Page 148 - konishipaper

274 K.Takahashietal./ProcedingsoftheC01'lbustionInstitute30(205)2271-2277
If the local liquid velocity is defined as u = αy2(0 ζ y ζ 五) and α = 1， liquid volumetric fiow !ate per unit width of the tray is:
2.3.Analyticalresults
SolutionsfrOlnEq.(17)wereplotedforfive diferentvaluesofwavelengthintheMa-Frcor- dinate.Thereisageneraltrendthatthecritical ManumberincreaseswithanincreaseinFrnum- ber.Liquidwilbecomeincreasingunstablewith decreasesbothinthewavelengthandinFrnum- ber.Thisindicatesthatliquid'sfresurface，stim- ulatedbyth~ heatfromthespreadingfiameunder microgravity(alargeFrnumber)condition，be- comesverystableifthewavelengthofsurface waveissuficientlylarge(aconditionsatisfiesthe NASA'smicrogravityexpernentswherenopul- sationwasobserved[1J).Gravitycontributesto createsurfacewavemotionthatenhancesinstabil- ityoftheliquidfresurface.
ThecriticalManumberversusWenumberwas inspectedusingthevaluesofthecriticallength scaleratioforthenormalgravityandmicrograv- ityconditions.ThecriticalManumberformicro gravityishigherthanthatfornormalgravity， indicatinggravitycontributestomakingtheliquid fresurfaceunstable.
Figure3showsthecriticalMαnumber_versus sub-surfacelayerdepth(definedinFig.2)where thetwoconstant Wenumbercasesareploted:
W e = 10.6 for normal gravity and W e = 53.8 for micro gravity. The sub-surface layer depth，
13.8m m，formicrogravityisaboutthretimes largerthanthecorespondingdepth，4.38m m， for nOlmal gravity. The critical M αnumber at h = 13.8 m m for micro gravity is M α = 0，4. which ismuchlargerthanthatofthecriticalMa= 0.1 fornormalgravity，sugestingthatwhenliquid surface becomes unstable and surface wave is formedundermicrogravity，thevaluehwilbe larger(whichmeansthediameterofsub-surface liquidconvectionwilbelarger).Thisposibility， ifva!idated，c.ouldexplainNASA'smicrogravity experimentalresults[1J，wherealargesub-surface circulationwasobservedforl-butanol，whileun- derthenormalgravityconditionthediameterof
r=月αY2dy=jGf，山 averageliquidvelocity
IS 玩=pi
，.L and the mOlnentum displacement thicknesiss=~. Eq.(9)canberewritenas:
バ/は¥
13 13 土
-3/ (g+二)
r~t3=竺 qj' (10) 15-cr¥ p)-cr pA[
_3 /
wherercristhecriticalfiowraterequiredforsur- facewavetoocur.
2.2.Thenon-dunensionalparameter Thefolowingnon-dimensionalparametersare
introduced，
r~(.3
TTT ゾgh
pAu2 vre=一一一
Mα-ασrqj
Fト=ゴニ UsingEq.(1)，Eq.(9)canberewritentonon-
(12)
σ dimensionalformofEq.(12):
pA[u2・
Anoveralenergybalanceandanoveralmomen- tumbalanceforsub-surfacelayereach，respec- tively，producesthefolowing:
え[I1T Us I1T
qj二一一?μσr-， (13)
αh
'h
L
I
A
T
where L and h are the thenal characteristic lengthanddepthofthesub-surfacelayercircula- tiondefinedinFig.1.UsingEq.(13)，threnon- dinlensional parameters shown in Eq. (1 1) can berewritenas:
σrl1T 1 h
門 r=一一 (14)
r
胸=等!hG) UsingEqs.(14)-(16)，Eq.(12)canbereducedto:
一 2vgμ vizL'
阪 4fA(1)?
U
1 ."h1
1-s=寸 +4n:"一一一一 (17)
ro
0.1 0.05。
。
Fr" . - - - A -Wを M α
Eqs.(14)-(17)，al1havingthecriticalengthratio intheirforms，describegenerationofliquidsur- face wav色 and its propagation; therefore，these fourequationsmaypredicttheonsetofiamepul- sationandsubsequentpulsatingfiamespreadover liquids. These predictions wil be validated by other researchers' experimental data as wel l as ournewandpreviousexperiments.
"'"話回国"""'"祖踏切
一-
(15) (16)
~
Fig. 3. M a number versus the thermal characteristic depthofthesub-surfacelayercirculationh.
h[1]
10 15 μ:gButanol 13.8mln
、l，ノ
噌EEム
、 f'I
4EEム
庁A M
l 一院 一hτA
π λ斗
十 l 一が
一
一nny