Critical velocity

Critical velocity is the lowest air velocity that stops smoke from flowing upstream against a ventilation airflow. In smoke control it is used to keep corridors, open doors and openings between spaces free of smoke by blowing fresh air towards the fire. The best-known estimate is an empirical relation by Thomas for corridors. In this relation the velocity grows with the cube root of the heat release rate divided by the corridor width.

For a wastebasket fire of 150 kW in a corridor 1.22 m wide, the relation gives about 1.45 m/s. For an intense fire of 2.4 MW, about 4 m/s is needed at an open door. Much lower values, between 0.25 and 1.25 m/s, may be used where sprinklers cool the smoke to near ambient temperature. The airflow that stops the smoke also brings oxygen to the fire, so the method calls for great care. In smoke detection the same term has a different meaning: the lowest gas velocity at which smoke enters the sensing chamber of a detector.

Principle

Smoke control relies on air velocities and pressure differences produced by fans. Across closed doors the appropriate quantity is the pressure difference, because the velocity through the gaps is difficult to determine. Smoke flow through an open doorway, in contrast, can be prevented with airflow. Doors in barriers are opened during evacuation and are sometimes left or propped open, and without smoke control smoke flow through such doors is common. In theory airflow can stop smoke movement through any space, but it is most often applied at open doorways and in corridors.

Opposed airflow is airflow supplied in the direction opposite to the smoke movement. It can replace a physical barrier between two spaces, for example between an atrium and a space that opens onto it. The airflow limits the smoke flow by countering the momentum of the smoke, and a minimum velocity must be reached at every point of the opening. If the airflow is too slow, or the smoke too hot, smoke can still flow back through the upper part of the opening, so that air and smoke pass the opening in opposite directions. Preventing this smoke backflow is the purpose of the critical velocity.

A report on the smoke management systems of the World Trade Center describes when the airflow method fits. It suits large openings where pressurisation cannot be applied, preferably openings that are small compared with the wall or plane that contains them. It is typically used for vertical openings such as doorways and hallways, and it works best when the smoke is diluted and relatively cool.

Thomas's relation for corridors

Thomas developed an empirical relation for the critical velocity that prevents smoke from flowing upstream in a corridor. The velocity is proportional to the cube root of gravity times the heat release rate, divided by the corridor width and by the density, specific heat and absolute temperature of the gases. Its form shows which factors matter: a larger fire needs a higher velocity, and a wider corridor a lower one:

$$V_k=K{\left(\frac{g\dot{Q}}{W\rho cT}\right)}^{1/3}$$

Symbol	Description	Unit
$V_k$	critical air velocity to prevent smoke backflow	m/s
$K$	constant of the order of 1	none
$g$	acceleration due to gravity	m/s²
$\dot{Q}$	heat release rate into the corridor	kW
$W$	corridor width	m
$\rho$	density of the upstream air	kg/m³
$c$	specific heat of the downstream gases	kJ/(kg·K)
$T$	absolute temperature of the downstream mixture of air and smoke	K

The downstream properties are taken far enough from the fire for them to be uniform across the corridor. Klote evaluates the relation with a density of 1.3 kg/m³, a specific heat of 1.005 kJ/(kg·K), a temperature of 27 °C and a constant of 1. The relation then reduces to a simple form, with the velocity in m/s, the heat release rate in kW and the width in m:

$$V_k=0.292{\left(\frac{\dot{Q}}{W}\right)}^{1/3}$$

The relation applies when the fire is in the corridor and also when smoke enters the corridor through an open door, an air transfer grille or another opening. Its results are approximate, because only an approximate value of the constant is known. They do indicate the type of air velocity needed to prevent smoke backflow from fires of different sizes. For fires of 500 to 2,000 kW in corridors 1 to 4 m wide, the relation gives velocities of about 1.5 to 3.7 m/s.

The cube root makes the velocity rather insensitive to the fire size. Doubling the heat release rate raises the critical velocity by only 26 %, and a tenfold increase raises it by a factor of 2.2. The ratio of heat release rate to width also follows the rules of Froude scaling. In a model in which the heat release rate shrinks with the length to the power 5/2 and the width with the length, the velocity shrinks with the square root of the length.

