Pressure Zones

Correct FDS Pressure Simulation

The heat emission from a fire source leads to an increase in temperature within the room. If the room is airtight, the pressure inside must increase. The operation of supply or exhaust ventilation increases or, respectively, decreases the mass of air in the airtight room. Consequently, the pressure in the room must also rise or fall.

Below is an example: there is a room with a fire source with the following characteristics:

Room volume = 48 m³.

Fire source material: Gasoline.

Fire source area = 0.25 m².

Fire development time = 10 s.

As shown in the picture, the pressure increase is approximately 20 kPa. That is, 0.2 times the atmospheric pressure. This pressure is equivalent to a load of 2 tons pressing on each square meter of the floor, walls, ceiling, doors, and windows.

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The walls of most civil and industrial premisses are not able to withstand such a pressure load. The building would burst like an overinflated balloon. Window glass cannot withstand a pressure difference of more than 0.03 atmospheres.

In reality, buildings do not burst from fires or the operation of smoke control ventilation systems. Therefore, in real fires, such a significant increase in pressure does not occur. This means that the large pressure increase obtained in fire simulation is incorrect. Thus, some factors affecting fire simulation results, including the spread of fire hazards, have not been accounted for.

Walls, doors, and windows, defined in the FDS file via the OBST parameter group, are assumed to be airtight by default.

In most cases, real rooms are not airtight enough to create such a significant pressure difference, so structural failures do not occur. Fire simulations are usually conducted taking into account that such a large pressure change in the room is not possible. Next, we review what is necessary to account for the non-airtightness of rooms when simulating fire.

Pressure Zones

For accurate pressure simulating, FDS splits the entire computational domain into pressure zones. A pressure zone is a part of the computational domain that is airtight in relaation to other parts. For example, a pressure zone can be a room with all doors and windows closed, or a corridor along with all rooms where doors are open to this corridor. Next, we refer to “pressure zones” simply as “zones.”

At any time, the pressure inside a zone is the same at every point.

FDS automatically splits the computational domain into zones and assigns each zone a number. The number zero is assigned to all space outside the computational domain (the surrounding open space) and to the part of the computational domain that is not hermetically separated from the surrounding open space.

You can assign zone numbers manually. To do this, specify a point within the zone using the ZONE parameter group in the FDS file.

&ZONE XYZ=2, 3.5, 0.5/

The zones specified in the FDS file are numbered in the order they are mentioned, starting from 1. All zones not specified in the file are numbered automatically, but these numbers are unknown and cannot be referenced in other parameter groups. Points within the same zone must not be specified more than once; otherwise, a calculation error occurs.

Zone numbers are important for simulating leaks.

Leaks

Realistic simulation of air exchange between rooms during a fire is an challenge. In addition to the direct exit of air and combustion products through open doors and windows, the air that seeps through the gaps of closed openings is important. These leaks become quite active during a fire because the increase in temperature creates a pressure difference between adjacent rooms.

The spread of combustion products is also affected by the operation of smoke control ventilation, including pressurization of elevator shafts and stairwells. Like the fire itself, smoke control ventilation can create pressure differences between rooms, leading to significant gas exchange through seemingly closed door openings. Therefore, to accurately simulate the operation of ventilation systems, it is also necessary to account for leaks.

When simulating a fire in the FDS system, the passage of air through open doors or windows is naturally accounted for, as there are no barriers to air flow in an unrestricted opening. Below we focus on the issue of simulating leaks.

According to [9], the mass flow rate of air (G) passing through the gaps of door and window openings depends on the pressure difference (Δp) on either side of the opening.

Air moves from higher pressure to lower pressure areas. The greater the pressure difference, the higher the air flow through the gaps and cracks. Therefore, the operation of ventilation or the presence of a fire source leads to leaks. Leaks reduce the pressure difference. As a result, the pressure difference between rooms (and the outside) remains at a reasonable level, and combustion products can leak through closed doors and windows. This corresponds to the real situation during a fire.

Structural Characteristics Which Determining Leaks

Gap Area

If the area of the gap through which the leak occurs is known, the mass flow rate of air can be calculated using the formula:

where Δp is the pressure difference on either side of the door or window opening,

ρ is the density of the air escaping through the gap;

f_g is the area of the gap. If the rooms are connected by multiple openings, the gap areas must be summed;

μ is the flow coefficient. For a gap (e.g., a door crack), μ = 0.8. The product μ·fщ is called the equivalent hydraulic area.

