Multidisciplinary Design Optimization in Aerodynamics and Aeroacoustics

Master Thesis: Analysis of the A-Pillar

Neeti Shetty (neesh311)

Link¨opingUniversity Division for Applied Thermodynamics and Fluid Mechanics Master Thesis 2018|LIU-IEI-TEK-A–18/03193-SE 2 Link¨opingUniversity Department of Management and Engineering Division of Applied Thermodynamics and Fluid Mechanics Master Thesis 2018|LIU-IEI-TEK-A–18/03193-SE

Master Thesis: Analysis of the A-Pillar

Neeti Shetty (neesh311)

Academic supervisor: Hossein Nadali Najafabadi Industrial supervisor: Jari Kesti Examiner: Roland G˚ardhagen

Link¨opingUniversity SE-581 83 Link¨oping, Sverige 013-28 10 00, www.liu.se 2 Abstract

A roof above your head, when in a car, is made possible due to the component called the A-pillar in the automotive industry. This component is not only responsible for holding up the roof but also in providing a point for the windscreen to be attached. Hence, it is deﬁnitely a part that can not be done away with and any problems aris- ing from it must be solved. The ﬂow over the A-pillar causes formation of vortices which causes an increase in the drag generated by the vehicle. These vortices also cause a high level of noise to be generated, which can cause discomfort inside the vehicle, when it is in motion. Hence, there is a need in the automotive industry to modify the A-pillar so as to reduce the generated drag and noise caused by it.

In this thesis, the flow around the A-pillar is analyzed and modifications are made accordingly to reduce the impact of the vortices formed due to it. The final resulting design of the A-pillar which has been modified from the aerodynamics and aeroacoustics point of view has been presented. This thesis project also includes the optimization of the method used to implement this. The method involved in obtaining an optimized design of the A-pillar started with the geometry cleaning phase in ANSA, followed by the meshing and simulation phase in FLUENT and finally concluding with the optimization phase in HEEDS. The process of doing this methodology has now been optimized resulting in lesser times between the models being cleaned and optimized.

The baseline model obtained from these simulations has been validated by comparing the ﬂow around the vehicle to other works and literature studies. This was done to be certain that the optimization method works to provide correct and accurate results. The optimized design, which called for an increased height was then compared against the baseline model, to understand the ﬂow behavior that lead to the reduction of the output variables.

Keywords: Aerodynamics, Aeroacoustics, A-Pillar, Optimization

Acknowledgements

A reﬂection on everyone who’s been a part of the last twenty weeks worth of work and helped make this project what it is, today.

- My teammate in this thesis project, Mattias Stridh for the endless discussions and eﬀorts spent in helping bring this thesis project to completion.

- My supervisor at CEVT, Jari Kesti for the vital support, guidance and assis- tance rendered throughout the project.

- The team of CAE-Energy at CEVT for their valuable insights and pleasant com- pany, that made working on this thesis a pleasure and delight.

- My supervisor Hossein Nadali Najafabadi and examiner Roland G˚ardhagen at LiU for their valuable inputs and advice on improving the work and report.

Thank You, Everyone.

Neeti Shetty Gothenburg, 2018

Nomenclature

Abbreviations and Acronyms

Abbreviation Meaning ASPL A-Weighted Sound Pressure Level CAA Computational Aero Acoustics CEVT China Euro Vehicle Technology CFD Computational Fluid Dynamics CFL Courant Friedrichs Lewy CPU Central Processing Unit DES Detached Eddy Simulations DDES Delayed Detached Eddy Simulations DNS Direct Numerical Simulations DoE Design of Experiments FFT Fast Fourier Transforms FWH Ffowcs William Hawkings HEEDS Hierarchical Evolutionary Engineering Design System IDDES Improved Delayed Detached Eddy Simulations LES Large Eddy Simulations LiU Link¨opingUniversity MDO Multi Disiplinary Optimization PIV Particle Image Velocimetry RANS Reynolds Averaged Navier Stokes RSO Response Surface Optimization SHERPA Systematic Hybrid Exploration that is Robust, Pro- gressive and Adaptive SPL Sound Pressure Level SRS Scale Resolving Simulations SST Shear Stress Transport URANS Unsteady Reynolds Averaged Navier Stokes

Notation

Symbol Description Unit A Frontal Area m2 c Speed of Sound [m/s] CD Drag Coeﬃcient [−] Cdes Calibration Constant [−] D Drag [N] k Turbulence Kinetic Energy m2/s2 Lt Turbulent Length Scale [m] M Mach Number [−] P Pressure [P a] Symbol Description Unit 2 Tij Lighthill Stress Tensor N/m v Velocity [m/s] Yk Dissipation term of k [−] β Volumetric Thermal Expansion K−1 δ Kronecker delta K−1 ∆ Characteristic Filter Width [−] Turbulence Dissipation Rate m2/s3 2 νt Kinematic Turbulent Viscosity m /s ω Turbulence Frequency s−1 ρ Density kg/m3 σ Stress Tensor N/m2

Subscripts and Superscripts

Character Meaning 0 Reference i, j, k Corresponding x, y and z Directions n Component Normal to the Surface Contents

1 Introduction 1 1.1 Background ...... 1 1.2 Previous Work ...... 2 1.3 Aim ...... 3 1.4 Scope and Limitations ...... 3 1.5 Problem Formulation ...... 4 1.6 Report Outline ...... 5

2 Theory 6 2.1 Flow Around Bodies ...... 6 2.1.1 Airﬂow Around a Ground Vehicle ...... 6 2.1.2 A-Pillar Vortex ...... 7 2.1.3 Drag ...... 8 2.1.4 Sound Pressure Level ...... 8 2.2 Turbulence Modeling ...... 9 2.2.1 Realizable k- (RKE) ...... 9 2.2.2 Delayed Detached Eddy Simulations (DDES) ...... 10 2.3 Computational Aeroacoustics ...... 11 2.3.1 Lighthill’s Analogy ...... 12 2.3.2 Ffows-Williams Hawkings ...... 12 2.4 Multi-Disciplinary Optimization ...... 13

3 Methodology 15 3.1 Geometry ...... 16 3.1.1 Morphing ...... 16 3.2 Mesh ...... 17 3.2.1 Aerodynamic Simulations ...... 17 3.2.2 Aeroacoustic Simulations ...... 19 3.3 Solver Settings ...... 20 3.3.1 Aerodynamic Simulations ...... 20 3.3.2 Aeroacoustic Simulations ...... 21 3.4 HEEDS Optimization ...... 22 3.5 Overall Optimization Method ...... 23

4 Results and Discussion 25 4.1 Baseline Design ...... 25 4.1.1 Pressure and Velocity Flow Field ...... 25 4.1.2 Vorticity ...... 27 4.1.3 Total Pressure on an Iso-surface of Q-Criterion ...... 28 4.2 Optimized Design ...... 29 4.2.1 Design of Experiments ...... 29 4.2.2 Parameter Optimization ...... 30 4.3 Comparison between the Results from the Baseline and Optimized Design ...... 34 4.3.1 Drag ...... 34 4.3.2 SPL ...... 35

5 Conclusion 38 5.1 Future Work ...... 39 5.2 Perspectives ...... 39

References 40

Appendix A Mesh (Aerodynamic Simulations) 42

Appendix B Frequency Range (Aeroacoustic Simulations) 43 List of Figures

1 Flow around the A-Pillar ...... 7 2 Project Workflow ...... 15 3 Vehicle geometry considered for simulations ...... 16 4 Changes due to Morphing ...... 17 5 Mesh showing refinement regions and inflations layers considered for aerodynamic simulations ...... 18 6 Mesh showing refinement regions considered for aeroacoustic simulations 19 7 Schematic of the domain and boundary conditions considered for the aerodynamic simulations ...... 21 8 Workflow of the optimization process in HEEDS ...... 22 9 Normalized contours of Pressure Coefficient along the car and Velocity Magnitude across a plane at the center of the car ...... 25 10 Velocity Pathlines along the junction between the windshield and A- Pillar ...... 26 11 Formation of vortices around the car plotted on an iso-surface of total pressure=0 ...... 27 12 Normalized Total Pressure plotted on a iso-surface of Q-criterion=1·106 s−2 ...... 28 13 Comparison of the effects the input parameters have on the outputs 29 14 Bubble Plot representation of the data in Table 2 ...... 31 15 Model of the optimized design superimposed on the baseline design (5 evaluations) ...... 33 16 Model of the optimized design superimposed on the baseline design (10 evaluations) ...... 33 17 Normalized Turbulent Viscosity Ratio plotted against sections along the Y-Z plane ...... 34 18 Normalized Total Pressure plotted on an iso-surface of Q-criterion=1·106 s−2 for the optimized design ...... 35 19 Normalized SPL contours in octave bands ...... 36 20 Wall Y+ around the car ...... 42 21 Contours of mesh cutoff frequency on a plane drawn at 700mm from the centre along Y-axis ...... 43 22 Plot of pressure monitored at four points in the wake behind the side mirror ...... 44 23 Normalized SPL contours in octave bands ...... 45 List of Tables

1 Inﬂuence of input variables on the desired output values ...... 29 2 Inﬂuence of input variables on the desired output values ...... 31 3 Normalized drag values ...... 35 4 Normalized area-weighted average SPL values on the front side window 37 5 Mesh Sensitivity Study for the baseline model (Aerodynamic Simula- tions) ...... 42 1 Introduction

This Master Thesis Project was carried out at CEVT (China-Euro Vehicle Technol- ogy AB), Gothenburg in 2018. Computational Fluid Dynamics (CFD) and Multidis- ciplinary Optimization (MDO) between aerodynamics and aeroacoustics is the focus of this thesis. It deals with the optimization of the A-pillar in terms of aerodynamics and aeroacoustics and also includes the optimization of the method in itself that is implemented to achieve this.

This section includes a basic introduction to the A-pillar and the impact the component as such has on the aerodynamic and aeroacoustic performance of the car. This lays the path for the motivation and aim behind this project followed by the implemented methodology.

1.1 Background A moving vehicle causes the displacement of the surrounding air and generates a resultant resistive force called drag which accounts for the major chunk of the total resistance to the motion of the vehicle. The study of this flow behavior falls under the study of aerodynamics while, the sound caused due to the flow behavior which includes the various mechanisms like vortex shedding and separated flow is under the domain of aeroacoustics (a combination of aerodynamics and acoustics).

