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Fire Dynamics Calculations

Compartment and pool-fire dynamics by the closed-form methods of the NRC handbook NUREG-1805, Fire Dynamics Tools, as revised in its Supplement 1: hot gas layer temperature (McCaffrey, Quintiere and Harkleroad for natural ventilation; Foote, Pagni and Alvares and Deal and Beyler for forced ventilation; Beyler for a closed compartment) with the Yamana and Tanaka smoke-layer height; pool-fire heat release rate, burning duration and flame height (Heskestad, Thomas); radiant heat flux to a target by the point-source and solid-flame models, with and without wind (Mudan tilted flame); Heskestad plume temperature and velocity and the Alpert ceiling jet; sprinkler, heat-detector and smoke-detector activation by the response time index; flashover heat release rate (MQH, Babrauskas, Thomas), Law's post-flashover temperature and fire severity; ignition and cable damage time (Tewarson, Mikkola and Wichman, Quintiere and Harkleroad, Janssens, Toal); smoke filling and visibility (Jin); and the SFPE hydraulic egress model. Material, fuel, cable and smoke-yield properties come from the handbook's tables; the default case is NUREG-1805 Example Problem 2-1.

  • Hot gas layer temperature and smoke layer height (MQH, FPA, Deal and Beyler, Beyler, Yamana and Tanaka) with a time history

  • Pool fire HRR, burning duration and flame height; radiant flux by point source and solid flame, in wind too

  • Plume and ceiling-jet temperatures, sprinkler and detector activation, flashover and post-flashover temperature

  • Ignition time of targets and cables, visibility through smoke and a hydraulic egress estimate

Fire Dynamics Calculations

Unit System: /

Analysis


Compartment (hot gas layer, flashover, smoke)








Lining and ambient (thermal properties in the handbook SI units: kW, m, kg, K; temperature plain °F or °C)









Fire (heat release rate in kW, time in minutes)






Pool fire (properties in kg/m²-s, kJ/kg, 1/m, kg/m³; spill volume plain gal or L)









Target (radiant heat flux)





Plume and ceiling jet





Detector or sprinkler







Flashover and fire severity (heats of combustion plain kJ/kg)





Ignition of a target (fluxes in kW/m², properties in the handbook SI units)















Smoke filling and visibility









Egress (hydraulic model; times in seconds, densities plain, speed constants in m/s)

















Method | Method page
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Fire Dynamics Calculations

Fire Dynamics Calculations

The tool brings together the closed-form methods of the U.S. Nuclear Regulatory Commission's handbook NUREG-1805, Fire Dynamics Tools (FDTs), as revised by its Supplement 1 spreadsheets, for the fire-hazard questions a building fire-protection engineer meets first: how hot the gas layer in a room becomes, how large a pool fire is and how high its flame reaches, how much heat radiates to a target, when a sprinkler or detector operates, whether the room flashes over, how soon a cable or a lining ignites, how fast the smoke fills the room and clouds the exit signs, and how long the occupants need to leave. Each analysis is one chapter of the handbook; the equations are printed with the substituted numbers, the chapter and equation numbers are named, and the material, fuel, cable and smoke tables of the handbook fill the property fields. The scope is compartment and pool-fire dynamics only: the handbook's explosion-overpressure and hydrocarbon-fireball chapters are vapour-cloud consequence analysis, process-safety work outside this tool.

Units and conventions

Lengths, areas, masses, the ventilation flow and the wind speed go through the unit menus; temperatures are plain numbers in °F (USCS) or °C (SI), heat release rates in kW, heat fluxes in kW/m², and the thermal properties are in the SI units of the handbook tables in both systems, as the NRC's English-unit spreadsheets keep them. Ambient air density is ρa = 353/Ta kg/m³ (Ta in K), the handbook's ideal-gas value. The results are the handbook's: the printed example problems of the chapters built are reproduced to their printed digits by the tool's test, and the Supplement 1 spreadsheets' cached values to six figures.

