Looking down the plughole

One of the more common uses of fire safety engineering is to compare the time available in a building before the onset of hazard, with the time required for safety. Where this 'time available' is determined by the deepening of a thermally-buoyant smoke layer beneath the ceiling, this deepening can be slowed or stopped by using smoke exhaust ventilators.

Plugholing is the unwanted phenomenon whereby an exhaust ventilator draws clean air from below the smoke layer, so that the ventilator exhausts a mixture of smoky gases from the smoke layer and clean air from below the smoke layer, see figure 1. The reduction in the exhaust rate of smoky gases from the smoke layer due to plugholing is very rarely taken into account by fire engineers when calculating how ventilators extend the time available before the onset of hazard. The key process for accurate calculation, namely the amount of smoke drawn into the ventilator while plugholing is occurring, remains unresearched. Nevertheless, a calculation method is proposed based on plausible arguments.

This new calculation procedure shows that "plugholing":
a) can have a significant effect on such calculations, and b) is strongly dependent on the circumstances of the fire growth and of the building geometry.

It is suggested that plugholing should no longer to be ignored in fire engineering calculations of this type. It is also suggested that research into the proportions of smoke and air drawn into a plugholing ventilator is highly desirable.

The plugholing phenomenon
The plugholing phenomenon is similar in appearance to the cone of air entering the plughole of a bath when the water level becomes low – hence the name plugholing. When in this condition the flow into the ventilator can be described as supercritical.

If the ventilator's exhaust rate is reduced, the proportion of air being drawn in reduces, until a condition is reached where the amount of air being drawn in becomes insignificant. This condition of the ventilator can be described as critical, see figure 2. It is also described as the onset of plugholing.

If the ventilator's exhaust rate is reduced further, and assuming no change in the layer's depth, the base of the layer below the ventilator appears undisturbed. This condition of the ventilator is described as subcritical, see figure 3.

Some research has been done to relate the critical condition to the layer's depth, to the layer's temperature, and to the size of the ventilator opening. Results from this past research into the critical limiting condition1,2 have been used to eliminate inefficient smoke exhaust designs where the smoke and heat exhaust ventilation system is based on steady-state design fires^3,4.

Plugholing can occur with natural smoke ventilators and with powered smoke ventilators, although it can be anticipated that a relatively smaller proportion of clean air will be drawn into a supercritical natural smoke ventilator opening than into the equivalent powered smoke ventilator opening.

There is currently no design formula in the published literature which allows the quantitative calculation of the proportions of clear air and smoky gases being drawn into a supercritical ventilator opening. It can be expected that the proportion of smoke will decrease as the layer's buoyancy decreases as a result of a reduction in temperature of the layer. It can also be anticipated that the proportion of smoke will decrease as the physical size of the ventilator opening increases. These qualitative statements follow from the known relationships at the critical condition².

Time dependent calculations
In the absence of smoke ventilation, one can calculate the position of the smoke layer base as a function of time, taking into account the assumed time-dependent behaviour of the fire, the building's geometry, and other relevant factors.

Most published guides to fire safety engineering describe methods for doing this^3,4,6,7. The result will be something like the 'no ventilation' curve in figure 4, predicting a time, t₁, to onset of hazard.

Many fire safety engineers will consider using smoke ventilation if this time, t₁, is shorter than the time required for safety, tsafety, however defined.

Commonly-used methods of introducing smoke ventilation ignore plugholing. Except for very simple geometry buildings, it is usually not practicable to adopt an analytical solution for smoke filling. Instead it is usual to adopt a quasi-steady-state method whereby the time is divided into a succession of small increments, and within each increment the fire and all other variables are regarded as being steady-state. Each parameter is changed from one increment to the next to approximate to the actual continuously-varying fire.

The quantity of smoke entering the smoke layer at each specified time in the fire's growth is calculated at that time using this quasi-steady-state approximation. The exhaust capacity from the layer (calculated for the same time and with the implicit assumption that all gases exhausted are taken from the smoke layer) is subtracted from this. Any positive difference is used to calculate the deepening of the layer prior to the start of the next increment. The result will be something like the 'with ventilators, ignoring plugholing' curve of figure 4, predicting a time to onset of hazard of t₃.

