Critical Fire Scenario Analysis

Automated Worst-Case Smoke Containment Verification

Abstract

A building's smoke-control system must perform under fire conditions originating in any occupied room. Manually simulating each possible fire location is time-consuming and in practice often replaced by a single "worst-case" guess — leaving unverified rooms as silent liabilities. This paper describes SootSafe's automated approach: a systematic search that simulates every candidate room in turn, determines the minimum fan capacity required to contain smoke in each scenario, and ranks the results so that the designer's attention is directed precisely where it is needed.

This paper assumes familiarity with the pressure-network model described in Nodal Pressure Network Analysis. The analysis here is built on top of that engine.

1. Problem Statement

Given a building network in which fire may originate in any one room:

Find, for each candidate fire room, the minimum fan-speed multiplier $m \geq 0$ such that no smoke reaches any protected space.

A protected space is any fire compartment (brandcell) in the building — dwelling units, offices, stairwells, and lobbies alike. Every protected space plays a dual role in the analysis: it is the fire source in the scenario where ignition occurs there, and it is the space that must remain smoke-free in every other scenario. This mirrors the Swedish regulatory requirement (BBR) that each brandcell must be protected from smoke originating in all adjacent brandcells, not only from smoke entering evacuation routes. Duct junctions, distribution plenums, and outdoor boundary nodes are not protected spaces and are never simulated as fire sources.

The answer to this question is not a single pressure map but a ranked list: which room demands the highest fan capacity, and by how much does the designed system fall short or exceed that demand?

2. Modelling a Fire Event

2.1 Fire as a Mass Source

A fire is modelled as a forced mass-flow injection at the fire node. Hot combustion gases increase the local air volume, creating an outward pressure gradient that drives smoke toward adjacent compartments. In the pressure-network model (see Nodal Pressure Network Analysis, §2.1), this is represented by setting the node's target mass rate:

$\dot{m}_i^{\text{target}} = -\dot{m}_{\text{fire}} \qquad \text{(negative = injection into the network)}$

with $\dot{m}_{\text{fire}}$ in kg/s chosen to represent a credible design fire intensity. The rest of the network — ducts, leakage paths, fans — responds to this source exactly as it would to any other forced flow condition.

2.2 Fan Capacity as a Continuous Variable

In practice, a designer might ask: "Does my system pass at nominal capacity? If not, how much more is needed?" Rather than re-running simulations for a discrete set of fan speeds, the model treats fan capacity as a continuous multiplier $m \in [0, m_{\max}]$ applied via the fan affinity law.

The affinity law states that for a geometrically similar fan operating at speed ratio $m$ relative to its rated speed, the pressure–flow curve scales as:

$\Delta P_{\text{fan}}(Q;\, m) = a Q^2 + (m b) Q + (m^2 c)$

where $a$ , $b$ , $c$ are the coefficients of the nominal fan curve ( $m = 1$ ). The linear term scales with $m$ and the constant term with $m^2$ , consistent with fan affinity relations. The quadratic term $a$ is speed-independent in this model (it represents system interaction, not shaft work).

This parameterisation means that scanning $m$ from $0$ to $m_{\max} = 5$ covers the range from completely off to five times rated capacity — sufficient for any realistic design margin.

3. Smoke Propagation and Leakage Detection

Smoke is carried by air. After the pressure-network solver has converged to an equilibrium pressure field $\mathbf{p}^*$ for a given fire scenario and multiplier $m$ , the question becomes: does smoke from the fire room reach any protected space?

Two physically distinct mechanisms can transport smoke across a boundary.

3.1 Convective Leakage

If a directed flow path exists from the fire node to a protected space — that is, every branch along the path carries positive volumetric flow from the fire side toward the protected side — then smoke is carried convectively with the air stream. This is the dominant leakage mode when the fire room is at higher pressure than the surroundings.

Detection is a directed graph traversal (breadth-first search) starting at the fire node, following only branches where the solved flow is directed away from the fire. If any protected space is reachable by this traversal, convective leakage has occurred.

