ion of a Vehicle Shape by CFD Code

8/8/2019 ion of a Vehicle Shape by CFD Code

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1 Introduction

The reduction of the aerodynamic resistance is an important aim pursued since many

years, in order to increase the efficiency (Agathangelou and Gascoyne, 1998; Basara,

2003; Emmelmann et al., 1990; Kobayashi and Kitoh, 1992; Koromilas et al., 2000;

Lietz et al., 2000; Pien et al., 2000; Werner et al., 1998; Yanagimoto et al., 1994;

Zhang et al., 2003). Today the experimental techniques use the wind tunnel in natural

or reduced scale; the study is executed recurring to the mechanical similitude theory

(Hucho, 1987; Milliken and Milliken, 1995). Empirical methods can also be used as

the White one (Morelli, 1974), as described in the Section 2.1 or CFD simulations

(Anderson, 1995; Basara, 2003; Kobayashi and Kitoh, 1992; Versteeg and

Malalasekera, 1995; Zhang et al., 2003), that in the last years have found great

diffusion, thanks to the great development of hardware and software. The fluiddynamic simulation permits the visualisation of the flux field around the vehicle and the

pressure distribution on its surface. The current trend is the development of automatic

optimisation software that gives satisfactory results reducing the working time.

The purpose of this work is to set up an efficient procedure able to reduce the

aerodynamic resistance of a vehicle, by its shape optimisation. The fluid dynamics

simulations have been executed using the module CFD, Tdyn, of the software GID

of Compass. The model examined, as an example, is Maserati Biturbo 222 of 1988

(Pasta and Virz Mariotti, 1989), digitised and modelled in Rhinoceros.

2 Manual optimisation

2.1 White methodThe vehicle design is manually varied by means of the software Rhinoceros, with the

aim of determining the geometry assuring the lower value of aerodynamics

penetration coefficient gh, respecting the constraints imposed by visibility,

habitability and necessary space for the mechanical parts, etc. The virtual model

of the vehicle is represented in Figure 1(a).

The White method (Morelli, 1974) divides the vehicle into nine parts and assigns

to every one a weight xi, that can be found in a table in depending on the part shape.

The weights are introduced in the following expression:

gh a0 9

i1

xi ai 0X16 0X00959

i1

xi 1

where the coefficients ai and a0 are obtained by statistical analysis of data obtainedby wind tunnel tests. The approximation of the White method is about 7%; a

gh 0X4735 is obtained for the examined vehicle.

2.2 CFD simulation

Due to the longitudinal symmetry of both model and motion field, half a vehicle was

analysed, in order to generate a more dense mesh on the model, and obtain more

accurate results. The model of Figure 1(a) presents a flat bottom, has no rear view

Optimisation of a vehicle shape by CFD code 27


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mirror or frontal opening, has a smooth cover rim and has no appendages such as

handles, rearview mirror, etc. Figure 1(b) shows the mesh of a half vehicle.

Figure 1(a) Maserati biturbo 222

Figure 1(b) Close up of the vehicle mesh

Simulations have been executed using a commercial code GID (free evaluation copy)that makes use of the Tdyn solver able to solve the RANS (Hucho, 1987; Kobayashi

and Kitoh, 1992) (Reynolds Averaged Navier Stokes) equations; it requires the choice

of turbulence model (the k 4 model in this paper) and the constraints conditions onsolid walls. An unstructured mesh of about 200,000 cells is used, with dimensions

moving between 0.56 m far away from the car surfaces and 0.005m close to.

At the end of the analysis a gh 0X472 is obtained, with a value very close to thatof the White method, so that parameters and turbulence model can be considered

correct.

C. D'Anca, A. Mancuso and G. Virz Mariotti28


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Another type of analysis has been executed determining gh versus the speed as

Figure 2 shows. One can note that gh stays almost constant, as expected, so that the

results of the successive CFD simulations at a speed equal to 130 km/h can be believed

suitable; the difference at low speed is probably due to a coarse mesh. Figures 3 and 4

show the pressure distribution on the model and the stream lines at the previous speed.

