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Incorrect formula for supersonic total pressure calculation

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September 21, 2021, 07:51	Incorrect formula for supersonic total pressure calculation	#1
sphani4391 New Member Sai Darbha Join Date: Aug 2019 Posts: 8 Blog Entries: 2 Rep Power: 6	The static pressure for the totalPressure boundary condition for compressible, supersonic flow in OpenFoam-v2012 is given in doxygen and the code as: $P_s = \frac{P_T}{\left( 1 + \psi \left( \frac{\gamma -1}{2 \gamma} \right) \|\vec{u}\|^2 \right)^{\gamma / (\gamma -1)}}$ where the compressibility, psi is related to the speed of sound, c as $\psi = \frac{1}{c^2}$ However, the isentropic relation for supersonic flows relate the static pressure to stagnation pressure as: $P_s = \frac{P_T}{\left( 1 + \psi \left( \frac{\gamma -1}{2 } \right) \|\vec{u}\|^2 \right)^{\gamma / (\gamma -1)}}$ For reference, have a look at: https://www.grc.nasa.gov/www/k-12/ai.../isentrop.html Is this a bug or am I missing something? Please suggest. Thanks, Sai

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