A simple strip of metal whose main functionality is to hold up the roof and provide a fixing point for the windscreen has now become one of the fiercely contested bat- tlegrounds in the development of a car. The ongoing battle between aerodynamics and aeroacoustics for the enhancement of this simple structure called the A-pillar has lead to various changes being done in terms of the design as very small changes can make a huge difference. It’s not ”what you hear” but rather ”what you don’t hear” that matters the most to vehicle safety and comfort. Hence, the quest for the quiet has now become a norm in the automotive industry. So, reduction of drag (aerodynamic optimization) and reduction of wind generated noise (aeroacoustic optimization) are two of the most important factors being considered in the designs of today.

Traditionally in engineering, the projects would start with certain designs and simulation softwares helped evaluate the performance of these designs. A new design based on the simulation reports would then be evaluated again to conﬁrm the design, making it a tedious and iterative process. MDO helps reduce this process time by deﬁning desired performance as inputs and allowing better designs to be developed faster as outputs. Hence, by automating the analysis process, better ways to review the performance with substantial savings in time is achieved. All relevant disciplines can be implemented simultaneously in MDO leading to better collaboration between disciplines with the common aim of achieving better results in terms of performance.

1 Aerodynamics and Aeroacoustics are the two major disciplines involved in this thesis project. Drag and noise level values are the important parameters related to these two disciplines, where lower values are desired. The noise level is dependent on the flow and hence any change to lower the drag value from the aerodynamic discipline will have an impact on the noise level value for the aeroacoustic discipline. CFD evaluations help evaluate the performance and flow around the vehicle. Based on these simulations, the parameters that can be altered, so as to optimize the performance, are chosen (possible variations include changes to the height and thickness of the A-Pillar). Using these, as input parameters that can be varied to achieve the desired output parameters (lower drag and noise levels in this case) helps reduce the total time taken from the initial design phase to the final output phase of having a single design that caters to both aerodynamics and aeroacoustics with the desired outputs. The use of MDO methods are much more rampant in today’s times than previously as it facilitates parallel designing techniques instead of the previously done sequential ones. It also does away with the time consuming iterative process.

1.2 Previous Work

An in-depth study of the work carried out in the aerodynamic and aeroacoustic domains related to the A-Pillar has been conducted in order to obtain a better understanding of the work carried out previously. The studies that have been the most helpful in addressing various aspects related to this thesis are summed up in this section.

The flow around the A-Pillar is quite important for understanding the impact it has on the drag and noise levels generated. A simplified model which contained a sharp edge as the A-pillar was considered as the geometry and the authors of [1] used Particle Image Velocimetry (PIV) to study the flow around the A-Pillar. The authors were able to measure the propagation of the vortex along the A-Pillar by capturing the flow quantities at various sections perpendicular to the A-Pillar. The interaction of the vortex with the side wall of the vehicle was also studied and the measurements of the wall pressure fluctuations were used as inputs to calculate the vibrations on the window. These data sets were also considered as worthy of being used as references in controlling the phenomenon.

For a more detailed understanding of the external wall pressure ﬂuctuations over the front side window, the author of [2] performed Large Eddy Simulations (LES) around the model to understand the eﬀect the A-Pillar vortex has on the window. These simulations results were also validated against the experimental data that the author obtained form the aeroacoustic wind tunnel, thereby reinforcing the analysis conducted.

In order to understand the impact the windshield geometry and the A-Pillar have on the pressure levels, the author of [3] used 5 different generic models and measured the fluctuating pressure values at different yaw angles and speeds. Flow Visualization was also used to supplement the pressure data. It was observed that the maximum pressure fluctuations occurred in the region between the separated and re-attached

2 areas instead of the reattachment points that had been proposed by others who had done similar tests.

The flow over the A-Pillar region was visualized by considering two different models with different A-Pillar configurations by the authors of [4]. The existing experimental data was used to validate the results obtained from the CFD simulations, thereby reconfirming the accuracy of the simulations.

The development of a method to predict the noise levels due to the flow over a vehicle using computational aeroacoustics was emphasized by the authors of [5]. It was observed that increased noise levels were generated in the separated flow regions when compared against the attached flow regions. Inspite, of computational aeroacoustics being a relatively new domain, the developed method served the purpose of forecasting the noise levels caused on the exterior surface of a vehicle.

Several parameters of the A-Pillar can be modiﬁed in order to obtain an optimal design that reduces drag and noise levels. However, most of the studies include changes made to the angle that the A-Pillar makes with the hood and the roof. The authors of [6] visualized the ﬂow over the A-Pillar by modifying it to have an increased rounded geometry. Doing so helped the authors obtain an A-Pillar vortex which was reduced in magnitude and size, when compared against a model with a lesser rounded A-Pillar geometry.

All the above mentioned works laid the foundation of the concepts involved in carrying out this thesis project. Emphasis was also laid on the methodology of how to solve aeroacoustic simulations.

1.3 Aim The main aim of this thesis project is to develop an optimization method that would improve the performance of the A-pillar. The objectives that lead to the fulfillment of this aim include adapting and improving the existing methods in the development of an efficient method towards optimization for the MDO between aerodynamics and aeroacoustics. It also includes various design parameter changes related to the A- pillar, the impact of which would be analyzed in terms of both aerodynamics and aeroacoustics. The purpose of doing so, helps in the reduction of drag and sound pressure levels (SPL) thereby improving the fuel efficiency and comfort respectively while the optimization method saves time and effort in obtaining an optimal design solution.

1.4 Scope and Limitations The scope of this project work includes the aerodynamic and aeroacoustic simulations to be carried out on the vehicle with emphasis laid on the A-pillar. The design of the A-pillar is then optimized to lower the drag and noise levels. Apart from

3 this, the development of a method that works towards optimization of the process in itself is also considered as part of the thesis work.

The thesis project in its entirety includes analysis of the A-pillar and the side mirror distributed between 2 students across 20 weeks. However, for simplicity and due to time constraints the A-pillar and the side mirror have been worked on simultaneously and optimized without considering the eﬀects of the other. Hence, a model that would have a reduction in drag and noise due to changes made in both the A-pillar and the side mirror is considered as out of scope of this thesis project. Only two parameters (height and thickness) have been considered for modifying the A- Pillar in order to obtain an optimized design that would reduce drag and lower the noise levels, due to the longer simulation times required for the aeroacoustic calculations. Apart from this, fewer evaluations are run in the design space due to time constraints which may not necessarily lead to the best optimal design of the A-Pillar but, nevertheless, it would result in an optimized design within the limitations of the thesis work.

1.5 Problem Formulation

The geometry of the parametric model of the vehicle (master model) has been cleaned and made watertight in ANSA. For simplicity, parts such as the engine bay and underbody panels have been deleted and the basic outer body of the car has been considered for analysis.

The geometry has then been morphed using the direct morphing method in ANSA in order to obtain several iterations from the master model. These iterations are dependent on the number of parameters that would need changing in the A-pillar so as to get an optimal design in terms of aerodynamics and aeroacoustics.

The car in its entirety has been simulated for the aerodynamics run as the vehicle is not a symmetric model (different angles of the side mirror and such) and the underbody (considered flat in this project for simplicity) would affect the aerodynamics of the vehicle as a whole. The aeroacoustic model only considers half the model of the vehicle, as emphasis for this study is more on localized areas.

The surface mesh for this cleaned geometry has been generated in ANSA after which a volume mesh has been generated in FLUENT Meshing. The mesh generated for the aerodynamic simulation is different from the one that has been generated for the aeroacoustic simulation due to the different mesh requirements for the aerodynamic model when compared to the aeroacoustic one. The aeroacoustic model requires a much more refined mesh for accurately capturing the noise generated due to the flow field whereas the mesh of the aerodynamic model needn’t be as refined as the aeroacoustic one for accurate results.

These volume meshes have then been read into FLUENT after which appropri- ate settings for the two separate simulations have been alloted. On convergence of the solution the results have been analyzed in HEEDS to obtain an optimized model

4 of the A-pillar that helps in the reduction of drag and noise.

Optimization of the entire process in itself has also been carried out. This includes the feasibility of using the same model for the aerodynamic and aeroacoustic simulation and the usage of similar scripts to ease the meshing process.

1.6 Report Outline The introduction in this report is followed by the theory related to performing the aerodynamic and aeroacoustic simulations on a car. This includes the basics of the ﬂow around a vehicle, turbulence models, computational aeroacoustics and optimization. This is then followed by the methodology adopted to do this project work which contains information about the geometry, mesh, implemented boundary conditions and the numerical settings for both the aerodynamic and aeroacoustic simulations. The results and discussions based on the simulations carried out are then presented, ﬁnally leading to the conclusion and a possible list of changes that can be made incase of further work is to be done in this domain.

5 2 Theory

This section introduces an unfamiliar reader to a few essential concepts that would help understand the work carried out in this thesis project. The thesis work has been based on these concepts and span from the basic aerodynamic ones to the more complex aeroacoustic ones.

2.1 Flow Around Bodies

Performance, comfort and safety play an important role when it comes to vehicles. All these factors are dependent on the flow around it. A body in motion displaces air and experiences a resistive force called drag on itself. The generation of noise due to turbulent flow is the most common effect experienced in the field of vehicle aeroacoustics rather than those generated by the externally applied forces to the fluid.

2.1.1 Airﬂow Around a Ground Vehicle

The airflow around the vehicle leads to the development of a boundary layer very close to the vehicle surface. The thickness of the boundary layer gradually increases as the distance from the front of the vehicle increases [7]. Laminar flow of the boundary layer is observed initially which causes the airflow to slide smoothly over one another at the very front edge of the vehicle. The outermost layers of the boundary layer move faster than the ones close to the vehicle due to the skin friction drag formed between the layers of the airflow. The boundary layer thickens, as this, eventually slows down the flow which spreads outwards. This laminar boundary layer gradually transitions to turbulent not very far off from the start of the vehicle.

