Evaporation (Chapter 14) Zan Wu Room: 5123

Transcription

1 Evaporation (Chapter 14) Zan Wu Room: 5123

2 Evaporation, Boilin vätska, liquid 1) Local boilin or subcooled boilin 2) Boilin with net evaporation q Pool boilin Forced convective boilin

3 Evaporation Nukiyama s experiment boilin curve t s I E t tråd-wire - t s värmande tråd, heatin wire q min q max q Heat lux increases/decreases

4 Evaporation Boilin Curve sinle bubbles nucleate boilin jets & colonns 3 transition reime ilm boilin q max Heat lux, [10 5 W/m 2 ] b 4 5 Saturated water on a plane surace at p = 1 bar 2 natural 2a convection q min t = twall - t s Wall temperature increases/decreases

5 Evaporation (a) (b) (c) Principal sketch o nucleate boilin ((a) and (b)), and ilm boilin (c).

6 Bubble nucleation, rowth and departure

7 Nucleate boilin heat transer mechanisms Micro-convection Transient conduction Microlayer evaporation Microlayer

8 Nucleate Boilin; theory, empiricism Nu = unction(re, Pr) u qw h L k ( ) 1/ 2 Re u L k L k is related to bubble departure diameter Nu 1 Nu C Re Pr k L 1n m s

9 Nucleate Boilin Rohsenow s ormula / w sl s s w p ) ( Pr ) ( h q C h t t c n = 1/3, 1+m = s Eq. (14-9) σ is the surace tension, σ = c 1 + c 2 t

10 Evaporation; Nucleate Boilin Reime 100 q h ( ) Eq. (2-9) 1 atm 26 atm 52.4 atm 82 atm 109 atm atm c p ( t h w t Pr s )

11 Evaporation- C sl and s in Rohsenow s equation Surace liquid C sl s Nickel water Platinum water Copper water Brass water Chrome benzene Chrome ethanol

12 Evaporation, nucleate boilin: Cooper s ormula A P ( ln R R P ) ( ln P R ) 0.55 M 0.5 q 0.67 w A = 55 P R p/ p critical is the reduced pressure Physical properties could be expressed as unctions o the reduced pressure M is the molecular weiht R P is the surace rouhness in m

13 Evaporation, nucleate boilin; Gorenlo s method F q R w p 0 PF qw0 Rp0 b (14-12) F PF 1.2P 0.27 R 2.5P R PR 1 P R b P 0.3 R 0 valid a certain reerence state, namely P P0 R0 Reerence values or 0 R m, 4 2 q 210 W/m w0 in Table 14-III.

14 Evaporation, nucleate boilin; Gorenlo s method or water F PF PR 6.1 P 1 P R 2 R b P 0.15 R

15 Evaporation-temperature distribution in liquid phase or pool boilin Temperature, o C Water Liquid surace100.4 o C Vapor 100 o C Distance rom the heatin surace, [cm] Bubble departure diameter in mm scale Lare temperature drop and hih heat transer coeicient near the wall

16 Evaporation: equilibrium-orce balance 2 r ( pbubble pliquid) 2 r r p r 2 ( p p ) bubble liquid

17 Surace tension A metal paperclip loatin on water Lotus eect

18 Evaporation eects on the boilin curve Subcoolin A liquid enclosed in a heated container will not stay a temperature below the saturation temperature very lon. Beore the liquid reaches the saturation temperature or i the warm liquid is continuously replaced by cold liquid (e.., by orced low) the subcoolin will, aect the boilin curve. It has been ound that the nucleate boilin reime is not very much aected but the values o qmax and qmin increase linearly with the subcoolin. The inluence on the transition reime is less known. Gravity The inluence o the ravity or other body orces is o interest as the boilin process also appears in rotatin or accelerated systems. Reduction o the ravity is important or boilin processes in space applications. Because the ravity acceleration is included in most expressions its role is evident. Surace rouhness A heatin surace miht be treated in various ways to ind out the importance o the surace rouhness. The eect o qmax on surace rouhness is very complicated. The ilm boilin reime is not aected siniicantly by surace properties which is understandable as the liquid phase is not in direct contact with the solid surace. The nucleate boilin reime is however aected by the surace rouhness.

19 Evaporation transition reime

20 Evaporation Taylor instability humid air Honey cold water Honey (a) (b) λ T unction (, ( )) An instability o an interace between two luids o dierent densities and with the denser luid at the top.

21 Evaporation Taylor instability, dimensional analysis λ T const ( ) a b c [m] [Nm 1 ] a [ms 2 ] b [km 3 ] c a 1/2, b c 1/2 λ T constant ( ) 2 3 or one-dimensional waves constant 2 6 or two-dimensional waves

22 Evaporation - arranement o vapor jets at q max T1 T 1 T /4 1 T2

23 Evaporation Kelvin-Helmholtz instability U Fla movement hih pressure low pressure

24 Evaporation Helmholtz instability T1 Details o instability in the jet surace surroundin liquid T /4 1 vapor jet surroundin liquid vapor jet u H heatin surace vapor jet u 2 λ H

25 Evaporation- estimation o q max or a horizontal surace q max h u A A j h A ( λ T j / Ah 2 λt / 4) q ( 1/ 4 1/2 max.149 h ) 0 λh λ T 1 (14-25) q ( 1/ 4 1/2 max h ) z (14-26)

