Method for considering real gas equations of state in through-flow programs

Numerical methods are significant in the turbomachine design process and off-design analysis. One of these methods is the through-flow method in the meridional plane, which is utilised in an early design phase. It provides a robust and quick numerical turbomachinery analysis by only giving a few characteristic geometric parameters. This work shows an extension of the through-flow method by considering real gas equations of state (EOSs) in throughflow programs. This is implemented in an in-house through-flow program called tFlow. This enables the method to support a more reliable calculation regarding, for instance, carbon dioxide (CO2) in a high-pressure region, where the gas does not behave like an ideal gas. The incorporation of real gas EOSs is validated with two-dimensional (2D) calculations of nozzle flows and with quasi-three-dimensional (3D) calculations of supercritical CO2 (sCO2) centrifugal compressors. A straightforward method for modifying the Riemann inlet boundary conditions for real gases is presented enabling a quick extension of through-flow codes to real gases and providing a stable solution process. Look-up tables (LUTs) are used instead of common high-degree polynomials to solve the real gas thermodynamic properties and reduce the computation time by a factor of about 20. Additionally, the calculation results verify the application of the Jameson-Schmidt-Turkel (JST) scheme in terms of real gas EOSs. Finally, the predictions are compared against 1D solutions for 2D cases and against the experimental data of the sCO2-HeRo compressor for 3D cases.