Numerical Investigation of Unsteady Crosswind Aerodynamics for Ground Vehicles

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Numerical investigation of unsteady crosswind aerodynamics for ground vehicles

Tristan Favre

Licentiate Thesis

Stockholm November 2009

Vinnova Centre of Excellence for ECO² Vehicle Design Department of Aeronautical and Vehicle Engineering

Postal address Visiting address Contact

Royal Institute of Technology Teknikringen 8 Tel: +46 8 790 80 15

Aeronautical and Stockholm Email: favre@kth.se

Vehicle Engineering SE-100 44 Stockholm Sweden

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Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm framläggs till offentlig granskning för avläggande av teknologie licentiatexamen Torsdag den 12 November 2009, 10:00 i sal E52, Osquars- backe 14, 3tr, KTH, Stockholm.

TRITA-AVE-2009:68 ISSN-1651-7660

ISBN-978-91-7415-446-7

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Abstract

Ground vehicles are subjected to crosswind from various origins such as weather, topography of the ambient environment (land, forest, tunnels, high bushes...) or surrounding traffic. The trend of lowering the weight of vehicles imposes a stronger need for understanding the coupling between crosswind stability, the vehicle external shape and the dynamic properties.

Means for reducing fuel consumption of ground vehicles can also conflict with the handling and dynamic characteristics of the vehicle. Streamlined design of vehicle shapes to lower the drag can be a good example of this dilemma. If care is not taken, the streamlined shape can lead to an increase in yaw moment under crosswind conditions which results in a poor handling.

The development of numerical methods provides efficient tools to investigate these complex phenomena that are difficult to reproduce exper- imentally. Time accurate and scale resolving methods, like Detached- Eddy Simulations (DES), are particularly of interest, since they allow a better description of unsteady flows than standard Reynolds Average Navier-Stokes (RANS) models. Moreover, due to the constant increase in computational resources, this type of simulations complies more and more with industrial interests and design cycles.

In this thesis, the possibilities offered by DES to simulate unsteady crosswind aerodynamics of simple vehicle models in an industrial framework are explored. A large part of the work is devoted to the grid design, which is especially crucial for truthful results from DES. Additional concerns in simulations of unsteady crosswind aerodynamics are highlighted, especially for the resolution of the wind-gust boundary layer profiles. Finally, the transient behaviour of the aerodynamic loads and the flow structures are analyzed for several types of vehicles. The results simulated with DES are promising and the overall agreement with the experimental data available is good, which illustrates a certain reliability in the simulations. In addition, the simulations show that the force coefficients exhibit highly transient behaviour under gusty conditions.

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Abstract

Effekten av plötsliga sidvindar behöver beaktas vid utformningen av väghållnings- och dynamikegenskaperna hos ett fordon, särskilt då for- donens vikt minskas. Väg- och spårfordon utsätts ofta för plötsliga sidvindar som uppstår genom omgivande topografi (slättland, skogar, tunnlar, hinder...), väderförhållanden eller omgivande trafik. Tyvärr kan en minskning av ett fordons bränsleförbrukning vara i konflikt med goda väghållnings- och dynamikegenskaper. Ett strömlinjeformat fordon med avsikt att reducera luftmotståndet är ett bra exempel på en sådan konflikt, eftersom strömlinjeformad geometri kan höja girmomentet vilket i sin tur medför en dålig väghållning.

Numeriska metoder utgör idag effektiva verktyg för att studera komplexa fenomen som är svåra att reproducera i t.ex. vindtunnelexperiment.

Storskaliga simuleringar, mer precist DES (Detached-Eddy Simulation), är intressanta därför de ger en bättre beskrivning av de instationära fenomenen. Dessutom, tack vare den konstanta ökningen av beräkningska- paciteten hos dagens datorer, blir den här typen av simuleringar mer och mer intressanta för industritillämpningar.

I den här avhandlingen studeras möjligheterna att använda DES för att simulera instationär sidvindsaerodynamik för enkla fordonsgeometrier i en industriell inramning. En stor del av avhandlingen fokuserar på design av beräkningsnätet, då detta är av yttersta vikt för tillförlitliga resultat från DES. Även andra parametrar som behöver beaktas vid simulering av instationär sidvindsaerodynamik belyses i denna avhandling, t.ex. nödvändigheten av god upplösning av vindbyarnas gränsskiktsprofil.

Slutligen är de instationära aerodynamiska krafterna och strömningsstruk- turerna analyserade för flera typer av fordon. Resultaten som erhålls från DES beräkningarna är lovande och stammer i stort väl överens med de experimentella data som finns tillgängliga, vilket implicerar en viss trovärdighet i de beräknade resultaten. Därtill visar beräkningarna att de aeroydnamiska lasterna är högst transienta då fordonet befinner sig i byig vind.

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Abstract

Les véhicules terrestres sont soumis à des vents latéraux de différentes origines telles que la météorologie, la topographie du milieu environnant (plaines, forêts, tunnels, haies...) et le trafic ambiant qui donnent à ces vents leur caractère instationnaire. La tendance voulant réduire le poids des véhicules impose de comprendre les mécanismes liant la stabilité aux vents latéraux, la forme extérieure et les propriétés dynamiques. Les moyens permettant de réduire la consommation des véhicules terrestres peuvent aussi rentrer en conflit avec la tenue de route. Ajuster le style d’une voiture pour en réduire la traînée est un bon exemple de ce dilemme. Si la conception n’est pas réalisée avec attention, le design à faible traînée peut entraîner une augmentation du moment de lacet, responsable de la détérioration de la tenue de route lors de vents latéraux.

Le développement des méthodes numériques a fourni des outils efficaces pour étudier ces phénomènes complexes, difficiles à reproduire expérimen- talement. Les méthodes de simulation aux grandes échelles, plus précisé- ment DES (Detached-Eddy Simulation), ont un intérêt particulier étant donné qu’elles offrent une meilleure description des fluides instationnaires.

En outre, grâce aux progrès constants des ressources numériques, ce type de simulations s’accorde de plus en plus avec les intérêts et les temps de rotations des industriels.

Dans cette thèse¹, les possibilités offertes par les DES pour simuler l’aérodynamique des véhicules simples, dans un cadre industriel, soumis à des vents latéraux instationnaires sont étudiées. Une large partie de ce travail est dédiée à la conception du maillage qui est particulièrement cruciale afin d’obtenir des résultats convenables avec les DES. Par ailleurs, le raffinement du maillage ainsi que la résolution du profil des rafales de vent sont également étudiés. Finalement, le comportement instationnaire des forces aérodynamiques est analysé pour différents types de véhicules.

