Stability Analysis of a Film Flow Down an Incline in the Presence of a Floating Flexible Membrane
19 Jul 2018-Vol. 308, pp 253-263
TL;DR: In this article, the effects of floating flexible membrane on the instability of a gravity-driven flow down an incline was explored using normal-mode analysis, where the influence of membrane tension was taken into account in terms of stress jump at the free surface.
Abstract: The present study deals with the effects of floating flexible membrane on the instability of a gravity-driven flow down an incline. Linear stability of the flow system is explored using normal-mode analysis. Free surface gravity-driven flow is unstable at much lower Reynolds numbers. Instability of such a flow can be controlled either by changing behavioral of the lower wall or by altering the surface waves at the free surface which is done here by including a floating flexible membrane at the top of the liquid layer. Influence of membrane tension is taken into account in terms of stress jump at the free surface. The Orr-Sommerfeld system of the flow is solved numerically using spectral collocation method. The results displays a destabilizing role of membrane tension for a wide range of parameters. The growth rate of the perturbation waves increases with an increase of membrane tension and the critical Reynolds number becomes smaller. Therefore, it is possible to enhance the instability of the flow system with help of membrane properties, which may be useful in Ocean engineering and coating industries.
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...[31] analyzed the role of a floating membrane in the linear stability of a film flow down an inclined plane....
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TL;DR: In this article , two dimensional Navier-Stokes have been applied to an incompressible viscous fluid motion down an inclined plane with net flow and boundary layer thickness analysis.
Abstract: Motion of uid elements can be described by the Navier-Stokes equations. They arise from the use of Law of motion to a uid. In this investigation, two dimensional Navier-Stokes have been engaged. Then they are applied to an incompressible viscous uid movement down an inclined plane with net ow. These leads to examining the effects to the velocity of the motion at various angles of inclination and finding the boundary layer thickness. Viscous laminar incompressible fluid ow also ow on an inclined position which makes it necessary to investigate the ow on an inclined plane. Results that have been achieved are of the ow over horizontal at plate. Solution that has been obtained involves a at photographic film being pulled up by a processing bath by rollers at an angle \(\theta\) to the horizontal. Quadratic polynomial function approximate velocity profile has been obtained under initial boundary layer conditions. This velocity profile has been used in momentum integral equation for ow over an inclined plane to get the boundary layer thickness. Boundary layer thickness is one of the parameters that is used to obtain the ow velocity down inclined plane.
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TL;DR: In this paper, the interaction of an incident wave with a moored floating membrane as a breakwater is analyzed for both the cases of finite water depth and shallow water approximation based on the linearized water wave theory, including the effect of changes in bottom topography.
34 citations
TL;DR: In this paper, the stability of a gravity-driven film flow on a porous inclined substrate is considered, when the film is contaminated by an insoluble surfactant, in the frame work of Orr-Sommerfeld analysis.
Abstract: The stability of a gravity-driven film flow on a porous inclined substrate is considered, when the film is contaminated by an insoluble surfactant, in the frame work of Orr-Sommerfeld analysis. The classical long-wave asymptotic expansion for small wave numbers reveals the occurrence of two modes, the Yih mode and the Marangoni mode for a clean/a contaminated film over a porous substrate and this is confirmed by the numerical solution of the Orr-Sommerfeld system using the spectral-Tau collocation method. The results show that the Marangoni mode is always stable and dominates the Yih mode for small Reynolds numbers; as the Reynolds number increases, the growth rate of the Yih mode increases, until, an exchange of stability occurs, and after that the Yih mode dominates. The role of the surfactant is to increase the critical Reynolds number, indicating its stabilizing effect. The growth rate increases with an increase in permeability, in the region where the Yih mode dominates the Marangoni mode. Also, the growth rate is more for a film (both clean and contaminated) over a thicker porous layer than over a thinner one. From the neutral stability maps, it is observed that the critical Reynolds number decreases with an increase in permeability in the case of a thicker porous layer, both for a clean and a contaminated film over it. Further, the range of unstable wave number increases with an increase in the thickness of the porous layer. The film flow system is more unstable for a film over a thicker porous layer than over a thinner one. However, for small wave numbers, it is possible to find the range of values of the parameters characterizing the porous medium for which the film flow can be stabilized for both a clean film/a contaminated film as compared to such a film over an impermeable substrate; further, it is possible to enhance the instability of such a film flow system outside of this stability window, for appropriate choices of the porous substrate characteristics.
30 citations
TL;DR: In this article, a third order differential equation is derived to describe the membrane covered free surface condition for wave energy relation for wave scattering by floating horizontal membrane is derived by the application of law of conservation of energy flux and alternately by the direct application of Green's second identity.
28 citations
TL;DR: In this paper, the interaction of incident monochromatic waves with a tensioned, flexible, circular membrane submerged horizontally below free surface is investigated in the frame of three-dimensional linear hydroelastic theory.
19 citations
TL;DR: In this article, the surface gravity wave interaction with circular floating elastic plates of finite radius is analyzed in both the cases of single and two-layer fluids in finite water depth under the assumption of small amplitude water wave theory and structural response.
13 citations