# Case 2 Help: Crossing Trains in a Tunnel

Case 2 simulates pressures and velocities when two trains travel through a simple tunnel. Each train carries its own pressure signature through the tunnel and also generates pressure waves as it enters and leaves the tunnel. The waves result from discontinuities at the noses and tails of trains and also from friction along the trains. Pressure fluctuations experienced by passengers on the trains are influenced by (i) waves caused by their own train, (ii) waves caused by the other train and (iii) the pressure signature carried by the other train.

Location of pressure and/or velocity output

## Output Locations

The principal use of Case-2 simulations is expected to be the prediction of pressures experienced by passengers on trains. However, some output is also provided at selected tunnel locations.

### Graphical output is provided as follows:

**Box-1:** Pressure histories in the tunnel

Tunnel-1 at x = LTUN / 4

Tunnel-1 at x = 3*LTUN / 4

**Box-2:** Pressure histories inside the front and rear coaches
of train-1

Solid lines - outside the train

Broken lines - inside the train

*NB: For unsealed trains, there is little difference between pressures
inside and outside coaches. For well-sealed trains, sufficiently rapid external
pressure changes are strongly damped. Large values of the sealing time constant
correspond to tight seals and small values correspond to poor seals. *

**Box-3:** Mean air velocity histories in the tunnel

Tunnel-1 at x = LTUN / 4

Tunnel-1 at x = 3*LTUN / 4

**Box-4:** Pressure histories inside the front and rear coaches
of train-2

(1) outside the train

(2) inside the train

### Text output is provided in the V01.txt file as follows:

- Pressure and mean-velocity histories at

Tunnel-1 at x = LTUN / 4

Tunnel-1 at x = LTUN/2

Tunnel-1 at x = 3*LTUN / 4 - Pressure histories in the leading and trailing coaches of both trains

(1) for an unsealed train

(2) for a sealed train with a time constant of 10 s - Train speed history

## LTUN, m: Length of the tunnel

For most purposes, the meaning of the tunnel length is self-evident. If you want to be more precise, give the distance between the centroids of the cross-sections of the tunnel portals. This is not a formal definition, but it is probably good enough.

In ThermoTun-Online, the length of the tunnel must be at least 300m. The full version of ThermoTun allows experienced users to choose any length greater than zero. ThermoTun-Online is intended only for applications in which one-dimensional analyses can be used with reasonable confidence.

## ATUN, m^{2}: Cross-sectional area of tunnel

For most purposes, the meaning of the cross-sectional area of the tunnel is self-evident. If you want to be more precise, calculate the total volume of air in the tunnel and divide this by the total tunnel length. This is not a formal definition, but it is probably good enough.

In ThermoTun-Online, the area of the tunnel must be at least 10m^{2}.
The full version of ThermoTun allows experienced users to choose any area greater
than zero. ThermoTun-Online is intended only for conventional train:tunnel applications.

With large cross-sectional areas, the assumptions of one-dimensional flow
can become suspect. It is recommended that the effective diameter of the tunnel
should not exceed 5-10% of its length. *(NB: The “effective diameter”
is the diameter of a circle with the same cross-sectional area as the tunnel).
*

## FTUN (*f*): Tunnel friction coefficient
(Fanning, not Darcy-Weisbach)

The tunnel skin friction coefficient determines the resistance to airflows
along the tunnel. There are * two* definitions in common use:

*Fanning (**f* ): Wall shear stress = *f* x ρ*U*^{
2}/2

** Darcy-Weisbach (λ )**: Wall shear stress =

*λ*x ρ

*U*

^{ 2}/8

where ρ is the density of the air and *U* is the mean velocity
along the tunnel.

It follows from the definitions that *λ=4f* so it is important
to know which one is used in any particular software. ThermoTun uses *f*,
not *λ*.

The Fanning friction coefficient for real tunnels will exceed 0.002. It will
usually be within the range 0.005 < *f* < 0.010.

## DXW0, m: Numerical grid length

Values of pressure and velocity are calculated at closely spaced points throughout the tunnel system. In Case 2 of ThermoTun-Online, the distance between adjacent calculation points (i.e. the numerical grid length) is 1% of the tunnel length. The full version of ThermoTun allows experienced users to choose any grid length greater than zero.

## LZUG1, LZUG2, m: Length of train

For most purposes, the meaning of train length is self-evident. If you want to be more precise and the train ends are strongly tapered, give the distance between the most extreme points. This is not a formal definition, but it is simple and it is probably good enough. The full version of ThermoTun allows experienced users to simulate trains comprising multiple coaches, each with any length greater than zero.

The prescribed length of the train must be at least 50m. The full version of ThermoTun allows experienced users to simulate trains comprising multiple coaches, each with any length greater than zero. ThermoTun-Online is intended only for applications in which one-dimensional analyses can be used with reasonable confidence. In reality, phenomena such as nose-entry and tail-entry to a tunnel exhibit three-dimensional behaviour that extends the period of development of pressure changes.

It is recommended that the train length should be equivalent to at least 10 tunnel diameters. This is because ThermoTun-Online is intended only for applications in which one-dimensional analyses can be used with reasonable confidence. The full version of ThermoTun allows experienced users to simulate trains comprising multiple coaches, each with any length greater than zero.