Hot gas layer temperature and smoke layer height (chapter 2)

For a room with a door or window the McCaffrey, Quintiere and Harkleroad correlation gives the layer temperature rise ΔTg = 6.85 [Q̇²/(Av√hv AT hk)]1/3, a fit to 100 room fires with the fire away from the walls; the effective heat transfer coefficient is hk = √(kρc/t) while the lining is still absorbing heat and k/δ after the thermal penetration time tp = (ρc/k)(δ/2)². With mechanical exhaust the Foote, Pagni and Alvares correlation ΔTg/Ta = 0.63 [Q̇/(ṁcpTa)]0.72 [hkAT/(ṁcp)]−0.36 and the Deal and Beyler energy balance ΔTg = Q̇/(ṁcp + hkAT) (with its own 0.4 √(kρc/t) coefficient, valid to 2,000 s) are both printed. For a closed room whose leaks prevent a pressure rise Beyler's non-steady balance gives ΔTg = (2K2/K1²)(K1√t − 1 + e−K1√t). The smoke layer descends by the Yamana and Tanaka filling equation z = [2kQ̇1/3t/(3Ac) + hc−2/3]−3/2 with k = 0.076/ρg; it ignores the smoke leaving the vent, so below the top of the vent the height is not credited and the handbook's "smoke exiting vent" caution is repeated. The table and chart follow the spreadsheet's schedule to 60 minutes. Limits: conventional rooms, a steady fire away from the walls, layer temperatures to about 600 °C (beyond that the room is at flashover), no ceiling vents.

Pool fire (chapter 3)

A liquid spill of area A burns as a circular pool of diameter D = √(4A/π) at Q̇ = m″ΔHc,eff(1 − e−kβD)A, Babrauskas's large-pool burning rate corrected for small diameters; the regression rate ν = m″/ρ gives the burning duration tb = 4V/(πD²ν); the flame height is Heskestad's Hf = 0.235Q̇2/5 − 1.02D (a mean height; a negative value means the fire is too weak for its diameter) and Thomas's Hf = 42D[m″/(ρa√(gD))]0.61. The fuel table is the handbook's Table 3-4 (butane to lube oil); a cable tray or a pallet stack is entered as a custom fuel with its bench-scale burning rate. The pool is assumed to involve instantly and fully, with no growth period.

Radiant heat flux to a target (chapter 5)

The point-source model radiates the fraction χr of Q̇ isotropically from the flame centre, q″ = χrQ̇/(4πR²), R = L + D/2; it is within 5 % of the better models only for L/D > 2.5 and overstates the flux near the fire. The solid-flame model treats the flame as a cylinder of diameter D and Heskestad height radiating with Shokri and Beyler's emissive power E = 58 × 10−0.00823D kW/m² (data from kerosene, fuel oil, gasoline, JP-4, JP-5 and LNG pools of 1 to 50 m); the target sees it through the view factor of a vertical cylinder, the horizontal and vertical factors combined as √(FH² + FV²) for a target at ground level, or the sum of the factors of the cylinders below and above the target height for a vertical target above ground (a flame below the target gives the upper cylinder a negative height, which the handbook spreadsheet and the tool treat as a negative factor). In wind the flame is tilted by Mudan's correlation, cos θ = (u*)−1/2 for u* = uw/(gm″D/ρa)1/3 above 1, shortened by Thomas's wind flame height, and seen through the tilted-cylinder view factors of Mudan (1984), with a = Hf/r and b = R/r as in Mudan's formula and the handbook's ground-level spreadsheet; the handbook's above-ground wind spreadsheet writes a1 = 2H1/r, twice that value, which the tool does not follow. The tilted formulas reduce exactly to the vertical-cylinder ones at zero tilt, and both were checked against a numerical integration of the view factor.

Plume and ceiling jet (chapters 9 and 10)

Above the mean flame height Heskestad's plume correlation gives the centreline temperature rise 9.1[Ta/(gcp²ρa²)]1/3Q̇c2/3(z − z0)−5/3 and velocity 3.4[g/(cpρaTa)]1/3Q̇c1/3(z − z0)−1/3, measured from the virtual origin z0 = −1.02D + 0.083Q̇2/5, with the convective part Q̇c = χcQ̇. Where the plume strikes an unconfined flat ceiling it turns into Alpert's ceiling jet: Tjet − Ta = 16.9Q̇2/3/H5/3 within r/H ≤ 0.18 and 5.38(Q̇/r)2/3/H outside, ujet = 0.96(Q̇/H)1/3 within r/H ≤ 0.15 and 0.195Q̇1/3H1/2/r5/6 outside. The Supplement 1 spreadsheets use the total Q̇ in these and the 0.18 bound; the original 2004 sheets used Q̇c and 0.15, which is why some printed 2004 example answers differ. The correlations assume a steady fire away from walls, a smooth ceiling and no hot layer yet under it.

