Validation and Development of Loss Models for Small Size Radial Turbines

Today an increasing need for gas turbines with extremely low flow rates can be noticed in many industrial sectors, e.g. power generation, aircraft or automotive turbo chargers. For any application it is essential for the turbine to operate at best possible efficiency. It is known that for turbines the specific optimum achievable power output decreases with smaller size. A major contribution for this reduction in efficiency comes from the relative increase of aerodynamic losses in smaller turbine stages. In the early turbine design stage, easy and fast to use two-dimensional calculation codes are widely used. In order to produce qualitatively good results, all of these codes contain a diversity of loss models that more or less exactly describe physical effects which generate losses. It emerges to be a real problem that most of these empirical models were derived for rather large scale turbo machines and that they are not necessarily suitable for application to small turbines. In this paper many of the commonly known and well established loss models used for the preliminary design of radial turbines were collected, reviewed, and validated with respect to their applicability to small-size turbines, i.e. turbines of inlet diameter smaller than 40 mm. Comprehensive numerical investigations were performed and the results were used to check and verify the outcome of loss models. Based on the results, loss models have been improved. Furthermore, new correlations were developed in order to raise the quality of loss prediction especially for the design of small-size turbines. After receiving an optimum set of loss prediction models, all of them were implemented into a two-dimensional solver program for the analytical iterative solution of a complete turbine stage. Hence a powerful tool for preliminary radial turbine design has been created. This program enables the user to analytically evaluate the effects of changing key design properties on performance. These are amongst others the optimum rotor inlet flow angle according to the slip-factor definition, the value of flow deviation, and hence the optimum blade outlet angle for a minimum adverse flow-swirl at turbine outlet. Complementarily the turbine key performance indicators, e.g. pressure ratio, power output, rotational turbine speed, and mass flow can be calculated for optimum efficiency of a given turbine geometry. The paper presents the most important loss models implemented in the new code and weights their relative importance to the performance of small size radial turbines. The data acquisition was done using the new code itself as well as accompanying full 3D CFD calculations.