Oscillatory rarefied gas flow inside a three dimensional rectangular cavity

The oscillatory rarefied gas flow in a three-dimensional (3D) rectangular cavity, which is frequently encountered in micro-electro-mechanical systems, is investigated on the basis of the gas kinetic theory. The effects of cavity aspect ratio, cavity depth ratio, and the oscillation frequency of the driving lid on flow characteristics and damping force are systematically studied using the discrete unified gas-kinetic scheme over a broad range of gas rarefactions. For the highly rarefied flow, when the lid oscillates at low frequency, as a consequence of the strong rarefaction effect, the damping force on the lid in a 3D cavity could even be smaller than that of a corresponding 2D one (i.e. the depth in the lateral direction approaching infinity). This finding contradicts our intuitive understanding that, the damping force is expected to be amplified due to the presence of the lateral walls. Meanwhile, when the lid oscillation frequency becomes sufficiently high, due to the effect of gas anti-resonance, the damping force on the oscillating lid will increase again as the depth reduces for the highly rarefied flow. In addition, the gas resonance and anti-resonance found inside the 2D cavity also appear in 3D ones, and the anti-resonance and resonance frequencies as a function of the cavity aspect ratio are nearly the same. However, the presence of the lateral walls will suppress their formation: the smaller the depth, the weaker intensity of the (anti-) resonance. These findings can help to design the structure of the micro-electro-mechanical devices.