(3) Falling film evaporation on a vertical wall

- differences with condensation

① start with a certain thickness of film

② reduce of film Re according to evaporation

- But, the reduction of RE is usually neglected since the evaporation rate is       much smaller than the film flow rate.

- Since [eqn: T_w > T_sat] , the liquid loser to the wall is superheated

∴ boiling or bubble cavitation in the feed liquid.

→ film disruption

- But, water evaporates into a vapor-air mixture

∴ total pressure >>[eqn: P_sat ~(T_w )] and little possibility of boiling.

- include mass transfer process

☞ film condensation : suction effect

☞ film evaporation : blowing effect

- Since evaporating films are mostly wary laminar or turbulent, by Chun and

Seban

[eqn: rm N u ~=~ 0.822 ~Re^-0.22 ~~,~~ 30~<~ Re ~<~Re_tr]      (wavy laminar)

[eqn: rm N u ~=~ 3.8 times 10^-3 ~Re^0.4 ~Pr_ell^0.65 ~~, ~~Re_tr ~<~Re]   (turbulent)      (5.2.44)

where  [eqn: rm Re_tr ~=~ 5800 ~Pr_ell^-1.06]

; same with condensation

(4) Methods of Improving the HT coeff is condensation

(a) changes to geometry of the surface to increase the available area.

(b) treatment of the surface to promote drop-wise rather than film-wise             force

(c) use of force fields

1) The influence of surface geometry

- At low[eqn: rm R_e , ~h_rough ~<~h_smooth]   ∵ the condensate retains due to the surface        tension.

- At high[eqn: rm R_e ( > 140), ~h_rough ~<~h_smooth]

- low-fin tubing in horizontal-tube condenser

∴ The HTC for fined surface is 15% less than that for the smooth                surface, but has larger net heat transfer rate due to increased transfer           area.

- roped or spirally indented tube

- by placing wires along vertical tube

; Optimum # of wire   [eqn: n~=~ {0.18 prod D} over d]

2) The promotion of drop wise condensation

- make the surface non-wetting

1) chemically coated surfaces

2) polymer coated surfaces

3) electroplated coated surfaces

3) The use of force field to enhance condensation

- In the film-wise condensation, the condensate film plays a role of the           resistance of heat transfer.

∴ use external force, centrifugal, vibrational and electrostatic force to              reduce the thickness and to promote chainage

- horizontal rotating disc

[eqn: bar h_f ~=~ 0.904 ~left[{h_f^3 rho_f^2 40^2 h_fg } over {mu_f (T_gi - T_w )} right]^0.25]                         (5.2.45)

- acoustic vibration

[eqn: h_vib over h_f ~=~ 1~+~0.0018 FA]

where A ; amplitude (mm)

F ; frequency (0～150Hz)

3. Condensation in Reactor Transients

★ Nuclear Reactor Safety Issues Relating to Condensation Mechanism

① Injection of subcooled water spray in to steam-filled regions

1) top spray for BWR ECCS

2) containment spray

② CCFL at top of fuel bundle

③ Steam discharge in to water-filled regions

1) steam bubble callapsed and "chugging" in suppression peals

2) IRWST

④ condensation-induced flow oscillation from subcooled water injection into

steam-voided regions

1) downcomer bypass of ECC flow

2) Oscillatory delivery of ECC injected in to the primary loops

3) water hammering in the S/G

⑤ noncondensible effects on condensation-induced national circulation flows        [eqn: (N_2 ,~ H_2 , ~~ orthers)]

- degrading national cliculation "reflux" cooling

(1) Condensation Heat Transfer in Stratified Flow (Steam / water)

○ measurement technique of local condensation rate

1) measuring local steam flow rate with traversing electrically heated pitot          tube

2) measuring local bulk temperature by T/C

○ condensation heat transfer coefficient in the stratified flow

[eqn: h^* ~==~ h_fg over {T_s -T_f} left vert dw_f over dx right vert]                                   (5.3.1)

where [eqn: T_f] : bulk liquid temperature

[eqn: W_f] : local liquid flow rate

Since[eqn: T_f] can be calculated from the energy equation for the liquid film          with[eqn: W_f] , we can obtain [eqn: h^*] from measuring either [eqn: T_f] or [eqn: W_f] .

In case of no noncondensible gas, the main resistance of condensation           heat transfer exists in the liquid side.

