Multicomponent-Liquid-Fuel Vaporization with Complex Configuration

Transcription

1 Multicompoet-Liquid-Fuel Vaporizatio with Complex Cofiguratio William A. Sirigao Guag Wu Uiversity of Califoria, Irvie Major Goals: for multicompoet-liquid-fuel vaporizatio i a geeral geometrical situatio, predict vaporizatio rate, iterface scalars ad scalar gas-phase profiles for ay value of the Lewis umber, with trasiet heat ad mass diffusio i the liquid iteriors.

2 Backgroud Defie mass-flux potetial Trasform the gas field equatio to Laplace s equatio assumig oly Stefa covectio Method of images to solve gas field with iteractio droplets Reduce scalar properties to fuctio of mass-flux potetial oly

3 Correlatios ad approach to solve the Cotiuity: S Species: Eergy: 0 gas phase V 2 ( V ) 0 0, determied by vaporizatio rates. ( VY DY) 0 ( Vh T) 0 D l[1 B ] / c Y h h Le B B p, S,,, S,, M, H, D Y, S Leff M, ad satisfy: 2 S 0 0; ; 1

4 Correlatios ad approach to solve the gas phase (cot.) Reduce scalar properties to fuctio of mass flux potetial oly: ' Y D d /( D) 0 [1 BM, ] Y S, Determie, h h, S Leff 0 [1 BM, ] L eff Y s, L Determie ad, eff D d /( / c ) N L / RT L / RT s, ls, k 1 ks, k Y W X Y W e e N 1/ Le M, H, ' p, b, s ( / ) ( 1,..., 2), [1 B ] 1 B ( 1,... N 2)

5 Goverig equatios for liquid phase Y D Y 2D Y 2. l, l, l, l, l, [ R] t R R T T 2 T 2. l l l l l [ R] t R R ICs : Y (, t 0) Y ; T (, t 0) T l, l, 0 l l0 Dl, Yl, BCs : Yl, ( 1, t) ( 1, t). RR T. l l ( 1, t) lrr[ N 2 1 k( hk, hk, S) k (1 B ) 1 Le, M, N 2 1/ k 1 L k k ]

6 Poits of umerical calculatio Eight droplets i a cubic array, with iitial distace betwee droplets 10 times of iitial droplet radius, ad the ambiet pressure 1 atm; The droplet is composed of three species: heptae, octae ad decae ; Variable gas-phase properties ; The gas-phase mass diffusivities are biary mass diffusivities i itroge ad vary i space ad time; The liquid-phase diffusivity of a species is determied by weightig its biary mass diffusivities i other two species based o mass fractio, the biary mass diffusivities are give by semi-empirical equatios.

7 Surface temperature ad species mass fractio at the liquid surface T s (K) 2000 ; [,0,1,,0,2,,0,3] [1/ 3,1/ 3,1/ l l l 3]. Surface temperature icreases with time. Surface mass fractio of volatile compoets decreases while mass fractio of o-volatile compoets icreases. T K Y Y Y t * 10-7 /R 2 0 (s/m 2 ) iteractive droplets isolated droplets Y l at surface decae octae 0.1 heptae t * 10-7 /R 2 0 (s/m 2 ) iteractive droplets isolated droplets

8 T b at surface Actual boilig poit 1/ Tbi 1/ Tbi, pure R.l( Xi, ls )/ Li. Actual boilig poit of volatile compoets icreases while actual boilig poit of o-volatile compoets decreases. The temperature at ay locatio i the droplet will ot exceed ay compoet's actual boilig poit at that locatio at ay time heptae octae decae T b, 1 / T l at 2% lifetime at 20% lifetime at 60% lifetime at lifetime t * 10-7 /R 2 0 (s/m 2 ) r (ormalized)

9 The shape of radius squared curves The rate of decrease of radius squared ormally become larger with time. But whe the ambiet temperature is very low, B M, may decrease with time due to a strog distillatio effect, ad 2 the ( R / R ) t curve may cosequetly become cocave K 400 K 500 K K 400 K 500 K (R/R 0 ) B M, t * 10-7 /R 2 (s/m 2 ) (R/R 0 ) 2

