intensity and spread rate interactions in unsteady firelines

Transcription

1 intensity and spread rate interactions in unsteady firelines Hinton, Alberta 2009 Hinton, Alberta 2009 John Dold Fire Research Centre University of Manchester, UK

2 intensity and spread rate interactions in unsteady firelines another way of characterising the spread of a bushfire Hinton, Alberta 2009 Hinton, Alberta 2009 John Dold Fire Research Centre University of Manchester, UK dold@man.ac.uk

3 topics bushfire chemistry turning vegetation into fuel vapour (at about 350 C) burning the fuel vapour with air (above about 900 C) basic fire spread phenomena and concepts the accumulation of fireline intensity spread rate and intensity interactions possible spread rate and intensity relations

4 how the vegetation responds to heating fast pyrolysis vapourises the fuel (around 350 C)

5 how the vegetation responds to heating fast pyrolysis vapourises the fuel (around 350 C) an electric toaster test

6 how the vegetation responds to heating fast pyrolysis vapourises the fuel (around 350 C) an electric toaster test a barbeque test

7 how the vegetation responds to heating fast pyrolysis vapourises the fuel (around 350 C) an electric toaster test a barbeque test schrubland fire (Portugal)

8 how the vegetation responds to heating fast pyrolysis vapourises the fuel (around 350 C) an electric toaster test a barbeque test schrubland fire (Portugal) a crown fire (courtesy Jack Cohen, USDA)

9 how the vegetation responds to heating fast pyrolysis vapourises the fuel (around 350 C) an electric toaster test a barbeque test schrubland fire (Portugal) a crown fire (courtesy Jack Cohen, USDA) compare: a chip-pan reaches flash-point at about 330 C

10 how the vegetation responds to heating fast pyrolysis vapourises the fuel (around 350 C) an electric toaster test a barbeque test schrubland fire (Portugal) a crown fire (courtesy Jack Cohen, USDA) compare: a chip-pan reaches flash-point at about 330 C slow pyrolysis produces charcoal (mainly below 300 C)

11 how the vegetation responds to heating fast pyrolysis vapourises the fuel (around 350 C) an electric toaster test a barbeque test d-glucose schrubland fire (Portugal) slow a crown fire (courtesy char pyrolysis Jack Cohen, USDA) e.g. compare: a chip-pan reaches flash-point at about 330 C C 6 H 12 O 6 cellulose plant growth fast pyrolysis e.g. levoglucosan C 6 H 10 O 5 slow pyrolysis produces charcoal (mainly below 300 C)

12 vegetation vapour burns above about 900 C bushfire flames are (normally) turbulent diffusion flames simply: air and fuel vapour have to mix to release heat. a small experimental fire

13 vegetation vapour burns above about 900 C bushfire flames are (normally) turbulent diffusion flames simply: air and fuel vapour have to mix to release heat. Slow mixing (in large flames) can t maintain the temperature so flames go out, leaving black smoke (soot) a small experimental fire

14 vegetation vapour burns above about 900 C bushfire flames are (normally) turbulent diffusion flames simply: air and fuel vapour have to mix to release heat. Slow mixing (in large flames) can t maintain the temperature so flames go out, leaving black smoke (soot) Buncefield fuel-depot a small fire experimental (11 Decemberfire 2005)

15 vegetation vapour burns above about 900 C bushfire flames are (normally) turbulent diffusion flames simply: air and fuel vapour have to mix to release heat. Slow mixing (in large flames) can t maintain the temperature so flames go out, leaving black smoke (soot) Weston Pier fire (29 July 2008) Buncefield fuel-depot a small fire experimental (11 Decemberfire 2005)

16 vegetation vapour burns above about 900 C bushfire flames are (normally) turbulent diffusion flames simply: air and fuel vapour have to mix to release heat. Slow mixing (in large flames) can t maintain the temperature so flames go out, leaving black smoke (soot) Weston Pier fire (29 July 2008) Buncefield fuel-depot a small fire experimental (11 Decemberfire 2005)

