optimization of race car front splitter placement using cfd

2019-01-5097 Published 30 Dec 2019

© 2019 SAE International. All Rights Reserved.

Optimization of Race Car Front Splitter Placement Using CFDSourajit Bhattacharjee, B.B. Arora, and Vishesh Kashyap Delhi Technological University

Citation: Bhattacharjee, S., Arora, B., and Kashyap, V., “Optimization of Race Car Front Splitter Placement Using CFD,” SAE Technical Paper 2019-01-5097, 2019, doi:10.4271/2019-01-5097.

Abstract

The behavior of flow over an automobile’s body has a large effect on vehicle performance, and automobile manufacturers pay close attention to the minimal of

the details that affect the performance of the vehicle. An imbal-ance of downforce between the front and rear portion of the vehicle can lead to significant performance hindrances. Worldwide efforts have been made by leading automobile manufacturers to achieve maximum balanced downforce using aerodynamic elements of vehicle. One such element is the front splitter. This study aims to analyze the aerodynamic perfor-mance of automobile at various splitter overhang lengths using

Computational Fluid Dynamics (CFD). For the purpose of analysis, a three-dimensional (3D) CFD study was undertaken in ANSYS Fluent using the realizable k-ε turbulence model, based on the 3D compressible Reynolds-Averaged Navier-Stokes (RANS) equations. The National Advisory Committee for Aeronautics (NACA) 4412 was taken as profile for the fixed-length splitter attached to a NASCAR 2019 model body. Vehicle speeds of 200, 250, and 300 km/h were considered in order to simulate the velocity of a race car. Drag coefficient, lift coef-ficient, and velocity contours were studied in order to examine the overall aerodynamic effect of overhang length on vehicle aerodynamic performance and optimize splitter geometry.

Introduction

Racing in modified stock cars has always been one of the most popular motorsports in North America [1]. The National Association for Stock Car Auto Racing

(NASCAR) is the world’s largest sanctioning body for stock car races. Since its introduction, the present Sprint Cup race cars, also called the Cup cars, have evolved through six genera-tions. The Generation 6 car is the common name for the Sprint Cup car that has been used since 2013. Since then the body structure has remained somewhat consistent and uniform with minor body changes introduced every year. The Generation 6 cars are usually designed to replicate the external features of street-legal versions of the same car produced by the manu-facturers. Like in every motorsport, aerodynamics plays a vital role in NASCAR race cars. A great amount of importance and budget is devoted to research on the same in order to reduce crucial aerodynamic drag and also increase downforce. Even a minute change in the aerodynamic features of the vehicle may alter the vehicle’s performance tremendously.

Over the years, various aerodynamic appendages have been added to the vehicle in order to improve vehicle safety at high speeds. Most of these, including hood and roof flaps which were

aimed at avoiding liftoff during high-speed races [2]. This occurs due to reduction in downforce on the vehicle and results in severe damage to vehicle and sometimes to driver. To avoid such accidents, a balanced distribution of high downforce acting on the vehicle is essential. There is a spoiler attached at the rear of the NASCAR vehicles which adds a large amount of down-force to the vehicle. If the downforce isn’t balanced at the front, a moment would be induced on the vehicle. This is where a front splitter becomes essential in stock racing vehicles. Splitters are attached to the bottom of the bumper of race cars. It is generally a flat plate which extends out of the vehicle up to a certain length. Its main purpose is to channel air flowing under-neath the vehicle in such a manner that a high-pressure zone is created above the splitter plate. Because of this high-pressure zone above the splitter, a significant amount of downforce is generated in front of the vehicle that keeps the car attached to the road even at tight corners. Also, a low-pressure zone is formed underneath the vehicle that restricts airflow through it, hence further improving the aerodynamics of the race car. Analyses have been previously performed on NASCAR vehicles, both experimental and analytical, but a parametric analysis on optimum splitter overhang length is yet to be performed.

