CHAPTER 5

ESTIMATING RADIANT HEAT FLUX FROM FIRE TO A TARGET FUEL Version 1805.1
ABOVE GROUND LEVEL IN PRESENCE OF WIND (TILTED FLAME) (English Units)
SOLID FLAME RADIATION MODEL

The following calculations estimate the full-scale cable tray heat release rate.
Parameters in YELLOW CELLS are Entered by the User.
Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Cable Type Selected.
All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected
and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Project / Inspection Title:

INPUT PARAMETERS
Mass Burning Rate of Fuel (m") 0.017 kg/m2-sec
Effective Heat of Combustion of Fuel (DHc,eff) 20000 kJ/kg
Empirical Constant (kb) 100 m-1
Fuel Area or Dike Area (Adike) 9.00 ft2 0.836 m2
Distance between Fire and Target (L) 10.00 ft 3.048 m
Wind Speed or Velocity (uw) 700 ft/min 3.56 m/sec
Ambient Air Temperature (Ta) 77.00 °F 25.00 °C
298.00 K
Gravitational Acceleration (g) 9.81 m/sec2
Ambient Air Density (ra) 1.18 kg/m3

Calculate
Note: Air density will automatically correct with Ambient Air Temperature (T a) Input

THERMAL PROPERTIES DATA

BURNING RATE DATA FOR FUELS Empirical
Mass Burning Rate Heat of Combustion Constant Select Fuel Type
Fuel
m" (kg/m2-sec) DHc,eff (kJ/kg) kb (m-1)
Methanol 0.017 20,000 100 Scroll to desired fuel type then
Ethanol 0.015 26,800 100 Click on selection
Butane 0.078 45,700 2.7
Benzene 0.085 40,100 2.7
Hexane 0.074 44,700 1.9
Heptane 0.101 44,600 1.1
Xylene 0.09 40,800 1.4
Acetone 0.041 25,800 1.9
Dioxane 0.018 26,200 5.4
Diethy Ether 0.085 34,200 0.7
Benzine 0.048 44,700 3.6
Gasoline 0.055 43,700 2.1
Kerosine 0.039 43,200 3.5
Diesel 0.045 44,400 2.1
JP-4 0.051 43,500 3.6
JP-5 0.054 43,000 1.6
Transformer Oil, Hydroca0.039 46,000 0.7
561 Silicon Transformer F0.005 28,100 100
Fuel Oil, Heavy 0.035 39,700 1.7
Crude Oil 0.0335 42,600 2.8
Lube Oil 0.039 46,000 0.7
Douglas Fir Plywood 0.01082 10,900 100
User Specified Value Enter Value Enter Value Enter Value
Reference: SFPE Handbook of Fire Protection Engineering, 3rd Edition, 2002, Page 3-26.

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 CHAPTER 5
ESTIMATING RADIANT HEAT FLUX FROM FIRE TO A TARGET FUEL Version 1805.1
ABOVE GROUND LEVEL IN PRESENCE OF WIND (TILTED FLAME) (English Units)
SOLID FLAME RADIATION MODEL

ESTIMATING RADIATIVE HEAT FLUX TO A TARGET FUEL IN PRESENCE OF WIND

Reference: SFPE Handbook of Fire Protection Engineering, 3 rd Edition, 1995, Page 3-276.

SOLID FLAME RADIATION MODEL IN PRESENCE OF WIND

q" = EF1->2
Where
q" = incident radiative heat flux on the target (kW/m2)
E = emissive power of the pool fire flame (kW/m2)
F1->2 = view factor between target and the flame in presence of wind

Pool Fire Diameter Calculation

Adike = pD2/4
D = √(4 Adike/p)

Where
Adike = surface area of pool fire (m2)
D = pool fire diameter (m)

D= 1.03 m

Pool Fire Radius Calculation

r = D/2
Where
r = pool fire radius (m)
D = pool fire diameter (m)

r= 0.52 m

Flame Emissive Power Calculation

E = 58 (10-0.00823 D)
Where
E = emissive power of the pool fire flame (kW/m2)
D = diameter of the pool fire (m)

