module v – advanced fire modeling · calculate fire plume and ceiling jet conditions, including...

Joint EPRI/NRC-RES Fire PRA WorkshopAugust 13-17, 2018

Kevin McGrattan – NIST

Fred Mowrer – Cal. Poly State University

Module V – Advanced Fire Modeling

Principals of Fire Behavior

A Collaboration of the Electric Power Research Institute (EPRI) & U.S. NRC Office of Nuclear Regulatory Research (RES)

2

Topics

Stages / elements of enclosure fires Ignition and heat release

– CHRISTIFIRE (Cable Heat Release, Ignition, Spread in Trays in Fire)

Fire plumes and ceiling jetsHeat and smoke detectionStructural response / damageCable response / damage

– CAROLFIRE (Cable Response to Live Fire)

3

Fire scenario development / analysis

To analyze fire scenarios, need to consider:

– Stage(s) of fire development to include in analysis– Elements to include in fire scenario (fuels, targets ...)– Data sources for elements (HRRs, properties, damage criteria)

– Fire modeling tool(s) to be used for the analysisEmpirical correlations (Heskestad plume, MQH, FPA ...) Zone model (CFAST, MAGIC)CFD model (FDS)

This module provides overview of fire modeling concepts

4

Stages of enclosure fires

5

Stage 1 - Fire plume / ceiling jet period

Buoyant gases rise to ceiling in fire plumeCeiling jet spreads radially until confinedPlume entrains surrounding airTemperature decays rapidly with height and radial distance

6

Stage 2 - Enclosure smoke filling period

Period begins when ceiling jet reaches wallsPeriod ends when smoke flows through ventsSmoke layer fills due to entrainment / expansion

7

Stage 3 - Preflashover vented period

Quasi-steady mass balance developsSmoke layer equilibrates at balance pointMass balance influenced by sizes, shapes and locations of

vents and by mechanical ventilationMass balance influences energy/species balances

8

Stage 4 - Postflashover vented period

Period begins when secondary fuels begin to ignite from radiant exposurePost-flashover fires frequently become ventilation-limited,

with flames extending out of ventsUnderventilation affects smoke production

9

Po Pi Po Pi

Po Pi

HoND

Po Pi

HoND

Vent flow stages

10

Elements of enclosure fires

Fire sourceFire plumeCeiling jetUpper gas layerLower gas layerVents / ventilationBoundariesTargets

11

DESIGN ELEMENT

EXAMPLE TYPES

PHYSICAL ATTRIBUTES

GEOMETRIC ATTRIBUTES

FUELS FINISHESFURNISHINGS

MATERIALSQUANTITIESRELEASE RATES

LOCATIONSDIMENSIONS

BOUNDARIES WALLSCEILINGSFLOORS

MATERIALS LOCATIONSDIMENSIONS

TARGETS PEOPLEEQUIPMENTPRODUCTS

DAMAGE CRITERIA

LOCATIONSDIMENSIONS

NATURAL VENTILATION

DOORSWINDOWS

STATUSACT. PARAMETER

LOCATIONSDIMENSIONS

MECHANICAL VENTILATION

INJECTIONEXTRACTIONBALANCED

FLOW RATESSTATUSACT. PARAMETER

LOCATIONSDIMENSIONS

Elements of enclosure fires

12

Design fire

HRR as function of time is termed the design fireApproaches to determining design fire:

– Knowledge of amount/type of combustiblesObject assumed to ignite and burn at known rateHRR history based on experimental data

– Knowledge of occupancy Little detailed data regarding specific fuelsDesign fire based on statistics / engineering judgment

13

The fire source

First item– Ignition– Growth rate– Peak HRR– Burning duration

Secondary items– Time to ignition– Burning histories

14

Factors controlling HRRs

Ignition scenarios– Ignition source magnitude– Ignition source duration

Fuel characteristics– Type– Quantity– Orientation

Enclosure effects– Radiation enhancement– Oxygen vitiation

15

Mass loss rate per unit area𝐴𝐴 Area of fuel that is burning∆𝐻𝐻𝑐𝑐 Fuel heat of combustion

