Shock Tube Simulation

Shock tube simulation

Introduction

In this project we will simulate the shock tube using converge simulation. Shocks are one of the important phenomena for the engineering design as especially in aerodynamics, recently shocks were more closely researched in the automotive industry for developing new i.c. engines technologies. More detail application is when there is a testing of the new fuel mixture for determining the chemical properties such as behavioral in high pressure, temperature conditions, by products of the reaction, determining chemical mechanisms etc. Here where shock tube is used which is basically extending or in this case slowing the engine chemical reaction happing in the power and exhaust stroke from few nan seconds to micro seconds. For this there are various techniques are developed over the past decades of research by the automotive companies since one of the techniques is the develop a code which somehow predicts these above mention qualities accurately, This is what I meant to achieve using CFD software.

What is shock tube?

This is a tube closed at both ends, with a diaphragm separating a region of high-pressure gas on the left (region 4) from a region of low-pressure gas on the right (region 1). The pressure distribution is also illustrated in Fig. The gases in regions 1 and 4 can be at different temperatures and have different molecular weights. When the diaphragm is broken (for example, by electrical current, or by mechanical means), a shock wave propagates into section 1 and an expansion wave propagates into section 4 This picture is sketched in Fig. 7.3. As the normal shock wave propagates to the right with velocity W, it increases the pressure of the gas behind it (region 2), and induces a mass motion with velocity up. The interface between the driver and driven gases is called the contact surface, which also moves with velocity up; across it the entropy changes discontinuously. However, the pressure and velocity are preserved: p1 = p2 and u3 = u2 = up. The expansion wave propagates to the left smoothly and continuously decreasing the pressure in region 4 to the lower value P3 behind the expansion wave.

Set up:

In converge the geometry was fairly simple to adapt. For simplicity I used Air as the test gas at 300 K temperature.

Initial conditions

• Pressure at High pressure region: 6 bar
• Pressure at Low pressure region: 1 bar
• Event initiated at : 0.001 seconds

What are events?

CONVERGE uses events to active or deactivate the disconnect triangles, which control when and where flow between regions is allowed. An OPEN event deactivates the disconnect triangles and thus allow flow between the specified regions. A CLOSE event activates the disconnect triangles and thus prohibits flow between the specified regions. When disconnect triangles are activated.

Here events were used to simulate the rupture of the diaphragm for shock tube.

In order to capture shock AMR was used to get a clear picture.

AMR level : 0.001 level with species N2 as the main concern since there is no reaction between o2 and n2 at the 300 K.

The entire run was simulated for 0.03 seconds.

The Grid was taken as 0.004 m for all the directions i.e. x, y and z.

Results.

Here are the results for the changes in the pressure and temperature over the whole time.

Pressure

As seen from the figure there is the change in the pressure across the shock it also state the start of the shock as event was set at 0.001 seconds. Since according to laws of thermodynamics there is loss of the pressure from high pressure region to low pressure region. Hence the zig zag pattern since these waves gets reflects from the wall at the end in the form of weaker shock.

Temperature:

Temperature also following the same pattern but if you see the slight rise on the both pressure and temperature this because of the expression came from simple energy analysis which can be found from any gas dynamics book but for the moving shock wave it is said that the temperature gets decreases when the shock is reflected and so the decrease in temperature.

Cell count:

As amr was setup in such a way that there was total nitrogen on the high pressure region whereas oxygen was setup for low region hence there is a change in number of cells for as. Here is animation for the mesh development across the domain.

In order to get the more clear picture i have also run the same simulation in more finer mesh just to get the clear picuture of N2 concentration and Velocity.

Litereracy source:
Modern Compressible Flow with historical perspective by John D Anderson Jr.

Converge science user manual.