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

The blade solidity, namely the blade chordtopitch ratio, largely affects the fluiddynamic performance of turbomachinery. 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 becomes questionable. Examples of such working fluids are the nonideal (dense) vapors of organic compounds (e.g., hydrocarbons, siloxanes) used to operate organic Rankine cycle (ORC) power systems. This study investigates the effect of both the working fluid and the flow compressibility on the optimum pitchtochord ratio of turbine stages. A first principle model for the profile losses is developed for this purpose. Charts providing the optimal pitchtochord ratio for unconventional turbine stages are then provided. Numerical simulations of the flow over a turbine stator cascade have been conducted to validate the model results and evaluate the influence of both working fluid, flow compressibility, and solidity value on the loss breakdown. The results show that the optimal solidity of turbine cascades value significantly increases with the flow compressibility. Therefore, models providing the optimal solidity based on the estimate of passage loss only are not suited for unconventional turbines.