17 vegetation vapour burns above about 900 C bushfire flames are (normally) turbulent diffusion flames simply: air and fuel vapour have to mix to release heat. Slow mixing (in large flames) can t maintain the temperature so flames go out, leaving black smoke (soot) Weston Pier fire (29 July 2008) a crown Buncefield fire (courtesy Jack fuel-depot a small Cohen) fire experimental (11 Decemberfire 2005)

18 vegetation vapour burns above about 900 C bushfire flames are (normally) turbulent diffusion flames simply: air and fuel vapour have to mix to release heat. Slow mixing (in large flames) can t maintain the temperature so flames go out, leaving black smoke (soot) Weston Pier fire (29 July 2008) a small experimental fire a crown Buncefield fire (courtesy Jack fuel-depot a small Cohen) fire experimental (11 Decemberfire 2005)

19 why is white smoke sometimes seen?

20 why is white smoke sometimes seen? vegetation vapour is produced at about 350 C but only burns or produces soot above about 900 C

21 why is white smoke sometimes seen? vegetation vapour is produced at about 350 C but only burns or produces soot above about 900 C For it to burn with enough energy to exceed 900 C, the vapour must exceed about 7% by mass in air so it must exceed this flash-point concentration to burn

22 why is white smoke sometimes seen? vegetation vapour is produced at about 350 C but only burns or produces soot above about 900 C For it to burn with enough energy to exceed 900 C, the vapour must exceed about 7% by mass in air so it must exceed this flash-point concentration to burn more dilute vegetation vapour does not burn

23 why is white smoke sometimes seen? vegetation vapour is produced at about 350 C but only burns or produces soot above about 900 C For it to burn with enough energy to exceed 900 C, the vapour must exceed about 7% by mass in air so it must exceed this flash-point concentration to burn more dilute vegetation vapour does not burn even above the flash-point concentration: Vapour stays unburnt unless it is heated above 900 C

24 why is white smoke sometimes seen? vegetation vapour is produced at about 350 C but only burns or produces soot above about 900 C For it to burn with enough energy to exceed 900 C, the vapour must exceed about 7% by mass in air so it must exceed this flash-point concentration to burn more dilute vegetation vapour does not burn even above the flash-point concentration: Vapour stays unburnt unless it is heated above 900 C In principle, there could be a delayed flash over as long as the concentration remains above about 7% Arnold & Buck (1954)

25 why is white smoke sometimes seen? vegetation vapour is produced at about 350 C but only burns or produces soot above about 900 C For it to burn with enough energy to exceed 900 C, the vapour must exceed about 7% by mass in air so it must exceed this flash-point concentration to burn more dilute vegetation vapour does not burn even above the flash-point concentration: Vapour stays unburnt unless it is heated above 900 C In principle, there could be a delayed flash over as long as the concentration remains above about 7% Arnold & Buck (1954) This may have happened in some large fires...

26 why is white smoke sometimes seen? vegetation vapour is produced at about 350 C but only burns or produces soot above about 900 C For it to burn with enough energy to exceed 900 C, the vapour must exceed about 7% by mass in air so it must exceed this flash-point concentration to burn more dilute vegetation vapour does not burn even above the flash-point concentration: Vapour stays unburnt unless it is heated above 900 C In principle, there could be a delayed flash over as long as the concentration remains above about 7% Arnold & Buck Corsica, (1954) 2000 This may have happened in some large fires...

27 topics bushfire chemistry turning vegetation into fuel vapour (at about 350 C) burning the fuel vapour with air (above about 900 C) basic fire spread phenomena and concepts some factors determining fire spread oscillatory and eruptive flame spread the accumulation of fireline intensity spread rate and intensity interactions possible spread rate and intensity relations

28 bushfire anatomy plume air flow u n normal wind air flow flame length char ω pyrolysis rate φ q heat flux flame angle vegetation load m R(t τ b ) d flame depth R(t ) spread rate

29 bushfire anatomy plume air flow u n normal wind pre-heating flame length air flow char ω pyrolysis rate φ T p q heat flux flame angle vegetation load m R(t τ b ) d flame depth R(t ) spread rate

