10 Sprinkler Activation Time 676738
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CHAPTER 11. ESTIMATING SMOKE DETECTOR RESPONSE TIME Version 1805.0 The following calculations estimate smoke detector response time. Parameters should be specified ONLY IN THE YELLOW INPUT PARAMETER BOXES. 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.
INPUT PARAMETERS Heat Release Rate of the Fire (Q) (Steady State) Radial Distance to the Detector (r) **never more than 0.707 or 1/2√2 of the listed spacing** Height of Ceiling above Top of Fuel (H) Activation Temperature of the Smoke Detector (T activation) Smoke Detector Response Time Index (RTI) Ambient Air Temperature (Ta) Convective Heat Release Rate Fraction (cc) Plume Leg Time Constant (l) (Experimentally Determined) Ceiling Jet Lag Time Constant (Ccj) (Experimentally Determined) Temperature Rise of Gases Under the Ceiling (DTc) for Smoke Detector to Activate r/H = 0.77
ESTIMATING SMOKE DETECTOR RESPONSE TIME METHOD OF ALPERT Reference: NFPA Fire Protection Handbook, 19 th Edition, 2003, Page 3-140.
tactivation = (RTI/(√ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation)) This method assume smoke detector is a low RTI device with a fixed activation temperature tactivation = detector activation time (sec) Where RTI = detector response time index (m-sec)1/2 ujet = ceiling jet velocity (m/sec) Tjet = ceiling jet temperature (°C) Ta = ambient air temperature (°C) Tactivation = activation temperature of detector (°C) Ceiling Jet Temperature Calculation Tjet - Ta = 16.9 (Qc)2/3/H5/3 Tjet - Ta = 5.38 (Qc/r)2/3/H Where
Tjet = ceiling jet temperature (°C) Ta = ambient air temperature (°C) Qc = convective portion of the heat release rate (kW) H = height of ceiling above top of fuel (m) r = radial distance from the plume centerline to the detector (m)
Convective Heat Release Rate Calculation Qc = cc Q Qc = convective portion of the heat release rate (kW) Q = heat release rate of the fire (kW) cc = convective heat release rate fraction
Where
Qc =
700 kW
Radial Distance to Ceiling Height Ratio Calculation r/H = 0.77 r/H > 0.15 >0.15 Tjet - Ta =
50.92
<0.15
5.38 ((Qc/r)^2/3)/H
Tjet - Ta =
50.92
Tjet =
75.92 (°C)
Ceiling Jet Velocity Calculation ujet = 0.96 (Q/H)1/3 ujet = (0.195 Q1/3 H1/2)/r5/6 ujet = ceiling jet velocity (m/sec) Q = heat release rate of the fire (kW) H = height of ceiling above top of fuel (m) r = radial distance from the plume centerline to the detector (m)
Where
Radial Distance to Ceiling Height Ratio Calculation r/H = 0.77 r/H > 0.15 >0.15
1.53
<0.15
ujet =
(0.195 Q^1/3 H^1/2)/r^(5/6)
ujet =
1.533
m/sec
Smoke Detector Response Time Calculation tactivation = (RTI/(√ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation)) tactivation =
0.42 sec
Answer
NOTE: If tactivation = "NUM" Detector does not activate METHOD OF MOWRER References: Mowrer, F., "Lag Times Associated With Fire Detection and Suppression," Fire Technology, August 1990, p. 244.
tactivation = tpl + tcj Where
tactivation = detector activation time (sec) tpl = transport lag time of plume (sec) tcj = transport lag time of ceiling jet (sec)
Transport Lag Time of Plume Calculation
tpl = l (H)4/3/(Q)1/3 Where
tpl = transport lag time of plume (sec) l = plume lag time constant H = height of ceiling above top of fuel (m)
tpl =
Q = heat release rate of the fire (kW) 0.42 sec
Transport Lag Time of Ceiling Jet Calculation tcj = (r)11/6/(Ccj) (Q)1/3 (H)1/2 Where
tcj = transport lag time of ceiling jet (sec) Ccj = ceiling jet lag time constant r = radial distance from the plume centerline to the detector (m) H = height of ceiling above top of fuel (m)
tcj =
Q = heat release rate of the fire (kW) 0.32 sec
Smoke Detector Response Time Calculation tactivation = tpl + tcj tactivation =
0.74 sec
Answer
METHOD OF MILKE References: Milke, J., "Smoke Management for Covered Malls and Atria," Fire Technology, August 1990, p. 223. NFPA 92B, "Guide for Smoke Management Systems in Mall, Atria, and Large Areas," 2000 Edition, Section A.3.4.
