Modeling gravity-driven flows on an inclined plane

1996 ◽  
Vol 101 (B5) ◽  
pp. 11565-11577 ◽  
Author(s):  
Barbara C. Bruno ◽  
Stephen M. Baloga ◽  
G. Jeffrey Taylor
Keyword(s):  
Inclined Plane ◽  
Gravity Driven

Contact line instability of gravity driven thin films flowing down an inclined plane with wall slippage

2020 ◽  
Vol 214 ◽  
pp. 115418 ◽  
Author(s):  
Chicheng Ma ◽  
Jianlin Liu ◽  
Shilin Xie ◽  
Yongqi Liu
Keyword(s):  
Thin Films ◽  
Contact Line ◽  
Inclined Plane ◽  
Gravity Driven ◽  
Wall Slippage

scholarly journals Flow of dense avalanches past obstructions

2001 ◽  
Vol 32 ◽  
pp. 281-284 ◽  
Author(s):  
Y. C. Tai ◽  
J. M. N.T. Gray ◽  
K. Hutter ◽  
S. Noelle
Keyword(s):  
Granular Flow ◽  
Laboratory Experiments ◽  
Flow Direction ◽  
Shock Formation ◽  
Finite Mass ◽  
Inclined Plane ◽  
Avalanche Flow ◽  
Gravity Driven ◽  
Velocity Changes ◽  
Curved Walls

AbstractOne means of preventing areas from being hit by avalanches is to divert the flow by straight or curved walls or tetrahedral or cylindrical-type structures. Thus, there arises the question how a given avalanche flow is changed regarding the diverted-flow depth and flow direction. In this paper a report is given on laboratory experiments performed for gravity-driven dense granular flows down an inclined plane obstructed by plane wall and tetrahedral wedge. It was observed that these flows are accompanied by shocks induced by the presence of the obstacles. These give rise to a transition from super-to subcritical flow of the granular avalanche, associated with depth and velocity changes. It is demonstrated that with an appropriate shock-capturing integration technique for the Savage-Hutter theory, the shock formation for a finite-mass granular flow sliding from an inclined plane into a horizontal run-out zone is well described, as is the shock formation of the granular flow on either side of a tetrahedral protection structure.

A falling film down a slippery inclined plane

2011 ◽  
Vol 684 ◽  
pp. 353-383 ◽  
Author(s):  
A. Samanta ◽  
C. Ruyer-Quil ◽  
B. Goyeau
Keyword(s):  
Travelling Waves ◽  
Falling Film ◽  
Inclined Plane ◽  
Local Flow ◽  
Navier Slip ◽  
Averaged Equations ◽  
Gravity Driven ◽  
The Waves ◽  
Navier Slip Condition ◽  
Good Agreement

AbstractA gravity-driven film flow on a slippery inclined plane is considered within the framework of long-wave and boundary layer approximations. Two coupled depth-averaged equations are derived in terms of the local flow rate $q(x, t)$ and the film thickness $h(x, t)$. Linear stability analysis of the averaged equations shows good agreement with the Orr–Sommerfeld analysis. The effect of a slip at the wall on the primary instability has been found to be non-trivial. Close to the instability onset, the effect is destabilising whereas it becomes stabilising at larger values of the Reynolds number. Nonlinear travelling waves are amplified by the presence of the slip. Comparisons to direct numerical simulations show a remarkable agreement for all tested values of parameters. The averaged equations capture satisfactorily the speed, shape and velocity distribution in the waves. The Navier slip condition is observed to significantly enhance the backflow phenomenon in the capillary region of the solitary waves with a possible effect on heat and mass transfer.

Developing Laminar Gravity-Driven Thin Liquid Film Flow Down an Inclined Plane

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
H. Lan ◽  
J. L. Wegener ◽  
B. F. Armaly ◽  
J. A. Drallmeier
Keyword(s):  
Surface Tension ◽  
Film Thickness ◽  
Liquid Film ◽  
Flow Rate ◽  
Film Flow ◽  
Thin Liquid Film ◽  
Inclined Plane ◽  
Liquid Film Flow ◽  
Gravity Driven ◽  
Surface Inclination

Three-dimensional (3D)—steady-developing-laminar-isothermal—and gravity-driven thin liquid film flow adjacent to an inclined plane is examined and the effects of film flow rate, surface tension, and surface inclination angle on the film thickness and film width are presented. The film flow was numerically simulated using the volume of fluid model and experimental verification was conducted by measuring film thickness and width using a laser focus displacement instrument. The steady film flow that is considered in this study does not have a leading contact line, however, it has two steady side contact lines with the substrate surface at the outer edge of its width. Results reveal that the film width decreases and the average film thickness increases as the film flows down the inclined plane. The film thickness and width decrease but its streamwise velocity increases as surface inclination angle (as measured from the horizontal plane) increases. A higher film flow rate is associated with a higher film thickness, a higher film width, and a higher average film velocity. Films with higher surface tension are associated with a smaller width and a higher average thickness. A ripple develops near the side contact line, i.e., the spanwise distribution of the film thickness exhibits peaks at the outer edges of the film width and the height of this ripple increases as the surface tension or the film flow rate increases. The width of the film decreases at a faster rate along the streamwise direction if liquid film has higher surface tension. Measurements of the film thickness and the film width compare favorably with the numerically simulated results.