In practice, sufficient smoke ventilation exhaust capacity will be specified to ensure that t₃ > t_safety by an acceptable margin.

Plugholing changes this picture
Initially the smoke layer will be shallow – although it may be the depth of the ceiling jet. Ventilator openings can be expected to exhaust a high proportion of clear air, with only a small proportion of smoke. Hence the initial curve will approximate to the 'no ventilation' curve.

As the layer becomes deeper, the proportion of smoky gases being exhausted will increase until the critical condition is passed and no more air is drawn in through the layer.

The resulting curve will look something like the 'with plugholing' curve in figure 4. Unfortunately, because the proportions of air and smoky gases entering a plugholing, supercritical ventilator opening cannot currently be calculated with confidence, it is not possible to predict t₂ quantitatively for any actual circumstance. As is illustrated in figure 4, it may be possible to have t₂ < t_safety even when t₃ appears satisfactorily larger than t_safety.

It can be expected that the importance of plugholing (ie the relative gap between t₂ and t₃) will vary from case to case. By analogy with the formulae for the onset of plugholing, it can be expected that plugholing will be less significant for deeper and/or hotter smoke layers; and will be more significant for layers whose depth approaches the size of the ventilator opening and/or which are cooler.

It is known that the critical condition representing the onset of plugholing can be eased for an entire reservoir by spreading the exhaust capacity over a larger number of smaller ventilator openings. This is the principle adopted in the draft BS 7346 Part 45 and elsewhere4 to avoid wasting exhaust capacity in smoke and heat exhaust ventilation systems design using steady-state design fires.

Similarly, spreading the exhaust capacity over a larger number of smaller ventilator openings as a part of time-dependent smoke and heat exhaust ventilation systems design will ensure that critical exhaust conditions will be reached earlier. This will in turn have the effect of moving the 'with plugholing' curve (c) in figure 4 closer to the 'with ventilators, ignoring plugholing' curve (b) – and hence moving t₂ closer to t₃.

An interim proposal
Until such time as research provides a better method, it is worth considering that the following method be adopted:

• Assume that the mass exhaust rate from a ventilator at the critical onset of plugholing remains the maximum mass exhaust rate of smoky gases from the smoke layer while plugholing in bulk.
  
• Introduce into the iterative calculation loop a calculation of the critical mass exhaust rate using the layer parameters applying to that time-increment. It is suggested that this calculation be based on Ghosh^2,4.
  
• This is compared with the fan (or natural ventilator) exhaust rate at that time increment, and the smaller value is subtracted from the plume mass flow rate into the layer, giving the contribution to the change in layer parameters needed for the next time-increment.

It is worth noting that this applies to either powered or natural ventilators and that the number and physical dimensions of openings in the smoke reservoir have to be specified as inputs, rather than being calculated.

It is appreciated that this method uses the critical mass calculation for a purpose outside its original scope and its accuracy cannot therefore currently be assessed. The assumption made is however plausible and is unquestionably a step forward from current design methods which will always underestimate the amount of ventilation required to a greater or lesser extent.

Illustrative examples
Methodology
An existing in-house FRS program implementing the iterative procedures described in Annex A of Ref 3, written by one of us (Morgan) was modified to include the proposals outlined in the previous Section of this paper.

  This program introduces into the iterative calculation loop a calculation of the critical mass exhaust rate using the layer parameters applying to that time-increment. This is compared with the fan (or natural ventilator) exhaust rate at that time increment, and the lower rate is subtracted from the plume mass flow rate into the layer to give the contribution to the change in layer parameters needed for the next time-increment. Note that this works for either fans or natural ventilators. Note also that the number and physical dimensions of openings have to be specified as inputs, rather than being calculated. A 2.5 m clear layer default safe limit has been set in the program: If a 3.0 m (or any other larger clear height) safe clear layer is preferred it is easy to interpolate.

