1. Ceiling Jets & Ceiling Flames
Fire Dynamics II
Lecture # 2
Ceiling Jets & Ceiling Flames
Jim Mehaffey
or CVG****
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

2. Ceiling Jets and Ceiling Flames
Outline
Review of models for unconfined fire plumes
Models for ceiling jets (temperature & velocity)
Models for response of sprinklers / heat detectors
Model for ceiling flame (flame extension)
Flames located against a wall or in a corner
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

3. Review of Models for Unconfined Fire Plume
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

4. Unconfined Fire Plume Comprises 3 Regimes
Persistent flame (flame is present 100% of time)
< z < Eqn (2-1)
z = height above fire source (m)
= heat release rate (kW)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

5. Unconfined Fire Plume Comprises 3 Regimes
Intermittent flame (flame present < 100% of time)
< z < Eqn (2-2)
Flame height = height where intermittency is 50%
(Correlation - Heskestad 1983)
l = D Eqn (2-3)
D = fuel diameter (m)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

6. Unconfined Fire Plume Comprises 3 Regimes
Buoyant (thermal) plume (no flame is ever present)
z > Eqn (2-4)
Assume heat is released at a virtual point source
zo = D Eqn (2-5)
zo = height of virtual source above burning item (m)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

7. Buoyant Plume Model (2) Correlations often expressed in terms of
= convective heat released rate (kW)
“Radius” of the plume, b (m)
b(z) = (z- zo) Eqn (2-6)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

8. Buoyant Plume Model (2) Upward axial velocity, uax (m s-1)
uax(z) = (z- zo)-1/3 Eqn (2-7)
Radial dependence of upward velocity, (m s-1)
u(r,z) = uax(z) exp(-r2/b2) Eqn (2-8)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

9. Buoyant Plume Model (2) Axial temperature, Tax = Tax - T (K)
Tax (z) = (z- zo)-5/3 Eqn (2-9)
Radial dependence of temperature, T(r, z) (K)
T(r, z) = Tax(z) exp[-(1.2r)2/b2] Eqn (2-10)
Average temperature, Tave
Tave (z) = (z- zo)-5/ Eqn (2-11)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

10. Buoyant Plume Model (2) Total upward mass flow, (kg s-1)
(z) = (z- zo)5/ Eqn (2-12)
****************************************************************
This is probably the simplest model available.
More complex models have been incorporated into computer models or into standards for smoke control.
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

11. Consider a Fire Plume Confined by a Ceiling
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

12. Unconfined Ceiling Jet
Need to model ceiling jet in order to predict time to activation of sprinklers or heat detectors
Properties of ceiling jet depend on
Rate of heat release
Diameter of fire base
Height of ceiling (above virtual source)
Models are available (Fire Dynamics I) to predict
Max. temperature as a function of radial distance
Maximum velocity as a function of radial distance
Time to activation of sprinklers or heat detectors if they are subjected to max. temp & velocity
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

13. Fire Plume Confined by Ceiling
Experiments - Alpert 1972
unconfined smooth ceiling
buoyant plume impinges on ceiling
steady fires / no hot layer
variety of fuel packages
heat release rate: 668 kW   98 MW
ceiling height 4.6 m  H  15.5 m
Findings
max temp & velocity close to ceiling (Y ~ 0.01 H)
ambient temp for Y > H
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

14. Alpert’s Correlations - Ceiling Jets
For “maximum” temperature and velcoity
Tmax - T = /3 (H - zo)-5/3 for r  0.18 H Eqn (2-13)
Tmax - T = 5.38( /r)2/3 (H - zo)-1 for r > 0.18 H Eqn (2-14)
umax = 0.96 { /(H - zo)}1/ for r  0.15 H Eqn (2-15)
umax = /3 (H - zo)1/2 r - 5/6 for r > 0.15 H Eqn (2-16)
r = radial distance under the ceiling (m)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

15. Comparison with Buoyant Plume Temperature in Ceiling Jet
Alpert: for r  0.18 H { ~ area of plume impingement as radius of plume is b(z) = (z- zo)}
Tmax - T = /3 (H - zo)-5/3
Axial Temperature in Buoyant Plume
Tax (z) = (z- zo)-5/3
or Tax (z) = /3 (z- zo)-5/3
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

16. Comparison with Buoyant Plume Velocity in Ceiling Jet
Alpert: for r  0.15 H { ~ area of plume impingement as radius of plume is b(z) = (z- zo)}
umax = 0.96 { /(H - zo)}1/3
Axial Velocity in Buoyant Plume
uax(z) = 1.14 { /(z- zo)}1/3
or uax(z) = 1.01 { /(z - zo)}1/3
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

