A forward and inverse three-dimensional linear design system for turbomachinery applications

The use of linear perturbation theory to produce a three-dimensional linear design system for turbomachinery applications is presented. The elements of the theory are: the construction of a linear sensitivity matrix using numerical differentiation; the theory of superposition to construct new geoemtries and flow fields; and, inverse design through matrix inversion and Quasi-Newton techniques. This paper discusses the underlying linear approximations behind the design method, with regard to complicated 3D viscous flows in turbomachines. Comparisons are made between results using the linear theory and those from full non-linear CFD solutions.