Chen-guang LAI, Cheng-ping YAN, Hong-qiang ZENG, Hai-lin ZHANG, Qing-yu WANG, Yu-ting ZHOU

(1School of Vehicle Engineering, Chongqing University of Technology, Chongqing 400054, China) (2Institute of Fluid Science, Tohoku University, Sendai 980-8577, Japan) (3School of Chemistry and Chemical Engineering, Chongqing University of Technology, Chongqing 400054, China)

Abstract: Multi-objective optimization design method based on kriging model and NSGA-II algorithm is adopted to investigate the influence of air-inlet grille to aerodynamic performance and underhood cooling performance of vehicle. Data mining technologies including total variation analysis and self-organizing map analysis are used to uncover the influence mechanisms of design variables on objective functions. Three parameters of the grille including the grille inclination angle, the number and width of grille bar are chosen as design variables. The optimization objectives are the drag coefficient, the lift coefficient and the air mass flow-rate into the underhood of vehicle. Data mining results shows out the effect degrees of variables to objectives, the relationship between variables and objectives, and the relationship between objectives. At last, aerodynamic performance and underhood cooling performance of the optimized models and initial model are compared.

Key words: Air-inlet grille, Multi-objective optimization, Aerodynamic performance, Cooling performance,Data mining

1 Introduction

Not only the heat dissipation of underhood, but also the vehicle aerodynamic performance is influenced by auto air-inlet grille, nevertheless, the latter is always ignored by designers. The coefficient of aerodynamic drag is mainly affected by car shape when only consider the external flow field. Actually, since the heat in the underhood need to be expelled, part of airflow would flow into the underhood through the grille which will consequently consumed some kinetic energy of the vehicle. The consumption of energy will give rise to extra aerodynamic resistance, which referred as internal flow drag. Thus, as the most important part that determines the airflow into the underhood, the structure of the air-inlet grille not just influence the underhood cooling performance, but determine the overall aerodynamic drag of the vehicle. Moreover, it may be a contradiction between the influence to underhood heat dissipation and to vehicle aerodynamic performance. That is, more airflow into the underhood will help improve heat dissipation performance, but will also increase the aerodynamic drag of the vehicle[1].

CFD numerical simulation technology is now more and more used in the aerodynamic analysis and thermal management of the automobile. Qing Jia et al. [2] investigated the influence of different grille bar number to the air inflow into the underhood. Jing Chang [3] in Jilin University studied and analyzed the influence of different parameters of air-inlet grille to vehicle aerodynamic performance and underhood heat dissipation performance by orthogonal experimental design method. Nowadays, evolutionary algorithms and genetic algorithms are widely used in the aerodynamic optimization. The biggest obstacle for their use in vehicle aerodynamic optimization is that the vehicle flow field is very complex and the optimization process needs excessive CFD calculations. In addition, as an approximate model, kriging model [4] can establish the mapping relationship between input and output instead of CFD calculations which will effectively help saving computing time and resources.

This paper illustrates a multi-objective optimization design method to investigate the influence of air-inlet grille to the vehicle aerodynamic performance and underhood heat dissipation performance. 50 sample points are used to fit the kriging model, and then a multi-objective genetic algorithm NSGA-II [5] is used to forecast the optimized models. At last, data mining technologies including total variation analysis and self-organizing map are used to analysis the influence mechanisms between design variables on objectives.

2 Multi-objective optimization designmethods

In most cases, improvement of one objective may cause the decline of other objectives, and it’s almost impossible to make all the objectives to be optimal [6]. Multi-objective optimization is a method which can help to achieve the relative optimal solutions when dealing with contradictory optimization objectives. Relatively optimal solution refers to those solutions which compromise among objectives and try their best to make each objective to reach a better performance. Usually, the solution set consist of the relatively optimal solutions is known as pareto-optimal solution set [7], among which there’s no solution shows dominant position to others. Fig.1 shows the flow chart of multi-objective optimization design.

Spatial uniformity of sample points is very important, which is related to the precision of approximate model. In this paper, Latin Hypercube Sampling (LHS) [8] which has good space filling features is employed to get the initial spatial uniformly distributed sample points. The sample data could be obtained by numerical simulation or experiment, and CFD simulation technology is used to get the objective data here. Then, the approximate model (here is kriging model) is fitted by the initial sample data. One should determine whether the accuracy of the approximate model meets the requirements. If satisfied, the optimization process stops and NSGA-II is used to seek the pareto-optimal solution set; otherwise, more sample points should be added to the initial sample point set and refit the approximate model. It should be noted that‘cross validation’is employed to check the accuracy of the approximate model in this paper.

