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

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 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

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

Normalized flame height versus dimensionless energy release rate 1< Q* <1000 See Table 2-1.2 [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)

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

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 Top hat = properties across section are constant Alpha is the entrainment coefficient (measured in experiments)

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

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

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

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

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

Heskestad; virtual origin

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

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

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)

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

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

Any questions? Next: Unit 5 – Vent flows