KEPS Refers to k-ε Realizable Model

xiii

Chapter 1

Introduction

Nowadays the automotive industry is one of the challenged sector on themarket. The companies has to fulfil the current regulations commissioned by theInternational Standards in means of the environmental field like the pollution,emission and safety for the passengers or manufacturing. Products has to meetthe expectation of the customers on the market in every possible aspect from thecomfort to performance or simply the fame in certain occasions. These conditionsleads to a high quality standards, what cannot be maintained without develop-ment of the current state. High demand needs investment and manufacturersare doing Research & Development projects in various fields of engineering inorder to accomplish their goals. Automotive industry is a collaboration of all me-chanical engineering discipline from thermodynamics to solid and fluid dynamicsthrough material science. In these fields the Computational Fluid Dynamics canbe applied as an efficient tool in the Research and Development projects.

As the CFD software packages are getting more common, and becomesreliable and rapid, it can be applied in multiple tasks. Automotive flows canbe separated into internal and external category. In terms of internal flows , theexhaust system and the vehicle engine simulations are the main research areas.Emission and environmental awareness can be reduced in the combustion process.The external flows are more in the common sense. Vehicles aerodynamics is anissue since the beginning of the 20th century [2]. Events such as crude oil priceincrease is accelerating the process. Recently one of the development field is thedrag reduction. This force plays a role in the fuel consumption, so it related tothe emission. All the newer designed electric cars are aerodynamically optimizedto reduce the losses correlated to the drag. Other problems like the cross windstability, cooling and mud deposition can be also modelled by the CFD simulationsand extreme cases like high-performance motor sports[3].

External aerodynamics point of view the main purpose is to reduce theacting drag forces around the vehicle to improve the overall efficiency. Gen-eral methodologies to investigate and develop the aerodynamic performance andcharacteristics are the following. First approach starts with a unique simplified

1

Introduction

bluff bodies or streamlined shapes , which represents the main flow features. In-vestigate and test these cases numerically and experimentally to draw conclusionfor the full scale vehicles [4]. In this thesis work such a task is evaluated. Theother approach is that the already finished mechanical design shape is optimizedlater with additional active of passive drag control elements.

The Thesis Report is focusing on the numerical modelling of a simplifiedvehicle model problem. The investigated shape is called Windsor model, devel-oped by the Rover company in the 80’s. Similarly to the Ahmed body it is usedto reproduce the basic flow features of a full scale car model. The Windsor modelhas different outlines to represent square-back, hatch-back and notch-back cases.The thesis originates to an experimental measurement published by Littlewood[5]with a square-back configuration with additional roughness elements. The mainobjective of the study was to test different element arrangements on the rear sur-face of the body. Placing slats horizontally along the back resulted in drag and liftreduction compared to the original clean shape.

The experiment has been redone by a current Phd student Anna Perryat Loughborough University in 2012. The newly obtained results have beenreferenced as the experimental validation case to the numerical investigation ofthe project by Iain Robertson [6] and Adrien Becot[7] at Cranfield University in2012. These works are the basis of the report.

Instead of further analysis of this experimental case the main focus ofthe thesis can be divided into two study. The Roughness Study investigatesthe baseline configuration without added surface element. The applied CFDsoftware package the Ansys FLUENT’s different roughness options were testedon the surfaces of the body. Another Study has been made on different addedroughness elements at the rear surface of the body similarly to the previous works.In this analysis these slats are vertically mounted on the back and the evaluationis focusing on the effect of these roughness elements to the overall characteristics.

1.1 Aims and Objectives

Summary of the aims and objectives:

• Perform a Roughness Study focusing on the surface roughness options ofthe available CFD tool on the Windsor body baseline configuration.

• Investigate the flow features and main characteristics and analyse the wakestructure of different vertically mounted roughness element configurations.

• Analyse the results and draw the conclusion between the cases on the aero-dynamics performance and drag.

2

Chapter 2

Literature Review

2.1 Aerodynamic Forces

The natural environment for a ground vehicle takes place in the atmo-spheric region, where the interaction with the atmoshpere creates forces. Therelative motion to the atmosphere generates aerodynamic forces on the vehicle’ssurfaces. In order to model the fluid motion properly it is essential to understandand apply the fluid dynamic and thermodynamic principles. In automotive aero-dynamics the analysis is divided into external and internal flow categories [8].Current thesis is concentrating on the external flows, thus this topic will be pre-sented along the chapter.

Figure 2.1: Acting Moments and Forces on a Car

Generally the external flows characteristics are governed by the geomet-rical configuration and Reynolds number of the flow. External flows are differ-entiated into three major term called the drag, lift and stability [3]. A movingvehicle relative to the atmosphere, with a velocity vector is effected with twotype of aerodynamic forces. On the opposite direction of the motion the forceis called drag, while the perpendicular component is defined as lift. The shapeof the vehicle and atmospheric conditions have a key role to determine the aero-dynamic loads. Based on the flow conditions (cross wind) and acting forces, thethree aerodynamic moments determine the vehicle’s road stability and handlingFigure 2.1. It is a sensitive balance of the lift (pitching moment) and side forces(yawing moment), while the rotating moment has a role only in extreme cases [9].

3

Literature Review

2.1.1 Drag

Drag is a sum of mechanical forces generated on the surface of an objectdue to the interaction with the fluid. In automotive aerodynamics drag is a majorconcern of investigation, since the magnitude of it is largely affect the vehiclecharacteristics such as fuel consumption. Acting drag force can be divided intotwo source, but the physical origin makes them dependent to each other. Incase of viscous flow the boundary layer has a strong influence on the externalflow development, like separation where the adverse pressure gradient causesthe deattachment. So the viscosity and the pressure distribution is related. Thedrag consist a pressure source term normal to the surface (pressure drag), anda viscosity originated shear stress term parallel to the surface (friction drag). Inother approach the aerodynamic drag is an integral of static pressure, friction andturbulence stresses over the surface of the vehicle [10].

The friction drag Df in a viscous flow is present all over the wall. Dueto the molecular friction, shear stress is acting on the surface. The integrationof this force component along the wall in the free stream direction is called thefriction drag. For streamlined bodies like airfoils or flat elongated bodies, whereseparation does not occur, this component is the dominant term of the drag [2].

The pressure drag is the dominant source for automotive flows, comparedto the friction drag from the shear stresses. Generally the pressure distributionalong a bluff body or a vehicle consist a high pressure area in front (stagnation),and a low pressure area at the rear in the separation zone (wake). The flow sepa-ration is highly determines the pressure drag, thus it is important to understandthe deattachment of the flow.

Flow separation which governs the pressure drag component can be di-vided into two types. The first type is where the separation line is perpendicularto the flow direction. The separation zone is unsteady and vortices are generatedwith a rotational axis perpendicular to the flow and parallel to the separation line.A significant pressure loss behind the body is occuring due to the vortex field ki-netic energy dissipation in the wake region (separation zone), where depressionand low velocities are characterising the flow. The other type is when the separa-tion line is closing an angle with the flow direction. It leads to a three dimensionalseparation, which induce suction (pressure drag) behind the body. These two sep-aration are in relationship and have a very complex three dimensional, unsteadyphenomenon. Different angle of attacks leads to vortex breakdowns and vortexburst which is a highly important area to understand the physics behind it. It is amajor research area in the topic of drag reduction.

The previous paragraphs are introducing the drag and the fluid mechan-ical background to understand this force component. As a measure of the drag, itcan be expressed as a dimensionless coefficient, so it is easier to compare differentvehicles. The expression Equation (2.1) contains the ratio of drag force D, whereD = Df + Dp, sum of friction and pressure drag over the multiplication of dynamicpressure and the largest area from the free stream direction AD

4

Literature Review

CD =D

12 · ρ · v

2∞ · AD

(2.1)

Traditionally this drag representation is used, but there exists advancedapproaches, where not only the surface integrals are in the formula, but it takesinto account the vortex evolution in the rear wake of the flow in order to under-stand the relationship between components. Onorato et al [11] is introducing asimplified model based on the momentum equation. Assume the flow incom-pressible, steady and the effect of turbulence and gravity are negligible comparedto pressure effects. The formula includes three particular expression as source ofthe drag Equation (2.2). Drag can be obtained by using the reference total pressurePi0 and actual Pi , with the free stream velocity V0 and the current local velocitycomponents Vx , Vy , Vz . The first integral term is related to the near wake ve-locity reduction, the next part is the drag coming from the longitudinal vortices,while the last term is representing the pressure loss between the downstream andupstream wake. The expression have been tried out as a User Defined Functionbut it does not give back the expected results.

Fx = −ρV2

0

2

∫S

(1 −

Vx

V0

)2

dσ +ρV2

0

2

∫S

V2y

V20

+V2

z

V20

dσ +

∫S

(Pi0 − Pi)dσ (2.2)

2.1.2 Lift

The perpendicular component of the acting load is the lift, which is basi-cally generated by the pressure difference between the upper and lower surfaceof the body involved in the flow. Similarly to the drag, the lift can be expressed bya dimensionless coefficient as well, depending on the free stream velocity v∞ andinitial conditions. Lift force in Equation (2.3) is denoted with L, the characteristichorizontal area AL, and the density of fluid ρ .

CD =L

12 · ρ · v

2∞ · AL

(2.3)

In a general passenger car case, the created lift force is significantly smallerthen the gravity force, thus the effect on the road characteristic is negligible. Thelift force is coming in the front for stability and tyre performance reason in thefield of race car aerodynamics. The downforce is an essential property in thehigh performance race cars. Greater downforce increases the turning speed,acceleration and stability conditions, improve braking performance.

5

Literature Review

2.2 Bluff Bodies

In aerodynamics the ground vehicles can be classified in the category ofbluff bodies. Beside vehicles another class the buildings can be placed in thisgroup, for external flow point of view. Both vehicles and buildings are influencedby the ambient conditions and natural wind. Major contribution for bluff bodiesare that the significant drag component originated to the generated pressure dragcompared to the friction type. In general if the streamlines are following thebody’s surface (streamlined body) due to the D’Alambert paradox the pressureforces are small, while the friction forces are dominating.

D’Alambert paradox states that in inviscuid fluid flow, if the streamlinesare follow the surface, applying the Bernoulli equation to determine the flowproperties, from the momentum equation we get the final result that the forcesacting on the body is zero [12]. In viscous case both pressure and rampant frictionforces plays a role.

Streamlined bodies such as aerofoils can behave as bluff bodies as theangle of attack reaches a certain value [13]. For streamlined bodies to reduce dragadvanced flow control methods are available to decrease skin friction. For bluffbodies to reach our goal it needs to be considered that pressure drag has to beminimized. Avoid separation of the boundary layer, keep flow attached to thesurface as much as possible.

Bluff body flows are characterised by separation of the boundary layer,thus an unsteady velocity field and a low pressure zone evolves in the rear bodycalled wake. In 2D bluff body cases these wake regions are generally character-ized by periodic vortex shedding. A common example for this phenomenon isthe Karman vortex for lower Reynolds number flows. Due to these conditionsthe wake has a large energy dissipation rate, thus a high drag arise behind thegeometry.

Figure 2.2: Streamlined and Bluff body

In order to reduce the drag it is essential to understand the physics behindit. So the main problem, the boundary layer separation must be investigated.Boundary layer remains thin and does not separate in accelerating flow, that’swhy in the forebody region near the stagnation point there is no separation. Thepressure forces can be related to the boundary layer

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Literature Review

Two basic condition for boundary layer separations is the vicinity of thewall, where the effect of the wall shear stresses arise (viscosity) and the adversepressure gradient related to streamwise velocity decreasing too. Separation takesplace if the decceleration effect of the wall shear stresses and the adverse pressuregradient tops the sum of momentum of velocity distribution.

