Heskestad Delichatsios and Beyler approach

Additionally assume an ambient room temperature of 22oC. Use gravity specific heat density of air and other constant values as provided in NFPA 72 Table B.7. Base calculations on a worst case scenario where a fire is centered between four detectors. Remember to account for ceiling height where necessary. The fire scenario for this problem will involve a chair with burning characteristics similar to that of chair F26 under test number 25 in Table B.2.3.2.6.2(e) of NFPA 72. Use FM’s time constant (τ0) for the given listed 15 ft spacing to determine the sprinkler RTI (Table B.3.2.5 NFPA 72). ft spacing of smoke detectors would provide advance detection over listed 15 ft spacing heat detectors. For the analysis assume an ambient temperature of 22°C and that the ceiling is smooth and flat. Assume ΔT is 5°C between the floor and ceiling. If needed use the values given in NFPA 72 Table B.7 for gravity specific heat of air and density of air. Assume worse-case scenario regarding fire location (centered between 4 detectors).

The fire scenario will involve a chair with burning characteristics similar to that of chair F26 under test number 25 in Table B.2.3.2.6.2(e) of NFPA 72. The chair cushion (5% of the mass of the chair) is made out of polyurethane foam with burning characteristics similar to that of PU foam GM21 in Table A.39 of the SFPE handbook (5th). Assume optical density properties of the polyurethane as provided in SFPE HB (4th) Table 2-13.5. 4. The owner of the building is concerned about the potential for a car fire in front of the entrance to ignite materials inside of the building if the front door is open. Assuming the front door is open and the chair described above is 1 m from the door opening in the lobby and the car is 2 m from the door opening outside of the building: Requirements: short answer a) Determine the heat detector activation times using Alpert’s correlations and the steady-state approach (assume a steady HRR of 800 kW). b) Assuming t2 fire growth and a convective heat release fraction of 70% determine heat detector activation times using the following approaches:Quasi-steady state with an initial time step Δt=5s. Perform a sensitivity analysis with at least two other time steps. Plot and compare the HRR and detector temperatures for all three time steps. For each iteration use the midpoint HRR value for the given time step.For example:First step (t=0 to t=5): HRR = α(Δt/2)2 = α(5/2)2Second step (t=5 to t=10): HRR = α(t1 +Δt/2)2 = α(5 + 5/2)2Method developed by Heskestad Delichatsios and Beyler (NFPA 72 Figure B.3.3.4.4 provides a helpful methodology). Quasi-steady state with an initial time step Δt=5s. Perform a sensitivity analysis with at least two other time steps. Plot and compare the HRR and detector temperatures for all three time steps. For each iteration use the midpoint HRR value for the given time step.For example:First step (t=0 to t=5): HRR = α(Δt/2)2 = α(5/2)2Second step (t=5 to t=10): HRR = α(t1 +Δt/2)2 = α(5 + 5/2)2 Method developed by Heskestad Delichatsios and Beyler (NFPA 72 Figure B.3.3.4.4 provides a helpful methodology).

c) Plot and compare the HRR gas and detector temperatures as a function of time for both methods used in (b). For the quasi-steady method only use the results for Δt=5s. d) Identify the limitations and assumptions inherent to each approach taken in (a) & (b) for calculating heat detection times. Assume the authority having jurisdiction requires that heat detection occurs at a HRR of no greater than 475 kW.a) Using the method developed by Heskestad Delichatsios and Beyler determine the required heat detector spacing to satisfy this requirement (based on same information as provided in (1)). Comment on the feasibility of this design.b) Assuming the detector activation temperature remains 57.2°C (135°F) and that the minimum feasible spacing for the heat detectors is 2.49m x 2.49m what measures could be taken to still meet the requirement of detection at 475 kW (Hint: think detector performance)? Support your answer by using the Heskestad Delichatsios and Beyler approach. a) Using the method developed by Heskestad Delichatsios and Beyler determine the required heat detector spacing to satisfy this requirement (based on same information as provided in (1)). Comment on the feasibility of this design. b) Assuming the detector activation temperature remains 57.2°C (135°F) and that the minimum feasible spacing for the heat detectors is 2.49m x 2.49m what measures could be taken to still meet the requirement of detection at 475 kW (Hint: think detector performance)? Support your answer by using the Heskestad Delichatsios and Beyler approach. The owner would now like to consider the benefit of installing smoke detectors within the enclosed roof deck space versus heat detectors. Specifically the owner questions whether the 30

a) Assuming use of the optical density approach that considers the entire volume of the roof deck what mass of smoke is required to be produced from the cushion if the detector is assumed to active at an optical density of 0.14 m-1? Assume the optical density outside and inside of the detector are the same. Based on information provided and this method to estimate response do you think there is enough fuel available in the cushion to result in the required optical density for detector response?