17. Proximity of Walls
Alpert correlations apply provided fire source is at least 1.8 H from walls
For fire against wall, air entrainment into plume is cut in half. Method of reflection predicts Alpert’s correlations can still be applied with
 2
For fire in corner, air entrainment into plume is cut in quarter. Method of reflection predicts Alpert’s correlations can still be applied with
 4
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

18. Example of Use of Eqn (2-13)
Calculate the maximum excess temperature under a ceiling 10 m directly above a 1.0 MW heat release rate fire. Assume z0 = 0.
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

19. Example of Use of Eqn (2-14)
Calculate minimum heat release rate of a fire against noncombustible walls in a corner 12 m below ceiling needed to raise temperature of gas below ceiling 50°C at a distance 5 m from the corner. Assume z0 = 0.
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

20. Example of Use of Eqn (2-16)
Calculate maximum velocity at this position. Assume z0 = 0.
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

21. Motevalli & Marks Correlation =Thickness of Ceiling Jet
= distance below ceiling at which
T - T = 1/ e {Tmax - T } with e = 2.718
Eqn (2-17)
for
H* = H - zo
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

22. Yuan & Motevalli Correlation Thermal Profile of Ceiling Jet
y = distance below ceiling (m)
Eqn (2-18)
for
T(r,y) = Tmax(r) when y/lT ~ 0.25
substituting into Eqn (2-17)
y / H* ~ [1 - exp( r / H*)]
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

23. Other Correlations - Ceiling Jets For “maximum” temperature
Tm = (Tmax - T) = 2/3 (H*) - 5/3 f(r/H*)
Replace
H  H*
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

24. Other Correlations - Ceiling Jets For “maximum” temperature
Replace
H  H*
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

25. Other Correlations - Ceiling Jets For “maximum” velocity
Umax = 1/3 (H*) - 1/3 f(r/H*)
Replace
H  H*
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

26. Other Correlations - Ceiling Jets For “maximum” velocity
Replace
H  H*
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

27. Thermal Response of Heat Detectors & Sprinklers
Simple model (convective heating)
= -1 (Tg - TD) Eqn (2-19)
TD = temp of detector / sprinkler link (K)
Tg = temp of ceiling jet (K)
 = time constant of device (s)
 = mD cD / (h AD) Eqn (2-20)
mD = mass of detector / sprinkler link (kg)
cD = specific heat of link (kJ kg-1 K-1)
AD = surface area of link (m2)
h = convective heat transfer coefficient (kW m-2 K-1)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

28. Thermal Response of Heat Detectors & Sprinklers
If Tg is independent of time
Eqn (2-21)
tr = time of activation (s)
TDr = manufacturer’s listed operation temperature (K)
T = initial temperature (K)
 can be characterized by device’s RTI
 = RTI u-1/ Eqn (2-22)
RTI = response time index (m1/2 s1/2)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

29. Thermal Response Index - Sprinklers
BSI 94/340340, “Draft Code of Practice for the Application of Fire Safety Engineering Principles to Fire Safety in Buildings”, British Standards Institute, London, p 115 (1994)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

30. More Detailed Detector Response Model
RTI = response time index (m1/2 s1/2 )
C = conductivity factor (m1/2 / s1/2 )
C is a measure of heat conduction from heat sensitive element to rest of heat detector or sprinkler
RTI and C can be determined for a detector
For C = 0, this model reduces to simpler model. Simple model is often accurate enough.
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

31. Detector or Sprinkler in a Channel
Delichatsios (1981)
In channel defined by corridor walls or ceiling beams
Eqn (2-23)
Eqn (2-24)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

32. Detector or Sprinkler in a Channel
Definition of terms
Tmax = Gas temperature near ceiling (K or °C)
Timp = Gas temperature where it impinges on ceiling
(K or °C). Given by Alpert Eqn (2-13).
umax = Gas velocity near ceiling (m s-1)
H = Height of ceiling above fire source (m)
Y = Distance along channel from point of impingement (m)
2 lb = Width of channel (m)
hb = Depth of channel (m)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

33. Detector or Sprinkler in a Channel
Limits of Application
For corridors correlations hold provided
Y > lb (gas is flowing along channel) (a)
lb > 0.2 H (ceiling jet impingement within channel) (b)
For beams must also have
hb / H > 0.1 (lb / H)1/3 (no spillage under beams) (c)
or combining (b) and (c)
hb / H > 0.17
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

34. Time Dependent Fires
In small room with slowly growing fire, Alpert’s (steady-state) correlations can ue used with 
In large industrial facilities
Travel time of fire gases from burning item to detector or sprinkler may be  10 s
If fire grows rapidly, steady-state model may yield overly conservative results
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

35. t2 Fire Growth Medium Eqn (2-26) Fast Ultra-fast
Growth of fire can often be characterized as
Eqn (2-25)
ti = time of “ignition” (s)
 = growth coefficient (kW s-2)
“Design” Fires, NFPA 72, National Fire Alarm Code
Slow
Medium Eqn (2-26)
Fast
Ultra-fast
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