There exist conditions what are influencing the separation, help it tohappen or avoid, decrease the possibility. Those conditions which acceleratethe process are the following. An obvious case is when the wall shear stressare larger in the turbulent layer when the roughness of the wall is bigger. Largerpressure gradient also affect the separation, it takes place where the flow directionis changing such as cases in front of a concave or behind a convex edge, smallrounding up radius. Low kinetic energy (slow velocity) near wall and suddenchange in radius also helps the separation. The techniques and methods to preventor relocate separation are trying to reduce the previous listed cases. Increase thekinetic energy by higher velocity near the wall or blowing in or suction of theboundary layer. For replacing the separation the easiest way is to interfere thelaminar-turbulent transition with turbulence generators

Figure 2.3: Boundary layer separation

Boundary layer separation is a mode of vorticity transport in potentialflows by convection. As a result of boundary layer separation, the shear layerenters the flow by creating a closed separation bubble or an open vortex tube.Both cases the characteristic pressure are smaller then the ambient. Separationbubbles and vortex tubes are the typical vehicle aerodynamic flow features in thewake region.

A closed separation bubble development process are containing the fol-lowing steps. First the boundary layer separation, the formation of shear layer,large velocity gradient across the shear layer and an intense turbulent mixingtakes place. Next section is the entrainment, which needs a reverse flow, whichhas pressure below ambient. It affects the curvature of the streamlines, reattach-ment or separation bubble closing and the final structure develops. [13].

Main features of the closed separation bubble are important to know if thetask is to reduce the size effectively. In the bubble compared to the undisturbed

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Literature Review

motion a relatively slow (20-30% of velocity) reverse flow takes place. The bubbleis surrounded by walls and the closed shear layer. An approximately constantlower pressure compared to the ambient, which is affected by the angle of theundisturbed flow and the tangent of the shear layer at the separation point.An intense turbulent mixing and high turbulence intensity region with a fairlydefinable passive flow structure[13].

The other structure the open vortex tube is generated when an edge andthe flow close a relatively small angle, eg. delta wings. The tube’s diameter isincreasing downwards with length. The pressure and velocity is decreasing asthe tube axis is approached. Open vortex tubes are active flow structures, withlower pressure then the ambient. This phenomenon arises at buildings top edgesand as well in hatchback cars[14].

Generally the separation’s place is fixed in case of sharp edges of thebodies. For rounded, curved shapes where is no sharp edge, the separationdepends on the pressure distribution and the position is moving until it reachesthe equilibrium. The place of separation can move periodically in time[15].

To sum it up the forces acting on a bluff body is mainly caused by theunbalanced pressure distribution along the geometry. The wall shear stress isplaying only a small role compared to streamlined bodies where this force is thedominant, but essential for the boundary layer separation. Bluff body flow arecharacterized by separation of closed bubbles or open vortex tube depending onthe geometry and flow conditions. This low pressure near wake region containsthe vortex structure which leads to the high drag [16]. Ground vehicles are cate-gorized as bluff body because of the geometry and aerodynamics flow features.In automotive aerodynamics streamlining is not a straightforward tool to reducedrag, since the shape of the body is determined by other designing constraintsand different purposes (heavy vehicles) [17]. Drag reduction can be reached bybase flow modifications by active and passive techniques.

2.3 Simplified models

Automotive industry has to face a lot of challenges these days. Companieshave to satisfy the customers, fulfil the international standard and maintain thefuture development. As the vehicles are getting more sophisticated and becomethe one of the state of the art technology in engineering. The fossil energy resourcesare finite and one of the main cause of global warming is the high amount of CO2produced by the industry and transportation, so the clever fuel consumption isessential. In case of vehicles one of the solution to the problem is the aerodynamicoptimization. The first fossil fuel crisis in the 70’s affect largely this sector of theindustry. Drag reduction came in to the front that time and since then this aspectis still and getting more important as hybrid technology and solar power drivengreen vehicles are the options for the prospective future. Important considerationto the road vehicles [14]:

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Literature Review

• Separation leads to high drag

• Ground effect influences both lift and drag

• Presence of wheels

• Wind is introducing yawed flow and turbulence

• Interference due to other vehicles

In the 20th century different tools were applied to reach aerodynamicperformance optimization goals. From wind tunnel measurements to nowadaysCAE techniques the motorsport, passenger and heavy duty vehicles can be man-aged. There are two ways to done the development process. The first and moreapplied method is to start aerodynamic concerns in a later phase of design de-velopment, the shape and detail optimization. Other approach is to start the fulldesign process with a genuine streamlined body and develop the whole vehicleon that configuration. To test and create such models, simplified or streamlinedbodies are used. This is a well approved methodology to investigate the aerody-namic characteristics. From the results of these reduced detailed models relationsand conclusion can be drawn to the original vehicles. Studies on these cases showthat these simplified bodies can perform realistic flow features as actual cars suchas of on Figure 2.4 .

Figure 2.4: Simplified Model Geometry,[18]

Due to the reduced complexity these models allow to prepare experimentsand CAE simulations. The simple geometry has a great potential to equip themeasurements cheaper, in simulation point of view the CAD model and CFDmesh are significantly easier to generate. The advantage of this approach appearsin the reproducing process, to measure and redo a simulation in order to validationor checking the case. For common models there exist a large range of availabledata both experimental and numerical, which is a good comparison possibilityand a good basis for investigation. Drawback of this approach is that an artificialcase is generated and some major details can be different to the actual vehicleconcepts, such as the underbody or the flow conditions. Furthermore this chaptercovers one of the most commonly applied simplified bluff body car model theAhmed body and the actually investigated shape the Windsor model.

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Literature Review

2.3.1 Ahmed Body

Ahmed Body is a well know study, what becomes a standard bench-mark problem formulation in ground vehicle flows, in order to investigate newturbulence solvers, CFD codes Figure 2.5. Researchers have been made severalmeasurements [1][19] and numerical simulations [20][21] in different configura-tions to analyze the backlight angle effect in the wake structure Figure 2.6. Thesecases are well documented and published. There original study [1] focused onthe backlight angle variation and it’s effect to the wake structure and base drag.This base model is able to reproduce the general vehicle aerodynamic.

Figure 2.5: Ahmed body baseline configuration

This base model is able to reproduce the general vehicle aerodynamicfeatures in the wake structure as a real vehicle configuration. Experiments havebeen carried out on different boundary conditions (moving ground) wide rangeof velocity and techniques from simple pressure, velocity measurements to PIV ,LDA [22]. Main CFD techniques were used to deal with the problem from RANS,URANS, LES to hybrid techniques. It is popular that added elements are testedon the original layout. Deflectors, splitters or induced cavities to investigate theeffects on the flow wake structure and drag coefficient.

Figure 2.6: Ahmed body flow structure [1]

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Literature Review

Significant differences arise in terms of modelling to real cases for wheelsand underbody. The wheel-house and wheel effect is neglected in most of theconfiguration, but there exist studies in this field too [23]. It can be furtherextended with rotating wheels and proper ground conditions, which is necessaryfor the diffuser studies. Usually the underbody is smooth for all type of simplifiedmodels, for actual cars it is very rare to have a covered smooth layout. It couldbe a possible future focusing area, since the combination of ground effect anddiffuser can reduce the drag and affect the whole wake structure

Figure 2.7: Ahmed body LDA mesurement layout[22]

Conclusions from the model can be utilized in the hatchback cars, sincethe geometry has a similar backlight angle configuration and the wake structure isalso very similar. For further studies the full model is a square back case what canbe applied for vans and heavy duty vehicle [24]. This case has the most similarityto the thesis Windsor model, due to the end, the difference is in the forebody whichis more ”hood” like for Windsor. The detailed and well documented Ahmed bodyis a good basis to understand what is happening in the wake behind a car.

2.3.2 Windsor Model

The Windsor model (Rover model) is a bit more sophisticated simplifiedcar concept then the Ahmed body. The shape is more automobile like. The frontbody with an A-pillar construction and hood resembles more to a full scale cardesign. The model represents a wide range of passenger cars depending on theapplied back configuration from square to notchback Figure 2.8 . In the last decadethe trends show that the frontal area of cars are increased and with the growingpopularity of the Sport Utility Vehicles (SUV) the aerodynamic optimization, dragreduction needs more focus.

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Literature Review

Figure 2.8: Windsor model different concepts

In the last few years at the Loughborough University different experi-ments have been made on the Windsor model with a square back configurationwith applied roughness element [5] as passive technique and steady blowing [25]as active method in order to reduce the base drag. The majority of measurementshave been done on a 1/4 and a full scale model at MIRA with an MPV. The appli-cation of slats at the back [5] of the model is linked to a previous roof trailing edgeinvestigation [26]. Experimental results show a considerable reduction both inbase drag and lift for different velocities and slat configurations Figure 2.9. Thismeasurement become the basis of two previous year MSc in CFD (2012) studentsIain Robertson and Adrian Becot.

Figure 2.9: Drag and Lift Coefficient evolution of the measurement[5]

Both thesis [6], [7] consist a numerical simulation on the basic concept, theclean layout square back model. The task was to investigate the Windsor modelon the same boundary conditions as the experiment. Generate a proper gridaround the Windsor body and investigate different turbulence models. Robert-son analyzed the same three type of configurations as Littlewood in the windtunnel with different grids and boundary conditions. Becot had to investigatethe backlight angle change similarly to the Ahmed body concept and additionalroughness elements at the underbody. Compared to the measured configurationboth of them get drag reduction for the back surface slats and the backlight anglearrangements. The added slats at the underbody affect in a drag and lift increase.The obtained wake structure analysis will be compared in later chapter of thethesis.

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Literature Review

2.4 Drag Reduction

In the previous sections the origin and physical phenomena is introducedto define drag. For vehicle aerodynamicist primary issue is to decrease drag.Companies objective is that is possible to reduce the drag with control solution by30% without confront the constrains [27]. Drag can be reduced by controlling theseparations location with flow intervention near the wall region with or withoutadditional external energy using devices [28]. Controlling can be used as acousticor noise regulation as well, not just drag reduction [28]. Methods can be cate-gorized into active and passive control systems. Passive approach applies shapemodification on the vehicle body, while the active techniques are introducing adirectly controlled external device.

The main objectives are to relocate the separation point to decrease theseparation effect and size of it or increase the base pressure. Keep the flow attachedto the wall as further possible or help to reattach (for trucks). If these conditionsare fulfilled the drag coefficient will be smaller, and the aerodynamic performancebecome more effective.

2.4.1 Passive Control

Passive techniques have been applied on a wide range, since the modifi-cation of the geometry is simpler to change. These methods are very effective forgeneral passenger cars, but plays an important role in heavy duty vehicles too.The most elementary step is to avoid the sharp edges if it’s possible and applyrounding or tapering.

In case of a square back geometry the boat tailing is one of the mostcommon technique what can be done in two ways limited by the constrains. Itis a gradual reduction of the cross section through the length till the base [29].Tailing with curvature for passenger cars or apply parallel elements for trucks orgeneric car models. For buses it is a well approved technique to round a certainpart of the end vertical edges. It helps to reduce the base area on the rear end anduses the underbody flow which comes up. As the separation zone gets smaller,de acting pressure also increases so the total drag is considerably lower.

Another method is to apply cavities near the rear roof edges [26] orcylindrical element along it for a slant Ahmed body as Pujals [30] with a smallerdrag reduction results. Similarly a base cavity with variable depth, which can beventilated by slots [31]. These approaches does not have a that significant changeas boat tailing but still achieve drag reduction. The study at Durham [31] showthat overall drag is decreased but a minimum drag is reached at a certain depth.With ventilation slots a greater reduction can be obtained with a bigger depthcavities. Add on devices or elements called splitters can be used both at the rearor front end, so the flow can be controlled.

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Literature Review

Figure 2.10: Ahmed body with added elements

These modifications are affect the deattachement or reattachment depend-ing on the position. The acting forces are different because of the area of the addedsplitters and it can change the wake structure in the back.

A very promising new technique which is using a porous layer on thesurface. For a square back Ahmed body with almost a full cover it resulted a 40%drag reduction by simulation. This approach very dependent on the boundaryconditions so the proper assumptions has to be made. [27]

Different passive techniques affect the total flow in different parts andeach method has a ”minimum” value where it is most effective, but it is possiblethat the other applied device has an optimal value on another condition. If moredevice is applied it has to be optimized together in order the reduce drag in themost efficient way Figure 2.11.