3.2 Dead-End Equalisation

A subtler mechanism arises when a protected space has a near-zero-flow connection to a smoke-contaminated node. Because flow through the connecting branch is approximately zero, the orifice law gives:

$|\Delta P| = k \, Q^2 \approx 0 \implies p_{\text{protected}} \approx p_{\text{contaminated}}$

The two compartments are at nearly equal pressure. Even though no net flow carries smoke, the pressure gradient is insufficient to drive clean air outward and prevent diffusive mixing across the boundary.

The leakage test for this case requires two simultaneous conditions:

The protected space has a neighbour that is reachable (directly or indirectly) from the fire node.
That neighbour node's pressure is not significantly below the protected space's pressure — i.e., the protected space is not actively pushing air out through that connection.

If both conditions hold, the protected space is considered at risk.

3.3 Safety Margin

For each protected space $s$ and each of its smoke-exposed neighbours $j$ , the local pressure margin is:

$\Delta P_{s,j} = p_s^* - p_j^*$

A positive margin means the protected space is above the contaminated zone and drives outward flow — smoke is being repelled. A negative margin means smoke is being drawn in.

The overall safety margin for a scenario is the minimum over all such pairs:

$\Delta P_{\text{margin}} = \min_{s,\, j \in \text{neighbours}(s)} \Delta P_{s,j}$

A scenario is safe if and only if there is no leakage (by either mechanism above) and $\Delta P_{\text{margin}} > 0$ .

4. Finding the Minimum Required Fan Capacity

4.1 Monotonicity

The leakage test is monotone in $m$ : increasing the fan multiplier raises the pressure in protected spaces relative to the fire room, making leakage progressively harder to sustain. This monotonicity — which follows from the strict positivity of the fan's pressure contribution and the continuity of the orifice flow law — guarantees that a well-defined minimum multiplier $m^*$ exists wherever the network topology permits containment at all.

4.2 Binary Search

Because the leakage test is monotone, binary search converges to $m^*$ in a guaranteed finite number of steps. The procedure for each candidate fire room is:

lo ← 0,  hi ← m_max
for each iteration:
    m_mid ← (lo + hi) / 2
    solve pressure network with fan multiplier m_mid
    if smoke reaches any protected space:
        lo ← m_mid          (need more capacity)
    else:
        hi ← m_mid          (can relax capacity)
        record best solution

After 12 iterations, $|hi - lo| < m_{\max} / 2^{12} \approx 0.001$ , giving a relative precision of 0.02 % on the required multiplier — more than sufficient for engineering purposes.

The solver is called once before the binary search to establish whether containment is even achievable at $m = m_{\max}$ . Each room simulation therefore involves at most 13 pressure-network solves (1 feasibility check + 12 search steps).

4.3 Result for Each Room

At the end of the binary search, the result for fire room $i$ is:

Output	Description
$m_i^*$	Minimum fan multiplier for containment
$Q_{\text{fan}}(m_i^*)$	Total volumetric fan flow at that multiplier (m³/s)
$\Delta P_{\text{margin}}$	Safety margin at the threshold (Pa)
`cleared`	Whether containment was achieved within $m_{\max}$
`infeasible`	Whether the network topology prevents containment regardless of fan capacity

5. Topology Validation and Infeasibility

Not every building network can achieve smoke containment purely through fan pressure, regardless of capacity. Two cases are detected before the binary search begins:

Case 1 — No other protected spaces exist. If the fire room is the only protected space in the network, there is no protected space to leak into. The required multiplier is trivially 0. (This can occur in single-zone networks used for component-level testing.)

Case 2 — Stranded protected space. A protected space is stranded if every path from it to a fixed-pressure boundary (outdoor) passes through the fire room. In that case, no air-supply fan can pressurise the protected space without drawing air through the fire room itself — a topological impossibility. The analysis flags this as infeasible and records the reason, directing the designer to add an independent supply path.

These checks are performed via a reachability search on the graph, excluding the fire node, before any pressure solve. They avoid running expensive solver iterations on configurations where the outcome is determined by topology alone.

6. Output and Ranking

After simulating all $N_{\text{fire}}$ candidate rooms, the results are ranked by $m_i^*$ in descending order. The top entries — the rooms that demand the highest fan capacity — are the critical scenarios. For each:

A required multiplier near 1.0 means the designed system barely passes.
A required multiplier well below 1.0 means the system has margin to spare.
A required multiplier above 1.0 means the current design fails and must be strengthened.
infeasible = true signals a layout problem that no fan upgrade can solve.

