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Chapter 1 Introduction In the design of turbomachinery blading, there are two problems that are of in- terest. One is the direct approach and the other is the "inverse" approach. In the direct approach the designer specifies the geometrical configuration and computes the performance at design or off-design operating point (e.g. possibly through the use of an Euler or Navier-Stokes code). In the inverse method, the blade geometry is deter- mined to yield a specified performance characteristic. In the next section, a review of previous work on inverse design of turbomachinery blading will be presented. The review has intentionally been focused on inverse design of turbomachinery blading in three-dimensional flow. Since the direct approaches based on Euler solver and Navier- Stokes solver are quite commonly known, no attempt will be made to review these works. Following the section on review, the technical objective of the present work is stated and the approach taken to accomplish the stated objective is described. Finally we present the organization of this thesis. 1.1 Review of Previous Work In contrast to the direct problem, research activities pertaining to the inverse design problem has not been extensive; this is especially so in three-dimensional flow. One of the earliest work is found in Ref. 4, in which Tan at al. presented an inverse design technique for highly loaded blades in annular cascades. The flow equations are solved by spectral methods in which the velocity is represented by a Fourier Series in the tangential direction and a Bessel Series in the radial direction. The blade wrap angle is represented by a Chebyshev Series in the axial direction and a Cosine Series in the radial direction. Borges (Ref. 22) applied this inverse design technique for the design of aPDF Image | Radial Inflow Splitter Blades in Three-Dimensional
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