Chapter 14: Förångning, g, Kokning; Evaporation, Boiling

Transkript

1 Chapter 14: Förånnin,, Koknin; Evaporation, Boilin vätska, liquid q 1) Lokal koknin eller underkyld koknin Local boilin or subcooled boilin 2) Koknin med nettoörånnin boilin with net evaporation kittelkoknin pool boilin, orcerad konvektiv koknin orced convective boilin

2 Evaporation Nukiyama s experiment boilin curve t s I E t s t tråd-wire - t värmande tråd, heatin wire q min q max q

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

4 Förånnin - Evaporation (a) (b) (c) Principal sketch o nucleate boilin ((a) och (b)), and ilm boilin (c).

5 Evaporation; Kärnkoknin, Nucleate Boilin Reime 100 q μ h σ ρ ( ρ ) Eq. (2-9) 1 atm 26 atm 52.4 atm 82 atm 109 atm atm c p ( t w t s ) h Pr

6 Nucleate Boilin; theory, empiricism Nu unction(re, Pr) u ρ q w h L k σ ( ) ρ ρ 1/ 2 Re ρu L μ k Nu α L λ k Nu 1 1 n m Re Pr C s

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

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

9 Evaporation, nucleate boilin: Cooper s ormula α A P ( ln RP ) R ( ln PR ) M qw M is the molecular weiht P R p/ p is the reduced pressure critical RP is the surace rouhness in μm A 55

10 Evaporation, nucleate boilin; Gorenlo s method, b q R w p 0 F PF q w0 Rp0 α α F (14-12) 0 F PF 1.2P 0.27 R + 2.5P R PR + 1 P R b P 0.3 R α valid a certain reerence state, namely P 0. 1 R q 4 w W/m 2. Reerence values or R0 α0 in Table 14-III. P0 μm,

11 Evaporation, nucleate boilin; Gorenlo s method or water, F PF PR P 1 P R 2 R b P R 0. 15

12 Evaporation-temperature distribution in liquid phase or pool boilin Tem mperature, o C Water Liquid sura ace100.4 o C Va apor 100 o C Distance rom the heatin surace, [cm]

13 Evaporation: equilibrium-orce balance σ σ Δp σ σ r π r 2 ( p p ) 2 π r σ bubble liquid r 2σ ( p p ) bubble liquid

14 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 and 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. Some studies indicate that is almost independent o the surace rouhness and whether the surace is clean or oxidized. 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.

15 Evaporation transition reime

16 Evaporation Taylor instability humid air Honey cold water Honey (a) λ Τ (b) λ Τ λ T λ unction ( σ, ( ρ ρ ))

17 Evaporation Taylor instability, dimensional analysis a b c const σ ( ρ ρ ) λt [m] [N m 1 ] a [m s 2 ] b [k m 3 ] c a 1/2, b c 1/2 λ T constant σ ( ρ ρ ) 2π 3 or one-dimensional waves constant t 2π 6 or two-dimensional waves

18 Evaporation - arranement o vapor jets at q max λ T1 λt 1 λ T /4 1 λ T2

19 Evaporation Helmholtz instability U Fla movement λ Η /2 Η hih pressure low pressure

20 Evaporation Helmholtz instability Details o instability in the jet surace λ T1 σ ρ surroundin liquid T 1 vapor jet surroundin liquid tλt /4 vapor jet u ρ λ H heatin surace vapor jet σ u 2πσ ρ λ H

21 Evaporation- estimation o q max or a horizontal surace q max ρ h u A A j h A j π( λ T / A 1 h 2 λ T / 4) 1 2 π 16 q ( ( ρ ρ ) 1/ 4 1/2 max.149ρ h ) 0 σ λ λ T 1 H (14-25) q ( ( ρ ρ σ) 1/ 4 1/2 max 0.131ρ h ) z (14-26)

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

23 Evaporation immersed bodies q max unction(we L, ρ / ρ ) ρ hu We L ρ 2 U L σ

24 Evaporation immersed bodies Low velocities q ρ h 1 [ 1/ ] 3 1+ (4/ We max D) U π (14-34) Hih velocities q ρ h max U ( ρ / ρ ) 169π 3 / 4 + ( ρ / ρ ) 19.2πWe 1/ 2 1/ 3 D (14-35)

