Mass-conserving cavitation model for dynamical lubrication problems. Part I: Mathematical analysis

Buscaglia, Gustavo C.; Talibi, M. El Alaoui; Jai, Mohammed

doi:10.1016/j.matcom.2014.11.026

Cited by 14 publications

(7 citation statements)

References 9 publications

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“…Our motivation in this paper is to design an efficient numerical solution algorithm based on an appropriate time‐space discretization for the unsteady Elrod‐Adams cavitation model. We pursue a different approach from the one found in []. By considering the flow along the characteristics, we derive a new variational formulation in a mixed form.…”

Section: Introductionmentioning

confidence: 99%

An active‐set mixed finite element solver for a transient hydrodynamic lubrication problem in the presence of cavitation

Tber

2018

Z Angew Math Mech

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In this paper, we study a moving free boundary problem related to the cavitation modeling in lubricated devices. More precisely, a characteristics method combined with a weak formulation in a mixed form is introduced for the Elrod‐Adams model. The formulation is suitable for the use of mixed finite element methods in the numerical approximation. It is proved that the time‐discrete problem and its finite element discretization have unique solutions. Further an efficient primal‐dual active‐set strategy is proposed to solve the resulting algebraic system. The performance of the overall algorithm is illustrated by numerical examples.

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Section: Introductionmentioning

confidence: 99%

An active‐set mixed finite element solver for a transient hydrodynamic lubrication problem in the presence of cavitation

Tber

2018

Z Angew Math Mech

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“…Cavitation is an effective mechanism of surface lubrication to reduce the friction coefficient. 7,8 Hirayama et al 9 found that the influence of cavitation occurrence should be considered in theoretical studies on bearing characteristics. Wahl et al 10 found that the cavitation phenomenon also exists in cross-groove texture surfaces.…”

Section: Introductionmentioning

confidence: 99%

Modeling and experiments of cavitation on a pocket-textured surface

Mao

Zhang

2019

Proceedings of the Institution of Mechanical Engineers, Part J:

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A two-dimensional computational fluid dynamics model was developed and an experiment was performed to investigate the role of pocket texture on fully lubricated motion with the cavitation effect. This paper discusses the cavitated simulation models and experiments to describe texture cavitation to solve the lubricating properties of the textured friction pair. The effects of velocity and texture scale on the support force and friction coefficient are discussed. It was found that the results of the two-dimensional computational fluid dynamics model with cavitation are nearly consistent with the experimental results; the hydrodynamic pressure decreased and the sliding speed dropped, and the effect of pressure became highly pronounced with ideal texture size. In addition, the simulation solution can show the internal flow field, and extend the solutions to large-scale textures and multiple textures. Meanwhile, appropriate texture parameters can optimize the friction coefficient and support force. The texture depth ratio plays a more important role on the value of the support force, and the width ratio has a greater influence on the friction coefficient.

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“…Numerous models have been introduced to couple this unilateral condition with the Reynolds equation, which is usually used to model the pressure evolution in thin film flow. Mathematical studies of these models can be found in [3,4,5,6,7,8] in which existence and uniqueness results are given for both the stationary and transient cases. Another approach has been proposed in [9] by considering cavitation as a multifluid problem with a free boundary between two immiscible fluids.…”

Section: Introductionmentioning

confidence: 99%

About a cavitation model including bubbles in thin film lubrication: A first mathematical analysis

Jaramillo

Bayada²,

Ciuperca

et al. 2019

Eur. J. Appl. Math

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In the lubrication area, which is concerned with thin film flow, cavitation has been considered as a fundamental element to correctly describe the characteristics of lubricated mechanisms. Here, the well-posedness of a cavitation model that can explain the interaction between viscous effects and micro-bubbles of gas is studied. This cavitation model consists of a coupled problem between the compressible Reynolds PDE (that describes the flow) and the Rayleigh-Plesset ODE (that describes micro-bubbles evolution). This coupled model seems never to be studied before from its mathematical aspects. Local times existence results are proved and stability theorems are obtained based on the continuity of the spectrum for bounded linear operators. Numerical results are presented to illustrate these theoretical results.

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Mass-conserving cavitation model for dynamical lubrication problems. Part I: Mathematical analysis

Cited by 14 publications

References 9 publications

An active‐set mixed finite element solver for a transient hydrodynamic lubrication problem in the presence of cavitation

An active‐set mixed finite element solver for a transient hydrodynamic lubrication problem in the presence of cavitation

Modeling and experiments of cavitation on a pocket-textured surface

About a cavitation model including bubbles in thin film lubrication: A first mathematical analysis

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