APPROX. HEATS OF COMBUSTIONFUEL ∆Hc (kJ/g)WOOD 15.0POLYURETHANE 30.0HEPTANE 44.5

cHAmQ Δ′′= &&

Heat release rate

m ′′&

q ′′&m ′′&

16

Phases of Fire Development

Total heat released by fire:

Approximate burnout time:

1. Incipient Stage2. Growth Stage3. Full-Developed4. Decay/Burnout

∫=t

odt)t(QQ &

maxobob Q

Qttt &≈−=

17

Fire growth characterizationPower law

Exponential

n

go t

tQQ

= &&

=

go τ

texpQQ &&

18

2

2

;kW 1055 ;g

oo

go t

QQ

ttQQ

&&&& ==

= α

t2 characterization

Growth rate tg (s) α (kW/s2)Slow 600 0.003

Medium 300 0.012Fast 150 0.047

Ultrafast 75 0.188

19

Fire growth characterization example

In the FMSNL fire test series, many of the tests were conducted using a gas burner programmed to grow as a t-squared fire to reach a HRR of 500 kW in 4 minutes, then to maintain a constant HRR of 500 kW for another 6 minutes– What does this HRR curve look like?– How much energy is released during the growth phase?– How much energy is released during the entire test?

20

Fire growth characterization

ExampleFMSNL HRR example

0

100

200

300

400

500

600

0 60 120 180 240 300 360 420 480 540 600 660Time (s)

HR

R (k

W)

MJ 403

240240500

3

3

2

3

2

240

0

22240 ==== ∫

ttQ

dtttQ

Qg

g

g

gs

&&MJ 180360500

600

240s 600 =⋅== ∫ dtQQ &

21

HRR example – cabinet fire

HRR taken from Appendix G, NUREG/CR 6850 (EPRI 1011989)

22

HRR example – cabinet fire

HRR taken from Appendix G, NUREG/CR 6850 (EPRI 1011989)

23

Secondary item ignition

Factors– Heat flux from primary fire– Ease of ignition of target

Point source estimate

)θcos(RπQχ

q frr 24

&& =′′

24

Secondary item ignition

Ignition time estimates (constant heat flux)– Thermally thick materials (most materials of interest in NPPs)

– Thermally thin materials

2

4

′′

−=

qTT

cρkπt oigig &

δcρ/qTT

t oigig &′′

−=

q ′′&

25

Summary

Engineers need to specify design fires– Judgment required– Some data available - relatively sparse– For NPP applications, data in NUREG CR-6850 typically used

Design fire specified in terms of HRR(t)– Simple case - incipient/growth/steady/decay– Complex case - multiple stages pieced together

Design fire drives consequence analysis– Single most important / uncertain factor

26

Kevin McGrattan, Andrew Lock, Nathan Marsh, Marc NydenNational Institute of Standards and Technology

Gaithersburg, Maryland, USA

David Stroup and Jason DreisbachU.S. Nuclear Regulatory Commission

Washington, D.C., USA

Cable Heat Release, Ignition, and Spread in Tray Installations during Fire

(CHRISTIFIRE) Phase I

27

What’s the Problem?Answer: Very little useful information on cables for fire modeling

Vertical Spread Rate?

Effectiveness of Wraps?

Ignition?

Tray to Tray Spread?

HorizontalSpread Rate?

28

Current Guidance for Modeling Cables

Problems going from“bench” to full-scale

Which HRR to Use?