30 bushfire anatomy plume air flow u n normal wind air flow flame length char ω ω pyrolysis rate pyrolysis rate φ q heat flux flame angle vegetation load m R(t τ b ) mass pyrolysing d (flame flame depth) depth R(t ) spread rate

31 bushfire anatomy plume flame air flow and flow interaction u n normal wind air flow flame length char ω pyrolysis rate φ q heat flux flame angle vegetation load m R(t τ b ) d flame depth R(t ) spread rate

32 bushfire anatomy plume flame air flow and flow interaction u n normal wind pre-heating flame length air flow char ω ω pyrolysis rate pyrolysis rate φ T p q heat flux flame angle vegetation load m R(t τ b ) mass pyrolysing d (flame flame depth) depth R(t ) spread rate

33 some current concepts in fire spread spread rate depends on: fuel properties (including moisture) fuel properties (including moisture) topography (slope) topography (slope) weather (wind) weather (wind)

34 some current concepts in fire spread spread rate depends on: fuel properties (including moisture) topography (slope) weather (wind) fire triangle topography topography spread rate fuel i.e. spread rate varies as wind, slope or fuel vary (the basis of most current fire-spread simulations) weather weather

35 some current concepts in fire spread spread rate depends on: fuel properties (including moisture) topography (slope) weather (wind) fire triangle topography topography spread rate fuel i.e. spread rate varies as wind, slope or fuel vary (the basis of most current fire-spread simulations) additional factors include: the width of the head fire (distance between flank fires) the width of the head fire (distance between flank fires) development of cellular fire fronts (or fingering) development of cellular fire fronts (or fingering) fireline rotation (up slopes) fireline rotation (up slopes) etc. weather weather

36 oscillatory flame spread and fireline intensity

37 oscillatory flame spread and fireline intensity

38 oscillatory flame spread and fireline intensity

39 oscillatory flame spread and fireline intensity

40 oscillatory flame spread and fireline intensity in other words: when intensity I is low, the fire surges ahead (increased R) then almost stops (reduced R) when intensity I is high after which intensity decreases to repeat the cycle that is: I QmR

41 oscillatory flame spread and fireline intensity in other words: in fact: when intensity I is low, the fire surges ahead (increased R) then almost stops (reduced R) when intensity I is high after which intensity decreases to repeat the cycle that is: I QmR Byram s first formula I = QmR (Byram-1) is an energy balance for steady rates of spread

42 oscillatory flame spread and fireline intensity in other words: in fact: when intensity I is low, the fire surges ahead (increased R) then almost stops (reduced R) when intensity I is high after which intensity decreases to repeat the cycle that is: I QmR Byram s first formula I = QmR (Byram-1) is an energy balance for steady rates of spread his second formula I = Qϖd (Byram-2) is better for unsteady rates of spread

43 eruptive flame spread eruptive fires: Viegas has pioneered the study of eruptive fires and identified many cases in the field these fires are essentially unsteady with an accelerating rate of spread they often occur under deceptively mild conditions resulting in many accidental deaths lives will be saved if they are better understood

44 an erupting field experiment. Portugal 2008

45 an erupting field experiment. Portugal 2008

46 an erupting field experiment. Portugal 2008 ignition (0 seconds) flow still separated (30 sec.) flow attached (37 sec.) 40 metre spread (70 sec.)

47 an erupting field experiment. Portugal 2008 ignition (0 seconds) flow still separated (30 sec.) flow attached (37 sec.) 40 metre spread (70 sec.)

48 an erupting field experiment. Portugal 2008 ignition (0 seconds) flow still separated (30 sec.) flow attached (37 sec.) 40 metre spread (70 sec.)

