Modeling of Cylindrical Couette Flow of Rarefied Gas. The Case of Rotating Outer Cylinder

Gospodinov, P.; Dankov, D.; Roussinov, V.; Stefanov, Stefan; Todorov, Michail D.; Christov, Christo I.

doi:10.1063/1.3265330

Cited by 4 publications

(6 citation statements)

References 10 publications

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“…In a previous research [12,13,14,15] it has been found that only for Kn = 0.02 and less both method solutions were in an excellent agreement. And here, our studies are for the cases with Kn = 0.02, 0.05, 0.1, 0.5 at: V 1 = 0,1, 0.3, 0.5, 0.7 and V 2 = 0 or V 1 = 0 and V 2 = 0,1, 0.3, 0.5, 0.7.…”

Section: Numerical Resultsmentioning

confidence: 90%

“…The Couette cylindrical flow is a fundamental problem in the rarefied gas dynamics [4,9,15,17,18,20,21]. Thus, its modeling and numerical solving is of a great importance for microfluidics, which serves for theoretical background of the analysis of new emerging Micro Electro Mechanical Systems MEMS [5,7,19].…”

Section: Introductionmentioning

confidence: 99%

“…We consider both molecular and continuum models treating the gaseous flow by using different level of mathematical description. Both models take into account the specific microfluidic effects of gas rarefaction and slip-velocity regime at the solid boundaries [10,11,13,14,15,16].…”

Section: Introductionmentioning

confidence: 99%

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Viscous drag in steady state gas flow between rotating cylinders

Gospodinov

Dankov

Roussinov

et al. 2012

AIP Conference Proceedings

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The viscous drag (wall shear-stress) exerted at the interface "gas-rotating cylinder wall" is numerically studied by using the Direct Simulation Monte Carlo (DSMC) method and the continuum model based on the Navier-Stokes-Fourier (NSF) equations for simulation of the cylindrical rarefied gas flow between two concentric cylinders with one of them rotating with a constant velocity and the other being at rest. Different cases were calculated for a set of velocities of rotating inner cylinder and another set for rotating outer one. These studies have been accomplished for several fixed Knudsen numbers. The NSF results have been obtained by setting a local value of Knudsen number in the corresponding first order slip boundary conditions. For the near planar case a typical averaged Knudsen number has been used. The fact of hydrodynamic self-similarity in steady state cylindrical Couette flow is investigated and confirmed. The flow characteristics obtained by both methods are: in an excellent agreement at small Knudsen numbers 0.02 and 0.05 and in a satisfactory agreement at 0.1 and 0.5. The work may be of interest to the analysis of various non-planar micro gas flows.

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Section: Numerical Resultsmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Viscous drag in steady state gas flow between rotating cylinders

Gospodinov

Dankov

Roussinov

et al. 2012

AIP Conference Proceedings

Self Cite

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“…The NSF model is completed with the equation of state for ideal gas: For the problem formulated first-order slip boundary conditions are imposed at both walls which can be written directly in dimensionless form as follows [19]:…”

Section: Continuous Model (Nsf) and Numerical Simulationmentioning

confidence: 99%

“…[20]      (11) In (11) with l is denoted the local mean free path,  -molecular diameter and  is the dimensionless density.…”

Section: Continuous Model (Nsf) and Numerical Simulationmentioning

confidence: 99%

Thermoacoustic waves in pulsed Pirani sensor MEMS. Numerical Investigation

et al. 2018

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Abstract. The transient heat transfer process is studied in rarefied gas confined between two stationary concentric cylinders. The inner cylinder (filament) is subjected to a periodically heating-cooling cycle. The energy transfer is modeled with continuous model based on Navier-Sockes Fourier equations of motion and energy transfer and with a statistical DSMC model. Numerical results for the temperature, thermodynamic pressure and pressure difference between thermodynamic pressure and radial stress tensor component are obtained for different circular frequencies of heating cooling cycle of filament and for different filament radii. The pressure variation at the end of any local heating stage of heating-cooling cycle is close to the value of equilibrium thermodynamic pressure. The results are applicable in designing the pulsed Pirani sensors.

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Cylindrical Couette flow with fixed outer cylinder: Rarefied effects

et al. 2021

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We consider the rarefied cylindrical Couette flow. The inner cylinder rotates at the constant angular velocity and the outer cylinder is at rest. We investigate the momentum and energy fluxes transferred to the cylinders and show that this flow is fundamentally different from the rarefied Couette flow with the fixed inner cylinder. For the free molecular mode, we derive the explicit analytical expressions for the fluxes. We find that momentum and energy fluxes transferred to the inner cylinder have a maximum with respect to the ratio of radii. The influence of the rarefaction on the energy and momentum transfer in the transitional regime is studied using the direct simulation Monte Carlo method. The shear stress and energy flux transferred to the inner cylinder increase with an increase in the angular velocity of the inner cylinder rather than tend to zero at high velocities, as in the Couette flow with the fixed inner cylinder with an increase in the angular velocity of the outer cylinder. In the transitional mode, for the flow with the fixed outer cylinder, the absolute value of the normal momentum flux transferred to the inner cylinder has a minimum as a function of the angular velocity of the inner cylinder. On the other hand, in the Couette flow with the fixed inner cylinder, this flux tends to zero at high angular velocities of the outer cylinder. The fundamental difference between these two flows at high velocities is associated with the degree of influence of dissipation on the flows.

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Modeling of Cylindrical Couette Flow of Rarefied Gas. The Case of Rotating Outer Cylinder

Cited by 4 publications

References 10 publications

Viscous drag in steady state gas flow between rotating cylinders

Viscous drag in steady state gas flow between rotating cylinders

Thermoacoustic waves in pulsed Pirani sensor MEMS. Numerical Investigation

Cylindrical Couette flow with fixed outer cylinder: Rarefied effects

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