Enclosure Fire Dynamics

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

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 101 300 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 • 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 0.6 < 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 CStratified case • Air flowing into compartment in lower level • Formation of neutral plane

25. Stage DWell 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?