10 detector activation time

CHAPTER 11. ESTIMATING SMOKE DETECTOR RESPONSE TIMEVersion 1805.0The 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 inputparameters. 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)

Height of Ceiling above Top of Fuel (H)

Smoke Detector Response Time Index (RTI)

for Smoke Detector to Activater/H = 0.77

ESTIMATING SMOKE DETECTOR RESPONSE TIMEMETHOD OF ALPERT

This method assume smoke detector is a low RTI device with a fixed activation temperatureWhere

Ceiling Jet Temperature Calculation

Where

Radial Distance to the Detector (r) **never more than 0.707 or 1/22 of the listed spacing**

Activation Temperature of the Smoke Detector (Tactivation)

Ambient Air Temperature (Ta)

Convective Heat Release Rate Fraction c)Plume Leg Time Constant (Cpl) (Experimentally Determined)Ceiling Jet Lag Time Constant (Ccj) (Experimentally Determined)Temperature Rise of Gases Under the Ceiling (Tc)

Reference: NFPA Fire Protection Handbook, 19th Edition, 2003, Page 3-140.tactivation = (RTI/(ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation))

tactivation = detector activation time (sec)RTI = detector response time index (m-sec)1/2ujet = ceiling jet velocity (m/sec)Tjet = ceiling jet temperature (C)Ta = ambient air temperature (C)Tactivation = activation temperature of detector (C)

Tjet - Ta = 16.9 (Qc)2/3/H5/3

Tjet - Ta = 5.38 (Qc/r)2/3/HTjet = 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

WhereQ = heat release rate of the fire (kW)

700 kW

Radial Distance to Ceiling Height Ratio Calculationr/H = 0.77 r/H > 0.15

>0.15 50.92 0.15

>0.15 1.53

Transport Lag Time of Plume Calculation

Where

H = height of ceiling above top of fuel (m)Q = heat release rate of the fire (kW)

0.42 sec

Transport Lag Time of Ceiling Jet Calculation

Where

r = radial distance from the plume centerline to the detector (m)H = height of ceiling above top of fuel (m)Q = heat release rate of the fire (kW)

0.32 sec

Smoke Detector Response Time Calculation

0.74 sec

METHOD OF MILKE

NFPA 92B, "Guide for Smoke Management Systems in Mall, Atria, and Large Areas," 2000 Edition, Section A.3.4.

Where

H = height of ceiling above top of fuel (ft)Q = heat release rate from steady fire (Btu/sec)

Where

Before estimating smoke detector response time, stratification effects can be calculated.NFPA 92B, 2000 Edition, Section A.3.4 provides following correlation to estimate smokestratification in a compartment.

Where

tcj = transport lag time of ceiling jet (sec)

tpl = Cpl (H)4/3/(Q)1/3

tpl = transport lag time of plume (sec)Cpl = plume lag time constant

tpl =

tcj = (r)11/6/(Ccj) (Q)1/3 (H)1/2

tcj = transport lag time of ceiling jet (sec)Ccj = ceiling jet lag time constant

tcj =

tactivation = tpl + tcjtactivation =

References: Milke, J., "Smoke Management for Covered Malls and Atria," Fire Technology, August 1990, p. 223.

tactivation = X H4/3/Q1/3

tactivation = detector activation time (sec)X = 4.6 10-4 Y2 + 2.7 10-15 Y6

Y = Tc H5/3 / Q2/3

Tc = temperature rise of gases under the ceiling for smoke detector to activate (F)

Hmax = 74 Qc2/5 / Tf->c3/5

Hmax = the maximum ceiling clearance to which a plume can rise (ft)


Where Q = heat release rate of the fire (Btu/sec)

663.47 Btu/sec

Difference in Temperature Due to Fire Between the Fuel Location and Ceiling Level

Where

H = ceiling height above the fire source (ft)1375.90 F

Smoke Stratification Effects

13.03 ftIn this case the highest point of smoke rise is estimated to beThus, the smoke would be expected to reach the ceiling mounted smoke detector.