tactivation = X H4/3/Q1/3 Where
tactivation = detector activation time (sec) X = 4.6 10-4 Y2 + 2.7 10-15 Y6 H = height of ceiling above top of fuel (ft) Q = heat release rate from steady fire (Btu/sec)
Where
Y = DTc H5/3 / Q2/3 DTc = temperature rise of gases under the ceiling for smoke detector to activate (°F)
Before estimating smoke detector response time, stratification effects can be calculated. NFPA 92B, 2000 Edition, Section A.3.4 provides following correlation to estimate smoke stratification in a compartment. Hmax = 74 Qc2/5 / DTf->c3/5 Where
Hmax = the maximum ceiling clearance to which a plume can rise (ft) Qc = convective portion of the heat release rate (Btu/sec) DTf->c = difference in temperature due to fire between the fuel location and ceiling level (°F)
Convective Heat Release Rate Calculation Qc = Q cc
Where
Qc = convective portion of the heat release rate (Btu/sec) Q = heat release rate of the fire (Btu/sec) cc = convective heat releas rate fraction
Qc =
663.47
Btu/sec
Difference in Temperature Due to Fire Between the Fuel Location and Ceiling Level DTf->c = 1300 Qc2/3 / H5/3 Where
DTf->c = difference in temperature due to fire between the fuel location and ceiling level (°F)
DTf->c =
Qc = convective portion of the heat release rate (Btu/sec) H = ceiling height above the fire source (ft) 1375.90 °F
Smoke Stratification Effects Hmax = 74 Qc2/5 / DTf->c3/5 Hmax =
13.03 ft
In this case the highest point of smoke rise is estimated to be Thus, the smoke would be expected to reach the ceiling mounted smoke detector. Y = DTc H5/3 / Q2/3 Y=
13.41
X = 4.6 10-4 Y2 + 2.7 10-15 Y6 X= 0.08 Smoke Detector Response Time Calculation tactivation = X H4/3/Q1/3 tactivation =
0.26 sec
Summary of Results Calculation Method METHOD OF ALPERT METHOD OF MOWRER METHOD OF MILKE
Smoke Detector Response Time (sec) 0.42 0.74 0.26
NOTE
The above calculations are based on principles developed in the NFPA Fire Protection Handbook 19th Edition, 2003, method described in Fire Technology, 1990, and NFPA 92B, "Guide for Smoke Management Systems in Atria, and Large Areas," 2000 Edition, Section A.3.4. Calculations are based on certain assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive capabili for a given situationsand, and should only be interpreted by an informed . 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 spreadsheet, please send an email to [email protected].
Prepared by:
Date
Checked by:
Date
Additional Information
Revision Log 1805.0 Original issue with final text.
Description of Revision
ESPONSE TIME
TER BOXES. values specified in the input a wrong entry in a cell(s).
1000.00 kW
r 1/2√2 of the listed spacing**
10.00 ft 13.00 86.00 5.00 77.00
947.82 Btu/sec 3.05 m
ft
3.96 m
°F
30.00 °C
(m-sec)1/2 °F
25.00 °C 298.00 K
0.70 0.67 1.2 18.00 °F
Calculate
h a fixed activation temperature
for r/H ≤ 0.18 for r/H > 0.18
o the detector (m)
10 °C
134.28
for r/H ≤ 0.15 for r/H > 0.15
o the detector (m)
6.07
Answer
ppression," Fire Technology, August 1990, p. 244.
o the detector (m)
Answer
re Technology, August 1990, p. 223.
ge Areas," 2000 Edition, Section A.3.4.
ling for smoke detector to activate (°F)
cation effects can be calculated. g correlation to estimate smoke
h a plume can rise (ft)
etween the fuel location and ceiling level (°F)
Location and Ceiling Level
etween the fuel location and ceiling level (°F)
13.03 ft
g mounted smoke detector.
Answer
the NFPA Fire Protection Handbook 19th Edition, A 92B, "Guide for Smoke Management Systems in Malls, tions are based on certain assumptions and ay or may not have reasonable predictive capabilities n informed . ed with the results of hand calculation,
eport an error(s) in the spreadsheet,
Organization Organization
Date January 2005
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
CHAPTER 10. ESTIMATING SPRINKLER RESPONSE TIME Version 1805.0 The following calculations estimate sprinkler activation time. Parameters in YELLOW CELLS are Entered by the . Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Sprinkler 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.
INPUT PARAMETERS Heat Release Rate of the Fire (Q) (Steady State) Sprinkler Response Time Index (RTI) Activation Temperature of the Sprinkler (Tactivation) Height of Ceiling above Top of Fuel (H) Radial Distance to the Detector (r) **never more than 0.707 or 1/2√2 of the listed spacing** Ambient Air Temperature (Ta) Convective Heat Release Rate Fraction (cc) r/H =
1.00
GENERIC SPRINKLER RESPONSE TIME INDEX (RTI)* Common Sprinkler Type
Generic Response Time Index (RTI) (m-sec)1/2
Standard response bulb Standard response link Quick response bulb Quick response link Specified Value
235 130 42 34 Enter Value
Reference: Madrzykowski, D., "Evaluation of Sprinkler Activation Prediction Methods" ASIAFLAM'95, International Conference on Fire Science and Engineering, 1 st Proceeding, March 15-16, 1995, Kowloon, Hong Kong, pp. 211-218.
*Note: The actual RTI should be used when the value is available.
GENERIC SPRINKLER TEMPERATURE RATING (Tactivation)* Temperature Classification Ordinary Intermediate High Extra high Very extra high Ultra high Ultra high Specified Value
Range of Temperature Ratings (°F) 135 to 170 175 to 225 250 to 300 325 to 375 400 to 475 500 to 575 650 –
Reference: Automatic Sprinkler Systems Handbook, 6 th Edition, National Fire Protection Association, Quincy, Massachusetts, 1994, Page 67.
*Note: The actual temperature rating should be used when the value is available.