Sprinkler, heat detector and smoke detector activation (chapters 10 to 12)

A heat-sensitive element is a lumped mass heated by convection in the ceiling jet, so its time to reach the rating is t = (RTI/√ujet) ln[(Tjet − Ta)/(Tjet − Tact)]; if the jet never reaches the rating the device does not operate. The response time index of a listed sprinkler should be the manufacturer's; the generic values of Madrzykowski (standard link 130, standard bulb 235, quick response 34 to 42 (m-s)1/2) and the generic temperature ratings are offered as defaults, and the RTI of a listed heat detector follows from its UL spacing and rating by the handbook's Table 12-2. A smoke detector has no rating; the handbook offers three estimates, which the tool prints together: the same RTI model with a low RTI and a small temperature rise (Alpert), the transport lags of the plume and ceiling jet (Mowrer), and the NFPA 92B temperature-rise form of Milke with its stratification check Hmax = 74Q̇c2/5/ΔTf→c3/5 in ft, Btu/s and °F. The worst position of a device in a square array is r = S/√2.

Flashover, post-flashover temperature and fire severity (chapter 13)

Flashover (a layer at 500 to 600 °C or 15 to 20 kW/m² on the floor) needs a fire of at least Q̇FO = 610√(hkATAv√hv) by MQH with the lining heated through (hk = k/δ), 750Av√hv by Babrauskas, or 7.8AT + 378Av√hv by Thomas; the lowest is the conservative threshold. After flashover Law's correlation of the CIB tests gives the maximum temperature 6000(1 − e−0.1Ω)/√Ω °C with Ω = (AT − Av)/(Av√hv); the handbook evaluates Ω with its AT already net of the opening, so the opening is deducted twice, and the tool keeps that evaluation so that its values match the handbook's. Law's fire severity turns the fuel load into its wood equivalent Leq = LΔHc/ΔHc,wood and the equivalent standard-furnace exposure tf = KLeq/√(AvAT) minutes with K = 1; it should not be used for openings under 0.4 m².

Ignition and cable damage time (chapter 6)

A thermally thick solid under a constant flux q″e above its critical flux ignites after a time that five correlations estimate from different data: Tewarson's t = (π/4)TRP²/(q″e − CHF)² with the critical heat flux and thermal response parameter of the FMRC apparatus (the handbook's cable table), Mikkola and Wichman's t = (π/4)kρc(Tig − Ta)²/(q″e − q″cr)², Quintiere and Harkleroad's t = [q″cr/(bq″e)]² from the LIFT flame-spread parameter, Janssens's t = 0.563(kρc/hig²)[(q″e/q″cr) − 1]−1.83, and the flux-time product t = FTP/(q″e − q″cr)n of Toal, Silcock and Shields. They diverge near the critical flux and differ among themselves by factors; the handbook prints them side by side, as the tool does. The IEEE-383 damage criteria of the handbook (10 kW/m² or 370 °C for qualified cable, 5 kW/m² or 218 °C for unqualified cable) are stated against the exposure.

Smoke filling and visibility (chapters 2 and 18)

The smoke analysis runs the natural-ventilation layer model and inverts the filling equation for the time at which the interface reaches a critical height (head height, the lowest cable tray, a detector); below the vent top it is a lower bound. Jin's relation S = K/(αmmp) then gives the visibility of an object from the particulate concentration mp = ypMf/V spread through the whole room (the handbook's well-mixed assumption; a layer holds the same particulate in a smaller volume), with K = 3 for reflecting signs and building components and 8 for illuminated signs, αm = 7,578 m²/kg (37,000 ft²/lb) for flaming and 4,301 m²/kg for smoldering combustion, and the particulate yields of the handbook's Table 18-3.

Egress time (SFPE hydraulic model)

The required safe egress time is estimated by the hydraulic model of the SFPE Handbook (Nelson and Mowrer, also in NIST's FPETool), used as mathematics with every constant an entered value: on each route element the speed is S = k(1 − aD) for the density D, the specific flow Fs = SD peaks at D = 1/(2a), the effective width is the clear width less the boundary layers, and the element with the smallest flow F = FsWe controls the queue, so that N occupants take N/F to pass it. The tool adds the entered pre-movement time, the travel time of the route at the applied density and the queue time, a conservative sum, and compares the total with an available time when one is entered (the smoke-filling time of the smoke analysis, for instance). Occupant loads, pre-movement times, minimum widths and travel limits are the code's (NFPA 101, NFPA 130 or the building code in force) and are cited only.