29

Current Guidance on Flame Spread

Based on only one experiment

Vague or ill-defined parameters

30

Cables used in CHRISTIFIRE

31

Thermoplastic cablestend to melt and drip;

Electrical failure ~200 °C

Thermoset cables tendto char and smolder;

Electrical failure ~400 °C

32

Multiple Tray Test 8

Time (s)

0 900 1800 2700 3600 4500

Hea

t Rel

ease

Rat

e (k

W)

0

200

400

600

800

1000Burner Off

Tray 2Tray 3

Tray 4

HRR (O2 cal.)HRR (mass loss) Thermoplastic Cable

33

Multiple Tray Test 12

Time (s)

0 300 600 900 1200 1500 1800

Hea

t Rel

ease

Rat

e (k

W)

0

50

100

150

200BurnerOffTray 1

Tray 2 Tray 3

HRR (O2 cal.)HRR (mass loss)

Thermoset Cable

34

Comparison of Thermoset and Thermoplastic Cable HRR

Time (s)

0 900 1800 2700 3600 4500 5400

Hea

t Rel

ease

Rat

e (k

W)

0

200

400

600

800

1000

ThermoplasticThermoset

35

External Heat Flux (kW/m2)

0 10 20 30 40

Hea

t Rel

ease

Rat

e Pe

r Uni

t Are

a (k

W/m

2 )

0

100

200

300

400

Cable #701Cable #700Cable #16Cable #367Cable #43Cable #46Cable #271Cable #11Cable #219Cable #220Cable #23Cable #270

}}

Thermoplastics

Thermosets

Results of Radiant Panel Experiments

36

Modeling

The Hard WayThe Easy Way

37

FLASH-CATFlame Spread over

Horizontal CableTrays

Required DataCable mass/length

Non-metal mass fractionIgnition

5-4-3-2-1 minute ruleUpward Spread35° spread angleBurning Rate

250 kW/m² thermoplastics150 kW/m² thermosets

Lateral Spread3.2 m/h thermoplastics

1.1 m/h thermosetsHeat of Combustion

16 MJ/kg for all

38

Measured Peak HRR (kW)

0 1000 2000 3000

Pred

icte

d Pe

ak H

RR

(kW

)

0

1000

2000

3000

Measured Energy Release (GJ)

0 1 2 3 4 5

Pred

icte

d En

ergy

Rel

ease

(GJ)

0

1

2

3

4

5

39

Fire DynamicsSimulator (FDS)

40

Vertical cable fire spread experiments at NIST

42

Corridor Fire Spread Experiments at NIST

43Cable fire spread in a corridor, courtesy NIST.

44

The spread rate of a fire can be estimated from:

If the cables are located within the Hot Gas Layer (HGL),

the spread rate could increase by a factor of 10.

45

FLASH-CAT

Flame Spread over

Horizontal Cable

Trays

Results of Hallway

Experiments

47

FLASH-CAT

Vertical Tray Results

48

Results of CHRISTIFIRE Phase 2

Average heat release rates for thermoplastic and thermoset cables are consistent with Phase 1 experiments

and FLASH-CAT modeling.

Fire spread rates are roughly a factor of 10 greater for multiple vertical trays or horizontal trays close to ceilings

(or within the hot gas layer).

49

CHRISTIFIRE Report, NUREG/CR-7010

[email protected]@nrc.gov

50

Fire plumes and ceiling jets

Describe fire plume and ceiling jet phenomenaDiscuss the theory behind fire plume correlationsAppreciate the role of plume entrainment on fire conditions

within an enclosureCalculate fire plume and ceiling jet conditions, including

temperatures and velocities, for different correlations

R

H

51

References – fire plumes

Enclosure Fire Dynamics– Chapter 4 - Fire plumes and flame heights

SFPE Handbook– Chapter on Flame Height– Chapter on Fire Plumes

52

Fire plume issues

Transports combustion products / entrained air vertically to ceilingCauses formation and descent

of smoke layerElevated temperatures and

velocities expose targets located in plume

53

Types of fire plumes

Axisymmetric plumesLine plumesWindow plumesBalcony spill plumesOther …

54

Axisymmetric fire plumes

Correlations– Morton-Taylor-Turner (ideal)– Zukoski– Heskestad– McCaffrey– Alpert– Alpert & Ward– Thomas

