Models of Turbulent Transport and Transfer of Disperse Phase Mass in Liquids

Table of contents

1.

???????????? ?????. ??? ????? ???? ?????????? ????? ??? ????? ??????????? ????????? ???????? ??? ??????? ? ???????????? ????????. ?????????? ???????? ? ????????? ?????????. ??????????? ??????? ? ???????????? ????????. ?????????? ???????? ? ????????? ?????????. ??????????? ????????????? ????? ????????? ???????? ?????? ??? ????????? ??????????????? ???????? ?????????? ???? ? ?????? ????????.

??? ????????????? ??????? ???? ???? ???????? ?????? ? ???????????? ?????? ?????? ??????????? ????????? ????????????? [14].

?.Ð?"?????? ?????? d ? ??? ?? ????????? ? ????????? ??????? ?? ????????????? ?????? ? ????????? â??": d ? << â??".

??? ????? ????????????? ?????? ??????? ????????? ????????, ????????? ? ???????? ???????? ?????.

??????????? ??????? ????????????? ??????? ????? ???????????? ?.?. ???????????????? (d ? <1 ???); ??????????????? (1< d ? <20 ???) ? ??????????????? (20< d ? <200 ???).

?. ??????? ????? ????? ??????? ? ???????????, ? ? ?????? ???????? ?????????? ?? ????? ???????? ??????????? ?????. ???????????????? ?????? ??????????????? ????????????.

2. ?. ????? ????? ???????

? = + y v v (6) , 6 . 11 , ò ? ? R y y v v ? < = + +(7)

????? ?????????????? (3) ???????? ????????? ( )

, / ln 1 1 1 * R R R u ? ? ? + = (8) ??? R 1 = * u ? 1 /? -???????????? ??????? ??????? ???????, ? ?????? ???????? R 1 = 11.6; ? = 0.4 - ????????? ??????????????.

???????? ???????? ????????? (5) ? (8). Ð?"?? ????? ?? ?????? ????????????????? ???????? ??????? ????? ????? ?????????????? ???????? ???????? ? ??????????? [7,10] (9) ??? ?? ???????-????????? n = 0,66. ??????, ??? ????????, ??? ???????? ? ????? ???????????????? ??????????? n = 0,6-0,57.

?? ????????? (5), (8) ? * u ???????????? ???????? ? ?????? ? ????????, ñ / ì [13].

Ð?"?? ??????? ???????? ????? C f?? = ?/4, ??? ???????????? ?????? ? ??????? ?????????? ??????; ?=0.316/Re ? 0.25 ; Re ? =U ?? d ? /? (??? ?????????????? ??????

d=d ? ); ý d -????????????? ??????? ???????, ?; ? = ñâ v ñâ ; / 4 ? ? à d ý ???????? ????????? ?????, 3 3 ì / ì ; v à -???????? ??????????? ???????,= ? ?? /? ? . ?????? ?=0.25d ? ? ???????? R ? . 25 . 0 * v u d R ý = ?(14)

??????????? ???? ????????? ??? ????????????? ???????? ???????? ??????????? ??? ???????????? ?????????? ???? ??? ???????????? ????, ????? ????????? ??? ??????????? ?????????? (????????, ??? ??????????? ????????).

3. III. ??????????? ???????? ??????

Ð?"???????????????? ?????????????? ????????? ?????? ? ???????????? ????? ?????????? ??????? ??????? ?????????? ? ??????????????, ??? ? ??????????. ??????? ??????????, ??? ?????? ?????????? ??????? ??????? ? ????????? (????? 3-5 ??, ? ??????????? ?? ????????????????? ??????? ????? ? ?????????? ????????????????? ???) ?? ????????? ? ???????????? ?????????? ?????. Ð?"?? ????? ?????? ?????? ??? ????????????? ????????????????? ????????? ? ??????????? ???????? ???????????? ????????????? ???????? ?????? ?????????? ?????????.

