A Reliable Update of the Ainley and Mathieson Profile and Secondary Correlations

Empirical correlations are still fundamental in the modern design paradigm of axial turbines. Among these, the prominent Ainley and Mathieson correlation (Ainley D. and Mathieson G., 1951, "A Method of Performance Estimation for Axial-Flow Turbines," ARC Reports and Memoranda No. 2974) and its derivatives, plays a crucial role. In this paper, the underlying assumptions of the aforementioned models are discussed by means of a descriptive review, whilst an attempt is made to enhance their reliability and, potentially, accuracy in performance estimations. Closer investigation reveals an intriguing misuse of the lift coefficient in the secondary loss. In light of this, an enhanced model that, notably, builds upon the Zweifel criterion and the vortex penetration depth concept is developed and discussed. The obtained accuracy is subsequently assessed through CFD computations, employing a database comprising 109 cascades. The results indicate a 50% probability of achieving the +/- 15% error interval, which is twice as good as the most recent Aungier model (Aungier R., 2006, "Turbine Aerodynamics: Axial-Flow and Radial-Inflow Turbine Design and Analysis", ASME Press, New York). Furthermore, the reliability of the proposed model is demonstrated by a reconstruction of the Smith chart, on the one hand, and a performance analysis, on the other. The reconstruction exhibits contours that conform to the original. The results of the performance study are compared with the CFD solutions of eight cascades working in off design conditions and confirm the need of the additionally included turbine design parameters, such as the axial velocity and the meanline radius ratios.