Balcony spill plume

A balcony spill plume is a plume of smoke that first flows horizontally under a balcony or similar projection and then turns upwards at its edge. It typically forms in atria and covered malls, where smoke from a fire in a shop or below a walkway spills from the walkway edge into the open space above. Because the smoke rises from a long edge rather than from a compact source, it behaves as a line plume and draws in more air than a round plume at short heights above the balcony.

At short heights above the balcony, a balcony spill plume therefore delivers appreciably more smoke to the smoke layer than a round plume from the same fire. This matters for smoke control in atria, where the exhaust rate must match the rate at which the plume supplies smoke to the layer. The SFPE Handbook contains two approaches. Milke gives an entrainment equation based on small-scale experiments, while Cooper treats the spill as a line plume rising from an imaginary line source below the balcony edge. The two approaches can give quite different results, and the width of the spilling smoke is uncertain.

Formation

A balcony spill plume starts as an ordinary fire plume that rises from the fire and meets a ceiling, balcony or other large horizontal projection. The smoke then travels horizontally under this projection towards its edge. At the edge it turns and rises into the larger space. Its properties depend on the fire, the width of the spill, the height of the ceiling or balcony above the fire and the path from the plume centreline to the balcony edge.

A common case is a fire in a shop next to an atrium. The smoke leaves the shop through its opening, flows under the walkway of the floor above and spills upwards from the walkway edge. The Introduction to Fire Safety Engineering describes such a plume, emerging from under a ceiling edge, balcony or gallery, as a line plume with an oval rather than round cross-section. Its larger perimeter compared with its cross-section leads to more mixing with fresh air.

Formation of a balcony spill plume: smoke from a shop fire flows under the walkway, spills at its edge and rises into the atrium, where it feeds the smoke layer. Based on Milke (2002b), pp. 4-301 and 4-308, and Ferreira and Strege (2005), p. 7.

The book also notes that a fire in a room next to an atrium is often the governing scenario in smoke calculations. The smoke passes through more mixing steps and forms a much larger volume. A calculation with only the atrium as one room is then not realistic if the adjacent room is not separated by fire- and smoke-resisting construction. A fire below a balcony inside the atrium itself can produce a similar spill, as in the example by Cooper described below.

Entrainment equations

As in any plume, most of the mass in a balcony spill plume is air drawn in from the surroundings, a process known as entrainment. For a fire in a space directly adjacent to an atrium, Milke gives an equation for the mass flow in the spill plume. It is based on Law's interpretation of small-scale experiments by Morgan and Marshall. In words, the mass flow grows with the cube root of the heat release rate multiplied by the square of the plume width. It also grows linearly with the height above the balcony plus a quarter of the balcony height above the fuel: $$\dot{m}=0.36{\left(\dot{Q}{L}^2\right)}^{1/3}(z+0.25H_{\mathrm{b}})$$ Without vertical barriers under the balcony, the smoke spreads sideways before it spills. An equivalent width can then be estimated from the width of the shop opening and the distance from the opening to the balcony edge: $$L=w+b$$

Symbol	Description	Unit
$\dot{m}$	mass flow in the spill plume	kg/s
$\dot{Q}$	heat release rate of the fire	kW
$L$	width of the balcony spill plume	m
$z$	height above the balcony edge	m
$H_{\mathrm{b}}$	height of the balcony above the top of the fuel	m
$w$	width of the shop opening	m
$b$	distance from the shop opening to the balcony edge	m

The equivalent width is the confined width that entrains the same amount of air as the unconfined spill plume, based on visual observations in the experiments. Vertical barriers attached to the underside of the balcony restrict the sideways spread and so fix the width. Because the plume width enters to the power 2/3, doubling it raises the mass flow by about 59%. Take a 5,000 kW fire under a balcony 3 m above the fuel, as in the handbook's own comparison. At 10 m above the balcony, the equation then gives about 193 kg/s for a 5 m wide plume and about 307 kg/s for a 10 m wide plume.

Plume width at the balcony edge: without barriers the smoke spreads sideways (equivalent width L = w + b); vertical barriers under the balcony limit the spill width. Based on Milke (2002b), pp. 4-301 to 4-302.

Because the spill plume grows linearly with height and a round plume with height to the power 5/3, the round plume eventually catches up. For large heights well above the balcony, the two give the same mass flow when the height is about 12.5 times the plume width. Above that height, Milke recommends the round plume equation with the height measured from the balcony to the smoke layer. For a 4.5 m wide spill, this rule places the crossover about 56 m above the balcony.

Mass flow against height above the balcony for a 5,000 kW fire with the balcony 3 m above the fuel: balcony spill plumes 5 m and 10 m wide and a round plume. Based on Milke (2002b), pp. 4-298 and 4-301.

Cooper uses a different approach. He treats the smoke at the balcony edge as a free line plume and places an imaginary line source below the edge. Its depth is chosen so that the line plume carries the same mass flow as the round plume that reaches the balcony. Above the edge, the mass flow per metre of spill then grows linearly with the height above this imaginary source, as in any free line plume.

Worked example

Cooper considers a pool-like fire with a total heat release rate of 5 MW on 4 m² of floor, 3 m below a balcony with a width of 3 m. The convective part is 65%, or 3.25 MW. The round plume reaches the underside of the balcony with a mass flow of 12.0 kg/s. The smoke is assumed to reach the balcony edge without significant extra entrainment or heat loss. The spill length is estimated at 1.5 times the balcony width, or 4.5 m, which gives a convective heat release rate of 722 kW per metre.

