1. 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
Each course unit represents breaking down the problem into individual pieces

2. 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

3. Define mean flame height
Height where flame is observed 50% of the time
Height above which flame appears half the time
Due to fluctuations, it is actually very difficult to measure flame height
Pure visual estimates tend to over predict flame height by 15-20%
Instead measure using video analysis or other lab measurements

4. Froude number in terms of heat release rate
Experiments show mean flame height, L, is a function of the square root of Fr:

5. Normalized flame height versus dimensionless energy release rate
1< Q* <1000
See Table [SFPE] for many different flame height correlations
Applies to several orders of magnitude
Similar results from many investigators
Most natural fires have Q* less than 10 to 100
Most correlations based on gas and not solid or liquid fires
Thus flame height correlates with Q* ^ 2/5, except at the low end of diffusion flames such as mass fires
Thus there are two regimes, one for tall flames with larger Q* and one for short flames (L/D < 1)

6. Flame height correlation of Heskestad
Reliable for 0.5 < Q* < 1000
Based on data fit for a number of different fuels
Not that it does not depend on type or form of fuel
Due to 2/5 power, use caution in solving for Q based on an observed L
There is naturally much fluctuation, since Heskestad equation is only for mean height
Plume equations to be developed are generally only valid above the flame

7. Formation of plume and ceiling jet

8. Plume centerline properties

9. The ideal plume (point source plume)
Goal: Derive simple algebraic equations for properties in plume
Assume top hat profile
Top hat = properties across section are constant
Alpha is the entrainment coefficient (measured in experiments)

10. 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]
A complete analytical solution is not possible, thus simplifications are necessary

11. Final form of the equations:
Notice how mass flow rate is a function of q 1/3 and z 5/3

12. Zukoski Plume Adjusted ideal plume theory to fit with experiments
Generally underestimates plume mass flow rate
Notice only a slight change in coefficient from 0.2 to 0.21

13. Zukoski plume experiments
Mass flow measurements from a hood are probably more accurate than those from integration of T and V across plume cross section

14. Plume equations that better represent reality
Many researchers have worked on developing plume equations
Derive through dimensional analysis and experiment
Heskestad plume equations
McCaffrey plume equations
etc

15. Heskestad; virtual origin

16. Heskestad plume correlations
z>L
Forms in EFD book with ambient properties already calculated
z>L
z<L

17. Measurements of centerline temperatures
Notice how centerline temperature is almost constant in flame region

18. 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
Convert buoyancy force into horizontal velocity (momentum)

19. 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)
Ceiling jet temps bounded by T ambient and T wall
Velocities bounded by 0 at wall and at interface

20. Alpert correlations r/H<0.18 r/H>0.18 r/H<0.15 r/H>0.15
Q is total heat release rate
r/H>0.15

21. Any questions? Next: Unit 5 – Vent flows