49 eruptive fires are responsible for many deaths they are poorly understood fatalities often include experienced firefighters

50 eruptive trench fires. Lousa, Portugal 2006

51 eruptive trench fires. Lousa, Portugal

52 topics bushfire chemistry turning vegetation into fuel vapour (at about 350 C) burning the fuel vapour with air (above about 900 C) basic fire spread phenomena and concepts some factors determining fire spread oscillatory and eruptive flame spread the accumulation of fireline intensity concepts behind Byram s second formula for I more detailed fuel descriptions spread rate and intensity interactions possible spread rate and intensity relations

53 intensity changes lag behind spread rate plume air flow u n normal wind air flow flame length char ω pyrolysis rate φ q heat flux flame angle vegetation load m R(t τ b ) d flame depth R(t ) spread rate

54 intensity changes lag behind spread rate plume a slow steady flame spread: u n normal wind air flow schematic illustrations steady spread rate and intensity air flow flame length char ω pyrolysis rate φ q heat flux flame angle vegetation load m R(t τ b ) d flame depth R(t ) spread rate

55 intensity changes lag behind spread rate plume a slow steady flame spread: u n normal wind air flow schematic illustrations after a jump in spread rate: steady spread rate and intensity air flow char R(t τ b ) intensity grows as flame depths grows until conditions become steady again d flame depth ω pyrolysis rate φ flame length q heat flux flame angle R(t ) spread rate vegetation load higher steady spread rate and intensity m

56 a simple model for intensity accumulation plume air flow u n normal wind air flow flame length char ω pyrolysis rate φ q heat flux flame angle vegetation load m R(t τ b ) d flame depth R(t ) spread rate

57 a simple model for intensity accumulation plume in a homogeneous fuel bed Dold and Zinoviev, CTM (2009) air flow intensity growth after a spread rate change u n normal wind air flow flame length char ω pyrolysis rate φ q heat flux flame angle vegetation load m R(t τ b ) d flame depth R(t ) spread rate

58 a simple model for intensity accumulation plume in a homogeneous fuel bed Dold and Zinoviev, CTM (2009) intensity growth after a spread rate change air flow consider: a burnout time τ b fuel load m un uniform pyrolysis rate ϖ = m/τ b flame depth d combustion energy Q spread rate R normal wind flame length air flow char ω pyrolysis rate φ q heat flux flame angle vegetation load m R(t τ b ) d flame depth R(t ) spread rate

59 a simple model for intensity accumulation plume in a homogeneous fuel bed Dold and Zinoviev, CTM (2009) intensity growth after a spread rate change air flow normal wind char consider: a burnout time τ b fuel load m un uniform pyrolysis rate ϖ = m/τ b flame depth d combustion energy Q spread rate R for which: intensity is I = Qϖ d (Byram-2) and flame depth is d = ω pyrolysis rate τb 0 flame length R(t ζ) dζ q heat flux φ flame angle air flow vegetation load m R(t τ b ) d flame depth R(t ) spread rate

60 a simple model for intensity accumulation plume in a homogeneous fuel bed Dold and Zinoviev, CTM (2009) intensity growth after a spread rate change air flow consider: a burnout time τ b fuel load m un uniform pyrolysis rate ϖ = m/τ b flame depth d combustion energy Q spread rate R normal wind for which: intensity is I = Qϖ d (Byram-2) and flame depth is d = flame length 0 q heat flux vegetation simply, flame depth is the distance travelled φ flame over the angleburnout time load char m ω pyrolysis rate τb R(t ζ) dζ and flame depth helps to determine the fireline intensity I air flow R(t τ b ) d flame depth R(t ) spread rate

61 a simple model for intensity accumulation plume in a homogeneous fuel bed Dold and Zinoviev, CTM (2009) intensity growth after a spread rate change air flow consider: this description acan burnout modeltime a flame-wind τ b resonance (Albini, fuel load 1982) m u uniform pyrolysis rate ϖ = m/τ b flame depth d combustion energy Q spread rate R n and eruptive fire growth (Dold and Zinoviev, 2009) normal wind for which: intensity is I = Qϖ d (Byram-2) and flame depth is d = flame length 0 q heat flux vegetation simply, flame depth is the distance travelled φ flame over the angleburnout time load char m ω pyrolysis rate τb R(t ζ) dζ and flame depth helps to determine the fireline intensity I air flow R(t τ b ) d flame depth R(t ) spread rate

62 more detailed considerations y flame B pyrolysing vegetation y = η(t, x) S A R(t) fuel load m h x X(t) d 1(t) X(t) spread and pyrolysis within a homogeneous fuel bed pyrolysis time τ p fuel burning speed S (internal spread) downwards burning time h/s (for bed height h)