E= 56.88 kW/m2

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 CHAPTER 5
ESTIMATING RADIANT HEAT FLUX FROM FIRE TO A TARGET FUEL Version 1805.1
ABOVE GROUND LEVEL IN PRESENCE OF WIND (TILTED FLAME) (English Units)
SOLID FLAME RADIATION MODEL

View Factor Calculation in Presence of Wind

tan-1(b+1/b-1)0.5-(a2 + (b + 1)2 - 2 (b + 1 +ab Sin q)/(AB)0.5 tan-1 (A/B)0.5((b - 1)/(b + 1))0.5 +

p F1->2,H = Sinq/(C)0.5 (tan-1 ((ab - (b2 - 1)Sinq)/ ((b2 - 1) (C))0.5)+ tan-1 ( (Sinq (b2-1))/(b2-1)0.5 (C)0.5)

(a Cosq/(b - a Sinq)) (a2 + (b + 1)2 - 2b (1 + a Sinq))/ (AB)0.5 (tan-1 (A/B)0.5 ((b - 1)/(b + 1))0.5+ Cosq/
p F1->2,V = (C)0.5((tan-1 (ab-(b2-1) Sinq)/((b2-1) (C))0.5+ tan-1 (b2-1) Sinq/((b2-1)0.5 (C)0.5)))-(aCosq)/(b-a Sinq)(tan-1(b-1/b + 1)0.5

a = Hf/r
b = R/r
A = a2 + (b +1)2 - 2a (b + 1) sinq
B = a2 + (b - 1)2 - 2a (b - 1) sinq
C = 1 + (b2 - 1) Cos2q
F1->2,max = √(F21->2,H + F21->2,V)

Where
F1->2,H = horizontal view factor
F1->2,V = vertical view factor
F1->2,max = maximum view factor
R = distance from center of the pool fire to edge of the target (m)
Hf = height of the pool fire flame (m)
r = pool fire radius (m)
q = flame tilt or angle of deflection (radians)

Distance from Center of the Pool Fire to Edge of the Target Calculation

R = L+r
Where
R = distance from center of the pool fire to edge of the target (m)
L = Distance between fire and target
r = pool fire radius (m)

R= 3.56 m

Heat Release Rate Calculation

Q = m"DHc,eff (1 - e-kb D) Adike

Where
Q= pool fire heat release rate (kW)
m" = mass burning rate of fuel per unit surface area (kg/m2-sec)
DHc = effective heat of combustion of fuel (kJ/kg)
Adike =
surface area of pool fire (area involved in vaporization) (m2)
kb = empirical constant (m-1)
D = diameter of pool fire (diameter involved in vaporization, circular pool is assumed) (m)

Q= 284.28 kW

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 CHAPTER 5
ESTIMATING RADIANT HEAT FLUX FROM FIRE TO A TARGET FUEL Version 1805.1
ABOVE GROUND LEVEL IN PRESENCE OF WIND (TILTED FLAME) (English Units)
SOLID FLAME RADIATION MODEL

Pool Fire Flame Height Calculation

Hf = 55 D (m"/r a (√g D)) 0.67 (u*)-0.21

Where
Hf = nondimensional wind velocity
m" = mass burning rate of fuel (kg/m2-sec)
D = pool fire diameter (m)
ra = ambient air density (kg/m3)
g = gravitational acceleration (m/sec2)
u* = nondimensional wind velocity

Hf = 1.02 m

Nondimensional Wind Velocity Calculation

u* = uw/(g m" D/r a)1/3

Where
u* = nondimensional wind velocity
uw = wind velocity (m/sec)
g = gravitational acceleration (m/sec2)
m" = mass burning rate of fuel (kg/m2-sec)
D = pool fire diameter (m)
ra = ambient air density (kg/m3)

u* = 6.765

Flame Tilt or Angle of Deflection Calculation

COS q = 1 for u* ≤ 1
COS q = 1 / √(u*) for u* ≥ 1

Since u* ≥ 1
q= ACOS(1/(u*)^0.5) = 1.176 Rad 67.39 degree
1.176 Rad 67.39 degree
a = Hf/r = 1.97
b = R/r = 6.91
A = a2 + (b +1)2 - 2a (b + 1) sinq = 37.61
B = a2 + (b - 1)2 - 2a (b - 1) sinq = 17.27
C = 1 + (b2 - 1) Cos2q = 7.91