Figure 2.11: Ahmed body with drag reduction element

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Literature Review

2.4.2 Active Control

Compared to passive methods active techniques are more fresh and hasmore potential as the technology improves and more radical solutions take place[27]. For example in the case of the Volkswagen XL1 prototype automobile, abig fan is applied in the back of the car to suck the air from the wake region.These techniques are using external energy source and control the flow. The greatadvantage compared to passive techniques is that it can be optimized dependingon the flow conditions, it has a feedback, so it’s kind of an interactive controlsolution for drag regulation.

A popular approach is the application of boundary layer suction or blow-ing so the separation zone and pressure distribution can be controlled. It ispossible to combine these two. The approach induce energy into the system so itcan counteract to the dissipation in the wake region. Numerical simulations andexperiments show that spanwise vortex weakening is coupled with the stream-wise vorticies along the backlight edges in the separated flow for an Ahmed body[28].

Figure 2.12: Ahmed body with applied Active Control

In [32] a 2D and 3D Ahmed body have been tested and investigated tofind the best position in terms of suction and blowing on Figure 2.12. The mainvortex structure were captured which determine the generated drag. The finalconclusion have three option. One of them is propose a transverse suction of thetop of slant edge or a transverse blowing in the bottom edge of slant, while the lastoption is to apply blowing on both sides of the slant to weaken the longitudinalvortices.

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Literature Review

2.5 Related Aeordynamics

In the previous chapters the fundamental physics, aerodynamics princi-ples and simple bluff body problem approach is presented in the topic of basicvehicle aerodynamics. The investigation and analysis studies of these simplifiedcases experimentally and numerically in this field is giving a good initial guessand understanding what happens around a vehicle. External automotive aero-dynamics can be divided into three type of set. The most common passengercars, the high performance race cars and the heavy vehicles including trucks andbuses. From these three group, the most relevant subsets for the thesis work is thesquare back vehicle terminology. Thus the aerodynamics of vans, pickups andSUV-s from the passenger cars, and the trucks and buses from heavy vehicles.The relationship between the simplified models and real cases can be seen in theLittlewood [5] experiment, which is the basis of the thesis.

Figure 2.13: Full Scale tested SUV horizontal slat configuration [5]

2.5.1 SUV

SUV is a marketing abbreviation of the Sport Utility Vehicle. These carsare generally equipped with four-wheel drive for off-road (4x4), with a largepassenger space capability and possible towing abilities [33]. It is a combinationof on and off-road vehicles. Original purpose of SUV’s were low speed off-roadapplication, where the aerodynamic effect are negligible, but the market evolution,increased usage on road and concern of road vehicles environmental impact leadsto the need of aerodynamic drag reduction. Due to the large frontal area, flat rear,tendency to four parallel side and sharp edges, the original SUV concept is largelyaffected by aerodynamic forces. A consequence of the previously listed designaspects causes a separation with an unwanted flow characteristic in the base anda vortex dominated downstream wake structure. Compared to normal passengercars, where the overall lift tends to zero, SUV studies prove that at typical highwayconditions, stability and handling is affected by the lift [34].

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Literature Review

Figure 2.14: SUV Drag Coefficient Evolution [33]

On Figure 2.14 the reduction of the total drag coefficient of SUV’s collectedby Land Rover and MIRA. There are several drag reduction techniques similarto a general passenger car such as tapering, boat tailing, but with considerationof the desired space limits. Shape optimization by chamfers and roundings cancause changes in drag. Vary the windscreen angle. Lowering the whole car andbonnet affect the overall lift, thus the stability in higher speed regions won’t beunstable. The listed modifications can be seen on Figure 2.15. Base pressureincreasing by bleeding technology, and application of cavities at the rear [35].

Figure 2.15: SUV Drag Reduction Techniques, [33]

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Literature Review

2.5.2 Heavy Vehicles

Heavy vehicles are obviously aerodynamically inefficient constructionssince the main purpose is to specialize in a certain type of job eg. construction site(excavator), agricultural (harvester) and transportation. In vehicle aerodynamicspoint of view the long distance transportation consume a significant proportion offuel consumption, thus the regulation and trends lead to the necessity of reducingaerodynamic resistance [2] [36].

The basic idea of trucks and buses is to transport as many goods, passen-gers as possible in one way, thus the primary importance is to extend the usefulspace as big as possible. It leads to a sharp edged box shape configuration, witha big length over height/width ratio, which is a specific bluff body situation. Itdescribes a flow field, with separations and reattachments, unsteady wake andthe interaction between the truck-trailers also makes it more complex, while theoverall lift is totally negligible. Because of the large side areas, the crosswindstability and handling is a big issue. Since the basic design is not dealing withaerodynamics, manufacturers must modify the basic shape. Studies says that athighway conditions the 50% of the energy consumption is due the drag, thus it isessential to reduce the resistance as much as possible[12][37].

Main areas of the generated drag can be divided into four section. Thefrontal area, interaction between truck elements, underbody and the rear wake.The proportion of these parts depends on the initial flow conditions (cross wind)[36].For buses this distribution suites as well except the interaction part.

Figure 2.16: Heavy Vehicle Drag Distribution,[29]

Despite the bus-truck flow similarities the drag reduction methodologyneeds a different approach. For buses it’s more likely to apply the general pas-senger car techniques. Rounding the sharp edges, simple boat tailing, add-ondevices, frontal inclination angle, underbody smoothening etc.

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Figure 2.17: Truck Boat Tailing Examples,[29]

Truck aerodynamic should handle the interaction-interference betweenbody parts with active and passive flow control devices [12] [37]. Some passivemethods as the upper surface curvature shape optimization (depends on thecountry, UK) ][38], different cab configurations, add-on devices, applied boattailing flaps like on Figure 2.17, cover the gap between the trailer and truck,smoothened underbody [29].

The active control devices are somehow affect the flow characteristic byinducing disturbance. Rotating elements on the roof top (moving surfaces) Figure2.18, autonomous self-adjustable add-on on devices (boundary layer manipula-tion), pressure rising at the base region by bleeding etc.

Figure 2.18: Truck Rotating Element Design,[29]

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Chapter 3

Theoretical Background

The origins of the fluid dynamics are going back to the 19th century untilthe famous Reynolds experiment. Since that milestone engineers try to modelthe flows with strong mathematical and physical background knowledge. Themain objectives are to understand the flow phenomena and try to describe it withnumerical tools and theory.

3.1 Governing Equations

In order to model the flow the continuum description of fluids based onthe Conservation Laws theory or simply called it as the Navier-Stokes Equations.In this approach three main conservation equation called Continuity, Momen-tum and Energy Equation is defined which represent the fluid motion. Theseexpression are having differential and integral forms too.

The following Equations (3.1),(3.2),(3.3) contain the variables of the pres-sure p, time t, density ρ, velocity vector U, viscosity τ, gravitational accelerationg and total energy E. These quantities are playing role in the fluid motion repre-sentation [39]. The differential form of the equations are the following.

• Conservation of mass, the Continuity Equation

The mass in the domain is conserved, what goes in goes out.

∂p∂t

+ ∇ · (ρU) = 0 (3.1)

20


• Conservation of momentum, the Momemtum Equation

Change of the momentum inside the volume is equal to the sum of flux ofmomentum through the surface, the change due to internal stresses and vol-umetric forces.It is in balance, like in the Newton’s Second Law phenomena.

∂pU∂t

+ ∇ · (ρU ⊗U) = ∇ · τ + ρg (3.2)

• Conservation of energy, Energy Equation

It can be described as the variation of total energy equals to the sum of theflux of total energy, work done by stresses and volumetric forces and theheat flux.

∂p∂t

+ ∇ · (ρU) = 0 (3.3)

In such a case as this vehicle aerodynamics problem the flow can beconsidered as incompressible flow. The acting velocities are low so as the Machnumber which leads to an assumption based on the negligible density changes.The density is assumed as constant, thus the continuity equation changes to thefollowing expression (3.4).

∇ ·U = 0 (3.4)

If this expression is applied to the momentum equation, there exist anequation between the velocity and pressure field, which can be solved with in-compressible specified numerical solvers.

These equations include partial derivative terms of the flow variables suchas the velocity and intensive quantities like pressure and density for compressiblecases. In the 20th century domain discretization methods have been developed toapply numerical schemes on fluid flow problems. One of the most proven methodis the Finite Volume Method which is used for incompressible cases very often.This approach uses control volumes all along the flow domain. To perform thenumerical study, it has to be made in all case, with a sufficiently refined controlvolume grid.

21


3.2 Numerical Models

There exists several numerical approach to solve the decoupling problemof the pressure and velocity. Most of the cases the well known Pressure Correctionmethods are used, or the solver based on the Vorticity Stream function where thevelocity is changed up with vorticity. Methodology which induces terms in orderto manipulate the solver are the Artificial Compressibility schemes. With thesea hyperbolic and hyperbolic-parabolic equations are resultant, which allows touse compressible numerical solvers into incompressible cases. So as this is alimitation to the method as well. Pressure projections methods are having twotype of approach with exact or approximate scheme [39].

Figure 3.1: SIMPLE Method Flowchart,[39]

22


The SIMPLE algorithm family is a Pressure Correction method which hasbeen widely used for low Mach number problems within the CFD community.It is a computationally fast scheme which produce acceptable range of accuracyin a short term. Its an iterative method with applied guess pressure field at thefirst step, which is used to solve the momentum equation. From the continuityequation the pressure correction is calculated. Then update with corrections tothe velocity and pressure field. This cycle goes until the convergence criteria isfulfilled.

Initial step is to apply boundary conditions. The original guess for pres-sure and velocity field is defined this way. In order to avoid instability in thenumerics, staggered grid is applied (see on Figure 3.2), which is used to store thescalar variables at node points, while velocities are on the faces.

Figure 3.2: Staggered Grid,[39]

In this class of solver between SIMPLE, SIMPLER, SIMPLEC methods,smaller changes are obtained to make it more stable and reliable. In the SIM-PLER case the continuity equation is derived to solve directly the pressure andnot the pressure correction equation, but the velocity field is still depending onthe correction. The SIMPLEC is the hybrid method of the previous two algorithmwith solving a changed momentum equation[39]. It has to be mentioned that forthis solver in FLUENT the applicable discretization scheme are different Upwindand MUSCLE method. To perform efficient simulations the Second Order Up-wind were used. This method is a solution for the Central Differencing Schemeproblem to outcome the flow direction determination. The scheme is conserva-tive, bounded and transportive, while the accuracy depends on the Taylor seriestruncation error [39].

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3.3 Turbulence Modelling

Turbulence is the first thing what comes to mind if flow physics arementioned. It is an important characteristic of the fluid motion. Turbulent flowsare governing our life from the bathroom whirls to the chimney plums. It can beobserved everywhere. From pipe flows to bluff body cases turbulence arise so itis essential to model it properly.

The classical modelling and phenomena is that the flow is characterizedby the balance of the inertial forces and viscous dissipation[39]. Turbulence arisesdue to instabilities in the flow caused by low velocity profiles or perturbations.Initial perturbation and vortex stretching with instability results into turbulence[40]. This fluid motion is highly unstable, three dimensional in space and causesa fluctuating velocity and pressure field.

For bluff body flows, two type of instabilities are connected. The Kelvin-Helmholtz appears at shear layers and the Tollmien-Schlichting which occur nearthe wall inside the boundary layer and increase the transition from laminar flow.

In the turbulent flow, the evolving eddies can be classified by their size. Ifthe whirl is bigger, it contains more energy, while the smaller ones are dissipating.This theory is best represented by the turbulence energy spectrum on Figure 3.3.Region classification is the following.

• Energy containing scales, Intergal scale

These whirls are containing the biggest portion of energy.

• Sub-Inertial range

The flow is called universal, neutral region between small and large scales.

• Dissipative scales, Kolmogorov scale

Defines the smallest eddy which is damping out by the viscous forces intoheat.

