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Direct contact condensation of vapor on turbulent, falling liquid film

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Abstract

The problem of condensation of pure vapor on turbulent falling liquid film of the same species is analytically solved. The gradual change in enthalpy of the coolant liquid film in the flow direction is considered to take place in three successive stages. The study brings out the influence of inlet Reynolds number, Prandtl number and degree of subcooling of the coolant on condensation heat transfer coefficients. The heat transfer coefficients predicted from the theoretical analysis are in reasonable agreement with the experimental data available in literature.

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Abbreviations

C p :

specific heat of liquid at constant pressure

F :

variable defined in equation (12)

F t :

variable defined in equation (10)

Gr x :

Grashof number, gx 3(ρ−ρ v )/(v 2 ρ)

g :

gravitational constant

h fg :

latent heat of condensation

h x , hv m :

local and average condensation heat transfer coefficients respectively

k :

thermal conductivity of liquid

L :

length of the plate

L + :

S Gr 1/3 L /Pr

\(\dot m\) :

mass flow rate of liquid per unit width of the plate

Nu x :

local Nusselt number, (h x /k)[v 2 ρ/tg(ρ−ρ v )]1/3

Nu m :

average Nusselt number, (h m /k)[v 2 ρ/g(ρ−ρ v )]1/3

Pr:

Prandtl number

q :

heat flux in y-direction at x=x

R :

q w /q i

Re:

local film Reynolds number defined in equation (3)

Re L :

film Reynolds number at the exit on the downstream

Re c,x :

local condensate Reynolds number, (Re − Re o )

Re C,L :

condensate Reynolds number at the exit, (Re L − Re o )

Re t :

variable defined in equation (11)

S :

subcooling parameter, C p (T s −T o )/h fg

T :

temperature

T + :

dimensionless temperature, k(T−T o )u*/(q i v)

T + s :

k(T s −T o )u*/(q i v)

u :

velocity along the x direction

U + :

u/u*

u*:

(τ w /ρ)1/2

x :

downstream distance

X + :

dimensionless downstream distance, S Gr 1/3 x /Pr

x 1 :

maximum limiting length as defined in equation (27)

x 2 :

maximum limiting length as defined in equation (28)

y :

direction normal to the plate

Y + :

yu*/v

0:

inlet at x=0

i:

vapor-liquid interface

s :

saturation

w :

wall

L :

exit at x=L

δ :

local liquid film thickness

δ + :

δu*/v

δ t :

thermal penetration depth

δ + t :

δ t u*/v

ε :

eddy viscosity

ν :

kinematic viscosity of the liquid

λ :

parameter appearing in equation (1a), g(ρ − p v )δ/(u* 2 ρ)

μ :

dynamic viscosity of liquid

ρ :

density of liquid

ρ v :

density of vapor

τ :

shear stress

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Authors and Affiliations

  1. Department of Mechanical Engineering, College of Engineering, Andhra University, 530003, Visakhapatnam, India

    J. Saibabu & P. K. Sarma

  2. Department of Chemical Engineering, College of Engineering, Andhra University, 530003, Visakhapatnam, India

    V. Dharma Rao

Authors
  1. V. Dharma Rao
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  2. J. Saibabu
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  3. P. K. Sarma
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Rao, V.D., Saibabu, J. & Sarma, P.K. Direct contact condensation of vapor on turbulent, falling liquid film. Appl. Sci. Res. 49, 31–48 (1992). https://doi.org/10.1007/BF00382741

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  • DOI: https://doi.org/10.1007/BF00382741

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