Predicting the rarefied gas flow through circular nano/micro short tubes: a semi-empirical model

Abstract

A new explicit semi-empirical model was proposed for predicting the steady state gas flow rate through short tubes under rarefied condition. The experimental data produced by Fujimoto and Usami and the DSMC data provided by Varoutis et al. were utilized to obtain the model coefficients. The model was further validated by the published experimental data. The proposed model was capable to make predictions while meeting all the criteria of the rarefied gas flow in the following ranges of the variables: 0<P r < 0.7, 0<δ < 4000 and 0<ω < 13. The model was capable to predict the reduced flow rate of rarefied systems, not only in the free molecular region and the hydrodynamic region, but also in the transition region, hence covering all the Knudsen number domain within the utilized data. It was also found that by increasing the pressure ratio and decreasing the length to diameter ratio, the transition region shifted to the higher values of the rarefaction parameter. The proposed model is useful in the vacuum gas community for engineering purposes by offering a practical closed form expression for the DSMC data to predict the rarefied gas flow rate.