12
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
ESTIMATING SPRINKLER RESPONSE TIME Reference: NFPA Fire Protection Handbook, 19 th Edition, 2003, Page 3-140.
tactivation = (RTI/(√ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation)) Where
tactivation = sprinkler activation response time (sec) RTI = sprinkler response time index (m-sec)1/2 ujet = ceiling jet velocity (m/sec) Tjet = ceiling jet temperature (°C) Ta = ambient air temperature (°C) Tactivation = activation temperature of sprinkler (°C)
Ceiling Jet Temperature Calculation Tjet - Ta = 16.9 (Qc)2/3/H5/3 Tjet - Ta = 5.38 (Qc/r)2/3/H Where
Tjet = ceiling jet temperature (°C) Ta = ambient air temperature (°C) Qc = convective portion of the heat release rate (kW) H = height of ceiling above top of fuel (m) r = radial distance from the plume centerline to the sprinkler (m)
Convective Heat Release Rate Calculation Qc = cc Q Where
Qc = convective portion of the heat release rate (kW) Q = heat release rate of the fire (kW) cc = convective heat release rate fraction
Qc =
700 kW
Radial Distance to Ceiling Height Ratio Calculation r/H = 1.00 r/H > 0.15 Tjet - Ta =
{5.38 (Qc/r)^2/3}/H
Tjet - Ta =
68.46
Tjet =
93.46 (°C)
Ceiling Jet Velocity Calculation ujet = 0.96 (Q/H)1/3 ujet = (0.195 Q1/3 H1/2)/r5/6 Where
ujet = ceiling jet velocity (m/sec) Q = heat release rate of the fire (kW) H = height of ceiling above top of fuel (m) r = radial distance from the plume centerline to the sprinkler (m)
Radial Distance to Ceiling Height Ratio Calculation r/H = 1.00 r/H > 0.15 ujet =
(0.195 Q^1/3 H^1/2)/r^5/6
ujet =
1.354
m/sec
13
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
Sprinkler Activation Time Calculation tactivation = (RTI/(√ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation)) tactivation = 139.89 sec The sprinkler will respond in approximately
NOTE: If tactivation = "NUM" Sprinkler does not activate NOTE The above calculations are based on principles developed in the NFPA Fire Protection Handbook 19th Edition, 2003. 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 . 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 spreadsheet, please send an email to [email protected].
Prepared by:
Date
Checked by:
Date
Additional Information
Revision Log Description of Revision 1805.0 Original issue with final text.
14
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
15
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
RESPONSE TIME
from the DROP DOWN MENU for the Sprinkler Selected. et and based on values specified in the input id errors due to a wrong entry in a cell(s).
re than 0.707 or 1/2√2 of the listed spacing**
1000.00 130 165 9.80 9.80 77.00
kW (m-sec)1/2 °F
73.89 °C
ft
2.99 m
ft
2.99 m
°F
25.00 °C 298.00 K
0.70
Calculate
Select Type of Sprinkler Standard response link
Scroll to desired sprinkler type then Click on selection
tivation Prediction Methods"
and Engineering, 1 st Proceeding,
the value is available. Generic Temperature Ratings (°F) 165 212 275 350 450 550 550 Enter Value
Select Sprinkler Classification Ordinary
Scroll to desired sprinkler class then Click on selection
Edition, National Fire Protection
d be used when the value is available.
16
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
for r/H ≤ 0.18 for r/H > 0.18
release rate (kW)
centerline to the sprinkler (m)
release rate (kW)
for r/H ≤ 0.15 for r/H > 0.15
centerline to the sprinkler (m)
17
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
2.33 minutes
Answer
does not activate
s developed in the NFPA Fire Protection Handbook certain assumptions and have inherent limitations. ot have reasonable predictive capabilities for a given
has been verified with the results of hand calculation, of these calculations. gestions, or to report an error(s) in the spreadsheet,
Organization Organization
Date January 2005
18
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
19
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
CHAPTER 12. ESTIMATING HEAT DETECTOR RESPONSE TIME
Version 1805.0 The following calculations estimate fixed temperature heat detector activation time. Parameters in YELLOW CELLS are Entered by the . Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Detector 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.
INPUT PARAMETERS Heat Release Rate of the Fire (Q) (Steady State) Radial Distance to the Detector (r) **never more than 0.707 or 1/2√2 of the listed spacing** Activation Temperature of the Fixed Temperature Heat Detector (T activation) Detector Response Time Index (RTI) Height of Ceiling above Top of Fuel (H) Ambient Air Temperature (Ta) Convective Heat Release Fraction (cc) r/H =
0.20
INPUT DATA FOR ESTIMATING HEAT DETECTOR RESPONSE TIME Activation Temperature Tactivation UL Listed Spacing r (ft) 10 15 20 25 30 40 50 70 Specified Value
Response Time Index RTI (m-sec)1/2
UL Listed Spacing r (ft) 10 15 20 25 30 40 50 70 Specified Value
Response Time Index RTI (m-sec)1/2
490 306 325 152 116 87 72 44 Enter Value
404 233 165 123 98 70 54 20 Enter Value 29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
UL Listed Spacing r (ft) 10 15 20 25 30 40 50 70 Specified Value
Response Time Index RTI (m-sec)1/2
UL Listed Spacing r (ft) 10 15 20 25 30 40 Specified Value
Response Time Index RTI (m-sec)1/2
UL Listed Spacing r (ft) 10 15 20 25 30 Specified Value
Response Time Index RTI (m-sec)1/2
UL Listed Spacing r (ft) 10 15 20 Specified Value
Response Time Index RTI (m-sec)1/2
321 191 129 96 75 50 37 11 Enter Value
239 135 86 59 44 22 Enter Value
196 109 64 39 27 Enter Value
119 55 21 Enter Value
Reference: NFPA Standard 72, National Fire Alarm Code, Appendix B, Table B-3.2.5.1, 1999, Edition .
