Smoke reservoir

Smoke reservoir is the upper volume of a space used to collect smoke before it is extracted or spills elsewhere. Walls, downstands or curtains can bound that volume and restrict horizontal spread. In a large open building, ceiling-mounted screens can divide the upper space into several smoke-collecting regions. A smoke barrier defines a boundary, while the reservoir contains the accumulating hot gas layer. Their depths and elevations are related but are not the same quantity.

A reservoir provides a place from which smoke and heat exhaust ventilation can remove gas. Its performance depends on the balance between plume supply, extraction and any spill beneath its boundaries. Layer temperature and heat transfer also affect the occupied volume. A large geometrical volume does not establish how long conditions remain acceptable. That requires the fire, plume, ventilation and layer-development calculation.

Reservoir boundaries and layer depth

Cooper describes large spaces subdivided by ceiling-mounted screens or draft curtains. The subdivisions remain freely connected below the curtains. Their purpose is to limit smoke spreading outside the curtained region of fire origin. They do not become separate full-height rooms merely because their upper volumes are divided.

Curtain depth is measured downwards from the ceiling to the curtain's lower edge. Smoke-layer depth is measured from the ceiling to the layer interface. Initially, the layer can be shallower than the curtain. As it deepens, its lower boundary can reach and then pass below the curtain edge.

The usable volume depends on the geometry above the chosen interface. A rectangular space of constant plan area has volume equal to plan area multiplied by layer depth. Where the shape changes with elevation, the same depth does not imply the same volume increment. Milke identifies changing cross-sectional area as a limitation of simple atrium calculations.

The surrounding building also affects the boundary conditions. A reservoir bounded entirely by curtains can discharge smoke along a different length from one partly bounded by walls. Cooper's spill calculation uses the total curtain length through which smoke can pass. The perimeter relevant to that calculation is therefore the open spill boundary, rather than automatically the complete room perimeter.

The reservoir is a geometrical and flow concept. The smoke within it can have changing temperature, mass and composition. Treating its volume as an empty container that simply fills at one fixed rate omits those changes. Zone calculations instead combine conservation relationships with models for the flows entering and leaving it.

How the smoke layer develops

A plume carries smoke upwards from the fire and entrains surrounding air during its rise. When it reaches the ceiling, the flow spreads horizontally. A layer forms as that ceiling flow reaches the bounding surfaces and additional gas accumulates. In large spaces, the transport needed to establish the layer can take an appreciable time.

The ceiling jet and the accumulated layer are related but distinct. Cooper estimates the jet depth as being of the order of one tenth of the fire-to-ceiling height in his model. His layer treatment is expected to work more reliably once the accumulated layer is thicker than that jet. An extremely shallow assumed reservoir layer may not satisfy that modelling condition.

Cooper's 2002 chapter accordingly reports a recommended curtain depth of at least one fifth of the fire-to-ceiling height for that treatment. This is guidance presented in the cited smoke-venting method. It is not a universal geometrical rule for every smoke-control system or a statement of current local building requirements. Its purpose is tied to the assumed relationship between the ceiling jet and the layer.

Once a layer exists, its interface can descend rapidly. A high interface allows a long plume rise and therefore substantial entrainment. As the interface descends, the distance over which the plume entrains air changes. The reservoir filling rate consequently depends on its current state as well as on the fire.

Layer position can also mean different things in different methods. An experimental observation may identify the first detectable smoke, while a zone model returns an idealised boundary between uniform regions. Milke explains that these definitions contribute to differences between predicted interface heights. Comparing an observed or calculated height with a curtain edge requires awareness of that distinction.

Mass supply, energy and plume selection

Entrainment adds surrounding air to the combustion products before they reach the reservoir. The smoke mass supplied can therefore greatly exceed the mass of fuel converted into gas. Its value depends on plume rise, fire characteristics and the geometry surrounding the plume. The reservoir balance uses this mixed plume flow, rather than the fuel-burning rate alone.

