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Vaporization of bi-component droplets in a turbulent over-heated flow : Experiments and Numerical Simulation

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(1)Open Archive TOULOUSE Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 11182. To cite this version : Moreau, Florian and Castanet, Guillaume and Bazile, Rudy and Lemoine, Fabrice Vaporization of bi-component droplets in a turbulent over-heated flow : Experiments and Numerical Simulation. In: 24th European Conference on Liquid Atomization and Spray Systems, September 2011 (Estoril, Portugal).. Any correspondance concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr.

(2)  

(3)        

(4)             

(5)   

(6)  .   !"#$% ' () $"*" !  . #$%)  ,-. #.',-/- )% 0 ) ))  1, %'  "

(7) 233    

(8) ',-,"

(9) 233     

(10)  455)6475 )!89" 5)5$5 9 $"4) 4 86:5 )87 8" )

(11) "5/;<$ 1. -) )   /.-18

(12) "5 ))$94  84 0 )) =54 )5840 ))5)$5 9 !9$)64) 4=84

(13) "5$5 4868)) 4=4 9   4)823< 475   8  8

(14) "5940 ))= 544$9 5)58)   9)4)  5) >=  4 )5 5  )4))5)-5544 58)4 0 )54$4  )$5 4=54 58)884 ? 5  =644  @847544.-: )!  88 )   !49==))5-45  84  )59=)9!4  64 4)$4 )5$54 )5  8) 5 !9675)    >)4=7 848   = =840 )54 ) 495.   48 ))=8)5$5 9 86AB8 )   )64 ? 55 $  8) 4  ? 8 0 ) 8   4 9  49  8   9  =  :$5  8  )$ )  54!   )  >=        )5  8  4  8   )5  9!  9   $5 7 848 $5 4=54 )  )5) $  6  9  8    5) ) 5 9 4 88  8  9   )5 $54$ ) !88 @44)  >A B46)4 9     ))5 $5@444) 488)5   9  8  9   ! ! 4 8$5  5 )6)64 $5A

(15) B -) ))4$585! 9 86 75)))4 8 4=4 9  $ 64  ) 9  49 ))4 -45 )! 8 5!)87 8" )

(16) "5/;<$ 1? ) 5 )4=  9 $4)868)  ) 0 ))= 54/$   9   4   )5)9 1645 8 0 ))=

(17) " 5   64 4)$)8."-) )   /.-1  4 !475 80 ))=86  69 5) 58)     64 4)>    488  8 9   ) )5 64)  5) >=  4)5 5A2B  )4))5)A;B69 )8 484 )  4 $5)

(18) "586=9675)  69) )4=4 849) )9!.-               

(19)   475" 5 $ 0  /3C=4 33D =1644=4  9   9=)9!5 !)=) 9  = !)$5)9!()) '$ AEB. )? ) !)   /=1448 )4 =44 984 !)  49 5 )9!2;4  49=

(20) )4? =84 2;45  $= ) !>)40  F4 4)$  4 9   !  423<64=)5!4?584868)AGB . 5)= 489 H5" !8.

(21) 4 4 64 440 45)  /D 7D  1 5)88 E3== )5 =45 = 33=)0 55)6460 6)6/33 73 1)6=.!76)6/37C  16=5  =4 4 474= )7 =84 84 44(74)74 =>4 840 45)  4 84 4-486=    69=$$  )*  )* 64 *+ D 46)484 4   4? )0 )7 8

(22) "5/;<1)" /C;<1 4 95"4) 52

(23) J9!84)49 >$ ! K -) 4 )5   ?   )9!5 = )686 5 )4 84 4 45849= ))*+3F44>)840 )86)=) =  )6=$ !84)5 4)EK64$4  4)5=8$!=49 =86  G3L/= 1 9"7586)5! ) 5 84  >$ ! 8 7 0 )8 7 ( 8 8

(24) "5 40 )7= 5  =0 ) :58  :5$ 8 . 2

(25) J. K 2

(26) =K 3

(27). =K ;<. D

(28) J.  <. ;3";.  

(29)  4$ ! 84   54 )9!:55!/:14 $ !))84)5 ) =.4:55!/.:1 4$ 84= )$ !84)55)8= 

(30) 7 548= 84? /M)*N3E1 4)5>)4 86486O6$ 4)5>)49==   4$  54$ !-) 94$ 8 )84)58)  "

(31). C. 73. G. ! -.%/. E. 75) ) $. ; 2

(32).  3. !" #$ 75" 5. 3. ;3. 33. ;3. 33. ;3.

