CAD-based shape optimisation of the NASA CRM wing-body intersection using differentiated CAD-kernel

In industrial design existence of a master CAD geometry of a product enables simultaneous multi-disciplinary collaboration. Adjoint CFD methods have become increasingly accepted for aerodynamic shape optimisations due to their low computational cost. However, use of CAD-based parametrisations for aerodynamic gradient-based shape optimisation is not widely used, one reason being that current CAD systems to do not compute derivatives. In this work, we present the automatically differentiated (AD) version of Open Cascade Technology (OCCT) CAD kernel which can provide derivatives with respect to CAD parameters. OCCT is differentiated in block-vector AD mode which significantly reduces the cost for computing the derivatives. This work contains further OCCT extension for NURBS-based optimisation with intersecting patches and a description of the surface mesh movement linked to the change of the intersection line. These techniques are applied to the drag reduction of the NASA Common Research Model via the modification of the intersection between the root fairing and the wing

Efficient CAD based adjoint optimization of turbomachinery using adaptive shape parameterization

The present thesis incorporates the CAD model into an adjoint-based optimization loop and uses it for the shape optimization of a 2D transonic turbine blade mid-section (profile). This is demonstrated by performing a single and multipoint optimization of the LS89 turbine, originally designed at the VKI. Substantial aerodynamic improvements are reported for both design point and off-design conditions.The case is deeply analysed from the flow analysis point of view. The present thesis is a step forward in three main aspects. First, the way the CAD model (for turbomachinery applications) is used within the shape optimization loop.To include the CAD model into the optimization loop, the CAD kernel and the grid generator (multiblock structured) are differentiated using the Algorithmic Differentiation (AD) tool ADOL-C. The advantage of including the CAD model in the design system is that assembly or manufacturing constraints can be imposed on the shape, allowing the optimized model or component to be manufactured. Second, a new definition of the parametric effectiveness indicator is proposed, based on the ability of a set of CAD-based design variables to produce a shape change using the adjoint sensitivities. An interesting thing is that parametric effectiveness considers the design variables can be non-orthogonal to each other and it can be applied to any type of constrained or unconstrained problems. If, in the beginning of the optimization, the parametric effectiveness is high, it is expected to reach a final solution with increased performance. Third, a new adaptive shape parameterization strategy is adopted, which is assisted by the above parametric effectiveness indicator in order to explore the design space more efficiently. The parametric effectiveness, which rates the quality of a CAD based parameterization for optimization, is used in a novel multilevel shape refinement procedure to: (1) introduce the minimum amount of design variables required to modify the shape in the direction the adjoint sensitivities dictate; (2) to create the best parameterization to be used during the optimization. By using the proposed methods and tools, not only the optimal geometry is defined by the CAD, which is the industry adopted standard for the design of components, but also, the designer avoids the use of either too few (slow improvements from cycle to cycle) or too many (increase the computational burden) design variables. The proposed methodology results to be an effective strategy to explore rich design spaces, to improve convergence rate, robustness and final solution of the adjoint-based optimization.Aquesta tesi incorpora el model de CAD en un procés iteratiu d'optimització basat en el mètode adjunt i l'utilitza per a l'optimització de la secció d'una turbina transónica 2D (perfil). Això es demostra realitzant una optimització de punt únic i multipunt de la turbina LS89, originalment dissenyada en el VKI. Es reporten millores aerodinàmiques substancials tant per al punt de disseny com per les condicions fora del disseny. El cas s'analitza en profunditat des del punt de vista aerodinàmic. Aquesta tesi representa un avanç en tres aspectes principals. Primer, la forma en què es fa servir el model CAD (per a aplicacions de turbomàquines) dins el procés d'optimització. Per incloure el model CAD en el bucle d'optimització, s'apliquen tècniques de diferenciació algorítmica (l'eina ADOL-C) al kernel del CAD i el generador de la malla (estructurada i multibloc). L'avantatge d'incloure el model CAD en el sistema de disseny és que es poden imposar restriccions de fabricació a la geometria, i això permet que el disseny ja optimitzat es pugui fabricar. En segon lloc, es proposa una nova definició de l'indicador d'efectivitat paramètrica, basat en la capacitat de produir el canvi en la geometria que dicta el mètode adjunt mitjançant l'ús de les variables de disseny que defineixen el model CAD. Cal destacar que l'efectivitat paramètrica considera que les variables de disseny poden ser no ortogonals entre si i es pot aplicar a qualsevol tipus de problemes restringits o no restringits. Si, al començament de l'optimització, l'efectivitat paramètrica és alta, s'espera que l'optimització arribi a una solució final amb major rendiment. En tercer lloc, s'adopta una nova estratègia de parametrització adaptativa, que és assistida per l'indicador d'efectivitat paramètrica anterior per explorar l'espai de disseny de manera més eficient. L'efectivitat paramètrica, que classifica la qualitat d'una parametrització basada en CAD per a l'optimització, s'utilitza en un nou procediment de refinament multinivell per: (1) introduir la quantitat mínima de variables de disseny requerides per modificar la geometria en la direcció que dicten les sensibilitats del mètode adjunt; (2) per crear la millor parametrització que s'utilitzarà durant l'optimització. En utilitzar els mètodes i eines proposats, no només la geometria òptima està definida en el model CAD, que és l'estàndard adoptat per la indústria per al disseny de components, sinó que també el dissenyador evita l'ús de molt poques (millores lentes de cicle a cicle) o massa variables de disseny (augmenten la càrrega computacional). La metodologia proposada resulta ser una estratègia efectiva per explorar espais de disseny enriquits, millora la taxa de convergència, la solidesa i la solució final de l'optimització basada en el mètode adjunt

