Journal Article10.1007/S100510051137
Improved modeling of flows down inclined planes
412
TL;DR: In this article, a second-order 2D model of film flows down inclined planes was derived by combining a gradient expansion at first or second order to weighted residual techniques with polynomials as test functions.
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Abstract: New models of film flows down inclined planes have been derived by combining a gradient expansion at first or second order to weighted residual techniques with polynomials as test functions. The two-dimensional formulation has been extended to account for three-dimensional flows as well. The full second-order two-dimensional model can be expressed as a set of four coupled evolution equations for four slowly varying fields, the thickness h, the flow rate q and two other quantities measuring the departure from the flat-film semi-parabolic velocity profile. A simplified model has been obtained in terms of h and q only. Including viscous dispersion effects properly, it closely sticks to the asymptotic expansion in the appropriate limit. Our new models improve over previous ones in that they remain valid deep into the strongly nonlinear regime, as shown by the comparison of our results relative to travelling-wave and solitary-wave solutions with those of both direct numerical simulations and experiments.
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Citations
Comparison of models for wave regimes of liquid film downflow in the linear approximation
TL;DR: In this paper, a number of the most well-known models of the wave flow of thin liquid films down a vertical plane are considered, and a linear stability analysis of plane-parallel motion is carried out.
4
Model of a wavy flow in a falling film of a viscous liquid
TL;DR: In this paper, a new model is developed for describing long wave perturbations in a falling film of a viscous liquid, based on an integral approach and an expansion of the velocity profile into a series in linearly independent basis functions of a boundary-value problem.
4
Thin films in the presence of chemical reactions
Antonio Pereira,Serafim Kalliadasis,Philip M. J. Trevelyan,Uwe Thiele +3 more
- 01 Dec 2007
TL;DR: In this article, the interaction between thin films and chemical reactions was investigated by using two prototype systems: a thin liquid film falling down a planar inclined substrate in the presence of an exothermic chemical reaction and a reactive mixture of insoluble surfactants on its surface.
4
New Model for Waves in a Falling Film
S.P. Aktershev,S.V. Alekseenko +1 more
TL;DR: In this paper, a boundary-layer approach and expansion of velocity into the system of linearly independent basic functions (harmonics), which satisfies boundary conditions, is developed for long-wave perturbations in a falling liquid film.
4
Dispersion in Shallow Moment Equations
Ullika Scholz,Julia Kowalski,Manuel Torrilhon +2 more
TL;DR: Dispersion in shallow moment equations with non-hydrostatic pressure is derived and analyzed. Dimensionally reduced dispersive equation systems are obtained for various orders and basis functions. Numerical experiments confirm the accuracy and efficiency of the reduced models.
References
•Book
Boundary layer theory
Hermann Schlichting
- 01 Jan 1955
TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.
•Book
Numerical analysis of spectral methods
David Gottlieb,Steven A. Orszag +1 more
- 01 Jan 1977
TL;DR: In this article, a mathematical analysis of spectral methods for mixed initial-boundary value problems is given, and the development of a mathematical theory that explains why spectral methods work and how well they work.
•Book
The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer
Bruce A. Finlayson
- 01 Jan 1972
Abstract: Preface to the classics edition Preface Acknowledgments Part I. The Method of Weighted Residuals: 1. Introduction 2. Boundary-value problems in heat and mass transfer 3. Eigenvalue and initial-value problems in heat and mass transfer 4. Applications to fluid mechanics 5. Chemical reaction systems 6. Convective instability problems Part II. Variational Principles: 7. Introduction to variational principles 8. Variational principles in fluid mechanics 9. Variational principles for heat and mass transfer problems 10. On the search for variational principles 11. Convergence and error bounds Author index Subject index.