In turbomachinery blade design, inverse methods and optimization techniques are often applied independently to produce high performance blade shapes. The idea of using an optimization algorithm to seek the optimal target distribution for an inverse design methodology has been explored. However, these efforts have been made mainly in the design of single aerofoils. In this paper, a new inverse design method is coupled with a simulated annealing algorithm to search for the optimum turbomachinery cascade shape. In order to speed up the algorithm, a database of generated designs is set up and the nearest match is selected to initialize subsequent calculation. The proposed computational procedure equips engineers with an automatic design tool with which the inverse method may be applied in isolation or combined with the optimization algorithm to produce the optimum.The inverse methodology is based on a cell vertex, nite volume time-marching ow solver that gives the viscous cascade ow solution in both the subsonic and the transonic ow regimes. The cascade shape is computed subject to an imposed distribution of the mass-averaged tangential velocity and a speci ed tangential thickness pro le. The solver code is validated using experimental data and the accuracy of the inverse method is veri ed by regenerating a known cascade geometry starting from a different one using its mass-averaged tangential velocity distribution. In combining the inverse methodology with the optimization algorithm, the mass-averaged tangential velocity distribution is parametrized using a cubic B-spline curve and the proposed simulated annealing algorithm is applied to predict the optimal distribution by minimizing loss. The overall procedure is demonstrated to produce optimum shapes of a transonic axial turbine and an axial compressor rotor.

The development and application of a three-dimensional inverse methodology in which the blade geometry is computed on the basis of the speci cation of static pressure loading distribution is presented. The methodology is based on the intensive use of computational uid dynamics (CFD) to account for three-dimensional subsonic and transonic viscous ows. In the design computation, the necessary blade changes are determined directly by the discrepancies between the target and initial values, and the calculation converges to give the nal blade geometry and the corresponding steady state ow solution. The application of the method is explored using a transonic test case, NASA rotor 67. Based on observations, it is conclusive that the shock formation and its intensity in such a high-speed turbomachinery ow are well de ned on the loading distributions. Pressure loading is therefore as effective a design parameter as conventional inverse design quantities such as static pressure. Hence, from an understanding of the dynamics of the ow in the fan in relation to its pressure loading distributions, simple guidelines can be developed for the inverse method in order to weaken the shock formation. A qualitative improvement in performance is achieved in the redesigned fan. The nal ow eld result is con rmed by a well-established commercial CFD package.

An inverse design methodology is presented for the design of turbomachinery blades using a cell-vertex finite volume time-marching algorithm in transonic viscous flow. In this method the blade shape is designed subject to a specified distribution of pressure loading (the difference in pressure across the blade) and thickness distribution. The difference between specified pressure loading and the pressures on the initial blade shape results in a normal velocity through the blade, which is then used to update the blade shapes. Viscous effects are represented by using a distributed body force. A simple and fast iterative scheme is proposed for automatically finding a suitable pressure loading that will provide a specified flow turning (or specific work). The method, therefore, can be applied to the design of new blade geometry without any need to supply information on the initial blade geometry or the blade loading corresponding to an existing design. The Euler solver is first validated by using experimental data for a turbine stage. The accuracy of the inverse procedure is then verified by designing the stator blade from the computed pressure loading. Finally the method is applied to the design of an axial transonic turbine stator and an axial compressor rotor and stator blade.

The development and application of a three-dimensional inverse methodology is presented for the design of turbomachinery blades. The method is based on the mass-averaged swirl, rV~θ distribution and computes the necessary blade changes directly from the discrepancies between the target and initial distributions. The flow solution and blade modification converge simultaneously giving the final blade geometry and the corresponding steady state flow solution. The flow analysis is performed using a cell-vertex finite volume time-marching algorithm employing the multistage Runge-Kutta integrator in conjunction with accelerating techniques (local time stepping and grid sequencing). To account for viscous effects, dissipative forces are included in the Euler solver using the log-law and mixing length models. The design method can be used with any existing solver solving the same flow equations without any modifications to the blade surface wall boundary condition. Validation of the method has been carried out using a transonic annular turbine nozzle and NASA rotor 67. Finally, the method is demonstrated on the re-design of the blades.