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Selected topics on physical modelling

Last modified by Omid Abouali on 2026/09/16 11:55

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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.

IDA Tunnel Application, Getting Started Guide-Beta1-2_html_439362c514c8b6bc.png

Figure 20. 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 21. 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.

IDA Tunnel Application, Getting Started Guide-Beta1-2_html_a47414f84e5a7b2d.png

Figure 22. 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.

IDA Tunnel Application, Getting Started Guide-Beta1-2_html_298f014c8e6b58f2.png

Figure 23. 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).

IDA Tunnel Application, Getting Started Guide-Beta1-2_html_5f847d2d103fc093.png

Figure 24. 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).

IDA Tunnel Application, Getting Started Guide-Beta1-2_html_ae507e5fff9ad648.png

Figure 25. 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.

IDA Tunnel Application, Getting Started Guide-Beta1-2_html_75e60e5d22736c8a.png

Figure 26. 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");

3. Warning: When importing or applying a temperature field from a previous model with multiple wall layers, the new model must contain the same number of layers to maintain consistency.

Emergency traffic (Rail tunnel)

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

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

IDA Tunnel Application, Getting Started Guide-Beta1-2_html_cf7d40cf5ca63b71.png

Figure 27. 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 incompressible 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.

Figure 28. 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 24). 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 29. 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.

Traffic flow model (Road tunnels)

Congestion model

The traffic (for one lane) is described by the following variables:

Vehicle flow q [pcu/h] where pcu is Passenger Car Unit (a conventional unit for measuring traffic flow consisting of vehicles of different type)
Vehicle speed v [km/h]
Density ρ [pcu/km]
Average road length per vehicle d [m/pcu].

The dependence between variables are expressed by equations

v.ρ= q , d.ρ=1000

For congested traffic, the vehicle speed is limited because of small distance between vehicles. Therefore we calculate the speed as a function of road length per vehicle v= f(d) :

v=	v_free	when d>d_free	Free traffic
	interpolated between v_free and v_cap	when d_free>d>d_cap	Medium traffic
	$v_{cap}\ e^(1-d_{cap}/d)$	when d_cap>d>d_cong	Congested traffic
	decreases linearly to zero	when d_cong>d>d_stop	Traffic stop

A graph of this dependence (for three vehicle types) is shown in Figure 30. In Figure 31 the same dependence is shown as flow-speed diagram, which is a more established way of describing traffic flow models.

Figure 30 Vehicle speed [km/h] as function of road length per vehicle [m]

Figure 31 The same dependence represented in flow [veh/h] and speed [km/h] coordinates

Unfortunately we cannot require the user to supply values for parameters used in this equation (except d_stop ), because they are not intuitive and depend on many different factors. Instead we calculate them from the tables described below.

Table 1 gives the value free speed v_free (i.e., vehicle speed in non-congested traffic). The free speed depends on vehicle type, slope, and allowed speed limit. In a realistic traffic model the free speed may exceed the allowed limit.

In this and the following tables, the slopes and the speed limits should be listed in the increasing order. The uphill sections have positive slopes.

Table 2 gives the steady speed that limits the free speed on long uphill sections, depending on vehicle type and slope. If a vehicle at the beginning of an uphill section moves faster than the steady speed, it slows down to steady speed at 1000 m of the uphill section and than continue moving with steady speed.

Table 3 gives the road capacity q_cap (maximal possible vehicle flow) as a function of number of lanes and speed limit. The capacity of the section after entrance is reduced proportionally to the vehicle flow from the entrance.

Table 4 gives the number of PCU (Passenger Car Units) per vehicle depending on vehicle type, slope, and slope length. Unlike other tables, this one is never extrapolated; the outmost rows and columns are used for slopes and length outside of the range given in the table.

Table 5 defines travel velocity at full capacity flow v_cap depending on speed limit and slope. This is the speed at traffic conditions that corresponds to maximal possible vehicle flow. It does not depend on vehicle type (i.e. all vehicles are moving with the same speed). Therefore the value of v_cap is reduced if v_free for some vehicle type is smaller then v_cap .

Table 6 defines the coefficient α for interpolation of the speed between v_free and v_cap .

The program uses the value of α at flow equal to 0, 43, 77, and 100% of full capacity, but only the value at 77% is calculated from table. The values at 0 and 43% are always 0 and the value at 100% is always 1.

The parameters used in the traffic equation are defined as:

$d_{cap}=\frac{v_{cap}}{q_{cap}}$

$d_{free}=\frac{v_{free}}{0.43\cdot q_{cap}}$

d_stop – calculated as an average road length per standing vehicle (that is given by the user for every vehicle type)

d_cong – a point between d_stop and d_cap calculated from the condition that the curve v= f(d) is smooth.

Tunnel connections

The traffic in every tunnel section is simulated using one or two (for bi-directional traffic) Way models. Adjacent Way models are connected so that every section receives from the previous one the traffic flow (for every vehicle type) and sends back the traffic density per lane.

