Trade-Off Between Hydraulic Performance and Structural Strength in Blade Thickness Design of High-Head Francis Turbines

Abstract

Francis turbine runners operated at high head conditions experience severe hydraulic loading and centrifugal stresses, making blade thickness a critical design parameter governing both hydraulic efficiency and structural integrity. Traditionally, blade thickness selection relies on empirical relations, leading to higher material usage or sub-optimal hydraulic performance. This study evaluates the Brekke empirical blade thickness formulation through a Fluid-Structure Interaction (FSI) framework applied to high-head Francis runners with speed number Ω = 0.24 and 0.29 operating at 500 m head. The Brekke model is first applied directly for the runners with Ω = 0.24 and Ω = 0.29, yielding leading edge thickness of 37.98 mm and 77.74 mm respectively, which the FSI analysis shows produces a minimum factor of safety of 1.4089 and 1.1729 respectively, below the IEC 60193 design threshold of 2.0, confirming its inadequacy at extreme head conditions. A parametric study varying the blade thickness ratio k = t_max/t_out across three configurations is then conducted, with hydraulic efficiency evaluated through CFD simulations and structural integrity assessed through one-way FSI. Results show that applying corrective multipliers of 0.83 to t_max,Brekke as t_max and 0.50 to t_max,Brekke as t_out yields an optimal design achieving a peak hydraulic efficiency above 93% with a factor of safety well above the IEC 60193 threshold, satisfying the structural integrity of the design. These corrective multipliers provide quantitatively grounded design guidance for high-head Francis turbine blade thickness selection, reducing reliance on iterative trial-and-error and offering a numerically validated calibration pathway for the Brekke empirical formulation at heads approaching 500 m.