Sources, checks and what is not covered

Every correlation and table comes from NUREG-1805 and its Supplement 1 (public domain), which print the equations, the property tables (compiled from the SFPE Handbook, Klote and Milke, the SFPE Engineering Guide and NFPA 72, credited there) and worked examples. The tool's test reproduces the handbook's example problems 2-1 to 2-6, 3-1 to 3-3, 5-1, 5-4, 6-1, 6-2, 9-1, 9-2, 10-1, 10-2, 11-1 to 11-3, 12-1, 13-1 to 13-3 and 18-1 to 18-3 and the cached values of the Supplement 1 spreadsheets, with every formula re-derived in an independent numpy script; the few printed answers that the revised spreadsheets no longer give (a 2004 answer computed with the convective HRR, a Celsius misprint) are recorded in the test and the references README. Not covered: the explosion, fireball, battery-room hydrogen, structural fire-resistance and THIEF cable-failure chapters of the handbook, fires against walls or in corners (chapter 4), growing (t²) fires, multi-room smoke movement, zone or field models, and the evacuation of whole buildings with merging flows.



References

Iqbal, N., and Salley, M. H. (2004). Fire Dynamics Tools (FDTs): Quantitative Fire Hazard Analysis Methods for the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program. NUREG-1805, U.S. Nuclear Regulatory Commission, Washington, DC.

Stroup, D., and Lindeman, A. (2013). Fire Dynamics Tools (FDTs): Quantitative Fire Hazard Analysis Methods for the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program, Supplement 1. NUREG-1805 Supplement 1, Vols. 1 and 2, U.S. Nuclear Regulatory Commission, Washington, DC.

McCaffrey, B. J., Quintiere, J. G., and Harkleroad, M. F. (1981). "Estimating Room Temperatures and the Likelihood of Flashover Using Fire Test Data Correlations." Fire Technology, Vol. 17, No. 2, pp. 98–119.

Foote, K. L., Pagni, P. J., and Alvares, N. L. (1985). "Temperature Correlations for Forced-Ventilated Compartment Fires." In Grant, C. E., and Pagni, P. J. (eds.), Fire Safety Science: Proceedings of the First International Symposium, Hemisphere Publishing, New York, pp. 139–148.

Deal, S., and Beyler, C. L. (1990). "Correlating Preflashover Room Fire Temperatures." Journal of Fire Protection Engineering, Vol. 2, No. 2, pp. 33–48.

Beyler, C. L. (1991). "Analysis of Compartment Fires with Overhead Forced Ventilation." In Cox, G., and Langford, B. (eds.), Fire Safety Science: Proceedings of the Third International Symposium, Elsevier Applied Science, London, pp. 291–300.

Yamana, T., and Tanaka, T. (1985). "Smoke Control in Large Scale Spaces, Part 1: Analytic Theories for Simple Smoke Control Problems." Fire Science and Technology, Vol. 5, No. 1, pp. 31–40.

Babrauskas, V. (1983). "Estimating Large Pool Fire Burning Rates." Fire Technology, Vol. 19, No. 4, pp. 251–261.

Heskestad, G. (1983). "Luminous Heights of Turbulent Diffusion Flames." Fire Safety Journal, Vol. 5, No. 2, pp. 103–108.

Thomas, P. H. (1963). "The Size of Flames from Natural Fires." Symposium (International) on Combustion, Vol. 9, No. 1, pp. 844–859.

Shokri, M., and Beyler, C. L. (1989). "Radiation from Large Pool Fires." Journal of Fire Protection Engineering, Vol. 1, No. 4, pp. 141–150.

Mudan, K. S. (1984). "Thermal Radiation Hazards from Hydrocarbon Pool Fires." Progress in Energy and Combustion Science, Vol. 10, No. 1, pp. 59–80.

Modak, A. T. (1977). "Thermal Radiation from Pool Fires." Combustion and Flame, Vol. 29, pp. 177–192.