scholarly journals A simple analytical model for pressure on obstacles induced by snow avalanches

2010 ◽  
Vol 51 (54) ◽  
pp. 1-8 ◽  
Author(s):  
Thierry Faug ◽  
Benoit Chanut ◽  
Rémi Beguin ◽  
Mohamed Naaim ◽  
Emmanuel Thibert ◽  
...  
Keyword(s):  
Analytical Model ◽  
Dead Zone ◽  
Granular Flows ◽  
Mitigation Measures ◽  
Snow Avalanches ◽  
Simple Analytical Model ◽  
Inclined Plane ◽  
Gravity Driven ◽  
D Model ◽  
Protection Dams

AbstractThe forces snow avalanches are able to exert on protection dams or buildings are of crucial interest in order to improve avalanche mitigation measures and to quantify the mechanical vulnerability of structures likely to be damaged by snow avalanches. This paper presents an analytical model that is able to calculate these forces taking into account dead-zone mechanisms. First, we present a 2-D analytical hydrodynamic model describing the forces on a wall overflown by gravity-driven flows down an inclined plane. Second, the 2-D model is successfully validated on discrete simulations of granular flows. Third, we provide ingredients to extend the 2-D model to flows of dry and cold snow. Fourth, we propose a simplified 3-D analytical model taking into account lateral fluxes. Finally, the predictions from the simplified 3-D analytical model are successfully compared to recent measurements on two full-scale snow avalanches released at the Lautaret site in France.

Interfacial Instabilities in Stratified Shear Flows Involving Multiple Viscous and Viscoelastic Fluids

1995 ◽  
Vol 48 (11) ◽  
pp. 763-776 ◽  
Author(s):  
Kang Ping Chen
Keyword(s):  
Couette Flow ◽  
Poiseuille Flow ◽  
Shear Flows ◽  
Film Flow ◽  
Viscoelastic Fluids ◽  
Interfacial Instabilities ◽  
Inclined Plane ◽  
Recent Developments ◽  
Gravity Driven ◽  
Further Development

This article reviews recent developments in the analysis of interfacial instabilities in systems involving multiple viscous and viscoelastic fluids. The scope of the review is limited to three basic problems in stratified shear flows: plane Poiseuille-Couette flow, circular Poiseuille flow, and gravity-driven film flow down an inclined plane. Important advances in this field of study are summarized and areas deserving further development are discussed.

Gravity-driven creeping flow of two adjacent layers through a channel and down a plane wall

1998 ◽  
Vol 371 ◽  
pp. 345-376 ◽  
Author(s):  
C. POZRIKIDIS
Keyword(s):  
Free Surface ◽  
Numerical Simulations ◽  
Channel Flow ◽  
Film Flow ◽  
Finite Amplitude ◽  
Creeping Flow ◽  
Plane Wall ◽  
Surface Velocity ◽  
Inclined Plane ◽  
Gravity Driven

We study the stability of the interface between (a) two adjacent viscous layers flowing due to gravity through an inclined or vertical channel that is confined between two parallel plane walls, and (b) two superimposed liquid films flowing down an inclined or vertical plane wall, in the limit of Stokes flow. In the case of channel flow, linear stability analysis predicts that, when the fluids are stably stratified, the flow is neutrally stable when the surface tension vanishes and the channel is vertical, and stable otherwise. This behaviour contrasts with that of the gravity-driven flow of two superimposed films flowing down an inclined plane, where an instability has been identified when the viscosity of the fluid next to the plane is less than that of the top fluid, even in the absence of fluid inertia. We investigate the nonlinear stages of the motion subject to finite-amplitude two-dimensional perturbations by numerical simulations based on boundary-integral methods. In both cases of channel and film flow, the mathematical formulation results in integral equations for the unknown interface and free-surface velocity. The properties of the integral equation for multi-film flow are investigated with reference to the feasibility of computing a solution by the method of successive substitutions, and a deflation strategy that allows an iterative procedure is developed. In the case of channel flow, the numerical simulations show that disturbances of sufficiently large amplitude may cause permanent deformation in which the interface folds or develops elongated fingers. The ratio of the viscosities and densities of the two fluids plays an important role in determining the morphology of the emerging interfacial patterns. Comparing the numerical results with the predictions of a model based on the lubrication approximation shows that the simplified approach can only describe a limited range of motions. In the case of film flow down an inclined plane, we develop a method for extracting the properties of the normal modes, including the ratio of the amplitudes of the free-surface and interfacial waves and their relative phase lag, from the results of a numerical simulation for small deformations. The numerical procedure employs an adaptation of Prony's method for fitting a signal described by a time series to a sum of complex exponentials; in the present case, the signal is identified with the cosine or sine Fourier coefficients of the interface and free-surface waves. Numerical simulations of the nonlinear motion confirm that the deformability of the free surface is necessary for the growth of small-amplitude perturbations, and show that the morphology of the interfacial patterns developing subject to finite-amplitude perturbations is qualitatively similar to that for channel flow.

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