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

Goals and expectations

Flames Calculate flame heights

Plumes Calculate plume mass flow (function of height z) Calculate plume centerline temperature (fnct of z) Know Zukoski plume and Heskestad plume

Ceiling Jets Use Alperts correlations

Define mean flame height

Height where flame is observed 50% of the timeHeight above which flame appears

half the time

Froude number in terms of heat release rate

Experiments show mean flame height, L, is a function of the square root of Fr:

gDHA

Q

gD

u

cv222

22

Fr

2

25

Since

Fr

DA

cv D

Q

gDHA

Q

D

L

Normalized flame height versus dimensionless energy release rate

1< Q* <1000

See Table 2-1.2 [SFPE] for many different flame height correlations

52

*QD

L

Flame height correlation of Heskestad

Reliable for 0.5 < Q* < 1000

mD m,L kW,HRR) (total Q

*

02.1235.0

02.17.3

52

52

D

Q

D

L

QD

L

DQL 02.123.0 52

Formation of plume and ceiling jet

Plume centerline properties

The ideal plume (point source plume)

Goal: Derive simple algebraic equations for properties in plume

Assume top hat profile

Derivation of ideal plume equations

Temperature as a function of height Difference above T

T(z) [oC or K] Plume radius as a function of height

b(z) [m] Upward velocity as a function of height

u(z) [m/s] Plume mass flow rate as a function of height

[kg/s])(zmp

Final form of the equations:

3/53/1.

3/12.

20.0 zQTc

gm

p

p

3/53/2.

3/1

220.5

zQ

cg

TT c

p

zb 5

6

3/13/1

3/1

94.1

zQ

Tc

gu c

p

Zukoski Plume

Adjusted ideal plume theory to fit with experiments

Generally underestimates plume mass flow rate

m.

p 0.21

2 g

cp T

1 / 3

Q. 1 / 3

z5 / 3

skgmmzkWQ

p

p

zQm/

.

3/53/1..

.

076.0

Zukoski plume experiments

Plume equations that better represent reality

Many researchers have worked on developing plume equations

Derive through dimensional analysis and experimentHeskestad plume equationsMcCaffrey plume equationsetc

Heskestad; virtual origin

Heskestad plume correlations

02/1

0 /12.0 zzTTb

T0 9.1T

gcp2

2

1 / 3

Q.

c2 / 3 z z0 5 / 3

3/10

3/1c

3/1

p0 zzQ

Tc

g4.3u

ccp QzzQm.

33/50

3/1..

1085.1071.0

0056.0..

L

zQm cp

z>L

z<L

z>L

Measurements of centerline temperatures

Plume interaction with a ceiling

Forms a ceiling jet (CJ)

Velocity of CJ driven by buoyancy of plume

Just as with plumes, there are a number of different CJ correlations

Temperature and velocity cross sections are not necessarily the same

Depth of CJ in the range 5%-12% of H Maximum u and T very near ceiling

(1% of H)

Alpert correlations

3/5

3/2

max

9.16

H

QTT

H

rQ38.5TT

3/2

max

3/1

max H

Q96.0u

6/5

2/13/1

max r

HQ195.0u

r/H<0.18

r/H>0.18

r/H<0.15

r/H>0.15

Any questions?Next: Unit 5 – Vent flows