Fire Dynamics. José L. Torero A. James Clark School of Engineering, The University of Maryland, USA

Transcription

1 Fire Dynamics José L. Torero A. James Clark School of Engineering, The University of Maryland, USA

2 Fire Dynamics: The combustion problem within Fire Safety Engineering 5/28/2018 2

3 What is the role of time?

4 RSET (Required Safe Egress Time)

5 t Solution Untenable Conditions (t f ) Evacuation Completed (t % e ) Structural Failure (t S ) 100%

6 ASET (Available safe Egress Time) Objectives t e <<<<t f RSET<<<<ASET t e <<<<t S t s Fire Safety Strategy

7 RSET o We need to establish egress times(t e ) o R.S.E.T. (t e ) Required Safe Egress Time

8 Egress Time (t e ) 0 t e = t de + t pre + t mov o t e Egress time o t de Detection time o t pre Pre-Movement time o t mov Displacement time t e = t pre + t mov

9 Pre-Movement Time (t pre ) o Purely statistical can be very long and brings great uncertainty

10 Movement Time o Travel distance d=d max o Conservative travel velocity: 1 m/s t dis =d/v t mov =t dis +t door <<150 s t door =N/W.d 2.5 min

11 ASET o A.S.E.T.: Available Safe Egress Time (t f )

12 Fire

13 Timeline Ignition Flashover too late for people t S t F

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15 The Pre-Flashover Compartment Fire H T U V S T S s V S a,0 T a e e a,i f

16 Approach o Zone Model Divides the room into two well defined zones o Upper Layer Hot combustion products o Lower Layer Cold air o Implies strong simplifications but help understand the dynamics of the problem

17 The Evolution of the Smoke Layer V S e H T S T U f s e T a V S a,0 a,i o Upper Layer - The parameters that need to be evaluated are: o The temperature of the upper layer: T u o The velocity at which the Upper Layer descends: V S = dh dt

18 Conservation Equations o These parameters can be obtained from, the ideal gas law and conservation of mass and energy in the Upper Layer ሶ ሶ P = ρrt u t Aρ T u H t = m s t Aρ T u H t C p T u = m s C p T s

19 Heat Transfer T ρc p t = k 2 T x 2 k T ቤ = q" ሶ x NET x=0 T ቤ = 0 x x=xs T t = 0 = T 0 Structural Analysis Fire Dynamics Post-Flashover Compartment

20 ሶ ሶ ሶ Q Net Qሶ out = A W q" ሶ r + ඵ m(y, ሶ z)cpt y, z dydz ම m CV CpT x, y, z dxdydz ሶ Q in = mcpt ሶ Q gen = H C m f d dt ම m CVCpT x, y, z dxdydz = ሶ Q gen + ሶ Q in ሶ Q out ሶ Q Net Net Heat Flux?

21 How does a fire grow in an enclosure?

22 Combustion o Heat of Combustion ( H C ): Energy released per kg of fuel burnt Complete Combustion Fuel H C [MJ/kg FUEL ] Hydrogen Propane Gasoline Paraffin Kerosene Coal (Lignite) Wood Peat (dry) PVC (Poly-Vinyl-Chloride) PE (Poly-Ethylene) 44.60

23 Burning Rate Q ሶ = H C F ሶ ሶ Q V S o F Burning Rate [kg/s] Q = H C A B m" ሶ F o ሶ m" F Burning Rate per unit area [kg/m 2 s] o A B Burning area [m 2 ]

24 Design Fire o A B = πr B 2 o r B burning radius o r B = V S t o V S Flame spread velocity o t time r B A B = πv S 2 t 2

25 ሶ ሶ ሶ Q ሶ = H A m" ሶ C B F A B = πv S 2 t 2 HRRPUA = H C m F Q = π H V2m" t 2 C S F Q ሶ = αt 2