? ???????????? ? ??????? ???????????? ???????? ????? ???????????????? ??????? ?? ??????? ?? ????????? ??????? ????????????? ? ? ? ? , ??? ? ???????? ??????? ???????????? ?????????????? ????????? ??????????? ??????, ? -1 , ? ?????? ??????????, ?. ?? ????????????????? ?????? ??? ???????? ? ? ? ? < 0.01, ??????? ????????? ?????? ????????????? ??????????? ????? ????????? 100% (µ 2 p =1), µ 2 p = (1-? E ? p ) -1 [14]. ??????? ??? ??????? ????????? ??? ?????? ??????????? ????????? ?????????? ????????????? ??????????? ????? ????? ???????? ???????:

. 01 . 0 9 ae 2 < ? = µ ? ? ? ? f d ÷ p E (15) ?????? ???????? [1] ????????? ??? ?????? ???????? ?????? ? ??????, ??? ?? ????????? ? E ? u * /(0.1R) ? ? ? = ?|?Î?"??|?d ? 2 /(18µ ? ), ?|?Î?"??|? ? 0: , 134 . 0 3 . 0 * ae ae u R f d ÷ ? µ ? ? µ ? = ? < (16) ??? ? ? = 2?f -??????? ??????? ??????????? ?????????, ? -1 ; f -??????? ???????????? ????????? ?????, ? -1 ; R -?????? ??????, ? (??? ??????? R=d ? /2,u R d u R ÷ ? µ ? µ ? < < ?

) ????? ?????????? ?? ????????? [14] .

1 ò p ÷ Å v D ? ? + = (19)

??????????? ???????? ???????? ?????? ? ? (???????????? ????????) ?????? ????? ?????????????? ????????? (3) ? ???????? ? ? = ? / (1+ ? E ? p ).

??????????? ???????? ?????? ?? ???????????, ?.?. ?? ??????? ?? ??????? ? ???????????? ?????? ????? ?????????????. ??????? ( ) ( )

. / ln 1 1 1 1 * ? ? ? ? ? ? + + = R R R u p E ÷ ? ? ? ? ? (20)

? ?????????????? ????????? ??????????? ??? ?????????? ?????????? ??????, ??????? ????????????? ?????????????? ??????, ????????????? ????????????? ???????? ?????????? ?????? ? ?????? ?????? ??? ? ??????????? ????????? ??????? ????? ???. ????????????? ???????? ????? ?????????? ? ?????? ??????? ?? ????? ???????????? ? ???? [6,7]. ???????? R 1 ??? ??????? (23) ???????? ? ???? [6].

ae 1 exp , ÷ F V ? ? ? ? = ? ? ? ? ? ?(

( )

2 1 1 * 1 ? ? ? ? ? ? ? = ? R arctg u u R ,(25)

? ??? ??????? (24) ( )

2 / 3 1 2 1 * 1 3 6 ? ? ? ? ? ? + + ? = ? ? k k u u R , (26)

??? ? 1 = 3 ln ( ) ???????? ? ? ??????, ????????? ??????? ???????? ???????? ?????????? ???????, ?????????? ????? ??????? ???????? ? ?????? [2,6,11].

1 ) 1 ( 1 2 + ? + Â Â Â ; ? 2 = 6 arctg 3 ) 2 ( Â Â ? ; ? = R 1 -0,3332 / 1 ae ae 2 / 1 ae ae ò 4 4 ? ? ? ? ? ? ? ? ? = ? ? ? ? ? ? ? ? = H PW ñð ? ? ? ? ? ? ? ? , (30)

??? ???????? ???????? ?????????? ???????, ??/? 3 ; Î?"P??????? ????????, ??;W ????????? ???????? ???????? ? ??????, ?/?; H????? ??????, ?.

????????? Î?" P ?? ????????? Ð?"????-???????? ?? (30) ???????.

2 / 1 3 ae ò 2 4 ? ? ? ? ? ? ? ? = d W ñð ? ? ? ? , (312 0 ? u u u k + = , (32)

??? u k???????? ??????????????? ????????, ?/?; u ???????? ????????, ????????? ????????????? ??????????? ?????, ?/?.

???????? u ? ??????????????? ??? ???????? ????????? ??????? ????????????? ??????????? ??????? ???????? ???????, ?????????? ????? ???????? ?????????? ??????? ? ??????.

( ) ???????????? ????????? ????????????? ??????????? (? 2 ????) ???????????, ???? ? ????? ????????? ?????? ???????????? ???????, ???????? «???????» [4].

3 / 1 3 3 / 1 2 ? ? ? ? ? ? ? ? = ? d W d d u ñð k k ? ? ?(

??????? ??????????? ?????????? ?? ??????????? ???????????? ?????????? ????????? ????????? ?? ????????? (Re ? >50) [11].

( ) ( ) 5 , 0 5 , 1 2 ae ò 2 / Re / 4 ? ? ? ? ý ý d = , (34)

??? Re ? = W ?? d ? / ?????? ?????????? ??? ???????; d ? = 4? ?? /? ?????????????? ??????? ???????, ?; ? ?????????? ????????? ????? ???????, ? 3 /? 3 ; ? ????????? ???????????, ? 2 /? 3 ; ???????????? ??????????????? ????????????? ??????????? ???? [4].