26 Evaporation-other eometries, pool boilin q unction(,,,, L, h ) max Y 1 q q max max z Y 2 L ( ) see Table 14-IV

27 Forced convective boilin or immersed bodies q max hu unction(we, / ) L We L U 2 L

28 Forced convective boilin or immersed bodies Circular cylinder in cross low Low velocities q h 1 max 1/ 1 (4/ WeD) U 3 (14-34) Hih velocities q h max U ( / ) 169 3/ 4 ( / ) 19.2We 1/ 2 1/ 3 D (14-35)

29 Forced convective boilin or immersed bodies q max hu ( 1/2 / ) 1 hih velocity ( 1/2 / ) 1 low velocity

30 Boilin in tubes, low reimeshorizontal tubes Bubbly Slu Plu Annular Stratiied Annular with liquid spray Wavy

31 Boilin in tubes, low reimes-vertical tubes (a) homoeneous bubbles (b) inhomoeneous bubbles (c) slus o the as phase (d), (e) partial annular low () annular low () annular low with liquid droplets in the as phase (a) (b) (c) (d) (e) () ()

32 Boilin in tubes, low pattern maphorizontal tubes Baker plot 100 G /k/(m 2 s) 10 Wavy low Annular low Slu low Bubbly low G = m /A cross, G = m / A cross air H O 2 1/2 1.0 Stratiied low Plu low G k/(m 2 s) H H 2O H 2O 2 O 2 1/ 3

33 Boilin in tubes, low pattern mapvertical tubes Hewitt and Roberts G 2 k/(s 2 m) Annular low Partial annular low Annular low with liquid droplets Bubbly low G = m /A cross, G = m / A cross 1.0 Slu low E+5 1.E+6 G 2 k/(ms 2 )

34 Two-phase low, deinitions and relations V V V V V F m m m m m X A m G / F GAX m ) 1 ( F X GA m R /u u u Void raction lowin mass quality mass velocity phase velocity ratio

35 Two-phase low, deinitions and relations F S ) (1 X G A m u F S GX A m u ) ) (1 F F X ε X ε u u F F S S ) (1 X X u u Supericial velocities (14-45) (14-47)

36 Pressure drop or two-phase lows: Lockhart-Martinelli method Re 1000 u S D G(1 X F ) D L 2 1 us p dz D Re usd GX 0 F D L 2 1 us p dz D 2 (dp/dx) TF / (dp/dx) t-v t-t v-t v-v Index Liquid Gas t-t Turbulent Turbulent v-t Laminar Turbulent t-v Turbulent Laminar v-v Laminar Laminar (dp/dx) / (dp/dx)

37 Pressure drop or two-phase lows: Lockhart-Martinelli method X 2 ( dp / dx) ( dp / dx) Martinelli parameter 2 2 ( dp / dx) ( dp / dx) C 1 X TF 1 X 2 two-phase multiplier C = 20 i turbulent low prevails in the liquid as well as in the as (tt) C = 12 i the liquid low is viscous (laminar) and the as low is turbulent (vt) C = 10 i the liquid low is turbulent and the as low is laminar (tv) C = 5 i laminar low prevails in the liquid as well as in the as (vv)

38 Pressure drop or two-phase lows: Friedel s method dp dx TF 2 LO dp dx LO LO means liquid only Formulas or 2 LO see book.

39 Oil recovery rom deep sea: presure drop Gas-oil or as-oil-water multiphase low Temperature alon the oil pipes rom deep sea aects thermophysical properties, e.., oil viscosity varies a lot with temperature Low low velocity, ravitational loss dominated Hih low velocity, rictional loss dominated

40 Forced convective boilin heat transer and temperature distribution TEMPERATURE PROFILE Outlet FLOW TYPE HEAT TRANSFER REGIMES x = 1 Sinle phase vapor H Convection to vapor Wall temperature Dryout Liquid drops in the vaporg Annular low F liquid drops in the vapor Annular low E Dry out Forced convection across a liquid ilm Slu low D Saturated nucleate boilin x = 0 Bubble low B,C Subcooled boilin Saturation temperature Fluid temperature Inlet Sinle phase liquid A Convection to liquid

41 Chen s method or estimatin the heat transer durin orced convective boilin TF S KK F C F = (Re TF /Re ) X tt 1 X X F X tt F ( dp / dx) ( dp / dx) 0.1 Approximative rane o data points /X tt

42 Chen s method or estimatin the heat transer durin orced convective boilin, continued F Re Re TF 0.8 F 1 1 i 0.1 X tt i 0.1 Xtt Xtt C 0.023Re 0.8 Pr 0.4 D Re G(1 X F) D/

43 Chen s method or estimatin the heat transer durin orced convective boilin, continued S Aproximative area or all data points S Re 1.17 TF E+4 1.E+5 Re TF = Re F E+6 KK c ts p p h 0.75 s p t s s t w t ps ( tw ) ps ( ts) s

44 Chen s method or estimatin the heat transer durin orced convective boilin, continued Calculate α TF or a number o t m accordin to TF S KK F C Then create a raph q = α TF t m vs t m At q = q w ind the true t m

45 Alternative method or estimatin the heat transer durin orced convective boilin- Gunor & Winterton S E TF KK C E Bo 1.37(1/ X tt ) 0.86 Bo q /( G h w ) S E 2 Re 1.17 Here α KK is taken rom Cooper s ormula, α C rom Dittus-Boelter s equation

46 Alternative method or estimatin the heat transer durin orced convective boilin- Steiner & Taborek TF n KK n C 1/ n Here α KK is taken rom Gorenlo s method, α C rom Gnielinski s ormula n = 3

47 Thank you very much!!