Gas Permeability Resistance

Often, the area of the gaps is not explicitly known, making it impossible to use formula (1) to determine the air flow rate through the gap. In such cases, the mass flow rate of air filtering through the door gaps is determined by the formula:

where Δp is the pressure difference,

S_res is the gas permeability resistance characteristic, 1/(kg·m), which is related to S_spec (specific gas permeability resistance characteristic).

where f is the area of the opening,

S_spec is the specific gas permeability resistance characteristic, m³/kg. It varies widely, with typical values ranging from 6000 to 200000 m³/kg.

The formula for flow rate can be altered as follows:

According to [10], the specific smoke and gas permeability resistance of fire-resistant smoke-tight doors of various sizes must be no less than 1.96·10^5 m³/kg.

Air Permeability Characteristic

The mass flow rate of air filtering out through gaps and openings is defined by the formula:

where J is the specific air permeability characteristic, kg/(s·m·Pa^1/2);

J = 7.5·10^-3 kg/(s·m·Pa^1/2) for single paired glazing;

J = 5·10^-3 kg/(s·m·Pa^1/2) for double separate glazing;

f is the glazing area, m²;

Δp is the pressure difference.

Volumetric Air Permeability at Δp = 100 Pa

Volumetric air permeability (at a fixed pressure difference) is defined as the ratio of the volumetric air flow to the surface area of the sample [13, 14].

Q = V/f

where Q is the volumetric air permeability, m³/(h·m²);

V is the volumetric air flow, m³/h;

f is the surface area, m².

The mass flow rate G can be obtained from the volumetric flow rate V by multiplying by the air density ρ, kg/m³. However, note that G is measured in kg/s, while V is in m³/h, so

G = (Q/3600)·f·ρ

This formula gives the correct air flow rate through leaks only if the pressure difference is equal to the value at which the volumetric air permeability was measured.

Most often, the volumetric air permeability is known at a pressure difference of 100 Pa. In this case, the air flow rate at any actual pressure difference can be calculated using the formula:

where Q is the volumetric air permeability, m³/(h·m²);

f is the surface area, m²;

ρ is the air density, kg/m³;

Δp is the pressure difference.

Where to Find Information on the Numerical Value for Leak Rate through Doors or Windows

The product may have a certificate in which the relevant value may be indicated. For fire resistant doors, the certificate often specifies the volumetric air permeability at Δp = 100 Pa or the specific gas permeability resistance characteristic.

If it is a standard product that does not have a certificate, there may be state technical specifications according to which the product is manufactured. In this case, you can find the relevant information in this certificate. For example, you can find typical values of volumetric air permeability for some classes of windows and balcony doors in [15, 16].

Importance of Accounting for Leaks

The result of fire simulation where leaks are accounted for is closer to reality than without it. No doors or windows are completely airtight. In real fires, smoke can leak through doors (even fire-resistant ones) and enter evacuation routes. Accounting for leaks allows you to anticipate such a situation.

It is also necessary to account for leaks in windows. Otherwise, heated air will only be vented from the room with the fire source through doors with leaks, leading to an overestimation of the amount of smoke passing through the door. Additionally, air will act as a cushion in rooms where occupants are present, preventing smoke from entering during fire simulation, whereas in reality, smoke can push the existing air out through windows.

For example, the picture below shows the comparison of the situation in three rooms during a fire in the corridor. The air in the corridor heats up and pressure increases.

In “Room 1,” there are no leaks through either the door or the window. Smoke does not enter at all.

In “Room 2,” there are leaks through the door but not through the window. Thus, a moderate amount of smoke enters this room from the corridor, but the pressure in the room increases, stopping smoke penetration.

In “Room 3,” there are leaks through both the door and the window. Smoke enters this room from the corridor, and the excess pressure is vented outside through the window. Therefore, smoke continues to enter the room through the door and even exits outside. This situation is typical for real fires. Only accounting for leaks in both doors and windows simultaneously allows for realistic simulation of smoke spread.