(33) 33.

(34) ;3. 233. ,-./ !" %$.:84)5 )*N3;)0 N2

(35) J. ."-) )   /.-18

(36) "5 ) )9!40 ) 5))P /  EE 1  6  )    )  4     8 

(37) "5    94  0 )  )  $5   54  4  -  40 9)454! 5488   F448   7 )9! 96$=4 )48   955   8   =   )  $    =  8  4=4  6$=4  4  4  7   =4  4   6= )   96.

(38) 7 )=' 4 98)54554 987 )  1 )  848  =    48      )4 )!

(39) "5 - 54"54!  55 4$9 6)!  ))/ACB)ADB184$5 544955  8

(40) "54#(7)8

(41) 3 

(42) 23645> C;;8=85 96 DC)2

(43) J4

(44) "5 8   =)96

(45) ;3);;3647 2 3465 )  5548   55=  )=J 4)OACB 96 DCJ)2

(46) J 48  845 4=8 8   5   )=  4;< )=@A3B48  8 0  4=  9!  7!=  $  4  =  8  5     ==9  -8  4  8    8  4  5    = ) 48   = 9664486=58)75  / (  1 1  3 1   1 

(47).  1  (  (. . 64(5458459$ 45 7849 

(48) 99=   6$=4 4 )!) 48   0  !) 4!=94)5) !84=45 5484 849 4 44 5/=(1 ) 959!

(49) "5 84 ) 949584  )= 4)84(74 48    = 96) 6! (. .  1  (  (.   / ( 1 1  3 1

(50) 3 64(4)  966  $  4 )>4 844 4/(+314 4575795   9 ))$4 988  = 4=54 64 4) !>) 4

(51) "5   84 $   (.   1  (  (  / ( 1 1 1  ( 1  3

(52) 3  /3 1  3 1.  =48   840 )54 9588  )) 45 84 )5 ) 4$ 8 84)5)54 4)83 "; -5!4  58)4=54==9!8  )9!40 ))5954 )8-755 ))P  64486= 4   N EE =!N

(53) 3 Q 580  !3O$  4 =)644 > 89 233 L4 8   =  )64E9 3 273 2578) /.-R". 1) ;C9? $

(54) 33";339)"58 )$ =) 45  84)5 @8459) 40 ))$5 54 -=4 55)) 9))8=/ =G7G  =148)=   9 )  8  4  5   =  4         =  =  4  4=4  5  80    8 54= 844) )) 9!=9)49!= 55)45 == =4$5 54)4 =40 )54 8!9)/=21AB  

(55)   )5884  8

(56) "5 40 )54  5) 8=  ; 8 )88)654 84 4/)*+3E31840 ) )4   8  4  4  )     4    5  8  ?   )$   4  5>  =  )  )  )6  )     94  )5  8  4  )5  9!   9       8  4  86  )  54  4=  =7"!!84)5  ) 40 )

(57) "586 5)==$ "  9)$)9!/=E1 

(58) . *. 3.  / 12&    64 2 &   . .  3 . . 2 3 ,

(59) 3. , 3 .

(60) 3. .

(61) 64   )4

(62) "50 )   3 4.:5=)7)  4  985) )9!4.: 4)5$ ! 2&     )9!6=4=4$ !))9!4.:8 4 )5)9!,4 ) 48 448)555,4 ;;. 33" 23S  3"E3S 23"C3S 3" ;S )=$ !. ;. $

(63) -)/. 2; 2. .

(64) ;

(65). ;. ;. 3. 3;. . ;. ;.

(66). )* !" &$ 7  $   8  )   = )$ ! (++3 8/)1 ))55 /)   8) $ )84 1. . . !" '$ 0 )"$5 54) . 4)5884  8

(67) "54$5 54/=G188 )*N

(68) 24)!! 975)9!58   8495849 4 

(69) "5    86    4  $5   54    9)     4  "   9!  ==  4    58  =  4  9 >  $ !  /=  C1  4  $     8  4  )    86 /58)9!4? )861 5)4$5840 ) 5449$)$  5)D

(70) <84? )86" 64 444)5 $5))*N;. . !" ($)5884  8

(71) " 540 )54)*N3E3/@1 )*N3

(72) /T1 )*N; /U1 )*NDE/"1. . !" )$ 7$ 84

(73) "5 8640 )54.

