Fire Physics, Nomenclature, and Modeling

Focus is on internal/enclosed fire situations. NPP applications are

emphasized.

There is one Significant Fire Event Every 10 Reactor Years.

Arthur Ruggles, UTNE

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Outline of Material

• Basics of Fire Modeling-Intro to Concepts• Definitions for phenomena

– Energy release rates and energy release vs. time– Combustion efficiency– Mass loss rate– Flash-over

• The Axi-symmetric plume• Enclosure flows• Smoke filling and combustion products

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Philosophy of Presentation

• The fire and fire induced plume drives the simulation-these physics are presented first.

• The fire responds to feedback from the enclosure such as reflected heat from walls, or restricted air/oxygen inflow.

• Relatively simple transport models and empirical models are introduced to develop understanding and intuition.

• A few parameters important to Nuclear Power Plant (NPP) Probabilistic Risk Assessment (PRA) are presented.

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Fire and Fire Plume Attributes

Continuous Flame Height-combustion and thermal energy addition occurs in the flameIntermittent Flame-flame is varying in time and position in this regionMean Flame Height-time and position average for flame height needed for steady state model development, this

is where energy addition due to combustion ends, and a buoyancy driven plume begins.Plume-buoyancy due to hot gasses from fire balanced by shear and mixing with entrained air to form a vertical

flow of air and combustion gasses in the “plume”. Momentum balance used to define plume mass flowand diameter are considered later.

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Context of Fire and Plume to Enclosure Fire Dynamics

Fire drives the energy addition and hot gas production that causes the plume and creates hazard to humans via smoke inhalation and heat exposure.

Mass flow in plume determines smoke filling rate in enclosure.Temperature in plume is important to buoyancy drive for flow into and out of the enclosure

openings. Air/oxygen inflow often limits fire progression in enclosures.Fire progression, which involves heating and vaporization of adjacent fuel, determines

energy release versus time, and fire duration.

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Energy release rate models-empirical. examine approaches to measurement and conventions for use.

Mass Loss rate models and burn efficiency-empirical.examine approaches to measurement and conventions for use.

Mean flame height models-empirical.measurement method and interface with plume parameters.

Plume models, including plume mass flow, temperature and diameter-mechanistic.mass, momentum and energy balance leading to plume models. Theseare related to buoyancy driven flows from thermal science. Models developed for the plume are quasi-steady.

Approach to Fire and Plume Modeling

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Empirical Model Development is based on Experimental Data

Mass loss rate-mass versus timeMass flow in plume-mass flow measurement with plume capture in hoodOxygen content-oxygen meter, air is normally 23% oxygen by mass.Plume temperature measurement-RTDs or ThermocouplesCombustion efficiency-mass flow with mass loss rate, oxygen content and

temperature used to infer this quantity.

Temperature

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Energy Release Rate, Mass Loss Rate, Heat of Combustionand Heat of Gasification.

Mass Loss Rate: The rate of fuel mass lost, Kg/s, some of which will combust,and some of which is gasified but does not combust.

Combustion Efficiency: Ratio of effective (actual) heat of combustion inthe fire over the complete heat of combustion, .

Heat of Combustion: Energy released per unit mass of fuel. There iseffective heat of combustion, Heff , which is equal to the combustionefficiency, , times the complete heat of combustion, Hc .

Heat of Gassification: Gases combust in fires. Some portion of the energy released from the fire must go back into gasification of liquid or solid fuels, Hg.

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Energy Release Rate or Heat Release Rate

The Heat Release Rate (HRR) is the total energy per unit time releasedby the fire. Units of KW are usually used in fire literature forpower, so the HRR is usually given in KW.

ceff HmHmQHRR

This definition of the HRR assumes the heat of combustion includesthe energy required to gasify the fuel. In most cases 70% to 80% of the fuel combusts, placing between 0.7 and 0.8.

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Pool Fires

• These fires are fairly common, machines with lube oil or transformer oil are dyked.

• Dyked area determines the pool fire area, which determines heat release rate.

• Lube oil or transformer oil inventory will fit in dyke by design.

• Do not put tools and components inside the dyke during component service.

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Pool Fires: Constant HRR

mLarge pool fire mass loss rate per unit area, , is larger than that for smaller pool fires. An approximation for smaller pool fire mass loss rate is provided below, where the parameter k is derived from data. The diameter of the fire, D, may be the diameter of a circle of equivalent area when the pool shape is not circular.

)1( Dkemm

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HRR and mass loss data per unit area for Common Combustible Materials: SFPE Handbook

MATERIAL Mass Loss Hc km-1)Polyethelene 0.026 kg/m2s 43.6 MJ/Kg Polypropolene 0.024 43.4Kerosene 0.065 44.1 3.5Gasoline 0.062 44.2 2.1Transformer oil(s) 0.025-0.030 44.8 0.7Polystyrene 0.034 39.2Methanol 0.025 20 infinitePolyurethane foams 0.021-0.027 23.2-28.0PVC 0.016 16.4Teflon 0.007 Kg/m2s 4.8 MJ/Kg

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Example Pool Fire

Diesel for emergency generators is compromised by a 40 year old fitting Failure. Approximately 90 gallons are released into an area 3m by 4m. The combustion efficiency is near 0.75, evaluate the heat release rate andduration of this fire. Assume this is an unrestricted (open) fire.