Based on the turbulence theory methodologies like LES, DNS, RANS andURANS are developed but this thesis work deals only with the RANS ReynoldsAveraged Navier Stokes models. This time averaged methods’s unique idea is todivide the variables into mean and fluctuation components Eq. 3.5, where φ canbe any flow variables like pressure or different velocity components.

φ = φ + φ′ (3.5)

24


Figure 3.3: Turbulent Energy SpectrumThe procedure is that the divided variables are applied on the Navier

Stokes Equations, then it is averaged it time. The resultant equations are notclosed because of more unknowns are presented in the equations. In case ofincompressible flows its 4 to 10 ratio. Modelling of the Reynolds Stress tensor is abasic assumptions. The model key feature is to apply the Boussinesq assumptionwhat allows to model turbulence by the eddy viscosity µt and the main straintensor S product.

The RANS modelling family has different approaches usually categorizedby its main features, so the one equation models like Spalart-Allmaras, or the 2equation k-ε and k-ω. In the thesis work these two type of turbulence modelshave been applied on the simulation cases, because of the reliable convergenceand relatively fast work. Based on the previous works on this Windsor bodymodelling the two best perfomer sub models are used within the k-ε and k-ωtubulence family.

3.3.1 k-ε Realizable

This method performs well in the separation region and far from the wallbounded regions, near the wall it uses the Wall Function Approach. The appliedk-ε Realizable model is the most stable from the optional types because it usesmathematical constrains on the Reynolds stresses and transport equations.

Governing equations of the model are solving the equation for kineticenergy k and the turbulent dissipation rate ε. These are containing the variationof the variables with diferrent constants and terms (3.6), (3.7). The turbulentviscosity used in the model is the Equation (3.8)

∂∂t

(ρk

)+∂∂xi

(ρkui

)=

∂∂x j

[(µ +

µt

σk

)∂k∂x j

]+ Gk + Gb − ρε − YM + Sk (3.6)

∂∂t

(ρε

)+∂∂xi

(ρεui

)=

∂∂x j

[(µ +

µt

σε

)∂ε∂x j

]+ ρC1Sε − ρC2

ε2

k +√νε

+ C1εεk

C3εGb + Sε

(3.7)

µt = ρCµk2

ε(3.8)

25


3.3.2 k-ω SST

The k-ω model has been developed by Kolmogorov [40] and extendedfurther into the SST model which is a combination of k-ε and k-ω [41]. It appliesthe good features of both models together. While the k-ω performs better nearthe wall, and in the boundary layer where the viscosity plays the dominant role,the k-ε is better on the free stream and separated flows. It has a built in filter todecide which 2 equation model has to be used in order to calculate the solutionto obtain convergence.

As it has been mentioned the k-ε approach is using wall function whilethe k-ω needs refined boundary layer. This phenomena is called the near wallapproach. The models separately has different grid refinement in order to performefficiently. The k-ε model doesn’t need too refined mesh only. It works fine fromthe y+ 30 region, but some added settings and near wall approach can be reducethis number until y+ 10, so the viscosity region is not resolved. While k-ω needs arefined mesh for y+ under 1, to adapt the boundary layer and simulate efficiently.Models are valid to perform on viscous region.

Figure 3.4: Wall Treatment of Turbulence Models,[42]

Governing equations of the model are solving the equation for kineticenergy k and the specific dissipation rateω (3.9), (3.10), while the tubulent viscosityis the following Equation (3.8). In these SST model expressions the S values referto the strain rate, and the α is the damping.

∂∂t

(ρk

)+∂∂xi

(ρkui

)=

∂∂x j

(Γk +

∂k

∂x j

)− Gk − Yk + Sk (3.9)

∂∂t

(ρω

)+∂∂xi

(ρωui

)=

∂∂x j

(Γω +

∂ω∂x j

)− Gω − Yω + Sω (3.10)

µt =ρkω

1

max[

1α ,]

SF2α1ω

(3.11)

26

Chapter 4

Methodology

In this section the applied methodology and problem formulation is de-scribed in details from the geometrical outline to the investigated simulations.The origin of the study is based on an experimental measurement on a Windsormodel carried out by Littlewood [5]. This experiment is the basis of the numericalsimulation for the baseline configuration.

4.1 Geometry

The measurements have been carried out on a 1/4 quarter scale Windsormodel in the wind tunnel. The lack of geometry information of the originalsimplified body used by Littlewood [5] lead to the need of creating a new one. Ithas been tested by a Phd student Anna Perry at Loughborough University. Thenew configuration has been generated in a CAD model file too, so the simplifiedcar layout could be performed with every detail. The proper cleaned geometry isthe first step for a numerical flow simulations.

Based on the technical drawings obtained by the previous year students[7, 6], the body has been built up in the SolidEdge modelling software. The aimwas to manipulate the geometry outline easier for the applied rear face slat con-figurations. In order to save computational time in the current CFD simulationsonly half car models have been made from the clean baseline configuration to thedifferent vertical element slat position arrangements.

The model is a square back Windsor body layout. It doesn’t have anywheels, so in order to perform the experiment four smaller cylindrical supportingelements are placed on the bottom Figure 4.1. A NACA0021 type wing is addedwhich serves as a cover for pressure tappings cabling for the measurement. Theairfoil trailing edge has been manipulated to generate a better grid. It had a verysmall edge which caused skewed cells close to symmetry plane proximity. Lastsection has been cut down for a 5 [mm] width at the end of the wing.

27

Methodology

Figure 4.1: Baseline GeometryOne of the main objective is to test the additional roughness elements on

the rear surface of the body. The previous two study [6, 7] and the experiment [5] isdealing with horizontally attached slats on the bottom part of the Windsor’s back.In this thesis work, these elements are added vertically along the surface. Theoriginal configurations has 3 or 4 piece of slats with a uniform 35 [mm] distancebetween each other. This was the assumption for the investigated cases too. Thedimensions of the clean body are the following Table 4.1.

Length of the car [L] 1.045 [m]

Height of the car [H] 0.29 [m]

Width of the car [W] 0.39 [m]

Slat dimensions 8x1 [mm]

Table 4.1: Windsor Model Geometry Dimensions

Beside the clean configuration, which have been used in the roughnessstudy, there are 4 other arrangement. Depending on the width of the total car,a uniform distance has been set between the slats. The full body width havebeen divided by the distance of 35 [mm] with a consideration of 35 [mm] offsetfrom the side faces of the car gives a 10 element case. So the half model contains5 slats on the back surface. Furthermore this 5 slats on a half model has beenmade simplified coarser to only 3 element options. These two previous modelhas the slat elements all along the rear back surface from bottom to top. Two extraconfiguration are obtained by shortening these slats. The shorter slat geometriesstarts from bottom until the height where the horizontal element cases werecarried out by Littlewood and former Master Students. The generated cases arethe following and the layouts are on the next page Figure 4.2, 4.3,4.4, 4.5

• C0 - Baseline configuration, clean from slats

• C1 - Full 3 Slats

• C2 - Short 3 Slats

• C3 - Full 5 Slats

• C4 - Short 5 Slats

28

Methodology

Figure 4.2: Configuration C1 with 3 total slats

Figure 4.3: Configuration C2 with 3 short slats

Figure 4.4: Configuration C3 with 5 total slats

Figure 4.5: Configuration C4 with 5 short slats

29

Methodology

4.2 Grid Generation

The flow domain dimensions are related to the geometry specification. Ithas to be mentioned that the size is based on previous simulations in the topic[6, 7] and relate to the wind tunnel measurement section dimensions. The crosssection of the domain for a half car model is 1.32[m] x 0.96 [m]. Meanwhile inlongitudinal direction in front of the Windsor is assumed 4L body length from theInlet and 7L after to have enough space for the wake evolution Figure 4.6.

Figure 4.6: Computational Domain

After the CAD model generation, the next step in the CFD simulation hi-erarchy is the mesh generation. For this current project the Ansys ICEM programhas been used. The generated mesh can hardly effect the numerical study. If thequality of the grid is not sufficient it loses the accuracy of the simulation, further-more it can slow it down as well. In order to analyse and validate the obtainedresults mesh dependence study has to be made. So all type of geometry has to bemodelled in several mesh refinement. Since the C0 baseline configuration has tocarry out the roughness study it has more grids to check the independence.

One of the important factors which determines the necessary refinementof the mesh is the wall y+ value (see at Chapter 3.3). Beside this condition othervariables such as Cell Quality, Skewness, Aspect Ratio are the main characteristicvariables which determine the goodness of the mesh. The governing numbersfor these cases are 1 million for Coarse mesh, 2-3 millions on the Medium and4-5 millions for the most refined Fine grids. Total cell numbers are varying onvertical element arrangements since the slat surface sizes are different and thesurface mesh, thus it has effect on the total cell number size.

30

Methodology

Despite the simplified geometry, it has curvatures and elements like thesupporting posts which makes complex tasks for the structured approach. E.g.the C-Grid on the wing section and O-Grid on the supports, and the proper prismlayer needs creates too many cells in the unimportant regions.

A roughness study has been tested on the clean body with structured meshin 2D. The aim was to find basic assumptions for 3D cases, such as the boundarylayer thickness around the body. Based on these assumptions an unstructuredmodel has been tested with varying prism layer height all along, but the approachhas failed in the grid generator, only Coarse mesh could have been generated.After this experience only constant height prism layer cases have been made dueto this generation issue. To determine the boundary layer thickness height, theflat plate formula has been used. Boundary layer thickness is determined by theacting Reynolds number and the characteristic length of the obstacle which givesback the developed height around the body by these equations (4.1). It givesaround 20[mm], which is also obtained from the 2D approach on the roof, whileit has different results on the underbody section.

δlam = 4.91 · x ·1√

Reand δturb = 3.82 · x ·

1Re1/5 (4.1)

In the simulation section the boundary layer thickness has been checkedby different segments on the symmetry plane at the roof. The methodology ofthe boundary layer analysis is described in a later section within the RoughnessStudy evaluation. The predefined assumptions were right, in the analysis sectionthe actual distributions shows similar values.

The determined boundary thickness is important to model separationaccurately. In the unstructured mesh approach the prism layer is applied forrefine the boundary section. A rule of thumb is that within this layer, at least 20cells should have been generated.

Figure 4.7: Meshing problem at the support

31

Methodology

The mesh has some parts which can lower the quality of the domain.Especially the prism layer on the slats and the support elements. Since in thesepositions the surfaces are perpendicular to each other and the surface mesh is notsufficiently fine to handle the growth of the two side prism layers. On the Figure4.7 the prism layer is 10[mm] height, but the bad quality elements are producedat the back of the wing support element and underbody connection face. Sameproblem arise at the back, if the slats are added to the surface Figure 4.8. Thecalculated height was 20 [mm] but for this prism the minimum quality could notbeen improved over 0.1-0.15 so the full height has been reduced to 10 [mm], wherethe minimum an general quality was higher.

Figure 4.8: Meshing problem at the slats

In the specification of the mesh setup, surfaces were treated differentlydepending on the position (support, Windsor body, rear ). Density regions havebeen applied to maintain the size of the surface mesh in the volume near mainbody edges. The front edges, the windshield-roof connection edge and the rearback lines have this refinement option. It has taken into account that the separationbubble could be an extended region behind the Windsor model, so at least 1 bodylength density region is defined behind the car. Beside the listed positions anotherregion is defined under the body related to the size of the surface mesh. Summaryof the applied density regions can be seen on Figure 4.9.

Figure 4.9: Mesh Densities Positions

32

Methodology

The mesh generation process was maintained the same for every case.First step is the surface mesh generation with the Octree Robust technique onPatch Dependent option, while the global size has been set to 150 [mm]. Then thefirst volume mesh is generated with Octree again. Afterwards the volume meshis deleted and the method is changed to Quick Delauney scheme with the prismlayers. This approach has a better smooth transition if densities are used alongthe domain, it avoids big neighbouring cell differences. For example two mediumand fine mesh can be seen in comparison in Figure 4.10.