(74) . !" *$)5884  8

(75) "54$5 54)*N

(76) 2/T1 )*N23C/R1 )*N2CC/@1. !" +$7$ 84

(77) "5 86"4=54$.    The experimental results were compared with a simplified model of droplet evaporation. This model considers that the heat and mass transfers inside the droplets results from pure diffusion and advection by the internal motions due to the friction between the liquid droplet surface and the external air flow. The evolution of the liquid composition is described by the discrete components approach presented by Tong and Sirignano [12], which consists in following each chemical species individually. Denoting      , the equation for mass and heat transports within a droplet can be presented in the following form:    5 5  5 5  ,

(78)     64          -40  5 5)45 048 6     

(79)     

(80)  

(81)  

(82)    

(83)   

(84)  9)'= A;B) )4  5888 $)88 $!4 84 484  5 97))40 )80 $)49 8 4 $ $9 4)88  88  ,  /44)88 $! ,  44)88 $!  +7 )8  1 )9!8 V==8 G   8488 84   ,

(85)   , 64V8  8444.  9 !

(86) =$A;B4  0   55)9!486=9 )! ) 0   "  1 0  0    &       3     "  ,&  :9   641)5 $!4 )4'46) 9 D is the diffusion coefficient of 6&   6&  48'5)= 9 5)=45 -4 specie i in air) :9     6&  v,i. 5   495  0  87)2

(87) J) 6$   )90 34 557? 8)9!48 44868

(88) "5)" $! 54868 =4 4 = 6$ N3 4$ 8 ! 98 ) !9!486=   6&   6&   .

(89) 4 )84   5) 85 )8 4 )56

(90) "5/N31NE<)0 -+/+ DCJ4$5) 9)6448840 ")! 55 4)484!A;B )'46) 94=$9! K

(91) 33GG    :0  "   ;

(92) !  7  ;

(93)   #% $  1 . :0. <  :0  $ % & ' K

(94) 33GG    :9   "   ;

(95)   7  ;

(96)   #% $   . :9 . <  :9   $ % & '        &   0  0     :   and :    3G where <  :    :  is the heat transfer Spalding number. 0   :     &   =    and B are linked by the following equation :. BT. M,i. :0   :9     (.  &   and 

(97)  "  "  " ,&  is the Lewis number. The composition of the vapor near the   

(98)  droplet surface is assumed to be in equilibrium with the liquid mixture. In addition the liquid and vapor mixtures are considered to be ideal so that the Raoult law can be applied: where ( . (&  ! (  !  0  where x denotes the molar fraction. P =1atm is the ambient pressure in the channel, T is the droplet surface temperature and P t is the saturating vapour pressure. To solve equation the droplet is divided into 100 regular segments along the radial coordinate and a CrankNicholson scheme is used. At each time step, the droplet radius is updated to account for the loss of mass and the swelling. Downstream distance from the injector is converted into time with the help of the space evolution of the droplet velocity measured using the PDA technique. Figure 3 shows the evolution of the droplet average axial velocity for different size classes. As expected, the smallest droplets have a relative velocity almost equal to 0. These droplets follow the free stream. -49 8 4?   )4 4  $ ! 84 )5 )5) 8 4  494$  9==!9$) 8  ? The axial velocity is also used to calculate the Reynolds number in equations and . a. s. sa. ;

(99)   $  $" , ) " The effect of turbulence on evaporation at any scale is not taken into account in the simulations, which are also reduced to a single dimension domain. In particular, the influence of the channel wall is ignored. In figure 4, it is also apparent that the mean liquid concentration is not uniform in a section of the channel near the injection but it tends to become uniform rapidly after. 4   6  58) 8  =  9 8 )5    == 8  *  

(100) 33 * /7 9$)9!4.:)*N3E145)884)59)75!)*N 3E5)468=  48)5)8 4 ) )4 9 8)59 )) 4$0 )86 8

(101) "5 59644   )* N 3E :=14 98)5 = 4 5 8. 1   K * 3E  . 

(102)    K * 3E  . 3.   ,.  ,

(103) 6

(104)  !  ,  ! K * 3E  ,  , E. where ! K * 3E  ,  is the size pdf at z/H=0.6. N decreases with z due to the disappearance of the droplets that have evaporated completely before reaching z. N is evaluated for any distance z as followed:.

