Stagnation Conditions of a Two-Phase-Flow

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.

Snippet Source:

Another excellent point from that thread,, was that the Homogeneous Equilibrium Model (HEM) averts the mathematical and theoretical difficulties associated with two-phase compressible flow and is somewhat conservative. As such, HEM has attained RAGAGEP status. RAGAGEP = Recognized And Generally Accepted Good Engineering Practice.