Typically use Heskestad correlation

55

D

Zf

D.Q.Z /f 021230 52 −= &

Heskestad flame height correlation

02.1*7.3 5/2 −= QDZ f

56

521660 /coL Q.zz &+=

Lcpl z/zQ.m && 00540=

c/

o/

cpl Q.)zz(Q.m &&& 001800710 3531 +−=

The Heskestad plume

Effective flame height

– Mass EntrainmentFlame region (z < zL)

– Mass EntrainmentPlume region (z > zL)

57

Plume centerline temperature

– Continuous flame region

– Plume region

CT °≈ 900Δ

3/5

3/23/5

3/2

)(085.0)(1.9

o

co

p

co

zzQzz

TcgQ

TT

−≈−

=

∆ −

∞∞∞

&&

ρ

3/5

3/2

)(25

o

co zz

QT−

≈∆&

The Heskestad plume

58

Fire location factors

Multiply HRR by fire location factor– Fires in the open: klf = 1– Fires along walls: klf = 2– Fires in corners: klf = 4

These values are going to change based on new research

59

Corner Fire Test, NIST, 2017, 400 kW Fire

VIDEO FILE REMOVED

60

Wall Fire Test, NIST, 2017, 400 kW Fire

VIDEO FILE REMOVED

61

Fire plume - example

In the FM/SNL fire test series, the room height was 6.1 m and the burner was 0.1 m above the floorFor many tests, the fire HRR was 500 kW and the burner

diameter was 0.9 mWhat would be the plume centerline temperature rise and

velocity at the ceiling based on the Heskestad plume correlation?

62


Solution – plume temperature– First calculate the virtual origin elevation

– Then calculate the plume centerline temp rise

Kzz

QTo

co

64)08.06(

)350(25)(

25 3/5

3/2

3/5

3/2

=−

=−

≈∆&

08.0)9.0(02.1)500(083.002.1083.0 5/25/2

=−=−= DQzo

&

63


Solution – plume velocity

smzz

Quo

co

/0.408.06

35003.103.13/13/1

=

−=

−

=&

64

Enclosure smoke filling

The ASET model

Analytical solutions– Expansion negligible – Leak at ceiling only

expVVdtdzA

dtdV

pluu && +==

H

zl

zu expVVpl&& +

expV&

plV&

expV&

pluu V

dtdzA

dtdV &==

65

Summary – fire plumes

Plume important for number of reasons– Temperatures/velocities/heat fluxes at targets– Smoke layer filling / exhaust rates– Smoke concentrations

Correlations available for some scenarios– Axisymmetric / line plumes– Windows / balconies (limited theory / data)

– For NPP applications, generally use Heskestad correlations

66

Summary – fire plumes

Limited/no correlations for other scenarios

– 3D fuel sources (e.g., racks, sprays …)– Obstructions in plume / flow field– Sloped / stepped ceilings– Wind / mechanical ventilation

CFD models can address scenarios where correlations are inappropriate

67

Ceiling jet topics

Unconfined ceiling jetsConfined ceiling jetsCeiling jet correlations

– Temperature– Velocity

68

References – ceiling jets

SFPE Handbook– Chapter on Ceiling Jet Flows

69

R

H

Unconfined ceiling jets

70

L

H

W

Confined ceiling jets

71

Temperature correlations – Alpert

– Alpert and Ward

( ) 3/2/32.0HRT

T

pl

cj =∆

∆

Unconfined ceiling jet

3/5

3/2

9.16HQTpl

&=∆

( ) 3/2/31.0HRT

T

pl

cj =∆

∆3/5

3/2

0.22HQT c

pl

&=∆

72

Temperature correlations


00.20.40.60.8

1

0 1 2 3 4 5 6 7 8 9 10

R/H

T cj/

T pl Alpert

A & WH & DCooper

73

Temperature correlation – Delichatsios

−

=

∆

∆ 3/13/1

16.0exp37.0HW

HL

WH

TT

pl

cj

Confined ceiling jet

74

Ceiling jet temperatures


00.20.40.60.8

1

0 1 2 3 4 5 6 7 8 9 10

L/H

T cj/

T pl H/W = 0.5

H/W = 1.0H/W = 1.5H/W = 2.0H/W = 2.5Unconfined

75

Velocity correlation– Alpert

– Note that according to this correlation the velocity decreases as the flow moves away from the source

