Shock Tube Simulation - Converge Studio

Aim

Study the effect of pressure and temp in Shock-tube.

Introduction

In a Shock Tube, the sudden expansion of a gas at high pressure into a gas at low pressure produces a plane shock wave that then propagates through a long-closed tube. The shock wave is used to produce a rapid increase in the pressure and the temperature of a reactive mixture. In most shock tubes, the shock wave is reflected at the end of the tube and produces during its way back the second rise in temperature. This technique is mainly used to study elementary steps, as well as pyrolysis and high-temperature autoignition in very dilute mixtures. 

The shock tube is a simple duct closed at both ends. A diaphragm divides this duct into two compartments called as a driver and driven sections. Schematic of the shock tube is as shown in Fig Driver section of the shock tube is the high-pressure section which is supplied by the high-pressure gas from the reservoir. Driven section of the shock tube is the low-pressure section which contains the low pressure-driven gas. These two sections are separated by a metal diaphragm.

Typical shock tube experimental set up is as shown in Figure. A high-pressure driver gas reservoir is connected with the driver section. However, a vacuum pump is connected to the driven section to arrive at the accurate driven section pressure. Pressure sensors are generally mounted along the driven tube for pressure measurement. These pressure sensors are connected to the data acquisition system.

Simulation Setup

1. Application > General Flow

2. Gas Simulation > Predefined Mixer > Air

3. Simulation Parameter

Run parameter > Transient 

Simulation Time parameters > 0.003 s

4. Boundary Conditions

High Pressure - Wall

Low Pressure - Wall

Other -  2D Wall

5. Initial Conditions and Events

Region and Initialization

  • High-Pressure Region
  • Low-Pressure Region

Events - Sequential 

Cell Count

Shock Tube Pressure 

Driver gas at high pressure in the region is being expanded through the expansion fan to a lower pressure behind the contact surface. Limits of expansion fan are formed by the head and tail of the rarefaction wave.

Growth of the boundary layer is interrupted as soon as the gas outflow across it becomes equal to the gas inflow across the shock wavefront. Owing to this, the shock wave and the contact surface velocities become equal, the plug size reaches a maximum and remains unchanged. The flow becomes steady as in the steady bow shock distance from the blunt-body in a supersonic flow, when the gas inflow across the shock wavefront becomes equal to the outflow across sonic lines and, to the flow along the side surfaces of the body. The gas flow between the shock wavefront and the contact surface is isentropic. The gas velocity behind the shock is determined in accordance with the conservation laws depending on the velocity of the shock wavefront.

Shock Tube Temperature

Density

Due to the viscous nature of the flow in the shock tube, the boundary layer is formed. Its thickness will be zero at the shock front and increases back through the shock heated region and the contact surface into the expanding driver gas and becomes zero again at the head of the rarefaction fan. Schematic of the boundary layer formed is shown in Figure. Important effects of the formation of the boundary layer are the following.

  1. Kinetic energy is dissipated as heat in the retarding layer of the boundary layer and this is conveyed to walls as by heat transfer.
  2. Deceleration of the shock front.
  3. Acceleration of the contact surface.


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