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).