6/5)/(2.0

HRuu

o

=


76

Velocity correlation– Delichatsios

– Note that according to this correlation the velocity does not change as the flow moves down the corridor

3/1)/(27.0HWu

u

o

=


77

Ceiling jet velocities

Ceiling jet velocity correlations

00.20.40.60.8

1

0 1 2 3 4 5 6 7 8 9 10

R/H or W/H

u/u o

Alpert

H & D

Delichatsios

78

Ceiling jet - example

In the FM/SNL enclosure, what would be the ceiling jet temperature and velocity at a radial distance of 3.0 m (10 ft) from the plume centerline for a HRR of 500 kW?

79

Ceiling jet - example

Solution– R/H = 3.0 / 6.0 = 0.5– Temperature rise

– Velocity

( )49.0

/31.0

3/2 ==∆

∆

HRTT

pl

cj

32)64(49.0

49.0

==

∆=∆ plcj TT

36.0)/(

2.06/5 ==

HRuu

o smuu o

/44.1)4(36.036.0

===

80

Summary – ceiling jets

Ceiling jets form when buoyant plume gases are trapped beneath ceilingTemperature / velocity correlations exist for some conditions

– Unconfined, horizontal, smooth ceiling– Confined, horizontal, smooth ceiling

For other conditions, such as obstructed or sloped ceilings, CFD model needed– In many NPP applications, the ceiling is highly obstructed (“cluttered”),

so CFD modeling may be necessary

81

Fire plume / ceiling jet summary

Fire plumes and ceiling jets are important aspects of enclosure fire dynamicsTemperature, velocity and entrainment correlations exist for

a few idealized geometries– These correlations are used for hand calculations and in zone models

Fire plume / ceiling jet flows are calculated directly in CFD models such as FDS

82

Heat and smoke detection

Understand terminology used to describe the activation of fire detection devicesAppreciate the role of different variables in estimating fire

detector activation and structural damage timesCalculate the response of fire detectors to fire plume and

ceiling jet conditions

83

References - detection

Enclosure Fire Dynamics– Chapter 4 - Fire plumes and ceiling jets

SFPE Handbook– Chapter on Fire plumes– Chapter on Ceiling jet flows– Chapter on Design of detection systems

84

Overview of methods to predict heat / smoke detector activation

Idealized geometry – smooth flat ceiling

85


Realistic geometry – obstructed ceiling

86


Step 1. Specify heat/smoke release rates

Smoke/ heat

source

Step 1

87


Step 2. Calculate temperature / smoke concentration outside detector

Smoke transport /

dilution

Smoke/ heat

source

Step 1

Step 2

Temperature / smoke concentration / velocity

outside detector

88


Step 3. Calculate detector response to local environmental conditions

Smoke transport /

dilution

Temperature / smoke concentration / velocity

outside detector

Detector temperature / smoke concentration

Detection activation criteria (e.g.,

temperature, %/m)

Smoke/ heat

source

Step 1

Step 3

Step 2

89

Tg, ug

M, cp, As

The DETACT model

A first order response model for predicting fire detector activation based on convective heating and a lumped capacity analysis

90

Bases

Heat balance at detector

Convective heating only

Lumped capacity analysis

Negligible losses (basic model)

outinabs qqq &&& −=

)( dgscin TTAhq −=&

dtdTmcq d

pabs =&

0≈outq&

91

Solution

Predictive equation for temperature rise

Definition of detector time constant

– Time constant not really constant because it depends on heat transfer coefficient, which depends on gas velocity

