Optimization design for aerodynamic elements of high speed trains
Introduction
As a large length-to-diameter ratio transportation vehicle, high speed trains (HST) run quicker and quicker. The speed of HST that running on the Beijing–Shanghai railway has already reached 300 km/h. In high speed conditions, the flow around the train reveals distinct unsteady characteristics due to the influence of the exposed structures (bogies, pantographs, etc.) and the ground effect [1]. Furthermore, the unsteady characteristics of the wake flow for a slender body are more predominant, which may lead to high fluctuations of aerodynamic loads, especially for the lift and side force of the trailing car. Large aerodynamic lift force will decrease the contact force between the wheels and the rail, which will lead to derailment in certain circumstance. For the flow around a slender body, asymmetric wake flow will emerge in crosswind conditions, and the shedding vortices around the nose of the trailing car will result in high lift and side force. Meanwhile, enough space should be ensured not only for the placement of equipments but also for the operation convenience of the drivers. Consequently, it is very necessary to ensure enough space of the streamlined head during the shape optimization of HST.
The streamlined part is very essential to the aerodynamic performance of HST. The aerodynamic performance could be effectively improved by optimizing the train shape [1]. However, the running environment of HST is very complex, and lots of design objectives (such as the aerodynamic drag force, the aerodynamic lift force of the trailing car, aerodynamic side force of the trailing car, the aerodynamic overturning moment of the trailing car, the aerodynamic rolling moment of the trailing car, the micro-pressure wave generated when the train pass a tunnel, the pressure wave generated when two trains crossing each other on a double railway and the aerodynamic noise.) have a serious effect on the running safety and amenity of HST. Dozens of design parameters are needed to accurately control the geometry of the high-speed train head, and several geometric constraints are also required to ensure the usefulness of the train head. Meanwhile, the aerodynamic shape optimization needs large amount of computational cost and hundreds of thousands times of flow field calculations should be required for one optimization. Thus, it is unbearable to take all of the design objectives into consideration when optimizing a train head. Limited by the computer technique and optimization algorithms, early studies on the streamline shape optimization of HST mainly rely on wind tunnel experiments and numerical simulations [2]. Meanwhile some methodology studies on two-dimensional profile of the streamlined head have been performed with gradient algorithms [3]. In order to reduce the computational cost and shorten the optimization cycle, some scholars introduce the response surface method (RSM) into the aerodynamic optimization [2], [3], [4], [5], [6], [7], [8], [9], [10]. In recent years, great progress has been obtained both for the response surface technique and the computer technique, which greatly improves the optimization efficiency and makes the engineering optimization of HST be possible.
Jongsoo and Junghui [3] conducted a two-dimensional optimization on reducing the micro-pressure wave with the RSM technique and sequential quadratic programming algorithm. Vytla et al. [4] performed a two-dimensional optimization study on minimizing the aerodynamic drag and noise based on the Kriging model and GA-PSO hybrid algorithm. In order to obtain the micro-pressure wave when the train passes by tunnel, both Jongsoo and Vytla [3], [4] used axial symmetric equations to simulate the flow field. Combined with GA and arbitrary shape deformation technique, Sun et al. [11] performed a three-dimensional aerodynamic shape optimization of HST. In order to reduce the computational cost, only the streamlined head has been considered in Ref. [11], which may decrease the computational accuracy of the flow field. Ku et al. [5] utilized the polynomial RSM to optimize the micro-pressure wave and obtained the optimal cross-sectional area distribution. Taking this distribution as the constraint, they then performed the three-dimensional optimization on minimizing the aerodynamic drag based on Kriging model. However, the whole process still belongs to a single objective optimization. Krajnovic [6] took the drag force coefficient, rolling moment coefficient and yawing moment coefficient as objectives to optimize a very simple train front for crosswind stability. Three kinds of RSM are adopted to reduce the CFD cost in his work. Because of difference of the three RSM methods prediction accuracy, Krajnovic found that the performance of the combination of RBNN and polynomial functions is better than the two others (polynomial functions and radial basis neural networks). Besides, in Ref. [6], Krajnovic also optimized the vortex generators to reduce the drag of the train. The study inspires us to make full use of RSM to reduce the CFD cost. In conclude, the aerodynamic shape optimization of HST found in the above references mainly focus on two-dimensional profiles or very simple three-dimensional shapes, and they mainly belong to methodology study and could hardly be used to engineering problems.