KeywordsComputational f luid dynamics, NASCAR, Aerodynamic performance, NACA 4412

Downloaded from SAE International by Vishesh Kashyap, Sunday, January 19, 2020


OPTIMIZATION OF RACE CAR FRONT SPLITTER PLACEMENT USING CFD 2

Wind tunnel tests performed by Britcher and Mokhtar [3] and Landman [4] showed the boundary profile along with the pressure distribution over the vehicle’s body. A high stagnation pressure at the front of the vehicle under the bumper makes it a vital spot for modification in order to extract downforce from the vehicle. Fu et al. [5] conducted wind tunnel tests as well as CFD simulations and checked the effect of turbulence model on the simulation of actual race conditions. Fu et al. [6] also validated numerical solvers with wind tunnel tests in predicting various parameters like coefficients of lift, drag, etc. It was one of the first attempts to visualize the flow characteristics in a Generation 6 NASCAR race car. During recent years, with a rapid development of computational resources, CFD has become an indispensable tool for racing aerodynamicists. Compared to wind tunnel testing, CFD simulation has its own advantage of providing a thorough description of the flow field interacting with a race car, instead of delivering only the force and moment coefficients. With proper modeling, CFD now can produce results that are comparable with the accuracy and repeatability of wind tunnel tests with significantly more details of the overall flow field. However, accurately simulating airflow by solving differential equations that govern the flow around an object requires time and huge computational resources. Because of the fast working pace and tight racing schedule, many race teams devote much effort to the development of accurate CFD methods with faster turnaround times.

In this paper, 3D CFD analyses have been performed in ANSYS Fluent using the realizable k-ε turbulence model on a stock NASCAR race car designed as per the 2019 rules in order to determine the effect of splitter overhang length on the aerodynamic performance of the vehicle. The overhang length of the splitter has been varied from 10 to 50 mm at a difference of 10 mm. The analyses have been carried out at velocities of 200 km/h, 250 km/h, and 300 km/h.

MethodologyFor the present study, modeling of the Computer-Aided Design (CAD) of the stock vehicle geometry was initially performed using SolidWorks 2018. In order to preserve the accuracy of the CFD analyses, grid independence tests were then carried out in order to ascertain an optimum mesh size with constraints of accuracy as well as computational resources. The computational model was then validated by comparison with reported data by analysis on bluff body as defined by Ahmed et al. [7]. A parametric study on NASCAR vehicle was then performed using this validated model.

CAD GeometryThe CAD of a 3D CAD model of a NASCAR Monster Series race car was carried out using SolidWorks 2018. The car was modeled as per the dimensions released in the official 2019 rules announced on October 2, 2018 [8]. The changes have been shown in Figure 1, while the stock body is the same as the Generation 6 vehicles.

The dimensions of the vehicle have been shown in Figure 2 along with the rendered CAD model in Figure 3. The splitter

FIGURE 1 2019 NASCAR rule changes.


FIGURE 2 Dimensions of NASCAR body for analysis.


FIGURE 3 CAD model of NASCAR 2019 vehicle (a) front trimetric view and (b) rear trimetric view.

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was modified in the models. It was designed in the form of an inverted wing having a profile of NACA 4412 airfoil, and is attached to the front bumper of the body. The modified profile is shown in Figure 4. The span of the splitter has been limited to the width of the vehicle body, and the chord length of the profile has been fixed at 100 mm. The overhang length X for the splitter has been modified in each model ranging from 10 mm splitter to a 50 mm splitter overhang. The overhang length has been limited due to the design criterion of 2019 rules.

MeshingThe flow visualization around the vehicle and an accurate calculation of resultant coefficients of drag and lift requires adequate space around the vehicle. A large flow domain is preferred for CFD studies, but the same must be limited as per the computational load and the nature of flow problem being solved. For the present study, the flow domain gener-ated around the vehicle consisted of the following dimen-sions: 3L in front of the vehicle, 5L behind the vehicle, 1.5L above the vehicle, and 1.5L towards the side of it, with L being the length of the vehicle [9], as shown in Figure 5. The analysis was performed on a half symmetric model to reduce compu-tation time but not at the expense of accuracy. The domain along with the model was cut into two halves with a symmetry plane passing right through the middle of the vehicle longitudinally.

ANSYS ICEM CFD was used for the meshing of the computational domain. A local refinement box of the following dimensions: 3L × 0.5L × L (length × breadth × height) was defined around the vehicle to concentrate the cell count close to the vehicle where the results are to be checked. This also resulted in a lower element count and better results. An edge sizing of 60 mm length was applied to the refinement box with advanced sizing set to proximity and curvature. Figure 6 shows the mesh generated around the vehicle. The domain had minimal blockage ratio as suggested by Connor et al. [10]. A grid independence test was carried out to determine the optimal edge length for the analysis. The same has been explained in a later section.

