# Aerodynamic shape optimization of high-speed trains using adjoint methods

Today’s high-speed trains, like those operating in China, convey passengers and goods with speeds reaching up to 350 km/h. thus even exceeding the landing speeds of commercial aircraft. Current developments of train manufacturers even aim for future traveling speeds of 400 km/h and more. Operating conditions like these make aerodynamic shape optimization a crucial factor during the entire design process of new high-speed trains. In order to meet the increasing requirements for safety, energy consumption, comfort, etc., and to reduce the demand for time-consuming and expensive wind tunnel experiments, we need design procedures, which can speed up or even automate the shape optimization process of high-speed trains.

There are many different strategies to improve specific aerodynamic features of vehicles, e.g. trains, defined by the corresponding objective functions. In case of gradient-based shape optimization, it is important to know the dependency of the considered objective function on small variations of the original shape. This dependency can be evaluated via sensitivity analysis, which computes the sensitivities, i.e. the derivatives or gradients of the objective function with respect to small modifications of the surface. The calculated sensitivities can be used to evaluate the necessary changes/modifications of the investigated geometry. This process can be run iteratively until the desired optimum is reached.

OneOne of the most important design aspects of high-speed trains is the influence of the aerodynamic loads on track side objects induced by the pressure wave generated by a passing train. First results of shape optimization applied to the conceptional Next Generation Train (NGT) aiming to minimize this pressure wave reveal the efficiency of the developed process chain. After five iterations, the pressure pulse could be decreased by a total of 20%, as can be seen in Table 1.

Iteration Value

0. 22.14

1. 20.64

2. 20.68

3. 19.46

4. 18.45

5. 17.60

Table 1: Values of the objective function (Δ_{tot} J_{Ω}≈20%)

Figure 1 shows the corresponding generated pressure waves for different optimization steps.

The enormous savings of adjoint-based shape optimization in computational effort have many advantages especially when dealing with complex geometries and large numbers of surface points as design parameters. In our procedure, we iteratively use continuous adjoint optimization and sensitivity analysis to evaluate the required shape modifications. To avoid the necessity of creating a new mesh after each optimization step - and thus to further reduce the costs of the entire process- we opted for a CAD-free approach using mesh morphing to modify the existing computational mesh instead of changing the original geometry. We developed an in-house tool using radial basis functions to determine the surface and volume mesh displacements from the calculated sensitivities and to provide the deformed mesh for a new calculation.

Figures 2 and 3 show an example of the sensitivity analysis of the NGT and as well as an animated detailed view of how the surface mesh has been deformed during the optimization process.

# References:

D. Jakubek, S. Herzog, C. Wagner “Shape Optimization of High Speed Trains using Adjoint-based Computational Fluid Dynamics”, IJRT Vol. 1, Issue 2, 67-88, 2012.

Dr. Keith Weinman

German Aerospace Center (DLR)

Institute of Aerodynamics and Flow Technology, Department Ground Vehicles

Göttingen

Phone: +49 551 709-2339