Fig.1 Flow chart of multi-objective optimization design

3 Geometry and simulation method

3.1 Research model and mesh strategy

The research model (see Fig.2) is a simplified model built in CATIA based on the standard model of Motor Industry Research Association (MIRA). The air-inlet grille and the key components in underhood are built, regardless of most pipes, connecters and other components which aren’t sensitive to temperature. The simplification has little influence on the aerodynamic and heat dissipation performance. Moreover, this paper mainly focuses on the optimization method. Layout of the underhood is shown in Fig.3.

Fig.2 Vehicle model

Fig.3 Layout of the underhood

Hybrid mesh is used to generate mesh in ICEM CFD software (see Fig.4). The mesh density is enhanced in underhood, and prism mesh is generated on the surfaces of carbody and underhood components. Tetrahedral mesh is generated in the computational domain near the vehicle while the outer domain is divided into hexahedral mesh. Total number of mesh elements is about 12 million.

Fig.4 Mesh strategy

3.2 Boundary conditions and material properties

CFD simulation is carried in the commercial software FLUENT. Simulation speed of the car is 20 m/s, and rotational speed of the radiator fan is 3 000 r/min. Condenser and radiator are assumed as porous medium and defined as heat source at the meantime. Two fan regions are set as rotation fields. The thermal boundary conditions are set according to the actual heat dissipation capacity under the same automotive operating condition. For simplicity, convection is considered to be the mainly heat transfer form and the heat radiation is ignored. Two materials are considered in this investigation, alumina for metallic components and engineering plastic for the other nonmetallic components. Material properties of the components are shown in Table 1.

Table 1 Material properties and corresponding components

MaterialDensity/(kg·m-3)Specific heat/(j/kg·k)Heat conductivity/(w/m·k)Corresponding componentsAluminum2 700871202.4Underhood, intake manifold, exhaust pipe heat shield, engine body, generatorEngineering plastic1 40015000.22Air filter, battery, fuse box, griller

4 Optimization

4.1 Variables and optimization objectives

Three parameters of the air-inlet grille including inclination angle of the grille (A), number of the grille bar (N) and width of the grille bar (L) are selected as design variables. The shape of the grille bar is shown in Fig.5. We define clockwise as positive just as the direction of ‘A’ shown in Fig.5. The coefficient of aerodynamic drag (Cd) and lift (Cl) as well as the air mass flow-rate (Um) into the underhood are the objectives to be optimized.

For good aerodynamic performance, the value ofCdshould be as low as possible. And for good handling stability, theClvalue should approach to 0.Umshould be as high as possible in consideration of the improvement of underhood cooling. The description above can be illustrated as:

Fig.5 Grille bar cross section diagram

Table 2 shows intervals of the design variables, whereNis an integer. 50 spatial uniformly distributed sample points are generate by LHS and CFD simulation are carried out to get the objective values. And then, the data of the 50 sample points is used to fit the kriging model. Theory of the kriging model is presented in the next section.

Table 2 Variable optimizing interval

variableOptimizing intervalInclination angle of grille A/(°)-5≤A≤30Width of grille bar L/mm10≤L≤29Number of grille bar N3≤N≤12

4.2 Fitting the kriging model

Since its high accuracy and can provide the predicted value and the predicted error at the same time, Kriging method is employed to fit the approximate model in this paper. For the unknown positionx, the objective function valuey(x) can be predicted as:

y(x)=μ+ε(x)

(1)

Where,xdenotes the m-dimensional vector; Right side of equation is a random function andμdenotes the mean of the stochastic process;ε(x) denotes the error term which follows the normal distribution i.e.,ε(X(i))～N(0,σ2),σ2denotes the process variance of kriging model.

Kriging model assumes that the different error termsε(x(i)) andε(x(j)) are spatially correlated. Letθhdenotes the correlation coefficient. Usually,phcan define as a constant, the correlation defined as:

corr[ε(X(i))，ε(X(j))]=

(2)

Where,θhandphcan respectively represent the activity and the smoothness ofxh. The unknown terms (μ,,θ1, …,θm) in the above equations can be are valued by choosing them to maximum the likelihood of the sample points, then one can get best linear unbiased estimation ofy(x), and the derivation process can be refers to [9].

Cross validation is used to determine the accuracy of kriging model. In this investigation, maximum errors ofCd,ClandUmof the observations are 5.32%, 3.48%, 6.7%. The errors are all below 10%, which means the model meeting the accuracy requirement and is valid for further analysis.

4.3 Seeking the optimal solutions

The optimal solutions were predicted on the basis of kriging model using NSGA-II algorithm. There are many multi-objective algorithms, such as: particle swarm algorithm, simulated annealing algorithm, ant colony algorithm, artificial neural network algorithm etc. Compare to the other algorithms, NSGA-II shows an excellent performance when dealing with the problems which have two or three objectives.