The boundary layer on the surface of the vehicle was captured accurately using prismatic cells. This was achieved by providing an inflation layer around the body and the road. The layers were set in such a manner that the first layer was 1.5 mm thick, and the remaining 10 layers increased by a growth rate of 1.1 (Figure 7). The thickness was set to the above settings due to a considerably low value of y+ at around 5. A number of cases were analyzed iteratively with different inflation layer thicknesses to determine the above value as the optimum one. The mesh outside the refinement box was set to a fine value of 60 mm near the refinement box and ranging up to 800 mm near the walls of the bounding box. The volume mesh hence produced consisted of tetrahedral elements along with a maximum skewness of 0.81 and an average of 0.34. The mesh comprised of approximately 8,000,000 elements.

FIGURE 4 Profile view for splitter.

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FIGURE 5 Computational domain.


FIGURE 6 Mesh generated in bounding box.


FIGURE 7 Zoomed-in view of the inflation layer.

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ModelingInflow velocities, v = 200 km/h (55.56 m/s), 250 km/h (69.44 m/s), and 300 km/h (83.33 m/s), are provided at the inlet wall for each model. Pressure outlet with atmospheric pressure condition was provided at the outlet boundary, and the remaining walls were defined as a stagnant wall with no-slip condition. Symmetry condition was given to the symmetry wall to replicate the analysis condition to the other side of the bounding box as well.

Figure 8 shows the algorithm which was used for predicting various parameters such as Coefficient of Drag and Coefficient of Lift of the geometry. Convergence was moni-tored and analysis was terminated when residuals reached the order of 10–6. When convergence was achieved, the results of the current analysis were plotted and the next parameter for the same model was chosen for analysis.

The realizable k-ε turbulence model was used for the analyses with nonequilibrium wall function for near-wall conditions. According to the required environment conditions as well as in accordance to research performed by Singh [11], the realizable k-ε turbulence model was found to be the most accurate in predicting values for real-life conditions especially with high velocity. Furthermore, the swirl component for the conditions of the given study is high, leading to the realizable model being ideal for analysis. The results were hence found to be most

accurate among the turbulence models provided in Fluent. The k-ε model has been represented in the following equations:

For turbulent kinetic energy k,

¶¶

+¶( )¶

= ¶¶

+æ

èç

ö

ø÷¶¶

é

ëê

ù

ûú+ + + - -r r

m m rku

x

k

t x

k

xP P S Yi

i j

t

k jk b ks

e mm

Eq. (1)

For dissipation ε,

¶¶

+¶( )¶

= ¶¶

+æ

èç

ö

ø÷¶¶

é

ëê

ù

ûú

+ +

re rm m

e

e

e

u

x t x x

Ck

P C P

i

i j

t

j

k e b

es

e

1 3(( ) + -S Ck

e ere

2

2 Eq. (2)

where Gk is defined as the turbulent kinetic energy gener-ated due to mean velocity gradients, Gb is defined as the turbu-lent kinetic energy generated due to buoyancy, and Ym defines the fluctuating dilation in compressible turbulence, which contributes to the overall dissipation rate. Sε and Sk are source terms defined by the boundary values taken defined to the analysis. C1ε, C2ε, and Cμ are experimentally determined constants and are given the following values for the analyses: C1ε =1.44, C2ε =1.92. Cμ in this model is variable, while σk and σε are turbulent Prandtl numbers for the turbulent kinetic energy and its dissipation rate. These have also been derived experimentally and are defined as follows: σk = 1.0, σε = 1.2. As the present study uses relatively moderate velocities, the dilation dissipation term, YM that stands for the turbulence from compressibility effects is defined as:

Y MM t= 2 2re Eq. (3)

The physical model is based on the 3D compressible RANS equations. The governing equations are as follows:

Continuity Equation

¶¶

+¶( )¶

=r rt

u

xi

0 Eq. (4)

where the medium’s density is shown by 𝜌, time by t, and flow velocity by ui.

Momentum Equation

¶( )¶

+ ¶¶

( ) + ¶¶

= ¶¶

+( ) +rr t t

u

t xu u

P

x xS

i

ji j

i jij ij

Ri Eq. (5)

where uj represents velocity in the xj direction, P repre-sents fluid pressure, τij represents the shear stress tensor, and Si represents body force.

