Development of a Sizing Method for Real Gas Applications

As a consequence, the mass flow rate through a nozzle or even a safety valve can no longer be determined by simple relations for ideal gases. 

In the case of flow of a real gas through an adiabatic nozzle, the stagnation enthalpy between the entrance and the narrowest flow cross section, the nozzle throat, remains constant (ht = constant). The change in enthalpy corresponds to the change in kinetic energy and the irreversible frictional pressure loss is expressed by the resistance coefficient  

The mass flow rate is obtained by a progressive variation of the state conditions in the nozzle throat at a constant stagnation enthalpy - or approximately in the case of isentropic flow (no heat transfer, = 0) - until the back pressure or a maximum of the mass flow rate (critical pressure ratio) is reached. 

This method is suitable when the state diagram of the gas is available or can be plotted. It applies not only for pure substances but also for mixtures of gases. If graphical methods are not efficient, the mass flow rate through a nozzle can also be determined with an equation for real gases, which can be derived from the first law of thermodynamics  

The second term corresponds to the Joule-Thomson effect, which includes the variation of the stagnation temperature during the expansion of the gas. This term is equal to zero for ideal gases. 

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