Solvability condition and its application to fast numerical solution of overposed inverse problems in compressible flows

A fast iterative inverse method for turbomachinery blade design

“…Since this has been analytically proved for incompressible flow it is expected the same to be true for transonic flow (Daripa, 1991).…”

“…Volpe and Melnik (1981) showed empirically that constraints similar to those for incompressible flow also exist for compressible flow. More recently, Daripa (1991) presented an analysis for the inverse problem in compressible flow, but the transonic problem with shock waves remains analytically unsolved (Demeulenaere and van den Braembussche, 1998;Lee and Mason, 2000).…”

A viscous inverse method for aerodynamic design

“…Lighthill discovered the solvability conditions that have to be respected by pressure distributions within an incompressible potential flow model [6], whereas the similar integral conditions for compressible flows and other issues were investigated in Refs. [13,11,3,8]. These issues are typical of problem as airfoil or blade inverse design since they are related to the closure of the body contour.…”

“…As an initial step, the study is limited to two-dimensional and axisymmetric flows, but the procedure can be straightly applied to threedimensional cases. The design case of wing or blade profiles is also feasible, but it is not considered here, since it merits a more extended discussion about the way of formulating the inverse problem and to satisfy or to overcome the related well-posedness issues [3,8,13,21].…”

“…First approaches to the solution of inverse problems were based on the potential flow theory and conformal mapping techniques [5][6][7][8]. Other methods replace the body surface with singularity distributions while also trying to simulate boundary layer blockage [9].…”