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Selected topics on physical modelling

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Selected topics on physical modelling

Selected topics on physical modelling

Specifying wall properties

The user can define one or more wall types with different thermal properties and use these wall types in tunnel section and platforms. The default wall type is used if no explicit wall type is selected.

To set the default wall type

Switch to "Global" tab;

In the "Wall" field, select a wall type to be used as a default one.

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Figure 45. Selecting default wall type

To choose wall type for station,

Double click the station on the schema to open the platform form;

In the "Wall" field, select either the default wall type (marked as "[default]") or a specific wall type.

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Figure 46. Selecting wall type for platform

A tunnel section may have segments with different wall properties along the tunnel.
To choose wall type for a segment in tunnel section,

Double click the section on the schema to open the section form;

Click "Edit segments" button to open the tunnel section dialog;

In the list at the top of dialog, select either the tunnel entry (the first row) or an "area change" point at the beginning of the required segment (if where is no "area change" point at desired position, add one);

In the "Tunnel wall" field, select the desired wall type;

Press "Ok" button to confirm the changes.

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Figure 47. Selecting wall type for a segment in tunnel section

To edit a wall type,

Switch to "Global" tab;

In "Resources" list, find the desired wall type and double click it to open the wall definition dialog.

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Figure 48. Select wall type for editing

Define the properties of wall layers (material and thickness). A wall may consist of one or more layers. Use buttons "Add", "Delete", "Promote", and "Demote" to arrange the layers. The properties of the selected layer are shown at the right part of the dialog. Choose the material and set the wall thickness for every layer. The thickness of the last layer is ignored (the last layer is infinite).

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Figure 49. Wall definition dialog

To edit the thermodynamical properties of the layer's material, click in the button at the right of "Material" field and select "Open" from menu. In the Material dialog, change the properties (heat conductivity, density, and specific heat) and click "Ok" (or "Save as" to keep both the old and the new material). Note that the materials are defined globally and a change of material properties affects all wall types that use this material.

End editing wall properties by pressing "Ok" button (or "Save as" to keep both the old and the new wall type).

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Figure 50. Material dialog

It is also possible to edit materials directly, without opening wall definition dialog. To do this, double click on the desired material in the "Resources" list on the "Global" tab.

To define a new wall type,

Edit the properties of an existing wall type as described above, but at the end press "Save as" button instead of "Ok".

In the "Create new resource" dialog select a name for the new wall type and click "Ok" button.

To remove an unused wall type or a material,

Switch to "Global" tab;

In "Resources" list, select the desired wall type or material and press "Delete" button on the keyboard (alternatively, right click it and select "Delete" from menu).

See also Section . Working with database.

Using computed wall temperature fields

During the simulation, IDA Tunnel Application computes the temperature fields in the tunnel walls and the ground around the tunnel sections and platforms. The computed temperatures may be used as start conditions in the following simulations.

To use the last computed temperature field in the next simulation,

Set all parameters for the new simulation;

Switch to "Global" tab;

Press "Set" button (under the heading "Ground temperature");

Start the simulation.

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Figure 51. Using computed temperature field

Note that the order of operation is significant because changing of parameters may affect the grid (the positions of the points where the temperatures are calculated) and therefore the start conditions should be recalculated.

To save the last computed temperature field (for using in other system),

Switch to "Global" tab;

Press "Save…" button (under the heading "Ground temperature");

In the dialog, select the file name and directory and press "Save".

To load a saved temperature field,

Set all parameters for simulation;

Switch to "Global" tab;

Press "Load…" button (under the heading "Ground temperature");

In the dialog, select the file containing the saved temperature field and press "Open".

Notes.

1. If the tunnel configurations in the system and in the saved field are different, only the matching part of the field is loaded (more precisely, the sections and platforms with the same name and overlapping coordinates).
2. If some parameters in the system are changed after loading a temperature field, press "Set" button before the simulation.

To restore the default start conditions for temperature field,

Switch to "Global" tab;

Press "Reset" button (under the heading "Ground temperature");

Emergency traffic

When simulating a fire, emergency traffic should be specified independently for every route.

The emergency traffic is given by the following parameters (see Figure ):

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Figure 52. Emergency traffic dialog

Action Determines the emergency action on this route.
Possible values:

Normal traffic: no emergency actions on this route
Closed entry: no new trains come into tunnel; the trains that are already in tunnel move according to the ordinary schedule;
Obstacle: the trains that have passed the obstacle go on according to the ordinary schedule; the trains that are behind the obstacle start braking; no new trains come into tunnel;
Burning train: same as obstacle except that the train that is the nearest to the given position moves according to the ordinary schedule to the first station.

