Abstract
It is an investigation of turbulent film condensation on an isothermal cone. The present paper describes the eddy diffusivity of two turbulent models. And then it discusses the film thickness and heat transfer characteristics under the different turbulent models. The results show the mean heat transfer coefficient on two forms of eddy diffusivity, and there is a variation on the two models. Furthermore, the current results are compared with those generated by previous theoretical investigations. It is found that in high vapor velocity, the mean heat transfer was greater than that of the laminar flow theory. Under the high vapor velocity region, the eddy effect will be an important factor for the heat transfer of turbulent condensate film. Besides, in the low vapor velocity region, the eddy diffusivity seldom influences the heat transfer of condensate film.
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Abbreviations
- C p :
-
Specific heat of condensate at constant pressure (J/kg/k)
- f :
-
Average friction coefficient τ/(ρ u 2/2)
- F :
-
Condensation parameter 1/(SFr)
- Fr :
-
Froude number, u 2∞ /gL
- Gr :
-
Modified Grashof number (gL 3/ν 2l )((ρl − ρv)/(ρl))
- g :
-
Acceleration due to gravity (m/s2)
- h :
-
Local heat transfer coefficient (w/m2 K)
- h fg :
-
Latent heat of condensate (J/kg)
- k :
-
Thermal conductivity (W/mK)
- k l :
-
Thermal conductivity of condensate film (W/mK)
- L :
-
Haracteristic length (m)
- Nu :
-
Nusselt number
- Pr :
-
Prandtl number
- Re :
-
Reynolds number, u ∞ L/ν
- L + :
-
Reynolds shear number, Lu/v t
- L * :
-
Wall shear parameter L +/Gr 1/3
- S :
-
Sub-cooling parameter C p(T s-Tw)/h fg Pr
- St :
-
Stanton number
- T :
-
Temperature (K)
- T + :
-
Dimensionless temperature (T− T w)/(T s− T w)
- U :
-
Velocity component in x-direction (m/s)
- u e :
-
Tangential velocity at edge of vapor boundary layer (m/s)
- u * :
-
Shear velocity \({\sqrt {\tau _{{\text{w}}} /\rho } }\)
- u ∞ :
-
The vapor velocity of the free stream (m/s)
- u + :
-
Dimensionless velocity u/u*
- x :
-
Coordinate of measured distance along cone wall (m)
- X :
-
Dimensionless coordinate along cone wall, X = x/L
- y :
-
Coordinate of measured distance normal to the cone wall (m)
- y + :
-
Dimensionless distance yu*/v t
- δ:
-
Condensate film thickness (m)
- δ+ :
-
Dimensionless film thickness δu */νl
- ϕ:
-
Shear parameter, \(C\frac{{\rho _{{\text{v}}} }}{{\rho _{{\text{l}}} }}{\left( {\frac{{\nu _{{\text{l}}} }}{{\nu _{{\text{v}}} }}} \right)}^{{ - 0.2}} Gr^{{1.4/6}} \)
- ν:
-
Kinematic viscosity
- ɛ m :
-
Eddy diffusivity for momentum
- ρ:
-
Density (kg/m3)
- τ:
-
Shear stress
- τδ :
-
Interfacial vapor shear stress
- s:
-
Saturation
- v:
-
Vapor
- l:
-
Liquid
- w:
-
Cone wall
- δ:
-
Vapor-liquid interface
- M :
-
Power of potential flow
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Acknowledgment
The authors gratefully acknowledge the support provided for this project by the National Science Council of the Republic of China under contract no. NSC-94-2212-E-165-001.