A direct design approach using the Euler equations

Self Cite

Inverse shape design in the context of fluid flow problems is commonly referred to the determination of the boundary shape corresponding to a given target surface pressure. Designers naturally turn to this class of problems whenever there are concerns regarding pressure-related phenomena such as cavitation, separation, shock waves, surface loading, etc. Numerical solution is often unavoidable and, therefore, three computational tools, i.e. a grid generator, a flow field solver and a shape updater, are required in an iterative solution procedure. In all existing iterative inverse design methods, the shape updater comes from separate mathematical or physical considerations that are not derived solely from the equations governing the flow field. In this paper, the currently used strategies to solve inverse shape design problems are categorized and reviewed, and then a truly physical-based iterative inverse shape design method is introduced in which the governing equations are not only used in the flow solver, but are also employed to update the shape. To explore the features of the proposed method, it is used to solve a number of shape design problems. The previously developed direct shape design method and a typical iterative solution approach are also explained and used for the solution of the same problems for the purpose of comparison. Computational results reveal that the proposed algorithm has a two to three times faster convergence rate as compared to the iterative algorithm. The convergence rate of the proposed algorithm usually stalls after three or two orders of magnitude reduction of the residual. For the test cases in this study, the direct design method is the fastest and most accurate method as compared to other algorithms. Both inhouse developed computer codes and commercial software are used as a field solver to show the general applicability of the proposed method in its current state of development.

Section: Inverse Problems In Science and Engineeringmentioning

confidence: 99%

Inverse shape design via a new physical-based iterative solution strategy

Nikfar

Ashrafizadeh

Mayeli

2014

Self Cite

“…Approaches to the inverse problem solution are based on the potential flow theory and conformal mapping techniques, [4,7,8] on stream-function base formulations, [9][10][11] on boundary elements replacing the body surface [12] and on direct design methods. [13][14][15][16] Several examples of inverse problem solution methodologies are presented in [5,17] and references therein.…”

Section: Introductionmentioning

confidence: 99%

A pseudo-compressibility method for solving inverse problems based on the 3D incompressible Euler equations

Ferlauto

2014

A numerical technique to solve the three-dimensional inverse problems that arise in aerodynamic design is presented. The approach, which is well established for compressible flows, is extended to the incompressible case via artificial compressibility preconditioning. The modified system of equations is integrated with a characteristic-based Godunov method. The solution of the inverse problem is given as the steady state of an ideal transient during which the flow field assesses itself to the boundary conditions, which are prescribed as design data, by changing the boundary contour. The main aspects of the Eulerian-Lagrangian numerical procedure are illustrated and the results are validated by comparing with theoretical solutions and experimental results.

“…This fully coupled shape design method was called the direct design method. Taeibi-Rahni et al [21] have employed the direct design approach to design ducts in the context of the Euler flow model. The direct design approach has not been applied in viscous flow shape design problems yet.…”

Section: Introductionmentioning

confidence: 99%

A semi-coupled solution algorithm in aerodynamic inverse shape design

Ashrafizadeh

Okhovat

Pourbagian

et al. 2011

The numerical solution of an inverse airfoil design problem requires computational tools for grid generation, flow solution and the geometry update to provide the desirable shape corresponding to a given surface target pressure. Un-coupled as well as fully and semi-coupled shape design strategies have already been developed and employed. The target pressure is directly imposed in the fully coupled approach in contrast to un-coupled methods. Available semi-coupled methods use additional computational tools to couple the flow solver and the shape updater to directly impose the target pressure. In this article, a semicoupled numerical shape design strategy is introduced, in the context of an ideal flow model, in which the target tangential velocity is directly imposed while no additional computational tool is employed. Numerical test cases, implemented on both structured and unstructured grids, are carried out to compare the performance of the proposed method with an adjoint-based optimization technique. Results show that the semi-coupled method has a two to three times faster convergence rate as compared to the adjoint approach. However, the semicoupled solution convergence rate usually stalls after three orders of magnitude reduction of the objective function, while the un-coupled optimization method provides a more accurate solution. Therefore, a hybrid solution methodology is also advised, which provides faster convergence as well as lower computational errors as compared to both semi and un-coupled methods.