Aerodynamics and Flow Field

induced by 2 HST trains

passing by each other

USING FDM/FVMMohit Prakash 12118049

Sourabh Hirau 12118077

Udit Kumar 12118084

Overview

IntroductionTheory of

Aerodynamic Simulations

NUMERICAL METHOD

Computation and

Discussion

Computed Results

Summary Conclusions

Introduction

The speed of trains has rapidly increased in recent years. Currently,

some of the high speed trains move at almost 300 km/h, which

corresponds to a Mach number of more than 0.2. With the increase

of speed, aerodynamic problems of such trains are emerging.

Due to the magnitude of the velocity of a high speed train (HST) the

flow of the air around the train becomes an important factor in the

movement of the train. This flow of air gives rise to the unsteadiness

and the different forces and moments that start acting on the train

and have a big impact on the stability of the train and safety and

comfort of the passengers and they can even cause the structural

fatigue .

Introduction(cont.)

A three-dimensional flow field induced by two trains passing by each

other inside a tunnel is studied based on the numerical simulation of

the three-dimensional compressible Euler/Navier-Stokes equations

formulated in the finite difference approximation.

A domain decomposition method with the interface scheme called

as FSA (fortified solution algorithm) is used to treat this moving-body

problem.

The computed results show the basic characteristics of the flow field

created when two trains pass by each other.

The history of the pressure distributions and the aerodynamic forces

acting on the trains are the main areas discussed.

The results also indicate the effectiveness of the present numerical

method calculating moving boundary problems.

Theory of Aerodynamic Simulations

To solve the flow of air around the trains CFD was used. CFD is based on the

finite volume approach. This means that the conservational principals are

applied for the properties describing the behaviour of a matter interacting

with its surrounding. The laws of conservation of mass and momentum for a

finite volume gives the continuity equation (2.1) and the equation of

motion (2.2).

Combining these together with the constitutive equations and assuming Stokes

condition(ƛ = -2µ/3) for an isotropic homogeneous Newtonian fluid (2.3), which air is, one

ends

up with the instantaneous compressible Navier-Stokes equations (2.4).

The Navier-Stokes equations are non-linear partial differential

equations and believed to precisely describe any type of flow.

However only a few exact solutions exists so the Navier-Stokes

equations have to be solved numerically. This is easier done by

splitting up the instantaneous variables into a mean and a fluctuating

part.

This is called Reynolds decomposition and the resulting equations are

called Reynolds averaged Navier-Stokes equations (2.5) (RANS). Note

that no incompressibility assumption were done in this project.

NUMERICAL METHOD

BASIC EQUATIONS : The basic equations are the unsteady three-

dimensional compressible Euler/Navier-Stokes equations

NUMERICAL METHOD (cont.)

The pressure is expressed by the equation of state for an ideal gas,

COMPUTATIONS AND DISCUSSIONS

Flow configuration

Two trains having the same shape

move at the same speed of Mach

number 0.22 (270 km/h) in opposite

directions inside the tunnel.

The blockage ratio of the cross-

sectional area of the train relative to

the tunnel is 0.12.

The length and the width of the train

are 2.5 and 0.34, respectively and the

lateral distance between the two

trains is 0.11. The trains are located 4.0

apart from each1 other at the

beginning.

COMPUTATIONS AND DISCUSSIONS

Figure shows the cut of the flow

field in the horizontal plane. In this

plane, the flow field is point

symmetric about the center point

under the condition that the same

trains cross each other at the same

speed.

Using this assumption, only the

upper left half of the flow field is

solved, which reduces both the

grid points and the computer time.

COMPUTATIONS AND DISCUSSIONS

The quasi steady-state solution

that is obtained for the trains

located in a finite distance from

each other is used as an initial

condition.

At the inflow boundary (right

boundary of the hatched region),

the point symmetry condition is

imposed.

COMPUTATIONS AND DISCUSSIONS

Pressure waves created by the trains can be captured by the Euler

equations.

The viscous effects on the tunnel wall is not important for this problem.

The flow near the train body surface may change the effective body

configuration and may have an influence on the unsteady pressure field.

The thin-layer Navier-Stokes equations are locally used in the zone for the train body.

The computation required about 50 h on VP200 supercomputer at the ISAS.

The integration time step is taken sufficiently small ( 4.5 x 10 s) to resolve flow

field.

Spatial discretization

The basic equations are discretized in the finite difference fashion. In the

right-hand side, the convective terms are evaluated using the flux

difference splitting by Roe.

The MUSCL interpolation( A FVM method) is used for the higher-order

extension. The metrics terms include the time derivatives to take care of the

grid movement.

All the details about the evaluation of the right-hand side except the

treatment of the Fortified source terms shown above can be found in the

paper by Fujii and Obayashi.

COMPUTATIONAL GRID

• The flow field is divided into four

zones, the tunnel zone, the zone

around the train (TRAIN ZONE), the

bottom of the train (BOTTOM ZONE)

and the interface zone.

• The train and the bottom zones

move at the train speed, the

position of the grids in the moving

zones relative to the tunnel grid

should be computed and the zone-

to-zone interpolation is necessary at

the zonal boundaries at each time

step.

