A falling film with waves on a vertical circular tube has been analyzed using the integral approach. Wavy flows, an important aspect of falling film absorption in refrigeration systems, have various shapes with flow rates. Within the wavy-laminar flow regime, capillary waves are known to exist below a Reynolds number of 100. A theoretical model of free surface deflection within the regime has been developed. The nonlinear equation obtained in the present work is similar to the deflection equation of wave on a flat plate. It becomes exactly the same as the wave equation on a flat plate in case of an infinite radius. The flow equations provided by this model are solved for various wave parameters at different Reynolds numbers. This study shows that the wave characteristics depend on the parameters such as wave number, dimensionless wave velocity, tube diameter and Reynolds number. As the tube diameter decreases, the intensity of wavy processes increases. The velocity distribution of the falling film was investigated in the present work. The cylindrical model appears to be more appropriate than the Cartesian model in case of small diameter tube and large Reynolds number. Calculated values are in good agreement with other published data. The new equation of annular film and the hydrodynamic description in the periodic field could serve as input for the analysis of heat and mass transfer processes in designing practical commercial devices.
Vapor absorption processes into a wavy falling liquid film of LiBr-$H_2O$ solution in a vertical circular tube are studied numerically. Transient, two-dimensional governing equations were formulated for simultaneous heat and mass transfer in the film, with wave hydrodynamics as input. The equations, coupled nonlinearly at the vapor-liquid interface, were solved by an iterative finite-difference scheme.
We considered the effect of solution mass flow rate, system pressure, solution inlet temperature, concentration, which can be controlled in an operation, to find out optimum operating condition and to investigate the effect of those parameters. The effect of tube diameter and length is presented to construct optimal design guidelines. It is shown that optimum film Reynolds number exists for maximum absorption mass transfer, beyond which mass transfer rate decreases. The mass transfer rates into wavy falling films are larger than those into smooth film. The waves in the falling film flowing on a vertical plate and in a vertical tube are responsible for the enhancement. The results supported the findings of other researchers who explained the enhancement of mass transfer at low Re by the convection associated with the vertical component of the velocity. By comparing the results of wavy flow on a vertical flat plate and in a vertical circular tube it is found that wave motion improves the heat and mass transfer rates in a vertical circular tube than on a vertical flat plate. The difference of heat and mass transfer rates between plate type and tube type absorber increases as the tube diameter decreases and as Reynolds number increases. We should take into account the tube diameter, length and solution mass flow rate simultaneously in design because the effects of those configuration and the operating parameter on the system performance, space constraints and material cost are coupled.