(105) . 1    1   K * 3E . ! K * 3E  ,  ,. ,. 64,4 )*N3E8)595)64 )584 $5>The size PDF is calculated as follows: ! ,  !  ,    K * 3E  ! K * 3E  ,  , ,. -475 )54$=, 4 4) , 646)* N 3E !40 )868

(106) "5$ ) =486=0    ,

(107) 

(108)     1      ,  6

(109)  !  ,  !  ,  , E 3 where Y (D) and + (D) corresponds to the results of the simulation obtained for a droplet of size distance z. 486"84

(110) "5/  "

(111)  14=54 9)$)9! l,3-p. l. D. at the.  "

(112)     

(113)    3   

(114)    . . ,    4 5 ))5)$ 8  84)655)8= D8 )88)5) 564

(115) "58 /64!1$ /=314 $584)59$)9 )*+8)5)4;3S- ) 4$!8)584

(116) "5 84)5 4)55568 49==

(117) ;3. C : 3 N;3S : 3 N33S : 3 N;3S : 3 N 33S : 3 N ;3S : 3N

(118) 33S. ;3. E. 9   4%

(119)  

(120) -?/. ,

(121)  

(122) 

(123) -./.

(124) 33. 33. ;3. 33. ;3. 2 . 3 C :3N;3S. E. :3N33S :3N;3S. 2. :3N 33S. :3N ;3S :3N

(125) 33S. 3 3. 3;. . ;. ;.

(126).

(127) ;. )*. !" -$ 5 ))5)$  8    8  4  )6  5  8  )88 )5). 3 3. 3;. . ;. ;.

(128).

(129) ;. )*. !" #.$ 5 ) 

(130) "5  "8  /64!1  $       8    8  4  )6 58)88)5). 4 5964 )) 5 )

(131) "50 ))=86")5!)8=  @44) 4  )

(132) "50 )86")0  >!$4 ) $  =-@444) 4 5964  )

(133) "586"4= 54  =644 )$ 8)*+

(134)  @84575  )9>)48  4488  8 9   >    9  ) 4$5) =) 84)54 $5 49   )9! 4 ? 84)5@444)  9   ) 488  8)5 64 4)) 4$5454 4  599!)  4  84$5 8

(135) "5  =644 75) 4   )  84)5 4 4 6 64 4!) 4 980 ))5 =! " .

(136) 4 )75  )98 )4.-  40  ! 4-= = 8  )5  !55 4)5 $ / 55  ,41 -8 4:  )!  )4!)9!49==)5/ ,7 , G3. 1  5)=4 E;;

(137) E=!$ 4) ))5)/,16 )9=$9! K

(138).    , ,7    E;;

(139) E  . . 64 4 !) )9!4: ) 444))4)88= 5 =55)) 40 ))54)! =8) )! )    23  64    4  =  5 =  5    ))  F4  ,7 , G3.  4    ) ))6 )9 , , C3. 0 ! 84)54,=)9!4 .- )9  )5))) ) $5 55 !44  )$5 9!$) )= )0 )

(140) "586    88 -"  955)  4=84) )! =88 . . " . . ,. .  ,

(141) 6

(142)   ,  !/ ,1, E. . 3.  ,

(143) 6

(144)   ,  !/ ,1, E. . . 4)75 98 )4 488   80 ))5))64 8   8 

(145) "5  :     4  =     8 

(146) "5    4  )5  4   ) 8     =    =!  88 )  9!  4  95  8  4   )    )    EE    4 546) 9))9!0 A

(147) B 4 84)5))64   )=0 A

(148) B 48   )9!)5 96  @ 3 

(149)  ,

(150)   

(151)  , . . 64 @       4   )    !  4%    4 

(152) "5       )   

(153)  ,  47 88  !84)5 >=  49584 ) 9    

(154)  ,   ( 

(155)  $. . . $. .   ( .

(156)  . . 3 $. . $.  64$4)5$ ) 4 7 ! 4 ( 5  )= 4)'A2B 488  ! 958).   

(157)  ,  ,

(158).  

