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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
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Overview Background on fluid flow Bernoulli equation
Flow through vents from well mixed compartments Flow through vents from stratified compartments Flow though ceiling vents
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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)
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Thermal expansion
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Fluid flows generated by fire
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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
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Relating density and temperature
Start with ideal gas law For properties of air T in [K] in [kg/m3]
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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
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Pressure differences produced by fluids
Hydrostatic pressure is a function of fluid density
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Pressures generated in buildings
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Bernoulli Remember your friend - the Bernoulli equation…
Static pressure head Hydrodynamic pressure term Hydrostatic pressure term
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A simple example for using the Bernoulli equation
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Pressures generated in buildings
Temperature inside building is warmer than temperatures outside building Only small openings at top and bottom of building
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Example – Flow through opening
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Bernoulli equation example for flows at the lower vent
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Fluid flow is restricted when passing through an opening
For vents in buildings, we usually use < Cd < 0.7
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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
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For the small openings in a building
Mass flow out the upper vent Mass flow in the lower vent
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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
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Neutral plane
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Neutral plane
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Vent flows and the neutral plane
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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
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Stage C Stratified case
Air flowing into compartment in lower level Formation of neutral plane
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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
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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
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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
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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
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Final form of the equations
Flow out of the compartment Flow into the compartment Expressions for neutral plane height
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A simplified form is available
Assume ambient properties Accurate when temperatures are over 300 oC and hot gases are uniformly distributed throughout compartment
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Mass flow rate through a ceiling vent
Mass flow in assumed equal to mass flow out Pressure difference across top vent is constant
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Pressure difference- stack effect
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Normal stack effect Air inside the building warmer than outside
Winter Greater pressure differences Taller spaces Larger temperature difference
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Reverse stack effect Air inside the building cooler than outside
Air-conditioned If the smoke is hot enough, it may overcome reverse stack effect
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Pressure differences - wind effect
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Additional reading material
SFPE Handbook Sec 2/Ch 5, Sec 3/Ch 9 Design of Smoke Management Systems by Klote and Milkie
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Any questions?
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