The energy in the turbulent boundary layer is dissipated in friction causing the velocity of the airflow to reduce, thereby increasing the pressure. This increase in the pressure causes a transfer of energy from the turbulent eddies in the boundary layer. A sudden and drastic increase in the pressure due to encountering sharp cor- ners and edges will lower the rate of mixing which would actually push forth the slower moving air causing the flow to stop following the surface of the vehicle and hence, separate [7]. The air downstream of the separation region cause an adverse pressure gradient when it starts moving towards the low pressure region which is in the direction opposite to that of the main flow. This imbalance of the forces over the body due to the separation of the flow, results in drag, making it important to have an attached flow over the surface. The separated airflow reattaches to the vehicle surface further downstream of the flow. Small regions of separation are encountered near the mirrors, windshield wipers and door handles whereas the A-Pillar, underside of the vehicles and wheel wells have larger separation regions.

6 2.1.2 A-Pillar Vortex

Quasi two-dimensional flow types also exist, inspite of the airflow around the vehicle at ground being majorly in three-dimensional form. This type of flow separates on the edge running perpendicular to the localized flow direction causing the vortices to roll up with their axis almost parallel to the separation line. The development of these vortices to continue as free trailing vortices is hindered as most of the kinetic energy of these vortices is dissipated by the turbulent mixing, making these vortices weak and untraceable. Air flowing at an angle forming a cone shaped helical vortex as shown in Figure 1 can cause separation. A-Pillars and C-Pillars mostly have these vortices. The axis of these vortices is in the direction of the freestream and since they are rich in energy, the containment of these is usually determined by the geometry of the vehicle.The A-Pillar vortex comprises of a primary vortex (the centre of which shifts away from the wall) and a secondary vortex (remains near the wall) which is smaller in dimensions and lesser in intensity than the primary one [7].

Figure 1: Flow around the A-Pillar

The conical vortex that arises from the separation of flow around the A-Pillar as shown in Figure 1 is a main source of turbulent flow. The blue arrows in Figure 1 represent the flow. The velocity of the flow around the A-Pillar is higher than the surrounding freestream velocity and the turbulent intensity is higher as well [7].The impingement of the vortex on the surface of the window causes surface pressure fluctuations on the side window. These fluctuations in the pressure on the surface of the car is a major source of the noise. The vortex generated by the A-Pillar has detrimental effects on the flow around the vehicle and is also a source of the noise. The pressure fluctuations on the front window surface are transmitted into the cabin via the glass surface of the window or through the body of the vehicle itself [3]. The sound intensity of the noise sources is proportional to the velocity.

7 This proportionality varies from the fourth power in monopole sources to the eighth power in quadrupole sources. Hence, an increase in the velocity causes an increase in the noise levels.

As the aerodynamic drag is a function of the time averaged mean pressure dis- tribution and the noise is dependent on the strength of the time dependent surface pressure ﬂuctuations which vary about a mean value, it can not be concluded that a vehicle with low aerodynamic drag would lead to a lower aerodynamic noise level.

2.1.3 Drag

The drag of a vehicle is represented as shown in Equation 1. 1 D = ρV 2AC (1) 2 D Drag is determined by the projected frontal area of the vehicle and its shape which is determined by the design requirements [7]. Drag increases with the square of the speed at which the vehicle moves, hence being of utmost importance at higher speeds. The product of the drag coeﬃcient and the frontal area is referred to as the drag area, which is a much more intuitive way of comparing the aerodynamic eﬃciency of various automobiles.

2.1.4 Sound Pressure Level

The local pressure deviation from the ambient pressure due to the acoustic wave propagation is termed as sound pressure [8]. Due to the huge range spanning between the threshold of hearing and threshold of pain, the logarithmic sound pressure level (SPL) is used in general. SPL is measured in decibels (db) and calculated using Equation 2.

P SPL = 20log rms (2) P0 where, −5 P0 is 2 · 10 Pa. This is the threshold of human hearing.

The human ear is not very sensitive at very low frequencies or too high frequencies. It responds more to frequencies between 500 Hz and 6000Hz. A standard weighting of the audible frequencies designed to reﬂect the response of the human ear to noise is the A-weighting method. A-weighting is a standard curve that closely matches the perception of the human ear by attempting to alter the sound pressure levels recorded by microphone measurements. These measurements are expressed as dbA or db (A).

Using these frequency weightings help analyze the data, but it is easier to analyze the diﬀerent sounds with the help of octave bands. The entire frequency range is divided into a set of frequencies called bands. When the highest frequency is twice

8 the lowest frequency, the frequency band is called an octave band. These bands are usually named by their center frequencies, the most common being 31.5 Hz, 63 Hz, 125 Hz, 250 Hz, 500 Hz, 1 kHz, 2 kHz, 4 kHz, 8 kHz and 16 kHeightHz.

2.2 Turbulence Modeling

It is computationally intensive to resolve and get accurate predictions of turbulence. Hence it is modeled. The flow parameters are obtained in CFD by solving the discretized form of the Navier-Stokes Equations. The equations can be solved in the steady state (time independent) as well as in the transient state (time dependent). As the Central Processing Unit (CPU) requirements by far exceed the available computing power, it is not practical to consider the usage of Direct Numer- ical Simulations (DNS) to resolve the wide range of scales in space and time. Hence, averaging procedures which, when, applied to the Navier-Stokes equations help filter out parts of the turbulent spectrum, if not all, are utilized. Time-Averaging is the most widely used one which results in the Reynolds- Averaged Navier-Stokes (RANS) equations. Doing so, allows a smooth variation of the averaged pressure and velocity fields to be obtained as the turbulent structures are eliminated from the flow. Scale Resolving Simulations (SRS) are an alternative to the RANS simulation where atleast a portion of the turbulent spectrum is resolved in the domain under consideration. Large Eddy Simulations (LES) is the most common one under the SRS models. As the SRS models require a relatively finer grid and smaller timestep, it is computationally more expensive than the RANS simulations. However, SRS simulations also consist of hybrid models which switch between RANS and LES thereby having a computational time that is more than that of the RANS simulations but less than the SRS ones. The formulation of the turbulence models used in this thesis project have been given in the following sections for completeness and are hence, not formulated in detail. The selection of the turbulence models is based on the details explained in the upcoming sections and reconfirmed by the use of it for similar works such as [5] and [9].

2.2.1 Realizable k- (RKE)

The turbulent length scale and the time scale can be determined by solving two separate transport equations in two-equation turbulence models. The transport equations for the turbulence kinetic energy (k) and its dissipation rate () forms the basis for the standard k- model [10]. The standard model holds good for fully turbulent flows as the assumptions made in the derivation of the model is that the flow is fully turbulent and the molecular viscosity effects are negligible.

The modeled equation for k is shown in Equation 3 ∂k ∂k ∂vi ∂vj ∂vi νt ∂θ ∂ νt ∂k +v ¯j = νt + + giβ − + ν + (3) ∂t ∂xj ∂xj ∂xi ∂xj σθ ∂xi ∂xj σk ∂xj

9 Similarly, the modeled equation is shown in Equation 4

2 ∂ ∂ ∂vi ∂vj ∂vi νt ∂θ ∂ νt ∂ +v ¯j = c1νt + +c1gi −c2 + ν + ∂t ∂xj k ∂xj ∂xi ∂xj k σθ ∂xi k ∂xj σ ∂xj (4)

The turbulent viscosity (νt) speciﬁed in Equation 3 and Equation 4 is computed as k2 ν = c (5) t µ

The coeﬃcients cµ, c1, c2, σk and σ have the values 0.09, 1.44, 1.92, 1 and 1.3 respectively which is expected to be universal for all types of ﬂows [11].

The shortcomings of the standard k- model, resulted in modifications being made, which lead to the development of the realizable k- model. Hence, this is an improvement over the standard, when dealing with flows concerning vortices, rotation and strong streamline curvature [10]. Certain mathematical constraints on the Reynolds stresses which are in-line with the physics behind the flows that are turbulent in nature is the reason behind the model being termed as realizable. The realizable model differs from the standard one due to the consideration of a variable Cµ in the new eddy-viscosity formula and also due to a new model equation for which is based on the dynamic equation of the mean-square vorticity fluctuation.

For the aerodynamic simulations, realizable k- turbulence model with enhanced wall treatment is considered, as it is more reliable and accurate for all external aerodynamic ﬂows at a lower computational cost.

2.2.2 Delayed Detached Eddy Simulations (DDES)

The increasing demand with respect to better accuracy at lesser simulation times has lead to the implementation of the DES which helps bridge the gap between RANS formulations and LES formulations. The DES is a hybrid of the LES and Unsteady RANS [11]. The boundary layer is treated by the RANS formulation while the Large Eddy Simulation (LES) is used to capture the outer detached eddies. The use of the unsteady RANS at the boundary layer is because the ﬂow in the boundary layer is strongly aﬀected by the unsteady LES in the outer region.

For the DES turbulence model, the dissipation term of the turbulent kinetic energy is modiﬁed from Equation 6 to that shown in Equation 7

∗ Yk = ρβ kω (6) where, ∗ β is equal to the coeﬃcient cµ which has a value of 0.09.

10 ∗ Yk = ρβ kωFDES (7) where, Lt FDES = max , 1 (8) Cdes∆max where Cdes has a value of 0.61 and is used as a calibration constant in this model and ∆max is the spacing of the grid. The turbulent length scale for this model is deﬁned as √ k L = (9) t β∗ω

The model switches between the models when

CDES∆max ≥ Lt → (RANS) (10)

CDES∆max ≤ Lt → (LES) (11) The point at which the switch between the RANS to LES model occurs causes a problem when there are cases of meshes generated carelessly and thick boundary layers due to which there is a possibility of the size of the cell in the boundary layer that is tangential to the wall being less than the boundary layer thickness[5]. This could cause the switch from RANS to LES to occur in the region where RANS should be activated. This would result in a premature separation point due to the under- prediction of turbulent viscosity and skin friction coeﬃcient. This was corrected by the implementation of a shielding function to preserve the use of RANS in the entire boundary layer. This method is referred to as the Delayed Detached Eddy Simulation (DDES) [10]. As, DDES provides access to the resolved turbulent scales at a computational cost that is less than the more accurate LES, it is shown to be a proven method for the sound generation of turbulent ﬂows. Based on the above reasons, DDES is considered for the aeroacoustic simulations.

