Compartment Fire Behaviour and Plume Modelling

Compartment fires are conventionally described in four phases. The phase classification is not merely academic: the pattern evidence at a scene, the toxicological environment during a fatal fire, the performance of detection systems, and the credibility of witness accounts all depend on which phase the fire was in at the relevant time.

Incipient phase: The fire is established but small. Heat release rate is low (typically below a few hundred kilowatts). The hot gas layer is thin and confined to the ceiling region; the neutral plane is high and the lower zone remains clear. Smoke production depends on fuel type; smouldering materials (upholstered furniture, cables) may produce visible smoke at very low heat release rates before visible flame appears. Ionisation smoke detectors and optical (photoelectric) detectors respond in this phase for smouldering and flaming fires respectively. Fire-fighters from the US National Institute of Standards and Technology (NIST), the UK Building Research Establishment (BRE), and the Australian Fire Research Group have all documented incipient phase durations ranging from a few seconds (fast-growth liquid pool fires) to hours (deep-seated smouldering fires in mattresses). The incipient phase is forensically significant because it is the phase during which the fire is most amenable to suppression and during which the evidence of cause (ignition source, first fuel) is best preserved.

Growth phase: Heat release rate increases, often following a t-squared growth curve (HRR proportional to time squared), governed by the fuel's burning rate and the progressively larger area of burning surface. The hot gas layer descends as more combustion products are generated. Visibility in the lower zone degrades. Temperature in the hot gas layer rises from a few hundred degrees toward the flashover threshold (590 to 650°C). This is the phase in which NFPA 921's origin determination methods are most reliable, because burn pattern gradients are still preserved and the fire has not yet homogenised the upper zone. The growth rate is characterised by an alpha coefficient in the HRR = alpha × t² model, with standard values: ultra-fast (0.1878 kW s⁻²), fast (0.0469), medium (0.0117), slow (0.0029). These standard growth curves are used in sprinkler activation calculations, evacuation modelling, and fire reconstruction.

Fully developed phase: The fire has reached its maximum heat release rate, constrained either by the available fuel (fuel-controlled) or by the ventilation opening area (ventilation-controlled). This is the phase of flashover transition. Post-flashover, the compartment burns at near-constant heat release rate until the fuel load begins to be exhausted. Temperatures in the hot gas layer range from 800 to 1,200°C. The lower zone is now also hot enough to sustain combustion in many cases. Structural elements begin to sustain permanent damage (steel yields above approximately 500 to 600°C; reinforced concrete spalls and loses strength above 300 to 400°C sustained exposure). Fire investigation in the fully developed and post-flashover phase must account for origin masking as discussed in the preceding topic.

Decay phase: As fuel is consumed, heat release rate falls. Ventilation-controlled fires may briefly intensify if additional air becomes available (a window fails, a wall collapses). The fire eventually extinguishes, leaving the charred remains that the investigator examines. Deep-seated smouldering may persist in heavy timber members, mattresses, baled materials, and sub-floor cavities long after visible flames have extinguished, posing re-ignition risk and complicating the interpretation of fire-fighter observations.

The fire plume is the buoyant column of hot gases and entrained ambient air rising above the burning fuel surface. Its structure has been characterised by decades of experimental work, most influentially by Gunnar Heskestad at Factory Mutual Research (now FM Global) and by Brian McCaffrey at the US National Bureau of Standards (NBS, now NIST) in the late 1970s and 1980s. Both researchers measured centreline temperature and velocity profiles in free-burning plumes above gas burners and pool fires of known heat release rate, then derived correlation equations that have become standard tools in fire engineering and forensic fire investigation.

The plume has three structural zones. The continuous flame zone extends from the fuel surface to the mean flame height, where temperatures are high and luminous. The intermittent flame zone above it shows fluctuating flame presence and is characterised by rapidly falling temperature. The convective plume zone above the intermittent zone consists of purely buoyant hot gas with no flame, and it is in this zone that the plume is most amenable to the analytical correlations.

Entrainment is the critical process by which ambient air is drawn into the rising plume from its periphery by turbulent mixing. The entrained air dilutes and cools the plume gases and increases the total mass flow rate as the plume rises. The mass flow rate in the plume approximately doubles for every 1.5 m of height above the fuel surface in large fires. This entrainment behaviour governs the smoke filling rate in the compartment, the dilution of toxic gases in the smoke layer, and the temperature at which the plume impinges on the ceiling.