Energy Equation

¶¶

+ ¶¶

= ¶¶

+( )+( )

- ¶¶

+ + +

r r t t

t re

H

t

u H

x xu q

u

xS u Q

i

i ij ij ij

Ri

ijR i

je i i HH Eq. (6)

FIGURE 8 Algorithm used for the analyses.

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where the total energy is represented by H, rate of heat dissipation by εe, and heat flux by qi.

Coupled pressure-velocity coupling scheme with second-order spatial discretization for pressure, momentum, turbu-lent kinetic energy, and turbulent dissipation rate and a least squares cell-based gradient were used to calculate the solutions.

Grid Independence TestThe grid independence test was performed on the NASCAR model without splitter at a velocity of 200 km/h. The coeffi-cient of drag was chosen as the parameter of study. Six meshes of successively finer element sizes were considered, between an element size of 100 mm and 50 mm. The results are illus-trated in Figure 9 (Table 1).

In the test, a decreasing trend of coefficient of drag is observed, and the difference between successive computed drag coefficients is seen to decrease. The number of elements varied from 3,984,000 for edge length 100 mm to 8,643,324 for edge length 50. It is observed that the difference between computed drag coefficients between element sizes 60 mm and 50 mm is minimal (<1%); hence further parametric study is carried out with a mesh size of 60 mm.

ValidationValidation of the computational model was carried out by analysis on an Ahmed body and comparison against

reported data. The model was validated against experi-mental data reported by Ahmed et al. [7] and CFD results obtained by Meile et al. [12]. The results are presented for slant angles of 25° and 35° using the realizable k-ε model. Values for coefficient of drag are observed to be in close agreement with the reported data considered as shown in Table 2. The velocity streamlines, as shown in Figure 10, are a lso seen to show good agreement with the experimental results.

For further validation, the coefficient of drag obtained for the current race car model was compared to the results of computational and experimental analyses of NASCAR race cars conducted by Fu et al. [13, 14] under similar analysis conditions. The results are tabulated in Table 3.

It is observed that the results obtained through the current analysis are well aligned with the results obtained through previous reported analyses, with a maximum error of 4.05%.

Through this validation study, it is hence concluded that the computational approach considered is suitable for predic-tion of the required aerodynamic characteristics with reasonable accuracy.

FIGURE 9 Grid independence test.

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TABLE 1 Number of elements for various edge lengths.

Edge length No. of elements100 3,984,000

90 4,889,235

80 6,487,562

70 7,445,098

60 8,093,647

50 8,643,324© 2019 SAE International. All Rights Reserved.

TABLE 2 Validation of computational model.

Angle of slant CD (Current study) CD (Reported) Error25° 0.294 0.299 1.6%

35° 0.271 0.279 2.86%© 2019 SAE International. All Rights Reserved.

FIGURE 10 Analysis on Ahmed body.


TABLE 3 Comparison with NASCAR analysis literature.

CD Current study 0.362

CD Experimental [13] 0.370

Error 2.16%

CD Computational [13] 0.355

Error 4.05%

CD Computational [14] 0.370

Error 2.16%© 2019 SAE International. All Rights Reserved.




FIGURE 12 Variation of coefficient of lift with respect to splitter overhang length.

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Results and DiscussionCFD analyses were conducted in order to predict the coefficient of lift for the NASCAR race vehicle as a function of the overhang length of the splitter attached to its bumper, for constant velocity, at velocities, 200 km/h to 300 km/h. Figure 11 depicts the velocity and pressure contours of the analysis conducted at 200 km/h with a splitter overhang of 50 mm.

Figure 12 presents the coefficient of lift as a function of the overhang length of the splitter on the NASCAR 2019

vehicle. From the graph, it is evident that the coefficient of lift exhibits an increasing negative trend with increase in the length of the front splitter. It is further observed that the coef-ficient of lift for all the cases under study has a greater negative magnitude than for the car with no splitter. It is also observed that while the negative magnitude of coefficient of lift increases substantially up to a splitter overhang of 30 mm, the marginal increase beyond this case is minimal.

Figure 13 presents the values of downforce as a function of the splitter overhang as compared to the car without a front splitter. The downforce is seen to exhibit an increasing trend with increase in splitter overhang. The increase is seen to be substantial up to an overhang of 30 mm, after which the marginal increase is gradual. It is also observed that the down-force for all cases under study is greater than for the car without a front splitter. The introduction of a front splitter leads to the interception of airflow in front of the car, with low pressure, high-velocity air being guided below the splitter surface and low-velocity air creating a high-pressure zone above the surface of the splitter. This high-pressure zone leads to an increase in the downward force experienced by the car. This also increases the coefficient of lift of the car. As the overhang length is increased, the area of the high-pressure zone also increases, leading to a further increase in the down-force and the coefficient of lift. As the distance of the splitter away from the car body increases, the difference between the velocities at the top and bottom surfaces decreases. This leads to a decrease in the impact of increasing splitter area with increasing splitter overhang.