τTT

TTmc

Ahdt

dT dgdg

p

scd )()(

−=−=

sc

p

Ahmc

τ ≡

92

Response Time Index

For cylinders in cross flow

Implications

Definition of RTI

Predictive equation

gc uh ~

guτ 1~ constuτ g =

guRTI τ≡

)( dggd TT

RTIu

dtdT

−=

93

RTI determination (1)

Plunge test– Tg = constant– ug = constant– Tact = known

Analytical solution

oτt

g

d eTT /1

ΔΔ −−= RTIut

g

act oacteTT /1ΔΔ −−=

94

Plunge test

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5

t/τ

∆T d

/ ∆T g τt

g

d eTT /1

ΔΔ −−=

95

DETACT formulation

Euler equation for Td

Substitute equation for dTd/dt

Evaluation requires RTI, Tg(t) and ug(t)

tdt

dTTT dtd

ttd Δ)()Δ( +=+

( ) tTTRTIu

TT td

tg

tgt

dtt

d Δ)()()(

)()Δ( −+=+

96

Detector activation

Fixed temperature devices

Rate-of-rise devices

– Typical value of dTact/dt: 8.3ºC (15 ºF) /min

actactd t

dtdT

dtdT

⇒>

actactd tTT ⇒>

97

Sprinkler activation

Generic sprinkler temperature ratings– From NUREG 1805

98

Sprinkler activation

Generic sprinkler RTIs– From NUREG 1805

99

Heat detector activation

Generic heat detector RTIs– From NFPA 72

100

Gas parameters - Tg, ug

Alpert correlation used in DETACT model (unconfined ceiling jet)– Temperature Velocity

3/2,

,

3/5

3/2

,

)/(3.0

ΔΔ

9.16Δ

HrTT

HQT

plg

cjg

plg

=

=&

6/5,

,

3/1

,

)/(2.0

0.1

Hruu

HQu

plg

cjg

plg

=

=

&

101

Sprinkler activation example

Assume sprinklers are installed on a 3m x 3m (10 ft x 10 ft) spacing in the FMSNL test roomThe FM/SNL test room is 18 m (60 ft) long x 12 m (40 ft) wide x 6 m (20 ft) highFor a quasi-steady fire with a HRR of 500 kW, estimate the activation time for a sprinkler with – Tact = 74 C – RTI = 130 (m-s)1/2

102


Solution– Step 1 – determine radial position of sprinkler

– Step 2 – calculate gas temperature / velocity at sprinkler

mSSSR 1.22

322

22

===+

= 35.00.61.2

==HR

CTHr

T

CHQT

plgcjg

plg

33)/(

3.0

549.16

,3/2,

3/5

3/2

,

=∆=∆

==∆&

smuHr

u

smHQu

plgcjg

plg

/1.2)/(

2.0

/4.40.1

,6/5,

3/1

,

==

=

=

&

103


Solution– Step 3 – Calculate sprinkler response– The next step would normally be to calculate the activation time of the

sprinkler– But note that the gas temperature at the sprinkler is only 53 C (20+33)

for this example, while the sprinkler activation temperature is 74 C– So the 500 kW fire would not activate the sprinkler until the hot gas

layer forms and the ceiling jet temperature exceeds the activation temperature

104

Smoke detector activation (temperature model)

Heat detector analogy– Treat smoke detector as low RTI deviceCannot use zero - Divide by zero errorHand calculations - use Td = Tg

– Assume ∆Tact ~ 15 ºC (or less)

– Questions regarding validityRelies on optical density analogySmoke detectors don’t always respond to optical density

105

Smoke detector activation (Heskestad model)

Smoke concentration in detector chamber, 𝑌𝑌c

𝑢𝑢 is the local gas velocity outside the detector𝐿𝐿 is the characteristic entry length of the detectorYs is the smoke concentration outside the detectorYc is the smoke concentration in the detection chamber