Figure 2 gh versus vehicle speed

Figure 3 Pressure distribution

Figure 4 Stream lines



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The successive simulations determine gh variations modifying some vehicle

surfaces. The obtained results, with the relative optimised surface, are shown in

Figure 5(a)(f):

Figure 5(a) ghversus fillet radius windscreen roof

Figure 5(b) ghversus fillet radius in the front corners

Figure 5(c) ghversus the shrinking of the back



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Figure 5(d) ghversus fillet radius roof rear window

Figure 5(e) ghversus fillet radius roof rear window (S.W.)

Figure 5(f) ghversus fillet radius roof rear window (S.W. with more inclined rear window)

Table 1 shows the values for the several particulars depicted in Figure 5. If all theconfigurations, assuring the lower gh values in Table 1, are considered, the model

shown in Figure 6(a) is obtained, that can be compared visually with the original one

in Figure 6(b). This model gives gh 0X456, with a reduction, with regard to theoriginal value, equal to 3.4%. It is not the minimum absolute value, because a linear

relation between all the adopted parameters does not exist, the relations are often

strongly non-linear, so that the superposition principle is not valid. A low gh value

can be obtained by carefully studying the streamlines and putting together the

solutions reducing phenomena such as the wakes, the separation, the vortices, etc.



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Table 1 gh values for all the examined configurations

Fillet variation between windscreen and roof Fillet 1.4m gh 0X446

Fillet variation of front corners Fillet 0.4m gh 0X427

Shrinking of the back Shrinking 0.48% gh 0X439

Fillet roof rear window variation Fillet 1.2 m gh 0X451

Fillet roof rear window variation (station wagon) Fillet 0.9m gh 0X464

Fillet roof rear window variation (station wagon with

more inclined rear window)

Fillet 1.2m gh 0X457

Figure 6(a) Optimised model

Figure 6(b) Original model

In this way the configuration shown in Figure 7(a) was found, having gh 0X429,with a reduction equal to 9.11% with regard to the original one. Figure 7(b) shows

the pressure distribution.



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Figure 7(a) Optimised model studying the stream lines configurations

Figure 7(b) Pressure distribution

3 Automatic optimisation

The chosen optimising surface is constituted by windscreen, roof and rear window,

shown with different grey levels in Figure 8. This surface has been approximated by

means of a bi-cubic NURBS surface having 15 6 control points (De Boor, 1978).Such control points have been assumed as design variables.



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Figure 8 Model before the optimisation

The control points belonging to the boundary curves A, B and C are fixed while that

belonging to D may change along y and z. In total one has 130 design variables, that

are h yiYjY ziYj with i 2Y F F F Y 14 and j 2Y F F F Y 6. To eliminate habitabilityproblems, some limit has to be fixed to the variation of the variables: the space in the

inside must not diminish and the height of the inside must not be lower than the

original so as not to annoy the driver and the passengers. In consequence the original

configuration is chosen as the lower bound (lb), while the surface far away 0.05 m (in

the z direction) from the original one is chosen as the upper bound (ub).

Besides constraints are imposed to avoid the optimisation routine going towards

unsuitable configurations, from the point of view of aerodynamics technology orstyle (penetration, bumps and similar). The following constraints are assigned, in

consequence:

yiIYj yiYj ! 0 for i IY F F F Y 13Y

ziIYj ziYj ! 0 for i IY F F F Y 8Y

ziIYj ziYj 0 for i WY F F F Y 13Y

2

Assuming as `an objective function' to be the aerodynamics resistance, the best

configuration attributes a minimum value to it, with the consequent values of the

independent variables.

3.1 Automatic loopThe problem, which is a typical constrained optimisation problem, has been solved

with the aid of the optimisation toolbox of MatLab. In particular, in order to use

efficient algorithms (Vanderplaats, 1976), the optimiser uses the BFGS quasi-Newton

method with a mixed quadratic and cubic line search procedure. This quasi-Newton

method uses the BFGS formula for updating the approximation of the Hessian matrix

since no information about the gradient of the objective function can be supplied.