Les résultats simulés avec les DES sont prometteurs et concordent bien avec les données expérimentales disponibles, ce qui illustre une certaine fiabilité dans ces simulations. De plus, les forces aérodynamiques exhibent un comportement fortement instationnaire lors de rafales de vent.

1Comprendre ‘Licentiate’ suédois et non ‘doctorat’

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Dissertation

A Licentiate of Technology is a intermediate Swedish academic degree that can be obtained half-way between the MSc and the PhD. While less formal than a Doctoral Dissertation, examination for the degree includes writing a thesis and a public thesis defence.

The work presented in this Licentiate was carried out within the ECO² Vehicle Design centre at the Department of Aeronautical and Vehicle Engineering, the Royal Institute of Technology (KTH) in Stockholm, Sweden.

This thesis consists of two parts. The first part gives an overview of the research with a summary of the performed work. The second part collects the following published scientific articles:

Paper A. T. Favre, G. Efraimsson and B. Diedrichs, "Numerical Investigation of Unsteady Crosswind Vehicle Aerodynamics using Time- Dependent Inflow Conditions", in Seventh World MIRA International Vehicle Aerodynamics Conference, England, ISBN 978 1 906400 05 7, October 2008

Paper B. T. Favre and G. Efraimsson, "An assessment of Detached- Eddy Simulations of unsteady crosswind aerodynamics of road vehicles".

Submitted to Flow, Turbulence and Combustion, September 2009

Paper C. T. Favre and G. Efraimsson, "Effects of deterministic wind gusts on unsteady crosswind aerodynamics of road vehicles".Internal Report number TRITA-AVE-2009:76, ISSN 1651-7660, September 2009

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Contents of this thesis has been presented in the following conference:

Paper A has been presented at the following conference:

• Seventh World MIRA International Vehicle Aerodynamics Confer- ence, Coventry, England (UK), October 2008

Parts of the work from Paper B has been presented at the following conferences:

• Third Symposium Hybrid RANS/LES methods, Gdansk, Poland (PL), June 2009

• Svenska Mekanikdagarna, Stockholm, Sweden (SE), June 2009

Other papers not included in the Licentiate

Proceeding T. Favre, B. Diedrichs and G. Efraimsson, "Detached- Eddy Simulations applied to Unsteady Crosswind Aerodynamics of Ground Vehicles", 3^𝑟𝑑 Symposium on Hybrid RANS-LES Methods, Gdansk, Poland 10-12 June 2009. To be published in Notes on Numerical Fluid Mechanics and Multidisciplinary Design Series, Springer.

Report T. Favre and D. Thomas, "Transient Crosswind Stability of Vehicles - A Literature Survey", in preparation, TRITA-AVE 2007:60.

Report M. Sima, T. Favre and D. Thomas, "Pilot Study in Scandinavia, the example of the West Coast Line.", AOA Internal report, Confidential, 080729-AOA-WP2.5, 2008.

Division of Work Between the Authors

Paper A. Favre created the computational meshes, performed the computations, and discussed the results with Efraimsson and Diedrichs.

Favre wrote and presented the paper under the supervision of Efraimsson and Diedrichs.

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Unsteady Crosswind Aerodynamics of Vehicles v

Paper B. Favre created the computational meshes, performed the computations, discussed the results and wrote the paper together with Efraimsson.

Paper C. Favre created the computational meshes, performed the computations, discussed the results and wrote the paper together with Efraimsson.

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Acknowledgements

This study is carried out within the crosswind project of the Centre for ECO² Vehicle Design. The study has benefited from computing resources at the Centre for Parallel Computers, (PDC) at KTH, which are granted by the Swedish National Infrastructure for Computing (SNIC).

My supervisor, Gunilla Efraimsson, is gratefully acknowledged for the time she devoted to me, for her guidance, advice and joyful support during the whole time I have worked at KTH. I am also thankful to Dr. Ben Diedrichs for the profitable discussions and his co-supervision.

Dr. JP Howell (Tata Motor) is acknowledged for the useful discussions concerning the Windsor model and the MIRA Ltd for the permission of using picture 2.4.

For the computer supports, PDC (Ulf Andersson, Elisabet Molin and the PDC support), Pär Ekstrand from the Mekanik Department and Urmas Ross from MWL, are greatly acknowledged.

The great working atmosphere wouldn’t be possible without the other PhD students at the AVE department, thanks in particular to Adrien, Dirk, Martin F., Tomas, Dima, Sathish, Hans, Nicolas F., Mac, Karl, Rémi and Crispin.

The life in Stockholm wouldn’t be that great without Martin, Nicolas, Janne or Cécile. Merci !

Without your daily support, your kindness or your different way to see life, Sveta, it would have been much tougher for me to make it.

Et pour ceux qui ont toujours crû en moi, Gérard, Joëlle, Philippe, Viviane et Anne-Laure, vous dire seulement merci est bien trop peu.

I am also particularly grateful to Ken Aston for the invention of the famous red and yellow penalty cards after the football world cup of 1966.

A surprise will be given to the first who will find how many times the word

"wind" is written in this thesis ...

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Nomenclature

Δ Grid spacing

𝜖 Dissipation

∇ Gradient operator

𝜔 Dissipation rate

𝜌 Density of air

˜

𝜈 Eddy viscosity

𝐶𝐹 Force coefficient 𝐶𝑆 or 𝐶𝑆𝑖𝑑𝑒 Side force coefficient

𝐶_𝐷𝐸𝑆 Adjustable constant in DES, usually 0.65 𝐶𝐷 or 𝐶𝐷𝑟𝑎𝑔 Drag coefficient

𝐶𝐿 Lift coefficient

𝐶𝑃 𝑖𝑡𝑐ℎ Pitch moment coefficient 𝐶_{𝑅𝑜𝑙𝑙} Roll moment coefficient 𝐶_{𝑌 𝑎𝑤} Yaw moment coefficient

𝑅𝑒 Reynolds number

𝑢𝑖 i^𝑡ℎ component of the velocity vector A, 𝐴𝑏𝑥 Frontal area

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x T. Favre

B Vehicle width

CFD Computational Fluid Dynamics CPU Central Processing Unit or processor d Distance to the walls