ESTIMATING FIXED TEMPERATURE HEAT DETECTOR RESPONSE TIME Reference: NFPA Fire Protection Handbook, 19 th Edition, 2003, Page 3-140.
tactivation = ( RTI/(√ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation)) Where
tactivation = detector activation time (sec) RTI = detector response time index (m-sec)1/2 ujet = ceiling jet velocity (m/sec) Tjet = ceiling jet temperature (°C) Ta = ambient air temperature (°C) Tactivation = activation temperature of detector (°C)
Ceiling Jet Temperature Calculation Tjet - Ta = 16.9 (Qc)2/3/H5/3 29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering andjet SpecialaProjects Section c
T
- T = 5.38 (Q /r)2/3/H Tjet = ceiling jet temperature (°C)
Where
Ta = ambient air temperature (°C) Qc = convective portion of the heat release rate (kW) H = height of ceiling above top of fuel (m) r = radial distance from the plume centerline to the detector (m) Convective Heat Release Rate Calculation Qc = cc Q Qc = convective heat release rate (kW) Q = heat release rate of the fire (kW) cc = convective heat release fraction
Where
Qc =
4004 kW
Radial Distance to Ceiling Height Ratio Calculation r/H = 0.20 r/H > 0.15 >0.15 Tjet - Ta =
194.99
<0.15
5.38 ((Qc/r)^2/3)/H
Tjet - Ta =
194.99
Tjet =
219.99 (°C)
Ceiling Jet Velocity Calculation ujet = 0.96 (Q/H)1/3 ujet = (0.195 Q1/3 H1/2)/r5/6 Where
ujet = ceiling jet velocity (m/sec) Q = heat release rate of the fire (kW) H = height of ceiling above top of fuel (m) r = radial distance from the plume centerline to the detector (m)
Radial Distance to Ceiling Height Ratio Calculation r/H = 0.20 r/H > 0.15 ujet =
(0.195 Q^1/3 H^1/2)/r^(5/6)
ujet =
7.300
m/sec
Detector Activation Time Calculation tactivation = ( RTI/(√ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation)) tactivation = 27.01 sec The detector will respond in approximately
NOTE: If tactivation = "NUM" Detector does not activate NOTE
The above calculations are based on principles developed in the NFPA Fire Protection Handbook 19th Edition 2003. 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 . Although each calculation in the spreadsheet has been verified with the results of hand calculation, 29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
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 spreadsheet, please send an email to [email protected].
Prepared by:
Date
Checked by:
Date
Additional Information
Revision Log Description of Revision 1805.0 Original issue with final text.
29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
ECTOR RESPONSE TIME
detector activation time.
d from the DROP DOWN MENU for the Detector Selected. heet and based on values specified in the input void errors due to a wrong entry in a cell(s).
5720.00 kW
re than 0.707 or 1/2√2 of the listed spacing** ure Heat Detector (T activation)
4.00 135 404.00 20.00 77.00
ft
1.22 m
°F
57.22 °C
(m-sec)1/2 ft
6.10 m
°F
25.00 °C 298.00 K
0.70
Calculate
RESPONSE TIME
Activation Temperature (°F) 128 128 128 128 128 128 128 128 Enter Value Activation Temperature (°F) 135 135 135 135 135 135 135 135 Enter Value
Select Detector Spacing Scroll to desired spacing then Click on selection
Select Detector Spacing 10
Scroll to desired spacing then Click on selection
29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
Activation Temperature (°F) 145 145 145 145 145 145 145 145 Enter Value Activation Temperature (°F) 160 160 160 160 160 160 Enter Value Activation Temperature (°F) 170 170 170 170 170 Enter Value Activation Temperature (°F) 196 196 196 Enter Value
Select Detector Spacing Scroll to desired spacing then Click on selection
Select Detector Spacing Scroll to desired spacing then Click on selection
Select Detector Spacing Scroll to desired spacing then Click on selection
Select Detector Spacing Scroll to desired spacing then Click on selection
, Appendix B, Table B-3.2.5.1, 1999, Edition .
