The Half-Range Moment Method in Harmonically Oscillating Rarefied Gas Flows
| Autor: | Dimitris Valougeorgis, Giorgos Tatsios, Alexandros Tsimpoukis |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
half-range moment method
oscillatory Couette flow lcsh:Thermodynamics 01 natural sciences 010305 fluids & plasmas Physics::Fluid Dynamics Collision frequency lcsh:QC310.15-319 0103 physical sciences rarefied gas flow Knudsen number Boundary value problem 010306 general physics Couette flow lcsh:QC120-168.85 Fluid Flow and Transfer Processes Physics Oscillation Mechanical Engineering Mechanics Stokes flow Condensed Matter Physics Stokes second problem Moment (mathematics) gas microflows Flow (mathematics) lcsh:Descriptive and experimental mechanics oscillation frequency |
| Zdroj: | Fluids, Vol 6, Iss 17, p 17 (2021) Fluids Volume 6 Issue 1 |
| ISSN: | 2311-5521 |
| Popis: | The formulation of the half-range moment method (HRMM), well defined in steady rarefied gas flows, is extended to linear oscillatory rarefied gas flows, driven by oscillating boundaries. The oscillatory Stokes (also known as Stokes second problem) and the oscillatory Couette flows, as representative ones for harmonically oscillating half-space and finite-medium flow setups respectively, are solved. The moment equations are derived from the linearized time-dependent BGK kinetic equation, operating accordingly over the positive and negative halves of the molecular velocity space. Moreover, the boundary conditions of the &ldquo positive&rdquo and &ldquo negative&rdquo moment equations are accordingly constructed from the half-range moments of the boundary conditions of the outgoing distribution function, assuming purely diffuse reflection. The oscillatory Stokes flow is characterized by the oscillation parameter, while the oscillatory Couette flow by the oscillation and rarefaction parameters. HRMM results for the amplitude and phase of the velocity and shear stress in a wide range of the flow parameters are presented and compared with corresponding results, obtained by the discrete velocity method (DVM). In the oscillatory Stokes flow the so-called penetration depth is also computed. When the oscillation frequency is lower than the collision frequency excellent agreement is observed, while when it is about the same or larger some differences are present. Overall, it is demonstrated that the HRMM can be applied to linear oscillatory rarefied gas flows, providing accurate results in a very wide range of the involved flow parameters. Since the computational effort is negligible, it is worthwhile to consider the efficient implementation of the HRMM to stationary and transient multidimensional rarefied gas flows. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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