All the surfaces are stored in an IGES format. In this work two IGES file were

created; the first contains information as far as the variable surface is concerned,



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while the other contains the remaining surfaces. IGES files are read by GID thanks

to a batch file containing all the instructions that GID has to execute. After the

reading of the batch file, GID imports the file IGES, loads all the boundary

conditions, creates the model of the simulating flux, generates the mesh, recalls the

solver and executes the simulation, as Figure 9 shows. At every step of the

optimisation loop, an IGES file of the optimising surface is modified and rewritten,

GID is rerun, the batch file is reloaded, the simulation is effected and the value of the

total resistance is stored in a text file; hence the design variables are modified, the

IGES file is updated and a new simulation runs. The loop is repeated until

convergence, or a maximum number of iteration is reached.

Figure 9 Flow chart of the optimisation loop

The lower bound (lb) and upper one (ub) are fixed, as detailed in the previous

section, while the linear constraints of Equation (2) can be arranged in a more

suitable matrix form by means of:

A x bY 3

x being a column vector containing the coordinates y and z of the design variables, A,

a matrix and b a column vector of zeros.

The optimisation programme was written for the more general case (i.e. a surface

of m n control points), successively some simplifications have been introduced dueto limited hardware resource. All the calculations are executed on a computer AMD

at 1.9 GHz.

Initially, for every line of control point (Figure 10(a)), only a point was

considered as independent variable, introducing some relation joining the remaining



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four points of the line to the above-mentioned point, in order to maintain unvaried

the windscreen curvature and the horizontal tangency of the surface across the

longitudinal plane of symmetry. Successively only seven out of 13 control points have

been considered variables, obtaining 14 design variables (providing that the control

point can change the y and z values); the variable control points are shown in

Figure 10(b).

Figure 10(a) Variable control points; general case

Figure 10(b) Variable control points; limited application



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4 Results

The convergence has been obtained after 147 iterations; Figure 11 shows the

normalised aerodynamics resistance (with regard to the initial value) versus the

iterations number.

Figure 11 Normalised aerodynamic resistance versus the iterations number

One can note as, varying the coordinates of only seven control points, in a range of

0.05 m, the lowering of the aerodynamics resistance is equal to 4.2% with regard tothe initial value. The obtained optimum configuration is shown in Figure 12. The

difference between initial and optimised configurations is evidenced in Figure 12(b),

where both the curves are obtained by the intersection of the surface with the middle

plane of the vehicle. The clear curve represents the initial configuration, while the

black one the optimised configuration.

The air flux near the optimised surface (Figure 13) is laminar without phenomena

of flux separation. Figure 14(a) shows that the optimised surface has a minor fluxseparation on the bonnet and on the windscreen; the wake is reduced with regard to

the non-optimised one (Figure 14(b)). This is due to a greater pressure recovery in the

rear, producing a lower resistance.

Finally the comparison of Figures 15(a) and (b) shows the differences between the

original geometry and that optimised automatically.



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Figure 12(a) Optimised surface (perspective view)

Figure 12(b) Optimised surface (side view)

Figure 13 Stream lines; close up on the windscreen



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Figure 14(a) Stream Lines around the optimised vehicle

Figure 14(b) Stream Lines around the initial vehicle

Figure 15(a) Optimised model

Figure 15(b) Initial model



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5 Conclusions

In the beginning, simulations were executed with the purpose of obtaining the

aerodynamics resistance according to the geometric configuration of some surfaces.

These simulations also furnished the pressure distribution on the vehicle surfaces,

and wake conformation; in all the cases a better configuration than the initial one

was found, with a reduction of the aerodynamic resistance coefficient of some

percent. The result of simulation is in very good accordance with the empirical White

method.

