Application of simulated annealing to inverse design of transonic turbomachinery cascades

Abstract

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.

Advances in Aerodynamic Design of Gas Turbines Compressors

“…Quite a new approach to the 3D design of axial compressor bladings has been recently proposed by Tiow, 2002. In this work, an inverse method was presented which is based on the flow governed by the Euler equations of motion and improved with viscous effects modelled using a body force model as given by Denton, 1987.…”

“…However, contrary to the methods cited above, the methodology is capable of providing designs directly for a specific work rotor blading using the mass-averaged swirl velocity distribution. Moreover, the methodology proposed by Tiow, 2002 joins the capabilities of an inverse design with the search potential of an optimization tool, in this case the simulated annealing algorithm (Kirkpatrick et al, 1983). The entire computation required minimal human intervention except during initial set-up where constraints based on existing knowledge may be imposed to restrict the search for the optimal performance to a specified domain of interest.…”

Study on adjoint-based optimization method for multi-stage turbomachinery

“…To eliminate the constraints of problem (3), flow equations (1) are introduced into the objective function (2) using Lagrange multiplier vector λ (also known as adjoint variable vector). A new equivalent objective function is,…”

“…Inverse design is intuitive and designers with plentiful experience are preferred. It can be further classified into conventional inverse design [1] and inverse optimization design [2]. Though the cost of conventional inverse design is relatively low, the method itself is very difficult.…”

Inverse-design and optimization methods for centrifugal pump impellers

“…the simplex method and the alternating-variables method. This approach was further extended by Tiow et al [67], who used simulated annealing as optimization algorithm. They successfully applied the method to the design of a compressor rotor and a turbine stator.…”