# Determining Detector Response

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).

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.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.

Sample Solution
Determining Detector Response 