26 Normalized Design Fires Class a Ultra Fast Fast Medium Slow

27 Conservation of Mass S = F + A S A F

28 0 F = A 10 cm 3 = 4 x x50x5 cm3 S = F + A S A Show Video

29 Conservation of Energy Q ሶ = A C p (T S T A ) o C p Specific Heat (J/kgK) o T S Smoke temperature o T A Ambient temperature T S = T A + Qሶ A C p

30 Entrainment A A A = E gρ A 2 C p T A Τ 1 3 Qሶ 1Τ3 H 5Τ3 o ρ A Ambient density o g gravity (9.81 m/s 2 ) o E = 0.2 Entrainment constant o H Entrainment height Qሶ H

31 Conservation of Mass: Hot Layer dm CV dt = A m CV = ρ H A H 0 H m CV H 0 H A

32 Conservation of Energy d m CV C p T H dt = A C p T S T H, m CV H A H 0

33 Can be solved using an Excel Spreadsheet ሶ o P = ρr T or ρ 2 = T 1 ρ T 1 2 o Q = αt 2 o T S = T A + ሶ Q ሶ m A C p o A = E gρ A 2 C p T A 1Τ3 Q ሶ 1Τ3 H 5Τ3 o dm CV dt = A m CV = ρ H A H 0 H H t = m CV,t+1 Aρ 2 o d m CVC p T H dt = A C p T S T H,t+1 = m CV,tT H,t + ሶ m CV,t+1 m A tt S

34 Example: Slow Growing Fire H 0 = 2.75 m, X 0 = 4.75 m, Y 0 = 3.5 m T H H 0 H

35 Implementation ሶ α(slow) W/s2 H m E 0.2 X m E gρ2 1Τ3 A C g 9.81 m/s2 Y0 3.5 m p T A ρa 1.2 kg/m3 A Cp 1 J/kg/K TA 290 K Δt 5 s t t+1 = t t + t Qሶ = αt 2 A = E gρ 2 1Τ3 A 1Τ3 Qሶ H 5Τ3 T = T A + Q H t+1 = H 0 H t C p T A AC p m ρ2 = T CV,t+1 = m CV,t + A t T H,t+1 = m CV,tT H,t + A tt S 1 m CV,t+1 ρ T 1 2 H t = m CV,t+1 Aρ

36 Compartment Evolution Flashover

37 Summary o Zone Model Divides the room into two well defined zones o Upper Layer Hot combustion products o Lower Layer Cold air o Provides the evolution of the height and temperature of the hot layer o It depends on an entrainment correlation o Results form a simple mass and energy balance between two control volumes o Breaks down when the smoke layer gets close to the floor, when the two control volumes become one and the entrainment correlation is no longer valid

38 Structural Analysis Post-Flashover compartment Fire

39 The collapse of the WTC towers emphasizes the need for a detailed structural analysis of optimized buildings ie. Tall Buildings

40 Existing Framework

41 Heat Transfer T ρc p t = k 2 T x 2 k T ቤ = q" ሶ x NET x=0 T ቤ = 0 x x=xs T t = 0 = T 0 Structural Analysis Fire Dynamics Back to the basics

42 Too Complicated! ሶ ሶ ሶ Q Net Qሶ out = A W q" ሶ r + ඵ m(y, ሶ z)cpt y, z dydz ම m CV CpT x, y, z dxdydz ሶ Q in = mcpt ሶ Q gen = H C m f d dt ම m CVCpT x, y, z dxdydz = ሶ Q gen + ሶ Q in ሶ Q out ሶ Q Net Net Heat Flux?

43 The Compartment Fire o It was understood that solving the full energy equation was not possible o The different characteristic time scales of structure and fire do not require such precision o Looked for a simplified formulation: The Compartment Fire

44 Typical Compartment

45 Thomas & Heselden (1972) o Realistic scale compartment fires (~4 m x 4 m x 4 m) aimed at delivering average temperatures o Simple instrumentation: Single/Two thermocouples Regime I Regime II Thomas, P.H., and Heselden, A.J.M., "Fully developed fires in single compartments", CIB Report No 20. Fire Research Note 923, Fire Research Station, Borehamwood, England, UK, 1972.

