This paper demonstrates a method for constraining blade thickness during the free-form based optimisation of transonic fan and compressor blades, and describes the effect that constraining thickness has. Constraining blade thickness is important to avoid issues such as excessive mechanical stress and flutter.

Free-Form Deformation is a parameterisation approach that enables the flexible design of turbomachinery components. It is less restrictive than other parameterisation methods, can perform 2D blade profile shaping as well as 3D blade perturbation and enables novel blade designs to be generated. Previous work has shown that FFD can produce blade designs capable of delaying and weakening the shock and reducing shock-induced separation for transonic compressor blades \[1\].

Baseline optimisations are carried out in this work using FFD to deform the geometry and Sequential Quadratic Programming (SQP) (making use of adjoint gradients) as the optimiser. The geometry is modified and meshed using PADRAM \[2\], and steady RANS CFD and adjoint simulations are carried out using Hydra \[3\]. It is demonstrated that significant efficiency benefit can be achieved with a small number of optimisation iterations thanks to the cost of adjoint optimisation being independent of the number of design parameters. Optimisations are carried out for a highly-loaded transonic compressor blade and a modern research transonic fan blade. It is shown that Free-Form Deformation has the tendency to reduce blade thickness for transonic compressor blades as a pre-compression geometry is formed during the optimisation.

A method is then implemented that uses finite difference of the maximum blade thickness at different spanwise locations to calculate thickness gradients with respect to each design parameter. This is inexpensive thanks to the capability of PADRAM to rapidly perturb the geometry. These gradients are then used during the SQP adjoint optimisation to constrain the blade thickness. Tests are carried out with thickness constraints at various spanwise positions, showing that it is necessary to have at least as many spanwise thickness constraints as radial control sections, to ensure the blade thickness is properly maintained.

Thickness constrained optimisations are then carried out on both the transonic compressor and fan blades. It is shown that a slight reduction in efficiency benefit is observed compared to the unconstrained optimisations, but the optimiser manages to find designs that still provide good efficiency increase while maintaining blade thickness throughout the span from hub to tip.  
 

 

\[1\]  A. John, S. Shahpar and N. Qin., “Novel compressor blade shaping through a free-form method.,” Journal of Turbomachinery, vol. 139, no. 8, 2017.  
\[2\]  S. Shahpar and L. Lapworth, “PADRAM: Parametric Design and Rapid Meshing System for Turbomachinery Optimisation,” in ASME Turbo Expo, Atlanta Georgia, 2003.  
\[3\]  L. Lapworth, “Hydra-CFD: a framework for collaborative CFD development,” in International Conference on Scientific and Engineering Computation (IC-SEC), Singapore, 2004.


The Influence of Parameterisation Setup on the Constrained Adjoint Optimisation of Transonic Fan Blades

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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