A sharp-interface elliptic two-phase numerical model of laminar film condensation on a horizontal tube

2016 ◽  
Vol 102 ◽  
pp. 1169-1179 ◽  
Author(s):  
Esam A. Saleh ◽  
Scott J. Ormiston
10.2514/3.931 ◽  
1997 ◽  
Vol 11 ◽  
pp. 526-532
Author(s):  
V. R. Murthy ◽  
Yu-An Lin ◽  
Steven W. O' ◽  
Hara Har ◽  
Sheng-An Yang

1961 ◽  
Vol 83 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Michael Ming Chen

The boundary-layer equations for laminar film condensation are solved for (a) a single horizontal tube, and (b) a vertical bank of horizontal tubes. For the single-tube case, the inertia effects are included and the vapor is assumed to be stationary outside the vapor boundary layer. Velocity and temperature profiles are obtained for the case μvρv/μρ ≪ 1 and similarity is found to exist exactly near the top stagnation point, and approximately for the most part of the tube. Heat-transfer results computed with these similar profiles are presented and discussed. For the multiple-tube case, the analysis includes the effect of condensation between tubes, which is shown to be partly responsible for the high observed heat-transfer rate for vertical tube banks. The inertia effects are neglected due to the insufficiency of boundary-layer theory in this case. Heat-transfer coefficients are presented and compared with experiments. The theoretical results for both cases are also presented in approximate formulas for ease of application.


Author(s):  
Foad Hassaninejadfarahani ◽  
Scott Ormiston

Laminar film condensation is an important phenomenon which occurs in numerous industrial applications such as refrigeration, chemical processing, and thermal power generation industries. It is well known that film condensation heat transfer is greatly reduced in the presence of a non-condensing gas. The present work performs a numerical analysis of the steady-state, laminar film condensation from a vapour-gas mixture in vertical parallel plate channels to demonstrate a computer model that could assist engineering analysts designing systems involving these phenomena. The present model has three new aspects relative to other current work. First, the complete elliptic two-dimensional governing equations are solved in both phases. Thus, the entire channel domain is solved rather than using an approach that marches along the channel from inlet to a prescribed length. Second, a dynamically determined sharp interface is used between the phases. This sharp interface is determined during the solution on a non-orthogonal structured mesh. Third, the governing equations are solved in a fully-coupled approach. The equations for two velocities, pressure, temperature, and gas mass fraction are solved in a coupled method simultaneously for both phases. Discretisation has been done based on a finite volume method and a co-located variable storage scheme. An in-house computer code was developed to implement the numerical solution scheme. Detailed results are presented for laminar film condensation from steam-air mixtures flowing in vertical parallel-plate channels. The results include velocity and pressure profiles, as well as axial variations of film thickness, Nusselt number and interface gas mass fraction. Detailed comparisons are made with results from a parabolic solution approach.


1971 ◽  
Vol 93 (3) ◽  
pp. 297-304 ◽  
Author(s):  
V. E. Denny ◽  
A. F. Mills ◽  
V. J. Jusionis

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.


1966 ◽  
Vol 88 (3) ◽  
pp. 265-272 ◽  
Author(s):  
C. E. Rufer ◽  
S. P. Kezios

A physical model is constructed for the stratified two-phase flow pattern with annular, laminar film condensation superimposed and the equivalent mathematical model is analyzed. Utilizing the principle of conservation of mass, energy, and momentum, an equation is derived which gives the slope of the vapor-bulk liquid interface along the tube. By varying the flow rate, inclination of the tube, tube radius, and film temperature difference, the effect of these variables on the flow level is illustrated in a typical example. A special case of this equation, namely, that describing the vapor-liquid interface when the rate of condensation is zero, is compared with several recent empirical horizontal tube holdup correlations and with flow-level data of Gazley for stratified air-water flow.


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