Velocity is seen to have a marginal effect on the coefficient of lift of the car. A marginal decrease in the coefficient of lift is observed with increase in velocity. This observation may be attributed to the viscous effect of the air medium. It is also observed that the magnitude of downforce increases with increase in travel velocity. This is due to the fact that lift force is directly proportional to the square of the velocity of travel.

Figure 14 showcases the percentage increase in downforce for the cases studied. It is observed that the velocity sparsely impacts the percentage change. The percentage change is seen to increase substantially up to a splitter overhang of 30 mm, while further increase is minimal. A maximum percentage increase in downforce of 7.3% is observed at 300 km/h for a splitter overhang of 50 mm.

FIGURE 11 (a) Velocity and (b) pressure contours at symmetry at velocity of 200 km/h for splitter overhang of 50 mm.

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FIGURE 13 Variation of downforce with respect to splitter overhang length.

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The advantage of using a splitter with an airfoil profile over a flat plate splitter may also be inferred from the study. Pelletier and Mueller [15] compared various aerodynamic characteristics for flat and cambered plates and observed a substantial increase in lift for cambered plates. The airfoil profile increases the velocity of air under the splitter, thereby increasing the downforce to a greater extent.

Figure 15 shows velocity and pressure contours for a car with splitter overhang of 50 mm and one with no splitter. It is evident from the figure that an area of concentrated high pressure is created on the top surface of the splitter. The region of low pressure is also seen to be greater for the car with splitter. It is also observed that the region above the splitter is

FIGURE 14 Percentage increase in downforce with respect to splitter overhang length.


FIGURE 15 (a) Velocity and (b) pressure contours for splitter overhang of 50 mm and (c) velocity and (d) pressure contours for car without splitter at 200 km/h.

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an area of relatively lower velocity for the car with splitter, thereby leading to a greater downforce and coefficient of lift.

ConclusionNumerical analysis of aerodynamic characteristics by para-metrically varying the splitter overhang length of a NASCAR 2019 vehicle was performed. The study indicated that the splitter plays an essential role in increasing the downforce of the vehicle in the front which in turn balances the forces acting on the race car body. Splitters with NACA 4412 profile and different overhang lengths of 10 to 50 mm were tested to understand the variation in downforce acting. 3D CFD analyses were performed to visualize the flow characteristics and understand the working of front splitters in NASCAR vehicle bodies.

The details regarding the flow simulations settings used were discussed and supported by the required validations of the applied numerical technique performed on an Ahmed body. Velocity and pressure contours along with velocity vectors were represented along with reported data to make accurate comparisons. On the basis of the results obtained, following conclusions are made:

1. Splitters play a significant role in addition of downforce to the vehicle body, especially at high speeds.

2. The negative magnitude of coefficient of lift increases with increase in splitter overhang length.

3. The coefficient of lift and downforce show similar trends of magnitude, with a substantial increase being observed up to a splitter overhang of 30 mm followed by a marginal increase up to 50 mm.

4. A maximum downforce increase of 7.3% is observed for a splitter overhang of 50 mm at a travel velocity of 300 km/h.

NomenclatureX - Splitter Overhang Lengthρ - Density of Mediumv - Inlet Velocityt - timeui - velocity of flow in the 𝑥𝑖 directionuj - velocity of flow in the 𝑥𝑗 direction𝑃 - fluid pressureτij - shear stress tensorSi - body force𝐻 - total energyqi - heat flux in the 𝑥𝑖 direction𝜀e - rate of dissipation of energyQH - thermal energyℎ - potential energy

Subscripti - xi directionj - xj directione - energy

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© 2019 SAE International. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE International.

Positions and opinions advanced in this work are those of the author(s) and not necessarily those of SAE International. Responsibility for the content of the work lies solely with the author(s).

ISSN 0148-7191

9OPTIMIZATION OF RACE CAR FRONT SPLITTER PLACEMENT USING CFD

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optimization of race car front splitter placement using cfd

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