Ghosh's plugholing formula^2,3 for openings away from walls has been used. The older Heselden formula1 is known to be inaccurate and is best avoided in this context.

The tabular outputs from the program have been plotted below in graphical form for greater clarity.

  Examples
Several imaginary single-storey scenarios were devised in order to identify trends. For each example there is a time-to-fill curve without any ventilation (Curve a in all cases); a curve with exhaust but no plugholing (Curve b in all cases); and one or more curves with exhaust and plugholing. These examples are shown as Examples 1 to 6. Details of each example are shown as part of each Figure. All these examples assume an upright plume, describable by the Large-Fire Plume Model (see for example ref 4) with a plume entrainment constant of 0.188.

Discussion
In all the examples, it is assumed that the smoke layer is constant at ceiling jet depth until the calculated depth exceeds the ceiling jet depth, which is itself defined as one-tenth of the floor to ceiling height⁹.

Example 1 shows a very similar behaviour to that predicted in Figure 4. It can be seen that curve c (with plugholing) predicts a time which is only about 5% shorter than curve b (without plugholing), when the layer reaches to 2.5 m above the floor. If this were the safety criterion for the design, it is clear that "plugholing" would have little effect on the outcome.

The most important difference introduced in Example 2 is that the growing fire is "capped" so that it remains constant once it has reached 5 MW. Apart from a change in the shape of curve b, there is little difference in the proportional effect of plugholing compared with Example 1.

Example 3 has a lower ceiling and larger fan exhaust, such that a steady asymptotic layer depth is reached slightly below 3.0 m above the floor. It can be seen that in this case, the effect of introducing "plugholing" into the calculation is to reach 3.0 m in approximately 50% of the time without "plugholing". If 3.0 m were the safety criterion in this case, it is clear that "plugholing" would be a very significant process which ought not to be ignored by a designer. It is clear from this and the foregoing examples that the significance of plugholing to the calculation is strongly influenced by the circumstances of the design.

Example 4 suggests that the number of openings has an effect, but not necessarily a strong effect, on the outcome.

Example 5, with a larger fan exhaust capacity, again shows the high significance of "plugholing" for all layer bases close to but higher than the asymptotic steady layer base height.

Example 6 has natural ventilators calculated to give a similar layer base height to the fan exhaust in Example 5, and also includes the cooling effect of sprinklers acting on the smoke layer. It is interesting that the effect of "plugholing" is greatly reduced compared to Example 5. This is likely to be the result of the much larger ventilator openings required for natural ventilators to move the similar mass of smoky gases.

The examples were chosen to be indicative, and to try to give an initial insight into the significance of plugholing. It is not suggested that these few examples give an answer to the problems. It is clear, however, that even this limited exercise in zone modelling has identified that there is a real problem which ought to be addressed.

It is suggested that the potentially significant effects of "plugholing" in reducing the time available before the onset of "hazard" are such that the phenomenon should be explicitly considered in all fire engineered designs where smoke exhaust is adopted to extend the "time available".

It is also suggested that there is a need for research to be carried out into the proportions of smoke and air drawn into a ventilator undergoing "plugholing", in order to improve the accuracy of calculations which include "plugholing". Suitable research methods could include physical scale modelling and/or CFD.

Conclusions

• Natural ventilators may be less susceptible to problems arising from plugholing than powered ventilators – probably because the holes are larger.
  
• Plugholing is more significant when the safe limit of layer depth is shallower.
  
• Plugholing is more significant when the safe limit of the smoke base is close to but is higher than the asymptotic steady depth of the smoke layer.
  
• Plugholing is more significant when powered exhaust capacities from the reservoir are relatively large.
  
• The effect of plugholing can be reduced by using a greater number of smaller capacity exhaust points.
  
• Based on the present examples, the effect of plugholing can vary up to 50% of the "ignoring plugholing" curve, but can be as small as 5%, depending on the circumstances of the example.
  
• It appears to be necessary for design calculations to include the effects of "plugholing" explicitly in design.
  
• There is a need for quantitative research into the relative proportions of smoke and air being drawn into a "plugholing" ventilator and for development of a representative design calculation based on that research.