Silver and Wallis used the concept of Re flux to derive f correction

[eqn: {f_i``^*} over f_i~ =~ phi over f_i~ +~ exp~ (-phi/2f_i )]                             (5.3.2)

where [eqn: f_i] : interfacial friction factor without condensation

[eqn: phi ~==~ 2 over {rho_g u_g} left vert dw_g over dx right vert]                                     (5.3.3)

[eqn: f_i``^* ~==~ 2tau_i over {rho_g u_g^2}]                                            (5.3.4)

By Whiteman film theory (Mickley at al.)

[eqn: {f_i``^*} over f_i~ =~ phi/f_i over {1- exp~ (-phi/f_i ) }]                                (5.3.5)

and  [eqn: {h^*} over h ~ =~ phi_H over {1- exp~ (-phi_H ) }] ,      [eqn: phi_H ~=~ mc_p over h ~=~ {c_p TRIANGLE T_{s ub}} over h_fg] (5.3.6)

From Eqs. (5.3.2) and (3.3.5),   [eqn: f_i`^* ~]～ [eqn: phi]   when  [eqn: phi]  is large.

Replacing [eqn: f_i`^* ~]in Eq. (5.3.4) by[eqn: phi ,] when the condensation effect is               dominant,  [eqn: tau_i] = condensation rate [eqn: times] average vapor velocity

i.e    [eqn: u_g left vert dw_g over dx right vert]

Linehan proposed

[eqn: {f_i`^*} over f_i = 1 + phi over f_i]                                           (5.3.7)

and      [eqn: tau _i = f_i `` {rho_g~ u_g^2} over 2 + u_g ~left vert dw_g over dx right vert]                             (5.3.8)

Another approach

[eqn: N u ~=~ {h^* delta } over k_f ~=~ CRe_g^N_1~~ Re_f^N_2~~Pr^N_3]                              (5.3.9)

where  [eqn: Re_k ~=~ W_k over mu_k ~~~~, ~~k~=~g ~~or ~~f]

Kim and Bankoff  ;  countercurrent stratified steam and subcooled water

in inclined rectangular channel (38 [eqn: times] 3.8 [eqn: times] 1.27m)

C       [eqn: N_1]     [eqn: N_2]       [eqn: N_3]

0.173     0.027    0.49      0.42       for smooth interface region

3.43[eqn: times][eqn: 10^-10]   2.1     0.56     1.16       for rough  interface region

- This appoach should be used very carefully due to the difficulty in the          expression of interfacial ware structure (thus, quite different C and              exponent for each experiment)

To account for turbulent structure, ([eqn: Re_t ``==`` lambda_t`` u_t`` /``nu_t] )

o Thomas

1) 0.1x0.1x1.09 m rectangular channel

2) hot-film anemometer and surface flow visualization

3) surface shear was negligible.

[eqn: u_t ~=~ 0.4 ```U_g,~~~~~~~lambda_t ~=~ m ~(12.7mm)~~~~~for~~ 0<x<0.15]

[eqn: =~ 0.15 ``U_g,]      [eqn: =~ delta]              [eqn: for~~ 0<x<0.15]

o Kim and Bankoff  ; strong effect of sheared and disturbed interface

[eqn: u_t ~=~ u^* ~=~ ( tau_i / rho )^1/2]

[eqn: lambda_t ~=~ a] ( maximum wave amplitude)

[eqn: therefore~~ N u ~=~ 0.061 Re_t^1.12``Pr^0.5]                               (5.3.10)

(2) Condensation Phenomena in Reactor Containment

- complex geometry and phenomena

- time-dependent peak pressure during accidents due to condensation

☞ Jubb's experiment

- large boiler (8'3" D, 30ft L)

▸ forced convection during blowdown : [eqn: St `` Pr^0.5 = 0.0576/Re^0.25]

▸ free convection post blowdown     :  [eqn: h ~=~ 0.0152``rho`` DeltaT^0.25]  (5.3.11)

☞ Uchida & Tagami

- 11 ft D , 21 ft L

- weight ratio of noncondensible gas (increasing decreases h)

[eqn: h_max = C`` LEFT ( Q over { V``t_p } RIGHT )^0.62]                                  (5.3.12)

where  V ; free volume

[eqn: t_p] ; time interval until peak pressure

☞ large scale experiment (CVTR)

- maximum h by Tagami is much lower

∴overshimated

☞ HDR experiment

By Almenas

[eqn: h ~=~ exp(7.4) LEFT [ 0.05 + rho_a over rho_v RIGHT ] TRIANGLE T^-0.58 `` P^1.2]                    (5.3.13)