FH1 FH2 FH3 FH4 FH5 FH6

F1->2,H = 0.002 0.858 0.998 0.906 0.328 -0.993 1.152
F1->2,V = 0.019 FV1 FV2 FV3 FV4 FV5 FV6
F1->2, max = √(F21->2,H + F21->2,V) = 0.019 0.149 1.077 0.906 0.137 -0.993 1.152

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 CHAPTER 5
ESTIMATING RADIANT HEAT FLUX FROM FIRE TO A TARGET FUEL Version 1805.1
ABOVE GROUND LEVEL IN PRESENCE OF WIND (TILTED FLAME) (English Units)
SOLID FLAME RADIATION MODEL

RADIATIVE HEAT FLUX CALCULATION IN PRESENCE OF WIND

q" = EF1->2

Answer q" = 0.10 Btu/ft2-sec 1.11 kW/m2

NOTE:
The above calculations are based on principles developed in the SFPE Handbook of Fire Protection Engineering, 3 rd Edition, 2002. Calculations are based on certain
assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive capabilities for a given situation and should only be
interpreted by an informed user. Although each calculation in the spreadsheet has been verified with the results of hand calculation, there is no absolute guarantee of the
accuracy of these calculations. Any questions, comments, concerns and suggestions or to report an error(s) in the spreadsheets, please send an email to
David.Stroup@nrc.gov or Naeem.Iqbal@nrc.gov.

Prepared by: Date: Organization:

Checked by: Date: Organization:

Additional Information:

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 CHAPTER 5
ESTIMATING RADIANT HEAT FLUX FROM FIRE TO A TARGET FUEL Version 1805.1
ABOVE GROUND LEVEL IN PRESENCE OF WIND (TILTED FLAME) (English Units)
SOLID FLAME RADIATION MODEL

The following calculations estimate the full-scale cable tray heat release rate.
Parameters in YELLOW CELLS are Entered by the User.
Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Cable Type Selected.
All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected
and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Project / Inspection
Title:

INPUT PARAMETERS
Mass Burning Rate of Fuel (m") 0.005 kg/m2-sec
Effective Heat of Combustion of Fuel (DHc,eff) 28100 kJ/kg
Empirical Constant (kb) 100 m-1
Fuel Area or Dike Area (Adike) 20.00 ft2 1.86 m2
Distance between Fire and Target (L) 30.00 ft 9.144 m
Vertical Distance of Target from Ground Level (H 1 = Hf1) 10.00 ft 3.048 m
Wind Speed or Velocity (uw) 700 ft/min 3.56 m/sec
Ambient Air Temperature (Ta) 77.00 °F 25.00 °C
298.00 K
Gravitational Acceleration (g) 9.81 m/sec2
Ambient Air Density (ra) 1.18 kg/m3

Calculate
Note: Air density will automatically correct with Ambient Air Temperature (T a) Input

THERMAL PROPERTIES DATA

BURNING RATE DATA FOR FUELSEmpirical
Mass Burning Rate Heat of Combustion Constant Select Fuel Type
Fuel
m" (kg/m2-sec) DHc,eff (kJ/kg) kb (m-1)
Methanol 0.017 20,000 100 Scroll to desired fuel type then
Ethanol 0.015 26,800 100 Click on selection
Butane 0.078 45,700 2.7
Benzene 0.085 40,100 2.7
Hexane 0.074 44,700 1.9
Heptane 0.101 44,600 1.1
Xylene 0.09 40,800 1.4
Acetone 0.041 25,800 1.9
Dioxane 0.018 26,200 5.4
Diethy Ether 0.085 34,200 0.7
Benzine 0.048 44,700 3.6
Gasoline 0.055 43,700 2.1
Kerosine 0.039 43,200 3.5
Diesel 0.045 44,400 2.1
JP-4 0.051 43,500 3.6
JP-5 0.054 43,000 1.6
Transformer Oil, Hy 0.039 46,000 0.7
561 Silicon Transfor 0.005 28,100 100
Fuel Oil, Heavy 0.035 39,700 1.7
Crude Oil 0.0335 42,600 2.8
Lube Oil 0.039 46,000 0.7
Douglas Fir Plywood 0.01082 10,900 100
User Specified ValueEnter Value Enter Value Enter Value
Reference: SFPE Handbook of Fire Protection Engineering, 3rd Edition, 2002, Page 3-26.

