Rothalpy Conservation and Loss Calculations in Turbomachinery for Improved Modeling of Leakage, Thrust, and Component Performance

Abstract Conservation of rothalpy in the rotating components of turbomachinery is a fundamental assumption in low-order models, including meanline analysis. Rothalpy is basically an energy term quantifying the initial total energy of the fluid stream minus the energy that is induced in the flow from the rotating components of the system. Though there is nothing fundamentally wrong with this concept, the typical formulations of the flowpath averaged rothalpy equations contain underlying assumptions that are not strictly true in all cases. These assumptions can be relatively modest in most centrifugal compressor impellers but not necessarily trivial. In other components, such as leakage paths, the errors associated with the conventional formulation for rothalpy can be much higher. Commonly used equations of rothalpy depart from the actual values when a given surface in the rotational domain is not actually rotating, as is the case with an open impeller or in a leakage path. In this work, we look at the common equations for averaged rothalpy and determine under what circumstances they do not strictly apply. Different correction methods for these terms are proposed and approximate magnitudes of these terms are shown. These methods can be easily applied in a meanline context where computational costs are a concern. Comparison to higher order models (specifically CFD) which have no simplified assumptions in their formulations for energy, are shown to indicate the effectiveness of the correction terms. Finally, a new formulation of leakage path modeling is proposed using these corrected rothalpy terms, which provides a higher level of fidelity to loss generation and pressure distributions calculated from meanline models. This new formulation can provide improved prediction, particularly for axial thrust magnitudes, that have typically been difficult to calculate accurately.