2.3 Computational Aeroacoustics

The noise levels generated due to aerodynamic flow can be directly obtained from Direct Numerical Simulations (DNS). However, due to the high computational resources required for this (caused because of the large differences in the length scale present between the acoustic variables and the flow variables), it is not deemed to be very practical. A more practical approach involves splitting the computational domain into several different regions in order to use different equations and numerical techniques to solve the governing acoustic or flow field. This would involve a Com- putational Fluid Dynamics (CFD) tool and then an acoustic solver. The flow field is used to calculate the acoustical sources which are then handed to the acoustic solver which helps calculate the acoustic propagation. The method of considering aeroacoustic analogies has been in use for aeroacoustic problems. Lighthill’s Analogy is

11 the most common one which is then altered to make it applicable for all problems in general. The formulation of Lighthill’s analogy and FW-H in the following sections are given for completeness and hence not formulated in detail.

2.3.1 Lighthill’s Analogy

Lighthill’s acoustic analogy is obtained by rearranging the Navier Stokes equations. All the sources are present as the analogy follows the Navier-Stokes equations without any simplification. A few of these sources are then identified as laminar or turbulent noise. The source term always includes physical sources and sources that would describe the propagation through an inhomogeneous medium. This was a major breakthrough in linking the sound wave properties with the flow properties[5].

Lighthill’s equation is represented as

2 2 2 ∂ ρ 2 ∂ ρ ∂ Tij 2 − c0 2 = (12) ∂t ∂xi ∂xi∂xj where Tij is the Lighthill stress tensor and represented as

2 Tij = ρvivj + (p − ρc0)δij − τij (13)

Equation 12 describes the linear motion of the sound waves that are generated due to flow fluctuations and it is valid provided, the flow is known at every instant of time [12] It is an inhomogeneous equation and a homogeneous wave equation would govern the acoustic wave propogation outside the turbulent region.

The acoustic field and the flow field are dependent on each other in reality. However, for lower Mach flows, the interaction between the two is considered as being coupled in one way only. Hence, the acoustic field depends on the flow field, but the flow field does not depend on the acoustic field [13].

2.3.2 Ffows-Williams Hawkings

Ffows Williams-Hawkings Model (FW-H) is a widely used analogy for the calcula- tion of the sound propagation at a receiver that is in the far field [14]. The far-field sound signal that is propogated from the near-field flow data from the CFD solution is taken into consideration. The work of Lighthill was extended to rearrange the momentum and continuity equations in the form of an inhomogenous wave equation in order to compute the sound pressure at various observer locations.

Equation 14 represents the FW-H equation. Arbitrary motion of solid bodies can be taken into account in this analogy [15]. The usage of generalized functions in order to rewrite the governing equations thus making it valid for the whole domain (which includes the solid body and the ﬂuid domain) is the main idea behind this

12 analogy. The terms on the right hand side of Equation 14 represent the quadrupole, dipole and monopole terms respectively.

2 Z Z 0 1 ∂ Tij ∂ Li p (x, t) = dV − xi dS 4π ∂xi∂xj r(1 − Mr) ∂ r(1 − Mr) V te S te (14) ∂ Z Q + dS ∂t r(1 − M ) S r te where, 0 2 0 Tij = ρuiuj + p − a ρ δij − τij (15)

Li = Pij + ρui (un − vn) (16)

0 Pij = p δij − τij (17)

Q = ρ0Uini (18)

ρ ρui Ui = 1 − vi + (19) ρ0 ρ0

As the FW-H formulation is based on Farassat’s formulation, it does not take into consideration effects such as reflections and refractions. However, it can give a fairly accurate prediction of the far field noise when it is coupled with second order dis- cretization schemes (for both temporal and spatial) and a significant mesh resolution and a resulting time step [14].

2.4 Multi-Disciplinary Optimization

Designing a relatively new design to be as good as possible is the main goal of any designer. The new design should be atleast as good as the old design in some areas while better at a few other areas. The improvement of various aspects of the design such that it results in a better end product is the basis of optimization. HEEDS, which is a robust optimization software package is used for the optimization process in order to obtain optimal designs by automating the analysis process and reducing the design time.

The optimization process can be speciﬁed by a set of variables that can be changed to improve the objective. The objectives are used for an initial judgment of how good the design is. Each of the chosen variables would be constrained within certain parameters to help determine the feasibility of the design. A baseline design would be the reference model against which all the iterations would be compared [16].

13 Several combinations of the variables are chosen and analysis are to be run for each combination, after which the output is evaluated to see how good of a ﬁt it is to the objectives and constraints decided in prior. This process is continued till a more optimal design from the baseline comes up. Due to the limitations on time and resources when doing the manual search method the ﬁnal solutions more often are not the best but are just good enough. HEEDS searches in the design space for the best design by automating the evaluation process and executing it several times in order to do so. The variables are changed each time, during execution [16].

HEEDS picks values for the variables considering the speciﬁed constraints. These variables are then used to modify the model and run the simulation process as per the baseline, while utilizing the same softwares that were used on the baseline design. Each design is given a performance rating based on whether the design constraints are satisﬁed. HEEDS does not discard infeasible designs. Instead, it can still use them to provide better results or even provide the best of all the infeasible designs which can be used as a tool to completely change the design from the existing [16].

Drag and noise level values are the two most important objectives that are related to the aerodynamics and aeroacoustic disciplines respectively. Lower values of these parameters are preferred for comfort and better performance. As the noise level is dependent on the ﬂow, any changes made in an attempt to lower the drag value will have an impact on the noise value as well. Hence, the use of MDO would result in an optimal and feasible design in terms of both the disciplines of interest.

14 3 Methodology

The methodology adopted during the working of this thesis project (including the optimization from the baseline design to the optimized design) along with the softwares used in achieving the results are detailed in this section. The existing method involves manually changing the design parameters, remeshing the model and then running the simulation again to obtain better results. This time consuming iterative process is repeated until an optimal design is obtained. In the improved method, this entire process is automated and the input scripts in HEEDS will accordingly morph the model, mesh it and simulate it. The basis of how the particular value of the parameter is chosen is dependent on the algorithm in HEEDS which uses the evaluations to pick suitable combinations of the parameters to yield optimized design solutions.

Figure 2 indicates the workflow of the project. The geometry is first cleaned and made watertight in ANSA after which the parameters that are to be changed during the morphing process are marked. The surface mesh is generated in ANSA for each of the configurations. This surface mesh is the geometry representation for the FLUENT MESHING software, which generates a volume mesh that is utilized for the simulations to be carried out. The aeroacoustic simulations require a very fine mesh for the transient run and also to capture the acoustic related data making the volume mesh different from the aerodynamic simulations. These different volume meshes are then simulated in the FLUENT SOLVER. The results (drag and SPL values) from the baseline model form the basis for the optimization to be carried out by the HEEDS software.

Figure 2: Project Workﬂow

The details of each of these are covered in the upcoming sections.

15 3.1 Geometry

Figure 3 shows the geometry of the vehicle used for the simulations in this thesis project. The geometry only consists of the outer structure of the car and all the internal parts such as the engine bay are deleted. This model is made watertight in ANSA so as to ease the process of working with it during the meshing phase.

(a) Isometric view showing the A-Pillar (b) Bottom view showing ﬂat underbody Figure 3: Vehicle geometry considered for simulations

The A-Pillar is highlighted in green in Figure 3a. A ﬂat underbody has been considered for the simulations as shown in Figure 3b. All these modiﬁcations have been done in order to simplify the model, which in turn, would simplify the simulations.

3.1.1 Morphing

The height and thickness of the A-Pillar have been varied in order to lower the drag and noise levels. These parameters were decided upon after considering only localized changes to be made to the A-pillar, so as to, make it easier for the changes to be accepted. Changes such as the angle the A-pillar makes between the hood and the roof could also be considered as a parameter, but doing so would cause several changes to be made in the design of the car itself. Hence, this particular parameter was discarded.

The direct morphing method of ANSA was used in order to make the required changes to the A-Pillar. The morphing script which serves as an input to the HEEDS optimization tool morphs the height and the thickness of the A-Pillar as per the values picked up by HEEDS.

Figure 4 shows the modiﬁcations made to the model when the height and the thickness of the A-Pillar is changed. The direction of the change in height is indicated by the blue arrow in Section C of Figures 4a and 4c , while the direction of the black arrow in the same ﬁgures indicates the direction of the change in thickness. Figure 4a shows the geometry when the height is increased by 5 mm and the distance from the windshield is increased by 4 mm from the existing baseline which is shown in

16 Figure 4b. Increasing the distance from the windshield by 4 mm causes a 3 mm decrease in the thickness of the A-Pillar. However, causing a further reduction of the thickness would cause the roof rail of the car to be pulled out even further causing a distortion.

(a) Geometry with highest parameter changes

(b) Baseline Geometry

Figure 4c shows the geometry when the height is reduced by 2 mm and the distance from the windshield is also reduced by 2 mm from the existing baseline which is shown in Figure 4b. This only causes an increase of 1 mm in the thickness of the A- Pillar. The range in which the height and thickness of the A-Pillar could be varied was also dependent on the impact these changes would have on the surrounding components.

3.2 Mesh

3.2.1 Aerodynamic Simulations A hexcore mesh was considered for the volume mesh generation as it would reduce the cell count and thereby the simulation time when compared against having a tetrahedral or hexahedral mesh alone throughout the domain. The region just around the vehicle comprises of tetrahedral cells as the prism layers are required to better capture the ﬂow physics around the car.

17 The region away from the car towards the end of the domain is made up of hexahedral cells which helps in reducing the ﬂow dissipation before it hits the car and also does its bit in reducing the cell count and thereby provides a computational advantage.

Figure 5: Mesh showing reﬁnement regions and inﬂations layers considered for aerodynamic simulations

Figure 5 shows the mesh which has been considered for the aerodynamic simulations as viewed from a plane at the centre of the domain. The reﬁnement regions around the vehicle which are visible in Section B and Section C of Figure 5 help capture the vortices while the prism layers which are visible in Section D and Section E of Figure 5 help capture the separation around the A-Pillar. The reﬁnement regions around the vehicle help provide a smooth transition from the inner most elements that are near the car to the outermost elements at the very end of the domain by adjusting the cell sizes and growth rates accordingly.

The mesh has approximately 45 million elements and is proven to work accept- ably after a mesh sensitivity analysis was done against meshes with approximately 33 million and 63 million elements (Refer Appendix A). The elements in the reﬁne- ment regions around the vehicle were increased by adjusting the element sizes and controlling the growth rates to increase the cell count from 33 million to 45 million and then ﬁnally onto 63 million elements.

The entire model and domain was considered for the aerodynamic simulations as the car as such is not symmetric. Since, the interest was in the drag values which are impacted by the entire car, the model and domain was considered in its entirety.

18 3.2.2 Aeroacoustic Simulations

The aeroacoustic mesh also contains hexcore elements like the aerodynamic mesh, for the same reasons stated previously. The difference between the two meshes is the addition of a refinement region around the A-Pillar for the aeroacoustic mesh and the removal of certain refinement regions around the car and changes in cell sizes of the refinement regions and domain when compared against the aerodynamic mesh. Half the car and half the domain is considered for simulations as the focus is on localized areas unlike aerodynamic simulations. Despite this, the cell count on the aeroacoustic mesh is quite high (47 million cells for half the car and domain) when compared to aerodynamic runs (45 million cells for the full car and domain) due to the very small cells in the refinement region around the A-Pillar.

The reduction in the number of reﬁnement regions around the car from the aerodynamic mesh has been done to ensure that the cell count does not increase drastically for the aeroacoustic mesh which would help in faster simulations. Also, it was rea- sonable enough to do this as the wake region behind the car is not of much interest when compared to the pressure ﬂuctuations on the side window in aeroacoustic simulations. The aeroacoustic mesh shown in Figure 6 has approximately 47 million elements.

Figure 6: Mesh showing reﬁnement regions considered for aeroacoustic simulations

Figure 6 is obtained by drawing a plane along Y-Axis at roughly 700 mm from the edge of the domain. The reduction of the reﬁnement regions when compared to the aerodynamic mesh is clearly visible in Section B of Figure 6 and the reﬁnement region around the A-Pillar and the front side window is highlighted in Section C of Figure 6. The region is designed such that it follows the path of the A-Pillar and is not just a rectangular box. This helps reduce the number of cells. As a rule of thumb, in order to maintain the accuracy of an acoustic simulation and the

19 subsequent analysis result, the mesh size should atleast be 20 divisions divided by the wavelength of the maximum frequency to be analyzed. This is considered as the ideal number of divisions to capture the resolution of the wavelength. This defined the mesh size of the refinement region around the A-Pillar and the front side mirror. The refinement regions around the car, allow a smooth transition from the inner-most cells which are quite small, to the outermost cells which are larger in comparison. These cell sizes vary from the aerodynamic ones ,in order, to reach a compromise between the faster run times and refinement at regions which are not of interest while simulating aeroacoustic runs.

3.3 Solver Settings

3.3.1 Aerodynamic Simulations

The volume mesh is exported to Fluent 19.0 for computational analysis. For the simulation, a velocity of 100 km/h (0.08 Mach) is considered. The analysis is done on a steady state, incompressible ﬂow (as the compressibility eﬀects for a Mach number with speed at 100 km/h is very low).

Pressure based solver has been considered for the simulations. Both, pressure and density based solver work over a wide range of ﬂows now, but the origins of the pressure based solver may provide an advantage over the density based solver for low speed incompressible ﬂows. Hence, the choice.

Realizable k- turbulence model with enhanced wall treatment is considered for running this simulation as it considered to be more reliable and accurate for a external aerodynamic ﬂows at a less computational cost.

Figure 7 indicates the size of the computational domain and the boundary conditions implemented for the aerodynamic run. The velocity inlet is approximately 4 vehicle lengths ahead of the car while the pressure outlet is approximately 10 vehicle lengths behind the car. The car is bounded on the top at a distance of approximately 7 vehicle heights while it is 4 vehicle widths to each side. The wake can be accurately captured in the regions of interest as per these dimensions and the effects from the boundaries are also minimized. The benefits of having a large computational domain reduces the blockage effects without unnecessary increase to the computational size and hence time. This is so because the size of the mesh cells are quite large at the very ends of the domain and reducing the domain will not result in substantial reduction in the cell size and therefore computational time.

20 Figure 7: Schematic of the domain and boundary conditions considered for the aerodynamic simulations

The vehicle is considered as a no slip wall. The face of the domain ahead of the vehicle is considered as a velocity inlet (100 km/h) and the face of the domain behind the vehicle is considered as the pressure outlet. The face of the domain on which the vehicle rest on is considered as a wall while all other faces are considered as symmetry. These boundary conditions help replicate the real life conditions as close as possible.

As standard initialization allowed for a faster convergence this method of initialization was considered over the hybrid one. Steadying out of the scaled residuals and CL and CD around the vehicle indicated convergence. The CD values are obtained at the end of each run. It is this value that needs to be reduced.

3.3.2 Aeroacoustic Simulations

The solver settings adopted for the aerodynamic simulations were implemented for the aeroacoustic simulations for the steady state run with a few minor changes (which are mentioned further down in this section), in order to obtain correct results with shorter simulation run times.

The wheels, powertrain and wind contribute to providing the overall noise that is heard in the cabin of a vehicle. This varies at diﬀerent vehicle speeds. Aerody- namic noise tends to dominate at speeds above 100 km/h [8]. Hence, the velocity at the inlet was considered to be 140 km/h instead of the 100 km/h considered in aerodynamic simulations. In order to speed up the simulations by reducing the mesh cell count, the domain considered for the aerodynamic simulations (shown in Figure 7) were reduced to approximately 2 car lengths ahead, 6 car lengths behind, 3 car heights above and 2 car widths to the left side when running the aeroaocustic simulations.

As the aerodynamic noise is dependent on the strength of the time dependent surface pressure fluctuations which vary about a mean value, transient cases are run. The results from the steady state simulation serves as an initialization to the upcoming transient run. DDES is considered for running this simulation as it is considered to provide a better shielding function than the DES when the switch occurs between RANS and LES. SST k-ω is considered in the RANS part of the simulations. A contour of the mesh cut-off frequency indicates the maximum frequency that the grid can resolve [17] (Refer Appendix A). A higher frequency resolution calls for a higher mesh refinement.

21 For the transient run, monitor points located in the wake region behind the side mirror and near the front side window are monitored for pressure to indicate convergence. The transient run is simulated until a statistically steady state is observed at around 0.1967 seconds. During this time the ﬂow has passed approximately four times through the reﬁnement region. After this, sampling of the acoustic data is done for another 0.0406 seconds. The FW-H model is activated and the front side window is considered as the source to collect the acoustics data. The noise at the front side window is the noise that is heard inside the cabin as no receivers are considered.

The area-weighted average SPL values across the octave bands 125, 250, 500 and 1000 Hz are calculated. The sampling run time dictates the lowest frequency that can be resolved while the smallest mesh size in the region of interest constrains the highest frequency (Refer Appendix B). The A-weighted correction is then applied to these values as this is an approximation for how the human ear perceives noise. The overall A-weighted SPL is then obtained at the end of each run. It is this value that needs reducing.

3.4 HEEDS Optimization

The generation of results from the baseline model is the basis for the optimization to be done on the model. Figure 8 shows the workﬂow adopted in HEEDS for the optimization process.

Figure 8: Workﬂow of the optimization process in HEEDS

An evaluation in HEEDS is referred to as the simulation run of a speciﬁc design. In this case, one analysis will be carried out for every design that needs evaluating. Each of these analysis would require a command that would execute the tool that is required for the analysis. Apart from this, input values to be used for the analysis are also required. After a successful simulation run the values will be stored in an output ﬁle.

The parameters (height and thickness of the A-Pillar) from the design form the inputs to the HEEDS run while the drag and SPL values constitute the outputs which are accordingly tagged in HEEDS. The optimization objectives are speciﬁed

22 which is to reduce the drag and noise levels in this case. The number of evaluations for HEEDS to run the optimization is set with the optimization method. SHERPA is considered as the optimization method for the HEEDS run as this method combines the best of all the methods and selects suitable variables from the design space in order to provide the best optimized result.

The variables in this case are set to continuous with a resolution that controls the fineness of the values that are picked out for the various evaluations. The higher the resolution value, the finer the set of values will be. SHERPA is the default optimization method in HEEDS for the optimization study. It combines various search methods at the same time in order to adapt and refine them as the search for the optimal design progresses. It helps find the best possible design based on the weighted combination of all the objectives.

3.5 Overall Optimization Method

Initially, an execution command from HEEDS starts ANSA and morphs the model. The initial evaluation from HEEDS is always the baseline between the minimum and the maximum values given for the parameters to be altered (having a value of 0 as the baseline has the simulations running on an unchanged model). After morphing, a surface mesh is generated in ANSA, which serves as a surface representation of the model for FLUENT to generate a volume mesh. This surface mesh is then imported to FLUENT MESHING and a volume mesh is generated. This volume mesh is then simulated for the aerodynamic and aeroacoustic runs simultaneously.

The drag and A-SPL results are reported at the end of the simulation runs, which are noted in HEEDS. The entire process is run in the same folders and running multiple evaluations causes the files to be overwritten. In order to avoid this, certain files (like the surface mesh, case and data files of both, the aerodynamic and aeroacoustic simulations, drag report from aerodynamic simulations, source files and SPL and A- SPL reports from the aeroacoustic simulations) are copied to new folders (named as per the design iterations from HEEDS) before the next evaluation is started. This helps in having a copy of all the simulations run.

The next evaluation is then begun to replicate the same process. As morphing the parameters, can cause the mesh to be skewed, the surface mesh is re-meshed in every single evaluation. Also, considering the number of licenses and nodes available to run the simulations, it was practical to run the volume meshing in FLUENT on less nodes than while running the simulations, inspite of FLUENT having the capability to switch from meshing mode to solver mode. Hence, a dummy file (in this case, a size-field file) has to be saved everytime the volume mesh is completed so that the solver mode could start. Not having this file, would cause the fluent meshing and solver to open up simultaneously, thereby using up licenses. Once this file is saved, the simulations start.

The next evaluation does not start until both the aerodynamic and aeroacoustic

23 simulations are completed. This is ensured by having another dummy file written out (in this case, a forces report) saved after the simulation. Once this file is saved from both simulations, HEEDS starts the next evaluation. These dummy files are deleted just before the volume mesh of the next evaluation is started. Not doing so, would result in the mesh and simulations not being run for the second evaluation, as the system would recognize these files are being present in the folder and imme- diately move onto the next evaluation. This would result in all evaluations having the same output values.

