Analysis of Flow Structures in the Wake of a High-Speed Train

Abstract

Slipstream is the flow that a train pulls along due to the viscosity of the fluid. In real life applications, the effect of the slipstream flow is a safety concern for people on platform, trackside workers and objects on platforms such as baggage carts and pushchairs. The most important region for slipstream of high-speed passanger trains is the near wake, in which the flow is fully turbulent with a broad range of length and time scales. In this work, the flow around the Aerodynamic Train Model (ATM) is simulated using Detached Eddy Simulation (DES) to model the turbulence. Different grids are used in order to prove grid converged results. In order to compare with the results of experimental work performed at DLR on the ATM, where a trip wire was attached to the model, it turned out to be necessary to model this wire to have comparable results. An attempt to model the effect of the trip wire via volume forces improved the results but we were not successful at reproducing the full velocity profiles. The flow is analyzed by computing the POD and Koopman modes. The structures in the flow are found to be associated with two counter rotating vortices. A strong connection between pairs of modes is found, which is related to the propagation of flow structures for the POD modes. Koopman modes and POD modes are similar in the spatial structure and similarities in frequencies of the time evolution of the structures are also found.

Appendix A: Trip Forcing

In [12] numerical and experimental results are compared for the ATM. The velocity profiles were considered to show a good agreement, except alongside the train. This was considered a promising first comparison, but the difference on the side of train implied that further investigation was needed. It was found that the reason for the difference in results in this region was caused by the installation of a trip wire in the experimental model. This trip wire is located on the middle of the first car and it is exactly at this position that the experimental and numerical results start to deviate. This lead to the conclusion that the trip wire was important for the flow and that it had to be included in the simulation. Including the trip wire geometrically and resolving the flow around it in the simulation could be very troublesome and computationally demanding. An approach to model the effect of the wire is investigated instead.

1.1 Method

The trip forcing model applied in this work is based on the trip forcing presented in [4]. In [4], the flow over a flat wall is considered hence, the y-coordinate is in the wall normal direction. The trip forcing in [4] is modeled via $F_S=(0,F_2,0)$, where

$$\begin{aligned} F_2 = exp \left( \left\{ x - t_{x0} / t_{xsc} \right\} ^2 - \left\{ y/t_{ysc} \right\} ^2 \right) f(z,t) \end{aligned}$$

(12)

with

$$\begin{aligned} f(z,t) = t_{amps}g(z) + t_{ampt}\left( \left( 1-b(t)\right) h^i(z) + b(t)h^{i+1}(z) \right) \end{aligned}$$

(13)

$$\begin{aligned} i = int(t/t_{dt}) , \;\;\;\;\;\;\;\;\; b(t) = 3p^2 - 2p^3, \;\;\;\;\;\;\;\;\; p = t/t_{dt} -i. \end{aligned}$$

(14)

The functions g(z) and $h^i(z)$ are Fourier series with $N_{zt}$ random frequencies, corresponding to steady and transient forcing respectively. Linked together with the Fourier series are the amplitudes $t_{amps}$ and $t_{ampt}$, s for steady and t for transient. The function b(t) is included in order for the forcing to be continuous in time. The constant $t_{x0}$ is the position of the trip forcing (the wall normal position is $y=0$) and $t_{xsc}$ and $t_{ysc}$ is the width of the Gaussian function in spanwise and wall normal direction. The variable $t_{dt}$ is the interval between different transient Fourier series for the trip. In this work, we used $N_{zt}=10$, $t_{amps}=t_{ampt}$, $t_{x0}=0.1713$, $t_{xsc}=0.04$, $t_{ysc}=0.005$ and $t_{dt}=0.0005$

The original formulation is valid for a flat plate. For simplicity, the curved surface of the train is considered as locally flat, where the y-coordinate is changed to the distance to the wall and z direction is considered to be along the curved surface. For any given point in the fluid, the distance to all the surface points are computed and minimized, in order to find the wall position closest to that cell. The vector from the point to the closest surface point is considered the normal direction and using $F_2$ from Eq. (12) the forcing in the cartesian coordinate system becomes $F_y = F_2 \times \cos (\theta )$ and $F_z = F_2 \times \sin (\theta )$, where $F_y$ and $F_z$ is the forcing term in the coordinate system of the train, and $\theta$ angle between the vector, of the point and the closest surface point, and the y-direction.

Fig. 11

Velocities and $u_{rms}$ alongside the train with three different amplitudes of trip forcing (4E5,6E5,1E6) compared to experimental results. Vertical line is the position of the trip wire

1.2 Results

The amplitudes of the forcing ($t_{amps}$ and $t_{ampt}$) are found to be important parameters. Too small amplitudes do not affect the flow significantly while too high amplitudes create a jet from the position of the trip forcing yielding too large impact on the flow on the side of the train. Different amplitudes are tested in order to find an optimum. Amplitudes that are very high or very low can be disregarded only by looking at the instantaneous flow. For these extreme values of the amplitudes, the simulation is stopped before the averaging starts and the results are not presented.

Even tough the results including a trip forcing show a large improvement in the region along side the train, no convergence towards the experimental data were found. There are two regions of the flow where the simulated results does not match experimental results. These two regions are directly after the location of the trip wire ($\approx -30 d_h$) and towards the end ($\left[ \approx -20 d_h,-5 d_h \right]$) where the velocity seem to be more or less constant with spanwise position. A higher amplitude of the trip forcing match the data just downstream of the trip wire but causes an overprediction of the velocity in the second region. A lower amplitude would give a good estimate towards the rear of the train, but underpredict the velocity close the trip wire. In addition, trying to match the $u_{rms}$ values is even more challenging. Results for different amplitudes are shown in Fig. 11. The black vertical line represents the position of the trip wire. In this study only the amplitudes are varied. Changing more parameters of the volume forcing would increase the computational cost extensivly. From the results in this section, we conclude that the the trip wire is needed in the numerical simulation in order to compare to experimental results and that the volume forcing improves the results but was unsuccessful to reproduce the experimental results.