??? ??????? ???????????? ??????????? ?? ?????? ? ???????????? ????????? ? ?????? ? ????????? ???????? ??????????????, ??? ?????????? ???? ?? ????????? ??????????? ???????. ???? ?? ?????????? ???? ?????? ????????? ??????????? ????????? ???????, ?? ?????????? ????????? ?????????????? ??????????? ?? ?????? ???????? ? ?????????, ??? ??????? ????????????? ??????????.

4. V. ??????????? ??? ?????????????

Ð?"???? ?????????? ?????????? ???? ?????????????? ????????? ??? ??????? ?????????? ?? ?????? ? ??????? ?????? ? ???????? ? ???????? ??? ???????????? ??????.

??????????? ??????? ???????? ?????????????? ???????? ?????????? ?????? ? ?????????????? ????? ???????? ??????? ???????, ??????? ???? ?? ????? ??????? ?????????????? ???????. ? ?????? [15] ???????????? ??????? ???????? ???????? ?????? ???????????? ??? ?????????????? ????????? (?????????? (32)):

2 îáò 2 2 0 u u u u k + + = ? ,(35)

??? u ??????????? ???????????????:

ì ê ì d d u u ae ê îáò 6 ? ? ? ? ? = , (36)??? u ? -???????? ???????? ????? ??????? ???????, ?/?: u ? = ? n d ? , n -??????? ????????, ? -1 ; d ? - ??????? ???????, ?; ? -??????????? ????????????? ??? ???????? ?????, ? k = f(Re ? ).

??????? ???????????? ???????? ?? ????????? ??????????? ????? ?????? ?? ????????? [6,7] ?????? ?????? ??????? ??????????? ? ???????? ???? ??? ??????????? ??????? ??????.

?? ??????? 2 ???????? ?????????? ????????? ? ????????????????? ?????? [15] ??? ??????????? ?????????????? ????? ? ???????? ??????? ???????. Ð?"?????? ?????? ?????????????? ????? -30, 8?10 -6 ; 593?10 -6 , ?.

Figure 1. 3 ?
3??? ?, ? ? (y)???????????? ?????????????? ???????????? ? ???????????? ????????, ? 2 /?; U ????????, ì/ñ . ?? ??????????? ??????, ?.?. ??? ? = 0, ???? ?? ????? ????? ???????? ? ????[12]: ???????? ????????, ?/?; ? ?U ???????? ???? ????????, ?/?.?????? ????????????? ????? ???????? ? * = ?(y)/? ?? . ????? ??????? ??????????????? ?????? ? ????????? (1), ???????? ??????????, ? ????????? ???????? ?? ??????? ???????????? ????, ???????[7,12]:????????? (3)???????? ?????????? ????? ? ????????? ?????????? ??????????? ?????????????? ?? ?????? ????????????? ???????????? ? ? ???????????? ???????? ? ? (y), ? ????? ?????????????? ???????????? ?????????? ? * (?????????????? ?????? ????????) ? ?????????? ????. ? ????? ???? ??????????? ???????? ???????? ????? ???????? ????? ?????????????? ????????? (3) ? ?????????? ????????? ????????????? ????????????? ?????? ? ? (y), ????????? ???????????????? ??????. ? ?????? ?????? ? ??????, ?????????????? Ð?"???????? ? ???????? ??????????????, ??? ????????? ???????????? ???????? ? ?????? ??????? ??????????????? D ? ~ y 4 . ?? ????????? ????? ???????????? ??????? ? ? (y) ? ?????(4) ??? y + = u * y/????????????? ??????????; ?=0.4 ?????????;
Figure 2.
??? C f????????????? ?????? ??? ???????? ?????? ?? ????????? ? U ????? ??????? ????????;
Figure 3.
??? ???????????? ??????????? ?? ????? (? ?????) ? ???????? ????, ?/?;? 1??????? ??????? ??????? ?? ?????, ?; y?????????? ?????????? ? ??????????? ????, ?.????? ?????????????? (22) ? ???????? ????????????? ?????? ?????? D ? = u * ? 1 (y/? 1 ) 2 , ??? ?????? ? ????????? ???????????? ??????? ??? (? * ? 1), ??????????? ??????????? ??????? ???[6]. ? ? * > 1, ? ????? ??????? ?????? ??? D ? = u * ? 1 (y/? 1 ) 3 ?????[6].
Figure 4.
??? R 1 = u * ? 1 /????????????? ??????? ??????? ???????; * u???????????? ???????? ?? ????????? ??????????? ?????, ?/?; ? ??????????? ?????????????? ???????? ???????? ????, ? 2 /?; z = (R 1 Sc) -0,333 ; Sc = ?/D????? ??????; ? * = ? d /? c????????? ????????????? ???????????? ???????? ?????????? ? ???????? ???.
Figure 5.
??? ??????? ????????? ???????
????????????? ? ? ? ? > 100 ??????? ????????? ???????????? ? ???? (µ 2 p ? 0). ?? ???????? ? (15) ? (16)
???????? ????????? ??? ??????, ?? ??????????
????????????? ???????????
? E ? p = ? 9 ae ? µ ? d ÷ 2 f > , 100 (17)
?????? ?????
d ÷ > 30 ? ae ? ? µ f = 13 . 4 * ae u µ R ? ? . (18)
?? ????????? (16) ? (18) ???????, ??? ???????, I
?????????? ? ???????????? ??????, ??? ?????? ??????? ?? ??????????? ?????, ??? ?????? ?? ?????? ? ???????? ?????????? ???, ??? ?????? ???????? ????? ? ???? ??????? ?? ?????????. ??????????? ???????????? ???????? ?????? * * (??? ??????? ae ae 4 . 13 134 . 0 ( ) C Volume XIV Issue II Version
Global Journal of Researches in Engineering
Note: ?); © 2014 Global Journals Inc. (US)
Figure 6.
?????? ?????????????? ?
?????? ???? ???????????? ???? //
????????????? ?????? ??????????
? ??????????????? ????????????, ?????? ?????????????? ? ?????????????
?????????????????? ?????????. -?.: ???????????,
2011. -?.336.
11. ??????? ?.?., ??????? ?.?. ??????????????
?????? ? ?????? ??????????????????
????????????? ?????????.
1