Efficient CAD based adjoint optimization of turbomachinery using adaptive shape parameterization

The present thesis incorporates the CAD model into an adjoint-based optimization loop and uses it for the shape optimization of a 2D transonic turbine blade mid-section (profile). This is demonstrated by performing a single and multipoint optimization of the LS89 turbine, originally designed at the VKI. Substantial aerodynamic improvements are reported for both design point and off-design conditions.The case is deeply analysed from the flow analysis point of view. The present thesis is a step forward in three main aspects. First, the way the CAD model (for turbomachinery applications) is used within the shape optimization loop.To include the CAD model into the optimization loop, the CAD kernel and the grid generator (multiblock structured) are differentiated using the Algorithmic Differentiation (AD) tool ADOL-C. The advantage of including the CAD model in the design system is that assembly or manufacturing constraints can be imposed on the shape, allowing the optimized model or component to be manufactured. Second, a new definition of the parametric effectiveness indicator is proposed, based on the ability of a set of CAD-based design variables to produce a shape change using the adjoint sensitivities. An interesting thing is that parametric effectiveness considers the design variables can be non-orthogonal to each other and it can be applied to any type of constrained or unconstrained problems. If, in the beginning of the optimization, the parametric effectiveness is high, it is expected to reach a final solution with increased performance. Third, a new adaptive shape parameterization strategy is adopted, which is assisted by the above parametric effectiveness indicator in order to explore the design space more efficiently. The parametric effectiveness, which rates the quality of a CAD based parameterization for optimization, is used in a novel multilevel shape refinement procedure to: (1) introduce the minimum amount of design variables required to modify the shape in the direction the adjoint sensitivities dictate; (2) to create the best parameterization to be used during the optimization. By using the proposed methods and tools, not only the optimal geometry is defined by the CAD, which is the industry adopted standard for the design of components, but also, the designer avoids the use of either too few (slow improvements from cycle to cycle) or too many (increase the computational burden) design variables. The proposed methodology results to be an effective strategy to explore rich design spaces, to improve convergence rate, robustness and final solution of the adjoint-based optimization.Aquesta tesi incorpora el model de CAD en un procés iteratiu d'optimització basat en el mètode adjunt i l'utilitza per a l'optimització de la secció d'una turbina transónica 2D (perfil). Això es demostra realitzant una optimització de punt únic i multipunt de la turbina LS89, originalment dissenyada en el VKI. Es reporten millores aerodinàmiques substancials tant per al punt de disseny com per les condicions fora del disseny. El cas s'analitza en profunditat des del punt de vista aerodinàmic. Aquesta tesi representa un avanç en tres aspectes principals. Primer, la forma en què es fa servir el model CAD (per a aplicacions de turbomàquines) dins el procés d'optimització. Per incloure el model CAD en el bucle d'optimització, s'apliquen tècniques de diferenciació algorítmica (l'eina ADOL-C) al kernel del CAD i el generador de la malla (estructurada i multibloc). L'avantatge d'incloure el model CAD en el sistema de disseny és que es poden imposar restriccions de fabricació a la geometria, i això permet que el disseny ja optimitzat es pugui fabricar. En segon lloc, es proposa una nova definició de l'indicador d'efectivitat paramètrica, basat en la capacitat de produir el canvi en la geometria que dicta el mètode adjunt mitjançant l'ús de les variables de disseny que defineixen el model CAD. Cal destacar que l'efectivitat paramètrica considera que les variables de disseny poden ser no ortogonals entre si i es pot aplicar a qualsevol tipus de problemes restringits o no restringits. Si, al començament de l'optimització, l'efectivitat paramètrica és alta, s'espera que l'optimització arribi a una solució final amb major rendiment. En tercer lloc, s'adopta una nova estratègia de parametrització adaptativa, que és assistida per l'indicador d'efectivitat paramètrica anterior per explorar l'espai de disseny de manera més eficient. L'efectivitat paramètrica, que classifica la qualitat d'una parametrització basada en CAD per a l'optimització, s'utilitza en un nou procediment de refinament multinivell per: (1) introduir la quantitat mínima de variables de disseny requerides per modificar la geometria en la direcció que dicten les sensibilitats del mètode adjunt; (2) per crear la millor parametrització que s'utilitzarà durant l'optimització. En utilitzar els mètodes i eines proposats, no només la geometria òptima està definida en el model CAD, que és l'estàndard adoptat per la indústria per al disseny de components, sinó que també el dissenyador evita l'ús de molt poques (millores lentes de cicle a cicle) o massa variables de disseny (augmenten la càrrega computacional). La metodologia proposada resulta ser una estratègia efectiva per explorar espais de disseny enriquits, millora la taxa de convergència, la solidesa i la solució final de l'optimització basada en el mètode adjunt.Postprint (published version

