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

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

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

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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)Persistent flame (flame is present 100% of time) 0.03 < z < 0.08 Eqn (2-1) z = height above fire source (m) = heat release rate (kW) = heat release rate (kW)

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Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2 5 Unconfined Fire Plume Comprises 3 Regimes Intermittent flame (flame present < 100% of time)Intermittent flame (flame present < 100% of time) 0.08 < z < 0.20 Eqn (2-2) 0.08 < z < 0.20 Eqn (2-2) Flame height = height where intermittency is 50%Flame height = height where intermittency is 50% (Correlation - Heskestad 1983) l = D Eqn (2-3) D = fuel diameter (m)

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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)Buoyant (thermal) plume (no flame is ever present) z > 0.20 Eqn (2-4) z > 0.20 Eqn (2-4) Assume heat is released at a virtual point sourceAssume heat is released at a virtual point source z o = DEqn (2-5) z o = height of virtual source above burning item (m) z o = height of virtual source above burning item (m)

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

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Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2 8 Buoyant Plume Model (2) Upward axial velocity, u ax (m s -1 )Upward axial velocity, u ax (m s -1 ) u ax (z) = 1.14 (z- z o ) -1/3 Eqn (2-7) u ax (z) = 1.14 (z- z o ) -1/3 Eqn (2-7) Radial dependence of upward velocity, (m s -1 )Radial dependence of upward velocity, (m s -1 ) u(r,z) = u ax (z) exp(-r 2 /b 2 ) Eqn (2-8) u(r,z) = u ax (z) exp(-r 2 /b 2 ) Eqn (2-8)

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Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2 9 Buoyant Plume Model (2) Axial temperature, T ax = T ax - T (K)Axial temperature, T ax = T ax - T (K) T ax (z) = 26 (z- z o ) -5/3 Eqn (2-9) T ax (z) = 26 (z- z o ) -5/3 Eqn (2-9) Radial dependence of temperature, T(r, z) (K)Radial dependence of temperature, T(r, z) (K) T(r, z) = T ax (z) exp[-( 1.2 r) 2 /b 2 ] Eqn (2-10) T(r, z) = T ax (z) exp[-( 1.2 r) 2 /b 2 ] Eqn (2-10) Average temperature, T aveAverage temperature, T ave T ave (z) = 14 (z- z o ) -5/3 Eqn (2-11) T ave (z) = 14 (z- z o ) -5/3 Eqn (2-11)

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Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2 10 Buoyant Plume Model (2) Total upward mass flow, (kg s -1 )Total upward mass flow, (kg s -1 ) (z) = (z- z o ) 5/3 Eqn (2-12) (z) = (z- z o ) 5/3 Eqn (2-12)**************************************************************** This is probably the simplest model available.This is probably the simplest model available. More complex models have been incorporated into computer models or into standards for smoke control.More complex models have been incorporated into computer models or into standards for smoke control.

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

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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 detectorsNeed to model ceiling jet in order to predict time to activation of sprinklers or heat detectors Properties of ceiling jet depend onProperties 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 predictModels 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

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

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Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2 14 Alperts Correlations - Ceiling Jets For maximum temperature and velcoity T max - T = /3 (H - z o ) -5/3 for r 0.18 H Eqn (2-13) T max - T = 5.38( /r) 2/3 (H - z o ) -1 for r > 0.18 H Eqn (2-14) u max = 0.96 { /(H - z o )} 1/3 for r 0.15 H Eqn (2-15) u max = /3 (H - z o ) 1/2 r - 5/6 for r > 0.15 H Eqn (2-16) r = radial distance under the ceiling (m)

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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- z o )}Alpert: for r 0.18 H { ~ area of plume impingement as radius of plume is b(z) = (z- z o )} T max - T = /3 (H - z o ) -5/3 Axial Temperature in Buoyant Plume T ax (z) = 26 (z- z o ) -5/3 T ax (z) = 26 (z- z o ) -5/3 or T ax (z) = /3 (z- z o ) -5/3 or T ax (z) = /3 (z- z o ) -5/3

