Turbomachinery Aerodynamic Shape Optimization Approach Using Adjoint Method And Its Applications For Blade Detail Design

Detail design can further improve blade aerodynamic loading. But turbomachin-ery aerodynamic shape design based on optimization algorithms and three-dimensional flow analysis is always too time-consuming. Manipulating hun-dreds of design variables to implement blade detail design with low computing cost is desirable for routine design. Differing with traditional gradient methods, the compu-ting cost of adjoint method is regardless of the number of design variables. In recent years, it has received considerable attentions in turbomachinery community. This pa-per presents investigations on multi-stage turbomachinery aerodynamic shape design using adjoint method, aiming to reduce design cycle and implement blade detail de-sign. The main contents with five parts are as follows:1. A general sensitivity-analysis modelCompare the sensitivity-analysis principle of adjoint method and traditional gra-dient methods. Results show that the computing cost of adjoint method is low and roughly equivalent to solve two sets of flow equations. Further, derive a general sen-sitivity-analysis model of objective function to design variables based on adjoint method. The model includes adjoint equations, adjoint boundary conditions, and a general sensitivity expression.2. Turbomachinery aerodynamic shape design approachThe objective functions of direct and inverse problems are specified. The pres-sure-ratio and mass-flow-rate constraints are introduced as penalty functions to re-main the low computing cost of adjoint method.3D blade perturbation parameteriza-tion based on Hicks-Henne hump functions is used to fit blade profile perturbation without blade geometry reconstruction. The thin shear-layer viscous body force and wall function with flow slip boundary condition can predict the wall boundary layer properly with low computing cost, and are adopted to detail the general sensitivity model. Further, an adjoint mixing-plane treatment is proposed to close the solution of adjoint equations, and thus sensitivity analysis is achieved in multi-stage tur- bomachinery conveniently. Integrated with the simple steepest method, a frame of an adjoint-based multi-stage turbomachinery aerodynamic shape design approach is con-structed and can be used for stage-matching design.3. Turbomachinery aerodynamic shape design softwareScheme of3D blade perturbation parameterization is given and simple H-type grid is generated using algebraic method. The numerical simulation of thin shear-layer N-S equations and adjoint equations is based on time-marching method and finite volume method. The way to implement boundary conditions depends on prorogation directions of characteristic information. Local time step method, multi-grid method, and blended second and fourth order numerical dissipation method are used to accel-erate the solving process. Sensitivity can be calculated as a post-process of flow field and adjoint field using complex method. And quantitative modifications of blade pro-files are searched by the simple steepest method and blade perturbation parameteriza-tion. Thus, turbomachinery aerodynamic shape design software is developed, includ-ing three main sub-solvers:flow solver, adjoint solver and sensitivity calculator.4. Validation of the model, approach and softwareFirstly, check flow-field prediction of NASA35transonic compressor stage us-ing flow solver against test data. Results show that it seizes key flow features and main aerodynamic parameters are agreed well. Secondly, calculate the value of sensi-tivity using adjoint method and finite difference method with the objective function of inverse problem for turbine annular cascade and1+1/2stage axial compressor. The error of the two method don’t exceed10%. Thirdly, again implement inverse optimi-zation design of the two cases to show the capability of the approach and software. The optimized blade profiles and pressure distributions agree well with the target, and thus the approach and software are validated.5. Applications to turbomachinery aerodynamic shape detail designTo increase aerodynamic efficiency and keep mass flow rate and stagnation pressure ratio unchanged, turbomachinery aerodynamic shape detail design aiming to minimize inlet and outlet mass-averaged entropy production rate and subjecting mass flow rate and stagnation pressure ratio constraints is investigated from lessons of NASA67rotor, NASA35transonic compressor stage,1+1/2stage transonic com-pressor,5+1/2stage transonic compressor and the first three rows of1+1stage coun-ter-rotating turbine. The optimised blades increases their adiabatic efficiency by1.38%、1.41%、0.91%、1.30%and0.42%points respectively while the two constraints are satisfied. The performance improvements are realized by minimizing peak Mach number, shock intensity and flow separation for transonic/supersonic flows, and fine tuning incidence angle distribution to reduce flow loss for subsonic flows.At last, this paper concludes the overall work and posts some prospects of tur-bomachinery aerodynamic shape design using adjoint method.