10 Comparisos of differet cases Higher ambiet temperature always leads to faster vaporizatio rate. The mixture with greater fractios of the more volatile compoets has slightly faster radius squared rate of chage case 1 case 2 case case 1 case 2 case 3 dr 2 /dt / (2D l, 0 ) (R/R 0 ) t * 10-7 /R 2 0 (s/m 2 ) t * 10-7 /R 2 0 (s/m 2 ) case 1: 2000K, 1/3,1/3,1/3; case 2: 1000K, 1/3,1/3,1/3; case 3: 2000K, 2/3,1/6,1/6.

11 Artificial liquid (R/R 0 ) t * 10-7 /R 2 0 (s/m 2 ) actual mixture artificial liquid 1 artificial liquid 2 A artificial sigle-compoet liquid is created to serve as a surrogate for the multicompoet. A average of the compoet properties is cosidered. The mass fractios of the more volatile compoets become smaller tha their iitial value i the process of the vaporizatio of the mixture, so less weightig should be put o the more volatile compoets i order to have a radius squared rate of chage closer to the value for the actual mixture. actual mixture: 2000K, 1/3,1/3,1/3; artificial liquid 1: 1/3,1/3,1/3; artificial liquid 2: 1/6,1/6,2/3.

12 2000K Profiles i the liquid phase ( ) T The profiles of temperature ad compositio iside the droplets chage with time while the chages of surface temperature ad surface compositio become slower with time. As heat coductio i the liquid phase is much faster tha mass diffusio, the temperature becomes early uiform ad costat after some time while the profiles of species mass fractio still varies. T l (K) at 1/20 lifetime 300 at 6/20 lifetime 290 at 11/20 lifetime at lifetime r (ormalized) Y l, at 1/20 lifetime at 6/20 lifetime 0.05 at 11/20 lifetime at lifetime r (ormalized)

13 Profiles i the liquid phase ( T 350K) Lower ambiet temperature always leads to more uiform profiles because it results i loger lifetime ad allows more time for heat ad species diffusio i the droplets. I the case of 350K ambiet temperature, the temperature profiles are early uiform all the time but the mass fractio profiles are ot, so the slow vaporizatio limit is ot strictly satisfied for multicompoet case eve at low ambiet temperature 350K. T l (K) at 1/20 lifetime 295 at 6/20 lifetime 290 at 11/20 lifetime at lifetime r (ormalized) Y l, at 1/20 lifetime at 6/20 lifetime at 11/20 lifetime at lifetime r (ormalized)

14 Profiles i the liquid phase ( T 3000K ) I the case of 3000K ambiet temperature, the temperature ad mass fractio profiles become steeper but still do't produce a sufficietly thi diffusio layer to satisfy strictly the fast vaporizatio limitig coditios. T l (K) at 1/20 lifetime 300 at 6/20 lifetime 290 at 11/20 lifetime at lifetime r (ormalized) Y l, at 1/20 lifetime at 6/20 lifetime 0.05 at 11/20 lifetime at lifetime r (ormalized)

15 Major coclusios The revised defiitio of the Lewis umber ad the ew heat trasfer umber BH, are show to be very useful i the aalysis ad calculatio. Liquid temperatures may exceed the pure-form boilig poit but are always lower tha the actual boilig poit i a liquid bled, thus o gasificatio iside the liquid occurs. At low ambiet temperature the rate of decrease of radius squared may decreases with time due to a strog distillatio effect. The slow vaporizatio limit model predicts the trasiet behavior well oly for sigle-compoet case at low ambiet temperature (350K). The fast vaporizatio limit model does t predict the trasiet behavior well eve at the ambiet temperature of 3000K.

16 Future work Exted the calculatio to ivolve forced covectio i the gas phase Cosider iteral circulatio i the liquid phase

17 Thak you!