36. Example of t2 Fire
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

37. Transient Ceiling Jets Heskestad and Delichatsios (1978)
Assumed
Dimensionless time
Dimensionless gas travel time (fire source to ceiling location)
For Tmax = umax = 0
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

38. Transient Ceiling Jets
Heskestad and Delichatsios (1978)
Eqn (2-27)
Eqn (2-28)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

39. Transient Ceiling Jets Heskestad and Delichatsios (1978)
For Tmax = umax = 0
For Early on, fire is small & transport time relatively long, transient effects are prominent. Eqns (2-27 & 28) apply.
For Later, fire is large & transport time relatively short, transient correlations revert to Heskestad and Delichatsios steady-state correlations (p 2-23 & 25)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

40. Example: Sofa p 2-35 with ti = 0 in room with H = 5 m
Example: Sofa p 2-35 with ti = 0 in room with H = 5 m. Calculate Tmax and umax for r = 4 m and t = 120 s.
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

41. Example: Sofa p 2-35 with ti = 0 in room with H = 5 m
Example: Sofa p 2-35 with ti = 0 in room with H = 5 m. Calculate Tmax and umax for r = 4 m and t = 120 s.
Tmax = 84 K +293 K = 377 K = 104°C
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

42. Steady-state: Heskestad & Delichatsios (p 2-23 & 25)
Example: Sofa p 2-35 with ti = 0 in room with H = 5 m. Calculate Tmax and umax for r = 4 m and t = 120 s.
Steady-state: Heskestad & Delichatsios (p 2-23 & 25)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

43. Steady-state: Heskestad & Delichatsios (p 2-23 & 25)
Example: Sofa p 2-35 with ti = 0 in room with H = 5 m. Calculate Tmax and umax for r = 4 m and t = 120 s.
Steady-state: Heskestad & Delichatsios (p 2-23 & 25)
umax = 2.8 m / s
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

44. Thermal Response of Heat Detectors & Sprinklers
Simple model (convective heating)
= -1 (Tg - TD) Eqn (2-19)
No simple solution when Tg and u are time-dependent
Must solve numerically (with computer)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

45. Eqn (2-19)  = - -1 {(TD - T) - (Tg - T)}
Detector Response for Simple Time-Dependent Tg(t) Assuming u is Relatively Constant
Eqn (2-19)  = - -1 {(TD - T) - (Tg - T)}
If (Tg - T) =  t  = - -1 {(TD - T) -  t }
Solution is (TD - T) =  { t -  [ 1 - exp (- t / ) ] }
If  is small & time of activation >>  then for t >> 
(TD - T) =  { t - }
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

46. Confined Ceilings
For large industrial or warehouse facilities, models for unconfined ceiling jet flows are often sufficient
In small rooms or for long times after ignition in large industrial or warehouse facilities, ceiling jet can become completely immersed in hot smoky layer
Hence ceiling jet entrains hot gas rather than cool air  temp of ceiling jet higher than for unconfined ceiling
Reduction in activation time of sprinkler or heat detector
To predict properties of ceiling jet, must know temp of hot layer & height of interface between hot layer and cool layer
Analytical and computer models are available for such scenarios
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

47. Ceiling Flames
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

48. Ceiling Flames
Flame impinges on ceiling & spreads out radially, even if ceiling is non-combustible
Heskestad & Hamada ( to 760 kW)
Flame extension, rf (m)
rf = 0.95 (l - H) Eqn (2-29)
Heskestad flame length (burning in open)
l = D Eqn (2-3)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

49. Ceiling Flames
Ceiling flames may ignite combustible or damage non-combustible ceiling elements, cables and pipes
Ceiling flames enhance thermal radiation to floor
augment burning rate of burning item
augment flame spread over burning item
augment heating or remote combustibles (targets)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

50. Ceiling Flame Increases Flame Spread & Burning
Consider burning of 0.76 m x 0.76 m slab of PMMA in an enclosure allowing air access from four sides
Max rate of burning ~ 3 x open-burning rate
Achieved in approximately 1/3 the time
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

51. Flames in a Corner
For flames above a burning object located against a wall or in a corner (of non-combustible materials)
asymmetric and therefore reduced entrainment of air have a major impact on the flame dynamics
flame length is increased
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

52. Temperature above fires in 1.22 m high wood pallets (x)
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2

53. References
D. Drysdale, An Introduction to Fire Dynamics,Wiley, 1999, Chap 4
B. Karlsson and J.G. Quintiere, Enclosure Fire Dynamics, CRC Press, 2000, Chap. 4
R.L. Alpert, “Ceiling Jet Flows”, SFPE Handbook of Fire Protection Engineering, 3rd Ed., 2002
Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2