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

Abstract

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 utilized 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.