When the plume impinges on the ceiling, it spreads radially outward as a ceiling jet, a shallow layer of hot gas flowing beneath the ceiling surface. The ceiling jet is the thermal environment in which ceiling-mounted heat and smoke detectors operate, and its temperature and velocity have been extensively characterised by Alpert (1972) at Factory Mutual Research. The Alpert correlation gives ceiling jet temperature and velocity as functions of heat release rate, ceiling height, and radial distance from the plume axis. Fire investigators use the Alpert correlation to determine whether, given a proposed fire size and location, a specific ceiling-mounted detector would have been expected to activate within a given time, a check on the consistency of alarm records with the proposed fire scenario.

The Heskestad plume correlation is the most widely used analytical model for fire plumes in engineering and forensic fire investigation. It was derived from a comprehensive experimental programme at Factory Mutual Research using pool fires and gas burners over a heat release rate range of approximately 100 W to 10 MW. The Heskestad correlation for centreline temperature rise above ambient at height z above the fire source is:

Delta-T = 9.1 × (T0 / g)^(1/3) × (cp × rho0)^(-2/3) × Q_c^(2/3) × z^(-5/3)

In simplified form, for standard ambient conditions, this reduces to:

Delta-T = C × Q^(2/3) × z^(-5/3)

where Q is the convective heat release rate in kilowatts, z is the height above the virtual origin in metres, and C is approximately 25 (in SI units). The key insight is the 2/3 power dependence on heat release rate and the -5/3 power dependence on height: a fire twice as large produces a 1.59-fold higher centreline temperature at the same height; a measurement point twice as high sees a 3.17-fold lower temperature rise.

The virtual origin correction accounts for the fact that the fire source is not a point source at the fuel surface: the effective point source (virtual origin) lies below the actual fuel surface for most fires, by a distance that depends on the fire diameter and heat release rate. For small fires on a large base, the virtual origin is close to the fuel surface; for small intense fires (a small pool fire), it lies above the surface.

The McCaffrey plume model divides the plume into three zones (continuous flame, intermittent flame, plume) and uses empirical power-law fits for centreline velocity and temperature excess in each zone, derived from experiments with gas diffusion flames at the NBS. The McCaffrey correlations are:

Centreline velocity: u = k_u × (Q/z^5)^(n_u) [m/s] Centreline temperature excess: Delta-T = k_T × (Q^2/z^5)^(n_T) [K]

with empirical constants k and n differing between the three zones. The zone boundaries are defined by a dimensionless height parameter z / Q^(2/5). The McCaffrey model is useful for estimating conditions in the lower flame zone where the Heskestad correlation is less reliable.

In practical fire investigation, both correlations are applied as follows. The investigator identifies physical evidence at the scene that constrains the plume parameters: the height of the neutral plane (from soot horizon on walls), the char damage on the ceiling surface above the probable origin (indicating the ceiling jet temperature), or the activation height of a detector. With these measurements, the correlations are solved in reverse to estimate the heat release rate consistent with the observed evidence. This back-calculated HRR is then compared with the expected HRR for the proposed first fuel to assess whether the proposed fire scenario could have produced the observed effects within the documented time frame.

The hot gas layer fills from the ceiling downward as combustion products are generated faster than they are removed through ventilation openings. The height of the hot gas layer boundary (the neutral plane height above the floor) at any time during the fire is governed by the balance between mass flow entering the layer from the fire plume and mass flow leaving through ventilation openings.

The two-zone model, originally formalised by Quintiere, Cooper, and others at the NBS in the late 1970s, divides the compartment into an upper hot zone and a lower cool zone. The upper zone temperature and depth are calculated from heat and mass conservation equations, given the fire's heat release rate, the compartment geometry, and the ventilation opening dimensions. This two-zone framework is the basis for zone fire models such as CFAST (Consolidated Fire and Smoke Transport, NIST) and FAST (Fire And Smoke Transport), which are widely used for evacuation modelling, detector placement analysis, and fire investigation reconstruction.

