Advances in research on inverse and hybrid problems of turbomachinery aerothermodynamics in China

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

“…A number of methods have been proposed for its solution such as conformal mapping, singularity method, hodograph method, channel method etc. (Dulikravich, 1992;Liu, 1995a;Yiu, 1994).…”

“…If, however, the second way is followed instead (Mangler, 1938;Dulikravich, 1992), the profile closure can be attained very easily by imposing simple boundary conditions, without resorting to any integral closure constraints. This not only significantly simplifies the solution process, but also allows full freedom of specifying wall velocity distribution (Liu, 1995a). Just for this reason, the second way is employed throughout the present author's research and is highly recommended for widespread application.…”

“…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):…”

The effect of variations in first- and second-order derivatives on airfoil aerodynamic performance

“…Based on G. L. Liu's (1995) variable domain theory for airfoil aerodynamic airfoil design, a numerical simulation program has been developed using a technique called the potential function method. The flow field around the airfoil can thus be modeled and analyzed relatively easily.…”