Abstract

The success of shape optimisation depends significantly on the parametrisation of the shape. Ideally, it defines a very rich variation in shape, allows for rapid grid generation of high quality, and expresses the shape in a standard Computer Aided Design (CAD) representation. While most existing parametrisation methods fail at least one of these criteria, this work introduces a novel parametrisation method, which satisfies all three. A tri-variate B-spline volume is used to define the volume to be optimised. The position of the external control points are used as design parameters, while the internal control points are repositioned to ensure regularity of the transformation. The grid generation process transforms a Cartesian grid (defined in parametric space) to the physical space using the tri-variate net of control points. This process guarantees a high grid quality even for large deformations, and has extremely low computational cost as it only involves a transformation from parameter space to physical space. This allows the computation of the grid sensitivities with respect to the design variables at a fraction of the cost of a Computational Fluid Dynamics (CFD) iteration, therefore allowing the use of one-shot methods. This novel parametrisation is applied to the shape optimisation of a U-bend passage of a turbine-blade serpentine-cooling channel with the objective to minimise pressure losses. A steady state, Reynolds-Averaged, density-based Navier-Stokes solver is used to predict the pressure losses at a Reynolds number of 40,000. The sensitivities of the objective function with respect to the control points 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, while still maintaining a CAD representation of the geometry. A large reduction in pressure loss is obtained, and the flow in the optimal geometry is analysed in detail.

Highlights

  • Internal cooling channels of modern gas turbine blades are a key enabler for high turbine inlet temperatures and higher efficiencies

  • The grid generation process transforms a Cartesian grid to the physical space using the tri-variate net of control points. This process guarantees a high grid quality even for large deformations, and has extremely low computational cost as it only involves a transformation from parameter space to physical space. This allows the computation of the grid sensitivities with respect to the design variables at a fraction of the cost of a Computational Fluid Dynamics (CFD) iteration, allowing the use of one-shot methods

  • In the present work we propose an alternative solution to the mesh deformation problem, while remaining closely linked to a Computer Aided Design (CAD) model

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Summary

Introduction

Internal cooling channels of modern gas turbine blades are a key enabler for high turbine inlet temperatures and higher efficiencies. They all highlight the presence of a separation bubble near the internal wall in the second part of the bend, as a result of a strong adverse pressure gradient Another group of authors studied the numerical modelling of the turbulent flow. In the present work we propose an alternative solution to the mesh deformation problem, while remaining closely linked to a CAD model. To this end, tri-variate B-splines will be employed, which. The mesh generation is significantly simplified as it Through this approach, all faces of the U-bend shape remain B-spline surfaces, which allows a suffices to transform a structured rectangular mesh in the computational domain to 3D space, leading straight forward link to a watertight CAD model. This allows the use of a oneshot method to speed up the convergence of the optimisation problem

Methodology
Geometry
Grid Generation
CFD Solver
Adjoint Solver
Computation of the Grid Sensitivities
Computation of the Design Variable Sensitivities
Steepest Descent
Results
Conclusions
Full Text
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