63 more detailed considerations y flame B pyrolysing vegetation y = η(t, x) S A R(t) fuel load m h x X(t) d 1(t) X(t) internal spread and pyrolysis in a mixed fuel bed pyrolysis time(s) τ p1, τ p2, τ p2,... fuel burning speed S downwards burning time h/s

64 including a stratified fuel bed density ϱ, energy content Q, burning speed S, vary with height: y flame pyrolysing vegetation ) y = η(t, x) S R(t) fuel load m h x X(t) d(t) X(t) sketch for the case τ pi h/s

65 including a stratified fuel bed density ϱ, energy content Q, burning speed S, vary with height: y flame pyrolysing vegetation ) y = η(t, x) S R(t) fuel load m h x X(t) d(t) X(t) sketch for the case τ pi h/s here the formula for intensity adopts the form (simplified for R S) I = τb 0 q(ζ) R(t ζ) dζ with q(ζ) = Q(y)ϱ(y)S(y) so that intensity is a weighted integral over previous spread rates

66 including a stratified fuel bed density ϱ, energy content Q, burning speed S, vary with height: y flame pyrolysing vegetation ) y = η(t, x) S R(t) fuel load m h x X(t) d(t) X(t) sketch for the case τ pi h/s here the formula for intensity adopts the form (simplified for R S) I = τb 0 q(ζ) R(t ζ) dζ with q(ζ) = Q(y)ϱ(y)S(y) so that intensity is a weighted integral over previous spread rates Qualitative features are still captured by (Byram-2)

67 topics bushfire chemistry turning vegetation into fuel vapour (at about 350 C) burning the fuel vapour with air (above about 900 C) basic fire spread phenomena and concepts some factors determining fire spread oscillatory and eruptive flame spread the accumulation of fireline intensity concepts behind Byram s second formula for I more detailed fuel descriptions spread rate and intensity interactions unsteadiness depends on spread rate and intensity relation Byram number B = QmR/I identifies different behaviour possible spread rate and intensity relations

68 the basic idea topography intensity spread rate fuel fire square for all fires weather if steady if steady fire triangle for steady fires topography topography spread rate fuel weather weather intensity depends on flame depth, accumulated by flame spread I = Qϖ τb 0 R(t ζ) dζ (or similar) and the spread-rate R depends on the intensity I and the spread-rate R depends on the intensity I R = F ( intensity, fuel, weather, topography ) This dependence is not yet known This dependence is not yet known

69 example: R/R s = ( I /QmR s ) ν if ν 1 or QmR = BI if ν = 1

70 example: the Byram number R/R s = ( I /QmR s ) ν if ν 1 B = QmR I is or QmR = BI if ν = 1 one for a steady fireline > 1 for a growing fire < 1 for a diminishing fire

71 example: the Byram number R/R s = ( I /QmR s ) ν if ν 1 B = QmR I is or QmR = BI if ν = 1 one for a steady fireline > 1 for a growing fire < 1 for a diminishing fire if ν < 1 then B = (R/R s ) (1/ν 1) { > 1 for R < Rs < 1 for R > R s so the steady spread-rate R s is stable ν > 1 B = (R/R s ) 1 1/ν { > 1 for R > Rs < 1 for R < R s so the steady spread-rate R s is unstable the fire erupts if R > R s

72 example: the Byram number R/R s = ( I /QmR s ) ν if ν 1 B = QmR I is or QmR = BI if ν = 1 one for a steady fireline > 1 for a growing fire < 1 for a diminishing fire { > 1 for R < Rs if ν < τ 1 1dR then B = ν (R/R = 1 s ) (1/ν 1) ν = 2 2 < 1 for R > R 0.2 2R s dt s 2 3 so the steady spread-rate R s is 3 stable 0.2 ν = 1 { > 1 for R > Rs ν > 1 B = (R/R s ) 1 1/ν < 1 for R < R s so the steady spread-rate 1 2 R s is unstable 2 the fire erupts if R > R s R/R s acceleration approximated using a truncated Taylor series

