(140i) Modelling Wave Enhanced Mass Transfer in Falling Films Using Effective Diffusion Coefficients

In chemical and life science industry numerous applications for heat and mass transfer in gas-liquid systems are designed to realize the liquid phase as a falling film. Examples for these applications are evaporation of solutions containing temperature sensitive substances in food industry, cooling in nuclear power plant, liquid/gas reaction with significant heat source and melt crystallisation in synthetic material production. The capability to transfer a large amount of heat and mass due to waviness of the liquid film with small pressure drop and controllable adjustment of the driving temperature gradient are the major advantages of falling films.

Appropriate field information about an interesting quantity, e.g. the concentration field of an absorbed component in the liquid phase is necessary for an optimal design of a falling film unit. State-of-the-art is a design using correlations of dimensionless numbers. The calculation of the integral behaviour and the geometric design is very fast but field information is missed. Exact field information can be obtained by solving the coupled system of nonlinear conservation equations for the gas and the liquid phase performing direct numerical simulations. The calculation duration is in the range of several weeks up to months for only one operating point and so much too long for an optimal design. Some analytical solutions exist describing the field of scalar quantities in the liquid phase for special cases but the wave enhanced transport is neglected in the basic models.

By introducing an effective diffusion coefficient it is possible to reduce the 3D non steady two-phase problem with free moving boundary to a 2D steady-state one-phase problem with a fixed surface. Thereby the effective diffusion coefficient incorporates the wave enhanced transport perpendicular to the wall and in flow direction of the liquid film. In the presentation a preliminary model of the effective diffusion coefficient based on experimental data for the absorption of oxygen into a wavy water film is introduced. This model provides detailed field information in short calculation times. Numerical results of the concentration field obtained by analytical solutions and the model based on effective diffusion coefficients will be shown.