The same model of the vehicle has been used for both the aerodynamic and aeroacoustic simulations. Also, similar scripts could be used for both simulations with differences being in the volume meshing phase of the aeroacoustic simulations. This was so, because of the change in domain, reduction of refinement regions around the car and the inclusion of a refinement region around the A-Pillar. The simulations scripts also different due to the steady runs for the aerodynamic simulations and transient runs for the aeroacoustic simulations. The naming convention of the parts were kept the same with suffixes being added for the parts related to the aeroacoustic simulations in order to facilitate this.

24 4 Results and Discussion

This section details the results obtained from running simulations with the settings speciﬁed in the previous sections. It begins with the ﬂow behavior around the car and the A-Pillar in particular. It then goes on to explain the reasoning behind the choice of the optimized design after which the optimized design is explained and compared against the baseline design. All this is based on the methodology mentioned in the previous section.

4.1 Baseline Design

The various plots and contours obtained from running the aerodynamic and aeroacoustic simulations on the baseline model are discussed in this section. These also serve as a validation of the method.

4.1.1 Pressure and Velocity Flow Field

Figure 9 shows the contours of pressure coefficient normalized against the maximum value plotted across the vehicle and the velocity contours plotted on the mid-plane of the vehicle. It is observed, that the flow around the vehicle encounters a stagnation point at the nose (increase in pressure and reduction in velocity) and the air tends to flow over and around the car instead of under the car due to the proximity the ground has with the vehicle.

Figure 9: Normalized contours of Pressure Coeﬃcient along the car and Velocity Magnitude across a plane at the center of the car

There is an accelerated ﬂow of air above and below the car where the velocity increases from the inlet velocity of 100 km/h. Towards the rear the ﬂow separates to form a low velocity and high pressure region of turbulence in the wake behind

25 the car. The upwash from the flat underbody is greater than the downwash from the roof providing a wake that is slightly unbalanced as the lowest drag is obtained when the upwash from the underbody matches the downwash from the roof, thereby giving a balanced wake at the rear of the car. Section B in Figure 9 shows that the flow around the A-Pillar has relatively high velocity and low pressure. This results in the fluid that is closest to the surface to change direction and separate as shown in Figure 10. The separation of flow around the A-Pillar also causes a low pressure region at the very top of the front side window as seen in Section B of Figure 9. This low pressure region occupies a fairly significant portion of the front side window after which the pressure increases when the flow reattaches eventually. This flow of air around the A-Pillar and the vehicle and the resulting pressure and velocity follows a similar pattern as explained in [7], where the surrounding flow field has been investigated on a simplified model of a vehicle.

Figure 10 shows the velocity streamlines around the base of the A-Pillar. The side mirror has been made transparent for clarity and the number of streamlines are quite less in number in order to clearly show the beginnings of the vortex formation.

(a) Side view of the pathlines showing the ﬂow behavior

(b) Zoomed-in view of the pathlines showing formation of vortices Figure 10: Velocity Pathlines along the junction between the windshield and A-Pillar

26 The separation of the flow and the formation of the vortices are clearly visible in Figure 10a. It is observed in Section B of Figure 10b that the oncoming flow from the hood faces an obstacle in the form of the windshield. As the air flows over the hood, the pressure reduces. On encountering the windscreen there is an increase in the pressure as seen in Figure 9. A part of the flow then tends to go over the windshield and onto the roof while a part of it tends to go around it, causing it to flow over the A-Pillar with an increased velocity from the freestream. The part of the flow that is deflected onto the A-Pillar, separates at the junction between the windshield and the base of the A-Pillar. The flow downstream from the A-Pillar base also aids in the formation of the vortex as this gets added to the flow that is already separated from the windshield. Hence, the downstream flow has a component from the windshield and from the base, which causes the generation of a vortex that is constantly fed by these two components. It is also evident in Section B of Figure 10b that the flow velocity around the base of the A-Pillar increases when compared to that of the freestream as the pressure in the A-Pillar region reduces causing the flow to separate. The flowfield around this model and the corresponding velocity pathlines that are obtained from this simulations are similar to the ones carried out by [5] where the beginnings of the vortex formation have been detailed.

4.1.2 Vorticity

Figure 11 shows the regions around the car where the vortices are generated. The main regions that cause the formation of the vortices include the A-pillar, side mirrors and the wheels. The wake at the rear forms the major bulk of the vortices all of which leads to an increase in the drag value.

The separation of the flow from the edges of the front window and the hood as the air flows over it causes a huge longitudinal vortex to develop along the A-Pillar as seen in Section B of Figure 11. The vortex then travels upward along the roof and downstream along the side window where the flow starts to expand. Design changes to reduce the flow separation along the A-Pillar will result in the reduction of strength of the A-Pillar vortex formed.

Figure 11: Formation of vortices around the car plotted on an iso-surface of total pressure=0

27 In principle, every vortex generated by the vehicle would travel downstream and then merge with the base wake. An attached ﬂow near the A-Pillar will help delay separation and prevent the onset of the vortices which will result in a reduced drag value. The separation of the ﬂow and the formation of the vortices due to the A- Pillar are explained in [7] and follow a similar path to the one’s obtained from this simulation.

4.1.3 Total Pressure on an Iso-surface of Q-Criterion

The existence of the vortex structure formed at the A-Pillar is observed in Figure 12. An iso-surface of the variable Q-criterion (which helps visualize vortices) has been used to represent the turbulent structures following which the regions of recirculation are noticed. The Q-criterion gives the local balance between the strain rate and the vorticity magnitude, making it widely used in order to visualize the turbulent fields in the flow regimes. A high level of turbulence and pressure fluctuations can be observed in the region close to the A-Pillar.

Figure 12: Normalized Total Pressure plotted on a iso-surface of Q-criterion=1·106 s−2

It is also observed that the flow at the base of the A-Pillar has low pressure causing the flow to separate and spiral upward forming vortices. Lower pressure on top when compared to beneath causes vorticity which forces the flow from below to move onto the top. As the flow around the A-Pillar is highly turbulent and separated it leads to high pressure fluctuations as seen in Figure 12.

The vortex covers the top half of the front side window (becoming stronger and wider as it travels downstream, where it mixes with the separated flow from the roof region) which is closest to the A-Pillar causing a region of low pressure at the very top of the window. This fluctuating impinging flow caused due to the geometry of the A-Pillar causes acoustic waves and the fluctuations in the pressure are a reason for the windows to vibrate and radiate noise to the interior of the vehicle.

28 4.2 Optimized Design

The Design of Experiments (DoE) was conducted in HEEDS to check the impact the chosen input variables have on the outputs. After this the parameter optimization study was conducted in order to come up with an optimized design. The DoE study was done only to improve the understanding of how changes to the height and thickness would inﬂuence the CD and A-SPL values and hence, the analysis from this study was not considered for obtaining the optimized design. The optimized design was chosen from the parameter optimization study.

4.2.1 Design of Experiments

The number of evaluations for the DoE study was maintained as 4, to just get an idea of the eﬀect the parameters have on each other. Since, only 4 evaluations were considered, a combination of the extreme values of the input parameters were considered by HEEDS for the simulations. Table 1 indicates the design options chosen for the DoE study. The values of CD and A-SPL have been normalized against the largest values in the respective columns.

Table 1: Inﬂuence of input variables on the desired output values

Design Id Height (mm) Thickness (mm) CD A-SPL 1 5 -4 1.0000 0.9921 2 -2 -4 0.9853 1.0000 3 5 2 0.9887 0.9909 4 2 2 0.9815 0.9847

Figure 13 shows the inﬂuence the height and thickness have on the drag and A-SPL.

Figure 13: Comparison of the eﬀects the input parameters have on the outputs

29 Based on the 4 evaluations done with a DoE study, it is observed that CD is influ- enced by the changes made to the height more than those made to the thickness. The thickness has a higher impact on the A-SPL while the height has less than a 2% influence on the A-SPL. The thickness has a larger effect on the A-SPL, when compared to the drag. As this comparison is done based on 4 evaluations (only the extreme values), it can not be considered as optimal.

Figure 13 also shows that an increase in the height causes a reduction in the CD value, while the A-SPL value increases as the height increases. It is observed that an increase in thickness causes a massive reduction in the A-SPL value and in the drag value as well.

Based on the 4 evaluations considered, it was decided to conduct the parameter optimization study with both the input variables as they have a considerable impact on the outputs. Hence, based on the screening done using the DoE method, the parameter optimization study was started.

4.2.2 Parameter Optimization

The rationale behind choosing the optimized design is detailed here. The study for ﬁnding the optimal design was done by using the parameter optimization study in HEEDS. Making localized changes to the A-Pillar aﬀects other parts in close proximity and hence, the lower and upper limits of the parameters to be morphed are limited.

It is desirable to monitor the changes over a wider range in order for easier understanding and to clearly understand the effects the parameters have on the outputs. However, this is not possible in the case of the A-Pillar as increasing the height of the A-Pillar or reducing the thickness, more than the specified values will cause a distortion of the roof rail of the car. Hence, increasing the limits and thereby the range of the optimization will account for more parts to be changed, to an extent that the changes are not concentrated around the A-Pillar alone. The design un- dergoes a massive change without the confirmation that these changes would lead to optimal results.

The design options, which include, the combination of variations of the design parameters, which in turn, helped yield the optimal design within the design space, considering the limited number of evaluations are shown in Table 2.

The column listing the thickness values indicate the value by which the A-Pillar has moved across the windshield from its current position. The values of CD and A-Weighted SPL have been normalized against the baseline model (Design Id-1). Equation 20 indicates how the values in the performance column of Table 2 have been computed. Performance indicates how well the design meets the objective while satisfying the constraints speciﬁed. The current model that is speciﬁed in Equation 20 refers to the Design Id under consideration for calculations. The weightage for both CD and A-SPL has been maintained the same as seen in the equation.

30 A − SPL C P erformance = current + Dcurrent (20) A − SPLbaseline CDbaseline

A height and thickness of 0 each indicate the baseline model which is represented by Design Id-1. A positive value of the height value indicates an increase in the height from the existing while a positive value of the thickness indicates a movement of the A-Pillar towards the windshield.