D-DES Delayed Detached-Eddy Simulation DES Detached-Eddy Simulation

DNS Direct Numerical Simulation

F Force

H Vehicle height

h Vehicle height

k Turbulent kinetic energy KTH Kungliga Tekniska Högskolan L, 𝐿𝑏𝑥 Vehicle length

LES Large Eddy Simulation LUD Second order upwind scheme

M Million

MARS Advection and Reconstruction Scheme

p Pressure

PDC Centre for Parallel Computers at KTH RANS Reynolds-Average Navier Stockes S Local deformation rate

S-A Spalart Allmaras turbulence model SEVM Radiused-Edges Vehicle Model

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Unsteady Crosswind Aerodynamics of Vehicles xi

SEVM Sharp-Edges Vehicle Model SGS Sub-Grid-Scale

SST Shear Stress Transport

SUV Sport Utility Vehicle, similar to a station wagon U Streamwise component of the velocity

URANS Unsteady RANS

W Spanwise component of the velocity x Streamwise coordinate

y Vertical coordinate

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Part I

Overview and Summary

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Chapter 1

Introduction

The decision to reduce the emission of six greenhouse gases, including carbon dioxide, has been taken in order to limit the climate change since the Kyoto protocol of 10 December 1997. In 1998, European, Japanese and Korean manufacturers signed with the European Commission a voluntary agreement to achieve an objective for the average specific emissions of CO2

at 140𝑔/𝑘𝑚 mainly due to technological developments. Then, in 2000, the European Commission via the decision No 1753/200/EC¹, introduced a strategy to impose the emissions at 120𝑔/𝑘𝑚² for the passenger cars by 2005 (or 2010 the latest). As a demonstration of the challenges in this regulation, the average specific emissions of CO2 was estimated around 186𝑔/𝑘𝑚 in 2000. In addition, the increasing cost of oil since 1973 and the first oil crisis are drivers for technological solutions for reducing the emissions. Therefore, efforts on reducing the fuel consumption became natural.

Lowering the air resistance, or drag, of the road vehicle is one of the technical achievements. However, styling trends to reduce drag tends to increase the yaw moment, Howell (1993), which in turns, is responsible of a poor handling, Hucho (1998). It is therefore essential to simultaneously study all the aerodynamic properties of a car including

1http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=CELEX:52001DC0643:EN:NOT last access: 04/09/2009

2The Commission is aiming to fill the gap between 140 and 120𝑔/𝑘𝑚 by informing the customers and tax measures.

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crosswind conditions. However, both experimental and computational methods need to be improved to properly deal with transient crosswinds.

Crosswind characteristics of a vehicle are usually described by two aerodynamic quantities, the side force and the yaw moment. The side force originate from the difference in pressure in the windward and leeward sides of the vehicle, Cairns (1994). High velocities around the leeward leading edge of the vehicle produces large negative pressure and hence is mainly responsible for the side force. Negative pressure is also observed at the rear, mainly depending of the design, and the unbalance in pressure between the front and the rear leads to a yaw moment tending to turn the vehicle front away from the crosswind. Baker (1986-1) considers this rotational instability as the only concern for passenger car safety. The two other types of instabilities, overturning and sideslip identified by Baker are not applicable for passenger cars, but more for trains and high-sided vehicles.

Crosswind originates from weather conditions, topology of the surroundings as well as the overall traffic. These conditions are in general too complex to be modelled properly. The gusts affecting passenger cars are mainly due to the surrounding topography since they may significantly increase the local crosswind component, Narita and Katsuragi (1981). These severe strong crosswind conditions can lead to accidents, for road, SHK (2001), and rail vehicles, Diedrichs (2006). Moreover, winds between 2.5 𝑚/𝑠 and 10 𝑚/𝑠 will already provoke steering corrections while driving on a motorway, Howell (1993). Thus, driver reaction and correction will have an impact on the dynamic behaviours of the car. Jarlmark (2002) found several combinations of driver behaviour and suggested that a vehicle should be designed for every driver pattern. After studying the correlation between drivers experience and reactions under crosswind, he also concluded that the sensitivity or ’feel’ for the movement of the vehicle can be enhanced by training. However, in contrast, the reaction time of the driver is not improved with training. Moreover, considering that driver corrections reduce lateral deviation, the crosswind performance can significantly be improved by the modification and optimization of the steering-wheel feel, Juhlin (2009).

Howell (1993) characterises the crosswind sensitivity by studying the yaw rate response to a given wind input. It is seen that the yaw rate increases

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Unsteady Crosswind Aerodynamics of Vehicles 5

inversely with the tyre cornering stiffness, the wheelbase and the vehicle mass. The yaw rate also increases directly with the aerodynamic yaw moment around the neutral steering point. For a given vehicle class, only the aerodynamic yaw moment is left to be optimized, mostly by shape design.

Figure 1.1: On-road and wind-tunnels wind profiles for crosswind. Figure from Cairns (1994).

Baker (1991) provides a dimensional analysis for the crosswind properties and defines requirements for a proper crosswind modelling. The aerodynamic forces and moments are functions of the vehicle geometry and velocity, the fluid properties and the wind characteristics. Therefore, the Reynolds number, the model geometry (especially its proportions), the yaw angle, the wind characteristics (velocity and turbulence variation with height) and the skewed boundary layer profile are essential parameters for elaborating realistic crosswind tests. The velocity variation with height of the wind and the skewed boundary layer are shown in Fig. 1.1 and considered are difficult to simulate, Baker (1991). Indeed, among the ways of making wind tunnel tests, the dynamic yaw tests in conventional wind tunnel and the test using oscillating aerofoils placed upstream of a model produce unrealistic variation in yaw angle and non-uniform flow respectively, Cairns (1994). None includes the effect of a realistic boundary

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layer. Further experimental setup using conventional wind tunnel and an impulsive gust from a shuttered adjacent nozzle suffers from practical difficulties preventing critical crosswind scenarios to be tested, Docton and Dominy (1996). Finally, a crosswind track in conjunction with a boundary layer wind tunnel, (Baker, 1986-2; Bocciolone et al., 2008), is believed to be the best experimental available for matching realistic crosswind scenarios, see Cairns (1994). However, this type of experimental track are still under development and further improvement or tests are usually required (Cairns, 1994; Chadwick, 1999; Bocciolone et al., 2008). Recent experimental setups concerning the transient loads on vehicles driven on bridges exposed to intermittent gusting, from a wind tunnel specifically designed for this, are giving promising results, (Kozmar, 2009). Finally, in industrial design loops, crosswind properties are most aften evaluated using yawed vehicles in steady crosswind conditions inside a wind tunnel facility.

Figure 1.2: Crosswind properties of the typical car designs. Figure from Cairns (1994).

