CFD based draft tube hydraulic design optimization

Abstract

The draft tube design of a hydraulic turbine, particularly in low to medium head applications, plays an important role in determining the efficiency and power characteristics of the overall machine, since an important proportion of the available energy, being in kinetic form leaving the runner, needs to be recovered by the draft tube into static head. For large units, these efficiency and power characteristics can equate to large sums of money when considering the anticipated selling price of the energy produced over the machine's life-cycle. This same draft tube design is also a key factor in determining the overall civil costs of the powerhouse, primarily in excavation and concreting, which can amount to similar orders of magnitude as the price of the energy produced. Therefore, there is a need to find the optimum compromise between these two conflicting requirements. In this paper, an elaborate approach is described for dealing with this optimization problem. First, the draft tube's detailed geometry is defined as a function of a comprehensive set of design parameters (about 20 of which a subset is allowed to vary during the optimization process) and are then used in a non-uniform rational B-spline based geometric modeller to fully define the wetted surfaces geometry. Since the performance of the draft tube is largely governed by 3D viscous effects, such as boundary layer separation from the walls and swirling flow characteristics, which in turn governs the portion of the available kinetic energy which will be converted into pressure, a full 3D meshing and Navier-Stokes analysis is performed for each design. What makes this even more challenging is the fact that the inlet velocity distribution to the draft tube is governed by the runner at each of the various operating conditions that are of interest for the exploitation of the powerhouse. In order to determine these inlet conditions, a combined steady-state runner and an initial draft tube analysis, using a stage interface between them, must first be performed for each operating condition. Due to the computationally intensive nature of the evaluation process, the efficiency of the optimization algorithm becomes important. Therefore, a state-of-the-art hierarchical-metamodel-assisted evolutionary algorithm is used.