Framework for real-gas compressible reacting flows with tabulated thermochemistry

• A framework is provided to deal with real-gas compressible reacting flows with tabulated thermochemistry.
• A cubic equation of state for tabulated thermochemistry is derived.
• The Jacobian matrix is detailed.
• Boundary conditions are expressed following the NSCBC formalism.
• Reactive and non-reactive test cases are performed with success to demonstrate the capacity of the new method.

Combustion in liquid rocket engines happens under severe thermodynamical conditions: pressure exceeds the critical pressure of injected propellants and temperature is cryogenic. Such a situation requires an important effort of modeling: real gas effects are incorporated through cubic equations of state along with pressure-correction terms, and transport properties follow specific rules. Modeling for turbulent combustion is also an issue and is presently considered with tabulated chemistry thus reducing the number of transported variables. In this study, a framework is provided to deal with real-gas compressible reacting flows with tabulated thermochemistry. As a consequence, a cubic equation of state for tabulated thermochemistry is derived with the adopted thermodynamic relations, and the temperature computation is adapted to incorporate real gas effects through the tabulated thermochemistry approach. Two-dimensional reactive and non-reactive theoretical test cases have been performed with success to demonstrate the capacity of the new method. Finally, the simulation of a three-dimensional non-reactive single injector derived from Mayer's experiment, that consists of a supercritical nitrogen jet injection into a warm nitrogen atmosphere, is also performed with success. The comparison between the tabulated approach and a fully coupled reference solution leads to similar results for the density values along the jet axis and for the spreading rate.

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