TECTOR RESPONSE TIME
n, 2003, Page 3-140.
ure of detector (°C)
for r/H ≤ 0.18 29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
for r/H > 0.18
heat release rate (kW)
me centerline to the detector (m)
209.48
for r/H ≤ 0.15 for r/H > 0.15
me centerline to the detector (m)
0.45 minutes
Answer
does not activate
s developed in the NFPA Fire Protection Handbook 19th Edition, mptions and have inherent limitations. ot have reasonable predictive capabilities for a given situation,
has been verified with the results of hand calculation, 29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
of these calculations. gestions, or to report an error(s) in the spreadsheet,
Organization Organization
Date January 2005
29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
29
INPUT PARAMETERS Heat Release Rate of the Fire (Q) (Steady State) Radial Distance to the Detector (r) **never more than 0.707 or 1/2√2 of the listed spacing** Height of Ceiling above Top of Fuel (H) Activation Temperature of the Smoke Detector (T activation) Smoke Detector Response Time Index (RTI) Ambient Air Temperature (Ta) Convective Heat Release Rate Fraction (cc) Plume Leg Time Constant (l) (Experimentally Determined) Ceiling Jet Lag Time Constant (Ccj) (Experimentally Determined) Temperature Rise of Gases Under the Ceiling (DTc) for Smoke Detector to Activate r/H = 0.77
ESTIMATING SMOKE DETECTOR RESPONSE TIME METHOD OF ALPERT Reference: NFPA Fire Protection Handbook, 19 th Edition, 2003, Page 3-140.
tactivation = (RTI/(√ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation)) This method assume smoke detector is a low RTI device with a fixed activation temperature tactivation = detector activation time (sec) Where RTI = detector response time index (m-sec)1/2 ujet = ceiling jet velocity (m/sec) Tjet = ceiling jet temperature (°C) Ta = ambient air temperature (°C) Tactivation = activation temperature of detector (°C) Ceiling Jet Temperature Calculation Tjet - Ta = 16.9 (Qc)2/3/H5/3 Tjet - Ta = 5.38 (Qc/r)2/3/H Where
Tjet = ceiling jet temperature (°C) Ta = ambient air temperature (°C) Qc = convective portion of the heat release rate (kW) H = height of ceiling above top of fuel (m) r = radial distance from the plume centerline to the detector (m)
Convective Heat Release Rate Calculation Qc = cc Q Qc = convective portion of the heat release rate (kW) Q = heat release rate of the fire (kW) cc = convective heat release rate fraction
Where
Qc =
700 kW
Radial Distance to Ceiling Height Ratio Calculation r/H = 0.77 r/H > 0.15 >0.15 Tjet - Ta =
50.92
<0.15
5.38 ((Qc/r)^2/3)/H
Tjet - Ta =
50.92
Tjet =
75.92 (°C)
Ceiling Jet Velocity Calculation ujet = 0.96 (Q/H)1/3 ujet = (0.195 Q1/3 H1/2)/r5/6 ujet = ceiling jet velocity (m/sec) Q = heat release rate of the fire (kW) H = height of ceiling above top of fuel (m) r = radial distance from the plume centerline to the detector (m)
Where
Radial Distance to Ceiling Height Ratio Calculation r/H = 0.77 r/H > 0.15 >0.15
1.53
<0.15
ujet =
(0.195 Q^1/3 H^1/2)/r^(5/6)
ujet =
1.533
m/sec
Smoke Detector Response Time Calculation tactivation = (RTI/(√ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation)) tactivation =
0.42 sec
Answer
NOTE: If tactivation = "NUM" Detector does not activate METHOD OF MOWRER References: Mowrer, F., "Lag Times Associated With Fire Detection and Suppression," Fire Technology, August 1990, p. 244.
tactivation = tpl + tcj Where
tactivation = detector activation time (sec) tpl = transport lag time of plume (sec) tcj = transport lag time of ceiling jet (sec)
Transport Lag Time of Plume Calculation
tpl = l (H)4/3/(Q)1/3 Where
tpl = transport lag time of plume (sec) l = plume lag time constant H = height of ceiling above top of fuel (m)
tpl =
Q = heat release rate of the fire (kW) 0.42 sec
Transport Lag Time of Ceiling Jet Calculation tcj = (r)11/6/(Ccj) (Q)1/3 (H)1/2 Where
tcj = transport lag time of ceiling jet (sec) Ccj = ceiling jet lag time constant r = radial distance from the plume centerline to the detector (m) H = height of ceiling above top of fuel (m)
tcj =
Q = heat release rate of the fire (kW) 0.32 sec
Smoke Detector Response Time Calculation tactivation = tpl + tcj tactivation =
0.74 sec
Answer
METHOD OF MILKE References: Milke, J., "Smoke Management for Covered Malls and Atria," Fire Technology, August 1990, p. 223. NFPA 92B, "Guide for Smoke Management Systems in Mall, Atria, and Large Areas," 2000 Edition, Section A.3.4.
