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Reynolds equation
About: Reynolds equation is a research topic. Over the lifetime, 5638 publications have been published within this topic receiving 111269 citations.
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TL;DR: In this article, the effects of fluid inertia on flows in simple cubic, face-centred cubic and random arrays of spheres are examined in lattice-boltzmann simulations.
Abstract: Lattice-Boltzmann simulations are used to examine the effects of fluid inertia, at moderate Reynolds numbers, on flows in simple cubic, face-centred cubic and random arrays of spheres. The drag force on the spheres, and hence the permeability of the arrays, is calculated as a function of the Reynolds number at solid volume fractions up to the close-packed limits of the arrays. At Reynolds numbers up to O(102), the non-dimensional drag force has a more complex dependence on the Reynolds number and the solid volume fraction than suggested by the well-known Ergun correlation, particularly at solid volume fractions smaller than those that can be achieved in physical experiments. However, good agreement is found between the simulations and Ergun's correlation at solid volume fractions approaching the close-packed limit. For ordered arrays, the drag force is further complicated by its dependence on the direction of the flow relative to the axes of the arrays, even though in the absence of fluid inertia the permeability is isotropic. Visualizations of the flows are used to help interpret the numerical results. For random arrays, the transition to unsteady flow and the effect of moderate Reynolds numbers on hydrodynamic dispersion are discussed.
455 citations
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09 Jan 1984
448 citations
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TL;DR: In this article, the authors present three broad classes of approaches: bypassing this region altogether using wall functions, solving a separate set of equations in the nearwall region, weakly coupled to the outer flow, or simulating the near-wall region in a global, Reynolds-averaged, sense.
432 citations
01 Jan 2014
TL;DR: In this article, a new numerical approach that is simple and robust, capable of handling three-dimensional measured engineering rough surfaces moving at different rolling and sliding velocities is presented.
Abstract: contacts is presented in this paper, using a new numerical approach that is simple and robust, capable of handling three-dimensional measured engineering rough surfaces moving at different rolling and sliding velocities. The equation system and the numerical procedure are unified for a full coverage of all the lubrication regions including the full film, mixed and boundary lubrication. In the hydrodynamically lubricated areas the Reynolds equation is used. In the asperity contact areas, where the film thickness is zero, the Reynolds equation is reduced to an expression equivalent to the mathematical description of dry contact problem. In order to save computing time, a multi-level integration method is used to calculate surface deformation. Sample cases under severe condition show that this approach is capable of analyzing different cases in a full range of l ratio, from infinitely large down to nearly zero (less than 0.03).
430 citations
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TL;DR: In this paper, a full numerical solution for the mixed elastohydrodynamic lubrication (EHL) in point contacts is presented, using a new numerical approach that is simple and robust, capable of handling three-dimensional measured engineering rough surfaces moving at different rolling and sliding velocities.
Abstract: A full numerical solution for the mixed elastohydrodynamic lubrication (EHL) in point contacts is presented in this paper, using a new numerical approach that is simple and robust, capable of handling three-dimensional measured engineering rough surfaces moving at different rolling and sliding velocities. The equation system and the numerical procedure are unified for a full coverage of all the lubrication regions including the full film, mixed and boundary lubrication, In the hydrodynamically lubricated areas the Reynolds equation is used. In the asperity contact areas, where the film thickness is zero, the Reynolds equation is reduced to an expression equivalent to the mathematical description of dry contact problem. In order to save computing time, a multi-level integration method is used to calculate surface deformation. Sample cases under severe condition show that this approach is capable of analyzing different cases in a full range of λ ratio, from infinitely large down to nearly zero (less than 0.03).
421 citations