Appendix A

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  2. Transport models and liquid extraction efficiency, A G Laptev . 2005. Kazan. 229. Kazan State Power Engineering University press
  3. Models of boundary layer and calculations of heat and mass transfer processes, A G Laptev . 2007. Kazan: Kazan University press. 500.
  4. Methods of intensification and modeling of heat and mass transfer processes, A G Laptev , N A Nikolaev , M M Basharov . 2011. Moscow: Teplotekhnik. 288.
  5. Efficiency of turbulent mixing of media in packed flowthrough mixers. Neftegazovoe delo, A G Laptev , T M Farakhov , O G Dudarovskaya . 2012. p. .
  6. A model of turbulence in the liquid phase of a bubble layer // Mezhdunarodnyi zhurnal prikladnykh i fundamental'nykh issledovanii, A G Laptev , E A Lapteva . 2013. p. .
  7. Mathematical models of momentum transfer in the boundary layer. A G Laptev , T M Farakhov . Journal of engineering physics and thermophysics 2013. (3) p. .
  8. Contact packings of industrial heat and mass transfer apparatuses. Kazan: Otechestvo, A M Kagan , A G Laptev , A S Pushnov , M I Farakhov . 2013. 454.
  9. Integrated treatment of sewer systems at industrial enterprises using the jet flotation method, D V Alekseev , N A Nikolaev , A Laptev . 2005. Kazan: Kazan State Technological University press. 156.
  10. Mathematical models and calculation of heat and mass transfer characteristics of apparatuses. Kazan: Otechestvo, E A Lapteva , T M Farakhov . 2013. 182.
  11. Turbulent transport and deposition of aerosols. Moscow: Nauka, E P Mednikov . 1981. p. 176.
  12. Mixing in liquid media: physical fundamentals and engineering calculation methods, L N Braginskii , V I Begachev , V M Barabash . 1984. Leningrad: Khimiya.
  13. Mathematical modeling of the process of dissolution of solid particles in apparatuses containing mixing devices. L P Klinova , N B Sosnovskaya , S G Dyakonov . Massoobmennye protsessy i apparaty khimicheskoi tekhnologii: mezhvuz. sb. nauch. tr. Kazan, KSTU, 1987. p. .
  14. Investigation of diffusion boundary layers by the holographic interferometry method. Doklady AN SSSR, S G Dyakonov , N B Sosnovskaya , L P Klinova . 1982. 264 p. .
  15. Dissolution of a solid particle in a stirred liquid. S M Oryol . Zhurnal prikladnoi khimii 1988. 61 (7) p. .
Notes
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Date: 2014-01-15