COMPUTATIONAL GRID

• The grid-to-grid correspondence and the coefficients necessary for the interpolation between the two moving grids and this interface square grid do not change in time because all these three grids move at the same speed.

• The interface grid is a Cartesian-like square grid, the interpolation between this interface grid and the tunnel grid becomes simple and does not require much computer time.

• The grid points of the TRAIN ZONE are distributed by the hyperbolic grid generation method and the other grid points are generated algebraically.

Fortified solution algorithm

The FSA took the basic concept from the idea of the Fortified Navier-Stokes

(FNS) approach that was originally developed by Van Dalsem and Steger.

to improve the performance of Navier-Stokes algorithms by using fast

auxiliary algorithms that solve subsets of the Navier-Stokes equations.

This FNS concept as an interface scheme and developed a zonal method

for a steady-state vertical flow problem.

The method was applied to present complicated flow problem between

trains. Since the basic equations need not be the Navier-Stokes equations,

this zonal method is now called FSA (Fortified Solution Algorithm) zonal

method.

When FSA applied to eular equations, and basic equation rewritten as

Fortified solution algorithm

The right-hand side term is the fortifying (forcing) term.

The solution is fortified to be Qr in other words, Qr = Q, when the switching

parameter X is set to be sufficiently large.

For the region that X values are set zero, the equations go back to the

original Euler equations.

By adding the forcing terms and modifying the solution procedure, we can

overlay the known solution Qr onto the solution Q in the appropriate region.

The required implementation for this algorithm is just to add the source term

to the right-hand side and to set the distribution of the X parameters,

whatever kind of domain decomposition (such as patched grid or overset)

grids may be used.

Computed results

To help understand the result, the

relative position of the train and

the imaginary opposite train at

several time stations is presented

At t = -9.09, the trains start moving

with the steady-state solution as

an initial condition.

At t = 0.0, both the train noses come to the point x = 0.0

Computed results

At t = 5.68, both the trains are

aligned side by side

At t = 11.36, both trains’ rear noses

are located at x = 0.0 and the

crossing is finished.

that the non-dimensional time 1.0

corresponds to 0.023 s. The top

view of the pressure contour plots

on the ground as well as the train

surface

Computed Result

red colour indicates high pressure

the blue colour indicates low

pressure.

as soon as the trains begin to

cross each other (t = 0.91), the

pressure at the front nose

(stagnation) of the trains begins

to decrease.

At the same time, the pressure at

the outer side of the train front

nose becomes low.

Velocity Profile

Velocity vector plots (shown here)

indicate that strong flows from the

inside high pressure region to the

outside low pressure region exists

over the train. When the bodies of

the trains are crossing each other

The pressure near the shoulders

between the train bodies strongly

decreases. The pressure at the

nose front still decreases.

Time history of the pressure coefficient on the side-wall surface facing to the opposite train.

Drag Coefficient

The aerodynamic forces acting on the train are important for the passengers’ comfort and safe train operation

drag coefficient, Co. When the trains start crossing, is described along side

When the trains start crossing, the drag force decreases since the pressure at the front nose decreases as described above.

the drag force recovers a little as the stagnation pressure recovers, but again starts decreasing as

the front nose approaches the rear shoulder of the opposite train.

Lift Coefficient

The C, increases when the crossing begins at t = 0.0, keeps almost constant value until t = 5.0, and then decreases.

The pressure on the upper surface of the train becomes low during the crossing. The pressure on the bottom surface also decreases but not as strong as the upper surface.

Therefore a lift force acts on the train while crossing. However, the fluctuation of the CL is much smaller compared to the other forces.

Pitching moment coefficient

The positive C, indicates the force to push the trains apart. As the trains come close, C, becomes large due to the high pressure between the front noses.

Then, it decreases until the shoulder of the train meets the shoulder of the opposite train.

The main reason for the increase of the C, at around t = 3.0 may be the pressure recovery at the front nose that pushes the train apart

As the trains move away from each other, the C, becomes small.

Summary

the mechanism of the aerodynamic forces is mainly governed by the movement of the high stagnation pressure at the nose and the strong low pressure region near the shoulder of the train.

The location of the nose and the shoulder relative to those of the opposite train basically explains the trend of aerodynamic forces and moments.

That means the improved design of the frontal part of the train may reduce the strong side force and yawing moments that would occur during the crossing of two trains.

The frontal part of the train is conventionally designed considering the reduction of the aerodynamic drag, and the interaction with the opposite train is not conventionally considered much.

The present paper discusses the aerodynamic characteristics of two trains passing by in a tunnel. The effect of the tunnel has not been discussed.

Conclusions

The flow field induced by two trains passing by each other inside the tunnel

has been numerically simulated using the Euler/Navier-Stokes equations.

The domain decomposition method was used to handle this moving

boundary problem. The computed result revealed the complicated flow

patterns. A strong side force acts on the train and it has several positive

and negative peaks.

It was revealed that the aerodynamic forces and moments strongly

depend on the relative position of the trains. Especially, the location of the

nose and the shoulder plays an important role.

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