Adjoint-Based Design Optimisation of an Internal Cooling Channel U-Bend for Minimised Pressure Losses

Abstract

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.

Comparison of large eddy simulation and Reynolds-averaged Navier–Stokes evaluations with experimental tests on U-bend duct geometry

“…The considered design and flow configuration has received particular attention both from research groups and industries, and various approaches and optimization strategies have been applied to it, focusing on pressure drop reduction 15–17 and heat transfer enhancement. 18,19 Shape optimization routines are usually coupled to an incompressible Reynolds-averaged Navier–Stokes (RANS) solver for the evaluation of the design performance, due to its low computational cost and its steady nature.…”

Adjoint shape optimization coupled with LES-adapted RANS of a U-bend duct for pressure loss reduction

“…The adjoint method continued to grow in the aeronautical industry framework bringing its use for: complete aircraft optimization [12], problems considering the compressible Navier-Stokes equations [13], aero-structural optimization [14,15]. The examples illustrated above are related to the aeronautical field but applications can be found in many other different domains, such as turbomachinery [16,17], automotive [18][19][20], energy [7], naval [21] and thermal exchange [22,23]. In the context of shape optimization, the coupling with deformation techniques [24,25] is necessary after the evaluation of the direction of improvement.…”

CAD Integrated Multipoint Adjoint-Based Optimization of a Turbocharger Radial Turbine

“…For example, the gradient of design variable 29, which is the exit width, suggests that both the efficiency and power increase when enlarging the exit area. The CEV assumption indeed affects the accuracy of the adjoint-based gradients, in particular for design parameters of the shroud meridional contour (design variables [21][22][23][24], where this assumption may not be valid due to the tip leakage vortex. However, they are accurate enough for shape optimization as will be shown in Section 4.…”

“…To overcome the limitations that are associated with finite-differences, an open-source CAD system was differentiated by [23] using algorithmic differentiation (AD), which was then applied to optimize a U-Bend shape found in high-pressure turbine blades as cooling devices. A trivariate B-spline parameterization was used by [24] for the same test case that allows a rapid meshing of the domain suitable for a one-shot optimization method while the geometry maintains the link to a CAD representation. A different approach was developed by [25,26] that employs the displacements of the control points of non-uniform rational B-spline (NURBS) patches as design parameters, which are available in the STEP file standard used to exchange data in a computer-aided engineering (CAE) framework.…”