Two different vehicle configurations were found: the first putting together the

particulars in Figure 5 having a minimum value of aerodynamic resistance, the other

deriving from a careful manual study of the stream lines around the vehicle. A better

result was obtained in the second case: the superposition of optimum particulars doesnot ensure the best result because a certain solution can influence the geometric

configuration of other vehicle parts in a different way. It demonstrates the difficulty

in the research of the shape, ensuring minimum aerodynamics resistance and the

importance of the designer experience.

The procedure of automatic optimisation is set creating a loop between a CFD

code that executes the simulations and an optimisation module. The procedure

permits the geometric configuration determination of the surface, which the

minimum value of aerodynamics resistance belongs. A gh reduction equal to

4.2% with regard to the initial value is obtained, only acting on seven amongst all the

control points. A better result can be obtained acting on other surfaces that were not

optimised because the resources of hardware and software were limited.

The potentialities of this method of automatic optimisation are remarkable if one

can realise a better grid and has the possibility of action on a greater number ofpoints; however its application requires hardware resources of high capacities.

References

Agathangelou, B. and Gascoyne, M. (1998) Àerodynamic design considerations of a Formula1 racing car', SAE Technical Paper Series 98039.

Anderson, J.D. Jr (1995) Computational Fluid Dynamics, McGraw-Hill, Inc.

Basara, B. (2003) Àutomotive engineering for intelligent vehicle systems, vehicleaerodynamics using CFD present status and future development', JUMV Congress,Belgrade, May 2003, paper YU-03009.

De Boor, C. (1978) A Practical Guide to Splines, New York: Springer-Verlag.

Emmelmann, H.J., Berneburg, H. and Schulze, J. (1990) `The aerodynamic development of theOpel Calibra', SAE Technical Paper Series 900317.

Hucho, W.H. (Ed) (1987) Aerodynamics of Road Vehicles, London: Butterworths.

Kobayashi, T. and Kitoh, K. (1992) À review of CFD methods and their applications toautomobile aerodynamics', SAE Technical Paper Series 920388.

Koromilas, C., Harris, C., Sumantran, V., Pachon, L. and Zeng, S. (2000) `Rapid aerodynamicdevelopment of two volume vehicle shapes', SAE Technical Paper Series 2000-01-0488.

Lietz, R., Pien, W. and Remondi, S. (2000) À CFD validation study for automotiveaerodynamics', SAE Technical Paper Series 2000-01-0129.



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Milliken, W.F. and Milliken, D.L. (1995) Race Car Vehicle Dynamics, Society of AutomotiveEngineers, Inc.

Morelli, A. (1974) Costruzioni automobilistiche in Enciclopedia dell'ingegneria, Milano:ISEDI.

Pasta, A. and Virz Mariotti, G. (1989) Ùn sistema CAD per lo studio del veicolo', Atti 6

congresso ADM, Palermo, 1216 Dec.

Pien, W.S., Zeuty, E.J. and Ranzebach, R. (2000) Àn integrated study of the Ford Prodigyaerodynamics using computational fluid dynamics with experimental support', SAETechnical Paper Series 2000-01-1578.

Vanderplaats, G.N. (1976) Numerical Optimization Techniques for Engineering Design withApplications, McGraw Hill Book Company.

Versteeg, H.K. and Malalasekera, W. (1995) An Introduction to Computational Fluid Dynamics The Finite Volume Method, Prentice Hall.

Werner, F., Frik, S. and Schulze, J. (1998) Àerodynamic optimization of the Opel Calibra ITCracing car using experiments and computational fluid dynamics', SAE Technical PaperSeries 980040.

Yanagimoto, K., Nakagawa, K., China, H., Rimura, T., Yamamoto, M., Sumi, T. andIwamoto, H. (1994) `The aerodynamic development of a small speciality car', SAETechnical Paper Series 940325.

Zhang, Y.J., Lv, Z.H., Xie, J.M. and Tu, S.R. (2003) Àn hybrid unstructured finite volumealgorithm for road vehicle flow computations with ground effects', Int. J. Vehicle Design,Vol. 33, No 4, pp.365380.


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