Francis full-load surge mechanism identified by unsteady 2-phase CFD

• Published in: IOP conference series. Earth and environmental science 2010-08, Vol.12 (1), p.012026-012026
• Main Authors: Dörfler, P K, Keller, M, Braun, O
• Format: Article
• Language: English
• Subjects: Cavitation; Computational fluid dynamics; Computer simulation; Computing time; Discharge; Downstream; Draft tubes; Dynamic stability; Finite element method; Flow stability; Fluid flow; Gain; Hydrologic data; Mass flow; Mathematical models; One dimensional models; Pressure dependence; Simulation; Stability analysis; Statistical analysis; Time dependence; Turbines; Vortices
• ISSN: 1755-1315; 1755-1307; 1755-1315
• DOI: 10.1088/1755-1315/12/1/012026

Francis turbines may produce spontaneous pulsations of pressure and output power when operating at very high discharge. In such cases there is a cavitating central vortex in the draft tube with variable cavity volume Vc. Until today, researchers agree that the main destabilizing agent is the so-called mass flow gain factor, defined as the derivative of cavity volume by the local discharge. Recent studies about 1D high-load stability analysis assumed that the mass-flow gain factor obtained from steady-state vortex data acts on the transient discharge downstream of the cavity. There are however good reasons to question this assumption. Most strikingly, the direct cause of the mass flow gain effect is the increase of swirl produced at the runner exit and hence upstream, not downstream of the cavity. To enhance the reliability of full-load stability predictions, the authors directly investigated the vortex dynamics. The development of the transient cavitating flow in the draft tube was simulated by means of unsteady 2-phase CFD. CFD work started with 1-phase calculations as presented by other authors. This was then extended to a more realistic 2-phase calculation. To contain the computing time within acceptable limits, given the very fine mesh and short time step required, the simulation domain was restricted to the draft tube and, at the same time, the problem was reduced to a basically 2-dimensional rotationally symmetric case. The response of the cavitating draft tube flow to a time-dependent inflow and time-dependent pressure at the draft tube exit was simulated. The results were input to a statistical identification procedure to check possible 1D transient models and find representative parameter values in the sense of a best fit between 1D model and CFD result. As we had suspected, the conventional vortex model with mass flow gain controlled by downstream discharge is not compatible with direct simulation and needs to be modified. The CFD results correspond to a model with the mass flow gain depending almost entirely on the runner exit discharge, delayed by a small dead time.