Computer Aided Design (CAD) tools are extensively used to design industrial components, however contrary to e.g. Computational Fluid Dynamics (CFD) solvers, shape sensitivities for gradient-based optimisation of CAD-parametrised geometries have only been available with inaccurate and non-robust finite differences. Here Algorithmic Differentiation (AD) is applied to the open-source CAD kernel Open CASCADE Technology using the AD software tool ADOL-C (Automatic Differentiation by OverLoading in C++). The differentiated CAD kernel is coupled with a discrete adjoint CFD solver, thus providing the first example of a complete differentiated design chain built from generic, multipurpose tools. The design chain is demonstrated on the gradient-based optimisation of a squared U-bend turbo-machinery cooling duct to minimise the total pressure loss.

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In order to optimise the shape of a three-dimensional CAD-based model using the computationally efficient adjoint methods, the calculation of shape sensitivities, the derivatives of the surface position with respect to the design parameters, is required. This sensitivity is usually not available with CAD systems, but can be obtained by applying the Finite Difference method to CAD-system. Finite-Differences or part-analytic differentiation have been proposed to obtain sensitivities, but have their drawbacks. If source code is available, automatic differentiation can provide accurate derivatives without incurring topology changes or requiring hand-differentiation. This paper proposes the differentiation of the open-source CAD kernel-OpenCascade Technology (OCCT) with AD software tool ADOL-C (Automatic Differentiation by Overloading in C++). As a case study we consider the optimisation of pressure loss in a U-bend pipe. The geometry of the U-bend is parametrised in OCCT with a number of cross-sections lofted along a guiding path line. The corresponding geometric derivatives are used in CFD optimisation loops with the resulting shape outperforming the initial design.

Over the past decades significant progress has been made with adjoint computational fluid dynamics solvers, which are an essential part of efficient high-fidelity aerodynamic shape optimisation. Shape parametrisation is much less mature, in particular the field is lacking efficient and automatic CAD-based parametrisation methods. The paper proposes a novel CAD-based parametrisation with CAD in the design loop such that the CAD shape can ultimately serve as a datum surface in multidisciplinary optimisation. Wing and fuselage are modelled with B-spline surfaces. The intersection line is calculated using an in-house implementation of a B-spline surface modeller and its derivative is efficiently calculated via finite differences. The proposed parametrisation method is applied to the redesign of the wingfuselage junction of the DLR-F6 model using an adjoint solver based on Reynolds-averaged Navier-Stokes equations. The moving intersection line capability enables the fuselage surface to be deformed and the resulting intersection line to move along the fixed wing during optimisation. The flow separation in the wing-body junction is substantially suppressed by an improved fuselage shape, at the cost of O(10) steady-state flow and adjoint solutions. The proposed parametrisation method represents an important step towards automated CAD-based optimisation for fully-featured aircraft characterised by complex intersecting surfaces.