Q1 Here is a simple differential equation modelling the smoke layer depth (y) in a large atrium provided with dynamic smoke extraction system.
dy/ dt = 1/A (m/p - Vo)
Where
A - Cross-section area of the floor (m2)
Vo - Volume extraction rate at the top of the atrium (m3/s)
Ts - Average temperature of plume (K) and can be derived by Ts = To + Q/mcp neglecting heat loss to walls and opening, To is the ambient temperature; cp is the specify heat of the plume gases (kJ/kg K)
p Smoke density at smoke temperature of Ts (kg/m3) and can be derived by Ρ = 353/Ts
m- Mass flow rate of the axisymmetric plume (kg/s) at the specified smoke layer height (z); It can be calculated from
m = 0.0711.2c1/3 zs/3 + 0.0018Qc
and Qc is the convective heat release rate (kW)
z is the height above the base of the fire (m)
Use numerical method to solve the differential equation and sketch the smoke layer depth and the clear smoke height as times goes from time zero to equilibrium status when the flows into and out of the smoke layer and the surrounding have reached equilibrium. Consider the following input parameters for the steady fire:
|
Ambient Temperature
Ceiling Height
Cross-section Area of Floor
Total Heat Release Rate
Convective Heat Transfer Fraction Fuel Height above Floor
Smoke Extraction Rate
|
25 °C 8.5 m 150 m2
4500 kW
0.7
Om
30 m3/s
|