73 example: the Byram number dr dt R/R s = ( I /QmR s ) ν if ν 1 B = QmR I is or QmR = BI if ν = 1 one for a steady fireline > 1 for a growing fire < 1 for a diminishing fire { > 1 for R < Rs if ν < τ 1 1dR then B = ν (R/R = 1 R s ) (1/ν 1) ν = 2 2 < 1 for R > R 0.2 2R s dt 1 0 s 2 3 so the steady spread-rate dr R s is 3 stable dr dt ν = 5 6 ν = 1 { > 1 for R > Rs ν > 1 B = (R/R s ) 1 1/ν < 1 for R < R s ν = 1 2 ν = 2 3 so the steady spread-rateν R= s is unstable 2 therfire erupts if R > R s R/R s acceleration approximated 1 using 0 a truncated Taylor series 0 1 dr dt numerical simulations (dotted) for ν < dt 1 R R

74 example: R/R s = ( ) ν I /QmR s or QmR = BI if ν 1 if ν = 1 dr R (1 ν)/ν spread-rate the Byram number B = QmR evolutions dr for one ν for > a1 steady fireline dt dt is > 1 for a growing fire I ν = < 1 for a diminishing fire ν = 5 6 { 0 > 1 for R < Rs if ν < τ 1 1dR 5 then B = ν (R/R = 1 R s ) (1/ν 1) 10 ν = 2 2 < 1 for R > R 0.2 2R s dt 1 0 s 2 R 3 dr so the steady spread-rate dr R s is 3 stable dt 3 2 { > 1 for R > Rs ν > 1 B = (R/R s ) 1 1/ν 3 ν = < 1 for R < R s ν = ν = 1 ν = 2 3 so the steady spread-rateν R= s is unstable 2 therfire erupts if R > R s R/R s 4 acceleration ν = 3 2 approximated 1 2 using 0 a 3truncated Taylor series 0 t numerical simulations 5 (dotted) 10for ν < dt t R 1 R

75 example: the Byram number R/R s = ( I /QmR s ) ν if ν 1 B = QmR I is or QmR = BI if ν = 1 one for a steady fireline > 1 for a growing fire < 1 for a diminishing fire if ν < 1 then B = (R/R s ) (1/ν 1) { > 1 for R < Rs < 1 for R > R s so the steady spread-rate R s is stable ν > 1 B = (R/R s ) 1 1/ν { > 1 for R > Rs < 1 for R < R s so the steady spread-rate R s is unstable the fire erupts if R > R s

76 example: the Byram number R/R s = ( I /QmR s ) ν if ν 1 B = QmR I is or QmR = BI if ν = 1 one for a steady fireline > 1 for a growing fire < 1 for a diminishing fire if ν < 1 then B = (R/R s ) (1/ν 1) { > 1 for R < Rs < 1 for R > R s so the steady spread-rate R s is stable ν > 1 B = (R/R s ) 1 1/ν { > 1 for R > Rs < 1 for R < R s so the steady spread-rate R s is unstable the fire erupts if R > R s if ν = 1 then B is constant so the fire erupts if B > 1

77 example: R/R s = ( ) ν I /QmR s or QmR = BI if ν 1 if ν = 1 R the Byram number QmR one for a steady fireline B = 3 is B > = 21 for a growing fire I 10 < 1 for a diminishing fire 1 { > 1 for R < Rs if ν < 1 then B = (R/R s ) (1/ν 1) B = 3 2 < 1 for R > R s so the steady spread-rate B = R1 s is stable 0.1 { > 1 for R > Rs ν > 1 B = (R/R s ) 1 1/ν B = 2 3 < for R < R s spread-rate evolutions for ν = 1 so the steady spread-rate R s is unstable t 0 1 the fire erupts if2 R > R s 3 if ν = 1 then B is constant so the fire erupts if B > 1