Table 2: Inﬂuence of input variables on the desired output values

Design Id Height (mm) Thickness (mm) CD A-SPL Performance 1 0 0 1.0000 1.0000 2.0000 2 -2 0 0.9928 1.0014 1.9940 3 1 0 1.0023 0.9950 1.9971 4 5 -2 1.0051 0.9942 1.9992 5 1.8 -2 0.9911 0.9985 1.9894 6 3.2 0 0.9747 0.9898 1.9645 7 5 0 0.9955 0.9891 1.9849 8 3.4 2 0.9733 0.9963 1.9698 9 5 2 0.9839 1.0033 1.9872 10 3.2 -1.4 0.9959 0.9940 1.9900

For easier representation, the data in Table 2 is plotted in Figure 14. The values of height and thickness are plotted on the x and y axis respectively. Drag is represented by the circles while the ﬁlled colours indicate A-SPL. Smaller the circle, lower is the drag value, while a darker colour (bottom of the colour map) indicates a lower A-SPL value.

Figure 14: Bubble Plot representation of the data in Table 2

31 It is observed from Figure 14 that the entire design space has not been explored in this study due to the lower number of evaluations considered. A thickness increase of 2 mm and a height increase of 3.4 mm of the A-Pillar generates the least drag (visible by the small circle), while the highest drag is generated when the height is increased by 5 mm and the thickness reduced by 2 mm (largest circle in the plot). Similarly, the least A-SPL is noticed when the height is increased by 3.2 mm with no change to the thickness, while the highest levels of A-SPL are observed when the height is increased by 5mm and the thickness by 2mm.

All the designs listed in Table 2 can be considered as optimized designs from the baseline as the performance of each of the designs is better than the baseline. How- ever, if emphasis is to be laid on only the reduction of the output values and not on the magnitude at which the reduction takes place, Design Id’s-2 and 9 can not be considered as a optimized design as it causes an increase in the A-SPL value inspite of causing a reduction in the drag. The same holds true for Design Id’s-3 and 4 as there is an increase in the drag value but a reduction in the SPL value. Hence, by the process of elimination, Design Id’s-5, 6, 7, 8 and 10 can be considered as optimized designs within the number of evaluations considered for this study.

Amongst these four designs, Design Id-6 has the best performance in terms of the reduction of both the desired output parameters. Hence, as per this, an increase in the height of the A-Pillar and maintaining the thickness as is, would provide the best performance within the limitations of the scope of this thesis. Having a closer look at the other feasible designs indicates that an increase in the height of the A-Pillar causes a reduction in the drag and SPL values. However, when this is coupled with an increase in the thickness, it causes a slight increase in the SPL values, which is nevertheless less than the baseline but more than a design that does not alter the thickness.

It is also observed from Design Id’s 6 and 7 that on increasing the height to the extreme values and keeping the thickness as is, does reduce the drag and SPL levels, but the design is not the optimal one in terms of design performance. The higher value of drag in the extreme case could be contributed to an earlier separation of the ﬂow when the ﬂow encounters the junction of the A-Pillar and the windshield.

Figure 15 shows the changes between the optimized design and the baseline when only 5 evaluations have been considered. Both the height and the thickness have been altered from the baseline. The model in blue represents the baseline design, while the changes made to the A-Pillar in the optimized design are represented in maroon. On considering 10 evaluations, the optimized design is the one that alters the height but not the thickness as shown in Figure 16.

32 Figure 15: Model of the optimized design superimposed on the baseline design (5 evaluations)

Increasing the height by 1.8 mm from the existing and having a reduction in the distance from the windshield by 2 mm causes most of the flow to move upwards onto the roof and a much less flow around the A-Pillar. The flow around the A- Pillar is much less and remains attached for a longer time at the base, leading to less separation and thereby causing a reduction in the strength of the vortex and a subsequent reduction in the drag value.

Figure 16: Model of the optimized design superimposed on the baseline design (10 evaluations)

Increasing the height by 3.2 mm from the existing and retaining the thickness from the baseline model also causes most of the flow to move upwards onto the roof resulting in a much less flow around the A-Pillar, which is similar to the optimized model detailed previously. As the thickness is almost doubled from the previous one, the flow around the A-Pillar is much less leading to a much more weakened vortex. Hence, the pressure fluctuations are reduced causing less noise at the side window.

The optimal design is chosen by HEEDS based on the performance values. However, this does not necessarily indicate the reduction of both the output parameters at all times, as the performance study will still be better than the baseline, if one of the output parameters decreases by a drastic amount while the other increases by a small value. The ﬁrst few iterations in HEEDS are chosen arbitrarily in the design space in order to judge the outputs. After, a few iterations the values start to inch towards the optimal values based on the study chosen in HEEDS. The feasibility of the optimal design are not considered by HEEDS either. In this particular case of the A-Pillar, an increased height and thickness can obstruct visibility and be a

33 reason for blind spots for the driver. Hence, it’s a trade-oﬀ between the design of the vehicle and improved output parameters.

4.3 Comparison between the Results from the Baseline and Optimized Design

The optimized design chosen on basis of reduced drag and SPL values and hence better performance after 10 evaluations is compared against the baseline model in this section.

4.3.1 Drag

Sections were extracted along the Y-Z plane in order to better visualize the flow around the A-Pillar. These sections were drawn at 2.2 m, 2.4 m, 2.6 m and 2.8 m from the origin along the X-axis. Doing so helps visualize the flow a little ahead of the A-Pillar and also at various locations downstream of the flow along the A-Pillar.

Figure 17 shows the turbulence generated along the A-Pillar in both the baseline and optimized design. The vehicle has been made transparent for clarity. High regions of turbulent viscosity ratio are observed in the sections drawn across the baseline model when compared against the optimized design.

(a) Baseline Design (b) Optimized Design

Figure 17: Normalized Turbulent Viscosity Ratio plotted against sections along the Y-Z plane

It is observed that a highly turbulent flow exists at the base of the A-Pillar where the flow accelerates from the freestream and separates giving rise to a vortex based on the very high amount of kinetic energy obtained at that region. This is represented in the very first section at the A-Pillar and windshield junction in Figure

34 17a. This high concentration of the kinetic energy decreases in magnitude as the distance from the base increases causing a reduction in the turbulence as noticed in the subsequent sections downstream of the A-Pillar. This separated ﬂow and the resulting turbulence plays an important role in the drag value of the car.

In the optimized design shown in Figure 17b the turbulence across the A-Pillar in all the sections is noticed to be considerably less. This is due to the increased height and reduced thickness of the A-Pillar which causes a larger part of the up- stream airflow to go over the windshield and onto the roof instead of around the A-Pillar, which results in less flow around the base of the a-Pillar. Hence, there isn’t a lot of flow accelerating around the base of the A-Pillar which gives rise to the formation of the vortex causing the magnitude of the vortex to be less when compared to the baseline design. Also, as a lot of the flow is deflected upward and not around the vehicle, the vortex is not being fed constantly by the flow from the separated by the windshield. Hence, less turbulence is observed across all sections of the A-Pillar which leads to a subsequent reduction in the drag value from the baseline model as shown in Table 3.

Table 3: Normalized drag values

Model Height (mm) Thickness (mm) CD Baseline 0 0 1 Optimized 3.2 0 0.9747

4.3.2 SPL

The reduction in the vortices formed at the A-Pillar of the optimized design is observed in Figure 18 when compared to the baseline.

Figure 18: Normalized Total Pressure plotted on an iso-surface of Q-criterion=1·106 s−2 for the optimized design

The optimized design caused by increasing the height which causes most of the ﬂow to go over instead of around. Hence, the A-Pillar vortex is now reduced and the

35 fluctuating pressure on the front side window is reduced considerably. The reduction in the formation of vortices and a reduction in the region between the separation and reattachment lines results in a reduction of the drag and SPL values. This shows how a simple modification in the geometry has a dramatic effect on the strength of the vortex.

The contours of SPL are normalized and plotted along the front side window as shown in Figure 19. The contours plotted against the baseline design for octave bands of 125 Hz, 250 Hz, 500 Hz and 1000 Hz are shown in Figures 19a, 19b, 19c and 19d, while the one’s plotted against the optimized design are shown in Figures 19e, 19f, 19g and 19h

It is observed that the SPL values are higher at the upper edge of the front side window which is closest to the A-Pillar, irrespective of the octave band frequencies. This indicates that the vortices formed due to the A-Pillar, generates the maximum ﬂuctuations in pressure which in turn correspond to higher noise levels. This covers a slightly less area of the side window at 125 Hz and goes on to increase with it being the highest at 500 Hz.

(a) 125 Hz (Baseline) (b) 250 Hz (Baseline) (c) 500 Hz (Baseline) (d) 1000 Hz (Baseline)

(e) 125 Hz (Optimized) (f) 250 Hz (Optimized) (g) 500 Hz (Optimized) (h) 1000 Hz (Optimized)

Figure 19: Normalized SPL contours in octave bands

The SPL values gradually decrease when moving away from the A-Pillar towards the extreme end of the front side window. This significant drop in the noise levels is due to the reduction in the intensity of the separated flow region caused by the A-Pillar and the subsequent reattachment of the flow. The region at the center of the window (SPL values between 0.65 and 0.74) are significantly lower than the regions at the very bottom which is affected by the wake caused due to the side mirrors as well. This trend holds true for both the baseline and the optimized design.

It is observed that on comparing the SPL contours of the baseline and the optimized design against a speciﬁed frequency, the SPL values are lower across a larger area in the optimized design which help in reducing the area weighted average of the SPL values across the front side window.

36 Table 4 gives the normalized SPL values against the maximum value from the baseline and the modiﬁed design across the frequency in the octave bands under consideration.

Table 4: Normalized area-weighted average SPL values on the front side window Normalised SPL Frequency (Hz) Baseline Modiﬁed 125 0.9821 0.9722 250 0.9978 0.9754 500 1.0000 0.9835 1000 0.9822 0.9644

It is observed that the normalized SPL values of the modified design are less than that of the baseline design across the frequencies of the octave bands. This is because of the lower SPL values occupying a larger area on the front side window as seen in Figure 19 which leads to a lower area-weighted averaged value due to the reduction in the formation of vortices in the optimized design. Hence, the overall A-weighted SPL value calculated from this set of octave bands is lower in the modified design when compared to the baseline. The contours plotted are based on the averaged SPL and hence, any local changes in specific are not captured. The noise levels if monitored at points across the side window would have different values based on the proximity of the point to the separation and reattachment regions of the flow. However, the averaged value over the frequency bands is a good judge of the noise levels heard inside the cabin as it is the collective effect of all the noise generated due to the pressure fluctuations on the side window.

