Towards Adaptive and Grid-Transparent Adjoint-Based Design Optimization Frameworks

With the growing environmental consciousness, the global perspective in energy production is shifting towards renewable resources. As recently reported by the Office of Energy Efficiency & Renewable Energy at the U.S. Department of Energy, wind-generated electricity is the least expensive form of renewable power and is becoming one of the cheapest forms of electricity from any source. The aeromechanical design of wind turbines is a complex and multidisciplinary task which necessitates a high-fidelity flow solver as well as efficient design optimization tools. With the advances in computer technologies, Computational Fluid Dynamics (CFD) has established its role as a high-fidelity tool for aerodynamic design.In this dissertation, a grid-transparent unstructured two- and three-dimensional compressible Reynolds-Averaged Navier-Stokes (RANS) solver, named UNPAC, is developed. This solver is enhanced with an algebraic transition model that has proven to offer accurate flow separation and reattachment predictions for the transitional flows. For the unsteady time-periodic flows, a harmonic balance (HB) method is incorporated that couples the sub-time level solutions over a single period via a pseudo-spectral operator. Convergence to the steady-state solution is accelerated using a novel reduced-order-model (ROM) approach that can offer significant reductions in the number of iterations as well as CPU times for the explicit solver. The unstructured grid is adapted in both steady and HB cases using an r-adaptive mesh redistribution (AMR) technique that can efficiently cluster nodes around regions of large flow gradients.Additionally, a novel toolbox for sensitivity analysis based on the discrete adjoint method is developed in this work. The Fast automatic Differentiation using Operator-overloading Technique (FDOT) toolbox uses an iterative process to evaluate the sensitivities of the cost function with respect to the entire design space and requires only minimal modifications to the available solver. The FDOT toolbox is coupled with the UNPAC solver to offer fast and accurate gradient information. Ultimately, a wrapper program for the design optimization framework, UNPAC-DOF, has been developed. The nominal and adjoint flow solutions are directly incorporated into a gradient-based design optimization algorithm with the goal of improving designs in terms of minimized drag or maximized efficiency

Eine adjungierte Aero-Struktur-Formulierung für eine effiziente multidisziplinäre Flügel-Optimierung

Computational fluid dynamics is today a reliable tool for the analysis of the flow past wings, and is increasingly used in aircraft design. Since the wing is a coupled fluid-structure system, stationary elastic deflection has to be taken into account during the design. If the design is performed by means of gradient-based optimization techniques, it is necessary to include the effect of static elasticity in the gradient computation, since this can significantly alter the values of the sensitivities. On the other hand, the prediction of highly non-linear effects such as shock arise in transonic flow, and shock-shock interaction in supersonic flow is critical to perform a detailed optimization; this demands the use of high fidelity flow models. Since these models are extremely computationally expensive, an efficient computation of the gradient in turn requires the use of an advanced mathematical tool: the adjoint method. Both these critical requirements can be met by a coupled aero-elastic adjoint formulation, where the coupling is carried out firstly in the physical variables of the two systems, and then in the adjoint variables, which are subsequently used to calculate the sensitivity. The multidisciplinary extension of the adjoint method also allows the evaluation of gradients of cost functions or constraints containing terms coming from the structure side, as in the case of the Breguet formula for aircraft range. In the present work, a completely continuous formulation of the aeroelastic coupled adjoint method is presented and applied to test cases relevant to aircraft design, through an implementation within the software FLOWer from DLR and MSC-Nastran. The test cases are based on the AMP wing in the transonic regime, while the shape parametrization is based on the free-form deformation method. A comparative study of optimization histories is presented, showing the necessity of a high number of design variables to maximize the effectiveness of the optimization, as well as the necessity for accurate sensitivities that contain the effect of aeroelasticity. The sensitivities obtained from the coupled adjoint have allowed to perform in relatively short time optimizations with high number of design variables, aimed to reduce drag at constant lift and angle of attack and to increase range by means of the Breguet formula, assuming a stress penalty for the structural weight and again constant lift and angle of attack. A comparison of these two cases shows that the aerodynamically optimal minimal drag design differs from the multidisciplinary optimal design.CFD (Computational Fluid Dynamics) ist heutzutage ein zuverlässiges Werkzeug für die Analyse von Strömungen und kommt deshalb in der Luftfahrtindustrie mehr und mehr zum Einsatz. Ein Flugzeugflügel ist jedoch ein Aero-Struktur-System, weshalb die durch die aerodynamischen Kräfte verursachte statische Deformation des Flügels während seines Entwurfes berücksichtigt werden muss. Wenn der Entwurf mittels deterministischen gradientenbasierten Optimierungsverfahren erfolgt, müssen demzufolge die statisch elastischen Effekte bei der Sensitivitätenberechnung mit einfließen und modelliert werden. Um sowohl auf der Struktur als auch auf der Aerodynamikseite hochgenaue und damit rechen- und zeitaufwändige Berechnungsverfahren verwenden zu können, wir ein gekoppeltes Aero-Struktur-Adjungiertenverfahren hergeleitet, implementiert sowie validiert und für den so genannten AMP-Flügel erprobt. Auf der Strömungsseite wird der DLR-Löser FLOWer und auf der Strukturseite der kommerzielle FEM-Löser MSC-NASTRAN verwendet. Schließlich wird eine multidisziplinäre Reichweitenoptimierung, mit der Breguet-Formel für die Reichweite als Zielgröße, für den AMP-Flügel durchgeführt – und zwar unter Berücksichtigung der statischen Deformation und der aerodynamischen Nebenbedingung, dass der Auftrieb konstant bleiben muss. Hierbei ermöglicht das effiziente gekoppelte Aero-Struktur-Adjungiertenverfahren die Parametrisierung des Flügels mit einer großen Anzahl an Entwurfsvariablen

