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.

水轮机的引流管对于整个系统的效率和功率特性起着重要作用。引流管的形状会影响其性能，从而导致对其设计进行数据驱动优化的需求不断增加。本文结合计算流体力学和多目标贝叶斯方法，对弯头式引流管进行了形状优化。选择的设计目标是使压力恢复最大化，并使沿几何形状的壁摩擦损失最小化。选择设计变量来探索潜在的新设计，使用流入锥，外跟和扩散器上的一系列细分曲线和样条曲线。优化运行是在Kaplan涡轮机的部分负荷下进行的。发现在帕累托前部具有最低能量损耗的设计具有直的锥形扩散器，倒角的鞋跟和凸的流入锥。对性能量的分析表明，在恒定的流出横截面情况下，通常使用的能量损失因子和压力恢复高度相关，因此不适合使用多目标优化。最后，在放电范围内测试了多种设计。由此发现减小鞋跟尺寸可在更宽的工作范围内提高效率。因此不适合使用多目标优化。最后，在放电范围内测试了多种设计。由此发现减小鞋跟尺寸可在更宽的工作范围内提高效率。因此不适合使用多目标优化。最后，在放电范围内测试了多种设计。由此发现减小鞋跟尺寸可在更宽的工作范围内提高效率。