Theoretical analysis of laminar film condensation in a rotating cylinder with a scraper

The rimming film condensation on the inside wall of a rotating cylinder with a scraper is analyzed. The whole cylinder is divided into two regions, one is the so-called boundary layer region where the radial velocity of the condensate is much smaller than the peripheric velocity so that the boundary layer theory is assumed to be valid; the other is the scraper region where because of the disturbance of the scraper the boundary layer theory does not apply. The boundary layer integral method in the boundary layer region coupling with the integral momentum theorem across the scraper region provides a method to determine the velocity, temperature, and film thickness distributions, and heat transfer coefficients. An extensive discussion about the previous models is given. The sublayer flow rate constancy principle and the variability principle of the boundary layer thickness (therefore the interface velocity) at the scraper position with respect to the rotational speed are proposed. The present model greatly improved the prediction of the average heat transfer coefficient. Received on 5 January 1998     

An analytical investigation into filmwise condensation on a horizontal tube in a porous medium with suction at the tube surface

An analytical investigation is performed into the problem of steady filmwise condensation flow over the outside surface of a horizontal tube embedded in a porous medium with suction at the tube surface. As in classical film condensation problems, an assumption is made that the condensate and vapor layers meet at a common boundary rather than being separated by an intermediary two-phase zone. Furthermore, it is assumed that the condensate film has constant properties and conforms to Darcy’s law within the porous medium. By introducing an effective suction function to represent the effect of the wall suction on the thickness of the liquid film, both the local condensate film thickness and the local Nusselt number are derived using a simple numerical shooting method. The analytical results indicate that the mean Nusselt number depends on the Darcy number, the Jakob number, the Rayleigh number and the suction parameter. Furthermore, it is found that the local Nusselt number has a maximum value at the upper surface of the horizontal tube and reduces toward zero at the lower surface as a result of the finite thickness of the condensate layer.     

Numerical study of condensing a small concentration of vapour inside a vertical tube

The purpose of this study is to analyse the combined heat and mass transfer of liquid film condensation from a small steam–air mixtures flowing downward along a vertical tube. Both liquid and gas stream are approached by two coupled laminar boundary layer. An implicit finite difference method is employed to solve the coupled governing equations for liquid film and gas flow together with the interfacial matching conditions. The effects of a wide range of changes of three independent variables (inlet pressure, inlet Reynolds number and wall temperature) on the concentration at exit tube, local Nusselt and Sherwood numbers, film thickness, accumulated condensate rate and temperature are carefully examined. The numerical results indicate that in the case of condensing a small concentration of vapours from a mixture, the resistance to heat and mass transfer by non-condensable gas becomes very intense. The comparisons of average Nusselt number and local condensate heat transfer coefficient with the literature results are in good agreement.     

Conjugate heat transfer inside a porous channel

Analytical and numerical analyses have been performed for fully developed forced convection in a fluid-saturated porous medium channel bounded by two parallel plates. The channel walls are assumed to be finite in thickness. Conduction heat transfer inside the channel wall is also accounted and the full problem is treated as a conjugate heat transfer problem. The flow in the porous material is described by the Darcy–Brinkman momentum equation. The outer surfaces of the solid walls are treated as isothermal. A temperature dependent volumetric heat generation is considered inside the solid wall only. Analytical expressions for velocity, temperature, and Nusselt number are obtained after simplifying and solving the governing differential equations with reasonable approximations. Subsequent results obtained by numerical calculations show an excellent agreement with the analytical results.     

Minimum wetting rate for a decelerating liquid film

The paper presents an analytical study of a laminar decelerating liquid film falling along a vertical plate. Approximate solutions are obtained for the boundary layer within the film, film thickness, entrance length, and minimum wetting rate. It is shown that the analysis may be extended also to a film flowing over a horizontal cylinder. The theory is in reasonable agreement with the parametric trends observed in experiments on horizontal cylinders.     

Integral analysis of condensation in a paper drum with a scraper

An integral analysis is made for laminar film condensation in a rotating paper drum with a scraper. The analysis includes the nonlinear inertial terms in the equation of motion, with the interface shear stress being considered. The results of numerical solutions show that the inertial terms cannot be neglected except in the cases of a very thin condensate film or a very large Froude number, that the condensation heat transfer will be, to some extent, enhanced by the inertial effect, and that the vapor shear at the vapor-liquid interface proves to be negligible. Distributions of the interface velocity and film thickness as well as heat transfer results are obtained and discussed. Included also in this paper is the investigation for transition of the condensate flow from steady state to unsteady one. Received on 6 December 1996     

Buoyancy-affected laminar film condensation

The flow and heat transfer in a laminar condensate flim on an isothermal vertical plate is modelled mathematically. The strict Boussinesq approximation is adopted to account for buoyancy due to local temperature variations within the film. A similarity transformation reduces the governing boundary-layer type equations to a coupled set of ordinary differential equations and the resulting three-parameter twopoint boundary value problem is solved numerically for Prandtl numbers,Pr, ranging from 0.001 to 1000 and Jakob numbers,Ja, between 0.0001 and 1.5. The principal effects of the favourable buoyancy are to reduce the thickness of the condensate film and increase the film velocity at the smooth liquid-vapour interface, whereas the friction and heat transfer at the plate are enhanced. In accordance with the classical Nusselt theory, it is found that the temperature varies nearly linearly across the film. The computed similarity profiles for velocity reveal, however, substantial departures from the parabolic distribution assumed in the simplified Nusselt analysis.     