Y = 13.41

X = 0.08

Smoke Detector Response Time Calculation

0.26

Calculation Method Smoke Detector Response Time (sec)METHOD OF ALPERT 0.42METHOD OF MOWRER 0.74METHOD OF MILKE 0.26

2003, method described in Fire Technology, 1990, and NFPA 92B, "Guide for Smoke Management Systems in Malls, Atria, and Large Areas," 2000 Edition, Section A.3.4. Calculations are based on certain assumptions and

Qc = convective portion of the heat release rate (Btu/sec)Tf->c = difference in temperature due to fire between the fuel location and ceiling level (F)

Qc = Q cQc = convective portion of the heat release rate (Btu/sec)

c = convective heat releas rate fractionQc =

Tf->c = 1300 Qc2/3 / H5/3

Tf->c = difference in temperature due to fire between the fuel location and ceiling level (F)Qc = convective portion of the heat release rate (Btu/sec)

Tf->c =

Hmax = 74 Qc2/5 / Tf->c3/5

Hmax =

Y = Tc H5/3 / Q2/3

X = 4.6 10-4 Y2 + 2.7 10-15 Y6

tactivation = X H4/3/Q1/3

tactivation = sec

The above calculations are based on principles developed in the NFPA Fire Protection Handbook 19

Summary of Results

NOTE

have inherent limitations. The results of such calculations may or may not have reasonable predictive capabilities for a given situationsand, 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 spreadsheet,please send an email to [email protected] or [email protected].

Prepared by: Date

Checked by: Date

Additional Information

Revision Log Description of Revision1805.0 Original issue with final text.

CHAPTER 11. ESTIMATING 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 inputparameters. This spreadsheet is protected and secure to avoid errors due to a wrong entry in a cell(s).

1000.00 kW 947.82 Btu/sec10.00 ft 3.05 m13.00 ft 3.96 m86.00 F 30.00 C

5.0077.00 F 25.00 C

298.00 K

0.700.671.2

18.00 F 10 C

Calculate

This method assume smoke detector is a low RTI device with a fixed activation temperature

for r/H 0.18for r/H > 0.18

**never more than 0.707 or 1/22 of the listed spacing**

(m-sec)1/2

r = radial distance from the plume centerline to the detector (m)

134.28

for r/H 0.15for r/H > 0.15


6.07

Mowrer, F., "Lag Times Associated With Fire Detection and Suppression," Fire Technology, August 1990, p. 244.

Answer


NFPA 92B, "Guide for Smoke Management Systems in Mall, Atria, and Large Areas," 2000 Edition, Section A.3.4.

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

Milke, J., "Smoke Management for Covered Malls and Atria," Fire Technology, August 1990, p. 223.

= temperature rise of gases under the ceiling for smoke detector to activate (F)

= the maximum ceiling clearance to which a plume can rise (ft)

Answer

Difference in Temperature Due to Fire Between the Fuel Location and Ceiling Level

13.03 ftThus, the smoke would be expected to reach the ceiling mounted smoke detector.

2003, method described in Fire Technology, 1990, and NFPA 92B, "Guide for Smoke Management Systems in Malls, Atria, and Large Areas," 2000 Edition, Section A.3.4. Calculations are based on certain assumptions and

= difference in temperature due to fire between the fuel location and ceiling level (F)

= difference in temperature due to fire between the fuel location and ceiling level (F)

The above calculations are based on principles developed in the NFPA Fire Protection Handbook 19 th Edition,

Answer

have inherent limitations. The results of such calculations may or may not have reasonable predictive capabilities for a given situationsand, and should only be interpreted by an informed user.Although each calculation in the spreadsheet has been verified with the results of hand calculation,

Any questions, comments, concerns, and suggestions, or to report an error(s) in the spreadsheet,

Organization

Organization

DateJanuary 2005

Office of Nuclear Reactor RegulationDivision of Systems Safety and AnalysisPlant Systems BranchFire Protection Engineering and Special Projects Section

19

CHAPTER 10. ESTIMATING SPRINKLER RESPONSE TIME Version 1805.0The following calculations estimate sprinkler activation time.Parameters in YELLOW CELLS are Entered by the User.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 inputparameters. 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)

Height of Ceiling above Top of Fuel (H)

r/H = 1.00

Common Sprinkler Type Generic Response

Standard response bulb 235Standard response link 130Quick response bulb 42Quick response link 34User Specified Value Enter Value

March 15-16, 1995, Kowloon, Hong Kong, pp. 211-218.*Note: The actual RTI should be used when the value is available.

Temperature Classification Range of TemperatureRatings (F)

Ordinary 135 to 170Intermediate 175 to 225High 250 to 300Extra high 325 to 375Very extra high 400 to 475Ultra high 500 to 575Ultra high 650User Specified Value

Activation Temperature of the Sprinkler (Tactivation)

Radial Distance to the Detector (r) **never more than 0.707 or 1/22Ambient Air Temperature (Ta)

Convective Heat Release Rate Fraction c)

GENERIC SPRINKLER RESPONSE TIME INDEX (RTI)*

Time Index (RTI) (m-sec)1/2

Reference: Madrzykowski, D., "Evaluation of Sprinkler Activation Prediction Methods"ASIAFLAM'95, International Conference on Fire Science and Engineering, 1st Proceeding,

GENERIC SPRINKLER TEMPERATURE RATING (Tactivation)*

Reference: Automatic Sprinkler Systems Handbook, 6th Edition, National Fire Protection


20

Association, Quincy, Massachusetts, 1994, Page 67.*Note: The actual temperature rating should be used when the value is available.