tactivation = X H4/3/Q1/3 Where
tactivation = detector activation time (sec) X = 4.6 10-4 Y2 + 2.7 10-15 Y6 H = height of ceiling above top of fuel (ft) Q = heat release rate from steady fire (Btu/sec)
Where
Y = DTc H5/3 / Q2/3 DTc = temperature rise of gases under the ceiling for smoke detector to activate (°F)
Before estimating smoke detector response time, stratification effects can be calculated. NFPA 92B, 2000 Edition, Section A.3.4 provides following correlation to estimate smoke stratification in a compartment. Hmax = 74 Qc2/5 / DTf->c3/5 Where
Hmax = the maximum ceiling clearance to which a plume can rise (ft) Qc = convective portion of the heat release rate (Btu/sec) DTf->c = difference in temperature due to fire between the fuel location and ceiling level (°F)
Convective Heat Release Rate Calculation Qc = Q cc
Where
Qc = convective portion of the heat release rate (Btu/sec) Q = heat release rate of the fire (Btu/sec) cc = convective heat releas rate fraction
Qc =
663.47
Btu/sec
Difference in Temperature Due to Fire Between the Fuel Location and Ceiling Level DTf->c = 1300 Qc2/3 / H5/3 Where
DTf->c = difference in temperature due to fire between the fuel location and ceiling level (°F)
DTf->c =
Qc = convective portion of the heat release rate (Btu/sec) H = ceiling height above the fire source (ft) 1375.90 °F
Smoke Stratification Effects Hmax = 74 Qc2/5 / DTf->c3/5 Hmax =
13.03 ft
In this case the highest point of smoke rise is estimated to be Thus, the smoke would be expected to reach the ceiling mounted smoke detector. Y = DTc H5/3 / Q2/3 Y=
13.41
X = 4.6 10-4 Y2 + 2.7 10-15 Y6 X= 0.08 Smoke Detector Response Time Calculation tactivation = X H4/3/Q1/3 tactivation =
0.26 sec
Summary of Results Calculation Method METHOD OF ALPERT METHOD OF MOWRER METHOD OF MILKE
Smoke Detector Response Time (sec) 0.42 0.74 0.26
NOTE
The above calculations are based on principles developed in the NFPA Fire Protection Handbook 19th Edition, 2003, method described in Fire Technology, 1990, and NFPA 92B, "Guide for Smoke Management Systems in Atria, and Large Areas," 2000 Edition, Section A.3.4. Calculations are based on certain assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive capabili for a given situationsand, and should only be interpreted by an informed . 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 spreadsheet, please send an email to [email protected].
Prepared by:
Date
Checked by:
Date
Additional Information
Revision Log 1805.0 Original issue with final text.
Description of Revision
ESPONSE TIME
TER BOXES. values specified in the input a wrong entry in a cell(s).
1000.00 kW
r 1/2√2 of the listed spacing**
10.00 ft 13.00 86.00 5.00 77.00
947.82 Btu/sec 3.05 m
ft
3.96 m
°F
30.00 °C
(m-sec)1/2 °F
25.00 °C 298.00 K
0.70 0.67 1.2 18.00 °F
Calculate
h a fixed activation temperature
for r/H ≤ 0.18 for r/H > 0.18
o the detector (m)
10 °C
134.28
for r/H ≤ 0.15 for r/H > 0.15
o the detector (m)
6.07
Answer
ppression," Fire Technology, August 1990, p. 244.
o the detector (m)
Answer
re Technology, August 1990, p. 223.
ge Areas," 2000 Edition, Section A.3.4.
ling for smoke detector to activate (°F)
cation effects can be calculated. g correlation to estimate smoke
h a plume can rise (ft)
etween the fuel location and ceiling level (°F)
Location and Ceiling Level
etween the fuel location and ceiling level (°F)
13.03 ft
g mounted smoke detector.
Answer
the NFPA Fire Protection Handbook 19th Edition, A 92B, "Guide for Smoke Management Systems in Malls, tions are based on certain assumptions and ay or may not have reasonable predictive capabilities n informed . ed with the results of hand calculation,
eport an error(s) in the spreadsheet,
Organization Organization
Date January 2005
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
CHAPTER 10. ESTIMATING SPRINKLER RESPONSE TIME Version 1805.0 The following calculations estimate sprinkler activation time. Parameters in YELLOW CELLS are Entered by the . Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Sprinkler 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.
INPUT PARAMETERS Heat Release Rate of the Fire (Q) (Steady State) Sprinkler Response Time Index (RTI) Activation Temperature of the Sprinkler (Tactivation) Height of Ceiling above Top of Fuel (H) Radial Distance to the Detector (r) **never more than 0.707 or 1/2√2 of the listed spacing** Ambient Air Temperature (Ta) Convective Heat Release Rate Fraction (cc) r/H =
1.00
GENERIC SPRINKLER RESPONSE TIME INDEX (RTI)* Common Sprinkler Type
Generic Response Time Index (RTI) (m-sec)1/2
Standard response bulb Standard response link Quick response bulb Quick response link Specified Value
235 130 42 34 Enter Value
Reference: Madrzykowski, D., "Evaluation of Sprinkler Activation Prediction Methods" ASIAFLAM'95, International Conference on Fire Science and Engineering, 1 st Proceeding, March 15-16, 1995, Kowloon, Hong Kong, pp. 211-218.
*Note: The actual RTI should be used when the value is available.
GENERIC SPRINKLER TEMPERATURE RATING (Tactivation)* Temperature Classification Ordinary Intermediate High Extra high Very extra high Ultra high Ultra high Specified Value
Range of Temperature Ratings (°F) 135 to 170 175 to 225 250 to 300 325 to 375 400 to 475 500 to 575 650 –
Reference: Automatic Sprinkler Systems Handbook, 6 th Edition, National Fire Protection Association, Quincy, Massachusetts, 1994, Page 67.
*Note: The actual temperature rating should be used when the value is available.
