Forced response freeform optimization of a radial turbine using the adjoint method

Abstract

Radial turbines equipped with inlet guide vanes are subject to a forced excitation: The guide vanes distort the pressure field upstream of the turbine wheel and induce a wake, that excites the blades as they pass. This is problematic as soon as resonance occurs. Hence, one is interested in studying whether and how one may reduce the induced forced response of the blades to avoid high cycle fatigue. Aiming at a reduction of the resulting forced response, a gradient-based freeform optimization is conducted for the studied radial turbine: Sensitivities are evaluated by means of the adjoint method. Herein, the complex step method is exploited to gather accurate derivatives of both dynamic stiffness matrix and excitation force. The resulting sensitivities are smoothed by means of the Vertex Morphing method before the mesh is updated. Few optimization iterations suffice to successfully reduce the blades' most prominent forced response. Hence, the method delivers a promising approach to make radial turbines more robust against guide vane induced excitations. A comparison of both baseline and optimized design illustrates how those have been altered by the optimizer and explains the improvements.