Optimal shape design with automatically differentiated CAD parametrisations

PhD ThesisTypical engineering workflow for aerodynamic design could be considered as a three-stage process: modelling of a new component in a CAD system, its detailed aerodynamic analysis on the computational grid using flow simulations (CFD) and manufacturing of the CAD component. Numerical shape optimisation is becoming an essential industrial method to improve the aerodynamic performance of shapes immersed in fluids. High-fidelity optimisation requires fine design spaces with many design variables, which can only be tackled with gradient-based optimisation methods. Adjoint CFD can efficiently calculate the necessary flow sensitivities on computational grids and ideally, also CAD parametrisation should be kept inside the loop to maintain a consistent CAD model during the optimisation and streamline the design process. However, (i) typical commercial CAD systems do not offer derivative computation and (ii) standard CAD parametrisations may not define a suitable design space for the optimisation. This thesis presents an automatically differentiated (AD) version of the open-source CAD kernel OpenCascade Technology (OCCT), which robustly provides shape derivatives with respect to CAD parameters. Developed block-vector AD mode outperforms commonly used finite difference approaches in both efficiency and accuracy. Coupling of OCCT with an adjoint CFD solver provides for the first time a fully differentiated design chain. Extension of OCCT to perform shape optimisation is demonstrated by using CAD parametrisations based on (a) user-defined parametric CAD models and (b) BRep (NURBS) models. The imposition of geometric constraints, a salient part of the industrial design, is shown for both approaches. Novel parametrisation techniques that can handle components with surface-surface intersections or simultaneously incorporate approaches (a) and (b) for the optimisation of a single component are demonstrated. The CAD-based methodology is successfully applied for aerodynamic shape optimisation of three industrial test cases. Additionally, advantages of the differentiated CAD is showcased for the commonly occurring CAD re-parametrisation and mesh-to-CAD fitting problems

Cad-based adaptive shape parameterisation for aerodynamic shape optimisation

Non-Uniform Rational B-Splines (NURBS) have become the industrial standard to represent and exchange a CAD geometry between CAD/CAE systems. CAD-based shape parameterisation uses parameters of a CAD model to modify the shape which allows to integrate a CAD model into the design loop. However, feature-trees of typical commercial CAD systems are not open and obtaining exact derivatives for gradient-based optimisation methods is not possible. Using the CAD-based NSPCC approach a designer can deform multiple NURBS patches in the design loop without violating geometric and/or thickness constraints. The NSPCC approach takes CAD descriptions as input and perturbs the control points of the NURBS boundary representation to modify the shape. In this work, an adaptive NSPCC method is proposed where the optimisation begins with a coarser design space and adapts to finer parametrisation during the design process where more shape control is needed. The refinement sensor is based on a comparison of smoothed node-based sensitivity compared to its projection onto the shape modes of the current parametrisation. Both static and adaptive parametrisation methods are coupled in the adjoint-based shape optimisation process to reduce the total pressure loss of a turbine blade internal cooling channel. The discrete adjoint flow solver STAMPS is used to compute the flow fields and their derivatives w.r.t. surface node displacements. The shape derivatives for gradient-based optimisation are obtained by application of reverse mode AD to the NSPCC CAD kernel. Since a CAD model is kept inside the design loop, the resulting optimal shape is directly available in CAD for further analysis or manufacturing. Based on the analysis regarding quality of the optima and rate of convergence of the design process adaptive NSPCC method outperforms static NSPCC approach

Development of parametric CAD models for gradient-based aerodynamic shape optimisation.