The soot horizon visible on vertical surfaces in a fire scene represents the physical boundary of the hot gas layer at the time soot was deposited. Since soot deposition requires a local temperature below approximately 200 to 300°C (at higher temperatures, soot is burned off), the soot horizon marks the smoke layer interface during the growth phase, before temperatures became uniformly high. Later in the fire, when the layer descends to floor level, the soot horizon on vertical surfaces is no longer clearly visible on walls. The investigator must therefore interpret soot horizons as records of the smoke layer height during the growth phase, not at the time of maximum fire intensity.

Practical extraction of a heat release rate estimate from the smoke horizon requires: measuring the soot horizon height above the floor, identifying (from witness accounts, alarm records, or building geometry) an approximate time at which the layer was at that height, and applying a mass balance calculation with the McCaffrey or Heskestad plume model to back-calculate the HRR that would position the layer at that height at that time. The result is validated against other evidence (char depth, detector activation, structural damage) before being incorporated into the investigator's report.

In large multi-storey buildings, smoke transport modelling requires corridor and stairwell flow analysis in addition to compartment models, because pressure differentials between floors, stack effect in high-rise buildings, and HVAC operation all influence where smoke migrates. These analyses are routinely performed using CFAST, FDS, or commercially maintained zone model software in the US (where NIST FDS and CFAST are freely available), the UK (where the fire service, BRE, and forensic science providers all use these tools), Australia, Canada, and increasingly in India's large-building fire investigation cases handled by CFSL and state FSLs.

The Fire Dynamics Simulator (FDS), developed and maintained by the National Institute of Standards and Technology (NIST) with contributions from VTT Technical Research Centre of Finland, is a large-eddy simulation (LES) computational fluid dynamics code that solves the Navier-Stokes equations for low-Mach-number buoyancy-driven flows, coupled with combustion chemistry and thermal radiation transport. It is freely available under a BSD licence, widely used in the fire protection engineering community, and has appeared as technical evidence in judicial proceedings in the United States, United Kingdom, Australia, Canada, New Zealand, and elsewhere.

FDS models a fire by dividing the computational domain (the building or fire compartment) into a three-dimensional grid of rectangular cells. At each time step, the solver computes velocity, temperature, pressure, and species concentration fields across the grid. Combustion is modelled as a single-step reaction between the fuel vapour (described by a prescribed heat release rate per unit area or a pyrolysis model for solid fuels) and oxygen. Radiation transport uses a Finite Volume Method (FVM) for the radiative heat equation. Smoke particles are tracked as tracer particles for visualisation, and sprinkler, detector, and HVAC models are implemented as boundary conditions.

For forensic reconstruction, FDS is used in the following workflows. Scenario testing: the investigator defines a computational model of the building with materials, geometry, ventilation, and a proposed fire scenario (location, heat release rate curve, first fuel). The simulation is run and the predicted temperature histories at specific locations (detector positions, body location, structural elements) are compared with the physical evidence (activation records, victim state, structural damage). If the predicted and observed evidence are inconsistent, the proposed scenario is rejected or revised.

HRR validation: the investigator uses the scene-derived HRR estimate (from Heskestad back-calculation, char depth analysis, or fuel load inventory) as the input fire for FDS, then checks whether the simulation predicts smoke conditions, alarm activation, and temperatures consistent with the observations. Inconsistency between the predicted and observed alarm activation time is a common discriminator between proposed fire scenarios.

Evacuation timeline: in fatal fire cases, the time available for safe egress is estimated by tracking the descent of the smoke layer and the toxic gas concentrations in the escape route. FDS outputs are post-processed using the NIST Fractional Effective Dose (FED) model (which combines CO, HCN, CO2, O2, and heat exposures into a physiological incapacitation estimate) to determine whether an occupant at a specific location at a specific time would have been incapacitated or could have escaped.

Several limitations are critical for forensic practitioners. FDS results are sensitive to grid resolution: a finer grid produces more accurate results but requires substantially more computation time. Subgrid-scale turbulence modelling introduces uncertainty in conditions near walls and in confined geometries. Pyrolysis modelling for solid fuels (the solid-phase thermal decomposition that produces the gas-phase fuel) is complex and requires material properties that may not be precisely known for the actual fuel involved. FDS simulations are not a replacement for physical evidence analysis; they are a hypothesis-testing tool that supplements systematic scene investigation.