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 CHAPTER 5
ESTIMATING RADIANT HEAT FLUX FROM FIRE TO A TARGET FUEL Version 1805.1
ABOVE GROUND LEVEL IN PRESENCE OF WIND (TILTED FLAME) (English Units)
SOLID FLAME RADIATION MODEL

ESTIMATING RADIATIVE HEAT FLUX TO A TARGET FUEL IN PRESENCE OF WIND

Reference: SFPE Handbook of Fire Protection Engineering, 3 rd Edition, 1995, Page 3-272.

SOLID FLAME RADIATION MODEL IN PRESENCE OF WIND

q" = EF1->2

Where
q" = incident radiative heat flux on the target (kW/m 2)
E = emissive power of the pool fire flame (kW/m 2)
F1->2 = view factor between target and the flame in presence of wind

Pool Fire Diameter Calculation

Adike = pD2/4
D = √(4 Adike/p)

Where
Adike = surface area of pool fire (m2)
D = pool fire diameter (m)

D= 1.54 m

Pool Fire Radius Calculation

r= D/2

r= 0.77 m

Flame Emissive Power Calculation

E = 58 (10-0.00823 D)
Where
E = emissive power of the pool fire flame (kW/m 2)
D = diameter of the pool fire (m)

E= 56.33 (kW/m2)

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 CHAPTER 5
ESTIMATING RADIANT HEAT FLUX FROM FIRE TO A TARGET FUEL Version 1805.1
ABOVE GROUND LEVEL IN PRESENCE OF WIND (TILTED FLAME) (English Units)
SOLID FLAME RADIATION MODEL

View Factor Calculation in Presence of Wind

p F1->2,V1 = (a1 Cosq/(b - a1 Sinq)) (a12 + (b + 1)2 - 2b (1 + a1 Sinq))/ (A1B1)0.5 (tan-1 (A1/B1)0.5 ((b - 1)/(b + 1))0.5 + Cosq/(C)0.5((tan-1 (a1b -(b2-1) Sinq)/((b2 -
1) (C))0.5+ tan-1 (b2-1) Sinq/((b2 - 1)0.5 (C)0.5)) - (a1 Cosq)/(b - a1 Sinq) (tan-1 (b - 1/b + 1)0.5

p F1->2,V2 = (a2 Cosq/(b - a2 Sinq)) (a22 + (b + 1)2 - 2b (1 + a2 Sinq))/ (A2B2)0.5 (tan-1 (A2/B2)0.5 ((b - 1)/(b + 1))0.5 + Cosq/(C)0.5((tan-1(a2b - (b2-1) Sinq)/((b2 -
1) (C))0.5 + tan-1 (b2-1) Sinq/((b2 - 1)0.5 (C)0.5)) - (a2 Cosq)/(b - a2 Sinq) (tan-1 (b - 1/b + 1)0.5

A1 = a12 + (b +1)2 - 2a1 (b + 1) sinq

A2 = a22 + (b +1)2 - 2a2 (b + 1) sinq
B1 = a12 + (b - 1)2 - 2a1 (b - 1) sinq
B2 = a22 + (b - 1)2 - 2a2 (b - 1) sinq
C= 1 + (b2 - 1) Cos2q
a1 = 2Hf1/r = 2H1/r
a2 = 2Hf2/r = 2 (Hf - Hf1)/r
b= R/r
F1->2,V = F1->2,V1 + F1->2,V2

Where
F1->2,V = total vertical view factor in presence of wind
R = distance from center of the pool fire to edge of the target (m)
Hf = height of the pool fire flame (m)
r = pool fire radius (m)
q = flame tilt or angle of deflection (radians)

Distance from Center of the Pool Fire to Edge of the Target Calculation

R = L+ r
Where
R= distance from center of the pool fire to edge of the target (m)
L= Distance between Fire and Target
r= pool fire radius (m)

