Optimization design of the elbow draft tube of the hydraulic turbine

Abstract

The draft tube of the hydraulic turbine serves to recover the kinetic energy of the water flow that leaves the runner. The amount of this energy depends on the turbine type, its specific speed and flow capacity. For high specific speed turbines, influence of the draft tube on the turbine efficiency is more essential. The height of the elbow-type draft tube has a considerable influence on its performance. Statistics show that increasing the height of the draft tube leads to a considerable increase of the turbine efficiency, but it also increases the scope and cost of civil works. The present paper presents the solution of the multi-objective optimization problem directed to minimization of the height of the toroidal elbow-type draft tube and maximization of the overall efficiency of the turbine. During optimization, 11-19 parameters that determine the shape and dimensions of the draft tube were subject to variation. In optimization, efficiency was maximized in two operating points: best efficiency point and full-load point. Cavitation qualities were defined as constraints. In order to correctly assess the turbine efficiency and cavitation, the computational domain included one channel of the distributor, one channel of the runner and draft tube; whereas losses in the spiral case and stay ring were determined using empiric formulae. Within the optimization the flow analysis was performed using 3D steady-state Reynolds averaged Navier Stokes equations closed by the k-ε turbulence model. On solid walls the method of wall functions was used. The turbine head, being the difference of specific energies in the inlet and outlet cross sections, was pre-set as a constant value, while the discharge was determined in the course of solution of the problem. A multi-objective genetic algorithm was used to solve the optimization problem. For the draft tube shapes obtained in the course of optimization, their performance characteristics and flow character were compared by means of CFD. It was found that it is possible to significantly reduce the height of the classical toroidal draft tubes without considerably affecting their performance characteristics.