Computational methods for aerodynamic shape design

A fast algorithm for inverse airfoil design using a transpiration model and an improved vortex panel method

“…There is no general accepted classification for airfoil design procedures. For instance, Yiu (1994) classifies them in four broad categories: (1) inverse methods (including iterative correction and nonlinear system approaches); (2) iterative modification methods (including here the very important optimization approach); (3) transformed plane method (including conformal mapping techniques); (4) special methods (including panel methods for incompressible potential flows). There is some superposition and mixing in this classification: for example, pure inverse methods can actually be implemented by means of both conformal mapping and integral equation formulations (for whose solution the panel method represents a classical numerical approach).…”

“…The method is based on a previously developed formulation employing a von Mises coordinate transformation (Barron, 1989). This approach was extended to general ideal steady flows (Latypov, 1993;Yiu, 1994), but it is also restricted to two-dimensional configurations.…”

A new generation of inverse shape design problem in aerodynamics and aerothermoelasticity: concepts, theory and methods

“…Although the first papers on inverse shape design of airfoils and cascades appeared as early as [1929][1930][1931][1932][1933][1934][1935][1936][1937][1938][1939][1940][1941][1942][1943][1944][1945] (Weinig, 1929;Mangler, 1938;Lighthill, 1945), the overwhelming majority of the literature on aerodynamics up to date deals only with the direct (analysis) problem (Dulikravich, 1992;Liu, 1995a;Yiu, 1994) and most turbomachine (TM) bladings and aircraft configurations are still designed by repeated use of direct problem methods in a cut-and-try manner, which is of course inconvenient, time-consuming and incapable of giving very rational results. This situation results possibly from the fact that, first, the inverse problem (to find the unknown boundary shape) is much more difficult to properly formulate as well as to solve than the direct one due to the presence of unknown boundaries, which is the origin of strong nonlinearity and possible ill-posedness, and second, the inverse design method often leads to airfoil/cascade shapes that are either unfeasible from practical design considerations or even unrealizable.…”

“…This situation results possibly from the fact that, first, the inverse problem (to find the unknown boundary shape) is much more difficult to properly formulate as well as to solve than the direct one due to the presence of unknown boundaries, which is the origin of strong nonlinearity and possible ill-posedness, and second, the inverse design method often leads to airfoil/cascade shapes that are either unfeasible from practical design considerations or even unrealizable. To circumvent these difficulties, it was proposed to extend the scope of aerodynamic problems to the following four categories (Table I) (Liu, 1980(Liu, , 1995aYiu, 1994):…”

A Cost Effective Approach for Subsonic Aeroelastic Stability Analysis of Turbomachinery 3D Blade Cascade. A Reduced Order Aeroelastic Model Numerical Approach

“…Since inverse optimization requires multiple iteration for small design change, there is not doubt why researchers in this field have favored BEM-PM or similar method. Some of the recent and more significant examples of use of PM for inverse optimization problem of axial compressor and turbine blade cascade optimization are [26,27,28,29]. Moreover, less sophisticated 3D unsteady vortex lattice method (UVLM) type boundary element method were used by [30,31,32].…”