THE ASSIMPTOTICAL SOLUTION FOR THE STUDY OF THE TRANSITION OF A GAS-LIQUID FLOW FROM COUNTER-CURRENT TO CO-CURRENT - Biage, M.; Campos, J. C. C. (Revista de Engenharia Térmica, 2007)
The transition of a flow of a liquid film from counter-current to co-current to a gas flow is known as the flooding phenomenon. In this paper is shown a quite criterions mathematical formulation in the form to identify with success the flooding point. One applies thus the conservation equations for a bi-dimensional and isothermical flow. Using the theorem of the PI of Vashy-Buckingham one makes a dimensional analysis in order to obtain parameters that make it possible to establish an asymptotic analysis for the a-dimensional equations and reduce a set of PDEs to a unique PDE for the thickness of the liquid film. This PDE will be decomposed in an equation for the permanent problem and another referring to the transient. It will be developed only the non–linear permanent equation applying the spectral method of collocation of Chebychev for its discretization. One intends in this paper to stress the physical interpretation of the equations for the thickness of the liquid film obtained through the asymptotic expansion and describe the characteristics of the used numeric method (spectral technique). The results are compared to others found in the literature proving that the spectral method of collocation is a very powerful technique for the solving of this kind of problem.