Abstract

Non-Uniform Rational B-Splines (NURBS) have become the industrial standard to represent and exchange a CAD geometry between CAD/CAE systems. CAD-based shape parameterisation uses parameters of a CAD model to modify the shape which allows to integrate a CAD model into the design loop. However, feature-trees of typical commercial CAD systems are not open and obtaining exact derivatives for gradient-based optimisation methods is not possible. Using the CAD-based NSPCC approach a designer can deform multiple NURBS patches in the design loop without violating geometric and/or thickness constraints. The NSPCC approach takes CAD descriptions as input and perturbs the control points of the NURBS boundary representation to modify the shape. In this work, an adaptive NSPCC method is proposed where the optimisation begins with a coarser design space and adapts to finer parametrisation during the design process where more shape control is needed. The refinement sensor is based on a comparison of smoothed node-based sensitivity compared to its projection onto the shape modes of the current parametrisation. Both static and adaptive parametrisation methods are coupled in the adjoint-based shape optimisation process to reduce the total pressure loss of a turbine blade internal cooling channel. The discrete adjoint flow solver STAMPS is used to compute the flow fields and their derivatives w.r.t. surface node displacements. The shape derivatives for gradient-based optimisation are obtained by application of reverse mode AD to the NSPCC CAD kernel. Since a CAD model is kept inside the design loop, the resulting optimal shape is directly available in CAD for further analysis or manufacturing. Based on the analysis regarding quality of the optima and rate of convergence of the design process adaptive NSPCC method outperforms static NSPCC approach.

Abstract

Low-order models are the first choice to find the initial design of turbomachinery components screening many configurations. The final optimisation of the three-dimensional geometry is crucial for the best performance. Because of the ability to accurately predict the performance of turbomachinery, fluid dynamic simulations became a powerful tool [10]. However, parameter studies for shape optimisation relying on fluid dynamic simulations are computationally expensive and might fail to reveal the optimal geometry. Gradient-based optimisation approaches allow a significant reduction of simulations and hence, determine the optimum efficiency. The adjoint method finds the optimisation gradient by calculating the derivatives of the state variables with respect to the design objective without the need for finite differences [6]. Thus, the adjoint optimisation is especially efficient for problems with many degrees of freedom and few design objectives, e.g. increasing efficiency. The application of the adjoint method for shape optimisation is demonstrated on the example of a centrifugal compressor impeller. The shape of the rotor blades is optimised, and the impact of different objection functions, i.e. reducing the required moment or increasing the achieved pressure ratio, and optimisation constraints, i.e. retaining the operating point or keeping an area ratio, is analysed. The results demonstrate that the compressor performance can be significantly improved using the adjoint method. However, the challenge is to obtain not only an optimised shape for operating points but also for the entire operating map. The final shapes, obtained for different operating points, are compared.

Abstract

Reynolds-Averaged Navier-Stokes (RANS) simulations are inaccurate in predicting complex flow features (ex: separation regions), and therefore deriving an optimised shape using the RANS-adjoint framework does not yield a truly optimal geometry. With the purpose of obtaining accurate sensitivity to objective function of interest, we improve the RANS flowfield using the strategy of Singh et al. [1]. This involves multiplying a corrective factor to the production term in the Spalart-Allmaras (SA) turbulence model equation and solving the inverse problem to determine the appropriate field, which enables the RANS solution to match the high-fidelity data.The geometry of our interest is the U-Bend which is widely studied in literature in the context of gas turbine cooling, and which is known to be a challenging case for RANS simulations to reproduce. We use the mean flowfield from a large-eddy simulation of the U-Bend geometry as the high-fidelity data to which the RANS flowfield is fit using the strategy outlined above. We observe a clear improvement in the RANS flowfield by optimising for the field, the objective function to be minimized being L2-norm of the mean velocity difference between RANS and LES. We further show that adding an additional corrective factor () to the destruction term in the SA turbulence equation and simultaneously optimising for the field alongside the field results in a better match of the RANS flowfield with the corresponding LES flowfield. We also show that surface sensitivity map for the improved LES-aided flowfield varies significantly in comparison to the baseline SA-based flowfield for an objective function of interest, the total pressure loss in the U-Bend.