12
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
ESTIMATING SPRINKLER RESPONSE TIME Reference: NFPA Fire Protection Handbook, 19 th Edition, 2003, Page 3-140.
tactivation = (RTI/(√ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation)) Where
tactivation = sprinkler activation response time (sec) RTI = sprinkler response time index (m-sec)1/2 ujet = ceiling jet velocity (m/sec) Tjet = ceiling jet temperature (°C) Ta = ambient air temperature (°C) Tactivation = activation temperature of sprinkler (°C)
Ceiling Jet Temperature Calculation Tjet - Ta = 16.9 (Qc)2/3/H5/3 Tjet - Ta = 5.38 (Qc/r)2/3/H Where
Tjet = ceiling jet temperature (°C) Ta = ambient air temperature (°C) Qc = convective portion of the heat release rate (kW) H = height of ceiling above top of fuel (m) r = radial distance from the plume centerline to the sprinkler (m)
Convective Heat Release Rate Calculation Qc = cc Q Where
Qc = convective portion of the heat release rate (kW) Q = heat release rate of the fire (kW) cc = convective heat release rate fraction
Qc =
700 kW
Radial Distance to Ceiling Height Ratio Calculation r/H = 1.00 r/H > 0.15 Tjet - Ta =
{5.38 (Qc/r)^2/3}/H
Tjet - Ta =
68.46
Tjet =
93.46 (°C)
Ceiling Jet Velocity Calculation ujet = 0.96 (Q/H)1/3 ujet = (0.195 Q1/3 H1/2)/r5/6 Where
ujet = ceiling jet velocity (m/sec) Q = heat release rate of the fire (kW) H = height of ceiling above top of fuel (m) r = radial distance from the plume centerline to the sprinkler (m)
Radial Distance to Ceiling Height Ratio Calculation r/H = 1.00 r/H > 0.15 ujet =
(0.195 Q^1/3 H^1/2)/r^5/6
ujet =
1.354
m/sec
13
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
Sprinkler Activation Time Calculation tactivation = (RTI/(√ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation)) tactivation = 139.89 sec The sprinkler will respond in approximately
NOTE: If tactivation = "NUM" Sprinkler does not activate NOTE The above calculations are based on principles developed in the NFPA Fire Protection Handbook 19th Edition, 2003. 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 . 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 spreadsheet, please send an email to [email protected].
Prepared by:
Date
Checked by:
Date
Additional Information
Revision Log Description of Revision 1805.0 Original issue with final text.
14
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
15
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
RESPONSE TIME
from the DROP DOWN MENU for the Sprinkler Selected. et and based on values specified in the input id errors due to a wrong entry in a cell(s).
re than 0.707 or 1/2√2 of the listed spacing**
1000.00 130 165 9.80 9.80 77.00
kW (m-sec)1/2 °F
73.89 °C
ft
2.99 m
ft
2.99 m
°F
25.00 °C 298.00 K
0.70
Calculate
Select Type of Sprinkler Standard response link
Scroll to desired sprinkler type then Click on selection
tivation Prediction Methods"
and Engineering, 1 st Proceeding,
the value is available. Generic Temperature Ratings (°F) 165 212 275 350 450 550 550 Enter Value
Select Sprinkler Classification Ordinary
Scroll to desired sprinkler class then Click on selection
Edition, National Fire Protection
d be used when the value is available.
16
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
for r/H ≤ 0.18 for r/H > 0.18
release rate (kW)
centerline to the sprinkler (m)
release rate (kW)
for r/H ≤ 0.15 for r/H > 0.15
centerline to the sprinkler (m)
17
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
2.33 minutes
Answer
does not activate
s developed in the NFPA Fire Protection Handbook certain assumptions and have inherent limitations. ot have reasonable predictive capabilities for a given
has been verified with the results of hand calculation, of these calculations. gestions, or to report an error(s) in the spreadsheet,
Organization Organization
Date January 2005
18
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
19
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
CHAPTER 12. ESTIMATING HEAT DETECTOR RESPONSE TIME
Version 1805.0 The following calculations estimate fixed temperature heat detector activation time. Parameters in YELLOW CELLS are Entered by the . Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Detector 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.
INPUT PARAMETERS Heat Release Rate of the Fire (Q) (Steady State) Radial Distance to the Detector (r) **never more than 0.707 or 1/2√2 of the listed spacing** Activation Temperature of the Fixed Temperature Heat Detector (T activation) Detector Response Time Index (RTI) Height of Ceiling above Top of Fuel (H) Ambient Air Temperature (Ta) Convective Heat Release Fraction (cc) r/H =
0.20
INPUT DATA FOR ESTIMATING HEAT DETECTOR RESPONSE TIME Activation Temperature Tactivation UL Listed Spacing r (ft) 10 15 20 25 30 40 50 70 Specified Value
Response Time Index RTI (m-sec)1/2
UL Listed Spacing r (ft) 10 15 20 25 30 40 50 70 Specified Value
Response Time Index RTI (m-sec)1/2
490 306 325 152 116 87 72 44 Enter Value
404 233 165 123 98 70 54 20 Enter Value 29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
UL Listed Spacing r (ft) 10 15 20 25 30 40 50 70 Specified Value
Response Time Index RTI (m-sec)1/2
UL Listed Spacing r (ft) 10 15 20 25 30 40 Specified Value
Response Time Index RTI (m-sec)1/2
UL Listed Spacing r (ft) 10 15 20 25 30 Specified Value
Response Time Index RTI (m-sec)1/2
UL Listed Spacing r (ft) 10 15 20 Specified Value
Response Time Index RTI (m-sec)1/2
321 191 129 96 75 50 37 11 Enter Value
239 135 86 59 44 22 Enter Value
196 109 64 39 27 Enter Value
119 55 21 Enter Value
Reference: NFPA Standard 72, National Fire Alarm Code, Appendix B, Table B-3.2.5.1, 1999, Edition .
