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.     

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.     

Study on laminar film condensation of saturated steam on a vertical flat plate for consideration of various physical factors including variable thermophysical properties

The extended theory of the steady state laminar film condensation process of pure saturated vapour at atmospheric pressure on an isothermal vertical flat plate is established. Its equations provide a complete account of the physical process for consideration of various physical factors including variable thermophysical properties, except for surface tension at the liquid-vapour film interface. First, similarity considerations are proposed to transform the governing system of partial differential equations and its boundary conditions into the corresponding dimensionless system. Then, the dimensionless new system is computed numerically in two steps: First neglecting shear force at the interface, so that the initial values of the boundary conditionsW _{xl, s} andW _{yl, s} are obtained. Then, the calculations of a problem of the three-point boundary-value for coupling the equations of liquid film with those of vapour film are carried out. Furthermore, the correlations for heat transfer coefficient and mass flow rate are proposed by analysis of heat and mass transfer and it is found that the heat transfer coefficient is function of dimensionless temperature gradient $\dot L$ , and that the condensate mass flow rate is function of the mass flow rate parameter (η _lδ W _{xl, s} ? 4W _{yl, s} )of liquid. In addition, the corresponding heat and mass transfer correlations expressed by subcooled temperature Δt are developed. According to Nusselt's theory four different assumptions are set up for an investigation of the effects of the film condensation of saturated vapour, so that the validity of Nusselt's theory can be further clarified. Quantitative comparisons from the results of the heat transfer coefficient and mass flow rate of the condensate indicate that the effect of variable thermophysical properties on the heat and mass transfer is appreciable. The effect of thermal convection in the condensate film is obviously larger than those of shear force at liquid-vapour interface, and the effect of the inertia in the condensate film is very small. Finally, it is also shown that Nusselt's theory, in using Drew reference temperature, will decrease the heat transfer coefficient by at most 5.11%, and will increase the mass flow rate of the condensate by at most 2.45%, provided that the effect of the surface tension is not taken into account.     

Pure steam condensation model with laminar film in a vertical tube

A new physical model for calculating the liquid film thickness and condensation heat transfer coefficient in a vertical condenser tube is proposed by considering the effects of gravity, liquid viscosity, and vapor flow in the core region of the flow. To estimate the velocity profile in the liquid film, the liquid film was assumed to be in Couette flow forced by the interfacial velocity at the liquid–vapor interface. For simplifying the calculation procedures, the interfacial velocity was estimated by introducing an empirical power-law velocity profile. The resulting film thickness and heat transfer coefficient from the model were compared with the experimental data and the results obtained from the other condensation models. The results demonstrated that the proposed model described the liquid film thinning effect by the vapor shear flow and predicted the condensation heat transfer coefficient from experiments reasonably well.     

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.     

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.     

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.     

Condensation heat transfer in a rotating horizontal cylinder with a scraper

A dryer used in the drying process of paper production is usually a rotating horizontal cylinder in which steam condenses. This study concerns some experiments and analyses of condensate flow and heat transfer in a dryer with a scraper.

A laminar film model and a solid film model are introduced for the theoretical analyses. In the former the condensate flow is assumed to be laminar. In the latter the condensate film is assumed to adhere to the cylinder wall. In the analysis with the laminar film model, the film thickness diverges at relatively slow rotations. A criterion for the critical condition at which the divergence commences is proposed. From the solid film model, analytical expressions can be derived for the film thickness and the heat transmission coefficient through the condensate film and the cylinder wall.

The experiments are conducted with an acrylic resin cylinder and a stainless steel cylinder. The experimental result on heat transmission agrees with the analytical result for the solid film model if a condensate film about 25 μm thick remains in spite of scraping.     

On condensation mass transfer in the presence of noncondensables

An analysis is made for the influence of the moving condensate film on the mass transfer rate from the gas-vapor mixture to the condensate. The governing energy and mass conservation equations are solved using the Crank-Nicholson method. The results show that the moving condensate film may have a considerable effect on condensation mass transfer.     

Wärmeübergang bei der Fallfilmverdampfung

At film evaporation in a vertical tube the heat transfer depends on the flow pattern of the falling film and the shear stress at film surface due to a significant flow in the gas phase. For heat transfer without superimposed gas flow equations exist which are checked experimentally. These equations have general validity for film evaporation and film condensation. By describing the influence of gas flow great differences occur between condensation and evaporation. The present work deals with a calculation method which was verified by condensation data. This method is compared and discussed with experimental results of film evaporation. It is shown that the presented method describing the shear stress influence is also applicable.     

Free- and forced-convection film condensation from a horizontal elliptic tube with a vertical plate and horizontal tube as special cases

A simple mathematical model is developed for the study of the mixed-convection film condensation with downward flowing vapors onto a horizontal elliptic tube. Analytical analysis for both the local condensate film thickness and heat transfer characteristics under simultaneous effects of interfacial vapor shear and pressure gradient has been performed by adopting a unified geometry parameter, eccentricity e. The present results for two limit cases, e = 0 (circular tube) and e = 1.0 (vertical plate) are in an excellent agreement with the earlier works. For very slow vapor flow, the present result for dimensionless mean heat transfer coefficient reduces to the same form as in the earlier works, , whose value is 0.728 for e = 0 and 0.943 for e = 1.0. As for very fast vapor flow, the dimensionless mean heat transfer coefficient, increase with increasing eccentricity under the effects of pressure gradient caused by potential flow and surface tension.     