The ranking lets the engineer focus immediately on the highest-risk rooms rather than sifting through all $N$ simulation results.

7. Computational Cost

The total number of pressure-network solves is at most $13 \, N_{\text{fire}}$ . Each individual solve converges in 3–8 Newton–Raphson iterations (see Nodal Pressure Network Analysis, §4.1). For a 50-room building, this amounts to at most 650 solver calls — a calculation that completes in a fraction of a second on modern hardware, making exhaustive coverage practical where manual methods allow only a single worst-case estimate.

8. Assumptions and Limitations

Assumption	Consequence	Direction
One fire at a time	Simultaneous multi-room fires are not considered	Non-conservative for simultaneous multi-room fires; accepted standard practice in single-origin fire safety design
Fixed fire intensity	$\dot{m}_{\text{fire}}$ is a scalar input; fire growth over time is not modelled	Dependent on the specified value — setting $\dot{m}_{\text{fire}}$ to the peak design-fire intensity is representative of the governing condition; lower values are non-conservative and will under-estimate the required fan multiplier
Steady-state pressure	The analysis finds the equilibrium state; transient pressures during door opening or fan spin-up are excluded	Mildly non-conservative — during fan spin-up after ignition, the pressure differential is less than the steady-state equilibrium this analysis resolves; the system is most vulnerable in the transient phase
Convective and pressure-equalisation leakage only	Radiation, conduction, and diffusive smoke transport through solid barriers are not included	Non-conservative — radiation heating and conductive transport through barriers are not modelled; accepted standard assumption in pressure-network analysis
Fan affinity law	The quadratic scaling assumes geometrically similar operation; it is an approximation for variable-speed drives at very low or very high multipliers	Neutral near $m = 1$ ; mildly non-conservative at very low multipliers where the model may over-predict fan effectiveness near stall; mildly conservative at very high multipliers
Fixed network topology	Doors and dampers are assumed to remain in their designed position during the fire event	Non-conservative — evacuation door-opening increases the effective leakage area and raises the true required fan multiplier; the analysis should be run with worst-case (doors open) leakage areas to compensate

The required multiplier $m^*$ produced by this analysis is a lower bound under idealised steady-state conditions. Two distinct steps are recommended before selecting a fan:

Model the evacuation scenario explicitly. Open doors are not a modelling limitation — they are a boundary condition. Re-running the analysis with evacuation-critical doors set to their open-position flow coefficients (typically two to three orders of magnitude larger than closed-door crack leakage) gives the governing $m^*$ for the worst-case occupation state. The higher of the closed-door and open-door results is the true design requirement.
Apply a selection margin above the governing $m^*$ . Even with an accurate worst-case model, fans are available only in discrete catalogue sizes and degrade over their service life. A margin at the fan-selection stage accounts for manufacturing tolerances, system aging, and the practical impossibility of procuring a fan that lands exactly on a computed threshold.

9. Relationship to Manual Practice

In current engineering practice (e.g. using general-purpose network solvers), a fire scenario analysis for a 50-room building requires 50 manual network edits and 50 separate solver runs — work that is often approximated by testing a single assumed worst-case room. The automated approach described here eliminates both the manual effort and the assumption: every room is tested, the worst cases are identified by computation rather than intuition, and the results are directly actionable.

10. Summary

The critical fire scenario analysis answers, for every room in a building, the question: "Is the smoke-control system strong enough if the fire starts here, and if not, by how much?" It does so by:

Modelling a fire as a mass-flow source at the fire node.
Scaling fan capacity continuously via the affinity law.
Detecting smoke leakage through two mechanisms — convective transport along flow paths, and pressure equalisation at near-zero-flow boundaries.
Locating the minimum required fan multiplier via binary search, exploiting the monotonicity of the leakage condition.
Flagging topologically infeasible scenarios before investing in solver iterations.
Ranking all rooms by required capacity so that engineering attention is directed to the highest-risk cases.

The result is exhaustive coverage of the scenario space at a computational cost that makes full building-wide analysis routine.