(159a) Choked and Near-Choked Real Gas and Two-Phase Flow Analysis of Discharge Piping

The methods of analysis of real gas and two phase gas-liquid flow in discharge piping of pressure relieve systems with possible multiple choking are discussed. General differential equations for real gas and two phase flow in the pipe in the form of pipe length, temperature, enthalpy and entropy derivatives via pressure for general thermodynamic conditions (including heat exchange with environment) are formulated. Right parts of these equations are regular functions of thermodynamic properties of the fluid and Mach number, so the equations can be effectively solved numerically using standard method.

The proposed approach was implemented in the software for unbranched discharge piping flow using different thermodynamic libraries. Some problems of implementation for mixtures with “narrow” phase envelope (almost azeotropic) are discussed. It found out that using pressure and enthalpy or pressure and entropy as basic thermodynamic parameters in this case is preferable over pressure and temperature to escape loss of accuracy. This also relates to Mach number calculation for two phase flow. For special cases of vapor-liquid flow of one-component fluid, and for non-flashing gas-liquid flow appropriate equations for Mach number are proposed, which take into account real properties of vapor/gas and compressibility of liquid. These equations are generalization of known equations for ideal gas and incompressible liquid mixtures and can be also used to improve accuracy of omega method.

The methods of calculating minor losses for high Mach numbers for elements typical in discharge piping are reviewed.

Different cases of crossing fluid envelope (flashing or condensation) in piping are considered and their influence to choked flow are discussed.

Flow rate distribution algorithms for branched discharge piping systems with multiple choked flow are proposed.