Multipoint Design Optimization of a Transonic Compressor Blade by Using an Adjoint Method

Abstract

This paper presents the application of a viscous adjoint method to the multipoint design optimization of a rotor blade through blade profiling. The adjoint method requires about twice the computational effort of the flow solution to obtain the complete gradient information at each operating condition, regardless of the number of design parameters. NASA Rotor 67 is redesigned through blade profiling. A single point design optimization is first performed to verify the effectiveness and feasibility of the optimization method. Then in order to improve the performance for a wide range of operating conditions, the blade is redesigned at three operating conditions: near peak efficiency, near stall, and near choke. Entropy production through the blade row combined with the constraints of mass flow rate and total pressure ratio is used as the objective function. The design results are presented in detail and the effects of blade profiling on performance improvement and shock/tip-leakage interaction are examined.

A discrete adjoint harmonic balance method for turbomachinery shape optimization

“…The difficulty in developing the adjoint form of the nonreflecting and the mixing plane boundary conditions has hindered its application for turbomachinery flows until recently [11,27,28,32,[43][44][45][46]. Frey et al [11] described a systematic approach to develop a discrete adjoint solver for turbomachinery optimization including the adjoint boundary conditions for the conservative mixing planes.…”

“…Marta et al [32] discussed physical meaning of steady adjoint solutions for turbomachinery. Luo et al [28] presented optimization of the NASA Rotor 67 fan by using a threedimensional viscous adjoint solver and redesigned the blades for three different operating conditions; namely, near peak efficiency, near stall, and near choke. Walther and Nadarajah [44] performed a constrained aerodynamic shape optimization for a transonic compressor in a multistage environment.…”

A Comparative Study of Two Different CAD-Based Mesh Deformation Methods for Structural Shape Optimization

“…[1][2][3] Gradient-free methods are non-intrusive and do not require source code access to implement. On the other hand, they require a high number of iterations to converge and are limited by the curse of dimensionality.…”

Adjoint-Based Constrained Aerodynamic Shape Optimization for Multistage Turbomachines

“…Moreover, while Li et al [24] utilized the continuous adjoint approach to perform aerodynamic shape optimization on a turbine cascade in two-dimensional turbulent flow, an adjoint-based optimization of a three-dimensional turbine stator in which the stagger angle was used as a design variable in addition to the profile shape was presented by Luo et al [25] in 2011. Luo et al [26] also applied the adjoint method to constrained multipoint optimization; they treated the constraints by a penalty function approach and redesigned Rotor 67 through blade profiling while considering three different compressor operation points. Finally, in 2010 and 2011, Mousavi and Nadarajah [27,28] used the continuous adjoint approach to optimize the heat transfer in cooled gas turbine blades by defining the profile shape, the location of the cooling hole and the coolant injection angle as the design variables.…”

“…Specifically, F 2 is a hyperbolic tangent function defined as 26) with the argument 27) where 28) and d is the distance from the field point to the nearest no-slip boundary. Note, in…”