Computational investigation and parametrization of the pumping effect in temperature-driven flows through long tapered channels

Abstract

The temperature-driven rarefied gas flow and the associated pumping effects through long channels with linearly diverging or converging cross sections are computationally investigated. The implemented kinetic modeling is well known and relies on the infinite capillary methodology coupled with the mass conservation principle along the channel. The net mass flow rate and the induced pressure difference between the channel inlet and outlet are parametrized in terms of the geometrical and operational data including the channel inclination and the inlet pressure. Specific attention is given to the diode effect. The investigated flow setups include (a) the maximum pressure difference scenario with zero net mass flow rate (maximum pumping effect), (b) the maximum net mass flow rate scenario with equal inlet and outlet pressures and (c) all intermediate flow cases where both the net mass flow rate and the pressure difference are different than zero. In the first limit case, the pressure difference is always increased with the channel inclination and, depending on the inlet pressure, it may be larger for either the diverging or converging channel. In the second limit case, the mass flow rate is always decreased when the channel inclination is increased and it is always higher for the diverging channel. In both limit cases, optimum operation scenarios, in terms of the diode effect and the overall performance, are extracted. For intermediate cases, the characteristic curves of the net mass flow rate versus the pressure difference have been developed, indicating that the mass flow rate is inversely proportional to the pressure difference. The results strongly depend on the channel inclination. The present work may support decision making on the suitability of tapered channel flow to meet certain pumping specifications and the design of cascade-type thermally driven micropumps.