ESTIMATING FIXED TEMPERATURE HEAT DETECTOR RESPONSE TIME Reference: NFPA Fire Protection Handbook, 19 th Edition, 2003, Page 3-140.
tactivation = ( RTI/(√ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation)) Where
tactivation = detector activation time (sec) RTI = detector response time index (m-sec)1/2 ujet = ceiling jet velocity (m/sec) Tjet = ceiling jet temperature (°C) Ta = ambient air temperature (°C) Tactivation = activation temperature of detector (°C)
Ceiling Jet Temperature Calculation Tjet - Ta = 16.9 (Qc)2/3/H5/3 29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering andjet SpecialaProjects Section c
T
- T = 5.38 (Q /r)2/3/H Tjet = ceiling jet temperature (°C)
Where
Ta = ambient air temperature (°C) Qc = convective portion of the heat release rate (kW) H = height of ceiling above top of fuel (m) r = radial distance from the plume centerline to the detector (m) Convective Heat Release Rate Calculation Qc = cc Q Qc = convective heat release rate (kW) Q = heat release rate of the fire (kW) cc = convective heat release fraction
Where
Qc =
4004 kW
Radial Distance to Ceiling Height Ratio Calculation r/H = 0.20 r/H > 0.15 >0.15 Tjet - Ta =
194.99
<0.15
5.38 ((Qc/r)^2/3)/H
Tjet - Ta =
194.99
Tjet =
219.99 (°C)
Ceiling Jet Velocity Calculation ujet = 0.96 (Q/H)1/3 ujet = (0.195 Q1/3 H1/2)/r5/6 Where
ujet = ceiling jet velocity (m/sec) Q = heat release rate of the fire (kW) H = height of ceiling above top of fuel (m) r = radial distance from the plume centerline to the detector (m)
Radial Distance to Ceiling Height Ratio Calculation r/H = 0.20 r/H > 0.15 ujet =
(0.195 Q^1/3 H^1/2)/r^(5/6)
ujet =
7.300
m/sec
Detector Activation Time Calculation tactivation = ( RTI/(√ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation)) tactivation = 27.01 sec The detector will respond in approximately
NOTE: If tactivation = "NUM" Detector does not activate NOTE
The above calculations are based on principles developed in the NFPA Fire Protection Handbook 19th Edition 2003. 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 . Although each calculation in the spreadsheet has been verified with the results of hand calculation, 29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
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 spreadsheet, please send an email to [email protected].
Prepared by:
Date
Checked by:
Date
Additional Information
Revision Log Description of Revision 1805.0 Original issue with final text.
29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
ECTOR RESPONSE TIME
detector activation time.
d from the DROP DOWN MENU for the Detector Selected. heet and based on values specified in the input void errors due to a wrong entry in a cell(s).
5720.00 kW
re than 0.707 or 1/2√2 of the listed spacing** ure Heat Detector (T activation)
4.00 135 404.00 20.00 77.00
ft
1.22 m
°F
57.22 °C
(m-sec)1/2 ft
6.10 m
°F
25.00 °C 298.00 K
0.70
Calculate
RESPONSE TIME
Activation Temperature (°F) 128 128 128 128 128 128 128 128 Enter Value Activation Temperature (°F) 135 135 135 135 135 135 135 135 Enter Value
Select Detector Spacing Scroll to desired spacing then Click on selection
Select Detector Spacing 10
Scroll to desired spacing then Click on selection
29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
Activation Temperature (°F) 145 145 145 145 145 145 145 145 Enter Value Activation Temperature (°F) 160 160 160 160 160 160 Enter Value Activation Temperature (°F) 170 170 170 170 170 Enter Value Activation Temperature (°F) 196 196 196 Enter Value
Select Detector Spacing Scroll to desired spacing then Click on selection
Select Detector Spacing Scroll to desired spacing then Click on selection
Select Detector Spacing Scroll to desired spacing then Click on selection
Select Detector Spacing Scroll to desired spacing then Click on selection
, Appendix B, Table B-3.2.5.1, 1999, Edition .
TECTOR RESPONSE TIME
n, 2003, Page 3-140.
ure of detector (°C)
for r/H ≤ 0.18 29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
for r/H > 0.18
heat release rate (kW)
me centerline to the detector (m)
209.48
for r/H ≤ 0.15 for r/H > 0.15
me centerline to the detector (m)
0.45 minutes
Answer
does not activate
s developed in the NFPA Fire Protection Handbook 19th Edition, mptions and have inherent limitations. ot have reasonable predictive capabilities for a given situation,
has been verified with the results of hand calculation, 29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
of these calculations. gestions, or to report an error(s) in the spreadsheet,
Organization Organization
Date January 2005
29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
29
Office of Nuclear Reactor Regulation Division of Systems Safety and Analysis Plant Systems Branch Fire Protection Engineering and Special Projects Section
29
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