In gas dynamics, the Kantrowitz limit refers to a theoretical concept describing choked flow at supersonic or near-supersonic velocities.
Setting the mass flow rates equal at the inlet and throat, and recognizing that the total temperature, ratio of specific heats, and gas constant are constant, the conservation of mass simplifies to, Solving for A4/A0, Three assumptions will be made: the flow from behind the normal shock in the inlet is isentropic, or pt4 = pt2 , the flow at the throat (point 4) is sonic such that M4 = 1, and the pressures between the various point are related through normal shock relations, resulting in the following relation between inlet and throat pressures,[1] And since M4 = 1, shock relations at the throat simplify to,[2] Substituting for
in the area ratio expression gives, This can also be written as,[3] The Kantrowitz limit has many applications in gas dynamics of inlet flow, including jet engines and rockets operating at high-subsonic and supersonic velocities, and high-speed transportation systems such as the Hyperloop.
[4] The Kantrowitz limit is a fundamental concept in the Hyperloop, a proposed high-speed transportation system.
The Hyperloop moves passengers in sealed pods through a partial-vacuum tube at high-subsonic speeds.
The first would increase the diameter of the tube in order to provide more bypass area for the air around the pod, preventing the flow from choking.
This would avoid the continuous increase of the vehicle drag due to the choking of the flow at the cost of the power required to drive the turbine and hence enable larger speeds.
The computer program NUMSTA has been developed in this context; it allows to simulate the dynamical interaction of several high speed vehicles in complex tunnel networks including the choking effect.
This idea has also been proposed by Elon Musk in his 2013 Hyperloop Alpha paper where a compressor is placed at the front of the pod.
[5] The compressor actively draws in air from the front of the pod and transfers it to the rear, bypassing the gap between pod and tube while diverting a fraction of the flow to power a low-friction air-bearing suspension system.