Aerodynamic optimization of railway motor coaches

F. Monnoyer, E. Lorriaux, N. Bourabaa

Laboratoire de Mécanique et d'Énergétique, University of Valenciennes, France

Abstract An aerodynamic optimization procedure using a genetic algorithm is presented. This multi-purpose procedure is first applied to drag minimization. In a preliminary phase, the feasibility of the method is assessed on two-dimensional profiles. In addition to specific features of the genetic algorithm, the implementation of automatic mesh generation and flow calculation is investigated. First three-dimensional results are discussed, where the shape generation process is automated. 1. Introduction The technological breakthrough in railways aerodynamics goes back to the putting into service of the very high speed trains in the early eighties. At operating speeds over 250 km/h, aerodynamic drag represents the largest part of traction power consumption and other phenomena related to fluid dynamics do appear: aerodynamic noise becomes louder than rolling noise; circulation in tunnels generates significant pressure fluctuations; cross winds have a stronger destabilizing effect; ballast floating is provoked in certain circumstances; the pantograph-catenary interaction is affected… Today, the 200 km/h commercial speed is reached or is planned for all rail modes, including freight. This, together with always more demanding customers and users in terms of safety, stability, comfort and cost-effectiveness, makes aerodynamic optimization an important issue not only to rolling stock, but also to railway infrastructure. The available engineering tools applying to fluid dynamics are experimental testing and numerical simulation. Experiment, either full scale or in wind tunnel, is the ultimate means of validating technological choices or numerical predictions, but it is too costly and time consuming to be heavily used at the design stage. On the other hand, computational fluid dynamics (CFD) is more flexible and economical, and has gained confidence on its ability to model complex flows accurately. CFD is widely used in aircraft and automobile design, and its implementation in railways is more recent [5], mainly because of the later emergence of aerodynamic concerns, but also due to specific difficulties involved by railway applications. Apart from drag in cruise conditions, the aerodynamic features mentioned above are mostly unsteady phenomena characterized by relatively large time scales, implying very costly calculations and requiring very large computing capacities. Moreover, all significant flow features are of global nature and therefore require taking the complete trains and their wake into account. Since the optimization of the aerodynamic performances of new rolling stock is hampered by design costs and durations that are inherent to the physical features to model but prohibitive for the railway manufacturing industry, new methods must be developed to make the most efficient use of CFD. One solution is to act on the models themselves, by adopting simplifying assumptions valid in specific cases. As an example, it is demonstrated that the pressure fluctuations in tunnels are predominantly one-dimensional; as a consequence, this phenomenon is very efficiently and accurately predicted by appropriate, simplified methods [11]. In most of the cases, however, there is no alternative to the general governing equations to guarantee a sufficient modeling accuracy [8]. The best way to achieve efficiency in the optimization process is then to reduce the number of simulations.

This paper is devoted to the first stage of a larger research project aiming at developing a multi-objective optimization procedure, applicable to all aspects of railways aerodynamics and able to seek optimum combinations of large numbers of parameters in a reasonable time and at an affordable cost. In the exploratory phase, the method is applied to drag minimization, but it was designed from the onset to be applicable to the other known aerodynamic issues.

The optimization procedure is based on a genetic algorithm, which was chosen because of its ability to survey complex search spaces and to escape the traps of local extrema. To improve efficiency and to reduce the number of simulations, a crucial point in our case, several complementary steps have been

developed as a complement to the standard genetic algorithm. Those which proved their efficiency have been implemented in the method.

In the present paper, the foundations of the method are presented and illustrated by two-dimensional applications. In a second part, the extension to realistic three-dimensional configurations is discussed.

2. The genetic algorithm Genetic algorithms are inspired by the principles of natural selection. Sciences engineering shows a growing interest for this type of metaheuristic optimization method [1-4, 6, 9]. The iterative process of the genetic algorithm reproduces the evolution of a constant population over its successive generations. Each individual corresponds to a distinct solution of the problem and its chromosomes are its parameters. The steps constituting a single iteration for the passage from a generation to the next are illustrated in Figure 1: - Selection: the individuals are opposed in competitions where the loser is eliminated, the survivors being

selected as new parents in an intermediate generation of half the initial population. Only the better-adapted individuals have a greater probability to be selected to reproduce and generate new individuals, thus perpetuating their genetic information.