ESTIMATING SPRINKLER RESPONSE TIME

Where


Where

H = height of ceiling above top of fuel (m)r = radial distance from the plume centerline to the sprinkler (m)



700 kW


{5.38 (Qc/r)^2/3}/H68.4693.46 (C)

Ceiling Jet Velocity Calculation

WhereQ = 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)


Reference: NFPA Fire Protection Handbook, 19th Edition, 2003, Page 3-140.tactivation = (RTI/(ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation))

tactivation = sprinkler activation response time (sec)RTI = sprinkler response time index (m-sec)1/2ujet = ceiling jet velocity (m/sec)Tjet = ceiling jet temperature (C)Ta = ambient air temperature (C)Tactivation = activation temperature of sprinkler (C)

Tjet - Ta = 16.9 (Qc)2/3/H5/3


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

c = convective heat release rate fractionQc =

Tjet - Ta = Tjet - Ta = Tjet =

ujet = 0.96 (Q/H)1/3

ujet = (0.195 Q1/3 H1/2)/r5/6

ujet = ceiling jet velocity (m/sec)


21

(0.195 Q^1/3 H^1/2)/r^5/61.354 m/sec

Sprinkler Activation Time Calculation

139.89 secThe sprinkler will respond in approximately

The above calculations are based on principles developed in the NFPA Fire Protection Handbook

The results of such calculations may or may not have reasonable predictive capabilities for a givensituation, 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 spreadsheet,please send an email to [email protected] or [email protected].

Prepared by: Date

Checked by: Date


ujet = ujet =

tactivation = (RTI/(ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation))tactivation =

NOTE: If tactivation = "NUM" Sprinkler does not activate

19th Edition, 2003. Calculations are based on certain assumptions and have inherent limitations.

NOTE


22

Revision Log Description of Revision1805.0 Original issue with final text.


23

CHAPTER 10. ESTIMATING SPRINKLER RESPONSE TIME

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 inputparameters. This spreadsheet is protected and secure to avoid errors due to a wrong entry in a cell(s).

1000.00 kW130165 F 73.89 C9.80 ft 2.99 m9.80 ft 2.99 m

77.00 F 25.00 C298.00 K

0.70Calculate

Select Type of Sprinkler

*Note: The actual RTI should be used when the value is available.

Generic Temperature Select Sprinkler ClassificationRatings (F)165212275350450550550Enter Value

(m-sec)1/2

**never more than 0.707 or 1/22 of the listed spacing**

Scroll to desired sprinkler type then Click on selection

Madrzykowski, D., "Evaluation of Sprinkler Activation Prediction Methods"ASIAFLAM'95, International Conference on Fire Science and Engineering, 1st Proceeding,

Scroll to desired sprinkler classthen Click on selection

Edition, National Fire Protection


24

*Note: The actual temperature rating should be used when the value is available.

for r/H 0.18for r/H > 0.18

r = radial distance from the plume centerline to the sprinkler (m)

for r/H 0.15for r/H > 0.15

r = radial distance from the plume centerline to the sprinkler (m)

= convective portion of the heat release rate (kW)



25

2.33 minutes

The above calculations are based on principles developed in the NFPA Fire Protection Handbook

The results of such calculations may or may not have reasonable predictive capabilities for a given

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,

Organization

Organization

= "NUM" Sprinkler does not activate

Edition, 2003. Calculations are based on certain assumptions and have inherent limitations.

Answer


26

DateJanuary 2005


41

CHAPTER 12. ESTIMATING HEAT DETECTOR RESPONSE TIME Version 1805.0The following calculations estimate fixed temperature heat detector activation time.Parameters in YELLOW CELLS are Entered by the User.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 inputparameters. 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)

Detector Response Time Index (RTI)Height of Ceiling above Top of Fuel (H)

r/H = 0.20

INPUT DATA FOR ESTIMATING HEAT DETECTOR RESPONSE TIME

Activation

UL Listed Spacing Response Time Indexr (ft)10 49015 30620 32525 15230 11640 8750 7270 44User Specified Value Enter Value

UL Listed Spacing Response Time Indexr (ft)10 40415 23320 16525 12330 9840 7050 5470 20

Radial Distance to the Detector (r) **never more than 0.707 or 1/22 of the listed spacing**Activation Temperature of the Fixed Temperature Heat Detector (T

Ambient Air Temperature (Ta)

Convective Heat Release Fraction c)