As highlighted previously, most of the initial knowledge in crosswind aerodynamics has been investigated using a steady approach. According to Hucho (1998), the side force is not as important as the yaw moment in influencing the crosswind sensitivity. Figure 1.2 shows the side force and

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yaw moment for three traditional car designs. Despite its larger side force, a squareback, with its lower yaw moment, is a more favourable design than fast or notchbacks. The strength of C-pillar vortices in the rear- slant of the two latter designs are responsible for this higher yaw moment values, Cairns (1994). In addition, the well rounded rear surfaces is found to increase the yaw moment, Howell (1993). The design of the A-pillar is of great importance as well since the control of the negative pressure in this area has a direct impact on both side force and yaw moment, Gilhaus and Renn (1986). Hucho (1998) suggests to use an aerodynamic device at this location which causes flow separation at yaw angle higher than 10^𝑜. Hence, low-drag design will dominate at lower yaw angle and limit suctions at higher yaw angle. Original solution like the ’aeroslit’, Sumitani (1990), may provide significant improvement for the lateral deviation and yaw rate properties of the vehicle. It is worth noticing than directional stability is influenced by the lift and pitching moment, and therefore shapes optimizing these quantities are beneficial. Howell (1993) found that certain low-drag designs may not have conflict with crosswind sensitivity such as the body side shaping (i.e. planform curvature of the body side).

Using experimental tracks similar to the one mentioned previously, Kobayashi and Yamada (1988), Cairns (1994) and Chadwick et al. (2001) for road vehicles, or Baker (1986-2) for rail vehicles, transient crosswind behaviours are analysed and lead to similar conclusions. Strong transients are observed in the yaw moment for the vehicles. Peaks are usually observed after 1 to 2 vehicle lengthes in the gust. Stabilisation of the loads towards steady crosswind values are observed after several lengthes in the gusts. The side force exhibits less pronounced peaks, mostly depending on the shape of the vehicle front. Sharp leading edges leads to well pronounced peaks whereas well rounded edges imply a smoother variation and no peak at all in many cases.

Initial numerical investigations have been carried out to reproduce already existing experiments involving steady crosswind aerodynamics (Hemida et al., 2005; Diedrichs, 2006; Bocciolone et al., 2008). However, the relative flexibility of numerical simulations propose larger possibilities than experiments for unsteady crosswind. Thus, Docton and Dominy (1996) used time dependent inlet boundary data on the lee side for 2D computational domain in order to match a similar experimental setup. A

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recent simulation by Krajnovic (2009) investigate the flow around an ICE2 train subjected to a gust with Detached-Eddy Simulations (DES) and using a similar side boundary condition for the gust: a function in space which varies in time. Demuth and Buck (2006) used periodic boundary conditions on the sides and a cosine-shape gust to investigate the crosswind properties of a production car.

Modern numerical techniques, such as DES, allows a better and accurate representation of the transient aerodynamic phenomena without involving unrealistic numerical resources, Spalart (1997). These advanced transient simulations require fine mesh spacing in the regions of separated flow and the mesh spacing may have an direct impact on the quality of the solution calculated. Therefore, a careful assessment of the mesh has to be realized.

Not only the flow field has to be studied but the quality of the advected crosswind inflows that may vary depending on the mesh quality which in turn provide different loads on the vehicles.

The objective of this work is to build a relevant and reliable numerical setup in order to investigate transient crosswind simulations. In addition, critical gust scenarios are to be defined and tested. Different vehicle shapes are also evaluated in order to relate the unsteady behaviour of the aerodynamic loads to the shape features of the considered models.

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Chapter 2

Vehicle and gust modelling

In this chapter, the geometries of the two different types of vehicles considered in this thesis are presented. Also, the numerical models for wind gusts used as boundary data for the unsteady simulations are described.

2.1 Geometries considered

In paper A, transient crosswind flows on two simple vehicle models are studied. The proportion of these models are similar to the proportions of a SUV. As pointed out in Chapter 1, steady crosswind analyses conclude that a larger side area implies a larger side force. This is not relevant for the yaw moment where the design itself (front and rear shape, edges radius of curvature) has the most influence. An illustration of this statement are the two simple box designs that have the same side area but different radius of curvature on the edges. These two models have been tested with unsteady crosswind using a crosswind track at the Cranfield University, UK, Chadwick et al. (2001). The side force magnitudes are about the same but the yaw moments have a different magnitudes and time histories during a deterministic gust.

The experimental setup used at the Cranfield University is described in Chadwick et al. (2001). Figure 2.2 illustrates the setup. The vehicle model is propelled at a constant speed on a track through the 2.4 𝑚×1.2 𝑚 boundary layer wind tunnel exhaust. The vehicle models are equipped

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(a) SEVM (b) REVM

Figure 2.1: The simple vehicle models studied at Cranfield University (UK) and in the paper A of this thesis.

with pressure sensors to visualise the surface pressure around the vehicle models. The data collected by the load balance were filtered with a low-pass Hamming window at 30 Hz. The filter properties were selected to eliminate track induced vibrations. The repeatability had been demonstrated in previous work Cairns (1994).

Figure 2.2: The track, model and wind tunnel exhaust, top and side views, from Chadwick et al. (2001).

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The same models and setup are studied in paper A of the present thesis.

The two models are referred as the Sharp-Edges Vehicle Model, SEVM, and the Radiused-Edges Vehicle Model, REVM. The streamwise length (box length, 𝐿𝑏𝑥), spanwise length and height (ℎ) are 0.48 𝑚, 0.2 𝑚 and 0.2 𝑚, respectively. The ground clearance is 0.15 ⋅ ℎ. The radii, 𝑟, of the REVM edges are 𝑟 = 0.1 ⋅ ℎ. The flow velocity used is the same as in the experiments of Chadwick et al. (2001), that is 13 𝑚/𝑠. The corresponding Reynolds number using the square-root of the frontal area, 𝐴𝑏𝑥, and the viscosity of air, is 𝑅𝑒𝐴𝑏𝑥 = 1.7 ⋅ 10⁵. Using 𝐿𝑏𝑥 as reference length yields a 𝑅𝑒𝐿_𝑏𝑥 of 4.1 ⋅ 10⁵. For crosswind applications, the magnitude of the crosswind velocity is 4.8 𝑚/𝑠 that leads a 𝑅𝑒𝐿_𝑏𝑥 of 4.4 ⋅ 10⁵. The flow around the SEVM is therefore highly separated whereas the radiused edges of the REVM tend to prevent large separation bubbles.

