An exact analytical solution for the second order slip-corrected Reynolds lubrication equation

Stevanovic, Nevena D.; Djordjević, Vladan

doi:10.5937/fmet1501016s

Cited by 2 publications

(3 citation statements)

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“…In order to increase the accuracy of the final steady-state solution at the solid walls' region, several different second-order accurate spatial schemes have been reported in the open literature [14,15,16,17]. Their main concept is based on the reconstruction of the first term of Equation (1) with the Taylor series [16,17].…”

Section: Velocity Slip and Temperature Jump Conditionsmentioning

confidence: 99%

“…Their main concept is based on the reconstruction of the first term of Equation (1) with the Taylor series [16,17]. Nevertheless, such a reconstruction is not a straightforward procedure when complex three-dimensional geometries, along with unstructured hybrid grids, are encountered; the calculation of the second derivative of the tangential velocity in the normal direction to the surface may introduce numerical errors, despite the a priori computational difficulty it entails in such test cases [14].…”

Section: Velocity Slip and Temperature Jump Conditionsmentioning

confidence: 99%

“…Since then, various studies have been conducted on the prediction of the attitude of rarefied gases,focusing on the utilization of two-or three-dimensional computational fields, structured or unstructured grids, various geometries, etc., [8,9,10,11,12,13]. Furthermore, significant efforts have been exerted for the development of higher-order spatial schemes to increase the accuracy of the final steady-state solution at the region of the solid wall boundaries [14,15,16,17]. Among them the model of Beskok and Karniadakis appears to be especially attractive, as it avoids the numerical difficulties, entailed by the evaluation of the second derivative of slip velocity when complex geometries along with unstructured hybrid grids are encountered [14,15].…”

Section: Introductionmentioning

confidence: 99%

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Numerical Analysis of Rarefied Gas Flows Using the Academic CFD Code Galatea

Klothakis¹,

Lygidakis²,

Nikolos³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. During the last decades considerable efforts have been exerted for the development of micro air vehicles as well as microelectromechanical systems in general, for a wide range of applications. However, such systems involve microscale rarefied gas flows, which appear to be significantly different comparing to flows at macroscale and continuum regime; it is this the reason the Navier-Stokes equations fail to simulate such phenomena without further modification. To this end, the enhancement of the in-house academic Computational Fluid Dynamics solver Galatea to encounter such simulations is reported in this study. In case of rarefied gas flows and particularly for fluids in slip flow regime (Knudsen number greater than 0.01) the no-slip condition on solid wall surfaces is no longer valid; hence, velocity slip conditions as well as temperature jump ones have to be included instead. Furthermore, to increase accuracy at the same region the second-order accurate spatial slip model of Beskok and Karniadakis has been incorporated, which avoids the numerical difficulties, entailed by the evaluation of the second derivative of slip velocity when complex geometries along with unstructured hybrid grids are encountered. Due to oscillations that might appear, especially during the initial steps of the iterative procedure, a normalization scheme is additionally employed, to allow for the gradual increase of the corresponding slip/jump values. Galatea has been validated against a benchmark test case concerning rarefied laminar flow (inside the slip flow regime) over a wing with a NACA0012 airfoil in different angles of attack. The obtained results were compared with those of a reference solver, and with those obtained with the paralleld open-source kernel SPARTA, based on the Direct Simulation Monte-Carlo method. According to this last approach, the flow domain is divided into a finite number of computational cells, while the required sample macroscopic flow properties are retrieved assuming intermolecular collisions of the simulated particles inside such cells. An excellent agreement was achieved between the results obtained by Galatea and SPARTA as well.

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Section: Velocity Slip and Temperature Jump Conditionsmentioning

confidence: 99%

Section: Velocity Slip and Temperature Jump Conditionsmentioning

confidence: 99%