Temperature Tactivation

RTI (m-sec)1/2

RTI (m-sec)1/2

T= 128 F

T= 135 F


41

User Specified Value Enter Value

UL Listed Spacing Response Time Indexr (ft)10 32115 19120 12925 9630 7540 5050 3770 11User Specified Value Enter Value

UL Listed Spacing Response Time Indexr (ft)10 23915 13520 8625 5930 4440 22User Specified Value Enter Value

UL Listed Spacing Response Time Indexr (ft)10 19615 10920 6425 3930 27User Specified Value Enter Value

UL Listed Spacing Response Time Indexr (ft)10 11915 5520 21User Specified Value Enter Value

ESTIMATING FIXED TEMPERATURE HEAT DETECTOR RESPONSE TIME

Where

RTI (m-sec)1/2

RTI (m-sec)1/2

RTI (m-sec)1/2

RTI (m-sec)1/2

Reference: NFPA Standard 72, National Fire Alarm Code, Appendix B, Table B-3.2.5.1, 1999, Edition.

Reference: NFPA Fire Protection Handbook, 19th Edition, 2003, Page 3-140.tactivation = ( RTI/(ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation))

tactivation = detector activation time (sec)RTI = detector response time index (m-sec)1/2ujet = ceiling jet velocity (m/sec)Tjet = ceiling jet temperature (C)Ta = ambient air temperature (C)

T= 145 F

T= 160 F

T= 170 F

T= 196 F


41


Where

H = height of ceiling above top of fuel (m)r = radial distance from the plume centerline to the detector (m)



4004 kW


>0.15 194.99 0.15

(0.195 Q^1/3 H^1/2)/r^(5/6)7.300 m/sec

Detector Activation Time Calculation

27.01 secThe detector will respond in approximately

Tactivation = activation temperature of detector (C)

Tjet - Ta = 16.9 (Qc)2/3/H5/3


Qc = c QQc = convective heat release rate (kW)

c = convective heat release fractionQc =

Tjet - Ta = Tjet - Ta = Tjet =

ujet = 0.96 (Q/H)1/3

ujet = (0.195 Q1/3 H1/2)/r5/6

ujet = ceiling jet velocity (m/sec)

ujet = ujet =

tactivation = ( RTI/(ujet)) (ln (Tjet - Ta)/(Tjet - Tactivation))tactivation =

NOTE: If tactivation = "NUM" Detector does not activate

NOTE


41

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

Prepared by: Date

Checked by: Date


Revision Lo Description of Revision1805.0 Original issue with final text.

The above calculations are based on principles developed in the NFPA Fire Protection Handbook 19

NOTE


41


41

CHAPTER 12. ESTIMATING HEAT DETECTOR RESPONSE TIME

The following calculations estimate fixed temperature heat detector activation time.

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 inputparameters. This spreadsheet is protected and secure to avoid errors due to a wrong entry in a cell(s).

5720.00 kW4.00 ft 1.22 m135 F 57.22 C

404.0020.00 ft 6.10 m77.00 F 25.00 C

298.00 K

0.70Calculate

INPUT DATA FOR ESTIMATING HEAT DETECTOR RESPONSE TIME

ActivationTemperature (F) Select Detector Spacing128128128128128128128128Enter Value

ActivationTemperature (F) Select Detector Spacing135135135135135135135135

**never more than 0.707 or 1/22 of the listed spacing**Activation Temperature of the Fixed Temperature Heat Detector (Tactivation)

(m-sec)1/2

Scroll to desired spacing thenClick on selection



41

Enter Value





ESTIMATING FIXED TEMPERATURE HEAT DETECTOR RESPONSE TIME




Scroll to desired spacing then

Click on selectionNFPA Standard 72, National Fire Alarm Code, Appendix B, Table B-3.2.5.1, 1999, Edition.


41

for r/H 0.18for r/H > 0.18


209.48

for r/H 0.15for r/H > 0.15


0.45 minutes

= activation temperature of detector (C)


= "NUM" Detector does not activate Answer


41

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,

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,

Organization

Organization

DateJanuary 2005

The above calculations are based on principles developed in the NFPA Fire Protection Handbook 19 th Edition,


41


41

Smoke_DetectorSprinklerFTHDetector

CommandButton4: CommandButton5: CommandButton1: CommandButton2: CommandButton3: CommandButton1_2: ComboBox1: ComboBox2: CommandButton2_2: OptionButton1: Off

OptionButton2: Off

OptionButton3: Off

OptionButton4: Off

OptionButton5: Off

OptionButton6: Off

CommandButton1_3: CommandButton1_4: ComboBox2_2: CommandButton2_3:

10 detector activation time

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