In paper B and C, a generic model of car, the so-called Windsor model Fig. 2.3, has been selected as a more realistic ground vehicle geometry. A longer geometry like a truck or a rail vehicle has a higher level of complexity for DES than a car since the boundary layers

Figure 2.3: The Windsor models.

are more developed and the transi- tion RANS/LES has to be carefully assessed. This motivated the use of a car like geometry as a benchmark model. The Windsor model has extensively been used in industry mainly to study the influence of the rear design of a car under different flow conditions. Most commonly, the backlight angle is varied while

the slant length remain the same. It is seen that the model with a rear angle of 15^𝑜 has the lowest drag whereas the 30^𝑜 configuration has the highest. In addition, the squareback version has the largest side force and the lowest yaw moment, Fig. 1.2.

In this thesis, the Windsor model with the squareback configuration is studied since the sharp trailing edges help to fix the separation at the rear. This geometry, unlike the Ahmed body, e.g. Guilmineau (2008), presents a realistic front for crosswind simulations that also prevents front separation. The flow velocity used is the same as in the experiments

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of Howell and Le Good (2005), that is 27 𝑚/𝑠. The car has a length 𝐿 of 1.045 𝑚, a width 𝐵 of 0.39 𝑚 and a height 𝐻 of 0.29 𝑚.

Figure 2.4: Squareback model (cour- tesy of MIRA Ltd).

The corresponding Reynolds number using the square-root of the frontal area 𝐴 and the viscosity of air, is 𝑅𝑒𝐴= 6.0 ⋅ 10⁵. Using 𝐿 as reference length yields a 𝑅𝑒𝐿of 1.9⋅

10⁶. For crosswind applications, the magnitude of the crosswind velocity is 9.8 𝑚/𝑠 that leads a 𝑅𝑒𝐿 of 2.0 ⋅ 10⁶. Howell and Le Good (2005), made experiments of the Windsor model without ground attachment, Fig. 2.4. The streamlined overhead is not included in the CFD model. Howell conducted headwind experiments with this model and the value for the drag coefficient is corrected to take into account the blockage of the wind tunnel. Cairns (1994) used a scaled Windsor model (with ground attachment) for crosswind applications. The value of the side force coefficient is compared to the calculated one.

2.2 Gusts models

Modelling crosswind gusts is a challenge since gusts can originate from

Figure 2.5: The crosswind velocity as a function of the non- dimensional length.

different situations. Both surrounding topography and weather conditions would require a streamwise and a vertical variation of the wind velocity. Gusty weather is also highly stochastic and such conditions can not be represented yet with CFD. However, deterministic models can be applied as boundary data for CFD models and the models considered in this thesis are introduced here- after.

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Cooper (1984) provides ratios of the approximate dimensions of ground vehicles relative to the typical atmospheric turbulence, i.e. gust length.

The ratios are reported in Table 2.1. In the experiments described Table 2.1: The approximate dimensions of vehicles relative to the length scale turbulence, i.e. the gust streamwise length, from Cooper (1984) and for the models considered in this thesis.

Vehicle ^𝑥𝐿𝑢(𝑚) 𝐿/^𝑥𝐿𝑢 𝐻/^𝑥𝐿𝑢 𝐵/^𝑥𝐿𝑢 𝐻0/^𝑥𝐿𝑢

Car 30 0.1 − 0.18 0.04 0.05 0.006

Bus 45 0.2 − 0.3 0.06 0.05 0.007

Truck 45 0.2 − 0.5 0.08 0.056 0.01

Train 45 0.5 0.08 0.06 0.007

(passenger coach)

Boxes 2.4 0.2 0.083 0.083 0.0125

Windsor 5.225 0.2 0.056 0.075 0.0096

Windsor 7.315 0.14 0.04 0.05 0.007

by Chadwick et al. (2001), a vehicle is propelled through a wind tunnel exhaust which is 5 times longer than the vehicle. As reported in section 2.1, the geometries are representative of a SUV and the values in Table 2.1 are not matching any of the vehicles considered by Chadwick et al. (2001).

Table 2.1 also shows that the ratios for the Windsor model, with a gust of 5𝐿(5.225 𝑚), are close to the typical values for a car. However, it is clear that the gust is too short to be representative of the typical dimensions.

Figure 2.6: Approximation of the atmospheric boundary layer close to the ground.

Therefore a gust of 7𝐿 (7.315 m) is also tested, Fig. 2.5.

Several wind gusts are tested along this thesis, especially in Paper C.

In order to match the Cranfield experimental gust, a first model with an overall length of 5𝐿 is used, Fig. 2.5. The cosine functions model the mixing zone at the entrance and exit of the gust and have been chosen according to the measurement presented in Schlicht- ing (1960). However, the steepness

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14 T. Favre

of the model, which is mathematically the period of the cosine function, is arbitrary chosen to be approx. 1.5𝐿 and is varied in Paper C (to 1𝐿 and 5𝐿), Fig. 2.5. The maximum speed corresponds to 20^𝑜 yaw angle (arctangent of the crosswind speed over the vehicle velocity). The ground vehicles are moving in the atmospheric boundary layer and therefore, the wind also has a vertical variation. The velocity profile will mainly be influenced by the surroundings and wind models that take these surrounding into account using classification, defined by Eurocode (1995), and are reported in Table 2.2. A simple approximation of the vertical profile, well known in wind engineering, Dyrbye and Hansen (1997) and Bocciolone et al. (2008) is

𝑈 (𝑦) = 𝑈𝑟𝑒𝑓

( 𝑦 𝑦𝑟𝑒𝑓

)𝛼

(2.1) The vertical profiles for the class I, II and III are shown in Fig. 2.6. The profiles for class I and II are found applicable for the work in this thesis.

Table 2.2: Classification of terrain categories.

Class. Description 𝛼

Class I Open land with little vegetation 0.12 Class II Farmland with few houses and trees 0.16 Class III Suburban areas or forest 0.22

Class IV Urban areas 0.30

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Chapter 3

Computational Methods

Accurate method for resolving the unsteady flow fields such as DES gives the opportunity to calculate unsteady flows with reasonable computational effort. This Chapter introduces the methodology used for solving the incompressible Navier-Stokes equations that is the principles of DES, the type of meshes, the tools for analysing the calculated flow and the numerical resources available for the work presented in this thesis.

