Shape optimisation of the sharp-heeled Kaplan draft tube: Performance evaluation using Computational Fluid Dynamics

Abstract

In the first of this two-part contribution, a methodology to assess the performance of an elbow-type draft tube is outlined. using Computational Fluid Dynamics (CFD) to evaluate the pressure recovery and mechanical energy losses along a draft tube design, while using open-source and commercial software to parameterise and regenerate the geometry and CFD grid. An initial validation study of the elbow-type draft tube is carried out, focusing on the grid-regeneration methodology, and the use of a steady-state assumption for evaluating the design's efficiency. The Grid Convergence Index (GCI) technique was used to assess the uncertainty of the pressure recovery to the grid resolution. It was found that estimating the pressure recovery through area-weighted averaging significantly reduced the uncertainty due to the grid.Simultaneously, it was found that this uncertainty fluctuated with the local cross-sectional area along the geometry. Subsequently, a study of the inflow cone and outer-heel designs on the flowfield and pressure recovery was carried out. Catmull-Rom splines were used to parameterise these components, so as to recreate a number of proposed designs from the literature. GCI analysis is also applied to these designs, demonstrating the robustness of the grid-regeneration methodology.

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

“…Steady-state and time-averaged transient simulations were carried out to assess the performance measures of the draft tube (see Sect. 2.1) with near-identical results as shown in our earlier paper (Daniels et al 2020). Sensitivity of the results to the inlet and outlet conditions was also investigated in this earlier work.…”

“…The reliability of the optimization process depends on the underlying CFD results; it is thus critically important to make sure that the CFD methodology is reliable. This has been the subject of an earlier paper (Daniels et al 2020) which assesses the numerical methodology for evaluating the performance of a draft tube design, the results of which are summarised here. The CFD simulations in this work were performed using the open-source code OpenFOAM-4.x.…”

“…The choice of the k − model was primarily based on existing studies in the literature (e.g. Abbas and Kumar 2017;Cervantes et al 2005) although in our previous paper (Daniels et al 2020) we also investigated the use of the k − − SST − SAS model. The sharp-heeled Hölleforsen-Kaplan draft tube was used as the base geometry.…”

“…López (2006) provides a 4-step methodology for the optimization process in turbomachinery, consisting of (1) Draft tube parameterization, (2) CFD methodology and validation, (3) Optimization algorithm and (4) Objective function. We have discussed i and ii in an earlier paper (Daniels et al 2020), so Sect. 2 reviews the methodology for evaluating the draft tube performance which has been presented in more detail there, including a discussion of the objective functions (Sect.…”

“…In this multi-objective shape optimisation, the energy losses along the draft tube are quantified by the frictional forces along the draft tube walls. In one form, the pressure losses at the walls can be quantified in terms of the nondimensional wall pressure, C p,wall (see Daniels et al 2020), as shown in Galván et al (2013a) or Galván et al (2013b). Alternatively, for this work, the frictional losses are quantified by the area-weighted average of skin friction across the draft tube walls:…”