This is the second part of a two-part paper. First, the design-optimization system basedon the adjoint gradient solution approach as described in Part I is introduced. Severaltest cases are studied for further validation and demonstration of the methodology andimplementation. The base-line adjoint method as applied to realistic 3D conﬁgurations isdemonstrated in the redesign of the NASA rotor 67 at a near-choke condition, leading toa 1.77% efﬁciency gain. The proposed adjoint mixing plane is applied to the redesign ofa transonic compressor stage (DLR compressor stage) and an IGV-rotor-stator conﬁgu-ration of a Siemens industrial compressor at a single-operating point, both producingmeasurably positive efﬁciency gains. An examination on the choice of the operating massﬂow condition as the basis for the performance optimization, however, highlights thelimitation of the single-point approach for practical applications. For the three-rowcompressor conﬁguration, a near peak-efﬁciency point based redesign leads to a mea-surable reduction in the choke mass ﬂow, while a near-choke point based redesign leadsto a signiﬁcant performance drop in other ﬂow conditions. Subsequently, a parallelmultipoint approach is implemented. The results show that a two-point design optimiza-tion can produce a consistently better performance over a whole range of mass ﬂowconditions compared with the original design. In the ﬁnal case, the effectiveness of thepresent method and system is demonstrated by a redesign applied to a seven-row indus-trial compressor at the design point, leading to a remarkable 2.4% efﬁciency gain.

Adjoint Aerodynamic Design Optimization for Blades in Multistage Turbomachines—Part II: Validation and Application

This paper presents the development of a collaborative optimization framework in combination with a variable-complexity modeling technique for the multidisciplinary coupling analysis and design of a shrouded turbine blade. The multidisciplinary optimization design of the shrouded turbine blade involves a high-fidelity detailed computational model and medium-fidelity models, which can become prohibitively expensive. In this investigation, a variable-complexity modeling methodology is introduced, where low-fidelity models and a scaling function are used to approximate the medium- and high-fidelity models through the optimizers in an inner-loop optimization to reduce computational expense. The optimization framework developed includes the collaborative optimization process, parametric modeling of the shrouded turbine blade, fluid–structure interaction solver using arbitrary Lagrangian–Eulerian formulation, an adaptive hexahedral structure mesh generator by establishing virtual blocks and parametric fixed poi...

Optimization Strategy for a Shrouded Turbine Blade Using Variable-Complexity Modeling Methodology

With the continuous growth in computing power, numerical optimisation is increasingly applied in shape optimisation using Computational Fluid Dynamics (CFD). Since CFD computations are expensive, gradient-based optimisation is preferable when the number of design variables is large. In particular the recent progress with adjoint solvers is important, as these solvers allow to compute the gradients at constant computational cost regardless of the number of design variables, and as a consequence enable the use of automatically derived and rich design spaces. One of the crucial steps in shape optimisation is the parametrisation of the geometry, which directly determines the design space and thus the final results. This thesis focuses on CAD-based parametrisations with the CAD model continuously updated in the design loop. An existing approach that automatically derives a parametrisation from the control points of a net of B-Spline patches is extended to include NURBS. Continuity constraints for water-tightness, tangency and curvature across patch interfaces are evaluated numerically and a basis for the resulting design space is computed using Singular Value Decomposition (SVD). A CAD-based shape optimisation framework is developed, coupling a flow solver, an adjoint solver, the in-house CAD kernel and a gradient-based optimiser. The flow sensitivities provided by the adjoint solver and the geometric sensitivities computed through automatic differentiation (AD) are assembled and provided to the optimiser. An extension to maintain the design space and hence enables use of a quasi-Newton method such as the BFGS algorithm is also presented and the convergence improvements are demonstrated. The framework is applied to three shape optimisation cases to show its effectiveness. The performance is assessed and analysed. The effect of parameters that can be chosen by the user are analysed over a range of cases and best practice choices are identified.

CAD-based geometry parametrisation for shape optimisation using Non-uniform Rational B-splines

An inverse design algorithm, called the ball-spine (BS) algorithm, is developed for the design of axial flow compressor blades. This algorithm has been previously applied to the design of 2D sharp leading edge airfoils. In the present study, the BS algorithm is extended to the design of blunt leading edge compressor blade sections. The algorithm receives a target pressure loading and an initial guess for its geometry. Through the design procedure, the geometry is evolved until the target pressure is achieved. The accuracy of the method is assessed against two airfoils, namely, NACA65-410 (with the initial guess for geometry as a flat-plate-airfoil) and NACA65-610 (with the initial guess for geometry as NACA65-410). The method is shown to be efficient and accurate, and can capture the target geometry in approximately 50 evolutions. As an application, a new airfoil with 5% more lift than NACA65-610 is designed, for which NACA65-610 geometry is used as the initial guess.

Applying the ball-spine algorithm to the design of blunt leading edge airfoils for axial flow compressors

Recently a new inverse design algorithm has been developed for the design of ducts, called ball-spine (BS). In the BS algorithm, the duct walls are considered as a set of virtual balls that can freely move along some specified directions, called ‘spines’. Initial geometry is guessed and the flow field is analyzed by a flow solver. Comparing the computed pressure distribution (CPD) with the target pressure distribution (TPD), new balls positions for the modified geometry are determined. This procedure is repeated until the target pressure is achieved. In the present work, the ball-spine algorithm is applied to three-dimensional design of axial compressor blades. The design procedure is tested on blades based on NACA65-410 and NACA65-610 profiles and the accuracy of the method is shown to be very good. As an application, the pressure distribution of the blade with NACA65-610 profiles is modified and the pressure gradient in the aft part of the blade is decreased and selected as target pressure distribution. The corresponding geometry which satisfies the target pressure is determined using the BS design algorithm.

https://jafmonline.net/JournalArchive/download?file_ID=37909&issue_ID=223

Three-Dimensional Design of Axial Flow Compressor Blades Using the Ball-Spine Algorithm

A blading design optimization system has been developed using an aeromechanical approach and harmonic perturbation method. The developed system has the capability to optimize aero-thermal performance with constraints of mechanical and aeromechanical integrity at the same time. ‘Aerodynamic mode shape’ is introduced to describe geometry deformation which can effectively reduce the number of design parameters while preserving surface smoothness. Compared to the existing design optimization practices, the present system is simpler, more accurate and effective. A redesign practice of the NASA rotor-67 at the peak efficiency point shows that the aero thermal efficiency can be improved by 0.4%, whilst the maximum static stress has been increased by 33%. Aeromechanical analysis of the optimized blade shows that the aerodynamic damping of the least stable first flap mode is still well above the critical value though the natural frequencies of the first 5 modes have been reduced by 1~4%. The present finding highlights the need for more concurrent integrations of mechanics, aerodynamics and aeromechanics design

Blading Aerodynamics Design Optimization With Mechanical and Aeromechanical Constraints

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Blading Aerodynamics Design Optimization With Mechanical and Aeromechanical Constraints