Shock Tube simulation

Problem Statement:

  • Setting up a transient shock tube simulation using Converge studio.
  • Obtaining plots of the pressure and temperature history in the entire domain and providing a suitable explanation for them.
  • Obtaining a plot for cell count as a function of time.

Setting up the simulation in Converge:

Geometry Setup:

  

The geometry is imported into Converge studio through the Stl file provided. After running initial diagnosis of geometry unwanted triangles are eliminated and we eliminate any intersection or open edge error. The manifold error remains to pursue just as it did in the conjugate heat transfer problem. Then we go for boundary flagging were respective boundaries are assigned to various geometric locations so that we can define boundary conditions accordingly.

Boundary Conditions:

  • High-Pressure Wall: Stationary Wall boundary with Law of the wall condition
  • Low-Pressure Wall: Stationary Wall boundary with Law of the condition.

   Apart from these two, we have four boundaries all of which are 2-D boundaries on the front and back side of the channel.

Grid setup:

The refined grid is 0.00075 in all directions with the approximate cell count amounting to 47000 without considering AMR.

Case Setup:                                                                                                           

  • Here we have transient solver as we are performing transient simulations.               
  • Our simulation end time is 3.0 milliseconds and minimum and maximum timestep are 1e-09 and 1.0 s respectively. Default CFL values are used                                                                         
  • The turbulence model is RnG K-epsilon                                                                   
  • We have also indicated the species (N2 and O2) present in each region and defined the pressure in the region containing N2 as 600000 Pa while the O2 region is at atmospheric pressure.       
  • We are also using AMR based on species (N2) and the subgrid-scale embedded level is 0.001.    Here we are also using the " events" option in the initialization tab to simulate the effect - the removal of the diaphragm has in shock tube experiments. 

Results:                                                                                                                               

Pressure Profile:                                                                                                   

https://youtu.be/JolyBdg1phw                                                                                                   

The above animation shows how the pressure is varied over the entire domain over the course of the entire simulation.                                                                                                                                                                                                                                                                       

Pressure profile over the entire domain at regular time intervals:                                       

  • From time t=30 to t=120 units                                                                                                                                                                                                                              
  • From the time t=150 to t-180                                                                                                                                                                                                                                

Pressure vector profile at t=232:                                                                                                                                                                                                                                   

Pressure vs Time plot:                  

                                                                                                                             

Explanation: Now after going through the animation, pressure profile at regular intervals and particularly the pressure vs time plot we can say that no significant change in the pressure takes place in either of the two regions till time 0.0001 s. But when we allow the mixing of high pressure and the low-pressure region at t=0.0001 the N2 present at a pressure of  0.6 Mpa in high-pressure region penetrates into the low-pressure region containing O2 at atmospheric pressure. Therefore there is a drop in the pressure in the high-pressure region accompanied by a rise of pressure in low-pressure-refer the graph below. However, this forward motion of N2 is thwarted by the retreating shock wave which also prevents the further mixing of N2 and O2 by creating a recirculating zone at the far end of the low-pressure region.Thus there is a backflow of N2 in the high-pressure region resulting in pressure rise which is accompanied by a corresponding pressure drop in the low-pressure region-refer figure below. The phenomenon gives rise to fluctuations in pressure which we can observe the pressure vs time plot.

Temperature profile:                                                                                                   

https://youtu.be/adQK4cnx8yo                                                                                                       

The above animation shows how the temperature varies over the entire domain for the course of the entire simulation.                                                                                                                                                                                                               

Temperature profile over the entire domain for regular time intervals:                

  •  From t=30 to t=120                                                                                                             
  • From t=150 to t=232                                                                                                              

Mean Temperature vs Time plot:

Explanation: Now after observing the animation, temperature profiles over the entire domain and from the Mean temperature vs time plot above we can state that the changes in the temperature start to take place after we allow the intermixing of gases at 0.0001s analogous to what happened in the case of pressure. Over the entire course of this simulation pressure and temperature vary proportionately. As the pressure decreases in the high-pressure region immediately after 0.001s there is the corresponding decrease in the temperature of that region - refer the figure below. Similarly with rise of pressure in the low-pressure region is accompanied by increases in temperature of the low-pressure region-refer figure below. This oscillation in temperature and pressure are caused due to the shock wave which continuously travels back forth in the channel.       

                                                                                                                                                                                 

Velocity profile:                                                                                                           

https://youtu.be/alPbgOTNKXo                                                                             

The above animation shows how the velocity changes over the entire domain for the entire course of the simulation.                                                                                   

Velocity profile over the entire domain at regular time intervals:                          

 

  • From t=30 to t=120                                                                                                                                                                                                                                                                   
  • From t=150 to t=232                                                                                                          

                                                                                                               

Velocity vector:

Cell count vs time plot:                                                                                                              

                                                                                                                            

Explanation: As mentioned in the case setup we have employed AMR in setting up this shock tube simulation. AMR-Adaptive mesh refinement helps achieve desire grid resolution and specific location by monitoring field variables. In our case, we have employed AMR based on species concentration and subgrid-scale is 0.001. The major advantage of AMR is that it helps us achieve consistent results by eliminating the dependence on users skill level as far grid resolution is concerned. Here we are monitoring the concentration of N2.                                                                                                 

Now the explanation for the above plot of cell count vs time is: In the case setup through an option called " events" we are enabling the mixing of N2 and O2 present at Higher and lower pressure region respectively. When this happens the N2 present in the higher pressure regions penetrates into the lower pressure region, therefore, its concentration increases in the low-pressure region. Now the converge which is actively monitoring the subgrid-scale N2 concentration increases the cell count as per AMR. As the N2 penetrates farther into the low-pressure region the cell count increases accordingly. However, this increase in cell count is not absolute, because as the shock wave created due to the initial pressure difference propagates forward it hits the end wall of the low-pressure region and is reflected back. This retreating shock front mitigates the mixing process by creating a recirculating zone. As a result, the rise of species concentration of N2 in the low pressure is curtailed and therefore the rise of cell count is also modified proportionately.                                                                                                                                                                                                                                                                                                                                                                              


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