Derivation of a Closed Form Expression for Estimating the Reduced Flow Rate for Pressure Driven Rarefied Gas Flow Through Circular Nano/Micro Pores

Abstract

In this paper, a new model to predict the gas flow rate through short tubes under rarefied condition based on the sigmoidal bahaviour of gas reduced flow rate (W) versus the rarefaction parameter (d) under rarefied condition was developed. The data produced by Varoutis et al. via Direct Simulation Monte Carlo (DSMC) method were utilised to obtain the model coefficients as functions of tube length to radius (w) and pressure ratio (Pr). Then, the model was tested against the published experimental data.There was a high degree of agreement between the model predictions and the experimental data. Moreover, the new model was capable to predict the reduced flow rate of rarefied systems, not only at free molecular region and hydrodynamic region, but also at transition region, hence covering all the Knudsen number domain within the utilised data. Therefore, the proposed model was capable to make predictions as well as meet all the criteria of the rarefied gas flow within the following conditions: 0<Pr<0.9, 0.01<d<1000 and 0.0<w<20. Thus, the proposed model provides a useful tool to make a valid prediction of  the rarefied gas flow behavior in a wide range of gas transport regime.