Kantrowitz Limit - The Aerodynamics Challenge

The goal of the SpaceX Hyperloop Competition II is to design a Pod which can achieve the maximum speed with a controlled acceleration and deceleration. So, the first step our team had to undertake was to design the aerodynamics of the pod. Since speed is the goal of the competition thus we gave aerodynamics the highest priority.

The competition environment is a closed one, that is the pod must run inside a tube creating additional challenges for our design. The aerodynamic drag decreases with a decrease in the ambient pressure and is almost negligible at near vacuum conditions. Achieving a near vacuum ~ pressures less than 1000 Pa is also a very tough task to achieve. To be in a safer zone, our team decided to design the pod to run inside the tube with a tube pressure of 4000 Pa. Realistically, pressures can be achieved less than 4000 Pa and considering the inaccuracies of numerical simulations or other unforeseen factors, a pressure of 4000 Pa was deemed sufficient to design a pod with stable aerodynamics. Effectively, the pod would be able to achieve higher speeds at pressures lowers than 4000Pa. One of the main problems posed by flows inside a tube is the Kantrowitz Limit. The Kantrowitz limit defines the maximum diameter of an object inside a tube at a certain speed above which the flow chokes, creating drag forces which build up in front of the object.

The way to tackle is to either go at speeds slower than the speed of sound or at speeds much higher than the speed of sound. Using a compressor at the front of the pod allows to eliminate this problem as well. A compressor driven by a motor transfers this high pressure build up at front towards the back of the pod.

The competition pod was designed without a compressor as the track length is only one mile which makes the use of compressed air a better option for propulsion. Using CFD Flow simulations in ANSYS Fluent, and after iterating through 15 designs, our team eventually came with an effective design that goes at 200 m/s in the tube. We tested the CAD models for lift and drag forces along with the Kantrowitz limit.