The applied mesh definition is in the following Table 4.2 The are densitiesrelated to the edges, they have the same size as the Windsor body surface whilethe ground has always a 50[mm] maximum cell size

Coarse Medium Fine Finest

Wall y+ 30 10 5 1

First Cell Height 0,2785 [mm] 0,095 [mm] 0,0475 [mm] 0,0095 [mm]

Number of Layers 20 24 28 36

Windsor Body 18 14 10 8

Supports 3 3 2 2

Wake Density 35 30 25 15

Rear Surface 14 10 6

Slats 10 8 4

Table 4.2: Applied Mesh Parameters

Figure 4.10: Applied Meshes for C0 baseline configuration

33

Methodology

4.3 Solver Setup

If the generated grid is acceptable the next step is the settings of theboundary conditions. All the domain and body surface has to be denoted toone of the conditions type. Some assumptions as the symmetry plane alreadydefines the needed condition. In the applied Ansys FLUENT software package,the following setup were used.

• Domain Inlet - Velocity Inlet

• Domain Ground - Wall, No-Slip

• Domain Side - Symmetry

• Domain Top - Symmetry

• Domain End - Outflow

• Domain Symmetry - Symmetry

• Windsor Body - Wall, No-Slip

• Windsor Supports - Wall, No-Slip

The aim is to reproduce the experiment so the conditions must fulfil that.That is why the ground and body surfaces are defined as a Wall condition withno-slip setting. The domain end section (outlet) for such bluff body incompress-ible flow the Outflow condition is suitable. Symmetry boundary is applied onthe Domain symmetry, top and side face to model the wind tunnel. The mostimportant surface is the inlet section with Velocity Inlet boundary. Later on at theGround Study section the domain inlet and domain ground will have differentboundaries.

Different turbulence models are tested in the analysis and the availableinlet profiles are varying depending on the method 4.12. The common velocityprofile, kinetic energy and turbulence intensity distribution can be seen on theFigures 4.11 and 4.13. In terms of the velocity there exist an inlet boundary layerand around the height of 70 [mm] the velocity reaches the free stream value. The40 [m/s] determines the Reynolds number what is 2.784 million for this case, sothe turbulent flow is expected in the domain.

34

Methodology

Figure 4.11: Velocity and Kinetic Energy Profiles

In terms of the velocity there exist a boundary layer which reaches thefree stream velocity 40 [m/s] at the height around 70 [mm] from the ground. Thisvelocity determines the Reynolds number what is around 2.784 million if theobstacle characteristic length is the 1.045 [m], so a turbulent flow is expected.

Figure 4.12: Turbulence dissipation ε and ω Profiles

Turbulent Intensity is varying all along the total height Fig. 4.13whichdissipates in the front domain during the simulation. If different turbulencemodels are applied each one of them needs their own boundary profile. Betweenthe k-ε and k-ω one can be calculated from the other if the hydarulic diameter andsome constants are obtained for the case.

Figure 4.13: Inlet Turbulence Intensity

35

Methodology

Other settings are listed to reproduce the simulation.

• Solver - Pressure Based, Steady, 3D

• Material - FLUENT Database, air, ideal-gas

• Scheme - SIMPLE

• Pressure - Standard

• Accuracy - Second Order Upwind

36

Methodology

4.4 Simulation Cases

In the analysis chapters three types of study are presented. The Rough-ness Study which investigated the C0 Baseline Configuration and the applicableFLUENT roughness determination options. The second part is the different slatconfiguration cases, to analyse the drag, lift and wake structure behind the ge-ometry layouts. Finally a moving ground case study, what is a widely appliedproblem formulation to test vehicle aerodynamic tasks.

In terms of the Roughness Study the Roughness Constant and RoughnessHeight variation have been tested. The first cell height has to be bigger then theapplied Roughness Height value according to the FLUENT Manual [42]. Onlythe Coarse and Medium mesh is under investigation since the y+ values are verysmall for finer meshes to test a realistic roughness height. The 0,2 [mm] and 0,075[mm] options have been tested. These values were applied on the ROOF and therear BACK surface to analyse the difference. This approach is a good baseline forstudies on real cars how to model the manufacturing small groves and cavities onthe top of a car.

All the slat cases have been carried out with the Roughness Constant of0.5 , what is the default in FLUENT without any Roughness Height. This appliesfor the moving ground cases as well. In the moving Ground Study, the ground issetted to 40 [m/s] similarly to the free stream velocity. The Velocity Inlet boundarycondition is changed [6] to constant 40 [m/s] initial velocity with the TurbulenceIntensity of 1 % and applied hydraulic diameter of 0,7822 [m] , on Table 4.3

Turbulence Intensity [%] 1

Hydarulic Diameter [m] 0,7288

Table 4.3: Ground Study Inlet Conditions

All the simulation what have been done on the Baseline configuration C0in order to investigate the Roughness on the body surfaces are in the Table 4.4.The values R0, R50 and R100 referes to the applied Roughness Constant whatare 0, 0.5 and 1. The second notations H0, H10, H20 are the Roughness Heightconstants where H10 are the cases belongs to the 0.075 [mm], and H20 to the 0.2[mm] option. The ROOF caption indicates that the roughness is applied only onthe Roof surface, while the BACK case is when both the Roof surface and Backsurface applies the current constant. The SST is the turbulence model of k-ω andKEPS refer to the k-ε Realizable model.

37

Methodology

Coarse Medium Fine Finest

R0 HO SST SST SST SST

R50 H0 SST, KEPS SST, KEPS SST, KEPS SST, KEPS

R100 H0 SST SST SST SST

R50 H10 ROOF SST, KEPS SST, KEPS

R50 H10 BACK SST, KEPS SST, KEPS

R50 H20 ROOF SST, KEPS SST, KEPS

R50 H20 BACK SST, KEPS SST, KEPS

R100 H10 ROOF SST

R100 H10 BACK SST

R100 H20 ROOF SST

R100 H20 BACK SST

Table 4.4: Baseline Configuration C0 All cases

After introducing the C0 cases, the Slat configuration comparison hasto be made. These were tested on the original setup and with moving groundboundary condition only with the k-ω SST turbulence model with RoughnessConstant of 0.5 (R50)and Roughness Height of 0 (H0). As it was mentioned beforeC1 is the case with 3 piece of full length slat, C2 is also with 3 but short layout.The C3 is full length with 5 elements at the back and C4 is with 5 but shorter case.

Coarse Medium Fine

C1 SST SST SST, GROUND




Table 4.5: All Slat configuration cases

38

Chapter 5

Results and Discussion I.

All the cases have been performed within the Ansys FLUENT softwarepackage with SIMPLE method solver. The numerical solver is an iterative methodso the residual values between two steps can be set as the convergence criteria.Initially it was 10E-5, but not all the cases have reached this criteria. Mostly thek-ε models, because in some sections of the body, the local y+ value is too small.If the convergence reaches this 10E-5 residual value the drag convergence havebeen checked. Afterwise the monitored drag and lift coefficients were denoted asthe convergence criterion. Generally the values were oscillating on lower digits.The simulations have been stopped at the mean value of the oscillating variables.

CF,corrected =CF,measured

(1 + 2E)(5.1)

For experimental validation the results from Anna Perry’s work havebeen applied. The obtained comparison drag and lift coefficient data is correctedthe same way as in the original approach [5] depending on the wind tunnelcorrection (5.1).The measurements results by Perry is focused only on the baselineC0 configuration. It has been measured with a 40 [m/s] velocity inlet and severaltimes it has been tested. The drag and lift coefficient is corrected by the Equation(5.1) and presented in Table 5.1

Cd Cl

Max 0.273 -0.0625

Min 0.2699 -0.0652

Table 5.1: Experimental Drag and Lift Coefficients

39


5.1 Roughness Study

In the Chapter 4.4 the provided simulation cases are introduced. Forfurther understanding the applied Rouhgness Constant and Roughness Height isdescribed in more details. The resultant cases are still comparable to the experi-mental results since the previous studies were using only smooth, non slip wallsin CFD. The applied roughness on the CFD model could have represent the realflow more accurate then with the smooth wall.

Fluid flows over rough surfaces where the turbulence is determined bythat roughness. To prove this phenomena examples like atmospheric flows onthe terrain or a well known sport case the golf ball flying can be mentioned[42].

Experiments shows that for rough pipe flows the near wall mean velocitymeasurements describe a semi logarithmic scale. This observation indicates tochange the Law of the Wall due to the roughness. In the following equations themain variables are the B additive constant in the loq-Law and fr (5.3) which is aroughness function what defines the shift of the intercept because of the roughnesseffect[42].

upu∗

τω/ρ=

1k

ln(Eρu∗yp

µ

)− ∆B (5.2)

u∗ = C1/4µ k1/2 and ∆B =

1κ

ln f r and K∗s = Ksρu∗

µ(5.3)

Generally ∆B is determined by the type and size of roughness. It iscorrelated to the non dimensional roughness height K∗s what can be expressed bythe physical roughness height value Ks in the Equation (5.3).

• Hydrodynamically smoothK∗s ≤ 2.25

• Transitional region2.25 < K∗s ≤ 90

• Fully rough region90 < K∗s

40


Figure 5.1: Wall Roughness Modelling

The three regimes which is introduced in FLUENT has been proposed byBradshaw [43] based on Nikuradse’s results. For the hydrodynamically smoothregion the ∆B is zero, while in the other two case it is a complex expression wherethe Roughness Constant plays an important role.

In the FLUENT wall boundary tab, there is the access to the RoughnessHeight Ks and Roughness Constant Cs values. When the Ks is zero, it means a totalsmooth surface[42]. If we increase this variable it will affect the calculations by theroughness’s impact in the numerical simulation. The default Cs of 0.5 [-] reproducethe Nikuradse’s[43] resistance for pipes with the k-ε model. Furthermore thisapproach has an assumptions that the applied Roughness Height must be smallerthen the first cell height near the wall. This means in order to analyse thisroughness effect the evaluated cases should be considered depending on the firstadjacent cell.

The applied height values are corresponding to the y+30 and y+10 cases.For the fine grids, the applicable roughness height is less then 0.001[mm] whichis smaller then the usually applied sand grain cases 5.1 correspond to D50 so theheight has been leveled up. Until a safe 0.075 [mm] and 0.2 [mm] value. So allthe roughness cases can be applied on the Coarse mesh and the smaller one onthe medium as well.

A short reminder what type of simulations are obtained. Dependingon the Roughness Constant the 0, 0.5 and 1 cases have been simulated on a 0Roughness Height smooth defined wall on all the meshes.

• Depending on the Roughness Constant the 0, 0.5 and 1 cases have beensimulated on a 0 Roughness Height smooth defined wall on all the mesheson the SST and k-ε turbulence model

• Apply Roughness Height on the Roof with both turbulence model anddifferent Roughness Constant

• Apply Roughness Height on the Roof and the Back surface

41


5.1.1 Grid Convergence

Grid convergence study has been made to verify the CFD model andprove the mesh independence. 3 different Roughness Constant cases has beensimulated from Coarse to Finest mesh. With the Rougness Constant of Cs=0.5 bothturbulence model were evaluated. The results of these simulations are presentedin the following sub chapters.

Drag and Lift

First step in the analysis is to present the acting aerodynamic force evo-lution for both drag and lift. In Chapter 2.2 several paragraphs contains thestatement that the bluff body flows are governed by the pressure forces, thusseparation and the turbulent wake structures are characterizing these flows. Thisstatement is true for such flows and later on it is proven in this project as well.

As the new experimental measurements and their drag coefficients arepresented on the Table 5.1, these were used as references for drag and lift coef-ficient convergence charts. The R50 H0 and R50 H0 KEPS cases are presented.The coefficients are calculated according to the Equations (2.1) (2.3) described inChapter 2.1. The following cases has grid convergence with abbreviation such asR0 H0, R50 H0, R50 H0 KEPS and R100H0. In order to present efficiently the dataonly the R50 H0 and R50 H0 KEPS will be presented to compare the differencebetween turbulence models.