The imaginary line source then lies 1.7 m below the balcony edge. At the design level of the smoke layer, 3 m above the balcony, the free line plume equation gives: $$\dot{m}=0.18\times 4.7\times 722^{1/3}\times 4.5=34.2\mathrm{k}\mathrm{g}/\mathrm{s}$$ For comparison, Cooper estimates that the same fire burning in the open, away from the balcony, would supply 26.0 kg/s at the same height of 6 m above the fire. The spill thus increases the smoke flow into the upper layer by 31%, from 26 to 34 kg/s.

Law's equation, which Milke gives for smoke from an adjacent shop, gives about 62.9 kg/s for the same dimensions with the total heat release rate. Cooper himself applies an equation of this form as an alternative solution to the same example. He uses a constant of 0.39 and the total heat release rate of the fire below the balcony. He obtains 68 kg/s, about 2.0 times his line plume estimate and about 2.6 times the estimate for the fire in the open. Milke presents his version of the equation for a fire in a space directly adjacent to the atrium. The comparison shows how strongly the predicted exhaust demand can depend on the chosen method.

Mass flow at the design level 3 m above the balcony (6 m above the fire) for the worked example, by method. Based on Cooper (2002b), pp. 3-232 to 3-233, and Milke (2002b), p. 4-301.

The temperature of the smoke follows from an energy balance on the layer: the convective heat release rate divided by the mass flow and the specific heat of air. The calculation assumes a specific heat of 1.0 kJ/(kg·K) and no heat loss. The smoke then reaches the layer about 95 K above ambient with Cooper's line plume estimate, but only about 48 K with his alternative estimate. The fire in the open would give about 125 K. The extra air drawn into a spill plume thus gives more smoke at a lower temperature.

Role in atrium smoke control

Atrium smoke control by the exhaust method keeps smoke 6 to 10 ft (1.8 to 3.0 m) above the highest occupied floor. The buoyant smoke rises to the upper part of the space, which acts as a smoke reservoir for the descending layer. In the most commonly used approach, fans extract smoke from this upper part at a rate equal to the flow of smoke entering the layer. The layer stops descending when the mass exhaust rate equals the mass flow supplied by the plume. Below the crossover height, a balcony spill plume therefore raises the required exhaust capacity.

In the United States, the calculation methods of NFPA 92B for such large spaces have been adopted in the atrium requirements of the model building codes. NFPA 92B also recognises that in very large spaces the entrained air can dilute the smoke so much that the descending layer presents little hazard.

Because the worst fire position may not be readily apparent, it may be necessary to evaluate design fires at several positions. The handbook to the Australian Fire Safety Verification Method gives the example of a large enclosure with overhanging projections and escape routes above floor level. There, design fires had to be evaluated in the centre, in a corner, near air inlets and under horizontal projections where line plumes may form. Under the projections, the larger smoke volume may compromise more escape routes in less time, although temperatures and toxic concentrations are lower.

Zone models represent the same process for smoke that flows between rooms. In CFAST, gas that leaves the upper layer of one room and enters the lower layer of the next rises into its upper layer as a spill plume. The entrainment of this plume follows a correlation of Poreh and co-workers, in which the mass flow grows with the width of the opening to the power 2/3. This mirrors the dependence on plume width in the balcony spill equation.

Limits and uncertainty

Law's equation rests on small-scale experiments with a single shop opening, a walkway and one turn of the smoke at the walkway edge. Its applicability is questionable when the smoke reaches the atrium through a long corridor, because the smoke then loses appreciable heat on the way. Milke calls it an approximation of the mass flow for a complex situation.

The width of the spilling smoke is another source of uncertainty. Cooper expects the spill length to lie between one and two times the balcony width and chooses 1.5 times. Without barriers, the equivalent width in Milke's method comes from visual observations in small-scale tests. Recalculating Cooper's example with a spill length of 3, 4.5 or 6 m gives about 28.6, 33.8 or 38.4 kg/s at the design level.

The constants in spill plume correlations also vary. For the CFAST spill plume, suggested values of the entrainment constant range from 0.44 to 0.66. For the same form of balcony spill plume equation, Milke uses a constant of 0.36 and Cooper's alternative 0.39.

The temperature of the smoke layer is usually estimated without heat loss to the walls, which is conservative. In spaces with ceilings lower than about 10 m, however, this assumption can overestimate the temperature significantly. The exhaust method itself needs a high space: it is not intended for low ceilings, where no smoke reservoir exists above the occupants. In such spaces, sprinklers may also cool the smoke so much that it loses its stratification and descends below the design level.

See also

• Smoke and heat exhaust ventilation
• Smoke barrier
• Plugholing
• Replacement air
• Smoke stratification

References

• Australian Building Codes Board. (2020b). Handbook: Fire Safety Verification Method (Print version 1.1).
• Cooper, L. Y. (2002b). Smoke and heat venting. 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. 3-219–3-242). National Fire Protection Association; Society of Fire Protection Engineers.
• Ferreira, M. J., & Strege, S. M. (2005). Smoke management systems (NIST NCSTAR 1-4D). National Institute of Standards and Technology.
• 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.
• Peacock, R. D., McGrattan, K. B., Forney, G. P., & Reneke, P. A. (2026). CFAST – Consolidated Fire and Smoke Transport: Vol. 1. Technical reference guide (Version 7, NIST Technical Note 1889v1). National Institute of Standards and Technology. https://doi.org/10.6028/NIST.TN.1889v1
• Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.