Modelling Shock Tube with Venting
 

Hello everyone,

I'm currently a PhD student studying the effect of blast on structures. Our facility is lucky enough to have an 8 meter long Shock Tube for simulating blast pressures. Out of personal interest, I decided to write a CFD code to model the development of the reflected pressure wave at the end of the test area. The code itself is a pretty basic 1D compressible Euler solver written in the conservation form (following Anderson's CFD book with some bells and whistles to make it easy to modify the domain, initial conditions, boundary conditions, etc).

Some background to my question:
As can be seen in the attached pressure-time history plot, the predicted pressure is reasonably compatible with what I recorded in the shock tube. However, notice that towards the end of the first positive phase (t~0.02-0.03 seconds) the code underpredicts pressure. Furthermore, for subsequent peaks caused by reflection of the shock wave within the shock tube (t>0.03 seconds), the code significantly overpredicts pressure.

In the real shock tube, we have sliding pressure relief vents at the test area which are initially closed, but slide open with the first positive phase. The pressure relief vents are intended to damp out subsequent pressure peaks as the shock wave reflects within the system. My code currently uses fully reflective boundary conditions for both ends of the shock tube. This clearly is not representative of the physical conditions at the location of the test area due to venting.

My question:
How can I model partially reflective BC's? I've done quite a bit of research by studying texts and looking online but I have not found a suitable answer (I've hit a wall! :confused:). I am OK with defining an empirical amount of venting, but I am not sure how to incorporate this into my BC. Any guidance you could provide would be greatly appreciated!

Anyone have any suggestions? Is there some type of boundary condition I could use to model a partial reflective boundary condition?