Enclosure Fire Dynamics Chapter 1 Introduction Chapter 2

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

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

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

Thermal expansion

Fluid flows generated by fire

Background information on flows in buildings Pascal [Pa] = force of 1 Newton [N] acting over an area of 1 m 2 ¢ At sea level, normal atmospheric pressure is 101 300 Pa ¢ Pressure differences in buildings due to fire: ¢ Small fraction of atmospheric pressure l << 100 Pa l Usually only a few Pa l

Relating density and temperature ¢ Start with ideal gas law ¢ For properties of air l T in [K] in [kg/m 3]

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

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

Pressures generated in buildings

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

A simple example for using the Bernoulli equation

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

Example – Flow through opening

Bernoulli equation example for flows at the lower vent

Fluid flow is restricted when passing through an opening ¢ For vents in buildings, we usually use 0. 6 < Cd < 0. 7

Mass flow through vents ¢ If pressure difference is constant over vent height, then the velocity is also constant l 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

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

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 ¢ l Flow in must equal flow out

Neutral plane

Neutral plane

Vent flows and the neutral plane

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 ¢

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

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

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

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

Integrating over the opening height ¢ Mass flow rate through vent ¢ Velocity is assumed constant across the width of the opening l ¢ ¢ 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

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

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

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

Pressure differencestack effect

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

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

Pressure differences - wind effect

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

Any questions?