37 5 Conclusion

The formation of vortices due to the ﬂow over the A-Pillar causes an increase in the drag generated by the vehicle. Apart from this, it also causes a high level of noise to be generated, which can cause discomfort in the cabin. Hence, there is a need in the automotive industry to modify the A-Pillar so as to reduce the drag and noise generated by the vehicle.

In this thesis project, the method of carrying out the optimization process from the geometry phase to the optimized design from the baseline is worked on. This was done by automating the process in HEEDS such that, the morphing, surface and volume mesh generation and simulations are run, for the respective settings as per the design parameters suggested by HEEDS within the design space suggested by the user. This entire process is done with a complete model for the aerodynamic simulations, while half the model is considered for the aeroacoustic simulations. This has been done so as to save time and computational resource when running the aeroacoustic simulations as the emphasis is laid on the localized changes and not on the model as a whole. From the simulations, the ﬂow around the car and the A-Pillar in particular of the baseline design is analyzed and validated against similar work carried out previously and from various literature studies. Various combinations of the height and thickness are altered accordingly, to reduce the impact that the vortices formed around the A-Pillar have on the drag and noise levels. 10 evaluations are run in order to get the optimized design (which has an increased height of the A-Pillar) from the aerodynamic and aeroacoustic simulations after which the ﬂow has been compared to the baseline model in order to validate the optimized design.

A working methodology to optimize the method of conducting aerodynamic and aeroacoustic simulations has been achieved. This has been done by carrying out evaluations, starting with an execution command from HEEDS which starts ANSA and morphs the model. Once, the model is morphed accordingly to the values specified by HEEDS (initial values form the baseline of the simulations), the surface mesh is generated. This surface mesh is the same for both the aerodynamic and aeroacoustic simulations. It is a surface representation of the model. Once the surface mesh is generated, FLUENT Meshing is started so that the volume meshes can be generated. The volume meshes for both the simulations are generated simultaneously. These volume meshes and the scripts to generate them are slightly different due to the difference in refinement regions. At the end of the generation of the volume mesh, a dummy size function file is saved which indicates FLUENT to move onto the next step of running the simulations. The simulations for both aerodynamics and aeroacoustics are run simultaneously. The scripts for running this also differ before of aeroacoustic runs being transient. The output from these simulations are the drag values from the aerodynamic runs and A-SPL values from the aeroacoustic runs. The entire procedure is repeated until an optimal design is obtained based on the number of simulations.

38 5.1 Future Work

The scope of the thesis has been limited on the basis of time and computational power. For further completeness of the simulation, usage of the complete model that includes internal parts and an underbody that is not flat will help provide results close to reality. Much more detailed results can be obtained on further refining the mesh in order to resolve for higher frequencies. Also, running the aeroacoustic simulations for longer flow through times and the sampling it for longer durations can help resolve lower frequencies. Doing so, would help obtain a wider understanding of the noise levels across a wide range of octave bands. Running the optimization process considering several more evaluations with smaller resolutions would help obtain an optimal design in a larger design space, thereby giving an optimal model that is not limited by the scope of the thesis.

5.2 Perspectives

From an industry perspective, multi-disciplinary optimization helps achieve better results in terms of performance which satisﬁes all the domains under consideration and not just one. Hence, developing a method that works towards optimizing the design of components, in the ﬁeld of aerodynamics and aeroacoustics does away with the results that would be optimal for one domain but not the other. Also, it helps saves time and computational resources as it couples various input parameters to provide the optimal results that suit all domains.

From an environment perspective, the reduction in the noise levels enhances the comfort level of the passengers. Road safety is also improved, as high levels of noise can lead to driver fatigue and a reduction in concentration. Reduction in drag would help improve the fuel eﬃciency.

39 References

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[2] Bambra DPS. Computational Analysis of A-Pillar Vortex Formation in Au- tomotive Applications. School of Engineering Computational Fluid Dynamics, Cranﬁeld University. 2013;.

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[4] Murad NM, Naser J, Alam F, Watkins S. Simulation of Vehicle A-Pillar Aerody- namics of Various Yaw Angles. 15th Australasian Fluid Mechanics Conference. 2004;.

[5] Radhakrishnan S, Nande I. Computational Aeroacoustics on an Electric Vehicle for Wind Noise Prediction and Analysis. Division for Applied Thermodynamics and Fluid Mechanics, Link¨opingUniversity, Link¨oping,Sweden. 2017;.

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[7] Wolf-Heinrich H. Aerodynamics of Road Vehicles. SAE Intl; 1987.

[8] Oettle N, Sims-Williams D. Automotive Aeroacoustic: An Overview. Journal of Automobile Engineering. 2017;.

[9] Dechipre H, Hartmann DM. Aeroacoustics Simulation of an Automotive A- Pillar Rain Gutter. European Automotive Simulation Conference. 2009;.

[10] ANSYS Fluent Theory Guide. ANSYS Manual. 2017;.

[11] Davidson L. Fluid Mechanics, Turbulent Flow and Turbulence Modeling. Divi- sion of Fluid Mechanics, Chalmers University of Technology. 2018;.

[12] Nagawkar BR. Numerical Study of Aeroacoustic Sources Generated from the Wake Behind the Car. Department of Fluid Dynamics, Chalmers University of Technology. 2016;.

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40 [16] Getting Started with HEEDS. HEEDS Manual. 2007;.

[17] Wagner C, H¨uttlT, Sagaut P. Large Eddy Simulation for Acoustics. Cambridge; 2006.

41 A Mesh (Aerodynamic Simula- tions)

A mesh sensitivity study was done for the mesh generated for the baseline model that would be used for the aerodynamic simulations. This was done by monitoring the residuals and the forces (CL and CD) around the vehicle. Table 5 shows the mesh sensitivity analysis done on the baseline model for aerodynamic analysis.

Table 5: Mesh Sensitivity Study for the baseline model (Aerodynamic Simulations)

Number of Elements % Diﬀerence in CD % Diﬀerence in CL 33 Million - - 45 Million 0.34 13.24 63 Million 0.37 3.4

The mesh with 45 million cells was selected to perform aerodynamic analysis for the baseline model. This mesh was selected as the 0.37% coefficient of drag (CD) and 3.4 % coefficient of lift (CL) difference between the 45 million and 63 million mesh cells is in the acceptable range of 5% changes. Also, the lesser mesh count mesh would help in reducing the computation time with no changes to the results.

The contours of y+ are plotted across the car as shown in Figure 20. The Re- alizable k- model with enhanced wall treatment works best when the ﬁrst cells are placed in the viscous layer (having a y+ in the range between 1 and 5). To achieve this 16 prism layers have been considered as this allows a smooth transition from the last cell in the prism layer to the very ﬁrst cell outside of it, considering the growth rate.

Figure 20: Wall Y+ around the car

42 B Frequency Range (Aeroacous- tic Simulations)

Post processing a steady state result by considering the mesh cutoff frequency helps decide in advance (before running the transient simulation) whether the mesh has the sufficient resolution to capture the turbulent flow structures in the frequency range that is of interest. The mesh cutoff frequency is defined as

q 2 3 k f = (21) MC 2∆ For a cell dimension of ∆ and the local turbulent kinetic energy k, 2∆ is the smallest length scale of a turbulent eddy structure that can be captured by the mesh while q 2 the associated ﬂuctuation velocity is 3 k. As this measure is derived from a steady state solution, its usefulness is only limited to approximate the frequencies of the turbulent scales that are modeled in RANS and can be resolved in SRS [17]. The mesh must be reﬁned in order to resolve a higher frequency.

Figure 21: Contours of mesh cutoﬀ frequency on a plane drawn at 700mm from the centre along Y-axis

A plane drawn at 700mm along the y-axis is used to visualize the cutoﬀ frequency that the mesh can resolve in Figure 21. It is observed that approximately 1000 Hz can be resolved during the transient run for the mesh generated for aeroacoustic simulations.

Figure 22 shows the vertex average plot of four points in the wake region behind the side mirror and near the front side window. The transient run was simulated for approximately 0.45 seconds. It is observed from the ﬁgure that a statistically steady state is observed at around 0.197 seconds.

43 Hence, it was decided to run the transient case before sampling to about 0.2 seconds, as the flow is considerably stable and any results obtained on sampling beyond this point can be considered as correct. Doing so would also help save simulation time and computational effort. The flow passes through the refinement region around the A-Pillar atleast four times during this period.

Figure 22: Plot of pressure monitored at four points in the wake behind the side mirror

Figure 22 also shows the sampling of the acoustic data for for another 0.25 seconds after the statistically steady state is achieved. Sampling for this long a time can help resolve a lower frequency at the cost of computational cost and eﬀort. Hence, this time has been reduced to 0.0406 seconds in the optimization simulations involving aeroacoustic data.

The SPL values obtained from this simulation of long transient runs and long sampling times was then compared against the ones obtained from a simulation of approximately 0.2 seconds to get to the statistically steady state and a further 0.0406 seconds of acoustic data sampling. The normalized SPL contours and values on the front side window obtained from both the simulations follow similar patterns as shown in Figure 23 and hence, the decision for the simulation times of the aeroacoustic simulations were considered in this thesis project.

The SPL contours shown in Figure 23a, 23b, 23c and 23d are obtained from the simulation run for a ﬂow time of approximately 0.7 seconds while Figure 23e, 23f, 23g and 23h are obtained from the simulation run for a ﬂow time of approximately 0.20406 seconds.

44 (a) 125 Hz (0.7s) (b) 250 Hz (0.7s) (c) 500 Hz (0.7s) (d) 1000 Hz (0.7s)

(e) 125 Hz (0.4s) (f) 250 Hz (0.4s) (g) 500 Hz (0.4s) (h) 1000 Hz (0.4s)

Figure 23: Normalized SPL contours in octave bands

Based on these simulation times and mesh resolution, a highest frequency of 1000 Hz can be resolved while, a lowest frequency of approximately 24 Hz can be resolved. However, only one wave is considered per period in this case. Hence, on considering 5 waves per period brings the least possible frequency resolution to approximately 125 Hz. This decides the frequency range of the simulations to be between 125 Hz and 1000 Hz.