On the Squire's transformation for stratified two-phase flows in inclined channels. (January 2017) - Barmak, I.; Gelfgat, A.Yu.; Ullmann, A.; Brauner, N.
Highlights: Squire's transformation for stability of stratified two-phase flow is studied. Squire's theorem rigorously holds for horizontal stratified two-phase flows. Additional constraints are required for transformation in inclined flows. Multiple solutions for the holdup in inclined stratified flow are considered. 2D perturbations are proven to be the critical ones for inclined stratified flows. Abstract: The applicability of the Squire's transformation for stability analysis of stratified two-phase flow in horizontal and inclined channels is examined. It is shown that for the considered flow such a transformation requires some additional constraints on the change of the inclination angle and flow rates of each of the phases. While the Squire's theorem (on the two-dimensionality of the critical disturbances) rigorously holds for the horizontal two-phase flow, for the inclined flow an exact mathematical theorem cannot be formulated. Nevertheless, it has been proven that 2D perturbations are the critical ones also for the case of inclined channel, since the transformation of a 3D stability problem to its 2D analog is associated with a stabilizing effect of reducing the system inclination, in addition to the reduction of the phases flow rates as in the case of horizontal flows.