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     

Condensation of a zeotropic CFC 114-CFC 113 refrigerant mixture in the annulus of a double-tube coil with an enhanced inner tube

Local heat transfer and pressure drop measurements were made during condensation of a zeotropic CFC114-CFCll3 refrigerant mixture in the annulus of a double-tube coil consisting of three U-bends and four straight lengths. The inner tube is a 19.1-mm O.D. corrugated copper tube with wire fins soldered onto the outer surface and the inner diameter of the outer duct is 25.0 mm. The vapor-phase mass transfer coefficient exhibited a sawtooth behavior with the U-bends showing higher coefficients than the straight lengths. The frictional pressure gradient data agreed well with a previously developed empirical equation for the condensation of pure refrigerants. A prediction method for the condensation heat transfer rate was proposed on the basis of the correlations of the vapor-phase mass transfer coefficient and heat transfer coefficient of the condensate film. The heat transfer data were correlated by the present method to a mean absolute deviation of 12.9%.     

A general treatment for non-Darcy film condensation within a porous medium in the presence of gravity and forced flow

Non-Darcy film condensation over a vertical flat plate within a porous medium is considered. The Forchheimer extended Darcy model is adopted to account for the non-Darcy effects on film condensation in the presence of both gravity and externally forced flow. A general similarity transformation is proposed upon introducing a modified Peclet number based on the total velocity of condensate, resulting from both gravitational force and externally forced flow. This general treatment makes it possible to obtain all possible similarity solutions including the asymptotic results in the four different limiting regimes, namely, Darcy forced convection regime, Forchheimer forced convection regime, Darcy body force predominant regime and Forchheimer body force predominant regime. Appropriate dimensionless groups for distinguishing these asymptotic regimes are found to be the micro-scale Grashof and Reynolds numbers based on the square root of the permeability of the porous medium. Correspondingly, the non-Darcy effect on the heat transfer rate are investigated in terms of these micro-scale dimensionless numbers.     

Effect of non-condensable gas on condensation in a highly-rotating drum with a scraper

The effect of non-condensable gas on condensation in a highly rotating drum with a scraper is explored analytically. The formulation is first carried out generally, and then the application of the general formulation to the steam-air system gives heat transfer results for a wide range of operating conditions. It is found that a very small amount of non-condensable gas can induce a significant reduction in heat transfer. The reduction is accentuated at larger temperature differences, thinner condensate thickness and, to one's surprise, at higher operating pressures. By comparison, it is indicated that the present situation is more sensitive to non-condensable gas than forced convection condensation along a horizontal plate. Received on 14 August 1997     

Effects of vapor pressure/velocity and concentration on condensation heat transfer for steam–ethanol vapor mixture

When a steam–ethanol vapor mixture condenses on a vertical flat plate, the form of the condensate film changes and many drops are created. This non-film condensation is called pseudo-dropwise or Marangoni condensation. This paper aims to study the main influencing factors on the Marangoni condensation of steam–ethanol vapor.The factors include the ethanol concentration, vapor pressure, vapor velocity and vapor-to-surface temperature difference. The experiments show that the heat transfer coefficient has a maximum value of approximately 42 kW/m² K when the ethanol concentration is 1%. At the low concentrations of 0.5, 1, 5.1 and 9.8%, the condensation heat transfer is greater than for pure steam. In addition, the heat transfer for all vapor mixtures increases with both the rise of vapor pressure and vapor velocity.     

Laminar film condensation from downward flowing superheated vapors onto a non-isothermal sphere

 A model is developed for the study of mixed convection film condensation from downward flowing superheated vapors onto a sphere with variable wall temperature. The model combined natural convection dominated and forced convection dominated film condensation, including effects of superheated vapor, pressure gradient and wall temperature variation can be solved numerically by the fourth-order Runge–Kutta technique. By the present numerical approach, the mean heat transfer is evaluated up to the critical angle of the condensate layer, φ_c. In general, the result of mean heat transfer shows that, as A, the wall-temperature amplitude, increases, the value of with inclusion of P, the pressure gradient effect, goes down slightly, however, the value of with the pressure gradient effect ignored will remain almost uniform. Further, for P=2.0, the mean heat transfer coefficient increases significantly, by 8.6–23.9%, depending on A, as the superheat parameter, S p, increases within a practical range. Received on 7 September 2000     

Steam chugging in a boiling water reactor pressure-suppression system

Results of a transient analysis predicting the general characteristics of steam chugging compare well with the results of two large scale experiments: GKM II, test 21 and GKSS, test 16. Predicted fundamental periods of chugging are within 5 and 16 per cent of the respective experimental values. The results of the analysis include effects of air in the drywell, momentum loss and heat transfer in the condensation pipe, direct contact condensation heat transfer at the gas-water interface and momentum and heat transfer in the wetwell water pool. Bubble shape is calculated in two-dimensional cylindrical coordinates.Required inputs to the analysis include the geometry, initial conditions and constants to determine both the steam inlet mass flowrate to the drywell as a function of time and conduction heat transfer through the wall of the condensation pipe. There are no arbitrary free parameters which must be specified to predict specific experiments. Rather, the analysis is based on fundamental physical phenomena, experimental coefficients documented for general heat transfer and fluid mechanics characteristics and standard analytical techniques.The random nature of steam chugging observed in some experiments is partially explained by predicted regimes of chugging and changes in the maximum extent of a bubble below the condensation pipe exit during each regime.     

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.