Two-way coupled Reynolds and Rayleigh–Plesset equations for a fully transient, multiphysics cavitation model with pseudo-cavitation

Snyder, Troy; Braun, M. J.; Pierson, Kristopher

doi:10.1016/j.triboint.2015.08.040

Cited by 24 publications

(22 citation statements)

References 24 publications

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“…Bearings which operate at very high ambient pressures (pressurized system) do not experience cavitation as the sub-ambient pressures are not low enough to reach the vapor pressure of the lubricant (vaporous cavitation) or the saturation pressure of dissolved gases within the lubricant (gaseous cavitation). Additionally, if the surface dilatational viscosity of the lubricant is sufficiently large, it is possible for large subcavity pressures to persist with the cavitation zone, and the full-Sommerfeld solution is nearly reproduced [40].…”

Section: Discussionmentioning

confidence: 99%

A CFD-Based Frequency Response Method Applied in the Determination of Dynamic Coefficients of Hydrodynamic Bearings. Part 1: Theory

Snyder

Braun

2019

Lubricants

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A general, CFD-based frequency response method for obtaining the dynamic coefficients of hydrodynamic bearings is presented. The method is grounded in experimental parameter identification methods and is verified for an extremely long, slider bearing geometry as well as short and long journal bearing geometries. The influence of temporal inertia on the dynamic response of the bearings is discussed and quantified through the inclusion of added mass coefficients within the mechanical models of the hydrodynamic bearing films. Methods to separate the dynamic stiffness into static stiffness and added mass contributions are presented and their results compared. Harmonic perturbations are applied to the bearings at varying frequencies to determine the frequency dependence of the dynamic coefficients and to facilitate the decomposition of the dynamic stiffness into its constituents. Added mass effects are shown to be significant for the extremely long slider bearing geometry and negligible for the short and long journal bearing geometries under operating conditions motivated by those typical of marine bearings.

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Section: Discussionmentioning

confidence: 99%

A CFD-Based Frequency Response Method Applied in the Determination of Dynamic Coefficients of Hydrodynamic Bearings. Part 1: Theory

Snyder

Braun

2019

Lubricants

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“…Consider that R n ij and R n−1 ij , for all cells, have already been calculated. The Staggered scheme (presented, e.g., in [13,29]) of discretization of the coupled RRP problem is defined by the following equations:…”

Section: Discretization: the Staggered Schemementioning

confidence: 99%

“…The geometrical and fluid/gas parameters are shown in Table 2. As in [13], the initial bubbles' radii is set to R(x, t = 0) = R 0 = 0.385 µm. The number of bubbles per unit volume n b is assumed to be constant in space and time.…”

Section: The Journal Bearingmentioning

confidence: 99%

A stable numerical strategy for Reynolds-Rayleigh-Plesset coupling

Jaramillo

Buscaglia

2019

Tribology International

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The coupling of Reynolds and Rayleigh-Plesset equations has been used in several works to simulate lubricated devices considering cavitation. The numerical strategies proposed so far are variants of a staggered strategy where Reynolds equation is solved considering the bubble dynamics frozen, and then the Rayleigh-Plesset equation is solved to update the bubble radius with the pressure frozen. We show that this strategy has severe stability issues and a stable methodology is proposed. The proposed methodology performance is assessed on two physical settings. The first one concerns the propagation of a decompression wave along a fracture considering the presence of cavitation nuclei. The second one is a typical journal bearing, in which the coupled model is compared with the Elrod-Adams model.

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“…Disregarding the inertial terms in Eq. (2.2) (as done in [14,21,38]) we obtain the following simplified version of the Rayleigh-Plesset equation where r 1 ∈ C Ω known and p ∈ W 1,q 0 (Ω) is the solution of (2.3).…”

Section: Well-posedness Without Inertial Termsmentioning

confidence: 99%

“…• To include bubbles convection by setting a non-null convective field u b . This could allow to consider more realistic physical settings, for instance taking u b equal to the velocity profile corresponding to the Reynolds equation, as done in some numerical works [21,19,38].…”

Section: Future Workmentioning

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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Two-way coupled Reynolds and Rayleigh–Plesset equations for a fully transient, multiphysics cavitation model with pseudo-cavitation

Cited by 24 publications

References 24 publications

A CFD-Based Frequency Response Method Applied in the Determination of Dynamic Coefficients of Hydrodynamic Bearings. Part 1: Theory

A CFD-Based Frequency Response Method Applied in the Determination of Dynamic Coefficients of Hydrodynamic Bearings. Part 1: Theory

A stable numerical strategy for Reynolds-Rayleigh-Plesset coupling

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

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