Heat transfer in laminar film condensation; local film resistance and local enthalpy allowing for variable viscosity and subcooling

In contrast to the conventional method of calculation account was taken of the dependence of viscosity on temperature and of the non-linear temperature profile due to subcooling of the condensate. Fully developed velocity and temperature profiles and a constant heat flux along the flow path are assumed. The local thickness of the film can be calculated with the usual equations provided the reference temperature of Drew [3] and Gregorig [4] for the viscosity (three-quarters of the wall temperature plus one-quarter of the film surface temperature) is used. The calculation of the local heat transfer coefficient and the mean condensate temperature (adiabatic mixing temperature), however, requires special equations taking into account the influences mentioned above.     

Film thickness measurement with an ultrasonic transducer

A technique for measuring condensate film thickness using an ultrasonic transducer is described. In the experiment, the condensate film thickness with R-113 and FC-72 (a fluorinert compound developed by the 3M Company) condensing on the horizontal lower surface of a rectangular duct was measured at several locations. From the measured values a power law relation between the condensate film thickness and the axial distance from the leading edge of the condensing surface was derived by regression analysis. Assuming a linear temperature profile in the condensate film, local and average heat transfer coefficients were computed from the condensate film thickness. The average heat transfer coefficients were compared with the values obtained by measuring the heat transfer rate to the coolant. The two values were within ±12% of each other. As yet there is no satisfactory analytical model to predict the local heat transfer coefficient even in the annular condensation regime. One of the main difficulties in modeling the condensation is the lack of a suitable model to predict the interfacial shear stress. With the measurement of the film thickness it is possible to determine the interfacial shear stress. It is hoped that the shear stresses so determined will lead to the development of a satisfactory model for interfacial shear stress with condensation.     

Turbulent film condensation on an isothermal cone surface

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.     

Development of a PLIC-VOF method for the dynamic simulation of entry region flow in a laminar falling film

The present work describes a numerical procedure to simulate the development of hydrodynamic entry region in a gravity-driven laminar liquid film flow over an inclined plane. It provides a better insight into the physics of developing film in entry region. A novel numerical approach is proposed which has the potential to provide solutions for the complex physics of liquid film spreading on solid walls. The method employs an incompressible flow algorithm to solve the governing equations, a PLIC-VOF method to capture the free surface evolution and a continuum surface force (CSF) model to include the effect of surface tension. To account for the moving contact line on the solid substrate, a precursor film model based wall treatment is implemented. Liquid film flow has been simulated for the Reynolds number range of 5 ≤ Re ≤ 37.5, and the predicted results are found to agree well with the available analytical and experimental data.     

Transient Film Condensation on a Vertical Plate Imbedded in Porous Medium

The present paper introduces a mathematical model that simulates the transient film condensation on a vertical plate imbedded in a porous medium. In this model, the Brinkman-extended Darcy model is adopted and the local macroscopic inertial term is included. Analytical solutions are presented that describe the transient behavior of the condensate film thickness, condensate mass flow rate and heat transfer coefficient. The current results show the effect of the permeability of the porous material on several issues including the velocity profiles, the film thickness and the time required to reach steady state conditions.     

T-RANS Simulations of Subcritical Flow with Heat Transfer Past a Circular Cylinder Surrounded by a Thin Porous Layer

We study flow and heat transfer to a cylinder in cross flow at Re = 3,900–80,000 by means of three-dimensional transient RANS (T-RANS) simulations, employing an RNG k − ε turbulence model. Both the case of a bare solid cylinder and that of a solid cylinder surrounded at some fixed distance by a thin porous layer have been studied. The latter configuration is a standard test geometry for measuring the insulating and protective performance of garments. In this geometry, the flow in the space between the solid cylinder and the porous layer is laminar but periodic, whereas the outer flow is transitional and characterized by vortex shedding in the wake of the cylinder. The results from the T-RANS simulations are validated against data from Direct Numerical Simulations and experiments. It is found that T-RANS is very well suited for simulating this type of flow. The transient nature of the flow underneath the porous layer is well reproduced, as well as the influence of vortex shedding on the heat transfer in the downstream stagnation zone. T-RANS results are found to be in much better agreement with DNS and experimental data than results from steady-state RANS.     