Several plume models address different fire configurations. Van Rossum describes the Thomas plume formulation in terms of fire perimeter and rise height. Other formulations use heat release rate and a virtual origin. Selection depends on the fire and the relevant plume region, so a convenient equation cannot be assumed applicable to every reservoir scenario.

A mass balance states that stored mass changes by the mass entering minus the mass leaving. For a reservoir, inflows can include the plume and any other gas introduced into the layer. Outflows can include the exhaust and spill to neighbouring spaces. The following time-step form makes the accounting explicit.

Δm = (ṁ_in − ṁ_out)Δt

Symbol	Description	Unit
Δm	Change in stored reservoir gas mass during the time step	kg
ṁin	Total mass flow entering the chosen reservoir boundary	kg/s
ṁout	Total mass flow leaving that boundary	kg/s
Δt	Time-step duration	s

Energy requires a separate balance. The convective part of the fire supplies energy through the plume. Energy leaves with extracted or spilled gas and through heat transfer to the bounding construction. The amount remaining affects the layer temperature and, through gas density, its volume.

A stationary interface therefore does not imply an absence of flow. Large inflows and outflows can occur while the stored quantity remains approximately constant. Conversely, matching a nominal volume supply and exhaust does not establish a mass balance if their temperatures differ. The quantities must be expressed at consistent gas conditions.

Smoke spilling below a curtain

When the layer interface descends below a curtain edge, smoke can enter the adjacent upper space. Cooper treats the gap below the curtain as a flow opening. The pressure difference across that opening varies with height. Buoyancy drives smoke from the hotter curtained region towards the initially cooler adjoining region.

For the particular two-layer assumptions, Cooper derives a spill mass rate from curtain length, spill depth and the density difference. The relationship below applies when the interface lies below the curtain edge. It assumes that the neighbouring space still has essentially its initial ambient conditions. Those assumptions limit its use after substantial smoke has spread into neighbouring reservoirs.

ṁ_spill = (L_c/3)√[8δ³ρ_s(ρ_a − ρ_s)g]

δ = z_curtain − z_interface > 0

Symbol	Description	Unit
ṁspill	Total smoke mass flow beneath the curtain boundary	kg/s
Lc	Total curtain length available for the modelled spill	m
δ	Depth of the smoke interface below the curtain edge	m
ρs	Density of smoke in the source reservoir	kg/m³
ρa	Density of ambient air in the adjoining region	kg/m³
g	Gravitational acceleration	m/s²

The expression gives zero spill while the modelled interface remains at or above the curtain edge. Once the interface falls below it, flow increases strongly with spill depth. The factor involving depth is proportional to its power of three halves. A small additional descent can therefore produce a meaningful change in the outflow.

Spill is not permanent storage outside the original reservoir. The adjacent spaces begin to develop their own layers. Cooper describes how continued spill can fill those spaces until smoke develops more widely across the building. A calculation that keeps the neighbouring region indefinitely clean would no longer represent that progression.

Worked reservoir and spill example

Cooper considers a square curtained region measuring 30 m by 30 m, away from surrounding walls. Its four sides give a total curtain length of 120 m. The curtains extend 3.0 m below the ceiling, while the smoke layer is 3.5 m deep. The interface consequently lies 0.5 m beneath their lower edges.

The corresponding plan area is 900 m². Multiplying by the curtain depth gives a geometrical volume of 2,700 m³ above the curtain edge. At the stated 3.5 m layer depth, the layer occupies 3,150 m³ within that plan area. These derived volumes describe the assumed rectangular geometry and do not establish a filling time.

The source takes ambient temperature as 293 K and smoke temperature as 393 K. Its ambient density is 1.2 kg/m³. The constant-pressure gas approximation gives a smoke density of approximately 0.895 kg/m³. Together with gravity of 9.8 m/s², these are the inputs to the spill equation.

Direct evaluation using those displayed inputs gives approximately 65.4 kg/s. Cooper reports approximately 66 kg/s for the example. The small numerical difference does not change the illustrated mechanism: smoke is leaving beneath the full curtain boundary. This is a modelled instantaneous flow under the specified conditions, rather than a measured reservoir performance.