Figure 5.2: Grid Convergence Drag Force R50

The first comparison and convergence charts are the total drag and liftforce acting on the half Windsor model. The diagrams are representing the pres-sure and viscous force relation as well. On the Figure 5.2 the proportion of theviscous and pressure forces can be observed, which is in the region of 1:4 or 1:5,so the viscous forces are getting around the 20% of the full drag. The convergence

42


Figure 5.3: Grid Convergence Lift Force R50

can be noticed too, but for better visualization later figures are more useful. TheFigure 5.2 of the lift states negative force so it is actually down force acting onthe body. At the lift force representation viscous forces are so small that it can beneglected.

The Figure 5.4 contains the two turbulence models, while the SST modelshows convergence and it is near the experimental region, the drag coefficientsare much higher for the k-ε model.The model is overestimating the acting forces.The difference is around 20% and the finest mesh is higher then all the othercases, so has to be mentioned that the actual y+ is too fine for the k-ε turbulenceapproach. Despite it is not suggested to apply in too refined grids but the solverstill converged. This overestimation can be seen on the lift evolutions as well. Thelift coefficients are almost the double of the measured cases with k-ε, plus the fineand finest grids are performing worse then the two coarser mesh on the Figure5.5 right side.

Figure 5.4: Grid Convergence Drag Coefficient R50 Turbulence

In order to see the more clear picture of the actual values, the difference isplotted on the same type of charts. Since the measurement has a maximum andminimum limit, the difference is calculated from these two numbers mean value.On the left side of the Figure 5.6 the SST model convergence can be noticed andthe finest mesh is within a few percent range, thus it is very accurate method.The k-εmodel’s over estimation was an expected phenomena, moreover the finer

43


Figure 5.5: Grid Convergence Lift Coefficient R50 Turbulence

grids are not working properly. In terms of the Lift Differences 5.7, both modelhave a significant difference compared to the measured down force.

To understand the drag mechanism, it has to be clear which parts of thecar model plays role in the force distribution. The biggest drag source is the rearsurface which is actually more then the total drag in axial direction. So all theother surfaces are balancing each other out and reduce the rear surface’s dragforce a bit. From the total drag the viscous forces are about to reach the 20 %. Liftforce points of view is different in this part the underbody is working as suctionusually 6x bigger then the final lift force, but the windshield and roof keeps thebalance with it.

Figure 5.6: Grid Convergence Drag Difference R50 Turbulence

Figure 5.7: Grid Convergence Lift Difference R50 Turbulence

Those cases R0 H0 and the R100 H0 has the same characteristics as theR50 H0 simulations. The difference occurs in the viscous forces, where a littleincrease can be observed. The actual viscous comparison is at a later sub chapterin this Roughness Study evaluation.

44


To see clearly the drag and lift evolutions the following Table 5.2 and 5.2contains the accuracy compared to the experimental results.

R50 H0 SST Coarse Medium Fine Finest

Drag Coeff. [-] 0.2805 0.2796 0.2683 0.2671

Accuracy [%] 3.33 3.00 1.16 1.60

Lift Coeff. [-] -0.0957 -0.1018 -0.1086 -0.1057

Accuracy [%] 50.21 59.74 70.50 65.82

Table 5.2: Drag and Lift Coefficients of R50 H0 SST Cases

R50 H0 KEPS Coarse Medium Fine Finest

Drag Coeff. [-] 0.2903 0.2899 0.2865 0.2908

Accuracy [%] 6.95 6.77 5.53 7.13

Lift Coeff. [-] -0.1269 -0.1236 -0.1389 -0.1329

Accuracy [%] 99.20 93.98 118.03 108.60

Table 5.3: Drag and Lift Coefficients of R50 H0 KEPS Cases

45


Pressure Coefficient

The Pressure Coefficient is a dimensionless characteristic variable whichcan represent the relative pressure field in the domain Eq.(5.4). The followingplots are representing the symmetry plane pressure coefficient distribution. Thisoutline consist of the back surface, roof, windshield, front, underbody and themain wing support element surface data.

Cp =p − p∞12ρ∞v2

∞

(5.4)

The distribution of Figure 5.9 is very similar to the following general carmodel Figure 5.8 by Hucho[2].In the front section, high pressure arise since theflow is stopped by the car then the velocity decreases and pressure increases basedon the Bernoulli Equation (5.5). Depression evolve in the front underbody sectionbecause the accelerating flow captured under the car. On the windshield closeto the roof the velocity is increasing and high value is reached at the roof edge.Along the roof the velocity damps into the free stream and pressure is normalizinguntil the back where separation occure due to the geometry.

12ρv2 + ρgH + p = const (5.5)

Figure 5.8: General Car Pressure Distribution[2]

The Figure 5.9 plot is normalized in the axial direction with the length ofthe car. The main parts can be recognized easily. On the left side at value zerothe pressure coefficient increases close to 1 which means that on the front bodysection is the place where the stagnation point lays. Underbody depression canbe observed and a secondary stagnation point on the support.

The following two pressure plots belongs to the same case with increasedzoom region on the front and back section Figure 5.10. On the left the front partcan be seen, but despite the zooming differences are small between the cases. Itcan be observe on the right plot that the finer mesh cases are working with higherpressures compared to the coarse grids but they are almost identical. So the meshindependence study can be validated.

46


Figure 5.9: Grid Convergence Pressure Coefficient Centerline R50

Figure 5.10: Grid Convergence Pressure Coefficient Centerline ZOOM R50

Skin Friction

In 2D simulations the skin friction coefficient can be used as a variablewhich allows to determine the separation and the reattachment. This dimension-less value is based on the wall shear stress Eq. (5.6).

C f =τω

12ρ∞v2

∞

(5.6)

If it changes the sign, it means separation occures and the shear layer isentrained in the flow, new sign change refers to the reattachment (only 2D). In 3Dspace this phenomena cannot be used to determine the separation because of thethree axial direction, but good assumptions can be made by analyzing it. It canbe applied only for 3D wing sections which is simplified to 2D approach. Alongthe roof is a good measure to see the boundary layer development.

47


The plot values show bigger differences, compared to the pressure dis-tribution. If can be noticed that the Coarse mesh is smaller then the other gridsalmost everywhere. It can be derived from that the actual prism layer appliedaround the body is smaller then required so the results are not accurate. Theoscillating behaviour is cased of the three dimensionality and turbulence at theroof section part of the chart.

Figure 5.11: Grid Covergence Skin Friction Coefficient R50

5.1.2 Roughness on Roof and Back

This section is comparing the applied Roughness Height cases. I havedifferentiate the cases called ROOF and BACK. In case the ROOF I refer to thesimulations where the wall boundary Roughness Height has been modified toone of the investigated value only on the roof top surface. The BACK name isreferring to those cases where the rear surface of the car has also applied withRoughness Height.

Two type of height has been investigated, the 0.075 [mm] refered as H10and 0.2 [mm] as the H20 nominated simulations. The Coarse mesh has beentested on all the listed configuration, while the Medium mesh is only appliedin the event of H10 defined height. Finer meshes cannot be tested because thewall y+ values violates to the rules of first adjacent cell height in the roughnessmodelling in FLUENT.

The comparison methodology is the same as in the Grid Convergence sec-tion. Acting aerodynamic forces, characteristic coefficients as drag, lift, pressureand skin coefficients has been evaluated.

48


Drag

Only the drag data are compared since viscous forces are negligible inthe terms of the lift force, so the change is minimal bewteen the rough andsmooth wall conditions. In these comparisons the ROOF and BACK values aredifferentiated into two and in first approach the H10 and H20 are also separated.The following list consist the content of this section on the compared cases withavailable turbulence models.

The first group of compared cases are for roughness H10 on the ROOFwith both turbulence model and the Coarse R50 H0 mesh is used as base initialdata. case. On the Figure 5.12, the increase of the total drag can be observed onthe Coarse mesh for both turbulence models. The k-ε is overestimating again, butthe Medium mesh is still smaller 5.13 and closer to the experiment.

Figure 5.12: Roughness Study Drag Coefficient R50 H10 ROOF

Figure 5.13: Roughness Study Drag Coefficient Difference R50 H10 ROOF

49


Similarly to the ROOF cases the SST model performs the same 5.14, forCoarse mesh the drag increase with roughness, and the Medium mesh is stillmore accurate. A small change can be seen on the k-εmodel where the roughnessassumption could have caused the change 5.15.

Figure 5.14: Roughness Study Drag Coefficient R50 H10 BACK

Figure 5.15: Roughness Study Drag Difference R50 H10 BACK

Based on the Equation (5.3) and the available constant density and rough-ness height, the minimal kinetic energy can be calculated to place the Law of Wallin the transitional or fully rough flow domain. With the smaller height this valueneeds a minimum kinetic energy value of 0.0003 . This is easily fulfilled so thesolver is working in the rough region over the roof.

50


The last two Figure 5.16 ,5.17 are the comparison of all the H20 caseson the coarse mesh with a reference value of the R50 H0 SST and k-ε. All thecoefficient showing increased drag as expected due to the roughness inductionproportional to the height condition. The k-ε models are still having twice as bigdifference then the SST model

Figure 5.16: Roughness Study Drag Coefficient R50 H20 ROOF and BACK

Figure 5.17: Roughness Study Drag Difference R50 H20 ROOF and BACK

To organize all the obtained drag and lift coefficient the following sum-mary Tables 5.4, 5.5, 5.6, 5.7 present the full data set on the ROOF and BACKstudy.

ROOFR50 H10

SSTR50 H10

KEPSR100 H10

SST

Coarse Medium Coarse Medium Coarse Medium

Drag Coeff. [-] 0.2821 0.2800 0.2910 0.2896 0.2817 0.2800

Accuracy [%] 3.91 3.16 7.20 6.69 3.76 3.14

Lift Coeff. [-] -0.0970 -0.1017 -0.1246 -0.1271 -0.0939 -0.09963

Accuracy [%] 52.28 59.63 95.54 99.47 47.35 56.29

Table 5.4: Drag and Lift Coefficients of ROOF H10 Cases

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BACKR50 H10

SSTR50 H10

KEPSR100 H10

SST

Coarse Medium Coarse Medium Coarse Medium

Drag Coeff. [-] 0.2823 0.2804 0.2894 0.2904 0.2824 0.2803

Accuracy [%] 3.97 3.29 6.62 6.99 4.01 3.27

Lift Coeff. [-] -0.0967 -0.1012 -0.1304 -0.1264 -0.0935 -0.1000

Accuracy [%] 51.73 58.81 104.65 98.37 46.79 56.91

Table 5.5: Drag and Lift Coefficients of BACK H10 Cases

ROOFR50 H20

SSTR50 H20

KEPSR100 H20

SST

Drag Coeff. [-] 0.2825 0.2919 0.2829

Accuracy [%] 4.05 7.53 4.20

Lift Coeff. [-] -0.0961 -0.1217 -0.0923

Accuracy [%] 50.76 90.94 44.81


BACKR50 H20

SSTR50 H20

KEPSR100 H20

SST

Drag Coeff. [-] 0.2826 0.2906 0.2832

Accuracy [%] 4.12 7.06 4.31

Lift Coeff. [-] -0.0939 -0.1287 -0.0919

Accuracy [%] 47.38 101.92 44.30


52


It belongs to the drag force investigation to check the roof surface viscousforce variation, how does it affect the full drag. The increase is proportional to theadded roughness from Figures 5.18,5.19. This additional viscous force can reachalmost 40-50% change compared to the R50 H0 reference case. The Roughnessmodel is working properly. For further investigate the concept it is advised toapply Roughness all along the body parts.

Figure 5.18: Roughness Study Viscous Forces on the roof ROOF

Figure 5.19: Roughness Study Viscous Forces on the roof BACK

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Pressure Coefficient

In terms of the pressure coefficient it is not expected to see significantdifference compared to the reference. It is observable on the Figure 5.20 as well.There is just minimal change between them.

Figure 5.20: Roughness Study Pressure Coefficients on Coarse Mesh Heights

Skin Friction

The Skin Friction represents the roughness height effect very clearly.When the shear layer reaches the roof surface with the roughness height setup.Significant change is observed for both height cases proportional to the RoughnessHeight itself.

