I’m trying to calculate the stagnation conditions of a water / steam - two-phase-flow in a horizontal constant diameter pipe.
The object is to calculate the stagnation pressure p_0 and mass flow quality x_dot_0 with given diameter d, mass flow m_dot, inlet pressure p_in and inlet mass flow quality x_dot_in.
I know how to calculate the stagnation mass flow quality x_dot_0 once I’ve calculated p_0. This ist done with an isentropic flash:
x_dot_0 = (s - s’_0) / (s’’_0 - s’_0)
Entropies will be calculated via REFPROP, where s = s(p_in,x_dot_in), but s’_0 and s’’_0 are dependent only from stagnation pressure p_0
So far I’ve found no real formula to calculate stagnation pressure conditions within two-phase-flows.
Stagnation pressure is indeed measured with a pitot tube, but I don’t think a stagnation pressure has merit when two-phase flow is involved. In compressible flow, stagnation pressure is the static pressure a gas retains when brought to rest isentropically from it’s flowing velocity/Mach number (M). In reality, a two-phase flow brought to rest will separate, and will no longer be the same two-phase mixture of interest. Also, liquid/solid parts of a two-phase flow are not compressible, and the thermodynamic relationships applied to the gas/vapor parts to calculate stagnation pressure will not apply to the liquid/solid parts. Forcing this calculation on the liquid/solid parts will not be rigorous, and depending on how much of the flow is liquid/solid initially, results may not be close enough to be practical.
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