Start time The time (in seconds from the beginning of the simulation) when the emergency action begins (i.e., alarm time + reaction time). This time does not necessarily coincide with the start of the fire.

Position The position (in meters from the beginning of the route) of the obstacle or the approximate position of the burning train at the time instance given by the parameter Start time.

Retardation The value of the emergency retardation.

The typical tasks of emergency traffic are:

Fire in tunnel section

Action: obstacle for routes that goes thru the section; closed entry for other sections.

Fire in train

The fire is modeled at the nearest station and starts when the train arrives to the station.
Action for traffic: burning train on that route; obstacle at the same position before the station – for other routes that goes thru the station (the position is evaluated so that the trains that passes the station before the burning one are allowed to go on); closed entry for other routes.

Overview of pressure and flow

Let us review some of the basic mechanisms which influence pressure and incompressible³ air flow in a tunnel. Starting from the barometric pressure at some reference level (defined to be 0), let us call it p_Amb, static pressure at the tunnel opening height, h, will be

$p_{\mathrm{Height\ }}=-\int_{0}^{h}\hairsp\rho(T,p(z))\cdot g\cdot dz\cdot+p_{Amb}$

where ρ is air density as function of height and g is the acceleration of gravity. The static pressure outside of the tunnel portal (away from the influence of tunnel air velocity) will then be p_Heigth + p_Wind, where the latter term is due to wind forces acting on the opening. (In IDA Tunnel, wind pressure is related to the dynamic pressure of the wind at some reference level away from the tunnel while in IDA RTV, any wind pressure is given directly.)

Presssure reference.png

Assuming an air velocity, v, into an empty tunnel, the (static) pressure, p_P₁, just inside of the entry will be reduced by two terms

$p_{P1}-p_{\mathrm{Height\ }}-p_{\mathrm{Wind\ }}={\underbrace{-k_{\mathrm{entry\ }}\frac{\rho}{2}\cdot v^2}}\below1{\underbrace{-\frac{\rho}{2}\cdot v^2}}\below2$

the first being viscous (friction) pressure loss due to turbulence forming at sharp features of the portal; the second is due to build-up of dynamic pressure $\frac{\rho}{2}\cdot v^2$ (kinetic energy). The magnitude of viscous losses are conventionally related to the dynamic pressure, here by a factor k_entry, which for a sharp-edged entry portal is around 0.5 (More about this below.)

Moving down into the tunnel to point P2, two more terms will influence the static pressure,

$p_{P2}-p_{P1}={\underbrace{-\frac{fL}{D}\frac{\rho}{2}\cdot v^2}}\below1-{\underbrace{\int_{h}^{P2}\hairsp\rho(T,p)\cdot g\cdot d z}}\below2$

Quantified by a so called friction factor, f, the first is a viscous pressure loss due to wall friction, also conventionally related to dynamic pressure, tunnel length, L, and hydraulic diameter, D. The second is an increase in pressure due to gravity of tunnel air.

In a tunnel with jet fans and traffic there will naturally be additional driving forces, see the Theoretical Reference for a full account. Pressure as presented in the path report of IDA is the static pressure as discussed above but less the ambient pressure at reference level (0 m height), P_Amb. 'Ambient static pressure' in a path report is the pressure one would have outside of the tunnel wall (should there not be any rock there). So if a small hole would be drilled in the tunnel wall, the difference between these two pressures would be the driving pressure across the hole.

Definition of pressure loss coefficients

In addition to friction at the boundary between air and tunnel wall, losses in total pressure will also occur at flow separation points that are induced by geometrical features such as sharp edges, area changes, obstructions etc. The magnitude of such losses is, as previously indicated, conventionally related to the dynamic pressure in an undisturbed ”normal” cross section by so called pressure loss coefficients. Figure shows a situation where the fittings around an open damper cause friction losses.

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Figure 53. Flow separation at an open damper with asymmetric geometry

The loss coefficient k₁₂ for flow from 1 to 2 is defined by

$p_{t_1}-p_{t_2}=k_{12}\cdot\frac{\rho}{2}\cdot v^2$

where $\rho$ = air density

v = air velocity (average over cross section)

p_t = total pressure before and after the single loss feature.

