Numerical optimization is becoming an essential industrial method in engineering design for shapes immersed in fluids. High-fidelity optimization requires fine design spaces with many desig...

/pdf/nurbs-based-and-parametric-based-shape-optimisation-with-3lzxc0cum0.pdf

NURBS-based and Parametric-based Shape Optimisation with differentiated CAD Kernel

This paper addresses the consideration of manufacturing effects of gas turbine blades in a probabilistic setting. Currently, during design these effects are covered by safety factors and conservative assumptions. The probabilistic investigation, on the other hand, will enable us to calculate the effect of variability on stresses and relevant aerodynamic quantities such as efficiency, thus providing the foundation for robust blade design. A set of 500 new and used turbine blades, provided by Rolls-Royce Deutschland, was digitised with an optical scan system. Cooling holes and abrasion effects were statistically analysed and removed from the scanned data set. Classical turbine parameters were identified. Finally, the variability (probability density functions and corresponding parameters) of the geometric parameters can be calculated according to the digitised geometries and the manufacturing process can be statistically analysed. The presented parametric model will provide the basis for upcoming numerical probabilistic assessment of the real geometric effects.

A parametric model for probabilistic analysis of turbine blades considering real geometric effects

Turbomachinery blades are an integral part of air breathing propulsion systems, gas and steam turbines and other energy conversion devices. The blade design is a very important process since it defines component performance. A parametric approach for the blade geometry design has been implemented. A variety of three dimensional blade shapes can be created using only a few basic parameters and limited interaction with a CAD system. Using a general approach for creating the blade geometries makes the process easy and robust for creating 3D blade shapes for various turbomachinery components. The geometry of the blade is defined by a very basic set of geometric and aerodynamic parameters. Parameters such as flow angles, axial chord, thickness to chord ratio and streamline meridional coordinates are defined. The leading edge and trailing edge are defined by curves as part of the input. Using these parameters, a specified number of 2D airfoils are created and are radially stacked on the desired stacking axis. The sweep and lean perturbations of the blade are defined by splines as a function of a few control points. The design tool generates a specified number of 3D blade sections and each section consists of a defined number of coordinates in the cartesian coordinate system. These sections can be lofted in a CAD package to obtain a solid 3D blade model, which has been demonstrated using Unigraphics-NX. Parametric update of the spline points defining the 3D blade sections creates new blade shapes without going back into the CAD interface. This approach for the design is very beneficial as the geometry can be modified quickly and easily as per the needs of the designer at any point of time. Using this tool, blade shapes of a 10 stage compressor similar to the GE/NASA EEE HPC, a 3 stage booster, a reverse engineered GE 1.5 MW wind turbine and a centrifugal compressor based on a NASA design are constructed as examples. The general capabilty of the design tool is demonstrated through these examples.

Parametric 3D Blade Geometry Modeling Tool for Turbomachinery Systems

The focus of the paper is on procedures and strategies to compute high-fidelity compressor maps for aero engines based on 3D CFD The developed automatic process starts with an operation point analysis where a convergence checker terminates the running 3D flow analysis as soon as physical quantities such as mass flow or aerodynamic blade row loss have converged Subsequently, the corresponding compressor speed line is determined, where operation limits like surge and choke are detected by solving optimization and root search problems, respectively Such speed lines also have to be calculated for various other shaft speeds to obtain the whole performance map This is achieved by adjusting shaft speed and boundary conditions, where the mesh for variable stator vanes and the amount of bleed mass flow are adapted automatically according to given schedules Finally, the developed process is applied to a 45-stage axial compressor to demonstrate feasibility of the proposed strategies

Compressor Map Computation Based on 3D CFD Analysis

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

This paper presents a full parametric model of a turbomachinery blade. The model forms the geometric backbone of a new aerodynamic design suite, which aims at speeding up the coupled 2D/3D aerodynamic design process. The approach employed here follows the basic design concepts of turbomachinery blades, which are typically defined by a series of cross-sectional aerofoils stacked at their radial location to a three-dimensional blade. Unlike the geometry management in current design systems, the paradigm of a CAD based Master Model has been incorporated in the geometry definition and the corresponding software architecture. Therefore all blade features have been modelled as computational components in the flexible object-oriented software environment. The blade parameterisation enables the 2D aerofoil construction either from the common superposition of the camber line and thickness distribution or the direct control of the suction and pressure side. The sensitivity of the aerofoil aerodynamic performance with respect to a design parameter can be quickly assessed with a fast 2D flow solver. The parameters of the radial stacking line define the axial and tangential shift of each section. The parametric concept facilitates the inclusion of specific shape control techniques such as curvature manipulation and surface smoothing. Furthermore the use of optimisation methods is greatly simplified by the modular program structure, which allows to access single modules of the blade design tool in a batch job. Since the blade design process involves different coordinate systems, unique mapping functions are essential for a consistent update of the blade geometry during a design cycle. The interface to the CAD system is based on the standard data exchange format STEP. The CFD interface makes use of the NetCDF data format for automatic grid generation.© 2004 ASME

Ju¨rgen Gra¨sel

Papers

A Full Parametric Model for Turbomachinery Blade Design and Optimisation