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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- z o )}Alpert: for r 0.15 H { ~ area of plume impingement as radius of plume is b(z) = (z- z o )} u max = 0.96 { /(H - z o )} 1/3 Axial Velocity in Buoyant Plume u ax (z) = 1.14 { /(z- z o ) }1/3 or u ax (z) = 1.01 { /(z - z o )} 1/3 or u ax (z) = 1.01 { /(z - z o )} 1/3

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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 wallsAlpert 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 Alperts correlations can still be applied withFor fire against wall, air entrainment into plume is cut in half. Method of reflection predicts Alperts correlations can still be applied with 2 2 For fire in corner, air entrainment into plume is cut in quarter. Method of reflection predicts Alperts correlations can still be applied withFor fire in corner, air entrainment into plume is cut in quarter. Method of reflection predicts Alperts correlations can still be applied with 4 4

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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 z 0 = 0.

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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 z 0 = 0.

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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 z 0 = 0.

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

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

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Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2 23 Other Correlations - Ceiling Jets For maximum temperature T m = (T max - T ) = 2/3 (H*) - 5/3 f(r/H*) T m = (T max - T ) = 2/3 (H*) - 5/3 f(r/H*) Replace Replace H H* H H*

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

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

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

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

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Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2 28 Thermal Response of Heat Detectors & Sprinklers If T g is independent of timeIf T g is independent of time Eqn (2-21) Eqn (2-21) t r = time of activation (s) T Dr = manufacturers listed operation temperature (K) T = initial temperature (K) can be characterized by devices RTI can be characterized by devices RTI = RTI u -1/2 Eqn (2-22) = RTI u -1/2 Eqn (2-22) RTI = response time index (m 1/2 s 1/2 )

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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)

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Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2 30 More Detailed Detector Response Model RTI = response time index (m 1/2 s 1/2 ) C = conductivity factor (m 1/2 / s 1/2 ) 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.

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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 beamsIn channel defined by corridor walls or ceiling beams Eqn (2-23) Eqn (2-23) Eqn (2-24) Eqn (2-24)

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

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

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Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2 34 Time Dependent Fires In small room with slowly growing fire, Alperts (steady-state) correlations can ue used withIn small room with slowly growing fire, Alperts (steady-state) correlations can ue used with In large industrial facilitiesIn 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

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

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

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Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2 37 Transient Ceiling Jets Heskestad and Delichatsios (1978) AssumedAssumed Dimensionless timeDimensionless time Dimensionless gas travel time (fire source to ceiling location)Dimensionless gas travel time (fire source to ceiling location) For T max = u max = 0For T max = u max = 0

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

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

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

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

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

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

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

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

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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 sufficientFor 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 layerIn 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 ceilingHence 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 detectorReduction 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 layerTo 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 scenariosAnalytical and computer models are available for such scenarios

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

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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-combustibleFlame impinges on ceiling & spreads out radially, even if ceiling is non-combustible Heskestad & Hamada ( 93 to 760 kW) Flame extension, r f (m) r f = 0.95 ( l - H) Eqn (2-29) r f = 0.95 ( l - H) Eqn (2-29) Heskestad flame length (burning in open) l = D Eqn (2-3) l = D Eqn (2-3)

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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 pipesCeiling flames may ignite combustible or damage non- combustible ceiling elements, cables and pipes Ceiling flames enhance thermal radiation to floorCeiling flames enhance thermal radiation to floor –augment burning rate of burning item –augment flame spread over burning item –augment heating or remote combustibles (targets)

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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 sidesConsider 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 rateMax rate of burning ~ 3 x open-burning rate Achieved in approximately 1/3 the timeAchieved in approximately 1/3 the time

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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)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

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

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Carleton University, (CVG****), Fire Dynamics II, Winter 2003, Lecture # 2 53References 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

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