The FDM solution of unsteady inverse problem for two‐dimensional oscillating airfoils

Abstract

PurposeThis paper seeks to develop an approach for the unsteady inverse problem of two‐dimensional oscillating airfoils based on the finite difference method (FDM) solution of the transient Euler equations.Design/methodology/approachThe solution strategies are determined according to the mathematical model for the inverse‐problem of oscillating airfoils. Then the unsteady nonreflecting far field boundary condition and the permeable wall boundary condition are employed to treat the boundary conditions. The applications are carried out for the modification of an oscillating airfoil according to the design targets of the unsteady pressure distribution in an oscillating period.FindingsThe results show that the pressure distributions over the new airfoils coincide with the design objects indicating that the mathematical model and solution strategy developed in this paper is rational and reliable.Research limitations/implicationsThis method is limited to frictionless flow.Originality/valueThe paper provides a new FDM solution of unsteady inverse problem for oscillating airfoils, which can be extended to treat the multipoint problem of airfoil design.