Analytical Investigation into Effects of Capillary Force on Condensate Film Flowing over Horizontal Semicircular Tube in Porous Medium

A theoretical investigation is performed into the problem of laminar filmwise condensation flow over a horizontal semicircular tube embedded in a porous medium and subject to capillary forces. The effects of the capillary force and gravity force on the condensation heat transfer performance are analyzed using an energy balance approach method. For analytical convenience, several dimensionless parameters are introduced, including the Jakob number Ja, Rayleigh number Ra, and capillary force parameter Boc. The resulting dimensionless governing equation is solved using the numerical shooting method to determine the effect of capillary forces on the condensate thickness. A capillary suction velocity can be obtained mathematically in the calculation process and indicates whether the gravity force is greater than the capillary force. It is shown that if the capillary force is greater than the condensate gravity force, the liquid condensate will be sucked into the two-phase zone. Under this condition, the condensate film thickness reduces and the heat transfer performance is correspondingly improved. Without considering the capillary force effects, the mean Nusselt number is also obtained in the present study as N u ¯ | V 2 ∗ = 0 = 2 R a D a / J a 1 / 2 ∫ 0 π 1 + cos θ 1 / 2 d θ .

Heat transfer performance of film condensation created by forced flow

In this work, condensate film on a vertical wall cooled on the external side by forced flow is analysed as a conjugate heat transfer problem. The treated case is that the condensate film and forced flow boundary-layer are in a parallel-flow arrangement. The mass, momentum and energy boundary-layer equations of the condensate film and forced flow are set in a dimensionless form to generalize the model. The parameters affecting the thermal communication between the condensate film and the forced flow are defined from the analysis. These parameters explain the relative impact of the three involved thermal resistances of solid wall, forced convection and film condensation on the local and mean Nusselt number. The study shows that the Nusselt number predicted by the present conjugate model is different from that predicted by a Nusselt-type model.

Study of condensation at the surfaces of tube with gradient heat flux measurement

Gradient heat flux measurement is used for study of heat transfer during condensation of water steam at inner and outer surfaces of tube. Experimental setups allow producing experiments with minimal distortion of condensate film flow. Experiments were carried out for different directions of steam and cooling water flows and for different angles of tube inclination relative to the vertical. Heat transfer coefficients and their change along the length and perimeter of tube were measured. The obtained data allow to study formation of condensate film and parameters of film motion. The results are corresponding to classical ideas.

Directional Passive Condensate Film Drainage on a Horizontal Surface With Periodic Asymmetrical Structures

Condensation of a highly wetting fluid on a horizontal surface with asymmetric millimeter-sized ratchets and periodically located film drainage pathways (DPs) in the spanwise direction is characterized. The hypothesis to be tested is whether the geometry would result in a net steady-state preferential drainage of the condensate film. Experiments are performed using PF5060 on a brass surface with ratchets of 3 mm pitch and 75–15 deg asymmetry. Drainage pathways are varied in density as nondimensional drainage pathways per meter depth ranging from 133 to 400. Experiments are performed at varied wall subcooling temperatures from 1 to 10 °C. Results of the asymmetric ratchet are compared against a control test surface with 45–45 deg symmetric ratchets. Both global and film visualization experiments are performed to characterize the differences in condensation between the symmetric and asymmetric surfaces. Global mass collection results indicate that all characterized asymmetric ratchet surfaces exhibit a net directional drainage of condensate while the symmetric control surface exhibited no preferential drainage. Among the asymmetric ratchets, the total mass flux rate increase with decrease in drainage pathway density, while the net mass flux rate increased with pathway density. Visualization of the condensate film was performed to explain the trends in net drainage with subcooling for different drainage pathway densities. For small drainage path density surfaces, a two-dimensional analytical model was developed to further characterize the effect of ratchet angle and Bond number on the net preferential drainage.

Condensation in Microchannels: Detailed Comparisons of Annular Laminar Flow Theory With Measurements

A relatively simple theory of annular laminar film condensation in microchannels, based on the Nusselt approximations for the condensate film and a theoretically based approximation for the vapor shear stress, has no empirical input and gives the local heat transfer coefficient and local quality for given vapor mass flux and vapor–surface temperature difference distribution along the channel. As well as streamwise vapor shear stress and gravity, the theory includes transverse (to the flow direction) surface tension-driven motion of the condensate film and gives a differential equation for the local (transverse and streamwise) condensate film thickness. As well as four transverse direction boundary conditions due to condensate surface curvature, a streamwise boundary condition is required as in the Nusselt theory. When the vapor is saturated or superheated at inlet, this is provided by the fact that the film thickness is zero around the channel perimeter at the position of onset on condensation. Most experimental investigations have been conducted with quality less than one at inlet and only approximate comparisons, discussed in earlier papers, can be made. The present paper is devoted to comparisons between theory and measurements in investigations where local heat flux and channel surface temperature were measured and the vapor at inlet was superheated. Measured and calculated heat transfer coefficients and their dependence on distance along the channel and on local quality are in surprisingly good agreement and suggest that the mode of condensation is, in fact, annular and laminar, at least where the quality is high.

Computational Fluid Dynamics Simulations of Convective Pure Vapor Condensation Inside Vertical Cylindrical Condensers

This paper presents the results from computational fluid dynamics (CFD) simulations of heat and mass transfer of pure vapor flowing and condensing in a vertical cylindrical condenser system at various inlet temperatures, mass flow rates, and operating pressure for the case where the vapor condensation is not completed inside the condenser tube. The heat and mass transfer inside the condenser tube is simulated as single phase flow, and the thin condensate film on the condensing surface is replaced by a set of boundary conditions that couple the CFD simulations inside the condenser tube and the coolant channel. The CFD results are compared with the experimental results, and good agreement has been found for the various measured temperatures. It is found that both the wall temperature and the heat flux vary significantly along the condenser tube, and it is necessary to consider the conjugate problem that consists of the whole condenser system (condenser plus coolant flow) in predicting the pure vapor condensation in a condensing system. The CFD results show that the heat flux along the condenser tube can be increasing for counter-flow condenser, and the condensate film may not be the main limiting factor in the pure vapor condensation. The results from the CFD simulations also show that the estimation of the interface shear stress cannot be based on the bulk velocity of the water vapor alone.