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Fire Progression in an Enclosure, Time Varying HRR

Ignition: self sustained combustion begins, PRA may provide list of ignitionsources and probability of occurrence.

Growth: Fire grows, smoke layer forms and descends, temperature in smokelayer increases, and fire radiative flux increases.

Flashover: Smoke layer/upper gas layer reaches 500F to 600F, and radiationfrom smoke layer and fire supports rapid fire spread to entire enclosure.

Fully Developed fire: Air/oxygen limited combustion in enclosure.

Ignition

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HRR versus Time

• Experiments with common fuel sources provide heat release rate versus time.

• NPP fuel sources include cable insulation, paint, and various fluids (e.g., lube oil, transformer oil, solvents, fuel).

• The HRR, along with fire base diameter, provide information on mean flame height.

• HRR, flame height and fire base diameter allow quantification of the plume.

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Fire Growth Phase: HRR=t2

• For Design Purposes, the growth phase is important since this is when protection and response systems should intervene.

• Some values for 1/8 inch plywood wardrobe with clothes (.86); Easychair 23Kg (0.19)

• “Fast” growth for greater than 0.047.

• “Slow” growth for less than 0.003. (NFPA 204M)

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Flame Height Modeling

• Dimensionless groups used in natural convection flow appear in empirical models.

L is flame height, D is fire diameter at base.

gDDTc

QQ

p2

DQL 02.1)(235.0 5/2

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The Plume Above the Flame

• The buoyancy in the plume above the flame is fixed if density is taken linear with temperature, and thermal losses are neglected.

• Plume model involves a balance of buoyancy with momentum losses due to mixing with adjacent air.

• Mixing also cools the plume average temperature, and increases the plume mass flow.

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Note that average of products is generally not equal to the product of averages.Funded by USNRC: EDU10-002

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Homework 1 Solution:The first two steps followalmost exactly the sequenceof the example earlier in the notes.Note that the oil evaporates more slowly than the diesel, but theheating value per unit mass forDiesel and the transformer oilare similar.

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NRC has these ModelsCoded into Spread SheetsAvailable on-line for Free!

These spreadsheets are in usenow for NPP fire safetyassessment.

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Plume Model AssumesPoint heat source at Z=0.

b

floor

Virtual Fire atVirtual Origin

Zoo

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Enclosure Dynamics using Two Zone Model

Plume feeds hot gases to hot layer.Hot layer fills enclosure and alters pressure distribution from that outside.Differential pressure drives flow into and out of the enclosure

through openings.Flow into enclosure may limit oxygen availability for fire

(ventilation controlled fire).

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Cables in Trays and Conduit are all over the Plant.Often smaller diameter cables for instrumentationare suspended in trays. Time to loss of cable functionis modeled in fire progression and plant response. PRAmay include cable integrity predictions. (NUREG 1805)

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Pressure Differences Drive flow Into and Out of EnclosureFire Induced Hot Layer Alters Pressure Gradient In Enclosure

Neutral Line

Hn Hd

Neutral Pressure at Hn

Density Change at Hd

Define z relative to Neutral Plane

Z+

Z-

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Pressure Differences can be related to Hot Gas Temperature, Hot Gas Layer Height, and Height of Neutral Pressure

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Mass flow is reduced to account for some flow physics not captured inIsentropic Bernoulli Model.

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Position of Neutral Pressure Plane is established using the Mass Balance

Mass flow into the enclosure must equal the mass flow outof the enclosure. If the enclosure has only one opening, then theNeutral pressure plane will cut through that opening, allowing both inflow and outflow through the same opening.

door

Neutral Pressure Plane

Note Velocity Profile for Inlet Flow is not Linear,Pressure Profile is linear, Velocity goes as Square root of Pressure for tall openings.

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Flows Through Openings are Modeled using Form LossesAnd Modified Bernoulli Equation for Horizontal flow

In Nuclear, Mechanical and Civil Engineering

f

h

CD

lf

vvp

vp

222

2

2

2

1

2

Upstream Flow is near zero, and downstream flow is also near zero, with maximum flow kinetic energy developed in the opening (actually just downstream of the opening), and later lost (actually thermalized via turbulence and shear), so our model reduces to:

fCvpp 221 2/1

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Cfast is a Two Zone Fire Modeling Code that wasSubjected to Verification and Validation (V&V) for

NRC

The code is general purpose, architectural enclosure fire modeling code developed by NIST

The code has a primitive GUI, and solves the equations we just covered, so a fire progression can be modeled.The output is available in tables, or can be examined graphically using a

package called Smokeview.Validation in this case means the code was run to predict experimental data from situations representative of a NPP. The predictions were

compared with the test data, the outcomes reviewed, and published.The code was Verified during previous examinations and tests during the

development by NIST.

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