78 numerical approach used here (reformulation as a PDE) define so that ϕ ( t, s ) = R ( t s ) ϕ t + ϕ s = ε 2 ϕ s 2 ( taking ε 0 ) ϕ ( t, 0 ) = R ( t ) I = τb 0 R ( t ) = F ( I ) q(s) ϕ(t, s) ds with suitable initial conditions ( ) ( ) ϕ 0 0, s = ϕ0 s

79 effect of the formula I = for some generic examples of q : τb 0 q(ζ) R(t ζ) dζ q Qm 1 3(τb 2 ζ2 ) τ b 2τb 3 3 τ b ζ 2τ 3/2 b 2(τ b ζ) τ 2 b 3(τ b ζ) 2 τ 3 b 6ζ(τ b ζ) τ 3 b 2ζ τb 2 sketch ζ ζ ζ ζ ζ ζ ζ τb τb τb case: a b c d e f g τb τb τb τb

80 effect of the formula I = for some generic examples of q : τb 0 q(ζ) R(t ζ) dζ q Qm 1 3(τb 2 ζ2 ) τ b 2τb 3 3 τ b ζ 2τ 3/2 b 2(τ b ζ) τ 2 b 3(τ b ζ) 2 τ 3 b 6ζ(τ b ζ) τ 3 b 2ζ τb 2 sketch ζ ζ ζ ζ ζ ζ τb τb τb case: a b c d e f g τb τb τb τb ζ 2 2 α e d c b a g f ν orγb τ 1 = Qm 2 τb ζ q(ζ) dζ 0 stability of the steady spread-rate for ν 1: R = R s + εe αt/τ 1 or growth rate dependence on B for ν = 1: R e αt/τ 1

81 interim summary accumulation of intensity is a key factor in unsteady fires the balance I = QmR (Byram-1) arises only for steady fire spread the balance I = Qmd/τ b (Byram-2) extends to unsteady fires in essence, intensity accumulates from earlier spread rates

82 interim summary accumulation of intensity is a key factor in unsteady fires the balance I = QmR (Byram-1) arises only for steady fire spread the balance I = Qmd/τ b (Byram-2) extends to unsteady fires in essence, intensity accumulates from earlier spread rates for any R = F( intensity, fuel, weather, topography ) stable steady spread arises if R = F(I ) is sublinear QmR a Byram number distinguishes fire growth or decay I

83 interim summary accumulation of intensity is a key factor in unsteady fires the balance I = QmR (Byram-1) arises only for steady fire spread the balance I = Qmd/τ b (Byram-2) extends to unsteady fires in essence, intensity accumulates from earlier spread rates for any R = F( intensity, fuel, weather, topography ) stable steady spread arises if R = F(I ) is sublinear QmR a Byram number distinguishes fire growth or decay I in modelling a non-homogeneous fuel bed the approach can deal with stratified and mixed vegetation types intensity involves a weighted accumulation of burning material Byram number has the same significance

84 interim summary accumulation of intensity is a key factor in unsteady fires the balance I = QmR (Byram-1) arises only for steady fire spread the balance I = Qmd/τ b (Byram-2) extends to unsteady fires in essence, intensity accumulates from earlier spread rates for any R = F( intensity, fuel, weather, topography ) stable steady spread arises if R = F(I ) is sublinear QmR a Byram number distinguishes fire growth or decay I in modelling a non-homogeneous fuel bed the approach can deal with stratified and mixed vegetation types intensity involves a weighted accumulation of burning material Byram number has the same significance more work is needed to determine R = F(I )

85 topics bushfire chemistry turning vegetation into fuel vapour (at about 350 C) burning the fuel vapour with air (above about 900 C) basic fire spread phenomena and concepts some factors determining fire spread oscillatory and eruptive flame spread the accumulation of fireline intensity concepts behind Byram s second formula for I more detailed fuel descriptions spread rate and intensity interactions unsteadiness depends on spread rate and intensity relation Byram number B = QmR/I identifies different behaviour possible spread rate and intensity relations

86 speculative spread rate and intensity relations in separated (buoyancy dominated) fire-plumes: flame length scales approximately as I 2/3 so for a given equilibrium spread rate R s (wind, slope, fuel) a possible relation is R ( I ) ν = for ν 2 R s QmR 3 s