Combining Parameterizations, Sobolev Methods and Shape Hessian Approximations for Aerodynamic Design Optimization

Aerodynamic design optimization, considered in this thesis, is a large and complex area spanning different disciplines from mathematics to engineering. To perform optimizations on industrially relevant test cases, various algorithms and techniques have been proposed throughout the literature, including the Sobolev smoothing of gradients. This thesis combines the Sobolev methodology for PDE constrained flow problems with the parameterization of the computational grid and interprets the resulting matrix as an approximation of the reduced shape Hessian. Traditionally, Sobolev gradient methods help prevent a loss of regularity and reduce high-frequency noise in the derivative calculation. Such a reinterpretation of the gradient in a different Hilbert space can be seen as a shape Hessian approximation. In the past, such approaches have been formulated in a non-parametric setting, while industrially relevant applications usually have a parameterized setting. In this thesis, the presence of a design parameterization for the shape description is explicitly considered. This research aims to demonstrate how a combination of Sobolev methods and parameterization can be done successfully, using a novel mathematical result based on the generalized Faà di Bruno formula. Such a formulation can yield benefits even if a smooth parameterization is already used. The results obtained allow for the formulation of an efficient and flexible optimization strategy, which can incorporate the Sobolev smoothing procedure for test cases where a parameterization describes the shape, e.g., a CAD model, and where additional constraints on the geometry and the flow are to be considered. Furthermore, the algorithm is also extended to One Shot optimization methods. One Shot algorithms are a tool for simultaneous analysis and design when dealing with inexact flow and adjoint solutions in a PDE constrained optimization. The proposed parameterized Sobolev smoothing approach is especially beneficial in such a setting to ensure a fast and robust convergence towards an optimal design. Key features of the implementation of the algorithms developed herein are pointed out, including the construction of the Laplace-Beltrami operator via finite elements and an efficient evaluation of the parameterization Jacobian using algorithmic differentiation. The newly derived algorithms are applied to relevant test cases featuring drag minimization problems, particularly for three-dimensional flows with turbulent RANS equations. These problems include additional constraints on the flow, e.g., constant lift, and the geometry, e.g., minimal thickness. The Sobolev smoothing combined with the parameterization is applied in classical and One Shot optimization settings and is compared to other traditional optimization algorithms. The numerical results show a performance improvement in runtime for the new combined algorithm over a classical Quasi-Newton scheme

Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers

An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat complete configuration designs subject to multiple design points and geometric constraints. Examples are presented for both transonic and supersonic configurations ranging from wing alone designs to complex configuration designs involving wing, fuselage, nacelles and pylons

Continuous adjoint approach for the spalart-allmaras model in aerodynamic optimization

In this paper, the continuous adjoint method to compute shape sensitivities in aerodynamic design with turbulence modeling is described and developed. The focus is on compressible flows described by the Reynolds-averaged Navier-Stokes equations and the classical Spalart-Allmaras model for turbulence. Turbulence modeling usually requires, in particular, computation of the distance to the surface. Here, this distance is incorporated to the system as a new variable, solving the Eikonal equation. The accuracy of the sensitivity derivatives obtained with the complete turbulent approach is assessed by comparison with finite difference computations and the classical continuous adjoint with frozen viscosity, showing substantial improvements in the convergence properties of the method and in the quality of the obtained gradients. The validity of the overall methodology is illustrated with several design examples, including the optimization of three-dimensional geometries in combination with advanced freeform techniques for mesh deformation

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