There is another example showing the need to account for leaks through doors and windows. In this example there is a fire source, exhaust, and supply ventilation in an enclosed space. This space may even have a substantial volume. The main point is that it is hermetically sealed from the external simulation area (the outside), meaning leaks are not activated on the doors or windows. The smoke control ventilation is designed with a deficit of supply relative to the exhaust (within the limits allowed by standards).

Since more air is being extracted from the sealed space than is being supplied, significant pressure drops are observed during simulation. Many users disregard this, considering it irrelevant to the simulation results. However, this is fundamentally incorrect, as pressure differences greatly influence gas exchange. Correct gas exchange simulation during a fire is crucial because it determines the spread of smoke and other hazards.

Moreover, there is another less obvious consequence. Evacuation routes can be blocked even far from the fire source, where smoke has not yet reached, due to a drop in oxygen level. The exhaust ventilation, which has a higher capacity than the supply, reduces the air mass in the entire enclosed space, thus decreasing the oxygen level (kg/m³). This occurs not so much due to oxygen burning but due to ventilation operation. Or more precisely, because the simulation of ventilation operation does not account for leaks through which air enters in real situations during ventilation operation. In real fires, the ventilation imbalance does not lead to significant pressure differences because the air is drawn in through doors and windows.

Thus, failure to take leaks into account when simulating fire leads to the false blocking of evacuation routes.

Summary:

In reality rooms are not airtight. They have openings and gaps through which air leaks. Accounting for leaks allows for accurate simulating of gas exchange during a fire.

When conducting fire simulation, it is recommended to account for leaks through doors and windows, even in rooms without fire sources, ventilation valves, or occupants. At least, in rooms near the fire source and ventilation valves. This affects the spread of smoke throughout the building.

In rooms with fire sources, ventilation valves, and occupamts, accounting for leaks is necessary. Otherwise, fire simulation results may contain significant errors.

Configuring Leaks in Fenix+

To enable leaks through a specific Door or Window, you need to enable the “Account for Leaks” option in the properties of the given topology element.

The leak rate through a Door/Window can be specified by setting the:

• leakage area,
• gas permeability resistance characteristic,
• specific gas permeability resistance characteristic,
• volumetric air permeability at 100 Pa,
• specific air permeability characteristic.

If you specify Leak area, you need to specify the equivalent hydraulic area S = μ·f of the gap, which already takes into account the flow coefficient μ (usually, μ=0.8).

Converting Leak Information into an FDS File

Unlike the case with unrestricted openings, you cannot simulate leaks through gaps directly in FDS, as the size of the gaps is much smaller than the cell sizes typically used for fire calculations. FDS has a specific mechanism for simulating leaks.

Air passes through a leak only if it connects rooms in different pressure zones. Otherwise, there is no pressure difference. To transfer leaks into the FDS file, you need to know the zone numbers that the door or window connects. Fenix+ 3 records the zones in the FDS file where doors and/or windows with leaks are located to identify their numbers.

All parameters characterizing leaks are defined in the FDS file in the ZONE, SURF, and MISC parameter groups.

If there are leaks between zones through doors or windows, when creating the zone in the FDS file, you need to specify the leak areas to all zones it connects to. This is done by setting the LEAK_AREA(i) parameter in the ZONE group, where i is the zone number into which the leak from the described zone occurs.

Below we demonstrate the use of the LEAK_AREA parameter with an example. We create two zones. The leak area from the first zone to the zero zone is 0.0001 m², from the second to the zero zone is 0.0003 m², and from the second to the first zone is 0.0002 m². The ZONE parameter groups look like this:

&ZONE XYZ=..., LEAK_AREA(0)=0.0001 /
&ZONE XYZ=..., LEAK_AREA(1)=0.0002, LEAK_AREA(0)=0.0003 /

This example shows why the order of the ZONE groups in the FDS file is important. It determines the zone numbers used in the LEAK_AREA parameter.

Below is an example of a scenario with three rooms, two of which have doors with leaks, and one has an open exit to the outside (see the picture).

In the FDS file for this scenario, two zones are created:

&ZONE XYZ=1,1.5,1 LEAK_AREA(0)=0.0029/  Zone 1
&ZONE XYZ=1.125,0.125,0.75 LEAK_AREA(1)=0.0029/ Zone 2

There is a leak area of 0.0029 m² from Zone 2 to Zone 1. There is also a leak from Zone 1 to Zone 0 (outside).