87 speculative spread rate and intensity relations in separated (buoyancy dominated) fire-plumes: flame length scales approximately as I 2/3 so for a given equilibrium spread rate R s (wind, slope, fuel) a possible relation is R ( I ) ν = for ν 2 R s QmR 3 s in attached (wind driven, low intensity) fire-plumes: without slope, attachment may arise below an intensity I a without slope, attachment may arise below an intensity I a spread rate would then be driven by wind or convection spread rate would then be driven by wind or convection

88 speculative spread rate and intensity relations in separated (buoyancy dominated) fire-plumes: flame length scales approximately as I 2/3 so for a given equilibrium spread rate R s (wind, slope, fuel) a possible relation is R ( I ) ν = for ν 2 R s QmR 3 s in attached (wind driven, low intensity) fire-plumes: without slope, attachment may arise below an intensity I a spread rate would then be driven by wind or convection there may be hysteresis between these two situations which would explain oscillatory flame spread

89 Albini s relation between R and I spread-rate formula of Albini (1982): (not yet tested) R (U R)3 = 1 + R 0 RA 3 I I 0

90 Albini s relation between R and I spread-rate formula of Albini (1982): (not yet tested) R (U R)3 = 1 + R 0 RA 3 I I 0 2 R m s 1 I = QmR U = 4.0 m s I/I 0 R A = 2 m s 1 and R 0 = 2 cm s 1

91 summing up accumulation of intensity is a key factor in unsteady fires flame depth and intensity generation can be tracked experimentally and in fireline simulation programs

92 summing up accumulation of intensity is a key factor in unsteady fires flame depth and intensity generation can be tracked experimentally and in fireline simulation programs we need R = F( intensity, fuel, weather, topography ) both experimental and theoretical considerations can provide valuable information and insight attached and separated flow should lead to different relations

93 summing up accumulation of intensity is a key factor in unsteady fires flame depth and intensity generation can be tracked experimentally and in fireline simulation programs we need R = F( intensity, fuel, weather, topography ) both experimental and theoretical considerations can provide valuable information and insight attached and separated flow should lead to different relations the potential unsteady phenomena over burnout or residence time scales can be described in a physically sound way the ideas extend readily to real (two-dimensional) topography

94 intensity and spread rate interactions in firelines acknowledging: with financial assistance from Malcolm Gill E. P. S. R. C. Jim Gould Bushfire C. R. C. Peter Ellis Leverhulme Trust Neil Cooper A. D. F. A. Matt Dutkiewicz MIMS AWE Rick McRae Phil Cheney Pat Barling errors and omissions are the responsibility of John Dold Jeff Cutting < > Cliff Stevens Domingos Viegas Albert Simeoni Forman Williams Eilis Leslie Charlie Westbrook Victoria John Gregory Sivashinsky J Barry Greenberg Rodney Weber Anna Zinoviev

95 intensity and spread rate interactions in firelines acknowledging: with financial assistance from Malcolm Gill E. P. S. R. C. Jim Gould Bushfire C. R. C. Peter Ellis Leverhulme Trust Neil Cooper A. D. F. A. Matt Dutkiewicz MIMS AWE Rick McRae Phil Cheney Pat Barling errors and omissions are the responsibility of John Dold Jeff Cutting < > Cliff Stevens Domingos Viegas Albert Simeoni Forman Williams Eilis Leslie Charlie Westbrook Victoria John Gregory Sivashinsky J Barry Greenberg Rodney Weber Anna Zinoviev

96 intensity and spread rate interactions in firelines acknowledging: with financial assistance from Malcolm Gill E. P. S. R. C. Jim Gould Bushfire C. R. C. Peter Ellis Leverhulme Trust Neil Cooper A. D. F. A. Matt Dutkiewicz MIMS AWE Rick McRae Phil Cheney Pat Barling errors and omissions are the responsibility of John Dold Jeff Cutting < > Cliff Stevens Domingos Viegas Albert Simeoni Forman Williams Eilis Leslie Charlie Westbrook Victoria John Gregory Sivashinsky J Barry Greenberg Rodney Weber Anna Zinoviev