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58th Annual Meeting
American Physical Society
Division of Fluid Dynamics
The Fluid Mechanics
of Fires
Howard R. Baum
National Institute of Standards and
Technology
Gaithersburg, MD. 20899
TOPICS
• Plume entrainment dynamics
• Mass fire induced flow fields
• Dispersion of smoke plumes
• Fire whirl dynamics
• World Trade Center fires
FIRE WHIRLS
Courtesy F. Battaglia
• Externally maintained circulation interactswith fire induced vorticity
• Fire concentrates vorticity along nominalplume centerline reducing entrainment
• Dramatically enhanced flame height
EMMONS - YING (1966)
• Burning acetone pool inside rotating screen
• Flame height reached ∼ 30 pool diameters
• Flame stable for long periods of time
INVISCID MODEL
• Low Mach number thermally expand-
able fluid
• Steady, axially symmetric flow
• No combustion or entrainment
∇ · (ρ~u) = 0
ρ(∇ (~u)2 /2− ~u× ~ω
)+∇p̃− ρ~g = 0
ρ~u · ∇T = 0
p0 = ρRT
p = p0 + p̃
ANALYSIS
• Yih Transformation
~u = u′√T/T0
∂ψ
∂z= −ru′
∂ψ
∂r= rw′
• Partial Integrals
(T − T0) /T ≡ θ0 (ψ) Γ ≡ 2πrv′ = Γ0 (ψ)
p̃/ρ0 +(u′)2/2 + gz ≡ H0 (ψ)
• Stream function equation
r∂
∂r
(1
r
∂ψ
∂z
)+∂2ψ
∂z2= r2
dH0
dψ+ gz
dθ0dψ
−Γ0dΓ0
dψ
TEMPERATURES
r/r0
T/T
0
0.0 1.0 2.0 3.0 4.01.0
2.0
3.0
4.0
S=0.0S=0.5S=1.0S=1.5S=2.0
Courtesy F. Battaglia
S = Γ∞/ (2πr0U0) U0 =
√√√√2gr0
(Tm − T0
T0
)
SWIRL VELOCITY
r/r0
v/U
0
0.0 1.0 2.0 3.0 4.0
2.0
4.0
6.0
S=0.0S=0.5S=1.0S=1.5S=2.0
Courtesy F. Battaglia
S = Γ∞/ (2πr0U0) U0 =
√√√√2gr0
(Tm − T0
T0
)
WORLD TRADE CENTER
TOWER COLLAPSE
ANALYSIS
- A SYNOPSIS -
c©2001 Sara K. Schwittek All rights reserved
TECHNICAL COMPONENTS
Fire Scenario Descriptions of building geom-
etry, materials, and initiating event(s).
m
Fire Dynamics Simulations of combustion, fluid
mechanics, heat and mass transport in gas.
m
Thermal Analysis Simulations of heating and
cooling of condensed phase materials.
m
Structural Analysis Calculation of displacements,
stresses, and loss of capacity of load
bearing structure.
FIRE DYNAMICS
From McGrattan and Bouldin 2004
• All fire simulations performed with NISTFire Dynamics Simulator (FDS).
• Geometry model as used by FDS basedon architectural rather than structural fea-tures.
• Window breaking times and locations ob-tained from photographic and video data.
FIRE DYNAMICS (2)
From McGrattan and Bouldin (2004)
• Predicted temperatures and heat releaserates compared with experiments.
• Experiments burned paper laden work sta-tions in limited ventilation compartments.
• Actual contents and completeness of burn-ing are sources of uncertainty.
FDS SIMULATIONS
From McGrattan and Bouldin (2004)
• North tower 96th floor ceiling temperaturesat 15 minute intervals.
• At 50 cm resolution, 150,000 cells per floorand 500,000 time steps required for 6000seconds simulated time.
• Parallel processing reduces computing timeto 2 days (8 processors/floor). 6-12 GBytesmemory required.
FDS SIMULATIONS (2)
From McGrattan and Bouldin (2004)
• Heating and cooling at any location as firesmigrate.
• FDS time step 102−103 times smaller thanthermal time scales. Allows simultaneousfire and thermal calculations if desired.
• Further details in (McGrattan and Bouldin2004).