For numerical accuracy, it is preferable for the train length to be at least 1% of the total tunnel length. This is because the numerical grid length used in ThermoTun-online is approximately ½% of the tunnel length. The full version of ThermoTun allows experienced users to vary the numerical grid size within wide limits.

## AZUG1, AZUG2, m^{2}:
Cross-sectional area of train

For many purposes, the meaning of the cross-sectional area of a train is self-evident. For the calculation of airflows in tunnels, a rather special meaning is implied (irrespective of which software you use). The key need is to simulate the blockage effect of the train. For a passenger coach, for example, the effective aerodynamic area is bigger than the cross-section of the passenger compartment, but smaller than the overall structural envelope including the underbody and bogies, etc.

The area of the train must be at least 5m^{2} and the blockage ratio in the
tunnel must not exceed 50%. The full version of ThermoTun allows experienced
users to choose any area greater than zero. ThermoTun-Online is intended only
for conventional train:tunnel applications.

## FZUG1, FZUG2 (*f*) Train friction coefficient (Fanning,
__not__ Darcy-Weisbach)

__not__

The train skin friction coefficient determines the main component of resistance
to airflows in the annulus between the sides of the train and the tunnel.
There are * two* definitions in common use:

*Fanning (**f* ): Wall shear stress = *f* x ρ*U*^{
2}/2

** Darcy-Weisbach (λ )**: Wall shear stress =

*λ*x ρ

*U*

^{ 2}/8

where ρ is the density of the air and *U* is the mean velocity
(relative to the train in this instance).

It follows from the definitions that *λ=4f* so
it is important to know which one is used in any particular software. ThermoTun
uses *f*, not *λ*.

If you have no experience of estimating train friction coefficients, the following values are indicative of some typical trains (but only indicative):

• modern streamlined passenger train: *f*
≈ 0.003

• conventional regional passenger train: *f*
≈ 0.005

• container-like freight train:
*f* ≈ 0.007

The Fanning friction coefficient for real trains will exceed 0.002. It will
usually be within the range 0.003 < *f* < 0.010.

## KNOSE1, KNOSE2: Loss coefficient, flow from open tunnel into annulus around train

In addition to skin friction on train and tunnel surfaces in the annulus around
a train, account is usually taken of local losses at the nose and tail. These
influence the amplitudes of pressure waves as well as the overall resistance
to flow. When the direction of airflow relative to the train is from the open
tunnel into the annulus, ThermoTun allows for a stagnation pressure loss given
by K_{NOSE} x ρ*U*^{ 2}/2, where ρ
denotes the air density and *U* is the air velocity *relative to the
train* in the annulus.

The prescribed value of the nose loss coefficient must be in the range 0 to 0.5. This range is sufficient for all conventional trains. The full version of ThermoTun allows experienced users to choose any value greater than zero.

## STAIL1, STAIL1: Shape factor, flow from annulus around train into open tunnel

When the direction of airflow relative to the train is from the annulus into
the open tunnel, ThermoTun allows for a stagnation pressure loss given by
K_{TAIL} x ρ*U*^{ 2}/2, where ρ
denotes the air density and *U* is the air velocity *relative to
the train* in the annulus. The most suitable value of K_{TAIL}
varies strongly with the train:tunnel blockage ratio. Instead of asking users
to prescribe different values for each tunnel area, ThermoTun calculates the
expected loss for a blunt-ended train and uses a shape coefficient S_{TAIL}
to define the actual loss as: S_{TAIL} x K_{BLUNT} x ρ*U*^{
2}/2.

The prescribed values of the tail shape coefficients must be in the range 0 to 1. This range is sufficient for conventional trains. The full version of ThermoTun allows experienced users to choose any value greater than zero.

## TSEAL1, TSEAL2, s: Sealing time constants for leakage through coach bodies

ThermoTun calculates pressures inside trains as a consequence of leakage of air through coach bodies.

Railways commonly use a sealing time constant to characterise the leakage characteristics of coaches. Typically, a test is undertaken in which the pressure inside a coach is held at a constant value for a period and is then allowed to decay freely.

The sealing time constant is usually defined as the time required for the pressure difference to reduce to (1/e) times the original value (where e = 2.718 is the base of natural logarithms. Beware: the sealing time constant is usually determined in a static test; the corresponding value for a coach in motion can be considerably smaller. Also, it is possible for different values to exist for positive and negative pressure differences between the inside and outside of a coach.

## VZUG1, VZUG2, km/h: Speed of train

In ThermoTun-Online, the train speed is constant and is defined in km/h. The full version of ThermoTun allows accelerating, decelerating, stopping, starting and reversing. It also allows speeds to be defined in other units if required.

The prescribed value of the train speed must be in the range 50 to 400 km/h. This range is sufficient for most practical purposes.

## TZUG1, TZUG2, s: Time of nose-entry to tunnel

The pressure histories experienced by passengers are strongly dependent on the relative entry times of the trains. You may specify any values that will cause the train noses to cross in the tunnel.