- Crossover: random combinations of the parents' chromosomes generate new individuals until the initial population size is recovered. These new individuals tend to be better fitted than their parents, which leads to the conclusion that after several generations the population will be composed of highly adapted individuals

- Mutation: Along with the recombination process, mutations are commonly introduced in the form of random modifications of the children parameters. Mutation acts as a diversity agent, to avoid all solutions tending to become very similar after multiple crossings, with th risk of stagnation at a local optimum.

3. Feasibility Study: two-dimensional applications 3.1. Problem setup In a first phase, the applicability of the genetic algorithm to aerodynamic optimization has been assessed. For this preliminary feasibility study, simplified configurations were considered: - the train is restricted to its longitudinal plane of symmetry, and the flow is assumed two-dimensional; - the rear of the train is included in the calculation, as it plays a significant role on the overall drag.

However, the central part of the train is shortened to reduce the size of the computational domain. Care was taken to keep a sufficient length to have a fully developed boundary layer upstream of the tail.

Figure 1: Evolution of a generation

The equations are solved in a Galilean reference frame attached to the train. Consequently, the train and its surrounding computational domain are fixed in space with the ground moving in the downstream direction at the speed of the incoming air flow. The computational domain and the classical conditions applied at its boundaries are shown in Figure 2.

The target variable to be minimized is the drag coefficient Cx:

=ρ 21

2

xx

FC

SV where Fx is the drag force, ρ the air density, S the train cross-sectional area and V its speed. Since the optimization process involves a large number of calculations, it is essential to reduce the computational effort as much as possible, while ensuring that the drag coefficient is computed with a sufficient accuracy. For this purpose, a sensitivity analysis has been carried out on the turbulence model and on the grid resolution, in order to find the right compromise between the required accuracy and the computational effort of the flow calculations. As a conclusion, calculations are performed on grids of about 35,000 cells, with the one-equation Spalart-Allmaras [10] turbulence model. The flow solver is the commercially available FLUENT software. 3.2. Grid generation The spatial discretization of the computational domain is realized with two constraints: - grid generation must be automated and provide valid meshes for all the possible configurations in

accordance with the geometric parameters defined for the optimization process; - the grid resolution must be adapted to the local physical properties of the flow field. The best way to fulfil these somewhat contradictory requirements is a hybrid grid. It combines a structured grid in wall proximity, to control the boundary layer resolution, and an unstructured triangular grid extending in the remainder of the spatial domain. A typical mesh around the forebody is illustrated in Figure 3. Grid generation is facing difficulties around sharp noses but the automatic procedure is yielding consistent meshes for this situation. Note that the afterbody is geometrically symmetric but that the grid is not identical in the unstructured region, where the cells are kept smaller for a better spatial resolution of the wake.

Figure 3: Mesh around the nose

Figure 2: Computational domain and boundary conditions

4. Shape Optimization 4.1. Shape definition The variable nose shape is generated by two connected NURBS defining the upper and lower parts of the nose, respectively. The two curves are passing through four control points, the position of which being controlled by means of the four parameters b, y1, y2 and y3, see Table 1. Figure 4 shows a typical geometry with the control points numbered from 1 to 4 and the remaining fixed points marked by solid circles.

1 2 3 4 x-coordinate fixed fixed ½b b

y-coordinate y1 y2 y3 fixed

Table 1: Control points coordinates

- The upper part of the nose is interpolated from four points: two fixed points at the ends and the two control points 1 and 2. Their x-coordinates are fixed and their y-coordinates y1 and y2 are variable parameters. The y2 parameter acts on the nose sharpness while the y1 parameter controls the curvature and the global shape of the profile;

- The lower part extends from the fixed point at the nose to the control point 4 and passes through point 3. The b parameter sets the x-coordinate of both of them and the y3 parameter controls the vertical position of the intermediate point 3.

- Smooth slope transition is imposed between the nose and the body of constant cross-section, both at the underside and at the roof.

4.2. Results 4.2.1. Random method An investigation of the search space has been performed prior to applying the genetic algorithm, in order to assess the sensitivity of the drag coefficient to the various parameters and to determine whether some parameters play a more significant role than others. Since an exhaustive survey of the whole palette of geometries would be too costly, a sample of 300 different nose shapes has been randomly generated by combinations of the geometric parameters

Figure 4: Two-dimensional nose shape

defined above. This random method is not intended to deliver the best solution but a representative population of train geometries. The most salient results are briefly discussed underneath. Figure 5 shows the evolution of Cx vs y1, the parameter controlling the global shape of the upper curve. The two configurations on the right of the figure are examples of individuals, where the lowest is characterized by a drag coefficient close to the minimum of the sample.