Need to know Yc that causes detector activation

c

csc

ttYtY

dtdY

δ)()( −

= uLtc /=δ

106

Structural steel damage

Same concept as DETACT for steel

Steel properties

( ) ( )DWcq

AVcq

VcAq

dtdT

pspp

ss

/

''r

''r

''r &&&

===ρρ

K)kJ/(m 666,3 3 ⋅≈pcρ

perimeterheatedtioncross

AV

s

sec−=

perimeterheatedlengthWeight

DW /

=

107

Structural steel damage

Steel critical temperature, Tc ≈ 550 ºCEvaluation of heat fluxes

– Flame radiant heat fluxApplies in flame only

– Plume convective heat fluxApplies in flame and plume

– Radiant flux outside flamePoint source estimate

– Based on Alpert & Ward FSJ article

2"c

)(3.0

HQk

q lf&

& =

2"r kW/m 160=q&

2"r 4 R

Qq r

πχ &

& =

EPRI/NRC-RES FIRE PRA METHODOLOGYModule 5Advanced Fire ModelingDevelopment of a Cable Response Model and Fire Model Verification and Validation

Kevin McGrattanNational Institute of Standards and Technology

Joint RES/EPRI Fire PRA WorkshopAugust 2018

109

CAROLFIRE (Cable Response to Live Fire)

Penlight heats target cables via grey-body radiation from a heated shroud

Well controlled, well instrumented tests

Allows for many experiments in a short time

Thermal response and failure for single cables and small cable bundles (up to six cables)

Cable trays, air drops, conduits

110

Typical Penlight setup

111

Intermediate-Scale Experiments

Courtesy Steve Nowlen and Frank Wyant,Sandia National Labs

• Less controlled, but a more realistic scale

• Hood is roughly the size of a typical ASTM E 603 type room fire test facility

• Propene (Propylene) burner fire (200 kW to 350 kW)

• Cables in trays, conduits and air drop

112

Simple Response Models in Fire

Solve for link temperature using velocity u and gas temperature from Fire Model. The RTI (Response Time

Index) is unique to each sprinkler.

Source: Gunnar Heskestad, Factory Mutual

Solve for smoke chamber concentration

using external smoke concentration and

velocity u from Fire Model. L is a length

scale unique to each detector.

113

Cable Failure Model

1-D heat conduction into homogenous

cylinder. Thermal conductivity (k) and

specific heat (c) assumed constant for all

cables. Density (ρ) obtained from cable

diameter and mass per unit length. Failure

temperature obtained experimentally.

The Fire Model provides the convective and

radiative heat flux at the cable surface.

Source: Andersson and Van Hees, SP Fire,

Sweden.

114

Single Cable

Penlight Test 1XLPE/CSPE

3/CTray

Time (s)

0 600 1200 1800 2400Te

mpe

ratu

re (C

)0

200

400

600

Courtesy Steve Nowlen and Frank WyantSandia National Laboratory

115

Cable in a Conduit

Penlight Test 7XLPE/CSPE3/CConduit

Time (s)

0 600 1200 1800 2400Te

mpe

ratu

re (C

)0

200

400

600

First Short2334 s

Shroud

Conduit

Cable

Courtesy Steve Nowlen and Frank WyantSandia National Laboratory

116

Measured or Inferred Failure Time (s)

0 600 1200 1800 2400 3000

Pre

dict

ed F

ailu

re T

ime

(s)

0

600

1200

1800

2400

3000Single Cable in TrayLoose Fill Cables in Tray6 Cable Bundle in Tray12 Cable Bundle in Tray3 Cable Bundle in ConduitAir Drop Cable(s)

Intermediate-Scale Experiments

117

Summary

Methods to calculate fire detector response and structural / cable damage have been discussed– First-order response characteristics– Lumped capacity analysis (Low Biot No.)

Methods require estimates for:– Heat flux or gas temperature at target– Thermal response properties of target

Basic models use fire plume/ceiling jet correlations– Same predictive equations used in computer fire models, but

temperatures / velocities calculated by models rather than specified by empirical correlations

module v – advanced fire modeling · calculate fire plume and ceiling jet conditions, including...

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