R= 9.91 m

Heat Release Rate Calculation

Q = m"DHc,eff (1 - e-kb D) Adike

Where
Q = pool fire heat release rate (kW)
m" = mass burning rate of fuel per unit surface area (kg/m2-sec)
DHc = effective heat of combustion of fuel (kJ/kg)
Adike = surface area of pool fire (area involved in vaporization) (m 2)
kb = empirical constant (m-1)
D = diameter of pool fire (diameter involved in vaporization, circular pool is assumed) (m)

Q= 261.06 kW

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 CHAPTER 5
ESTIMATING RADIANT HEAT FLUX FROM FIRE TO A TARGET FUEL Version 1805.1
ABOVE GROUND LEVEL IN PRESENCE OF WIND (TILTED FLAME) (English Units)
SOLID FLAME RADIATION MODEL

Pool Fire Flame Height Calculation

Hf = 55 D (m"/r a √(g D))0.67 (u*)-0.21

Where
Hf = flame height (m)
m" = mass burning rate of fuel (kg/m2-sec)
D = pool fire diameter (m)
ra = ambient air density (kg/m3)
g = gravitational acceleration (m/sec2)
u* = nondimensional wind velocity

Hf = 0.55 m

Nondimensional Wind Velocity Calculation

u* = uw/(g m" D/r a)1/3

Where
u* = nondimensional wind velocity
uw = wind velocity (m/sec)
g = gravitational acceleration (m/sec2)
m" = mass burning rate of fuel (kg/m2-sec)
D = pool fire diameter (m)
ra = ambient air density (kg/m3)

u* = 8.904

Flame Tilt or Angle of Deflection Calculation

COS q = 1 for u* ≤ 1
COS q = 1 / (√u*) for u* ≥ 1

Since u* ≥ 1
q = ACOS(1/(u*)^0.5) = 1.229 Rad 70.42 degree
1.229 Rad 70.42 degree
0 Rad 0.00 degree

A1 = a12 + (b +1)2 - 2a1 (b + 1) sinq = 48.29

A2 = a22 + (b +1)2 - 2a2 (b + 1) sinq = 404.94
B1 = a12 + (b - 1)2 - 2a1 (b - 1) sinq = 26.61
B2 = a22 + (b - 1)2 - 2a2 (b - 1) sinq = 328.92
C = 1 + (b2 - 1) Cos2q = 19.55 ###
a1 = 2Hf1/r = 2H1/r = 7.93
a2 = 2Hf2/r = 2 (Hf - Hf1)/r = -6.49 ###
b = R/r = 12.89

F1->2,V1 0.04059 FV1 FV2 FV3 FV4 FV5 FV6 FV7

F1->2,V2 -0.00487 0.490 1.045 0.895 0.076 -0.755 1.221 0.366
F1->2 = F1->2,V1 + F1->2,V2 = 0.03572 FV1 FV2 FV3 FV4 FV5 FV6 FV7
-0.114 1.005 0.799 0.076 -1.338 1.221 -0.085

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 CHAPTER 5
ESTIMATING RADIANT HEAT FLUX FROM FIRE TO A TARGET FUEL Version 1805.1
ABOVE GROUND LEVEL IN PRESENCE OF WIND (TILTED FLAME) (English Units)
SOLID FLAME RADIATION MODEL

RADIATIVE HEAT FLUX CALCULATIONS IN PRESENCE OF WIND

q" = EF1->2

Answer q" = 0.18 Btu/ft2-sec 2.01 kW/m2

NOTE:
The above calculations are based on principles developed in the SFPE Handbook of Fire Protection Engineering, 3 rd Edition, 2002. Calculations are based on certain assumptions and
have inherent limitations. The results of such calculations may or may not have reasonable predictive capabilities for a given situation and should only be interpreted by an informed
user. Although each calculation in the spreadsheet has been verified with the results of hand calculation, there is no absolute guarantee of the accuracy of these calculations. Any
questions, comments, concerns and suggestions or to report an error(s) in the spreadsheets, please send an email to David.Stroup@nrc.gov or Naeem.Iqbal@nrc.gov.

Prepared by: Date: Organization:

Checked by: Date: Organization:

Additional Information:

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