The flow in the draft tube cone of Francis turbines operated at partial discharge is a complex hydrodynamic phenomenon where an incoming steady axisymmetric swirling flow evolves into a three-dimensional unsteady flow field with precessing helical vortex (also called vortex rope) and associated pressure fluctuations. The paper addresses the following fundamental question: is it possible to compute the circumferentially averaged flow field induced by the precessing vortex rope by using an axisymmetric turbulent swirling flow model? In other words, instead of averaging the measured or computed 3D velocity and pressure fields we would like to solve directly the circumferentially averaged governing equations. As a result, one could use a 2D axi-symmetric model instead of the full 3D flow simulation, with huge savings in both computing time and resources. In order to answer this question we first compute the axisymmetric turbulent swirling flow using available solvers by introducing a stagnant region model (SRM), essentially enforcing a unidirectional circumferentially averaged meridian flow as suggested by the experimental data. Numerical results obtained with both models are compared against measured axial and circumferential velocity profiles, as well as for the vortex rope location. Although the circumferentially averaged flow field cannot capture the unsteadiness of the 3D flow, it can be reliably used for further stability analysis, as well as for assessing and optimizing various techniques to stabilize the swirling flow. In particular, the methodology presented and validated in this paper is particularly useful in optimizing the blade design in order to reduce the stagnant region extent, thus mitigating the vortex rope and expending the operating range for Francis turbines.

No abstract

The aim of this paper is to present the results obtained with a 3-D numerical method allowing the prediction of the cavitation behavior of a centrifugal pump and to compare this prediction to model tests. The influence of the diffuser on the pump performances, for a cavitating flow, is taken into account by performing coupled computations. The proposed method, which allows the performance drop prediction, consists of assuming the cavity interface as a free surface boundary of the computation domain and in computing the single phase flow. The unknown shape of the interface is determined using an iterative procedure matching the cavity surface to a constant pressure boundary (pv). The originality of the method is that the adaptation process is done apart from the flow calculation, allowing to use any available code.

No abstract

The objective is to define a prediction and transposition model for cavitation erosion. Experiments were conducted to determine the energy spectrum associated with a leading edge cavitation. Two fundamental parameters have been measured on a symmetrical hydrofoil for a wide range of flow conditions: the volume of every transient vapor cavity and its respective rate of production. The generation process of transient vapor cavities is ruled by a Strouhal-like law related to the cavity size. The analysis of the vapor volume data demonstrated that vapor vortices can be assimilated to spherical cavities. Results are valid for both the steady and unsteady cavitation behaviors, this latter being peculiar besides due to the existence of distinct volumes produced at specific shedding rates. The fluid energy spectrum is formulated and related to the flow parameters. Comparison with the material deformation energy spectrum shows a remarkable proportionality relationship defined upon the collapse efficiency coefficient. The erosive power term, formerly suggested as the ground component of the prediction model, is derived taking into account the damaging threshold energy of the material. An erosive efficiency coefficient is introduced on this basis that allows to quantify the erosive potential of a cavitation situation for a given material. A formula for localization of erosion is proposed that completes the prediction model. Finally, a procedure is described for geometrical scale and flow velocity transpositions.

The predictive control of the self-sustained single spiral vortex breakdown mode is addressed in the three-dimensional flow geometry of Ruithet al.(2003) for a constant swirl number$S=1.095$. Based on adjoint optimization algorithms, two different control strategies have been designed. First, a quadratic objective function minimizing the radial velocity intensity, taking advantage of the physical mechanism underpinning spiral vortex breakdown. The second strategy focuses on the hydrodynamic instability properties using as objective function the growth rate of the most unstable global eigenmode. These minimization algorithms seek for an optimal volume force in an axisymmetric domain avoiding therefore expensive three-dimensional computations. In addition to considering eigenvalues around the base flow, we also investigate the stability around the mean flow and we find that it correctly predicts the frequency of the self-sustained single spiral vortex breakdown mode for Reynolds numbers up to$Re=500$. Close to the instability threshold, at a Reynolds value of$Re=180$, all these control strategies successfully quench the spiral vortex breakdown. The related volume force is found identical for the base and mean flow eigenvalue control even if the uncontrolled growth rates differ significantly. The control of the least unstable eigenvalue of the mean flow is not only found optimal at$Re=180$, it also stabilizes the flow at a Reynolds value as large as$Re=300$, which opens promising extensions to industrial applications.

No abstract

Pumps running as turbines are pointed out as a cost-effective solution for energy recovery in pressurised water supply systems. However, these hydraulic machines feature low efficiency under variable discharge operation due to the lack of an inlet flow control component. Variable speed operation is an approach for controlling the discharge at the pump as turbine inlet aiming at increasing the operational efficiency. This research work presents the experimental investigation for measuring the variable speed characteristic curves of pumps running as turbines, focusing on the turbine and on the extended operation modes. Three single-stage end-suction closed-impeller centrifugal pumps with different unit specific speed values are tested. Turbine mode test results show that the discharge-specific energy operating range is broadened with increasing efficiency if the machines are operated with variable speed. Extended operation results show that these hydraulic machines do not feature the instability region near the runaway conditions, the so-called the "s-curve". Outcomes of this experimental investigation provide the required insights for establishing the design technical specifications of micro hydropower plants with variable speed pumps running as turbines, aiming at maximizing the energy recovered in pressurised water supply systems.