b) Determine smoke detector activation time assuming the cylindrical volume approach with-1detector activation at optical density of 0.14 m . Assume the time delay associated withsmoke lag into the detector is 25 seconds. State all assumptions.

c) Determine the minimum steady-state fire size required to have smoke reach the ceiling without stratifying and the minimum fire size required for the ceiling jet reach critical velocity for smoke detection. State all assumptions.

d) Identify critical limitations and assumptions inherent calculating smoke detection times.

a) Assuming you would specify a flame detector what type would you specify (e.g. UV IR UV/IR) and why?

b) Assuming you would mount the detector(s) near the hotel doorway what would you need to know about the response characteristics of the detector in to detect a pool fire under the car involving 1 gallon of gasoline? (Flame heat flux data such as from SFPE Hb Table 36.7 will be useful in developing your response.) a) Determine the heat detector activation times using Alpert’s correlations and the steady-state approach (assume a steady HRR of 800 kW).b) Assuming t2 fire growth and a convective heat release fraction of 70% determine heat detector activation times using the following approaches:Quasi-steady state with an initial time step Δt=5s. Perform a sensitivity analysis with at least two other time steps. Plot and compare the HRR and detector temperatures for all three time steps. For each iteration use the midpoint HRR value for the given time step.For example:First step (t=0 to t=5): HRR = α(Δt/2)2 = α(5/2)2Second step (t=5 to t=10): HRR = α(t1 +Δt/2)2 = α(5 + 5/2)2Method developed by Heskestad Delichatsios and Beyler (NFPA 72 Figure B.3.3.4.4 provides a helpful methodology).c) Plot and compare the HRR gas and detector temperatures as a function of time for both methods used in (b). For the quasi-steady method only use the results for Δt=5s.d) Identify the limitations and assumptions inherent to each approach taken in (a) & (b) for calculating heat detection times. Quasi-steady state with an initial time step Δt=5s. Perform a sensitivity analysis with at least two other time steps. Plot and compare the HRR and detector temperatures for all three time steps. For each iteration use the midpoint HRR value for the given time step.For example:First step (t=0 to t=5): HRR = α(Δt/2)2 = α(5/2)2Second step (t=5 to t=10): HRR = α(t1 +Δt/2)2 = α(5 + 5/2)2Method developed by Heskestad Delichatsios and Beyler (NFPA 72 Figure B.3.3.4.4 provides a helpful methodology). Assume the authority having jurisdiction requires that heat detection occurs at a HRR of no greater than 475 kW.a) Using the method developed by Heskestad Delichatsios and Beyler determine the required heat detector spacing to satisfy this requirement (based on same information as provided in (1)). Comment on the feasibility of this design.b) Assuming the detector activation temperature remains 57.2°C (135°F) and that the minimum feasible spacing for the heat detectors is 2.49m x 2.49m what measures could be taken to still meet the requirement of detection at 475 kW (Hint: think detector performance)? Support your answer by using the Heskestad Delichatsios and Beyler approach.The owner would now like to consider the benefit of installing smoke detectors within the enclosed roof deck space versus heat detectors. Specifically the owner questions whether the 30 a) Using the method developed by Heskestad Delichatsios and Beyler determine the required heat detector spacing to satisfy this requirement (based on same information as provided in (1)). Comment on the feasibility of this design.b) Assuming the detector activation temperature remains 57.2°C (135°F) and that the minimum feasible spacing for the heat detectors is 2.49m x 2.49m what measures could be taken to still meet the requirement of detection at 475 kW (Hint: think detector performance)? Support your answer by using the Heskestad Delichatsios and Beyler approach. a) Assuming use of the optical density approach that considers the entire volume of the roof deck what mass of smoke is required to be produced from the cushion if the detector is assumed to active at an optical density of 0.14 m-1? Assume the optical density outside and inside of the detector are the same. Based on information provided and this method to estimate response do you think there is enough fuel available in the cushion to result in the required optical density for detector response?b) Determine smoke detector activation time assuming the cylindrical volume approach with-1detector activation at optical density of 0.14 m . Assume the time delay associated withsmoke lag into the detector is 25 seconds. State all assumptions.c) Determine the minimum steady-state fire size required to have smoke reach the ceiling without stratifying and the minimum fire size required for the ceiling jet reach critical velocity for smoke detection. State all assumptions.d) Identify critical limitations and assumptions inherent calculating smoke detection times. a) Assuming you would specify a flame detector what type would you specify (e.g. UV IR UV/IR) and why?b) Assuming you would mount the detector(s) near the hotel doorway what would you need to know about the response characteristics of the detector in to detect a pool fire under the car involving 1 gallon of gasoline? (Flame heat flux data such as from SFPE Hb Table 36.7 will be useful in developing your response.)