FDS is validated against a large experimental database maintained by NIST. The primary validation reference is the FDS Technical Reference Guide (McGrattan et al., NIST Special Publication 1018) and the FDS Validation Guide (Hostikka, Floyd, et al., NIST SP 1018). Expert witnesses presenting FDS results in court proceedings are expected to demonstrate familiarity with the validation database and to quantify the uncertainty in their simulation results.

NFPA 921, the Guide for Fire and Explosion Investigation published by the National Fire Protection Association (United States), mandates a scientific method framework for fire investigation: observation, hypothesis formulation, and hypothesis testing against all available data. Fire modelling, whether analytical (Heskestad, McCaffrey, Alpert) or computational (FDS, CFAST), is a tool for hypothesis testing, not for generating hypotheses independently of physical evidence.

The correct integration of models into a fire investigation follows a specific sequence. The investigator first develops an origin and cause hypothesis from physical evidence: scene examination, burn pattern analysis, victim location, material evidence of ignition source. The hypothesis is explicit: "the fire originated at location X, with ignition source Y, in fuel Z, at time T, and grew at rate R." Each of these parameters has a physical value associated with it.

The investigator then applies the analytical models to compute what observable evidence this hypothesis would predict. What temperature should be present at the smoke detector location at the time of alarm activation? What soot horizon height is predicted at the time indicated by witness accounts? What HRR is back-calculated from the measured char damage, and is it consistent with the expected burning rate of the proposed first fuel? If the predicted evidence matches the observed evidence within the uncertainty of the models and measurements, the hypothesis is supported. If it does not, the hypothesis is revised or a different origin or cause is considered.

This framework is explicitly adopted in the ENFSI guideline for fire investigation (European Network of Forensic Science Institutes, 2021) and is consistent with the ISO 17025-governed quality management requirements applied at accredited fire investigation laboratories. In the United Kingdom, fire investigation reports prepared for the Crown Prosecution Service and used in arson prosecutions are expected to follow the structure: scientific question, method, result, interpretation, and limitation, a format directly compatible with the hypothesis-testing model.

In India, expert witness testimony from CFSL fire investigators is given before courts operating under the Bharatiya Sakshya Adhiniyam (BSA) 2023, which replaced the Indian Evidence Act 1872 with updated provisions governing expert opinion (Section 39 BSA). The evidentiary standard for expert fire investigation testimony in India is whether the opinion is based on recognised scientific principles and is reproducible, a standard that fire modelling with documented validation supports. In US federal proceedings, the Daubert standard (Daubert v. Merrell Dow Pharmaceuticals, 1993) requires expert scientific testimony to be based on methods that have been tested, peer-reviewed, and generally accepted; FDS and the Heskestad correlations satisfy all three criteria. In the UK, R v. Robb (1991) and subsequent case law define the admissibility threshold for expert opinion as one based on specialised knowledge reliably applied.

1. Define the geometry and materials
   Build the computational or analytical model from scene measurements: room dimensions, ventilation opening positions and sizes, fuel load inventory with material classifications, and compartment construction materials. Accuracy at this stage limits the reliability of everything downstream.
2. Establish the fire input parameters
   Assign the heat release rate curve (t-squared growth with appropriate alpha coefficient, peak HRR from fuel load or ventilation factor, decay curve). Use laboratory burning rate data for the proposed first fuel where available.
3. Apply analytical correlations for plume and ceiling jet
   Use the Heskestad correlation to estimate centreline plume temperature at ceiling height. Apply the Alpert correlation to estimate ceiling jet temperature and velocity at the detector location. Compare against scene evidence (char on ceiling, detector activation record).
4. Run FDS simulation for spatial and temporal detail
   If the scene geometry is complex or the hypothesis requires detailed spatial predictions, run a validated FDS simulation on an appropriate grid. Document grid sensitivity analysis. Post-process for temperature histories at key locations, smoke layer height as a function of time, and toxic gas concentrations.
5. Test predictions against all evidence streams
   Compare model outputs against: alarm activation timing, witness accounts of smoke and fire visibility, victim location and condition, char depth measurements, structural damage, and suppression system activation. Document agreements and discrepancies.
6. Document uncertainty and alternative hypotheses
   Quantify sensitivity of key predictions to uncertain input parameters (HRR uncertainty, material property uncertainty, grid resolution). Explicitly state whether alternative origin or cause hypotheses were tested and rejected, and on what evidence basis.