Perturbation analysis to the nonlinear stability characterization of thin condensate falling film on the outer surface of a rotating vertical cylinder

Viscous falling film instability around a vertical moving cylinder

“…Figure 5 represents the temporal growth rate at Re = 10, λ = 2.5, = 0.05 and the Weber number We = 800. As regarding this figure, for small values of k (k ≤ 0.09) the system is unstable, on growing the value of k the system becomes stable, as already noticed by Chen et al [15], in Fig. 4a the case when the rotation number vanished, as they consider a configuration of an axisymmetric flow of an incompressible, condensate flow on the outer surface of a vertical cylinder which rotates with a constant velocity.…”

Weakly nonlinear stability analysis of a falling film with countercurrent gas flow

“…The approximation | H 0x | 1 gives qualitative results for the constant film thickness assumption at the zeroth order. Substituting for H (x, t) in (27) and retaining terms up to the order of η 3 , the evolution equation for η is obtained as…”

“…These properties are of primary importance for the design of process devices, and it is therefore desirable to have a better understanding of these mechanisms that occur under various conditions and to develop a theoretical behavior that allows nonlinear effects. Apart from a detailed analysis by Chang [22], Chang et al [23], and Cheng and Chang [24] on the nonlinear stability of falling films, there have been many investigations on the weakly nonlinear stability analysis of the falling film flow system (down an inclined/vertical wall or on the surface of the cylinder) which include the investigations by Usha and Uma [25], Uma and Usha [26], Chen et al [27], Lai et al [28], Ünsal and Thomas [29] and Hung et al [30]. These investigations have examined the growth of an initially unstable periodic surface perturbation and its nonlinear interaction with the higher harmonics.…”

Nonlinear stability analysis of thin condensate falling film inside a rotating vertical cylinder

“…By the method of multiple scales [18], the GinzburgLandau equation [19] can be derived following the same procedure as Chen et al [1] oa…”

“…The authors previously studied the thin condensate film falling on the outer surface of a rotating vertical cylinder [1]. In this paper, the falling condensate film inside the rotating vertical is reexamined to show the difference between these two cases.…”