A novel Navier-Stokes procedure has been developed to investigate the LiBr-$H_2O$ absorption phenomena about the free-falling film flow on a horizontal tube. The fully elliptic equations of momentum, temperature and concentration are solved by using the SIMPLER algorithm, which incorporates the QUICK scheme and the incomplete Cholesky conjugate gradient method for accuracy and efficiency. Taking account of the surface-tension effects, the free-surface location is carefully traced by the MAC method in a time-accurate manner. The flow field including the free-surface location is obtained using a cylindrical orthogonal grid while a nonorthogonal general grid is fitted over the film region for the heat/mass transfer calculation.
When the flow rate is low, the surface tension is found to play an important role in dictating the flow field especially near the stagnation points due to the abrupt change of film surface curvature. There forms a recirculation zone next to the free surface near the upper stagnation point, which is induced by the film-thickening friction force from the tube wall. The calculation without the surface-tension effects, on the other hand, is unable to capture this recirculating motion. For large flow rate, however, the surface-tension effects diminish and all the calculations give nearly identical results. At the tube side, the calculated film thickness follows closely the Nusselt's fully-developed profile for small flow rates but deviates substantially as the flow rate increases since it takes longer to attain the fully developed state.
To examine the absorption process, calculations have been made for various inlet temperature and flow-rate conditions. Until the temperature and concentration fields fully develop, the absorption feeds on itself: The higher rate of absorption generates more heat and sends the temperature higher. This in turn increases the normal temperature gradient and also the rate of absorption. For low inlet temperature, the absorption rate is large in the upstream region but the mean temperature also increases and as a result the absorption decreases as the film flows to downstream while high-inlet-temperature case does the opposite. The difference in the absorption rate due to the inlet temperature change becomes smaller in the downstream than that in the upstream. For large flow rate, the heat transfer to the wall becomes poor due to the thick film and so does the absorption rate.
The analyses have also been carried out for multiple tube arrangement. After a few tube rows, the absorption characteristics show a converged fully developed state: The mean temperature and concentration decrease linearly; the absorption rate and the newly defined equilibrium parameter, which is the measure of deviation from the equilibrium state, converge to finite values. The convergence becomes rapid as the flow rate decreases.