Fenix+ 3 automatically creates zones, so that the user does not need to take any action.

The number of pressure-isolated zones used in the project is specified using the MAX_LEAK_PATHS parameter in the MISC group.

&MISC MAX_LEAK_PATHS=2/

FDS has a default value for the maximum number of zones, but Fenix+ 3 always writes the actual number of zones used into the FDS file to avoid limitations.

If a zone borders the calculation domain boundary (see Calculation Area), there are two possible situations:

1. The computational domain boundaries adjacent to the zone are open. The zone is considered connected to the external Zone 0, and the pressure in it is equal the background pressure.
2. The computational domain boundaries adjacent to the zone are closed. Such a zone will function as isolated from Zone 0.

The FDS file must also specify the surfaces (SURF) through which the leak occurs. In Fenix+ 3, such a surface is automatically placed on closed doors and windows where the “Account for Leaks” option is enabled.

The LEAK_PATH parameter in the SURF group specifies the zone numbers that the surface connects via leaks.

&SURF ID='1',..., LEAK_PATH=1, 2 /

As a result, all OBST elements in zones 1 and 2 with the surface type SURF_ID=‘1’ exchange air through leaks according to the pressure difference. Such a leak can work in both directions.

Note that an object with zero thickness cannot be covered by such a surface. Therefore, Fenix+ 3 represents doors and windows with the “Account for Leaks” option enabled as OBSTs with a thickness equal to the MESH cell size in the FDS file. In SmokeView, this appears as a thickening of the doors and windows with leaks when viewing the project.

Leak Rate in FDS

The leak rate (m³/s) in FDS is determined by the formula [11]:

where:

Cd is the discharge coefficient (Fenix+ uses the default FDS value of Cd = 1),

AL is the area of the gap,

Δp is the pressure difference,

sign(Δp) is the sign of the pressure difference,

ρ is the ambient air density.

Unlike in formula (1), density is in the denominator in formula (6) because formula (6) calculates volume, whereas formula (1) calculates mass.

G = Vleak·ρ

The AL (LEAK_AREA) parameter corresponds to the total area of leaks from one zone to another, so if there are multiple door openings, the areas of leaks through them are summed.

Regardless of which leak characteristic the user sets in Fenix+ 3, it is converted to an area when transferred to the FDS file.

If the user sets the Leak Area (S) in Fenix+ 3, then for calculating AL, it is sufficient to directly compare formulas (1) and (6). From this, it can be seen that:

AL = μ·f_gap = S, (7)

meaning that the value S is transferred to FDS as the AL parameter without conversion.

If the Specific Gas Permeability Resistance Characteristic (S_spec) is set, then by comparing formulas (3) and (6), we get:

From which:

If the Gas Permeability Resistance Characteristic (S_res) is set, then by comparing formulas (2) and (6), we get:

From which:

If the Specific Air Permeability Characteristic (J) is set, the formula for calculating AL can be obtained by comparing formulas (4) and (6):

From which:

If the Volumetric Air Permeability at 100 Pa (Q) is set, the formula for calculating AL can be obtained by comparing formulas (5) and (6):

From which:

Example Scenario with Leaks

Below is an example scenario where two rooms are separated by a fireproof door with a specific resistance to gas permeability of 200,000 m³/kg. One room contains the fire source, while the other has an open door leading outside.

The scenario has a door which separates two isolated rooms with the “Account for Leaks” option enabled. In this case, two zones are created in the FDS file:

&ZONE XYZ=0.02, 0.48, 1/
&ZONE XYZ=1.625, 0.625, 0.75 LEAK_AREA(1)=0.00288675134594813/

The leak area (LEAK_AREA) corresponds to the specified resistance to gas permeability of the door.

The door is represented by an OBST element:

&OBST XB=0.5,0.75,0,1,0,2 SURF_ID='1' RGB=50,205,50/

It is covered by a SURF surface, specifying that it connects Zones 1 and 2 through leaks:

&SURF ID='1' LEAK_PATH=1, 2/

The picture below shows how smoke seeps between the rooms through the closed door. The smoke that seeps into the right room then exits freely through the open door outside.

