1. Enclosure Fire Dynamics
Chapter 1: Introduction
Chapter 2: Qualitative description of enclosure fires
Chapter 3: Energy release rates, Design fires
Chapter 4: Plumes and flames
Chapter 5: Pressure and vent flows
Chapter 6: Gas temperatures
(Chapter 7: Heat transfer)
Chapter 8: Smoke filling
(Chapter 9: Products of combustion)
Chapter 10: Computer modeling
Each course unit represents breaking down the problem into individual pieces

2. Overview Background on fluid flow Bernoulli equation
Flow through vents from well mixed compartments
Flow through vents from stratified compartments
Flow though ceiling vents

3. What causes the flow of gases in a building?
Flows driven by fire
Expansion due to heating
Pressure differences caused by buoyancy
Flows driven not by fire
Pressure differences caused by temperature variations throughout a building
Atmospheric conditions (wind against a building)
Mechanical ventilation (fans, heating system)

4. Thermal expansion

5. Fluid flows generated by fire

6. Background information on flows in buildings
Pascal [Pa] = force of 1 Newton [N] acting over an area of 1 m2
At sea level, normal atmospheric pressure is Pa
Pressure differences in buildings due to fire:
Small fraction of atmospheric pressure
<< 100 Pa
Usually only a few Pa

7. Relating density and temperature
Start with ideal gas law
For properties of air
T in [K]  in [kg/m3]

8. Types of pressure Hydrostatic pressure Hydrodynamic pressure
Due to fluid at rest
Hydrodynamic pressure
Due to fluid in motion
For a compartment fire
Hydrostatic pressure will be converted into hydrodynamic pressures
Fluid flows from high pressure to low pressure
Produces flow through vent

9. Pressure differences produced by fluids
Hydrostatic pressure is a function of fluid density

10. Pressures generated in buildings

11. Bernoulli Remember your friend - the Bernoulli equation…
Static pressure head
Hydrodynamic pressure term
Hydrostatic pressure term

12. A simple example for using the Bernoulli equation

13. Pressures generated in buildings
Temperature inside building is warmer than temperatures outside building
Only small openings at top and bottom of building

14. Example – Flow through opening

15. Bernoulli equation example for flows at the lower vent

16. Fluid flow is restricted when passing through an opening
For vents in buildings, we usually use < Cd < 0.7

17. Mass flow through vents
If pressure difference is constant over vent height, then the velocity is also constant
Narrow vents
Discharge (flow) coefficient, Cd, accounts for edge effects
When velocity is not constant, it is necessary to integrate over profile to arrive at mass flow rate

18. For the small openings in a building
Mass flow out the upper vent
Mass flow in the lower vent

19. What is the neutral plane height?
Problem is we do not know hu and hl at this point
Use conservation of mass to derive a relation for hu and hl
Flow in must equal flow out

20. Neutral plane

21. Neutral plane

22. Vent flows and the neutral plane

23. Pressure profiles for a room with a vent
Consider a compartment with a large opening
Pressure difference and velocity will vary over the cross section of the opening
We will look at 4 different cases that occur during the development of the fire

24. Stage C Stratified case
Air flowing into compartment in lower level
Formation of neutral plane

25. Stage D Well mixed case Hot smoke layer extends to the floor
Post-flashover
Can also apply to a small fire in a well mixed room

26. Begin with the equations for the well mixed case
Assume a large opening
Mass flow rate in equals the mass flow rate out
Mass of the fire is assumed very small
Uniform temperature throughout the compartment

27. Flow from a well mixed compartment
Velocity is a maximum where the pressure difference is greatest
Since the pressure difference (and velocity) is a function of height, it is necessary to integrate over the height, z

28. Integrating over the opening height
Mass flow rate through vent
Velocity is assumed constant across the width of the opening
It only changes with height
Integrate above the neutral plane for flow out the compartment
Integrate below the neutral plane for flow into the compartment

29. Final form of the equations
Flow out of the compartment
Flow into the compartment
Expressions for neutral plane height

30. A simplified form is available
Assume ambient properties
Accurate when temperatures are over 300 oC and hot gases are uniformly distributed throughout compartment

31. Mass flow rate through a ceiling vent
Mass flow in assumed equal to mass flow out
Pressure difference across top vent is constant

32. Pressure difference- stack effect

33. Normal stack effect Air inside the building warmer than outside
Winter
Greater pressure differences
Taller spaces
Larger temperature difference

34. Reverse stack effect Air inside the building cooler than outside
Air-conditioned
If the smoke is hot enough, it may overcome reverse stack effect

35. Pressure differences - wind effect

36. Additional reading material
SFPE Handbook Sec 2/Ch 5, Sec 3/Ch 9
Design of Smoke Management Systems by Klote and Milkie

37. Any questions?