Thomas's relation is not appropriate for sprinklered fires with small temperature differences between the upstream air and the downstream gases. For such cases Shaw and Whyte developed a method for the velocity through an open doorway, verified by experiments. For a sprinklered fire with a temperature difference of only 2 °C, it gives a minimum average velocity of 0.25 m/s, and larger values may be appropriate in many situations.

Doors and stairs

When doors in the boundaries of a smoke control system are open, smoke can flow into refuge areas or escape routes unless enough air flows through the door. One criterion for the design velocity is that no smoke backflow should occur during the evacuation of the building. The choice depends on the evacuation time, the rate of fire growth, the building layout and the presence of a suppression system.

Klote notes that much is still to be learned about the critical velocity at an open door. In the absence of a specific relation for doorways, the corridor relation can be used with the door width in place of the corridor width, assuming uniform smoke properties across the opening. For an intense fire of 2.4 MW this gives about 4 m/s, and for a much smaller fire of 125 kW about 1.5 m/s. In a sprinklered building, smoke away from the fire may be cooled to near ambient temperature, and design velocities of 0.25 to 1.25 m/s may be used.

Air velocity through open doors is also a criterion for stair pressurisation systems. In Australia, the 2020 data sheets for the Fire Safety Verification Method summarise a reliability study of such systems by Fazio. That study treated door opening forces above 110 N or air velocities below 1 m/s as failure. The effectiveness with respect to airflow was estimated at between 30 % and 63 %, depending on the system and the treatment of extreme estimates. The data sheets add that in some scenarios smoke spread to the stair may be adequately retarded at velocities below 1 m/s.

Atrium openings

In atrium smoke control, opposed airflow can keep smoke from passing between the atrium and the spaces that open onto it. Milke gives two empirical correlations for the minimum average velocity over the whole opening, based on limited experimental data. One applies to smoke that comes from the communicating space and depends on the square root of a height and of the temperature rise of the smoke. The other applies when the smoke at the opening belongs to a plume rising along the atrium wall, and depends on the cube root of the heat release rate divided by a height.

The average velocity from these correlations is higher than the minimum velocity needed at any single point. The excess ensures that the minimum is reached everywhere, given the turbulence caused by the edges and corners of the opening. The opposed airflow velocity should not exceed 1 m/s. Above that value the airflow may push the plume away from the wall, exposing more plume surface to the entrainment of air and so increasing the amount of smoke produced.

The required air supply is the opening area times the velocity, and for several openings the areas are added. The method may therefore be infeasible when many openings with a large total area need protection. When the airflow protects a communicating space from smoke in the atrium, the extra air enters the atrium. If an exhaust system keeps the smoke layer there at a constant height, all of this extra air must also be exhausted.

Car parks and tunnels

In the Netherlands, a 2021 report on indoor car parks with electric vehicles discusses displacement ventilation. This creates a sufficiently high air speed along the full cross-section of the car park, for example 1.5 m/s according to the Dutch standard NEN 6098, which might easily mean 40-fold ventilation. Its aim is a clear view of the fire for an offensive interior attack by the fire service. The ventilation usually starts only after people have escaped, so it improves firefighting conditions but not escape. The principle works only in tunnel-shaped car parks, and its added value is not yet fully known.

In Dutch practice, tunnels do not fit the building regulations on several aspects, because these are aimed mainly at buildings where people stay. Fire safety engineering is therefore applied to tunnels on several aspects. Tunnels are usually fitted with a smoke management system, and computational fluid dynamics can be used to study how effective it is. The Fire Dynamics Simulator offers a special solution scheme for long tunnel geometries made up of dozens of computational meshes placed end to end. Its documentation also refers to work that couples a three-dimensional model of the fire region with a one-dimensional network model of the ventilation of a tunnel fire. The ventilation systems used in tunnels, including jet fan ventilation, are described in separate articles.

Side effects of the airflow

Airflow that stops smoke also supplies oxygen to the fire. For most materials in building fires, about 13.1 MJ of energy is released per kilogram of oxygen consumed, and air is 23.3 % oxygen by mass. As a result, 1.0 m³/s of air at 21 °C contains enough oxygen for a fire of 3,660 kW. In Klote's corridor example, the airflow needed to stop the smoke of a 150 kW fire could support a fire more than 100 times larger. Klote concludes that extreme caution is needed when airflow is used.

