Shock Tube Simulation
Problem Statement:
To set up the problem of Transient Shock Flow through a tube using Converge CFD and to analyze the pressure and temperature over the domain. The cell count as a function of time is also investigated.
Case Setup:
The geometry consists of a rectangular tube with a diaphragm in between. One side of the tube is filled with N2 and the other side is filled with O2. The flow through the tube when the diaphragm gets removed is studied.
The base grid is set as 0.8 mm and a permanent adaptive mesh refinement with SGS 0.001 at 3 levels are given. The geometry and grid generation is as shown below.
Boundary and Initial Conditions:
Since this is assumed to be a 2-D simulation the front and back boundaries are given 2-D B.Cs. The top, bottom and two sides are given wall boundary conditions. The top and bottom boundaries follow the law of the wall whereas the sides are given no-slip conditions. The high-pressure region filled with N2 is at a temperature of 300 K and 6 bar pressure whereas the low-pressure region filled with O2 is at atmospheric conditions.
Results and Observations:
The pressure and temperature profiles in the High-Pressure and Low-Pressure Regions are as given below:
It can be observed from the graph that for the initial 0.001s nothing happens. That is due to the fact that the diaphragm remains closed for that duration. As soon as the diaphragm is opened N2 from the high-pressure region begins to flow into the Low-pressure region. Thus, the pressure and temperature keep decreasing. Once it flows through a certain distance the O2 particles hit the wall and get reflected. These O2 particles, in turn, collide with the N2 particles causing them to flow in the reverse direction and hence the pressure and temperature rise. As the wave keeps on colliding with the wall the amplitude of pressure and the temperature gradually decreases and it will finally reach a steady state. In the form of waves, energy gets transferred with the goal of attaining equilibrium. Shocks are formed due to the coalescing of the waves during the process of attaining equilibrium.
Cell Count:
Adaptive mesh refinement was used to increase the number of cells based on the N2 concentration to make more accurate predictions about the region. Since the level of AMR was given as three there are four more grid points that are getting generated. The AMR is as shown below.
From the above graph it can be seen that the number of cells remain constant at somewhere around 5000 for the initial 0.001s. When the diaphragm is opened a change in N2 concentration is noticed and thus the AMR starts to kick in. The cell count thus increases and decreases with respect to the concentration. It is around 20000 at the end of the simulation. The shock wave will keep propagating until the pressure dies down. A recirculation region is created due to the reflection from the wall and hence mixing is prevented.
The link to the animations are given below: