The Effect of Noncondensable Gas on Laminar Film Condensation of Liquid Metals

1973 ◽  
Vol 95 (1) ◽  
pp. 6-11 ◽  
Author(s):  
R. H. Turner ◽  
A. F. Mills ◽  
V. E. Denny
Keyword(s):  
Liquid Metals ◽  
Dominant Role ◽  
Boundary Layer Separation ◽  
Vertical Surface ◽  
Film Condensation ◽  
Vapor Flow ◽  
Interfacial Resistance ◽  
Noncondensable Gas ◽  
Laminar Film ◽  
Laminar Film Condensation

The effect of noncondensable gas on laminar film condensation of a liquid metal on an isothermal vertical surface with forced vapor flow is analyzed. Where necessary the interfacial resistance due to thermodynamic nonequilibrium is included for a condensation coefficient σ = 1. A computer program has been developed to solve a finite-difference analog of the governing partial differential equations and is applied here to the mercury–air and sodium–argon systems. Heat-transfer results are presented for vapor velocities in the range 1 to 100 fps with mass fraction of gas varying from 10−5 to 3 × 10−2. The overall temperature difference ranged from 0.1 to 30 deg F while the temperature levels were 1200 and 900 deg R for mercury–air and 2000 and 1500 deg R for sodium–argon. The effect of noncondensable gas is most marked for low vapor velocities and high gas concentrations. At the lower pressure levels the inter facial resistance plays a dominant role, causing maxima in the curves of q/qNu versus x. For the mercury–air system the adverse buoyancy force causes vapor boundary-layer separation when the free-stream vapor velocity is low.

Laminar Film Condensation From a Steam-Air Mixture Undergoing Forced Flow Down a Vertical Surface

1971 ◽  
Vol 93 (3) ◽  
pp. 297-304 ◽  
Author(s):  
V. E. Denny ◽  
A. F. Mills ◽  
V. J. Jusionis
Keyword(s):  
Liquid Film ◽  
Numerical Solution ◽  
Finite Difference Methods ◽  
Vertical Surface ◽  
Forced Flow ◽  
Film Condensation ◽  
Two Phase ◽  
Noncondensable Gas ◽  
Laminar Film ◽  
Laminar Film Condensation

An analytical study of the effects of noncondensable gas on laminar film condensation of vapor under going forced flow along a vertical surface is presented. Due to the markedly nonsimilar character of the coupled two-phase-flow problem, the set of parabolic equations governing conservation of momentum, species, and energy in the vapor phase was solved by means of finite-difference methods using a forward marching technique. Interfacial boundary conditions for the numerical solution were extracted from a locally valid Nusselt-type analysis of the liquid-film behavior. Locally variable properties in the liquid were treated by means of the reference-temperature concept, while those in the vapor were treated exactly. Closure of the numerical solution at each step was effected by satisfying overall mass and energy balances on the liquid film. A general computer program for solving the problem has been developed and is applied here to condensation from water-vapor–air mixtures. Heat-transfer results, in the form q/qNu versus x, are reported for vapor velocities in the range 0.1 to 10.0 fps with the mass fraction of air ranging from 0.001 to 0.1. The temperature in the free stream is in the range 100–212 deg F, with overall temperature differences ranging from 5 to 40 deg F. The influence of noncondensable gas is most marked for low vapor velocities and large gas concentrations. The nonsimilar character of the problem is especially evident near x = 0, where the connective behavior of the vapor boundary layer is highly position-dependent.

Paper 6: Effect of Vapour Drag on Laminar Film Condensation on a Vertical Surface

1965 ◽  
Vol 180 (10) ◽  
pp. 280-287 ◽  
Author(s):  
Y. R. Mayhew ◽  
D. J. Griffiths ◽  
J. W. Phillips
Keyword(s):  
Reynolds Number ◽  
Liquid Film ◽  
Atmospheric Pressure ◽  
Vertical Surface ◽  
Simple Theory ◽  
Experimental Results ◽  
Film Condensation ◽  
Laminar Film ◽  
Laminar Film Condensation

A simple theory is presented for laminar film condensation of a pure vapour on a vertical surface which takes account of the drag induced on the liquid film by the flow of the condensing vapour. Experiments were carried out with steam at atmospheric pressure condensing inside a vertical 1.824 in diameter tube 8 in high. The downward vapour velocity was varied from 5 to 150 ft/s, the corresponding range of the film Reynolds number at the bottom of the tube being 200-500. Experimental results agreed well with the theory.

Laminar Film Condensation of a Flowing Vapor on a Horizontal Cylinder at Normal Gravity

1969 ◽  
Vol 91 (4) ◽  
pp. 495-501 ◽  
Author(s):  
V. E. Denny ◽  
A. F. Mills
Keyword(s):  
Boundary Layer ◽  
Normal Gravity ◽  
Numerical Solutions ◽  
Horizontal Cylinder ◽  
Vertical Surface ◽  
Film Condensation ◽  
Laminar Film ◽  
Laminar Film Condensation ◽  
Fluid Properties ◽  
Finite Difference Analog

An analytical solution, based on the Nusselt assumptions, has been obtained for laminar film condensation of a flowing vapor on a horizontal cylinder. In so doing, a reference temperature for evaluating locally variable fluid properties is defined in the form Tr = Tw + α (Ts − Tw) and accounts for both the effects of fluid property variations and minor errors introduced by the assumptions in the analysis. Verification was obtained by comparison with exact numerical solutions based on a finite-difference analog to the conservation equations in boundary-layer form. In the analytical as well as the numerical developments, vapor drag was accounted for through an asymptotic solution of the vapor boundary layer under strong suction. It was found that, for angles up to 140 deg, there was less than a 2 percent discrepancy between the analytical predictions and the numerical results. As 180 deg is approached an increased discrepancy is expected due to a gross violation of the Nusselt assumptions. The values of the reference parameter α, which were previously derived for condensation on a vertical surface, were found to be appropriate for the horizontal cylinder as well.

Flow Regimes for Laminar Film Condensation on a Vertical Plate With an Upward Vapor Flow

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Kentaro Kanatani
Keyword(s):  
Nusselt Number ◽  
Film Thickness ◽  
Average Nusselt Number ◽  
Vertical Plate ◽  
Film Condensation ◽  
Integral Model ◽  
Vapor Flow ◽  
Plate Length ◽  
Laminar Film ◽  
Laminar Film Condensation

Abstract Laminar film condensation on a vertical plate with an upward vapor flow is studied. An approximate integral model of the condensate film and the boundary layer of the vapor is numerically solved, taking into account both gravity and interfacial shear. Here, three types of solution are examined: (i) zero film thickness at the bottom; (ii) zero flowrate with a finite film thickness at the bottom; and (iii) negative flowrates at the bottom. The film thickness and the average Nusselt number are shown as functions of the distance along the plate and the plate length, respectively. The terminal lengths of the solutions of the types (i) and (ii) are calculated against the degree of the subcooling. Moreover, the results are compared with those derived using the approximation method where the shearing stress on the vapor–liquid interface is composed of only the momentum transferred by the suction mass (the Shekriladze–Gomelauri approach). It is found that the average Nusselt number is well described by the Shekriladze–Gomelauri model in the range of the solution type (ii), while the average Nusselt number for the thinnest-film solution of the type (iii) is asymptotically consistent with the Shekriladze–Gomelauri value for long plates.

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