25 Evaporation immersed bodies q max ρ hu ( 1/2 ρ / ρ ) 1 hih velocity < + π > + π ( 1/2 ρ / ) 1 low velocity ρ

26 Evaporation-orced convection in tubes, low reimes-horizontal tubes Bubbly Slu Plu Annular Stratiied Annular ua with liquid qudspray Wavy

27 Evaporation-orced convection 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) () ()

28 Evaporation-orced convection in tubes, determinin low reimes- horizontal tubes Baker plot (m 2 s)] G /λ [k/( Wavy low Annular low Slu low Bubbly low G m /A cross, G m / A cross 1.0 Stratiied low Plu low 0.1 ρ ρ λ ρair ρ 2 H O 1/ G 2 ψ [k/(m s)] σ ψ σ μ μ H H 2O H 2O 2 O ρ ρ 2 1/ 3

29 Evaporation-orced convection in tubes, determinin low reimes- vertical tubes G m /A cross, 2 G /ρ [k/(s 2 m)] Annular low Partial annular low Annular low with liquid droplets Bubbly low G m / A cross Slu low E+5 1.E+6 G 2 /ρ [k/(ms 2 )]

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

31 Two-phase low deinitions and Two-phase low, deinitions and relations F S ) (1 ρ ρ X G A m u & F S ρ ρ GX A m u & Supericial velocities ρ ρ ) ) (1 F F X ε X ε u u (1 ρ ρ ) ) (1 S S X ε X ε (1 ρ ρ F F S S ) (1 ρ ρ X X u u F ρ (14-45) (14-46) (14-47)

32 Pressure drop or two-phase lows: Lockhardt-Martinelli method Re u D S G(1 X F ) ν Δ p μ D L ρu D 2 2 S Re u ν S D Δp p GX μ F D L ρ D 2 2 u S 1000 ε 1.0 (dp/dx) (dp/dx) TF / 100 φ t-t 10 φ v-v vv ε 1 ε φ v-t Index Liquid Gas t-t φ t-v v-t Turbulent Turbulent Laminar Turbulent t-v Turbulent Laminar v-v Laminar Laminar (dp/dx) / (dp/dx)

33 Pressure drop or two-phase lows: Lockhardt-Martinelli method ( dp / dx) 2 X Martinelli parameter ( dp / dx) φ 2 ( dp / dx) ( dp / dx) TF two-phase multiplier 1 C X + 1 X φ C20 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 id low is turbulent t and the as low is laminar (tv) C 5 i laminar low prevails in the liquid as well as in the as (vv)

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

35 Forced convective boilin heat transer and temperature distribution FLOW TYPE HEAT TRANSFER REGIMES TEMPERATURE PROFILE Outlet x 1 Sinle phase vapor H Convection to vapor Wall temperature Dryout Liquid drops in the vapor G 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

36 Chen s method or estimatin the heat transer durin orced convective boilin α TF Sα KK + Fα C X tt 1 X X F F 0.9 ρ ρ 0.5 μ μ 0.1 X tt ( dp / dx) ( dp / dx) F (R Re TF /Re ) Approximative rane o data points /X tt

37 Chen s method or estimatin the heat transer durin orced convective boilin, continued F Re Re TF i 0.1 X tt F i > 0.1 Xtt Xtt α C 0.023Re023Re Pr 0.8 Pr 0.4 λ D Re G(1 X F) D / μ

38 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 α KK λ c ρ Δts Δp σ p μ h ρ 0.75 s Δt s t w t s Δp s ps ( tw ) ps ( ts)

39 Chen s method or estimatin the heat transer durin orced convective boilin, continued Calculate α TF or a number o Δt m accordin to α TF Sα KK + Fα C Then create a raph q α TF Δt m vs Δt m At q q w ind the true Δt m

40 Alternative method or estimatin the heat transer durin orced convective boilin-gunor & Winterton α S α + E α TF KK C E Bo (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

41 Alternative method or estimatin the heat transer durin orced convective boilin-steiner & Taborek α TF ( n n ) α 1/ n KK + αc Here α KK is taken rom Gorenlo s method, KK, α C rom Gnielinski s ormula n 3