Application of multi-objective Bayesian shape optimisation to a sharp-heeled Kaplan draft tube

Abstract

The draft tube of a hydraulic turbine plays an important role for the efficiency and power characteristics of the overall system. The shape of the draft tube affects its performance, resulting in an increasing need for data-driven optimisation for its design. In this paper, shape optimisation of an elbow-type draft tube is undertaken, combining Computational Fluid Dynamics and a multi-objective Bayesian methodology. The chosen design objectives were to maximise pressure recovery, and minimise wall-frictional losses along the geometry. The design variables were chosen to explore potential new designs, using a series of subdivision-curves and splines on the inflow cone, outer-heel, and diffuser. The optimisation run was performed under part-load for the Kaplan turbine. The design with the lowest energy-loss identified on the Pareto-front was found to have a straight tapered diffuser, chamfered heel, and a convex inflow cone. Analysis of the performance quantities showed the typically used energy-loss factor and pressure recovery were highly correlated in cases of constant outflow cross-sections, and therefore unsuitable for use of multi-objective optimisation. Finally, a number of designs were tested over a range of discharges. From this it was found that reducing the heel size increased the efficiency over a wider operating range.

Shape optimisation of a hydrodynamic separator using expensive and constrained multi-objective computational modelling

“…We have previously used homoscedastic Gaussian Process (GP) models with zero noise to generate several different infill criteria. This is suitable for cases where zero noise is present in the CFD simulations, such as steady single-phase flow in a duct (Daniels et al, 2022). Choosing the appropriate infill criterion is essential to the success of the optimisation and partially depends on the number of objectives (Rahat et al, 2017).…”

“…However, it was not clear how noise in the CFD simulations should be treated in the optimisation process. Another issue raised by the current authors was the problem of parallelisation (Daniels et al, 2022). The developers of previous work have looked at synchronous (González et al, 2016) and asynchronous (Alvi et al, 2019) forms of this approach.…”

A Review on the Modelling of Wave-Structure Interactions Based on OpenFOAM

“…Uni-directional waves interacting with a fixed cylinder [41] HOS-NWT approach to assess the wave load on a fixed wind turbine, according to the statistics in non-Gaussian seas. In addition, the coupling of Machine Learning with CFD can also significantly speed up the computational investigation, in particular when a large amount of simulations is required [88,89].…”

Optimization of the Shape of a Hydrokinetic Turbine's Draft Tube and Hub Assembly Using Design-by-Morphing with Bayesian Optimization

“…Marjavaara and Lundström [20] and Marjavaara [15] use a Response Surface Method (RSM) surrogate modeling strategy, as well as a commercial CFD code (ANSYS CFX4.4) to create new designs with different parametrizations (circular and elliptical, respectively) of the elbow section. More recent improvements include those of Daniels et al [21,22] who use multi-objective Bayesian optimization to maximize pressure recovery using a series of subdividing curves, optimizing over the inflow cone, outer-heel, and secondary straight diffuser. Other improved designs focus on the optimization of the draft tube for low-head applications while retaining the sharp-heel shape [23,24].…”

“…Some of the baselines that we chose were used previously in literature so that we were able to exploit any inherent advantageous features they might have, while other baselines were chosen to have non-intuitive features that would lead to radical designs, rather than incremental improvements. In the past, the fundamental design features of the Kaplan draft tube were formed through experimental observation and quasi-empirical formulae derived from geometries already installed and in use in HEPPs [21]. The works of Gubin [17], Cervantes [11], Mulu [52] and Nilsson et.…”