3.1 Flow physics

The commercial solver STAR-CD v4.08 developed by CD-Adapco¹is used for all simulations reported in this thesis. In the code, the Navier-Stokes equations are solved using the finite volume method. Due to the low speed of the ground vehicle considered, the flow is assumed to be described by the incompressible Navier-Stokes equations:

∂𝑢_𝑖

∂𝑡 + 𝑢_𝑗∂𝑢_𝑖

∂𝑥𝑗

= −∂𝑝

∂𝑥𝑖

+ 𝜈∇²𝑢_𝑖 𝑖 = 1, 2, 3 (3.1)

∂𝑢_𝑖

∂𝑥𝑖

= 0 (3.2)

Equations 3.1 are the momentum equations representing the advection of the flow whereas the Equation 3.2 is the continuity equation representing the conservations of mass.

1www.cd-adapco.com

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16 T. Favre

3.2 Turbulence models

In Spalart (1997), it is concluded that Reynolds-Average Navier-Stokes (RANS) methods seem insufficient for transient flows. Instead, Spalart proposed a new scale resolving method, DES, that appears to be more suitable. DES joins the modelling efficiency of RANS close to the walls and the scale resolution of Large-Eddy Simulation (LES) far from the wall, especially in regions of separated flows. The success of this method provided an extensive set of published simulations, see e.g. Travin et al.

(1999, 2002) and Constantinescu and Squires (2001). An update of DES, called Delayed-DES (D-DES), Spalart (2006), is the current standard in most of the codes available. Although DES is recognized for its reliability for giving good results, Spalart (2001), there is risks of excessive dissipation in the LES regions and on erroneous location of separation.

The formulation of DES was originally defined by Spalart (1997). As stated above, the global idea is to use a simple RANS model, the Spalart-Allmaras (S-A) model, close to the wall and the traditional Smagorinsky’s as a Sub- Grid-Scale (SGS) model in the separated flows where the LES applies. In the S-A model Spalart (1992), the eddy viscosity ˜𝜈 is adjusted to scale with the local deformation rate 𝑆 and 𝑑 such that: ˜𝜈 ∝ 𝑆𝑑², where 𝑑 is the distance to the closest wall. In the Smagorinsky model, Smagorinsky (1963), the eddy viscosity scales with 𝑆 and the grid spacing Δ, such that:

˜

𝜈 ∝ 𝑆Δ². Therefore, if the term 𝑑 in the S-A model is replaced by ˜𝑑, defined as:

𝑑 ≡ (𝑑, 𝐶˜ 𝐷𝐸𝑆Δ), (3.3)

this acts as S-A in the regions where 𝑑 ≪ Δ, and as a SGS model when Δ ≪ 𝑑. Traditionally, Δ is defined as the largest spacing in all three directions which ensures 𝑑 ≪ Δ in the boundary layers where usually the prismatic layer cells are highly anisotropic. This model has only one adjustable constant 𝐶𝐷𝐸𝑆 and is set at 0.65 in this study.

Especially for geometries where the boundary layer becomes large enough, the model can switch to LES and leads to poor modelling in these areas.

Therefore, Spalart (2006) presented an extension of DES, called Delayed- DES, (D-DES), to be more robust for ambiguous grid design. The D-DES is used throughout this thesis.

In paper A, other RANS models have been used for DES, especially the 𝑘 − 𝜔 𝑆𝑆𝑇 from Menter (1992), for the REVM. This model was intended to improve the existing 𝑘 − 𝜔 model by removing its strong dependency

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on arbitrary freestream values. This was resolved by keeping the 𝑘 − 𝜔 formulation close to the wall and by gradually switching to the 𝑘−𝜖 towards the end of the boundary layers and in far field. The Shear Stress Transport (SST) improvement, relying on the assumption that the principal shear- stress is proportional to the turbulent kinetic energy, enhanced the 𝑘 − 𝜔 ability to predict flow in adverse pressure gradients.

3.3 Grid structure and spacial discretization

The computational meshes are composed of unstructured polyhedral cells.

Characteristics and benefits of polyhedral cells compared to tetrahedral cells are described in Peric (2004). Polyhedral cells contain more faces than tetrahedral or hexahedral cells (typically, 1M Poly cells ≡ 2M hexa

≡3M tetra for the same amount of faces). The mesh topology has been designed for DES simulations according to the guidelines in Spalart (2001).

A homogeneous core of fine cells is placed around the vehicle model, Fig. 3.1

Figure 3.1: Topology of the computational domain used for the Windsor model, papers B and C.

or Fig. 3.2(a). Typically, this area extends down to 1𝐿 behind the vehicle

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18 T. Favre

models. In this area, the flow structures are simulated using LES and demands a fine spatial discretization. Several refinement zones are created to reduce the far field cell size down to the finest core of the mesh, see Fig. 3.1 or Fig. 3.2(b).

(a) (b)

Figure 3.2: Polyhedral mesh of the Windsor model. (a) Successive refinement zones. (b) Fine vs Coarse meshes close to the car model.

The numerical schemes for discretization in space used in this thesis are a second order accurate upwind (LUD), Price (1966), and the Monotone Advection and Reconstruction Scheme (MARS). The MARS scheme is developed by CD-Adapco and is a scheme constituted by a reconstruction step and an advection step. The MARS scheme is used in paper A whereas LUD is utilised in papers B and C. It should be mentioned that STAR-CD restricts the discretization of the continuity equation to Central Difference (CD).

3.4 Flow visualisation and force coefficients

The coherent structures of the flow, defined in e.g. Hussain (1986), are investigated by using the second invariant of the velocity gradient, the so- called 𝑄 criterion. The second invariant of the velocity gradient Δ𝒖 is

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defined for incompressible flow as

𝑄 = 1

2(∥ Ω ∥²− ∥ 𝑺 ∥²) (3.4) where ∥ Ω ∥²= 𝑡𝑟[ΩΩ^𝑡]^1/2 and ∥ 𝑺 ∥²= 𝑡𝑟[𝑺𝑺^𝑡]^1/2; 𝑺 and Ω are the symmetric and antisymmetric component of Δ𝒖. Thus 𝑄 can be seen as the local balance between the rotation rate relative to the strain rate. Positive and high values of 𝑄 correspond to a high level of flow vorticity. Jeong and Hussain (1995) demonstrates that this is a necessary condition for vortex cores. In addition, to ensure a sufficient condition, the pressure shall decrease in this area of the flow. More details on the theoretical aspects regarding flow visualization can be found in Chakraborty et al.

(2005). However, it should be pointed out that the pressure condition is subsumed in 𝑄 > 0.

