Linear harmonic oscillatory rarefied gas flow with arbitrary frequency in comb finger blocks

Abstract

Abstract The linear oscillatory two-dimensional rarefied gas flow in the zig-zag channel between the shuttle and stator fingers of typical comb elements, due to the harmonic motion of the shuttle finger with arbitrary frequency, is numerically investigated, via the linearized unsteady Shakhov kinetic model equation, subject to purely diffuse boundary conditions. The amplitude and phase distributions of the velocity components, normal and shear stresses, density and temperature are thoroughly investigated in the whole range of the gas rarefaction and oscillation parameters, characterizing the flow. The low, moderate and high flow oscillation regimes are defined by the ratio of the gas rarefaction over the oscillation parameters. It is shown that in the low oscillation regime the flow may be approximated by the corresponding steady-state analysis, while in the high oscillation one by the superposition of the associated oscillatory one-dimensional normal sound propagation and Couette flows. In the former case edge and compressibility effects are considerable and in the latter one the flow is characterized by gas trapping along the shuttle finger. In the moderate oscillation regime the fully oscillatory two-dimensional flow must be analysed. Here, the antiresonance and resonance states of the flow are considered. The ratios of the gas rarefaction over the oscillation parameters, where the average normal and shear stresses acting on the shuttle finger are minimized are computationally specified. Changing the main geometry parameters of the comb finger block, significantly affects the normal and shear stresses acting on the shuttle finger, mainly in the low oscillation regime. The present work may be applied to minimize the damping forces in comb finger blocks, as well as to optimize the design of new generation devices operating in moderate and high frequencies.