10 sprinkler 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 Activate

r/H = 0.77

ESTIMATING SMOKE DETECTOR RESPONSE TIMEMETHOD OF ALPERT

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

Where

Ceiling Jet Temperature Calculation

Where

Radial Distance to the Detector (r) **never more than 0.707 or 1/2√2 of the listed spacing**

Activation Temperature of the Smoke Detector (Tactivation)

Ambient Air Temperature (Ta)

Convective Heat Release Rate Fraction (cc)

Plume Leg Time Constant (Cpl) (Experimentally Determined)

Ceiling Jet Lag Time Constant (Ccj) (Experimentally Determined)

Temperature Rise of Gases Under the Ceiling (DTc)

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)1/2

ujet = 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/H



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

5.38 ((Qc/r)^2/3)/H

50.92

75.92 (°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 detector (m)


>0.15 1.53 <0.15

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

1.533 m/sec

Smoke Detector Response Time Calculation

0.42 sec

METHOD OF MOWRER

Where

Qc = cc Q


cc = convective heat release rate fraction

Qc =

Tjet - Ta =

Tjet - Ta =

Tjet =

ujet = 0.96 (Q/H)1/3

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


ujet =

ujet =


tactivation =

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

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

tactivation = tpl + tcj


tpl = transport lag time of plume (sec)

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


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 + tcj

tactivation =

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

tactivation = X H4/3/Q1/3


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

Y = DTc H5/3 / Q2/3

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

Hmax = 74 Qc2/5 / DTf->c

3/5

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 ft

In 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


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)

DTf->c = difference in temperature due to fire between the fuel location and ceiling level (°F)

Qc = Q cc


cc = convective heat releas rate fraction

Qc =

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

DTf->c = difference in temperature due to fire between the fuel location and ceiling level (°F)


DTf->c =

Hmax = 74 Qc2/5 / DTf->c

3/5

Hmax =

Y = DTc 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 th Edition,

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 Revision

1805.0 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/sec

10.00 ft 3.05 m

13.00 ft 3.96 m

86.00 °F 30.00 °C

5.00

77.00 °F 25.00 °C

298.00 K

0.70

0.67

1.2

18.00 °F 10 °C

Calculate

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

for r/H ≤ 0.18

for r/H > 0.18

**never more than 0.707 or 1/2√2 of the listed spacing**

(m-sec)1/2

F13

This default value (86 °F) is the most appropriate value for the majority of analyses. You may change this value for your specific application. If you change this value please ensure that it is appropriate.

F14

This default value (5.0) is the most appropriate value for the majority of analyses. You may change this value for your specific application. If you change this value please ensure that it is appropriate.

F17


F20

This default value (18 °F) is the most appropriate value for the majority of analyses. You may change this value for your specific application. If you change this value please ensure that it is appropriate.


134.28

for r/H ≤ 0.15

for 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 ft

Thus, 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)


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

Date

January 2005

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

14

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 170

Intermediate 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)



Convective Heat Release Rate Fraction (cc)

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


15

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}/H

68.46

93.46 (°C)


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)

Radial Distance to Ceiling Height Ratio Calculation



tactivation = sprinkler activation response time (sec)

RTI = sprinkler response time index (m-sec)1/2




Tactivation = activation temperature of sprinkler (°C)

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

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




Qc = cc Q


cc = convective heat release rate fraction

Qc =

Tjet - Ta =

Tjet - Ta =

Tjet =

ujet = 0.96 (Q/H)1/3

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



16

r/H = 1.00 r/H > 0.15

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

1.354 m/sec

Sprinkler Activation Time Calculation

139.89 sec

The 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 =

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

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

NOTE


17

Revision Log Description of Revision



18

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 kW

130

165 °F 73.89 °C

9.80 ft 2.99 m

9.80 ft 2.99 m

77.00 °F 25.00 °C

298.00 K

0.70

Calculate

Select Type of Sprinkler

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

Generic Temperature Select Sprinkler ClassificationRatings (°F)

165

212275350450550550Enter Value

(m-sec)1/2


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 class

then Click on selection

Edition, National Fire Protection

F18



19

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

for r/H ≤ 0.18

for r/H > 0.18

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

for r/H ≤ 0.15

for r/H > 0.15

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

= convective portion of the heat release rate (kW)



20

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


21

Date

January 2005


32

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 Index

r (ft)10 490

15 306

20 32525 15230 11640 8750 7270 44User Specified Value Enter Value


r (ft)10 404

15 233

20 16525 12330 9840 7050 5470 20


Activation Temperature of the Fixed Temperature Heat Detector (Tactivation)


Convective Heat Release Fraction (cc)

Temperature Tactivation

RTI (m-sec)1/2

RTI (m-sec)1/2

T= 128 F

T= 135 F


32

User Specified Value Enter Value


r (ft)10 321

15 191

20 12925 9630 7540 5050 3770 11User Specified Value Enter Value


r (ft)10 239

15 135

20 8625 5930 4440 22User Specified Value Enter Value


r (ft)10 196

15 109

20 6425 3930 27User Specified Value Enter Value


r (ft)10 119

15 55

20 21

User 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.


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


RTI = detector response time index (m-sec)1/2




T= 145 F

T= 160 F

T= 170 F

T= 196 F


32


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

5.38 ((Qc/r)^2/3)/H

194.99

219.99 (°C)


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 detector (m)


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

7.300 m/sec

Detector Activation Time Calculation

27.01 sec

The detector will respond in approximately

Tactivation = activation temperature of detector (°C)

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

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




Qc = cc Q

Qc = convective heat release rate (kW)

cc = convective heat release fraction

Qc =

Tjet - Ta =

Tjet - Ta =

Tjet =

ujet = 0.96 (Q/H)1/3

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


ujet =

ujet =

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

tactivation =

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

NOTE


32

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 Revision



NOTE


32


32

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 kW

4.00 ft 1.22 m

135 °F 57.22 °C

404.0020.00 ft 6.10 m

77.00 °F 25.00 °C

298.00 K

0.70

Calculate

INPUT DATA FOR ESTIMATING HEAT DETECTOR RESPONSE TIME

Activation

Temperature (°F) Select Detector Spacing128

128

128128128128128128Enter Value

Activation


135

135135135135135135


Activation Temperature of the Fixed Temperature Heat Detector (Tactivation)(m-sec)1/2

Scroll to desired spacing then

Click on selection


Click on selection

F18



32

Enter Value

Activation


145

145145145145145145Enter Value

Activation


160

160160160160Enter Value

Activation


170

170170170Enter Value

Activation


196

196

Enter Value

ESTIMATING FIXED TEMPERATURE HEAT DETECTOR RESPONSE TIME


Click on selection


Click on selection


Click on selection


Click on selection

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


32

for r/H ≤ 0.18

for r/H > 0.18


209.48

for r/H ≤ 0.15

for r/H > 0.15


0.45 minutes

= activation temperature of detector (°C)


= "NUM" Detector does not activate

Answer


32

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

Date

January 2005



32

10 sprinkler activation time

Documents

reasonable

special projects

heat release

avoid errors

ambient air

ul listed

subsequent

smoke management