Weighing factors for each objective are set according to the design requirements, and the Pareto-optimal solution set that fits the demands well could be obtained by NSGA-II algorithm. Table 3 presents two of the Pareto-optimal solutions.

5 Results and discussion

5.1 Data mining

Data mining is a technology that can analyzes large amounts of data [10]. Based on the kriging model, total variation analysis and self-organizing map analysis are carried out to investigate the interactions between variables and objectives. Total variation analysis (see Fig.6) can investigate the interactions in a quantitative way and reflect the sensitivities of the objectives to each variable.

Fig.6 Total variation analysis map

As shown in Fig.6, all the variables have influence onCd,ClandUm. Inclination angle of grille has the greatest impact on the aerodynamic drag, which accounted for 53.1%. The second important factor is the number of grille bar, accounted for 33.5%. It should be noted that, number of grille bar has the greatest impact on bothClandUm. The width of grille bar also has a relatively high influence toCl, while the inclination angle of grille has the least impact onCl. The sum variance proportion of the inclination angle of grille and the number of grille bar onUmreached 99.6%, however the impact of the width of grille bar onUmcan be ignored.

Self-organizing map [11], which can keep the topological structure of the original data unchanged, is a technique to analyze the data by project high dimensional data to one or two dimensional. The relationship between variables and objectives can be intuitively reflected through the self-organizing map (see Fig.7).

Fig.7 Self-organizing map

Red part in Fig.7 denotes the high value while the blue denotes the low value. For example, as shown in the black circles, the lowestCdoccurs when the number of grille bar is large and the inclination angle of grille is relatively low. For good underhood cooling performance,Umneeds to be high, and the number of grille bar should be low. It means that the optimization of aerodynamic drag and the optimization of underhood cooling performance are contradictory. For good underhood cooling performance, one needs to sacrifice some aerodynamic performance. Moreover, we can infer that the optimization ofCdand the optimization ofClare also contradictory. Considering the contradictions, one can get a relative optimal solution according to Self-organizing map. For example, in the optimization design of automobile,CdandUmcould be set with larger weighting factors, whileClcould be set with a relatively small weighting factor, and thus a pareto solution meet the design requirements well could be obtained.

5.2 Comparison of optimization results

Two relative optimal models (a51 and a52) are selected to construct the geometry model and be simulated by CFD, and the results are compared with the original model a0. Details of comparison models are shown in table3.

When compared with the original model, three objectives includingCd,ClandUmof the two optimal models are all optimized. Wherein,Cdof a51 has a greater optimization, whileUmof a52 has a greater optimization.

Pressure contours ony=0 section of the comparison models are shown in Fig.8. It can be seen the pressure drag caused by the differential pressure between the head and rear of a0 is larger than that of a51 and a52. And that’s the main reason whyCdof a0 is higher.

Fig.9 and Fig.10 are the temperature contours ony=0 andz=0.279 5 section of the comparison models. It’s obvious that the average temperatures in the underhood of a51 and a52 are lower than that of a0, and the average temperature of a52 is the lowest. This is in agreement with the air mass flow-rate (Um) into the underhood. That is, the more air flow into the underhood, the better cooling performance of the underhood is.

Table 3 Relevant parameters of comparison model

A/(°)L/mNCdClUm/(kg·s-1)a011.4322.0280.356 20.114 11.118a51-3.5715.04110.336 50.101 91.467a5213.5722.8040.341 40.100 61.526

Fig.8 Pressure contour ony=0 m section

Fig.9 Temperature contour ony=0 section of the underhood

Fig.10 Temperature contour onz=0.279 5 m section of the underhood

6 Conclusions

(1) Multi-objective optimization design is employed to investigate the impact of the air-inlet grille on vehicle’s aerodynamic performance and underhood cooling performance. Compare to the original vehicle, the relative optimal models have effectively optimized the aerodynamic and underhood cooling performance.

(2) Different effect degrees of air-inlet grille to aerodynamic drag, aerodynamic lift, and the air mass flow-rate into the underhood are obtained by total variation analysis. The relationship between variables and objectives is found through the self-organizing map analysis.

To summarize, it’s demonstrated that the optimization strategy combine kriging model, NSGA-II algorithm and data mining technologies is promising for multi-objective problems such as the optimization and analyses of the aerodynamic and cooling performance of vehicle.

Acknowledgements

This research was sponsored by Key technology innovation projects of key industries in Chongqing (No.cstc2015zdcy-ztzx60011) and Graduate Innovation Fund of Chongqing University of Technology (No.YCX2016109).