Hi @jousefm and @Get_Barried,
Would love to have your help. Hyperloop is getting more media attention, and it could be good PR for SimScale if the high-speed flow problems can be explained.
The ‘Kantrowitz Limit’ was proposed in Elon Musk’s original proposal, about page 5 http://www.spacex.com/sites/spacex/files/hyperloop_alpha-20130812.pdf
He correctly stated that flow thru an orifice can never exceed Mach1, then used the incompressible calculations of back-flow to propose the “Kantrowitz Limit” which no pod could exceed. He then proposed a large compressor to divert most of the frontal airflow thru a small duct to the tail. Kantrowitz has dominated Hyperloop aerodynamic theory, and most designs show some form of compressor, although the idea is losing support.
In my (totally unqualified) opinion, the Kantrowitz Limit is wrong, and it’s an absurd solution to have a complex compressor with a 20:1 ratio forcing air thru a small duct. It’s wrong to apply incompressible theory to a high-speed situation. Compression is required, but only 2:1 in the throat using the thrust of the wheels or linear motors.
At a pod speed of Mach 0.5, the back flow (with my 2:1 area ratio) is also M0.5. If we only consider incompressible, we than have an airflow of M 1.0 vs the pod, and M 0.5 vs the tube. So its not really like a choked orifice.
But we must consider compressible flow. At a pod speed of Mach 1 (our max is about M 0.7), the flow in the orifice would be a simple outward compression of about 2:1. There would be shock waves and increased drag, but acceptable with very low pressure in the tube.
Hyperloop is a really fascinating airflow situation, with high speed in a confined tube. It would be great if SimScale could do the simulations, it would contribute to the future of high-speed transportation!