The source then contrasts a vented arrangement with continued spill when no ceiling vents are open. Its point is that the reservoir boundary alone does not remove the gas entering from the plume. Exhaust can balance that supply under the stated steady conditions. Without sufficient removal, smoke spreads beneath the curtains and fills neighbouring upper spaces.

Exhaust effectiveness and inlet interaction

A reservoir's extraction points need access to the smoke layer. Excessive local withdrawal can cause plugholing, drawing relatively clean air from beneath the interface. Some nominal extraction then bypasses the smoke. A shallow layer is more susceptible because the clean air is closer to the outlet.

Distributing extraction between more points reduces the flow demanded at each point. Increasing layer depth can also reduce the tendency to draw through the interface. These measures concern local extraction effectiveness, while the total required exhaust still depends on plume supply. A reservoir calculation therefore needs both the total balance and an appropriate extraction arrangement.

Replacement air can disturb the same balance. Milke describes supplying it below the interface, because air introduced directly into the smoke layer adds to the extraction demand. Strong supply near the plume can increase entrainment or alter burning. The reservoir cannot be assessed independently of the inlet flow that supports the exhaust.

Natural vents also depend on inlet capacity and external pressure. Cooper shows that restricted inlet area reduces the effective exhaust capability. Wind changes the pressure distribution around the building and can alter opening flows. A nominal vent area therefore has to be interpreted within the complete flow path serving the reservoir.

Limits of an idealised reservoir model

A two-layer model assumes uniform conditions within each layer. Van Rossum identifies this as a simplification, because real temperature and composition vary across a space. A reservoir can also contain local flow disturbances near the plume, curtains and exhausts. The model's average state does not resolve each of those locations individually.

The thermal boundaries influence the result as the layer deepens. More wall area comes into contact with smoke, while the ceiling remains exposed above. Heat transfer depends on that area, material properties and the temperature difference. Reservoir geometry therefore affects both storage volume and the thermal exchange used to predict the layer state.

Steady design and transient development answer different questions. Cooper's steady formulation selects a fire and interface elevation, then finds the removal needed to maintain them. His transient discussion includes changing plume flow, layer conditions and vent actuation. A steady solution cannot establish the earlier smoke conditions before the assumed exhaust arrangement is operating.

Fire and actuation scenarios

The design fire represents a plausible assembly of combustibles in the space being assessed. Cooper relates it to the material, arrangement and burning characteristics expected in the facility. A reservoir above storage therefore needs a fire description consistent with that storage. Its plan area alone does not define the smoke supply entering from below.

Fuel elevation also changes the available plume rise. Cooper's steady formulation explicitly includes the elevation and area of the fire as well as the selected layer position. Moving the source upwards changes the distance between fuel and interface, even when the ceiling and curtains remain fixed. The plume calculation consequently retains a defined vertical datum for those quantities.

The assessment also identifies which vents are open at the time under consideration. Cooper discusses systems where individual vents are actuated by fusible links and their available area changes as fire develops. The eventual total opening area is different from the area available earlier. Reservoir conditions during that earlier interval require the appropriate operating state.

Where different performance objectives are assessed, the relevant time can also differ. Cooper distinguishes maintaining conditions for escape from maintaining access for subsequent firefighting and protecting adjacent contents. These objectives connect the developing layer to the period of interest. They do not follow automatically from a reservoir having a particular volume or curtain depth.

See also

• Smoke control
• Atrium smoke control
• Replacement air
• Balcony spill plume

References

• Cooper, L. Y. (2002). Smoke and heat venting. In P. J. DiNenno (Ed.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-219–3-242). National Fire Protection Association.
• Milke, J. A. (2002). Smoke management in covered malls and atria. In P. J. DiNenno (Ed.), SFPE handbook of fire protection engineering (3rd ed., pp. 4-292–4-310). National Fire Protection Association.
• Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.