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47 ሶ ሶ ሶ Assumptions Regime I o The heat release rate is defined by the complete consumption of all oxygen entering the compartment and its subsequent transformation into energy, Q = my O2, Hc O2. o o o o o o Eliminates the need to define the oxygen concentration in the outgoing combustion products Eliminates the need to resolve the oxygen transport equation within the compartment. Limits the analysis to scenarios where there is excess fuel availability Chemistry is fast enough to consume all oxygen transported to the reaction zone The control volume acts as a perfectly stirred reactor. The heat of combustion is assumed to be an invariant/ the completeness of combustion is independent of the compartment. o Radiative losses through the openings are assumed to be negligible therefore Q out is treated as an advection term (3% of the total energy released (Harmathy)). o There are no gas or solid phase temperature spatial distributions within the compartment. o Mass transfer through the openings is governed by static pressure differences ( m ሶ = CA O H O ) o o all velocities within the compartment to be negligible Different values of the constant were derived by Harmathy and calculated by Thomas for different experimental conditions.

48 ሶ ሶ Maximum Compartment Temperature d dt m CVCpT S = ሶ Q gen + S.S. ሶ Q in ሶ Q out ሶ Q in Qሶ Net Qሶ out d ሶ Q Net T g,max ሶ Q out = m CV CpT g,max mcpt ሶ g,max ሶ Q in = mcpt ሶ T g,max in = ሶ Q gen = ሶ Q out = out = m=ca ሶ O my ሶ O2, Hc O2 mc ሶ p T g,max H O Q gen = H C m f T H 0 Qሶ Net = Ak T g,max T δ

49 ሶ ሶ Maximum Compartment Temperature 0 = ሶ Q gen ሶ Q out ሶ Q Net Substituting and solving for T g,max d ሶ Q Net T g,max ሶ Q out = m CV CpT g,max mcpt ሶ g,max ሶ Q in = mcpt ሶ T g,max T g,max = T F = 1 + T TCD 1 + T F T CD T F Y O2, Hc O2 ΤC p Q gen = H C m f T H 0 T CD = CY O2, Hc O2 Τ k δ A O A H O

50 The Data Regime I Theory Regime II Theory Τ A A 0 H 0 Regime II Regime I

51 Design Method Φ = A 0 H 0 (Law, M., A Basis for The Design of Fire Protection of Building Structures, Struct. Eng., no. February, pp , 1983.) T [ o C] Heating T g,max Cooling R = 0.1 A 0 H 0 1/2 (kg/s) Kawagoe (1958) Thomas & Heselden (1972) t BO t [min] t BO = M f R

52 Parametric Fires (Pettersson, O. Magnusson, S. E. and Thor, J. Fire Engineering Design of Steel Structures, Stockholm, Jun ) ሶ Q Net o Recorded temperature evolution effect of structural heating o Average temperature single thermocouple rack (6 TC)

53 Realistic Fire T g,max

54 Regime II? o Data scatter is very large o Factors such as aspect ratio, nature of the fuel and scale were shown by Thomas & Heselden to have a significant effect on the resulting temperatures o The relationships between T g,max and R with Τ A A 0 H 0 and A 0 H 0 are no longer valid

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56 (SFPE Engineering Guide Fire Exposures to structural Elements May 2004) A A 0 H 0 Quintiere McCaffrey Pettersson Rockett Tanaka, etc.

57 Summary o An elegant framework was established that provided an answer to a fundamental question o Assumptions were clearly established o Limitations were clearly established o A simple design methodology was developed that provided a worst case: T g,max vs t curve for the purposes of structural analysis.

58 The End of the Compartment 1960 s 1970 s 2000 s 1990 s

59 To me there has never been a higher source of earthly honour or distinction than to be remembered through the advances I brought to science. Isaac Newton Philip Humphrey Thomas (16 June January 2014)