Thus, the main propose of our work in this paper is to introduce the popular optimization algorithms and RSM technique into engineering problems with amounts of CFD cost, adopt a procedure to shorten the design cycle of new streamlined parts of HST as much as possible, and shed light on aerodynamic shape design based on the unsteady flow field. Aerodynamics design objectives that seriously influence the running safety and amenity of HST (such as the aerodynamic lift force of the trailing car, aerodynamic side force of the trailing car, the aerodynamic overturning moment of the trailing car, the aerodynamic rolling moment of the trailing car, the pressure waves generated when the train pass a tunnel) are considerate in this paper. Besides, the aerodynamic drag force is also considerate in our work to make sure that the optimal train is friendly to environment. However, some other design objectives (such as two trains crossing each other on a double railway and the aerodynamic noise) are not discussed in this paper. Only the lift force of the trailing car and the volume of streamlined part are taken to be optimal objectives so as to reduce the CFD cost and make the optimal problem be practical. So we mainly take the shape of the trailing car into consideration in this paper and discuss the influence of the leading car shape to pressure waves in Section 6.4 carefully. The Kriging model is adopted together with the multi-points criterion based on minimum response surface method to reduce the CFD cost and improve the optimization efficiency. Meanwhile, a cross-validation training approach has been proposed in this paper which greatly reduces the number of training samples. Based on the Kriging model of which the accuracy meets the engineering requirement, the Pareto front has been obtained with NSGA-II. Then four typical design points are chosen from the Pareto solutions for comparative study with the original shape known as CRH380A, and one of these points is chosen for the unsteady aerodynamic study together with the original shape.
Section snippets
Optimization process
Although the RSM has been utilized, the design cycle of the streamlined parts of HST is still very long. Any unreasonable operating during the optimization process may deteriorate the optimization solutions, even result in disagreeable solutions. Thus, the optimization process should be designed reasonably and reduce unnecessary steps as many as possible. The whole optimization process in the present paper is listed as below, as Fig. 1 shows:
- (1)
Determine the design variables and their ranges based
Geometry
Optimization of the head of HST mainly focuses on the streamlined part, of which the key design variables are as follows: the cross-sectional area distribution and the slenderness ratio of the streamlined part, the longitudinal-type line and horizontal-type line of the streamlined part, the drainage around the nose, the cab perspective and the bogie shield. In the present paper, a CRH380A 1:1 model with three carriages has been utilized for aerodynamic shape optimization. The connection part
Rans
CFD accuracy that directly affects the construction of the Kriging model and efficiency of optimization algorithm is the foundation for the whole optimization process. In this paper, the speed of high-speed train is 300 km/h, so the Mach number is 0.245. Under this condition, the air compression characteristic has an obvious effect on the aerodynamic performance of HST. Therefore, the steady compressible Reynolds-averaged Navier–Stokes equations [12] based on the finite volume method are used to
Construction of Kriging model
The Kriging surrogate model is an interpolation model based on statistical theory [18]. Compared to the polynomial RSM model, the Kriging model could obtain more precise global optimal results. This model is composed of regression model and related model. The former is a global approximation in the design space, while the latter could reflect the variables’ distribution structure in the design space, which impacts directly on the predicting accuracy of the model. The essence of constructing the
Steady aerodynamics discussion
The volume of the streamlined part (Vol) and the lift force of the trailing car (Cl) are treated as the optimization objectives, and the real-coded genetic approach with a population number of 300 and 1500 generations has been performed in the optimization process. Fig. 10 shows the Pareto front of the two objectives. It can be found that the volume of the optimal solutions is limited in a small zone, while Cl varies a little bigger, indicating that Cl is more sensitive to the change of
Conclusions
The complex wake flow of HST severely influences on the running safety and amenity of the trailing car. In order to improve the aerodynamic performance of the trailing car and weaken the influence of the wake flow, a multi-objective optimization on the CRH380A streamlined head has been performed in the present paper, taking the lift force of the trailing car and the volume of the streamlined part as the optimization objectives, and a complete high efficiency optimization strategy based on the
Acknowledgements
This work was supported by 973 program (2011CB711100) and national key technology R&D program (2009BAQG12A03). Computing Facility for Computational Mechanics Institute of Mechanics, Chinese Academy of Sciences is gratefully acknowledged.
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