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
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