Figure 5.21: Roughness Study Skin Friction Coefficient on Coarse Mesh Heights

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5.1.3 Boundary Layer Evolution

Generally in the incompressible bluff body flow cases the governing flowstructure is determined by the separation. If the aim is to reduce the effect of itit has to be monitored to understand and manipulate it. The prism layer criteriahas beend defined by the flat plate case 5.22. Similarly to this assumption, theboundary layer evolution is monitored on several points at the centerline of thecar, on the symmetry plane.

Figure 5.22: Boundary Layer Description

The methodology to extract data of the boundary layer is to analyse thevelocity profile near the wall. For this purpose 5 different line is applied on thesymmetry plane heading upside from the roof shown in Figure 5.23. The lines aredefined on the following axial positions. X = 4.8, 4.95, 5.05, 5.15, 5.22 [m].

Figure 5.23: Boundary Layer Monitoring

55


If the actual velocity profiles reaches the 99 % of the free stream velocity,that point can be considered as the edge of the boundary. That is the reasonof the yellow colored isosurface in the 5.23, and the growing boundary layerhas been showed with this technique. With the representation of this currentisosurface, the roof can be analysed. On the Figure 5.24, with a closer look on theend section of the roof, there exists a wavy part. This phenomena is caused bythe turbulent boundary layer. Depending on the roughness height concept, thisregion is moving forward or backward.

Figure 5.24: Boundary Layer Velocity Isosurface

Qualitatively some of the cases has been compared in plots. The process isthe same as in the drag comparisons, that the Coarse R50 H0 is the reference. Thefirst Figure is the Grid Convergence plot 5.25, then a roughness height comparisonon the R50 ROOF cases, then a k-ε analysis. In the convergence comparison Figure5.25 the fine mesh is around the mean value of the previous two, so it can bestated that the layer is stabilized. But is has to be taken account that the turbulentboundary can hardly effect these values despite it is a RANS model case.

The Roughness Height Study applied on the Roof has a quite stable out-come Figure 5.26. The clean H0 cases has the same characteristics while theapplied roughness is increase the boundary layer height at the section at 5.05 [m]

Conversely to the force comparison section the k-ε gives back almost thesame height distribution as the SST models despite the model is using differentapproach for boundary layer description Figure 5.27.

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Figure 5.25: Boundary Layer Evolution Grid Convergence R50

Figure 5.26: Boundary Layer Evolution Roughness Height ROOF

Figure 5.27: Boundary Layer Evolution KEPS

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5.1.4 Flow Features

This section contains a general analysis, a representation of the evolvedflow structure for the basic configuration. The investigated Roughness Studyhas only minor differences between each other since the only variable was thesurfaces roughness feature. Relevant comparison can be applied only on the twoturbulence model. My previous experiences are indicated this decision [4]. Thetask was to set up an Ahmed body simulation and analyse the models. Qualitativeand quantitative analysis have been made and the final conclusion was that thetwo turbulence method has different vortex structure behind the body. So themotivation for this comparison is analyse the models extensively and draw theconclusion on the two turbulence approach.

Pressure

The pressure distribution on the body seen on Figure 5.28 allows to iden-tify the separation regions along the model. In a case like this square back vehicleit is not a question, where does the flow separate. Nevertheless the distributionallows to optimize a duct or intake for different purposes on a full scale modelwith this kind of shape. Local maximums are placed on the supporting elementsboth the cylindrical and wing section, where small separations occur. The edgeof the left bottom underbody conical shape surface has also negative values, soanother separation is expected on this part.

Figure 5.28: General Pressure Coefficient Distribution

58


For further investigation the rear surface pressure distribution has beencompared all along the global legend not specific local distribution. The Figure5.29 are comparisons of the Coarse and the Fine mesh for both turbulence model.On the right side of the sub plots are the finest mesh cases, while the left is thecoarse grid results. In terms of consistency the SST models is reliable but a smallpressure region arise close to the side edge. This disturbance can be caused bythe averaging RANS model imperfection. The difference between k-ε remarkable,this issue has been mentioned earlier that the mesh is to fine for the method.

Same type of plots with the previously mentioned cases but the coarsewith coarse and fine with fine mesh to see the difference between the RANSmethods 5.30.

Figure 5.29: Pressure Coefficient Back Coarse-Fine SST (left) KEPS (right)

Figure 5.30: Pressure Coefficient Back Coarse-Coarse (left) Fine-Fine (right)

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Symmetry

The advantage of the symmetry boundary condition is that the centre lineof the model can be examined on the main flow variables. The pressure Figure 5.31and velocity Figure 5.32 are related to each other based on the Bernoulli Equation.The frontal area has a high pressure small velocity flow which develops furtheron the upstream and downstream of the body. At the sharp edge rear surfacethe main separation bubble is evolving. In the velocity contour it can be seenwhere the local velocities are decreasing until the 10% of the free stream flow. Onthe extended turbulent kinematic energy contour Figure 5.33, the slow turbulentenergy dissipation can be observed on the downstream section. It still has someeffect until the end of the domain. From the velocity and TKE contour, theassumption to create a density region in the mesh behind the Windsor model byone body length has been proven 5.32, 5.33.

Figure 5.31: General Symmetry Pressure Distribution

Figure 5.32: General Symmetry Velocity Distribution

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Figure 5.33: General Symmetry Turbulent Kinetic Energy

Wake

The two symmetry plane streamline plots on Figure 5.35 are remarkablydifferent. As it has been mentioned, former experience in the vehicle aerodynamicsimulation topic has a similar outcome. The great difference between the modelscan derived from the turbulence model features working on the viscous layer.The Wall functions are handling the flow differently.

The k-ε model has an almost symmetric vortex in the separation bubble.This can be happening only if the velocities are the same on the up and downstream. Vortex cores are close to each other and the extension of the separationzone seems smaller. This structure explains the k-ε model symmetric pressuredistribution on the back surface. The SST approach also has the two vortex config-uration but the upper whirl is pushing down the bottom one, it has more energyFigure 5.33. The experimental PIV measurements [5] are showing correspon-dence to the SST wake structure. Based on this conclusion the Vertical Slat Studyis simulated only with SST model.

Figure 5.34: General Symmetry Streamline SST (left) and KEPS (right)

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The symmetry plane vortex structure is proved again with the full wakestreamlines on Figure 5.35. The right hand side k-ε model is still represent nearlythe synchronous vortex pair with the same dimensions. Similar behaviour can beextracted from the data with an isosurface lined to pressure on Figure 5.36.

Figure 5.35: General Wake Streamline SST (left) and KEPS (right)

Figure 5.36: General Vortex Structure SST (left) and KEPS (right)

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Chapter 6

Results and Discussion II.

6.1 Vertical Element Study

The configurations has been introduced in the Chapter 4.1. A short recallto know what are the applied cases. The distance between the configuration isbased on the same dimensions as the original experiment [5] and CFD simulation[6] but vertically. The so called Configuration 0 is the baseline geometry C0, theothers differentiate by the additional elements. C1 is the case when 3 total heightslat is modelled on the half car body. C2 is the shortened variation of the previouscase, it goes up from the bottom to the height where the previous year studiesadded the last horizontal element. C3 is defined by 5 total length slat on the backsurface while the C4 is the shortened type of this configuration.

6.1.1 Drag and Lift

The experimental drag and lift coefficient is obtained from Table 5.1 andthe differences are calculated from these measurement result mean values. At thedrag difference plots these values are used as reference.

On the Figure 6.1 significant drag coefficient drop can be observed. Com-pared to the mean value these values are going under the measurement drag.On the difference plot of 6.1 right side the two closest cases are the short slatconfigurations, these values are within the 0.05 region. The long slat cases are onthe same accuracy as the C0 clean body, but the smallest overall drag coefficientsare reached by those two.

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Figure 6.1: Vertical Slats Drag

Figure 6.2: Vertical Slats Lift

All the applied model has been collected in a Table 6.1. The drag coeffi-cients are within the 5% difference for every cases, where the negative percentagemeans that the current case is lower then the reference measurement data. Liftvalues are up the very high close to 100%. Every Lift Coefficients case data isgetting lower, so the acting down force on the car is increasing further 6.2, almostdoubled force. Increasing grip is a good feature for a car characteristic but thedifferences are reaching to high values compared to the validation data, it is avery poor performance.

SLATS C0 C1 C2 C3 C4

Drag Coeff. [ - ] 0,2797 0.2626 0.2666 0.2610 0.2662

Accuracy [ %] 3.76 -4.08 -2.28 -4.85 -2.43

Lift Coeff. [ - ] -0.1018 -0.1141 -0.1206 -0.1129 -0.1249

Accuracy [ %] 61.70 80.98 91.16 79.04 97.90

Table 6.1: Vertical Slats Coefficients and Accuracy

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6.1.2 Pressure

The comparison can be started with the pressure coefficient plots alongthe centerline of the body. To avoid too many data in the visualization plots, caseshas been differentiated into C0,C1,C2 and C0,C3,C4 branches on Figure 6.3 andextended ZOOM views are applied Figure 6.4 too analyse the plots easier. Fromthe full plots it can be stated that the pressure at the front regions and generallyall around the body is slightly decreased compared to baseline. The ZOOMplots indicates an increase at the support back end and the roof and underbodyend section pressures are also smaller. To analyse the back pressure full surfaceinvestigation is needed.

Figure 6.3: Vertical Elements Pressure Coefficient along Centerline

Figure 6.4: Vertical Elements Pressure Coefficient along Centerline ZOOM

The pressure coefficient distribution on the back of the car is validatedto the experimental data. The original plot of this can be seen on the Figure6.5. Local distribution is different then the measured data. This problem arosefor previous simulations as well [6, 7]. The great difference can be caused bymeasurement errors or simply the RANS turbulence approach is not suitable torepresent the rear surface instantaneous pressure field what has been monitoredin the experimental case. This conclusion can be used to explain why the liftcoefficient is so different from the experimental results. The underbody flowpossibly has an unsteady characteristic like the separation zone at the back whichleads to this uncertainty.

65


Figure 6.5: Pressure Coefficient Comparison Experimental (left) and C0 (right)

The comparison plots have been made for all the possible configurationswhere the order of the comparison plots are for Figure 6.6 is C1, C2 and 6.7 is C3,C4. To understand the difference between each cases, it has to be stated, that ifthe contour colour is getting more redish it increases the pressure on the surface.That is why the slat configurations are having smaller drag coefficient, since theaverage pressure is greater then the baseline configuration and the main dragcomponent is the rear surface of the total body. Slight increase in pressure can bemonitored

Figure 6.6: Pressure Coefficient Comparison C0 (left) and C1 C2 (right)

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On both comparison Figures 6.6 6.7 close to the side and top edge ofthe body the pressure increased which is in connection with the separation andwake zone development by and shear layer at the edge. This indicates that theseparation bubble for vertical slat arrangements has a smaller extension. The corecentre of the C0 configuration is basically sliced up and and slightly increasedbetween two slat elements. This can be related to the small scale turbulence scalesdissipation between the roughness elements.

Figure 6.7: Pressure Coefficient Comparison C0 (left) and C3 C4 (right)

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6.1.3 Symmetry

During the roughness study presentation, different variables were shownlike pressure and velocity. For the better understanding and visualization of thecompared cases the most useful plots were the kinetic energy distribution and thestreamline plots. With the help of these contours the wake vortex structure canbe investigated on the symmetry plane seen on Figure ?? 6.9

The double vortex core structure has been checked. The position of upperand lower vortex has been compared. Kinetic energy is higher in the upper coreof the 5 slat configurations compared to the 3 slat and baseline options. Betweenthe short and total length slats the full cases shows bigger energy. In case of thestreamlines this phenomena can be observed. The short element cases are havinga more compressed lower vortex while the upper whirls have more stretcheddomain.

Figure 6.8: Vertical Elements Turbulent Kinetic Energy and Streamline C0 C1 C2

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Figure 6.9: Vertical Elements Turbulent Kinetic Energy and Streamline C0 C3 C4

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6.1.4 Wake

The analysis of the wake region is the essential part of the investigationto perform the flow structure evolution for different geometries. For better un-derstanding some analysing isosurface variables such as total pressure and the Qcriterion have been used. These variables has to be introduced to have a pictureon why is it useful to compare them.

