A stable numerical strategy for Reynolds-Rayleigh-Plesset coupling

Jaramillo, Alfredo; Buscaglia, Gustavo C.

doi:10.1016/j.triboint.2018.08.022

Cited by 11 publications

(4 citation statements)

References 27 publications

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“…• 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%

“…• The liquid phase of the mixture is continuous while the gas phase corresponds to a high number of spherical bubbles dispersed in the liquid [14,39,40,41,21,42,19];…”

Section: Future Workmentioning

confidence: 99%

“…In the lubrication area, this phenomenon has been ignored until the works of Someya's group [13,14] who proposed to couple the full Rayleigh-Plesset equation (which describes the evolution of a bubble) with the Reynolds equation (which describes the fluid). Numerous works follow in the lubrication literature using simplified forms of the Rayleigh-Plesset equation for various kind of applications [15,16,17,18,19,20]. The paper of Snyder et al [21] can be considered as a review paper in this field.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Future Workmentioning

confidence: 99%

“…• The liquid phase of the mixture is continuous while the gas phase corresponds to a high number of spherical bubbles dispersed in the liquid [14,39,40,41,21,42,19];…”

Section: Future Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…By means of the proposed numerical method, simulations of the Journal Bearing mechanism (Section 2.4.1) are performed and a comparison of these results with the ones for the state-of-the-art Elrod-Adams cavitation model (Section 2.3.2) is made. These findings are part of an article published in a peer-reviewed journal (JARAh'IILLO;BUSCAGLIA, 2019) during this work.…”

Section: Stability Analysismentioning

confidence: 85%

New models and numerical methods in hydrodynamic lubrication

Palma¹

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When the value of as is small enough (e.g., as : 7.85 x 10'6 N-s/m) the pressure profiles that develop in the journal bearing are observed to satisfy the condition p 2 pcav, with pcav computed from Eq. (4.11). In fact, a large region where p 2 pcav is observed, which resembles the cavitation regions predicted by more traditional models. This motivates to incorporate pGav = ~0.77 atm into the Elrod-Adams and Reynolds cavitation models in order to perform comparisons with the RRP model. Doing so, the resulting pressure profiles are shown in Fig. 6.1.15 for rotating speeds of 1000 and 5000 rpm and as : 7.85 x 10-5 and 7.85 x 10"6 N-s/m. Notice that the rupture point for both the Elrod-Adams and Reynolds models are the same (which is a well-known fact), while for the RRP coupling the rupture is placed further along the fluid's movement direction. On the other hand, it is also known that the Reynolds model fails to accurately predict the reformation point when compared to a mass-conserving model (AUSAS at (Ll., 2007). Remarkably, when as is small enough the RRP model predicts a reformation point similar to that of the Elrod-Adams model. Furthermore, Fig. 6.1.16 shows the comparison of the fluid fraction produced by the RRP model, 1 _ a, with the fluid fraction produced by the Elrod-Adams model, 0. Qualitatively both fluid fraction fields are similar, the one corresponding to the RRP model being a regularized version of the other, in some sense. Notice that increasing as to 7.85 x 10"5 N's/m significantly reduces the similarities between the two models.Let us remark that the results shown in these last comparisons were obtained with a mesh having A951 = 27rJr/512 and A332 : JW/64 (i.e., N9; : 512) and with the time step fixed to 400 steps per cycle (CFL:1.3). l'ribology International 130 (2629) T9] "205 contents listsfavafla'ble at Sciencet 're a.' iournat homepage: we, etsevlemomfiocate'J-'t riboiat,

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