Continuous Adjoint Shape Optimization of Internally Cooled Turbine Blade

Authors

Xenofon Trompoukis - National Technical University of Athens (NTUA)
Konstantinos Tsiakas - National Technical University of Athens (NTUA)
Varvara Asouti - National Technical University of Athens (NTUA)
Marina Kontou - National Technical University of Athens (NTUA)
Kyriakos Giannakoglou - National Technical University of Athens (NTUA)

Abstract

This paper presents a continuous adjoint-based optimization framework with applications in Conjugate Heat Transfer (CHT) problems involving compressible fluid flows. The objective function gradient, necessary for the shape optimization, is computed based on the continuous adjoint technique. For computationally demanding optimization problems, such as those encountered in CFD-based shape optimization, adjoint techniques are very attractive since the cost of computing the objective function gradient does not scale with the number of the design variables. Once the primal and adjoint equations are solved, the objective function gradient is computed based on volume and surface integrals including primal, adjoint fields and grid sensitivities. However, especially in cases with large number of design variables, computing grid sensitivities may be time consuming. An alternative approach (proposed by the same group) involves the solution of extra PDEs governing the so-called adjoint grid displacement field and computes the objective function gradient solely based on surface integrals, hence reducing its computation cost. Comparison of objective function gradients computed by both continuous adjoint approaches and finite differences is included in the full paper. In this work, the turbulence model is also included in the adjoint formulation without making the “frozen turbulence” assumption. The method developed is used for the shape optimization of a turbine blade for minimizing the total pressure losses between inlet and outlet and controlling the high temperature areas over the blade. The blade geometry is controlled by an in-house free form deformation tool based on volumetric NURBS. All computations are carried out on a GPU cluster. In both primal and adjoint solvers, data exchange overlaps with computations, minimizing communication overhead. Besides, mixed precision arithmetics, renumbering and coloring techniques together contribute in exploiting the computing capabilities of modern GPUs. The coupling of the flow and heat conduction primal and adjoint solvers is based on three different schemes, the performance comparison of which is also shown in the full paper.This project has received funding from the European Union's Horizon 2020 research and innovation programme under Grant Agreement No 769025.