The total pressure is the sum of the dynamic and static pressure variable.If this value is set to zero it is a good measure and estimation of the generatingwake structure expansion without. Actual vertical elements arrangements arepresented on the Figure 6.10 left side. The order of the plots from top to downis C0, C1, C2, C3, C4. Iso plots have similar layout but the cases could havebeen differentiated. At the baseline configuration a tail can be highlighted. Forthe roughness elements options the tail is only observable for the long slat cases,while the short cases are having a shorter barrel like shape. These observationshave been noticed on the other type of comparison of Q criterion isosurface.

Q criterion is a scalar used to visualize 3D flows. It is a well approvedvortex identification method. In a turbulent flow it can highlight the coherentstructure. It contains the symmetric and skew symmetric components of thevelocity gradient tensor. The Q criterion is defined as the velocity gradient tensor’ssecond invariant. This variable shows the ratio between rotation and deformation.The positive values of this scalar are representing the vortex structure.

Q =12

(u2i.i − ui. ju j.i) = −

12

ui. ju j.i =(‖Ω‖2 − ‖S‖2

)(6.1)

In the equation (6.1) the Ω is the vorticity magnitude and S represent themean strain rate [44]. Similarly to the pressure plots these Q isosurface data hasthe same conclusion that the baseline configuration has a stronger and longertail structure. The plotting isosurface was set to Q=250, which value shows thestructure without the ground turbulence small scales but visualize the actual wakevortices. The plots are in the Figure 6.10 right side for all configuration options.All the vertically mounted arrangements has a more straight conical structurecompared to the spiral tail seen on the baseline. For the total slat cases this coneis wider compared to the short simulations. Beside the

70


Figure 6.10: Vertical Elements Total Pressure (left) and Q criterion (right) From C0to C4

71


To Analyse the wake structure qualitatively certain velocity and kineticenergy profiles are extracted from behind the car. The wake is around the size ofthe half body length so the investigation lines are placed in this region. In axialdirection there have been set 6 different extraction data presented at Table 6.2. Inthe width of the body the applied planes are the symmetry plane noted as Y1 andthe side plane refer as Y2.

X105 X110 X120 X130 X140 X150

Axial Position [m] 5.25 5.35 5.45 5.55 5.65 5.75

Table 6.2: Extracted data axial position

The following pages consist the summerized plots of the extracted datafor velocity and turbulent kinetic energy. To avoid too many variable on a singleplot visualization the C0 C1 C2 and C0 C3 C4 branch plots are used. It results in4 big plots. Figures 6.11, 6.12 corresponds to the velocity comparisons for the twogroup, while Figures 6.13, 6.14 refers to turbulence comparison. The conclusionsare drawn in this page while the plots are later presented. Table 6.3 contains thegeneral layout of the plots.

X105 Y1 X105 Y2

X130 Y1 X130 Y2

X150 Y1 X150 Y2

Table 6.3: Plot explanation

The Y1/X105 section plots shows that all slat cases has lower velocityprofile for the lower vortex. The long element cases are slightly smaller whichindicates that the longer slats are capturing the vortex more. It is proven bythe fact that the C3 configuration has the smallest velocity distribution. Kineticenergies are smaller because of the proximity of the slats, what had the effect tocapture the vortex between them.

At Y2/X105 the closing of the separation bubble can be seen since its onthe body’s side plane. The velocities are bigger then the clean case which canlead to a mildly extended separation bubble. Similarly to the symmetry planesection the kinetic energies are smaller then the baseline case. This indicates thatthe separation separation bubble is smaller then C0 case.

The Y1/X130 charts represents the stronger upper vortex and lower smallone connection and the end section of the weak one. For the slat configurationsthe top of the weak vortex is on a lower vertical position. This observation hasbeen already identified by the symmetry streamline comparison on Figure 6.8,6.8. The energy distribution are very similar to all arrangements at the symmetryplane, there is no significant difference.

72


Y2/X130 plots show the squashed lower vortex has the effect only nearthe symmetry which also proven by the Q criterion Figure 6.10 Reversely tothe symmetry plane consistence the on the side plane extension the energies aresignificantly smaller and the C3 and C4 case have the lowest values. This meansthe bottom vortex is weaker and its more pressed by the upper whirl.

At the position Y1/X150 the vortex and separation zone end is approached.The decreasing bubble maximum height can be monitored to see the actual zoneclosing the region. In terms of turbulence the plots are consistent, cases are almostidentical at the symmetry plane.

Charts of Y2/150 are more interesting compared to the previous section.Plots are indicating the effect of the very stretched compressed lower vortexchanging the distribution. At the kinetic energy there is no such a characteristic,it only appeared at the velocity distribution.

The findings corresponds to other analysis parts. The investigated vari-ables and features like the streamline, pressure or isosurface comparisons. Inthis analysis the lower velocity and kinetic energy distributions are indicatingthe conclusion that the slats are capturing the double vortex between the rough-ness elements and this leads to the pressure increase along the back surface. Thisgrowth on pressure variable results into drag reduction on the surface. Previouslyit has been stated the most significant drag is coming from the back surface, so theroughness element study proves the purpose to apply them in order to decreasethe overall drag.

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Figure 6.11: Slat Velocity Comparison Y1 (left) Y1 and Y2 (right) for C0 C1 C2

74


Figure 6.12: Slat Velocity Comparison Y1 (left) Y1 and Y2 (right) for C0 C3 C4

75


Figure 6.13: Slat TKE Comparison Y1 (left) Y1 and Y2 (right) for C0 C1 C2

76


Figure 6.14: Slat TKE Comparison Y1 (left) Y1 and Y2 (right) for C0 C3 C4

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6.1.5 Moving Ground Study

The motivation to examine the moving ground condition is due to thegeneral picture of the vehicle aerodynamic problems. Moving ground conditionis closer to the real life experiences and matches the fluid dynamic phenomenonstheoretically. That is why the main wind tunnels are applying moving ground forfull scale model experiments, like the Pininfarina Wind Tunnel in Torino, Italy. Toperform the study the Table 4.3 input data were used with the 40 [m/s] movingground boundary condition. In this case the inlet condition is a constant not aprofile as it has been used for the other studies. All the vertical roughness elementarrangements are tested with the reference baseline model.

Drag and Lift

The acting aerodynamic characteristics are presented in the followingtwo Figure 6.15, 6.16. Results from the plots shows a common increase in dragcoefficient for all the cases with almost the same value. A huge decrease appearsin terms of the lift coefficient which indicates a bigger down force on the car.Because of the slight increase in drag the slat configurations are closing on theexperimental results within a few percent region.

Figure 6.15: Ground Study Drag Coefficients

78


Figure 6.16: Ground Study Lift Coefficient

In this analysis part the significant plots in the topic, streamlines andthe velocity distributions are evaluated similarly to the method in the VerticalSlat comparisons. On the Figure 6.17 all the streamlines are compared, in everyconfiguration. On the left side with the Ground Study results. The lower vortexstructure within the separation zone almost disappeared. The upper strong vortexexpending in the lower region along the back surface. The size of the wake ismaintained but the upper vortex is governing the full zone.

The plots for velocity investigation are in the Figure 6.18 and6.19, thesetwo have the same layout as in the Table 6.3. It has to be mentioned that the C0case which is used in the charts refers to the original baseline configuration, withthe velocity inlet profiles.

At the position X105 both symmetry and side plane results near theground reaches the boundary condition velocity on the ground. Beside this nearground region the velocity distribution is very similar.

This finding is true for all the other compared section as well. On the sideplots it is the difference is significant. It can be derived from that under the bodythe flow can accelerate but on the side the slow boundary is working all along theground.

79


Figure 6.17: Ground Study Streamlines Ground (left) and original (right)

80


Figure 6.18: Ground Velocity Comparison Y1 (left) Y1 and Y2 (right) for C0 C1 C2

81


Figure 6.19: Ground Velocity Comparison Y1 (left) Y1 and Y2 (right) for C0 C3 C4

82

Chapter 7

Conclusions and Recommendations

7.1 Conclusions

Initial aims and objectives were to carry out an aerodynamic study ona simplified Windsor model with the available software package based on ameasurement and previous numerical investigations in the topic. In order tosatisfy these goals an extensive CFD simulations has to be done and deepen theknowledge on the drag mechanism acting on bluff body flows. The basic theoriesand approaches that helps to improve the quality of the work are presented in theLiterature Review and Theoretical Background. After this problem initializationprocess the CFD model can be generated.

Based on experiences and previous works [7, 6] on the topic, a successfulpre-processing is assigned to the problem formulation. After generating the basicconcepts and cases the numerical studies have been settled. The main focus wason the understanding of the drag mechanism and analyse the wake structure ofthe Windsor body.

The Roughness Study was an investigation FLUENT’s capabilities on theroughness theory. Two main turbulence model k-ε Realizable, k-ω SST have beenexamined on a baseline configuration. The study consist optional roughness con-stant and roughness height settings comparisons on the Windsor body. Betweenthe turbulence models the k-ω SST model showed reasonably good performance,while the k-ε Realizable model failed to analyse the flow features. The meshindependence study is only valid for the k-ω SST model and the results provesthat as well. The simulation data have been compared to the measurement resultsdone by Perry. In terms of drag and wake structure the k-ω model is workingon an acceptable range within 5-10% accuracy on the drag coefficient and a wellresolved wake structure. The problem arise on the pressure distribution alongthe rear surface of the car and the lift coefficient values what has a range of 50%inaccuracy compared to reference experiment. The rear surface pressure distri-bution difference can be caused by the 2 equation models incapability for the case

83

or the reason is the RANS time averaged model or the errors in the measurementdata. k-ε model can not even reproduce the wake, it overestimates the drag andlift coefficient too.

Based on the conclusion that the k-ε model is inefficient for such a case,the additional vertically mounted roughness element case study has been carriedout only with Sk-ω SST model. The configurations are based on the originaldimension but the direction of the adjusting is different. Numerical results areshowing drag reduction compared to the baseline configuration. To prove thedrag drop, the wake and rear surface has been analysed. The drag reduction issourced on the base pressure increase which was proven with kinetic energy andvelocity profiles near the wake. The vortex structure change is also playing arole in the drag reduction, which has been shown in the analysis section. Despitethe promising drag evaluation the lift analysis big inaccuracy indicates the needof further investigate the model. As a final conclusion of the roughness elementstudy is that the full length slats has the lowest drag coefficients and the additionalparts are weakening the bottom vortex strength on the wake structure.

The study has been extended into a moving ground comparison, wheredrag increase and further lift decrease has been noticed. It has been examinedbecause this boundary condition is more realistic and results like that can bepotentially applied in full scale vehicle aerodynamics.

7.2 Recommendations for Future work

In this Master Thesis report two main studies have been carried out ona simplified car model. The results and previous works on this case shows thatthe additional roughness elements are capable to reduce the drag or increase thedown force. In order to further improve the Windsor Body test case I wouldsuggest the following:

• If the computational capacity is great I would suggest URANS or LES sim-ulation. Test those models because the rear surface pressure distributionis not accurate compared to the experimental data. One of the reason canbe the applied RANS time averaged model which cannot handle the flowfeatures so instantaneous approach needs to be tested.

• A suggestion mentioned by Robertson [6] and Littlewood [5] that the smoothunderbody assumptions leads to unreliable results, and cannot be appliedin the full scale models. Since this work contains a Roughness Study, I canonly encourage to work on this field and solve the problem.

• Different slat geometry configurations can be tested either T-shape or V-shape or additional cavities on the roof. These approaches can be too com-plex, but the geometry variation can bring new features and findings whatcan be applied in the full scale industry.

• New measurements could be performed based on the CFD projects. Frombacklight angle testing [7] to additional rotating wheels application thereexist numerical study.

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Appendix

A. Actual Appendix Title A

- Matter -

B. Actual Appendix Title B

- Matter -

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title of work · msc computational fluid dynamics msc thesis academic year : 2012 - 13 supervisor :...

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