Page 146 - konishipaper

2272 瓦 Takahashietα.1/ProcedingsoftheCombustionInstitute30ρ05)2271-2277 Nomenclature
A theamplitudeofsurfacewave(m)
a theadjustabl己faptorofalocalliquid
velocity，(m-1s-l)
C土 theforwardandreversepropagation
velocitiesofdynamicwave(m/s)
Co thepropagationvelocityofkinematic
wave(m/s)
thewavevelocity(m/s) theFroudenumber theacelerationduetogravity(m/s2) theinitialfuelayerthicknes(m) thesub-surfacefiowheight(m) thethermalcharacteristicdepthofthe sub-surfacelayercirculation(m)
k thewavenumber三(2π/A)(m-1)
L the thermal characteristic length of
thesub-surfacelayercirculation(m) Ma theMarangoninumber 2 qi theheatfiuxfromthewal(W/m)
U a local liquid ve10city (=ay2(0ζ y ζ 五) ) (m/s)
GreekSymbols
s the momentum displacement thick-
nes s (三 J~1 U切 /u初)
i1T the temperature dif ference between flashpointandliquidbulktempera- ture(K)
surfacewavetoocur(ml./s) wavelength(m) thedensityoftheliquid(kg/mj thesurfacetensioncoeficient(N/m) theshearstresintheliquid(Pa) the surface shear stres due to Marangoniefect(Pa)
subscripts
b liquidphase
theinterfacebetweengasandliquid
phase
t thepartialderivativesintime
x the partial derivatives in the
x-direction
icallengthscaleratio，h/L，obtainedexperimen- tal1ybytheSchlierentechnique[10]tocorelate flame spread rate over four diferent alcohol (methanol，ethanol，propanol，andbutanol)fuels. T h e c r i t i c a l l e n g t h s c a l e r a t i o h / L c o n s i s t s o f c h a r - acteristic thermal-fluid length in liquid surface， and subsurface liquid circulation (or thermal structure) depth，both created by the spreading 丑ame. Figure 1 shows those two lengths deter- minedinaSchlierenimage.Wiliamshimselfin
Us theliquidsurfacevelocity(m/s) U t4e average liquid velocity
J;Udy/h)(m/s) theWebernumber thefiowdirectioncordinate thenormaldirectiontothewal
fiameleadingedgetounderstandthemechanism ofpulsatingfiamespread[6-8].Asaresult，adual pulsationstructureforflamepulsationwasfound consistingofamain-pulsationofabout0.5-1Hz， a n d a s u b - p u l s a t i o n o f a b o u t 5.:. . .-10 H z [8]. T h e main pulsation created the generation and disap- pearanceofacoldtemperatureval1eyintheliquid surface ahead of the fiame [7]. Based on these experimentaldata，weproposedapulsatingfiame spreadmodel[7]consistingofsub-surfacelayer circulation and the surface wave. Other groups (NASAandtheUCI)numericalycalculatedpul- satingfiamespreadbothundernormalgravity andmicrogravityconditions[9，10Jandindicated that the control mechanism over the pulsating spreadundernormalgravitymightbediferent fromthatundermicrogravity.
To benefit from al these experimental and numericalstudies，andtoupdatethetheoryon fl.amespreadoverliquidsformulatedbyWi1iams [1J，weconductedstabilityandscai1nganalyses ontheseresultswiththehopetofindaunifiedthe- oreticalbasiswithwhichtocorelatethem.Our instability analysis was focused on the liquid sub-surfacelayeraheadofafiame'sleadingedge， whereasurfacewavewasinitiatedandacoldtem- p e r a t u r e v a l1 e y w a s c r e a t e d . W e i n t r o d u c e d t h r e e pi-numbers，Ma，砂'e，andFrnumbers，andacrit-
Fig.1.A Schlierenphotographandde白ledcharacter- isticlength，L，andthedepth，hofsub司 surfacelayer c i r c u l a t i o n ( f u e l is ル p r o p a n o l ， H = 7 m m ， a n d t h e i n i t i a l fue1temperature=16.3OC).
F liquidVolunletriC.fio~ rateperun件 widthofthet町(=必 αy2dy=id3)
(m2/ s ) ¥ / rcr the critical fiow rate r~quired for
)
c肝 gHh-h
阪 xy
APσ 九日
一