The higher drag coefficients systematically observed for values of y1 below 2.5 m indicate that this parameter is significant, as it is directly associated with poor quality solutions whatever the values of the other parameters. In other words, a "bad" value of y1 overrides any effect of "good" values of the other parameters. On the other hand, the solutions are more scattered for higher values of y1, indicating that other parameters are playing a role, though it is clear that an optimum region exists around y1=2.7m. The y2 parameter is also playing a role, although to a less extent than y1. The pattern of Figure 6 shows that the best solutions are obtained for higher values of y2, i.e. y2>1.3m. Two distinct zones can be clearly identified. They correspond to values of y1 below and above 2.5m, respectively, and this is consistent with the significant behavior of y1 identified previously. The two profiles illustrate how the y2 parameter acts on the nose sharpness.

Figure 6: Influence of the parameter y2

Figure 5: Influence of the parameter y1

4.2.2. Application of the genetic algorithm The application of the genetic algorithm to a population of 28 individuals provided a best solution after 10 generations, as shown in Figure 7. 90 different configurations have been calculated.

The best profile according to the genetic algorithm is shown in Figure 8. The values of the y1 and y2 parameters are consistent with the conclusions drawn in the previous section and the resulting nose bluntness may be surprising at the first sight. For the sake of comparison, the particular solution drawn in Figure 5 and characterized by a slender nose is reproduced in Figure 9.

The lower drag produced by the blunt shape is due to its wake. Indeed, a deeper insight into the pressure and shear forces distributions shows that the contributions of the front parts are practically identical for both geometries. On the other hand, the downstream flow patterns differ significantly. This is visible in Figure 10, showing the total pressure field behind the trains. The wake of the sharper nose is indisputably wider, reflecting larger energy losses. This phenomenon constitutes the major part of the drag force and is completely driven by the shape of the train nose.

Figure 7: Best solution for each generation

Figure 8: Best solution Figure 9: Sharp nose individual

Extensive testing has been carried out with the two-dimensional model. The effect of population sizes, selection procedures, mutations and of several other features was investigated. In addition, the automated meshing and calculation procedure of train geometries has been adapted to parallel computer architectures, with the ability to evaluate several individuals simultaneously. The genetic algorithm has demonstrated its good search capacity. Moreover, it is able to bring out solutions that would probably have been eliminated by classical engineering approaches. However, the solution obtained from the genetic algorithm may depend on the initial population, in particular if its size is small. The use of large populations is unaffordable for aerodynamic optimization because the calculation of the drag is a computer intensive task, and mutations introduce the necessary diversity to make up for degeneration by consanguinity. The ability of the genetic algorithm to preserve the diversity of the possible solutions and to seek global optimums in complex search spaces is balanced by a relatively slow convergence of the process. This is a serious drawback since it involves numerous costly flow calculations, and a strong improvement of the overall convergence has been achieved by coupling the general genetic algorithm with an embedded Simplex [7] method 5. Three-dimensional model 5.1. Shape design The definition of real three-dimensional train geometries must rely on a high-quality CAD platform that has to be included in the iterative optimum search. For this purpose, the code must be linked to the agent defining the new individuals and to the grid generation tool for the flow calculation. The Open CASCADE1 platform fulfils these requirements: it includes components for 3D surface and solid modelling and it provides extensive data exchange capabilities; moreover, this open source software is freely available and can be modified according to any particular needs. The choice of the governing parameters for the nose shape is a difficult task: their number must be reduced as much as possible to limit the size of the search space, but they must guarantee to cover a wide range of realistic geometries. Their definition is still work in progress, and use is made at the present stage of local parameters analogue to those implemented for the two-dimensional applications. Starting from a central part of constant, fixed section, the train's ends are generated by the Open CASCADE module with the following rules: 1 www.opencascade.org

Figure 10: Total pressure field (Pa) in the wakes

- the surface is subdivided into an upper and a lower face. These two faces are defined by their bounding curves;

- the bounding curves in the longitudinal plane of symmetry are controlled by the same parameters as those applied to the two-dimensional models discussed in the previous section, excepted that y2 and y3 are replaced by vectors to control the surface tangency;

- the upper and lower faces share a common bounding b-spline curve, controlled by an additional parameter;

- first-order continuity with the train body is imposed as well as in the plane of symmetry. Figures 11 and 12 show two examples of shapes produced by the method, with their bounding curves. Both trains have an overall length of 28 m and a 20 m long, 4.5 m high central part. The parameter setting was intentionally chosen to generate profiles similar to the two-dimensional nose shapes presented in section 4.2.2.