You can see that accounting for leaks significantly enhances the realism of fire simutation.

Best Practices of Using Leaks

1. It is important to understand that leaks are not intended to simulate openings. A leak is always a small gap. The equations used in FDS to calculate leaks are only valid for such small gaps. If the gap area is specified as the leak characteristic, it must be much smaller than the area of the door or window. Regardless of the specified area, leaks only function with a pressure difference. Do not attempt to simulate open doors using leaks, i.e., by specifying a leak area equal to the door opening area. This will not produce the expected simulation results.
2. Do not place the boundary of the calculation domain close to windows and doors with leaks enabled. There must be at least one cell gap, preferably several. Otherwise, FDS will not be able to correctly simulate the leaks.
3. Sealing the fire source or ventilation elements in an airtight room increases the probability of simulation termination due to numerical instability. Leaks allow air to escape from the room, increasing the stability of the simulation.
4. If two zones are connected by multiple closed doors or windows with leaks, the AL is calculated for each door and/or window, then the areas are summed to get the total LEAK_AREA. The total leak rate will be divided among all doors and windows connecting the two zones, proportional to the surface area of these doors and windows.

Due to this feature of leak simulation in FDS, if there is a fireproof door with low air permeability and a window with high air permeability between two zones, smoke may exit through the fire door even more intensively than through the window if the door’s area is larger than the window’s. Moreover, the higher the leak rate of the window, the larger the total leak area between the zones, and the more smoke will exit through the door.

However, doors and windows from the room with the fire source often exit into different zones, so this issue rarely arises.

To avoid this problem, when designing a fire scenario in a building, ensure that the doors and windows from the building to the outside are closed. This means that windows from the room with the fire source lead outside, while doors lead to a corridor that does not have a direct connection to the outside. If there are leaks through the windows and doors in the room with the fire source, they will not combine but will be simulated independently. If the window’s air permeability is significantly higher than the door’s, smoke will primarily exit through the window leaks, rather than the door, and relatively little smoke will enter the corridor.

The following pictures illustrate this point.

The first picture shows an undesirable configuration. The window and fireproof door exit from the room with the fire source into one zone since the door from the corridor to the outside is open. Leaks are devided between the window and door proportionally to their area. This results in a lot of smoke entering the corridor during simulation, even if the door’s resistance to gas permeability is much higher than the window’s.

The second picture shows an acceptable configuration for simulating leaks. The window and fireproof door exit from the room with the fire source into different zones since the door from the corridor to the outside is closed. Leaks through the window and door from the room with the fire source are calculated independently. If the door’s resistance to gas permeability is much higher than the window’s, smoke will mainly be forced through the window to the outside rather than into the corridor.

It is also advisable to activate leaks on the door from the corridor to the outside. Otherwise, the simulating of leaks from the room with the fire source into the corridor is not accurate. The air entering from the room with the fire source increases the pressure in the corridor, and the leak from the room to the corridor gradually stops. With leaks on the exterior door, air from the corridor exits outside, preventing the pressure in the corridor from rising. This results in more accurate gas exchange simulation.

5. When coducting a fire simulation with leaks, it is necessary to cover the entire building or its airtight part with calculation areas. Otherwise, if the building is divided by the calculation domain boundary, it will depressurize the building’s interior, making it one pressure zone with the outside. This can cause incorrect leak simulation through fireproof doors due to combined leak rate with window leak rate.

This situation is illustrated in the picture. Here, the window and door from the room with the fire source exit into one zone because the closed door from the corridor to the outside is not included in the calculation domain. Leaks will work incorrectly.

A correct placement of the calculation domain is shown below.

6. It is highly recommended to add leaks not only in the room with the fire source or ventilation but also along the path of the potential outgoing/incoming air. This includes all doors in the corridor/hall and preferably the windows in at least the nearest rooms. These leaks allow air to continue flowing through the building’s corridors and, eventually, outside. Air can exit to the outside through leaks in both windows and entrance doors, so it is necessary to activate leaks on entrance doors as well.

If this is not done, the air exiting from the room with the fire source (through door leaks) will begin to increase the pressure in the corridor and adjacent parts of the building. This will reduce the effectiveness of leaks as their rate depends on the pressure difference.