Adjoint Aerodynamic Design Optimization for Blades in Multi-Stage Turbomachines: Part I—Methodology and Verification

The adjoint method for blade design optimization will be described in this two-part paper. The main objective is to develop the capability of carrying out aerodynamic blading shape design optimization in a multistage turbomachinery environment. To this end, an adjoint mixing-plane treatment has been proposed. In the first part, the numerical elements pertinent to the present approach will be described. Attention is paid to the exactly opposite propagation of the adjoint characteristics against the physical flow characteristics, providing a simple and consistent guidance in the adjoint method development and applications. The adjoint mixing-plane treatment is formulated to have the two fundamental features of its counterpart in the physical flow domain: conservation and nonreflectiveness across the interface. The adjoint solver is verified by comparing gradient results with a direct finite difference method and through a 2D inverse design. The adjoint mixing-plane treatment is verified by comparing gradient results against those by the finite difference method for a 2D compressor stage. The redesign of the 2D compressor stage further demonstrates the validity of the adjoint mixing-plane treatment and the benefit of using it in a multi-bladerow environment. DOI: 10.1115/1.3072498

[1]  Michael B. Giles,et al.  The harmonic adjoint approach to unsteady turbomachinery design , 2002 .

[2]  Meng-Sing Liou,et al.  Transonic Axial-Flow Blade Optimization: Evolutionary Algorithms/Three-Dimensional Navier-Stokes Solver , 2004 .

[3]  J. H. Horlock,et al.  A Review of Some Early Design Practice Using Computational Fluid Dynamics and a Current , 2005 .

[4]  A. Jameson,et al.  A COMPARISON OF THE CONTINUOUS AND DISCRETE ADJOINT APPROACH TO AUTOMATIC AERODYNAMIC OPTIMIZATION , 2000 .

[5]  P. Rentrop,et al.  An adjoint approach to optimal design of turbine blades , 2005 .

[6]  Antony Jameson,et al.  OPTIMAL CONTROL OF UNSTEADY FLOWS USING A TIME ACCURATE METHOD , 2002 .

[7]  Fernando Gisbert,et al.  Profiled End-Wall Design Using an Adjoint Navier-Stokes Solver , 2006 .

[8]  K. Giannakoglou,et al.  COMPRESSOR BLADE OPTIMIZATION USING A CONTINUOUS ADJOINT FORMULATION , 2006 .

[9]  Shahrokh Shahpar,et al.  Turbomachinery Design Optimization Using Automatic Differentiated Adjoint Code , 2007 .

[10]  Luis Santos,et al.  Aerodynamic shape optimization using the adjoint method , 2007 .

[11]  Feng Liu,et al.  Optimum Aerodynamic Design of Cascades by Using an Adjoint Equation Method , 2003 .

[12]  Kenneth C. Hall,et al.  Sensitivity Analysis of Unsteady Inviscid Flow Through Turbomachinery Cascades , 2001 .

[13]  Li He,et al.  Adjoint Aerodynamic Design Optimization for Blades in Multistage Turbomachines—Part II: Validation and Application , 2010 .

[14]  V. N. Vatsa,et al.  Computation of sensitivity derivatives of Navier-Stokes equations using complex variables , 2000 .

[15]  H. Starken,et al.  Redesign and performance analysis of a transonic axial compressor stator and equivalent plane cascades with subsonic controlled diffusion blades , 1984 .

[16]  Gianfranco Guidati,et al.  Automated Design Optimization of Compressor Blades for Stationary, Large-Scale Turbomachinery , 2003 .

[17]  Meng-Sing Liou,et al.  Multi-Objective Optimization of Transonic Compressor Blade Using Evolutionary Algorithm , 2005 .

[18]  Dieter Bestle,et al.  Modern Compressor Aerodynamic Blading Process using Multi-objective Optimization , 2006 .

[19]  J. Eric,et al.  Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations , 1998 .

[20]  Kazuhiro Nakahashi,et al.  Discrete Adjoint Method for Unstructured Navier-Stokes Solver , 2005 .

[21]  A. Jameson,et al.  Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation , 1996 .

[22]  A. Jameson,et al.  Optimum Shape Design for Unsteady Three-Dimensional Viscous Flows Using a Nonlinear Frequency-Domain Method , 2006 .

[23]  André Pierre Saxer,et al.  A numerical analysis of 3-D inviscid stator/rotor interactions using non-reflecting boundary conditions , 1992 .

[24]  R. A. Van den Braembussche,et al.  A Novel Two-Dimensional Viscous Inverse Design Method for Turbomachinery Blading , 2003 .

[25]  W. Ning,et al.  Efficient Approach for Analysis of Unsteady Viscous Flows in Turbomachines , 1998 .

[26]  Li He,et al.  Analysis of Rotor-Rotor and Stator-Stator Interferences in Multi-Stage Turbomachines , 2002 .

[27]  Weilin Yi,et al.  Design Optimization of Transonic Compressor Rotor Using CFD and Genetic Algorithm , 2006 .

[28]  Thong Q Dang,et al.  Improving aerodynamic matching of axial compressor blading using a three-dimensional multistage inverse design method , 2007 .

[29]  Antony Jameson,et al.  Aerodynamic design via control theory , 1988, J. Sci. Comput..

[30]  Her Mann Tsai,et al.  Aerodynamic Design of Turbine Blades Using an Adjoint Equation Method , 2005 .

[31]  Li He,et al.  Blade Forced Response Prediction for Industrial Gas Turbines , 2005 .

[32]  John D. Denton,et al.  Three-dimensional time-marching inviscid and viscous solutions for unsteady flows around vibrating blades , 1993 .

[33]  J. D. Denton,et al.  The Calculation of Three-Dimensional Viscous Flow Through Multistage Turbomachines , 1992 .

[34]  Niles A. Pierce,et al.  An Introduction to the Adjoint Approach to Design , 2000 .

[35]  Zhenping Feng,et al.  Inverse Problem in Aerodynamic Shape Design of Turbomachinery Blades , 2006 .