Reduction in drag and vortex shedding frequency through porous sheath around a circular cylinder

A numerical study on the laminar vortex shedding and wake flow due to a porous‐wrapped solid circular cylinder has been made in this paper. The cylinder is horizontally placed, and is subjected to a uniform cross flow. The aim is to control the vortex shedding and drag force through a thin porous wrapper around a solid cylinder. The flow field is investigated for a wide range of Reynolds number in the laminar regime. The flow in the porous zone is governed by the Darcy–Brinkman–Forchheimer extended model and the Navier–Stokes equations in the fluid region. A control volume approach is adopted for computation of the governing equations along with a second‐order upwind scheme, which is used to discretize the convective terms inside the fluid region. The inclusion of a thin porous wrapper produces a significant reduction in drag and damps the oscillation compared with a solid cylinder. Dependence of Strouhal number and drag coefficient on porous layer thickness at different Reynolds number is analyzed. The dependence of Strouhal number and drag on the permeability of the medium is also examined. Copyright © 2009 John Wiley & Sons, Ltd.     

Finite-amplitude stability analysis of liquid films down a vertical wall with and without interfacial phase change

The generalized kinematic equation for film thickness, taking into account the effect of phase change at the interface, is used to investigate the nonlinear stability of film flow down a vertical wall. The analysis shows that supercritical stability and subcritical instability are both possible for the film flow system. Applications of the result to isothermal, condensate and evaporate film flow show that mass transfer into (away from) the liquid phase will stabilize (destabilize) the film flow. Finally, we find that supercritical filtered waves are always linearly stable with regard to side-band disturbance.     

Forced convective film condensation inside vertical tubes

A theoretical study of forced convective film condensation inside vertical tubes is presented. We propose a unified procedure for predicting the pressure gradient and condensation heat transfer coefficient of a vapor flowing turbulently in the core and associated with laminar or turbulent film on the tube wall. The analysis for the vapor flows is performed under the condition that the velocity profiles are locally self-similar. The laminar and turbulent film models equate the gravity, pressure and viscous forces, and consider the effect of interfacial shear. The transition from laminar to turbulent film depends not only on the liquid Reynolds number but also on the interfacial shear stress. In this work we also proposed a new eddy viscosity model which is divided into three regions: the inner region in liquid condensate near the wall; the interface region including both liquid and vapor; and the outer region for the vapor core. Comparisons of the theory with some published experimental data showed good agreement.     

活塞环组摩擦及润滑特性的综合分析

基于二维平均流量模型和微凸体接触模型，提出了一种分析内燃机活塞环组润滑的模型，同时还对油膜厚度进行了实测，理论值与实测值具有良好的一致性，并且运用这种模型求出了活塞环－缸套之间油膜厚度的三维分布，发现油膜厚度沿圆周方向存在不均匀性．在分析中还考虑了贫油的影响，而且首次探讨了活塞系统的二阶运动对活塞环组润滑特性的影响，给出了不同结构下活塞系统的摩擦力和摩擦功耗．     

航空发动机轴承腔中油滴运动与沉积的特性分析

本文在获得轴承腔中气相介质流场的基础上,采用Lagrangian方法建立油滴在气相介质流场中运动的分析模型,通过瞬时步进法数值模拟油滴的运动过程,获得了油滴直径和旋转轴转速对油滴运动过程中的速度和轨迹影响的规律.基于获得的油滴与腔壁碰撞前的运动状态,以及结合油滴与腔壁的碰撞模型,实现了油滴直径和旋转轴转速对碰撞后油滴沉积率和动量转移率影响规律的分析.结果表明:油滴直径和旋转轴转速对油滴速度及轨迹,以及油滴沉积率及动量转移率都有很大影响,而且前者的影响更为明显.与国外同等条件下的试验结果对比表明,本文提出的油滴运动与沉积特性分析方法具有较好的可靠性和精度.碰撞前后油滴运动状态和沉积率及动量转移率的计算,为下一步油膜厚度和速度的计算,继而为轴承腔润滑设计和换热分析提供了初始条件.     

Simultaneous heat and mass transfer inside a vertical tube in evaporating a heated falling alcohols liquid film into a stream of dry air

A numerical study of the evaporation in mixed convection of a pure alcohol liquid film: ethanol and methanol was investigated. It is a turbulent liquid film falling on the internal face of a vertical tube. A laminar flow of dry air enters the vertical tube at constant temperature in the downward direction. The wall of the tube is subjected to a constant and uniform heat flux. The model solves the coupled parabolic governing equations in both phases including turbulent liquid film together with the boundary and interfacial conditions. The systems of equations obtained by using an implicit finite difference method are solved by TDMA method. A Van Driest model is adopted to simulate the turbulent liquid film flow. The influence of the inlet liquid flow, Reynolds number in the gas flow and the wall heat flux on the intensity of heat and mass transfers are examined. A comparison between the results obtained for studied alcohols and water in the same conditions is made.     

Binary diffusion and heat transfer in laminar mixed convection channel flows with uniform wall heat flux: extremely thin film thickness

A detailed numerical study has been performed to investigate the combined heat and mass transfer in laminar mixed convection channel flows with uniform wall heat flux. In an initial effort the liquid film on the channel wall is assumed to be extremely thin in thickness. Major dimensionless groups governing the present problem areGr _T,Gr _Mx,Pr,Sc, φ andRe. Results are specifically presented for an air-water system under various conditions. The effects of wall heating flux, the Reynolds number and the relative humidity of the moist air in the ambient on the momentum, heat and mass transfer in the flow are investigated in great detail.