The same information is sent also to and from other traffic models (Queue, Split, Merge).

The splitting branch is modelled using two models, Split and Queue. The Split model is a simple model that removes the given fraction of the traffic flow from the main stream and adds it to the exit stream. The beginning of the exit stream is modelled in the same way as the tunnel entry (Queue model).

The merging branch (Merge model) joins two traffic streams into one stream. Both ingoing sections use the value of traffic density from the outgoing section to calculate the traffic speed. The traffic flow from the branch stream reduces also the capacity of the outgoing stream. The smallest of the incoming traffic flows reduces the capacity of the outgoing stream.

Tunnel entry and exit

The traffic speed and flow at tunnel entries (Queue model) are calculated as functions of the density at the beginning of the tunnel. If the ingoing traffic flow exceeds the calculated one, the extra vehicles line up in the queue. If the ingoing traffic flow is smaller than the calculated one then the vehicles from the queue (if any) are used to raise the actual flow.

At the tunnel exit, the single required value is the traffic density directly after the tunnel. It is used to calculate the traffic speed at the end of the last tunnel section.

If the density is set to –1 (left blank in the Entry/Exit form), the Way model will use the traffic density in the last segment instead.

Multiple vehicle types

Vehicles of different types are modelled as traffic components. Vehicle speed and flow are calculated separately for every component. Vehicle density is first calculated for every component, but the flow equations use the total density.

In case of congested traffic all vehicles have the same speed. Therefore the vehicles with low speed constrain the speed of other vehicles. Clearly the traffic components with zero density cannot hinder other vehicles. Therefore the model assumes that only the components with density 1 veh/km or higher constrain the speed; for density between 0 and 1 veh/km the constrained speed is interpolated.

The concentration of traffic components may change dynamically. These changes are not delayed by the queue because the order in the queue is not modelled.

Multi-lane traffic

The model does not simulate every lane separately. All lanes have equal traffic conditions. Multi-lane traffic is modelled by defining the road capacity depending on the number of lanes (table 3 in vehicle flow model). The overtaking possibility is included in this dependency and not considered elsewhere.

Simplified traffic models

The congestion model is not the most appropriate for modelling a traffic situation with given vehicle flow or density. For this purpose IDA RTV defines two simplified traffic models: moving traffic and standing traffic.

In the moving traffic model the road capacity and possible speed are unlimited. The actual vehicle speed is equal to the given speed limit and vehicle flows are given at each entry.

The user can specify the default speed limit in the Global tab and the particular limits in section forms.

In the standing traffic model, all exits are closed so the tunnel fills completely by vehicles, except sections that are not available for traffic. Traffic lights are ignored, so they do not prevent the filling of the tunnel. Note that it takes some time to fill the tunnel. If the tunnel is not completely filled after the simulation, try to increase the simulation time.

The vehicle density is given by the parameter "Road length per standing vehicle".

The distribution of vehicles of different types is calculated from the traffic flows at entries and exit fractions in splitting branches.

Specifying transversal ventilation

Long tunnels with bidirectional traffic may be ventilated by separate, continuous supply and exhaust ducts. In IDA RTV, stretches of road sections can be supplied with transversal ventilation (supply or exhaust). These stretches may overlap.

Defining location of transversal ventilation is done as follows (Figure 32).

Open the section model and press ‘Edit segments’.

Press Add and select Transversal duct.

Give (left) position and length.

Figure 32. Edit segments dialog with Transversal duct selected

By default, air flow through the duct is given, independent of pressure, as specified in the Edit segments dialog. In this case, ambient values of temperature, turbidity, CO and NO₂ as defined in (Section: Specifyinng ambient data ) are used as boundary values. If the check box ‘The volume flow is given here’ is unchecked, the transversal duct must be connected to some other component outside of the section model. Connecting the ventilation duct (shown as a square at the bottom of the tunnel section component) is done in a Connect dialog similar to that of Figure 18.

To summarize, air flow in a transversal ventilation duct can be generated in three different ways.

Explicitly given air volume flow is achieved by checking ‘The volume flow is given here’ and then either specifying a constant value or binding to a function of time by connecting it to an input table, see Section Error: Reference source not found.
‘The volume flow is given here’ is unchecked. The external interface of the transversal duct is connected to an external given flow component. This could either be the library ‘Given flow’ component or another transversal duct of a neighbouring section model in which the ‘The volume flow is given here’ has been checked.
‘The volume flow is given here’ is unchecked. The external interface of the transversal duct is connected to an external component combination and flow is determined by actual pressure difference. In this case, the total pressure drop of the supply duct and its dampers should be specified in the external system, i.e. the transversal duct itself does not have any resistance to pressure nor does it have any volume.

Specifying ambient data

To set ambient air properties press the ‘Ambient’ button at the bottom of the system form (Figure 33).

Figure 33. The ambient air properties form

Ambient temperature and reference pressure as well as the air quality measures turbidity, carbon monoxide and nitrogen dioxide are specified here.