(159)  

(160)  ,. . 64 

(161)  47  88 840 )

(162) "548 4  658) 644$ 8 

(163)   5)=0 ) =$9!0 A

(164) B 9 89$  80 )

(165) "5 47 88  !8 5)8=  8  84

(166) "5"8  8 )88 )5)488  !)  4)5))

(167) "5"8     )=0 ) 40 )

(168) "586" 9  )9! 88  -# >=   4=7 644)5) 95. . # . . 3. @

(169)  ,

(170)   

(171)  ,  ! / ,1,. . 3. @

(172)  ,

(173) ! / , 1,. . 4   88 -" )-# 9  )475) 9 )   4 ) )*N3E/01)4  )$ 840 )

(174) "5864 )))65.

(175) 4   )  $       5)    8=     4    $       >)    95 544  5)4) )! =4)5 /4)8 

(176) <1 9  !4)5  !=8

(177) "5 88 )4 $555 46484   )$  96)*N3))*N3E ) 45  89=)54 64 4 488 )9!955445 84 54)) 884)654)5) ) $5 O6$ )58455)   4 ))584

(178) "50 )86 =4!4=4445) )9!4  4=964 58) 4=54)4     1 75)9)-40 )54 75)9)-4= 54  )75) S im u la tio n fo r th e u n c o rre c te d m e a s u r e m e n ts S im u la tio n fo r th e c o r re c te d m e a s u r e m e n ts. 3C 3G. 0 .9 5 0 .9 0 .8 5. 3E. 

(179)  B. 4%

(180)  

(181)  ' 

(182) -A")/. 3D. 3; 32 3

(183). 0 .8 0 .7 5 0 .7. 3. 0 .6 5. 3. 0 .6. D D D D D D. 3 3;. = = = = = =. 40 80 12 16 20 24. µm µm 0 µm 0 µm 0 µm 0 µm. 0 .5 5 . ;. ;.

(184).

(185) ;. 2. 2;. ;. ;;. )*. !" ##$ 0 )  ) 

(186) "5  86" 59675/"  ))  )1)  $ . 0 .5. 0. 2. 4 6 8 10 12 14 16 9   4%

(187)  

(188) 

(189) 

(190) 6 4%. 18. 20. !" #%$ $   8  4  7   88  ! 8 84)58  84

(191) "5 "8 ))5). /   .- 80 ))=  8

(192) "54$958) 9 $" 4) 486 645!)89!7 8" )

(193) "56? ) ."5 =8475)>   "4 9)88 84.-$!)5$ )4)! 848   = ) = "47 84 ))40 ))5 5   9)4))5)))  555 446 9=964)9)4=54)4  4= 8 !40 )54$8  8475)      , 8 &   * !-C/ ! ;

(194) $ (. 4)88 $!A "B   A"B '5 8 4 5 !AQ>=J"B :5)AB :!A>=W"

(195) B 48$5AQ>="B 4 ) $!AQJ""B 86A>="B :! $ !A."B .99!8C .) 9 !) 9 :5$ !A"B 7 )AB.

(196)  6 ' 9 5 ". ) )AB 8 . = 0 ). ,   AB  >  X>5- ! "

(197) 

(198) " # 

(199) 

(200) 

(201) 23C"2

(202) / 33E1 A B  >  4 $  '4 Z =  >5-  # 

(203) 

(204) 0

(205) . "

(206) /12

(207) " 2 C/DDE1 A

(208) B '>Q :94 O  # < 

(209)  3/212GDI2D/ 3331 A2B '=F < ,0   ,

(210)   9)=#$!./DDD1 A;B 9 '=F >D>*

(211) 90 

(212) 

(213) E3;"EC/DCD1 AEB (): '$   # 

(214) 

(215) 

(216) . "GE;D"E2/DD1 AGB  4   ' (

(217) 

(218) < 2G/

(219) 1 

(220) GDI

(221) D2/ 33D1 ACB J 4 Q)O  

(222) !:GE 

(223) D"

(224) 2/ 33

(225) 1 ADB ) (  9.  

(226) !:CGD

(227) " 32/ 33G1 A3B@   4 6  " E<   

(228) 

(229) 0

(230) 

(231) 

(232) <0 F    5  . E"D59/ 33C1 AB  !,>0

(233)  - .! 40 )  "#$%)  / 331 A B=P '=F  # < 

(234) EE. "

(235) ;/DCE1 A

(236) B0  :5%) )(   F88  (

(237) 

(238) < 2

(239) DGD"DD / 33G1 A2B 4: 'Q/ 331  

(240)  33"322/ 331.

(241)

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