The component of the aerodynamic loads projected in the vehicle axis, are the drag in the streamwise direction, the side force in the lateral crosswind direction and the lift in the upward vertical direction. The non-dimensional coefficients are based on the vehicle and the crosswind velocity as 𝐶𝐹 =

𝐹

1

2𝜌𝑈²𝐴 for the force, where 𝐹 is the force considered, 𝐶𝐹 the coefficient associated, 𝜌 the density of air, 𝐴 the projected frontal area of the vehicle model and 𝑈 the velocity considered.

3.5 Computational Resources

The work benefited from the computational resources at the Centre for Parallel Computers, PDC², at KTH. The characteristics of the two clusters used are:

• Lenngren: Dell consisting of 442 PowerEdge 1850 servers. Each node have two 3.4GHz "Nocona" Xeon processors and 8GB of main memory. A high performance Infiniband network from Mellanox is used for MPI traffic.

2www.pdc.kth.se

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20 T. Favre

• Lucidor 2: Lucidor is a distributed memory computer (a cluster) from HP. It consists of 106 HP rx5670 servers each with four 1.3 GHz Itanium 2 "McKinley" processors. 22 of the nodes have 48 GB of main memory and the rest have 32GB. The interconnect is Myrinet.

The typical time for 45000 time steps achieved for each simulation (DES of headwind) on the three grids is reported in Table 3.1, together with the number of CPU cores used.

Table 3.1: Computational time for three typical simulations and meshes.

Cases Total No. Cluster type Time No.

of cells ×10⁶ in CPU h of CPU cores

Coarse 6.8 𝐿𝑢𝑐𝑖𝑑𝑜𝑟 2 16 000 64

Medium 9.3 𝐿𝑒𝑛𝑛𝑔𝑟𝑒𝑛 9 000 64

Fine 11.3 𝐿𝑒𝑛𝑛𝑔𝑟𝑒𝑛 14 500 84

The author benefited of 16 parallel licenses of STAR-CD from Spring 2007 to Spring 2008, then 20 licenses till winter 2009 and finally 84 up to now.

The total number of CPU hours on the clusters for the simulations is approximately 395 898 that is, taking the 24 672 hours since the first day of employment, a constant simulation on an average of 16 computers...

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Chapter 4

Results and Discussion

The contributions of this thesis is an assessment of the numerical methods in order to treat unsteady crosswind properly. Unsteady crosswind blends headwind and crosswind situations therefore the mesh size and structure is analysed and discussed for all the cases cited. In addition, the unsteady crosswind properties of a realistic simple car model is tested for several wind gust profiles simulating mainly a jet flow that has a ‘step’ shape.

4.1 Simple vehicle geometry

Two simplified vehicle geometries with the same dimensions and based on a sharp edges vehicle model (SEVM) and a radius edges vehicle model (REVM) are subjected to an unsteady gust that has a spacial extension of 5𝐿, 𝐿 being the vehicle length. Aerodynamic loads for SEVM are reported in Fig. 4.1 and for the REVM in Fig. 4.2.

First of all, it is noticeable that the agreement with the experimental data is fair. As anticipated in the literature, the difference between the two models in the side force is less pronounced than the yaw moment. It is found that the massively separated flow due to the sharp edges of the SEVM give a centre of pressure closer to the mid point of the vehicle and therefore reducing the yaw moment. The well-rounded edges efficient for drag reduction (the peak of drag is reduced by 40% compared to the SEVM) penalizes the yawing properties and by consequence the potential handling properties. However, it is observed that the developement of the

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22 T. Favre

Figure 4.1: 𝐶𝑆𝑖𝑑𝑒and 𝐶𝑌 𝑎𝑤 calculated with URANS and DES for the SEVM.

The corresponding values obtained at the Cranfield University, Chadwick et al. (2001), are represented with the hallow circles.

yaw moment is smoother for this geometry whereas the SEVM has strong peaks at the entrance and the exit of the gust.

4.2 The Windsor model

4.2.1 Mesh analysis

As mentioned in section 3.2, DES acts as a LES in the wake region. The theoretical limit of this model as the mesh is refined is a Direct Numerical Simulation (DNS), that is the flow is fully resolved down to the mesh size.

Therefore the influence of the mesh size for any DES is of great interest.

Several levels of refinement in the area close to the car detailed in section 3.3 and illustrated in Fig. 3.2(a), are therefore tested for headwind simulations.

As expected, the finest grid is providing the most extensively resolved flow field. The comparison between the coarse and the fine meshes concerning

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Figure 4.2: 𝐶𝑆𝑖𝑑𝑒and 𝐶𝑌 𝑎𝑤calculated with URANS and DES for the REVM.

The corresponding values obtained at the Cranfield University, Chadwick et al. (2001), are represented with the hallow circles.

𝐶𝑆𝑖𝑑𝑒 and 𝐶𝑌 𝑎𝑤 calculated with DES for the SEVM are also plotted.

the resolved turbulent kinetic energy (k) is shown in Fig. 4.3. As expected, more k is captured with the fine mesh. The peak of production is observed at the end of the recirculation bubble. Also, the coarse mesh fails to predict the experimental drag coefficient by 14% whereas the medium and fine are 4%and 3%, respectively, off the experimental mark.

Steady crosswind simulations have been performed in order to investigate a possible improvement when using a specific extension of the finest cells in the leeward side of the model. However, no significant differences in the results were observed. Both meshes tested yielded very good agreement with the side force coefficient from Cairns (1994) (within 2%) and the calculated flow field are consistent to each other.

Since the ground is moving only in the streamwise direction, the crosswind has a boundary layer that develops. In order to resolve properly this

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24 T. Favre

Figure 4.3: k plotted for the coarse and the fine mesh in the section 𝑦/ℎ = 0.31 of the wake. Vertical variation of k is shown at two discrete points corresponding to 𝑥/𝐿 = 0.5 and 𝑥/𝐿 = 1.

boundary layer, the refinement of the upstream zone, see Fig. 3.1, should be analysed. The original discretization, 0.4 𝑚 (0.38𝐿), is refined to 0.1 𝑚 and 0.07 𝑚 and the velocity profile is shown in Fig. 4.4. The value of 0.1 𝑚is found sufficient to capture the gradient. With this improved grid, the same magnitude for the side force, a slight improvement of the drag force but an impressive 50% change in the lift force, greatly sensitive to the ground clearance flow.

4.2.2 Various wind gust scenarios

A wind gust with the similar spacial extension is implemented for the Windsor model. The aerodynamic loads, the flow and pressure development are shown on Fig. 4.5. It is seen that the development of the

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Figure 4.4: Vertical resolution of the crosswind boundary layer for different levels of refinement of the upstream zone. 0, in the vertical axis refers to the ground and 1 to the under- body of the vehicle.

