A review on slip models for gas microflows

Zhang, Wenming; Meng, Guang; Wei, Xueyong

doi:10.1007/s10404-012-1012-9

Cited by 273 publications

(187 citation statements)

References 218 publications

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“…However, more rigorous kinetic analyses of the Boltzmann equation for planar flows (Cercignani & Daneri (1963)) have shown that α s = 1.1466, (for more details see Barber & Emerson (2006)). Following Maxwell's original work, many other slip models have been proposed in the literature including results for atomically rough walls, for more details see the review article by Zhang et al (2012). Additionally Lilley & Sader (2008) studied the Knudsen layer, which is a rarefaction effect that extends to a distance of the order of one mean free path from the solid wall, by using existing linearized Boltzmann equation solutions of Kramers problem for hard sphere molecules with partial thermal accommodation.…”

Section: Air Flow Modelmentioning

confidence: 99%

“…This type of first-order slip model has been implemented for many different types of slip flow successfully reproducing flow characteristics in the slip regime, see Gad-el-Hak (2006), Wei & Yogendra (2007), Nieto et al (2011). Higher order slip models, where the jump velocity at the walls is also proportional to higher order derivatives of the fluid velocity, have been proposed in the literature to extend slip flow predictions into the transition regime (for more details see Zhang et al (2012)). …”

Section: Introductionmentioning

confidence: 99%

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Dynamics of a small gap gas lubricated bearing with Navier slip boundary conditions

2017

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A gas lubricated bearing model is derived which is appropriate for a very small bearing face separation by including velocity slip boundary conditions and centrifugal inertia effects. The bearing dynamics are examined when an external harmonic force is imposed on the bearing due to bearing begin situated within a larger complex dynamical system. A compressible Reynolds equation is formulated for the gas film which is coupled to the bearing structure through an axial force balance where the rotor and stator correspond to spring-mass-damper systems. Surface slip boundary conditions are derived on the bearing faces, characterised by the slip length parameter. The coupled bearing system is analysed using a stroboscopic map solver with the modified Reynolds equation and structural equations solved simultaneously. For a sufficiently large forcing amplitude a flapping motion of the bearing faces is induced when the rotor and stator are in close proximity. The minimum bearing gap over the time period of the external forcing is examined for a range of bearing parameters.

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Section: Air Flow Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics of a small gap gas lubricated bearing with Navier slip boundary conditions

2017

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“…During the past decade a significant effort has been exerted by various researchers for the development of micro air vehicles as well as microelectromechanical systems in general [1,2,3]. However, such systems may involve rarefied gas flows, which appear to be considerably different, compared to flows at the continuum regime; thus, the Navier-Stokes PDEs (Partial Differential Equations), used at macroscale CFD (Computational Fluid Dynamics) solvers, appear to fail simulating such phenomena without further adaptions and modifications [1].…”

Section: Introductionmentioning

confidence: 99%

“…However, such systems may involve rarefied gas flows, which appear to be considerably different, compared to flows at the continuum regime; thus, the Navier-Stokes PDEs (Partial Differential Equations), used at macroscale CFD (Computational Fluid Dynamics) solvers, appear to fail simulating such phenomena without further adaptions and modifications [1]. In practice the rarefied gas flows are categorized depending on the computed Knudsen number, a classification originally proposed by Schaaf and Chambre [4]: For Knudsen numbers less than 1.0E-2 (continuum regime) the Navier-Stokes PDEs are valid without any further modification, allowing ordinary CFD (Computational Fluid Dynamics) solvers to be employed.…”

Section: Introductionmentioning

confidence: 99%

“…In practice the rarefied gas flows are categorized depending on the computed Knudsen number, a classification originally proposed by Schaaf and Chambre [4]: For Knudsen numbers less than 1.0E-2 (continuum regime) the Navier-Stokes PDEs are valid without any further modification, allowing ordinary CFD (Computational Fluid Dynamics) solvers to be employed. Nevertheless, for values between 1.0E-2 and 1.0E-1 (slip flow regime) special treatment of wall boundary conditions is required; velocity slip conditions as well as temperature jump ones have to be applied (as in this work) [1]. If greater than 1.0E-1 Knudsen numbers are encountered (transition regime and free molecular regime) the rarefaction effects become the sovereign ones, necessitating for alternative methodologies, depending on the DSMC (Direct Simulation Monte Carlo) [5] approach or the solution of the Boltzmann Equation [6].…”

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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Nanoscale grain boundary channels in fracture cement enhance flow in mudrocks

et al. 2016

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Hydrocarbon production from mudrock or shale reservoirs typically exceeds estimates based on mudrock laboratory permeability measurements, with the difference attributed to natural fractures. However, natural fractures in these reservoirs are frequently completely cemented and thus assumed not to contribute to flow. We quantify the permeability of nanoscale grain boundary channels with mean apertures of 50–130 nm in otherwise completely cemented natural fractures of the Eagle Ford Formation and estimate their contribution to production. Using scanning electron imaging of grain boundary channel network geometry and a digital rock physics workflow of image reconstruction and direct flow modeling, we estimate cement permeability to be 38–750 nd, higher than reported permeability of Eagle Ford host rock (~2 nd) based on laboratory measurements. Our results suggest that effective fracture‐parallel mudrock permeability can exceed laboratory values by upward of 1 order of magnitude in shale reservoirs of high macroscopic cemented fracture volume fraction.

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A review on slip models for gas microflows

Cited by 273 publications

References 218 publications

Dynamics of a small gap gas lubricated bearing with Navier slip boundary conditions

Dynamics of a small gap gas lubricated bearing with Navier slip boundary conditions

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

Nanoscale grain boundary channels in fracture cement enhance flow in mudrocks

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