09 Plume Temperature Calculations

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Office of Nuclear Reactor Regulation

Division of Systems Safety and Analysis

Plant Systems Branch

Fire Protection Engineering and Special Projects Section

CHAPTER 9. ESTIMATING CENTERLINE TEMPERATURE

BUOYANT FIRE PLUMEVersion 1805.0The following calculations estimate the centerline plume temperature in a compartment fi

Parameters should be specified ONLY IN THE YELLOW INPUT PARAMETER BOXE

All subsequent output values are calculated by the spreadsheet and based on values speparameters. This spreadsheet is protected and secure to avoid errors due to a wrong ent

The chapter in the NUREG should be read before an analysis is made.

INPUT PARAMETERS

Heat Release Rate of the Fire (Q)

Elevation Above the Fire Source (z)

Area of Combustible Fuel (Ac)

Ambient Air Temperature (Ta)

AMBIENT CONDITIONS

Specific Heat of Air (cp)

Ambient Air Density (ra)

Acceleration of Gravity (g)

Convective Heat Release Fraction (cc)

Note: Air density will automatically correct with Ambient Air Temperature

ESTIMATING PLUME CENTERLINE TEMPERATUREReference: SFPE Handbook of Fire Protection Engineering, 3

rdEdition, 2002, Page 2-6.

Tp(centerline) - Ta = 9.1 (Ta/g cp2ra

2)1/3 Qc2/3 (z - z0)

-5/3

Where Tp(centerline) = plume centerline temperature (C)

Qc = convective portion of the heat release rate (kW)

Ta = ambient air temperature (K)

g = acceleration of gravity (m/sec2)

cp = specific heat of air (kJ/kg-K)

ra = ambient air density (kg/m3)

z = distance from the top of the fuel package to the ceiling (

z0 = hypothetical virtual origin of the fire (m)

Convective Heat Release Rate CalculationQc = cc Q

Where Qc = convective portion of the heat release rate (kW)

Q = heat release rate of the fire (kW)

cc = convective heat release fraction

Qc = 3500 kW

Fire Diameter Calculation

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Ac = pD2/4

Where Ac = area of combustible fuel (m2)

D = fire diameter (m)

D = (4 Ac/p)

D = 2.02 m

Hypothetical Virtual Origin Calculation

z0/D = -1.02 + 0.083 (Q2/5

)/D

Where z0 = virtual origin of the fire (m)

Q = heat release rate of fire (kW)

D = fire diameter (m)

z0/D = 0.22

z0 = 0.44 m

Centerline Plume Temperature Calculation

Tp(centerline) - Ta = 9.1 (Ta/g cp2ra

2)1/3

Qc2/3

(z - z0)-5/3

Tp(centerline)

- Ta

=218.97

Tp(centerline) = 516.97 K

Tp(centerline) = 243.97 C 471.15

The above calculations are based on principles developed in the SFPE H

Protection Engineering, 3rd

Edition, 2002.

Calculations are based on certain assumptions and have inherent limitati

calculations may or may not have reasonable predictive capabilities for a

should only be interpreted by an informed user.

Although each calculation in the spreadsheet has been verified with the rthere is no absolute guarantee of the accuracy of these calculations.

Any questions, comments, concerns, and suggestions, or to report an err

please send an email to [email protected] or [email protected].

Prepared by: Date Organization

NOTE

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Checked by: Date Organization

Additional Information

Revision Log Description of Revision

1805.0 Original issue with final text.

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F A

e.

.

cified in the inputry in a cell(s).

5000.00 kW

25.00 ft 7.62 m

34.50 ft 3.21 m2

77.00 F 25.00 C

Calculate 298.00 K

1.00 kJ/kg-K

1.18 kg/m

9.81 m/sec2

0.70

(Ta) Input

m)

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F

ndbook of Fire

ns. The results of such

given situation, and

sults of hand calculation,

r(s) in the spreadsheet,

Answer

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Date

January 2005

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09 Plume Temperature Calculations

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