PhD Thesis.Shape optimisation is widely used in industry to improve the performance of the product. When performing aerodynamic analysis with CFD (Computational Fluid Dynamics), gradient-based optimisation methods are normally preferred if the number of design variables is high. These methods require the evaluation of the total derivatives, which can be split into two terms: the flow and the shape derivatives. While evaluating the flow derivatives with the adjoint CFD method, this thesis demonstrates that the shape derivatives can be calculated with algorithmically differentiated parametric CAD models. The development of such CAD models allows to compute the derivatives exactly and, by utilising the reverse mode variant of algorithmic differentiation, independently of the number of design parameters. This makes the computation of the shape derivatives efficient and robust. The parametrisation of the test-cases (a cooling channel and a compressor stator blade) is defined by intuitive and designer-friendly variables which capture the shape modes which mainly affect the objective function. The optimised parametric CAD models are compared to reference results. These results are set as the optimal shapes given by parametrisations with refined design space. The reference results of the cooling channel are identified in the literature. For the blade test-case, the design space of the parametric-based CAD model is enlarged (almost quadrupled). The optimised shape obtained with the parametricbased design is able to reproduce the same design modes provided by the enlarged design space. The fit of the assembly constraints of the blade’s test-case (four mounting bolts) during the flow optimisation has never been demonstrated. This is due to the arduous identification of a differentiable assembly constraints’ function. This thesis demonstrates that an approach based on the detection of a signed distance between the blade and the bolts succeeds in fitting the assembly constraints.

An Adaptive Parameterisation Method for Shape Optimisation Using Adjoint Sensitivities.

PhD Theses.Adjoint methods are the most e cient approach to compute the design sensitivities as the entire gradient vector of a single objective function is obtained in a single adjoint system solve. This in turn opens up a wide range of possibilities to parameterise the shape. Most shape parameterisation methods require manual set-up which typically results in a restricted design space. In this work, two parameterisation methods that can be derived automatically from existing information are extended to include adaptive design space in shape optimisation. The node-based method derives parameterisation directly from the computational mesh employed for simulation and normal displacements of the surface grid nodes are taken as design variables. This method o ers the richest design space for shape optimisation. However, this method requires an additional surface regularization method to annihilate high-frequency shape modes. Hence the best achievable design depends on the amount of smoothing applied on the design surface. An improved adaptive explicit surface regularization method is proposed in this thesis to capture superior shape modes in the design process. The NSPCC approach takes CAD descriptions as input and perturbs the control points of the NURBS boundary representation to modify the shape. The adaptive NSPCC method is proposed where the optimisation begins with a coarser design space and adapts to ner parameterisation during the design process. Driven by adjoint sensitivity information the control points on the design surfaces are adaptively enriched using knot insertion algorithm without modifying the shape. Both parameterisation methods are coupled in the adjoint-based shape optimisation process to reduce the total pressure loss of a turbine blade internal cooling channel. Based on analyses regarding the quality of the optima and the rate of convergence of the design process the adaptive NSPCC method outperforms both adaptive node-based and the static NSPCC approach

CAD-based geometry parametrisation for shape optimisation using Non-uniform Rational B-splines

PhDWith the continuous growth in computing power, numerical optimisation is increasingly applied in shape optimisation using Computational Fluid Dynamics (CFD). Since CFD computations are expensive, gradient-based optimisation is preferable when the number of design variables is large. In particular the recent progress with adjoint solvers is important, as these solvers allow to compute the gradients at constant computational cost regardless of the number of design variables, and as a consequence enable the use of automatically derived and rich design spaces. One of the crucial steps in shape optimisation is the parametrisation of the geometry, which directly determines the design space and thus the nal results. This thesis focuses on CAD-based parametrisations with the CAD model continuously updated in the design loop. An existing approach that automatically derives a parametrisation from the control points of a net of B-Spline patches is extended to include NURBS. Continuity constraints for water-tightness, tangency and curvature across patch interfaces are evaluated numerically and a basis for the resulting design space is computed using Singular Value Decomposition (SVD). A CAD-based shape optimisation framework is developed, coupling a flow solver, an adjoint solver, the in-house CAD kernel and a gradient-based optimiser. The flow sensitivities provided by the adjoint solver and the geometric sensitivities computed through automatic differentiation (AD) are assembled and provided to the optimiser. An extension to maintain the design space and hence enables use of a quasi-Newton method such as the BFGS algorithm is also presented and the convergence improvements are demonstrated. The framework is applied to three shape optimisation cases to show its effectiveness. The performance is assessed and analysed. The effect of parameters that can be chosen by the user are analysed over a range of cases and best practice choices are identifi ed.China Scholarship Council [No. 201306230097] and Queen Mary University of London