Adjoint based design optimisation of an internal cooling channel u-bend for minimized pressure losses

Abstract

Copyright © by the Authors. The aim of this paper is to reduce the pressure losses of a U-bend passage of a turbine blade serpentine cooling channel. A steady state Reynolds-Averaged density based Navier-Stokes solver is used to predict the pressure losses at a Reynolds number of 40,000. A novel geometry representation approach is used defining directly the volume of the passage rather than its exterior boundary, which is now the most common approach in CAD systems. The U-bend volume is parameterised using tri-variate B-splines, the deformations of the shape are controlled by the external control points of the B-spline volume, while the internal control points are repositioned using a transfinite interpolation to ensure a smooth and regular internal representation of the shape. This approach ensures a good grid regularity at a large reduced computational cost compared to traditional approaches. The sensitivities of the control points with respect to the objective function are computed using a hand-derived adjoint solver and geometry generation system. A one-shot approach is used to simultaneously converge flow, gradient and design, resulting in a rapid design approach with a design time equivalent to approximately 10 normal CFD runs. A large reduction in pressure loss is obtained, and the optimal geometry is analysed in more detail.