In the asymmetric damper example, two loss coefficients are needed, one for each flow direction. However, we have no problem in finding a dynamic pressure to relate the pressure loss to, since the duct away from the damper has a constant cross section and therefore velocity and in turn dynamic pressure. In cases where the cross section of the tunnel changes at the flow feature, the situation is more complicated and we have to introduce a convention for the selection of a suitable dynamic pressure to relate the loss coefficient to.

In IDA Tunnel and RTV, the convention is to relate the loss coefficient to the smallest of the two cross sections that are adjacent to the single loss feature, i.e. to the largest dynamic pressure. Loss coefficients in sections are called Expansion and Contraction respectively to indicate their relation to the direction of flow.

In a situation without area change, such as in the damper example above, the “Contraction” coefficient is valid for flow from left to right (positive direction) and correspondingly the “Expansion” coefficient is for negative flow.

At tunnel portals, losses in total pressure are naturally defined with respect to dynamic pressure in the adjacent tunnel. Flow direction is also easily managed by distinction between flow into or out of the portal.

Pressure loss coefficients at tunnel area changes

The area change is treated as a node in IDA Tunnel and the corresponding total pressure loss is calculated based on loss coefficient. This coefficient mainly depends on the geometry and the area ratio of two adjacent cross sections. Typically, the user is responsible for entering the proper value for the loss coefficient based on every single project. But there are two common types of the area change which are the sudden and gradual Expansions/contractions. The values of the loss coefficient for the area sudden change can be found with either an analytical approach using the control volume mass, momentum, and energy balance method (for example, Kloss= $\left(1-\frac{d^2}{D^2}\right)^2$ for a sudden expansion) or using some empirical coefficients. In Edit segments form when the user adds an area change node to the segment, selecting the Loss coefficients radio button one can select different options for specifying the loss coefficients (Figure 54). The default is the manual entering the Contraction and expansion loss coefficients. The default value is 0.2. One can select the automatic calculation of loss coefficient for two types of area changes: Sudden or gradual types. In this case IDA Tunnel calculates the loss coefficient for both contractions and expansion based on the adjacent cross sections of the connected segments. This can be very useful when the user does a parametric run simulation changing the area of one of the adjacent segments.

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Figure 54. Form for selecting manual entry or automatic calculation of loss coefficients for area changes.

Pressure losses at tunnel branches

At tunnel branches (junctions), estimation of total pressure losses is much more complex. A manageable part of the problem is to introduce a suitable convention for definition of loss coefficients. (see Section 2.1.8 of the Theoretical Reference for the chosen definitions.) More difficult is to find reliable data for pressure losses in the literature. Available data is almost exclusively valid for typical duct geometries rather than for tunnels, which typically have sharp angles between branching tunnels.

In IDA Tunnel and RTV, empirical expressions by Gardel have been implemented for automatic estimation of viscous losses in branches. These are not valid for all geometries that may occur in real tunnels and in cases where branch losses are critical, one should instead give explicit loss coefficients. User-defined loss coefficients may be given using the Outline view of the branch model.

Orifice flow situations

For flows through orifices, when there is no natural surrounding duct dynamic pressure to relate losses to, it is common practice to define a so called Equivalent Leakage Area, ela, rather than a loss coefficient. The (common) definition of ela used in IDA Tunnel and RTV is

$\Delta p=\frac{1}{2\cdot\rho\cdot e l a^2C_d^2}\cdot{\dot{m}}^2$

where $\mathrm{\Delta p}$ = difference in static pressure before and after the orifice

$\rho$ = air density

ela = Equivalent Leakage Area

C_d = Discharge coefficient, by default set to 0.65

$\dot{m}$ = mass flow through orifice.

For sharp-edged opening geometries, the default discharge coefficient is chosen so that the equivalent leakage area roughly corresponds to the physical area of the opening. This provides a simple way to estimate pressure drop without access to any table data.

Should the orifice in fact be surrounded by a duct with a well-defined area, as for example in the Damper component in closed position, the following holds

$\Delta p=\frac{A_t^2}{ela^2C_d^2}\cdot\frac{\rho}{2}\cdot v_t^2$ and therefore,

$k=\frac{A_t^2}{ela^2C_d^2}$

where A_t = surrounding duct (tunnel) area

v_t = duct air velocity (average over cross section)

k = loss coefficient.