Heskestad, G. (2002). "Fire Plumes, Flame Height, and Air Entrainment." In DiNenno, P. J. (ed.), SFPE Handbook of Fire Protection Engineering, 3rd ed. National Fire Protection Association, Quincy, MA, pp. 2-1–2-17.

Alpert, R. L. (1972). "Calculation of Response Time of Ceiling-Mounted Fire Detectors." Fire Technology, Vol. 8, No. 3, pp. 181–195.

Heskestad, G., and Bill, R. G. (1988). "Quantification of Thermal Responsiveness of Automatic Sprinklers Including Conduction Effects." Fire Safety Journal, Vol. 14, No. 1–2, pp. 113–125.

Madrzykowski, D. (1995). "Evaluation of Sprinkler Activation Prediction Methods." ASIAFLAM '95, Proceedings of the First International Conference on Fire Science and Engineering, Interscience Communications, London, pp. 211–218.

Mowrer, F. W. (1990). "Lag Times Associated with Fire Detection and Suppression." Fire Technology, Vol. 26, No. 3, pp. 244–265.

Milke, J. A. (1990). "Smoke Management for Covered Malls and Atria." Fire Technology, Vol. 26, No. 3, pp. 223–243.

Babrauskas, V. (1980). "Estimating Room Flashover Potential." Fire Technology, Vol. 16, No. 2, pp. 94–103.

Thomas, P. H. (1981). "Testing Products and Materials for Their Contribution to Flashover in Rooms." Fire and Materials, Vol. 5, No. 3, pp. 103–111.

Law, M. (1978). "Fire Safety of External Building Elements: The Design Approach." Engineering Journal, American Institute of Steel Construction, Vol. 15, No. 2, pp. 59–74.

Walton, W. D., and Thomas, P. H. (2002). "Estimating Temperatures in Compartment Fires." In DiNenno, P. J. (ed.), SFPE Handbook of Fire Protection Engineering, 3rd ed. National Fire Protection Association, Quincy, MA, pp. 3-171–3-188.

Tewarson, A. (2002). "Generation of Heat and Chemical Compounds in Fires." In DiNenno, P. J. (ed.), SFPE Handbook of Fire Protection Engineering, 3rd ed. National Fire Protection Association, Quincy, MA, pp. 3-82–3-161.

Society of Fire Protection Engineers (2002). SFPE Engineering Guide: Piloted Ignition of Solid Materials Under Radiant Exposure. Society of Fire Protection Engineers, Bethesda, MD.

Quintiere, J. G., and Harkleroad, M. F. (1984). New Concepts for Measuring Flame Spread Properties. NBSIR 84-2943, National Bureau of Standards, Gaithersburg, MD.

Jin, T. (1978). "Visibility Through Fire Smoke." Journal of Fire and Flammability, Vol. 9, pp. 135–155.

Klote, J. H., and Milke, J. A. (2002). Principles of Smoke Management. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, GA.

Nelson, H. E., and Mowrer, F. W. (2002). "Emergency Movement." In DiNenno, P. J. (ed.), SFPE Handbook of Fire Protection Engineering, 3rd ed. National Fire Protection Association, Quincy, MA, pp. 3-367–3-380.

Nelson, H. E. (1990). FPETOOL: Fire Protection Engineering Tools for Hazard Estimation. NISTIR 4380, National Institute of Standards and Technology, Gaithersburg, MD.

National Fire Protection Association (2021). Life Safety Code. NFPA 101, Quincy, MA.

National Fire Protection Association (2022). National Fire Alarm and Signaling Code. NFPA 72, Quincy, MA.

National Fire Protection Association (2021). Standard for Smoke Control Systems. NFPA 92, Quincy, MA.

Electric Power Research Institute and U.S. Nuclear Regulatory Commission (2005). EPRI/NRC-RES Fire PRA Methodology for Nuclear Power Facilities. EPRI 1011989 and NUREG/CR-6850, Palo Alto, CA, and Washington, DC.

Worked Examples

Published examples this tool reproduces; each page lists the inputs to enter and the printed answers.

All worked examples

DISCLAIMER: The methods and calculation on aNOWysis.com are provided as means to educate the reader. There is no warranty, expessed or implied, as to the relevance or accuracy of the methods or calculations. All calculations should be checked by a qualified analyst for appropriateness and accuracy. We will not be held liable for any damages, injuries or deaths caused by using methods or calculations from this site.