Performance analysis and optimization considerations for a Knudsen compressor in transitional flow

Abstract

The Knudsen compressor can be applied as either a vacuum pump or compressor for gases. Earlier investigations have indicated that there are several interesting potential applications of the Knudsen compressor because it has no moving parts and requires no lubricants or supplementary working fluids. However, its energy efficiency tends to be low, so that careful optimization is necessary. An important aspect of the optimization is an understanding of the Knudsen compressor’s operating characteristics in the transitional flow regime of rarefied gas dynamics. This article presents a formulation of Knudsen compressor operation in transitional, rarefied flow. In certain simplified but meaningful situations the formulation provides essentially analytical results for the sensitivity of key performance indicators, such as the energy use and device volume per unit of upflow, to changes in operating and geometric parameters. A numerical study of more complicated situations, using the most general form of the formulation developed here, is substantiated by the analytical investigation. The numerical results also extend the understanding of the Knudsen compressor’s performance characteristics to conditions that cannot be addressed by the simplified analytical form. Specifically, minimization of the device’s volume per unit of upflow is found when the entire cascade operates in transitional flow, which can only be studied using the complete formulation. The results make clear that operation in the transitional flow regime can lead to very significant (factor of 5 to 10) reductions of energy use and device volume for a given task.

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“…In equilibrium, the pressure ratio is given by p 2 /p 1 = √ T 2 /T 1 , where p 2 and T 2 are the pressure and temperature in the warmer chamber and p 1 and T 1 are the pressure and temperature in the colder chamber. Muntz et al (2002) showed that at…”

Thermal Transpiration Based Pumping and Power Generation Devices

“…In the limits relevant to this study where Kn << 1 and the transpiration-induced pressure rise is small compared to the inlet pressure, the transpiration-induced volumetric flow rate ( ), Eq. 4 in (4) reduces to the Eq. (1) below, where is the mass flow rate, P the pressure, ρ the density, c the sound speed, A the membrane area, γ the gas specific heat ratio, L the membrane thickness, T the temperature, Q T (Kn) a flow coefficient (for Kn << 1, Q T ≈ 0.64 Kn) and the subscripts 1 and 2 refer conditions at the low-temperature inlet and high-temperature outlet of the transpiration device.…”

A MEMS Knudsen pump for high gas flow applications.

“…Previous work by Muntz and others on quantifying efficiency resulted in the development of parameters, which, when optimized, improved pump performance [14]. It was determined that minimizing the energy required per molecule of upflow would reduce the total power consumed, while minimizing the volume per molecule of upflow would reduce the total volume of the pump.…”

“…al. have shown that the power consumption of a series of cascaded pumps is greatly reduced by allowing operation during the transition stage, where both the pressure and the thermal transpiration flow are significant [14]. The efficiency of the pump is reduced as the differential pressure increases due to thermal transpiration moving molecules against the pressure gradient.…”

“…The generated mass flow rate through an aperture is obtained by multiplying the flux by the cross-sectional area of the aperture. Muntz and his group have done substantial work on the Knudsen pump and the thermal transpiration effect through long channels in transitional flow [14]. They obtain the following equation for the mass flow through a capillary tube:…”