5.2. Flow simulations The streamline patterns around the two shapes presented in Figures 13 and 14 show that the flow fields are globally similar, with the formation of horseshoe vortices behind the tail. The onset of these structures takes place on the lower part of the rear end, where the fluid arriving from behind the train is recompressing in the wake. The vortices are fed by air flowing from the sides and the top of the train, and build a strong wake extending far behind.

Figure 12: Train shape B

Figure 11: Train shape A

The drag coefficients of shapes A and B are 0.21 and 0.23, respectively. Unlike the two-dimensional analysis, the second shape is not a better solution than the sharper nose. This is due to the fact that the steeper rear windshield leaves more room to air flowing from the sides toward the hood and eventually feeding the vortices, which in turn spread over a larger area in the wake. This behavior is essentially three-dimensional and points out that aerodynamic optimization cannot rely upon conclusions drawn from simplified cases.

6. Conclusions First investigations of the genetic algorithm applied to the aerodynamics of railway vehicles have confirmed its feasibility and its efficiency. The optimization process has been successfully implemented with standard state-of-the-art CFD software and the influence of various geometric parameters has been assessed on two-dimensional configurations. Emphasis has been laid on the development of coupled optimization methods, to improve the efficiency of the optimum search compared to the sole genetic algorithm, without losing the flexibility required to cope with complex search spaces and multiple parameters. In addition, careful attention has been paid to the efficient use of the embedded flow simulation method, regarding automatic grid generation and parallel computation. The extension to three-dimensional configurations is in progress. Surface modelling requires sophisticated tools that have to be open to modifications in order to be included in the automatic process. In addition, specific constraints like the trains’ length and the need to optimize nose shapes operated both in front and at rear position make the process a very demanding task in terms of three-dimensional flow simulation effort. These issues are addressed and the Open CASCADE platform has already proven its suitability. Automatic grid generation is a challenging task but the developments realized so far are encouraging.

Figure 14: Flow around shape B

Figure 13: Flow around shape A

Acknowledgements This work is supported by the Regional Research Group on Ground Transport (GRRT), in the research program TAT of the Région Nord-Pas de Calais. Financial support is granted by the ERDF program of the European Community. References [1] D. Dupont, A.-M. Kökösky, Ph. Biela, and A. Saadane. "Vie Artificielle : application à la résolution de problèmes complexes". In Techniques de l’ingénieur, volume HA. (2002) [2] V. Gautard-Yzquierdo. "Optimisation automatique de formes en aérodynamique. Application à la conception d’aéronefs". PhD thesis, Université de Paris Nord (1999) [3] K.C. Giannakoglou. "Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence". Progress in Aerospace Sciences, Vol. 38, pp. 43-76 (2002). [4] S. Maouche, C. K. Bounsaythip, and G. Roussel. "Optimisation du placement de formes irrégulières". In Techniques de l’ingénieur, volume S.(2000). [5] F. Monnoyer, M. William-Louis. "Application of CFD to High-Speed Trains Aerodynamics". in Computational Methods in Applied Sciences '96, John Wiley & Sons, p. 153-159 (1996). [6] F. Muyl, L. Dumas, and V. Herbert. "Hybrid method for aerodynamic shape optimization in automotive industry". Computers & Fluids, Vol 33, pp. 849-858 (2004) [7] J. Nelder, R. Mead. “A simplex method for function minimization”. Computer Journal, Vol. 7, pp. 308-311 (1965) [8] R. S. Raghunathan, H. D. Kim, and T. Setoguchi. "Aerodynamics of high-speed railway trains". Journal of Wind Engineering and Industrial Aerodynamics, Vol 38, pp. 469–514 (2002) [9] K. M. Rachid. "GADO, a Genetic Algorithm for continuous Design Optimization". PhD thesis, University of New Jersey (1998) [10] Ph. Spalart and S. Allmaras. "A one-equation turbulence model for aerodynamic flows". Technical Report AIAA-92-0439, American Institute of Aeronautics and Aeroacoustics (1992) [11] M. William-Louis, R. Grégoire. "1-d Calculations of Pressure Fluctuations Outside and Inside a Pressure Sealed High-Speed Trainset Travelling through Tunnels". in TRANSAERO, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Vol. 79, Springer Verlag, pp. 342-357 (2002)