Computational Study on Micro Shock Tube Flows with Gradual Diaphragm Rupture Process

Arun Kumar Rajagopal,Toshiaki Setoguchi,Heuy Dong Kim

doi:10.4236/ojfd.2012.24a027

Abstract

Gas flows through micro shock tubes are widely used in many engineering applications such as micro engines, particle delivery devices etc. Recently, few studies have been carried out to explore the shock wave excursions through micro shock tubes at very low Reynolds number and at rarefied gas condition. But these studies assumed centered shock and expansion waves, which are generally produced by instantaneous diaphragm rupture process. But in real scenario, the diaphragm ruptures with a finite rupture time and this phenomenon will significantly alter the shock wave propagation characteristics. In the present research, numerical simulations have been carried out on a two dimensional micro shock tube model to simulate the effect of finite diaphragm rupture process on the wave characteristics. The rarefaction effect was simulated using Maxwell’s slip wall equations. The results show that shock wave attenuates rapidly in micro shock tubes compared to conventional macro shock tubes. Finite diaphragm rupture causes the formation of non-centered shock wave at some distance ahead of the diaphragm. The shock propagation distance is also drastically reduced by the rupture effects.

Highlights

Shock tube is a device which generates a moving shock front and associated expansion and contact waves, by the sudden expansion of gas from high pressure to a low pressure region
Numerical simulations have been carried out on a two dimensional micro shock tube model to simulate the effect of finite diaphragm rupture process on the wave characteristics
The results show that shock wave attenuates rapidly in micro shock tubes compared to conventional macro shock tubes

Summary

Introduction

Shock tube is a device which generates a moving shock front and associated expansion and contact waves, by the sudden expansion of gas from high pressure to a low pressure region. There numerically study showed that the shock propagation distance increases due to the slip effects These studies on micro shock tube assumed an instantaneous opening of diaphragm which produces centered expansion and shock wave. The diaphragm ruptures gradually and the flow evolves from the high pressure chamber to the low pressure chamber progressively This produces non centered waves in the shock tube and the propagation characteristics of the wave shows differences compared to the sudden rupture process. Matsuo [9] assumed a quadratic opening function for the opening radius with respect to time for their shock tube studies to determine the diaphragm rupture effects at different pressure ratios. The optimum opening function obtained from the macro shock tube studies were later used to simulate the diaphragm rupture process for micro shock tube

Mesh Independence Study

Governing Equations

Gradual Diaphragm Rupture Modeling

Results and Discussion

Conclusion