The World Trade Center report on smoke management makes a similar point. The airflow method should not produce excessive airflow towards a fire, because this could intensify the fire, disrupt the plume or interfere with people leaving the building. The report adds that the ASHRAE text by Klote and Milke does not recommend the method in general. The exceptions are a suppressed fire and the rare cases in which the amount of fuel can be limited with confidence. At atrium openings, too much air can also deflect the plume and increase smoke production, as described above.

Worked example

Klote illustrates the corridor relation with a wastebasket fire of 150 kW in a corridor 1.22 m wide with a ceiling height of 2.44 m. All the following steps were recalculated for this article with the simplified relation. The critical velocity is:

$$V_k=0.292{\left(\frac{150}{1.22}\right)}^{1/3}=0.292\times 4.97=1.45\mathrm{m}/\mathrm{s}$$

Over the full cross-section of 1.22 m by 2.44 m, this velocity corresponds to an airflow of 4.3 m³/s. That airflow carries enough oxygen for a fire of about 15,800 kW, which is more than 100 times the wastebasket fire. The example shows why the airflow method is risky when the fire is not controlled.

The cube-root dependence becomes clear with a larger fire in the same corridor. An average living-room sofa fire releases about 2.5 MW. The relation then gives 3.71 m/s, only 2.6 times the velocity for the wastebasket, although the heat release rate is 16.7 times higher. The airflow becomes 11.0 m³/s, with enough oxygen for a fire of about 40 MW. If the corridor were sprinklered and the smoke cooled to near ambient temperature, design velocities between 0.25 and 1.25 m/s may be used instead.

Limitations and other meanings

The relations for critical velocity are simple estimates with a limited basis. Thomas's relation uses an approximate constant and assumes uniform properties across the corridor, and it does not cover sprinklered fires with small temperature differences. There is no specific relation for doorways, and further research is needed on the effect of sprinklers. The correlations for atrium openings rest on limited experimental data. The choice of a design velocity therefore still depends on experience and engineering judgement.

The term has a different meaning in the design of smoke detector systems. There, the critical velocity is the lowest gas velocity at which smoke enters the sensing chamber of a detector in sufficient amount to raise an alarm at a given threshold. Experiments found a value of about 0.15 m/s for the detectors tested in one study. This is close to the low velocity of 0.16 m/s at which a detector must respond in the UL sensitivity test. A common mistake is to mix up the two meanings. In smoke control the critical velocity is a minimum airflow that keeps smoke out, while in detection it is a minimum flow that lets smoke in.

See also

• Smoke control
• Smoke movement
• Smoke barrier
• Replacement air

References

• Australian Building Codes Board. (2020a). Data sheets: Fire Safety Verification Method (Handbook annex, Print version 1.1).
• Ferreira, M. J., & Strege, S. M. (2005). Smoke management systems (NIST NCSTAR 1-4D). National Institute of Standards and Technology.
• Klote, J. H. (2002). Smoke control. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 4-274–4-291). National Fire Protection Association; Society of Fire Protection Engineers.
• McGrattan, K., Hostikka, S., Floyd, J., McDermott, R., Vanella, M., Mueller, E., & Paul, C. (2026). Fire Dynamics Simulator technical reference guide: Vol. 1. Mathematical model (6th ed., NIST Special Publication 1018-1). National Institute of Standards and Technology. https://doi.org/10.6028/NIST.SP.1018
• Milke, J. A. (2002b). Smoke management in covered malls and atria. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 4-292–4-310). National Fire Protection Association; Society of Fire Protection Engineers.
• Schifiliti, R. P., Meacham, B. J., & Custer, R. L. P. (2002). Design of detection systems. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 4-1–4-43). National Fire Protection Association; Society of Fire Protection Engineers.
• Van der Graaf, J., Hessels, T., & Rosmuller, N. (2023). Fire safety of indoor car parks accommodating electrically powered vehicles. Nederlands Instituut Publieke Veiligheid. (Original work published 2021)
• Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.