Kinetic modeling of a tapered Holweck pump

Naris, Steryios; Tantos, Christos; Valougeorgis, Dimitris

doi:10.1016/j.vacuum.2014.04.006

Cited by 16 publications

(13 citation statements)

References 17 publications

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“…The understanding of the gas behavior in this regime is a key element in the above developments, and we consider the present contribution as a step towards such analysis. Considering other applications, relatively high-speed shear flows at rarefied conditions prevail in vacuum pump machines, such as the Holweck pump, where flow Mach numbers as high as ≈0.5, and Knudsen numbers reaching ≈0.5, are reported [28][29][30]. Several works [21,31] have mentioned the relevance of the nonlinear Couette problem for the analysis of microelectromechanical systems operating at high (≈100 GHz) frequencies and oscillation amplitudes of several nanometers.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear thermal effects in unsteady shear flows of a rarefied gas

Ben-Ami

Manela

2018

Phys. Rev. E

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We study the response of a rarefied gas in a slab to the motion of its boundaries in the tangential direction. Different from previous investigations, we consider boundaries displacements at nonsmall Mach (Ma) numbers, coupling the dynamic and thermodynamic gas states, and deviating the system from its low-velocity isothermal condition. The problem is studied in the entire range of gas rarefaction rates, combining limited case ballistic-and continuum-flow analyses with direct simulation Monte Carlo computations. A nonlinear solution is derived in the ballistic regime for arbitrary velocity profiles and amplitudes. At near-continuum conditions, a slip-flow timeperiodic solution is obtained for the case of oscillatory boundary motion, by expanding the flow field in an asymptotic Mach power series. The effect of replacing between isothermal and adiabatic surfaces is examined. The results indicate that, at all Knudsen (Kn) numbers, the thermodynamic fields and normal velocity component are dominated by double-frequency (and descending higher-order even-frequency harmonic) time dependence, different from the fundamental-frequency time dependence dominating the tangential gas velocity. At continuumlimit conditions, this stems from the quadratic viscous dissipation term (negligible at low-Mach conditions), coupling the square of the tangential velocity gradient as a forcing term. System nonlinearity also results in an unsteady normal force acting on the boundaries, overcoming the tangential force with increasing Ma. A marked difference from the latter is that the normal force either decreases with Kn or, at sufficiently small actuation frequencies, varies nonmonotonically with Kn, reaching a maximum at some intermediate rarefaction conditions.

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Section: Introductionmentioning

confidence: 99%

Nonlinear thermal effects in unsteady shear flows of a rarefied gas

Ben-Ami

Manela

2018

Phys. Rev. E

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“…The steady isothermal gas flow through long capillaries still remains an active research topic and a subject of many investigations [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Recently, simple closed-form expressions for the reduced flow rate in long tubes in all flow regimes were deduced in [18] and [19] based on direct simulation Monte Carlo (DSMC) and kinetic simulations, respectively.…”

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confidence: 99%

Predicting the Knudsen paradox in long capillaries by decomposing the flow into ballistic and collision parts

2015

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The well-known Knudsen paradox observed in pressure driven rarefied gas flows through long capillaries is quantitatively explored by decomposing the particle distribution function into its ballistic and collision parts. The classical channel, tube, and duct Poiseuille flows are considered. The solution is obtained by a typical direct simulation Monte Carlo algorithm supplemented by a suitable particle decomposition indexation process. It is computationally confirmed that in the free-molecular and early transition regimes the reduction rate of the ballistic flow is larger than the increase rate of the collision flow deducing the Knudsen minimum of the overall flow. This description interprets in a precise, quantitative manner the appearance of the Knudsen minimum and verifies previously reported qualitative physical arguments.

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“…Motivated by the overwhelming complexity of channels networks contained in microfluidic chips (Thorsen, Maerkl & Quake 2002), the study of heat and mass transfer phenomena in non-straight channel geometries has become the focus of several works. In the context of rarefied gas flows, these have included, among others, studies on the effects of channels bending (Sharipov & Graur 2012;Liu et al 2018), gradual section expansion (Naris, Tantos & Valougeorgis 2014;Graur et al 2015;Hemadri, Parade & Bhandarkar 2016;Tatsios et al 2017) and geometrical irregularities, including sudden expansion and contraction (Agrawal, Djenidi & Antonia 2005;Gat, Frankel & Weihs 2008;Hong, Zhen & Yang 2008;Varade, Agrawal & Paradeep 2014).…”

Section: A22-2mentioning

confidence: 99%