A DSMC-MD Investigation of Wall Effects in a Shock Tube Operating at High Knudsen Numbers

Introduction

The use of micro shock tubes in novel applications such as drug delivery, microengines and chemical kinetics demand accurate predictions of flow parameters. A shock tube operating at micro scales or under rarefied conditions has a relatively high Knudsen number (Kn), and under this condition the gas-wall interactions significantly affect the flow duration time. Numerous studies of low driver pressure (0.2-5 mm of Hg) shock tubes have been carried out, wherein the decrease in the flow duration time due to wall effects was established [1, 2, 3]. The nature of the flow in a shock tube is unsteady and typically high speed, and hence the time for a molecule to be in complete equilibrium with walls is less. As a consequence the reflection of the molecules is expected to take place with incomplete accommodation [4]. Zeitoun et al.[5] performed the numerical simulations of micro shock tubes using Direct Simulation Monte Carlo (DSMC) method with diffuse reflection at the wall and observed decreases in shock wave strength and velocity. Diffuse reflection occurs as a result of complete accommodation at the wall, whereas the reflection is specular when there is no accommodation at all. For intermediate levels of accommodation, the CLL model [6] is often employed. In a previous investigation by the present authors [7], DSMC analysis of a high Knudsen number shock tube was performed with the CLL model of gas-surface interaction using arbitrary values of accommodation coefficients.