Values are taken at the centroids of the cells.

Figure 4.5: History of the aerodynamic forces under an unsteady gust together with the development of the flow structures and pressure coefficients.

leeward vortices combined with the large drop of pressure at the leeward A- pillar are responsible for the increase of the side force. The slight decrease

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26 T. Favre

of the frontal pressure is decreasing the drag at the gust entrance. In Fig. 4.5, it is observed that the forces’ history from the simulation using the coarse mesh is not consistent with the two other refined meshes.

Further, by varying different types of wind gusts as explained in Sec. 2.2, the loads exhibit similar trends for all the cases. Figure 4.6 illustrates the aerodynamic loads for wind gust with 5𝐿 as streamwise extension and Fig.

Figure 4.6: Time history of the aerodynamic loads. Only the gusts with 5𝐿 as streamwise extension are considered..

4.7 provides the loads for the baseline and two gusts with a streamwise extension of 7𝐿.

As for the REVM in Sec 4.1, smooth variations in the side force history

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Figure 4.7: Time history of the aerodynamic loads. Only the gusts with 7𝐿 as streamwise extension are considered.

are observed that are partly explained by the well rounded edges in the model’s front. The drag and pitch moment have an opposite behaviour under gusts. Both exhibit very large peaks at gust exit: the drag increase up to 88% whereas the pitch decrease down 63%. Moreover, overshoots up to 18% higher than the steady value are observed for the yaw moment at gust entrance. In general, the steeper the gusts tend to provide higher peaks in the loads as it is illustrated for 𝐶𝑌 𝑎𝑤, 𝐶𝐷 and 𝐶𝑃 𝑖𝑡𝑐ℎ. Therefore, improving the design in order to lower the severe excess of drag in the gust and reduce the overshoot and magnitude of the yaw moment, would enhance the crosswind characteristics of the model.

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Chapter 5

Conclusions and Future Work

The results collected in this thesis illustrate the possibilities of DES to provide reliable results for crosswind without an excessive computational time for simple geometries. It is seen that grid converged results are obtained for the aerodynamic loads. The accuracy of the solutions obtained is fair using industrial tools but can be improved.

Large vortices are found in the leeward side of the vehicles under crosswind.

These structures are well captured and provide reliable side coefficients.

The characteristics of these vortices, together with the large amount of negative pressure at the front, are responsible for the crosswind properties of a given vehicle.

The work presented also demonstrates the necessity of a careful grid design while doing unsteady crosswind simulations. Not only the wake discretization matters but the resolution of the crosswind flow upstream is of importance.

Although the extension of this present work can be utterly wide considering the topic, the author suggest the following extension for his work:

• The improvement of the accuracy of the solution computed with DES

28

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can be realized by changing the cell design. Indeed, the numerics computed on a grid of hexahedrals limit the numerical dissipation and enhance the solution from the LES region of the DES.

• So far, a simple vehicle model has been used to provide information on how to deal with unsteady crosswind aerodynamics. However, sensitivity of different vehicle designs can be carry out based on this study. Indeed the different flows between the typical rear backs of cars is nowadays well known for headwind or steady crosswind, see Hucho (1998). However, the flow history under unsteady crosswind scenarios would provide some depth for the real understanding of the car design. Moreover, the study from the Paper A of this thesis illustrate the noticeable differences between models with two radii of curvature for the edges. A more extensive work with different radii of curvature for a more advance road or rail vehicle geometry can be interesting.

• Also, a natural extension of this work is to apply the knowledge gained to longer vehicles such as trains, trucks or buses. The model used in Maddox et al. (2004) for the truck geometry seems to be serious option. Crosswind are of great concern for high-speed trains, Diedrichs (2006, 2009), Krajnovic (2009), and the Aerodynamic Train Model, Muld et al. (2009), might be of interest for a modern high- speed train geometry to use for the extension of the thesis work to rail vehicles.

• Finally, advanced methods like the Partial Orthogonal Decomposi- tion might be of interest to extract more information from the flow field simulated.

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Chapter 6

Summary of Appended Papers

6.1 Paper A

Numerical Investigation of Unsteady Crosswind Vehicle Aerody- namics using Time-Dependent Inflow Conditions

T. Favre, G. Efraimsson and B. Diedrichs

In this article, simple vehicle models are exposed to an unsteady wind gust. Similarities with the experimental data available are fair, especially considering the basic numerical setup and the few differences in the results between experiments and numerical simulation. The side force and yaw moment are fairly close to the experimental ones. Differences in the pressure distributions on the leeward surface highlights room for further improvements in the numerical simulations. Flow visualisation helped to understand how the flow field develops as well as the difference between the two designs. The vehicle models (SEVM and REVM) have the same side area but different radii of curvature on all the edge: sharp for the SEVM and well-rounded for the REVM. Although the magnitudes of the side force are the practically the same, the yaw moments are quite different:

a higher value is found for the REVM and demonstrate that styling trends that improve the drag can be disastrous for the crosswind properties.

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6.2 Paper B

An assessment of Detached-Eddy Simulations of unsteady crosswind aerodynamics of road vehicles

T. Favre and G. Efraimsson.

An assessment of a proper mesh design in order to perform unsteady crosswind simulation is realized using DES. The squareback version of the so-called Windsor model is used in this study. The typical Reynolds number of the cases studied is 2.0⋅10⁶based on the vehicle length. The level of refinement of the finest cells close to the car is analysed for headwind simulation. Since the ground is moving only in the streamwise direction, the crosswind has a boundary layer that develops. In order to properly resolve this boundary layer, a refinement study of the upstream mesh is also performed. A modification is realized on the mesh to improve the resolution of the leeward side of the car. Finally, a description of the flow structures and force coefficients under an unsteady gust is provided.

6.3 Paper C

Effects of deterministic wind gusts on unsteady crosswind aerodynamics of road vehicles

T. Favre and G. Efraimsson.

In this report, different deterministic models of wind gusts that are varied in the streamwise and the vertical directions are tested on the Windsor model using DES. The 𝑅𝑒𝐿 of the corresponding flow case is 2.0 ⋅ 10⁶. The magnitude of the gusts models corresponds to a yaw angle of 20^𝑜. The overall behaviour of the aerodynamic loads follows a similar trend for all the wind gusts considered. Besides, the aerodynamic loads calculated show a large excess of drag coupled with a reduction of the pitch moment.

Although the side force has a smooth variation in the gust, overshoots up to 18% higher than the steady value of yaw moment are also observed.

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Part II

Appended Papers

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