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- Amoignon, Olivier, 1969-
(författare)
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Numerical Methods for Aerodynamic Shape Optimization
- 2005
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Gradient-based aerodynamic shape optimization, based on Computational Fluid Dynamics analysis of the flow, is a method that can automatically improve designs of aircraft components. The prospect is to reduce a cost function that reflects aerodynamic performances.When the shape is described by a large number of parameters, the calculation of one gradient of the cost function is only feasible by recourse to techniques that are derived from the theory of optimal control. In order to obtain the best computational efficiency, the so called adjoint method is applied here on the complete mapping, from the parameters of design to the values of the cost function. The mapping considered here includes the Euler equations for compressible flow discretized on unstructured meshes by a median-dual finite-volume scheme, the primal-to-dual mesh transformation, the mesh deformation, and the parameterization. The results of the present research concern the detailed derivations of expressions, equations, and algorithms that are necessary to calculate the gradient of the cost function. The discrete adjoint of the Euler equations and the exact dual-to-primal transformation of the gradient have been implemented for 2D and 3D applications in the code Edge, a program of Computational Fluid Dynamics used by Swedish industries.Moreover, techniques are proposed here in the aim to further reduce the computational cost of aerodynamic shape optimization. For instance, an interpolation scheme is derived based on Radial Basis Functions that can execute the deformation of unstructured meshes faster than methods based on an elliptic equation.In order to improve the accuracy of the shape, obtained by numerical optimization, a moving mesh adaptation scheme is realized based on a variable diffusivity equation of Winslow type. This adaptation has been successfully applied on a simple case of shape optimization involving a supersonic flow. An interpolation technique has been derived based on a mollifier in order to improve the convergence of the coupled mesh-flow equations entering the adaptive scheme.The method of adjoint derived here has also been applied successfully when coupling the Euler equations with the boundary-layer and parabolized stability equations, with the aim to delay the laminar-to-turbulent transition of the flow. The delay of transition is an efficient way to reduce the drag due to viscosity at high Reynolds numbers.
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| 2. |
- Amoignon, Olivier
(författare)
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Adjoint-based aerodynamic shape optimization
- 2003
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- An adjoint system of the Euler equations of gas dynamics is derived in order to solve aerodynamic shape optimization problems with gradient-based methods. The derivation is based on the fully discrete flow model and involves differentiation and transposition of the system of equations obtained by an unstructured and node-centered finite-volume discretization. Solving the adjoint equations allows an efficient calculation of gradients, also when the subject of optimization is described by hundreds or thousands of design parameters.Such a fine geometry description may cause wavy or otherwise irregular designs during the optimization process. Using the one-to-one mapping defined by a Poisson problem is a known technique that produces smooth design updates while keeping a fine resolution of the geometry. This technique is extended here to combine the smoothing effect with constraints on the geometry, by defining the design updates as solutions of a quadratic programming problem associated with the Poisson problem.These methods are applied to airfoil shape optimization for reduction of the wave drag, that is, the drag caused by gas dynamic effects that occur close to the speed of sound. A second application concerns airfoil design optimization to delay the laminar-to-turbulent transition point in the boundary layer in order to reduce the drag. The latter application has been performed by the author with collaborators, also using gradient-based optimization. Here, the growth of convectively unstable disturbances are modeled by successively solving the Euler equations, the boundary layer equations, and the parabolized stability equations.
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| 4. |
- Amoignon, Olivier, et al.
(författare)
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Adjoint of a median-dual finite-volume scheme : Application to transonic aerodynamic shape optimization
- 2006
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The sensitivity analysis is a crucial step in algorithms for gradient-based aerodynamic shape optimization. The analysis involves computing the gradient of functionals such as drag, lift, or aerodynamic moments, with respect to the parameters of the design. Gradients are efficiently calculated by solving adjoints of the linearized flow equations. The flow is modeled by the Euler equations of gas dynamics, solved in Edge, a Computational Fluid Dynamics (CFD) code for unstructured meshes. The adjoint equations and expressions for the gradients are derived here in the fully discrete case, that is, the mappings from the design variables to the functional's values involve the discretized flow equations, a mesh deformation equation, and the parameterization of the geometry. We present a formalism and basic properties that enable a compact derivation of the adjoint for discretized flow equations obeying an edge-based structure, such as the vertex-centered median-dual finite volume discretization implemented in Edge. This approach is applied here to the optimization of the RAE 2822 airfoil and the ONERA M6 wing. In particular, we show a method to parameterize the shape, in 2D, in order to enforce smoothness and linear geometrical constraints.
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| 7. |
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| 8. |
- Amoignon, Olivier, et al.
(författare)
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Shape optimization for delay of laminar-turbulent transition
- 2006
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Ingår i: AIAA Journal. - : American Institute of Aeronautics and Astronautics (AIAA). - 0001-1452 .- 1533-385X. ; 44:5, s. 1009-1024
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Tidskriftsartikel (refereegranskat)abstract
- A method using gradient-based optimization is introduced for the design of wing profiles with the aim of natural laminar How, as well as minimum wave drag. The Euler equations of gasdynamics, the laminar boundary-layer equations for compressible flows on infinite swept wings, and the linear parabolized stability equations (PSE) are solved to analyze the evolution of convectively unstable disturbances. Laminar-turbulent transition is assumed to be delayed by minimizing a measure of the disturbance kinetic energy of a chosen disturbance, which is computed using the PSE. The shape gradients of the disturbance kinetic energy are computed based on the solutions of the adjoints of the state equations just named. Numerical tests are carried out to optimize the RAE 2822 airfoil with the aim to delay simultaneously the transition, reduce the pressure drag coefficient, and maintain the coefficients of lift and pitch moments. Constraints are also applied on the geometry. Results show a reduction of the total amplification of a large number of disturbances, which is assumed to represent a delay of the transition in the boundary layer. Because delay of the transition implies reduction of the viscous drag, the present method enables shape optimization to perform viscous drag reduction.
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