A Novel Reduced-Order Mathematical Model for Radial Turbines

Abstract Radial turbines are commonly used to extract otherwise unused energy from engine exhausts, and are therefore an important component of many emission reducing technologies. There is a desire to quickly and reliably predict the performance of radial turbines over a variety of different operating conditions. Reduced-order models meet the computational speed requirements but often do not obtain sufficient accuracy without the tuning of multiple unknown parameters. In order for a model to be predictive, we need a way to reduce the number of unknowns and find ways to calibrate these parameters to known geometric values. In this paper, we develop a new reduced-order model from first principles by averaging the fundamental Navier–Stokes equations of fluid motion. All losses are derived from the deviatoric stress tensor to ensure consistency. Only four unknown parameters are required, each with a physical interpretation and showing evidence of universality. The model simulates gas properties throughout the turbine, shows the loss distribution over the operating range, and predicts turbine performance curves. Validation is provided by a remarkable fit to experimental data. Therefore, this model has the potential to become a valuable tool for turbine manufacturers during early design stages.