The effect of working fluid and compressibility on the optimal solidity of axial turbine cascades

The blade solidity, namely the blade chord-to-pitch ratio, largely affects the fluid-dynamic performance of turbomachinery and its cost. For turbomachines operating with air or steam, the optimal value of the solidity which maximizes the efficiency is estimated with empirical correlations such as the ones proposed by Zweifel (1945) and Traupel (1966). However, if the turbomachine operates with unconventional fluids, the accuracy of these correlations is questionable. Examples of such fluids are the organic compounds (e.g., hydrocarbons, siloxanes) used in organic Rankine cycle (ORC) power systems. This study concerns an investigation on how the working fluid, its thermodynamic state, and flow compressibility influence the optimum pitch-to-chord ratio of turbine stages. A first principle reduced-order model (ROM) for the computation of profile losses was developed for this purpose. The ROM results are compared with those obtained from numerical simulations of the flow over two axial turbine cascade geometries. The influence of both the working fluid, the flow compressibility, and the solidity value on both the boundary layer state at the blade trailing edge and the base pressure are evaluated. Models to compute mixing and passage losses in the compressible regime as a function of the axial solidity are proposed and discussed. Results show that the value of the optimal solidity of turbine cascades significantly increases with the flow compressibility, and mildly increases if the fluid is in the dense vapor state. Moreover, the optimal solidity value is strongly affected by the mixing process occurring downstream of the blade trailing edge. Therefore, currently available models for its estimation, which are solely based on the minimization of the profile losses, are inaccurate.