the fluid mechanics of fires - aps physics of fluid dynamics the fluid mechanics of fires howard r....

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).