Numerical Simulation of Nonlinear Self Oscillations of a Full Load Vortex Rope

Self excited instabilities or oscillations of a cavitating full load vortex rope occur due to an interaction between the gas volume and the acoustic waves. From the onset of the oscillations, the amplitudes grow until they reach a maximum, called the “limit cycle”. The aim of this paper is to predict and to simulate this full load instability with its corresponding “limit cycle”. The test case is a reduced scale model installed on test rig in the Laboratory for Hydraulic Machines at the EPFL. An advanced hydro acoustic vortex rope model is developed to take into account the energy dissipation due to thermodynamic exchange between the gas and the surrounding liquid. Three key hydro acoustic parameters are set up using both steady CFD simulations and analytical models. First of all, parameters are assumed to be constant and time domain simulation is divergent without reaching the limit cycle. However frequency of instability is well predicted. Then inclusion of nonlinear parameters is found to lead to a limit cycle of finite amplitude. Prediction is compared with results from experiments and is in good agreement. It is shown that nonlinearity of the viscoelastic damping parameter, modelling the energy dissipation, is decisive to reach the limit cycle. Moreover, an energy approach is developed to understand the interaction process between the mass source and the system dissipation to reach the equilibrium at the limit cycle. It brings out that over one period the dissipation can provide energy to the system whereas the mass source dissipates to ensure the equilibrium.

Experimental investigation of the local wave speed in a draft tube with cavitation vortex rope

François Avellan, Arthur Tristan Favrel, Christian Landry, Andres Müller, Christophe Nicolet, Keita Yamamoto

Hydraulic machines operating in a wider range are subjected to cavitation developments inducing undesirable pressure pulsations which could lead to potential instability of the power plant. The occurrence of pulsating cavitation volumes in the runner and the draft tube is considered as a mass source of the system and is depending on the cavitation compliance. This dynamic parameter represents the cavitation volume variation with the respect to a variation of pressure and defines implicitly the local wave speed in the draft tube. This parameter is also decisive for an accurate prediction of system eigen frequencies. Therefore, the local wave speed in the draft tube is intrinsically linked to the eigen frequencies of the hydraulic system. Thus, if the natural frequency of a hydraulic system can be determined experimentally, it also becomes possible to estimate a local wave speed in the draft tube with a numerical model. In the present study, the reduced scale model of a Francis turbine was investigated at off-design conditions. In order to measure the first eigenmode of the hydraulic test rig, an additional discharge was injected at the inlet of the hydraulic turbine at a variable frequency and amplitude to excite the system. Thus, with different pressure sensors installed on the test rig, the first eigenmode was determined. Then, a hydro-acoustic test rig model was developed with the In-house EPFL SIMSEN software and the local wave speed in the draft tube was adjusted to obtain the same first eigen frequency as that measured experimentally. Finally, this method was applied for different Thoma and Froude numbers at part load conditions.

IOP Publishing Ltd2014

Experimental investigation of the local wave speed in a draft tube with cavitation vortex rope

François Avellan, Arthur Tristan Favrel, Christian Landry, Christophe Nicolet, Keita Yamamoto

Hydraulic machines operating in a wider range are subjected to cavitation developments inducing undesirable pressure pulsations which could lead to potential instability of the power plant. The occurrence of pulsating cavitation volumes in the runner and the draft tube is considered as a mass source of the system and is depending on the cavitation compliance. This dynamic parameter represents the cavitation volume variation with the respect to a variation of pressure and defines implicitly the local wave speed in the draft tube. This parameter is also decisive for an accurate prediction of system eigen frequencies. Therefore, the local wave speed in the draft tube is intrinsically linked to the eigen frequencies of the hydraulic system. Thus, if the natural frequency of a hydraulic system can be determined experimentally, it also becomes possible to estimate a local wave speed in the draft tube with a numerical model. In the present study, the reduced scale model of a Francis turbine (v=0.29) was investigated at off-design conditions. In order to measure the first eigenmode of the hydraulic test rig, an additional discharge was injected at the inlet of the hydraulic turbine at a variable frequency and amplitude to excite the system. Thus, with different pressure sensors installed on the test rig, the first eigenmode was determined Then, a hydro-acoustic test rig model was developed with the In-house EPFL SIMSEN software and the local wave speed in the draft tube was adjusted to obtain the same first eigen frequency as that measured experimentally. Finally, this method was applied for different Thoma and Froude numbers at part load conditions.

Iop Publishing Ltd2014

RANS computations for identification of 1-D cavitation model parameters: application to full load cavitation vortex rope

Sébastien Alligné, François Avellan, Andres Müller, Christophe Nicolet

Due to the massive penetration of alternative renewable energies, hydropower is a key energy conversion technology for stabilizing the electrical power network by using hydraulic machines at off design operating conditions. At full load, the axisymmetric cavitation vortex rope developing in Francis turbines acts as an internal source of energy, leading to an instability commonly referred to as self- excited surge. 1-D models are developed to predict this phenomenon and to define the range of safe operating points for a hydropower plant. These models involve several parameters that have to be calibrated using experimental and numerical data. The present work aims to identify these parameters with URANS computations with a particular focus on the fluid damping rising when the cavitation volume oscillates. Two test cases have been investigated: a cavitation flow in a Venturi geometry without inlet swirl and a reduced scale model of a Francis turbine operating at full load conditions. The cavitation volume oscillation is forced by imposing an unsteady outlet pressure conditions. By varying the frequency of the outlet pressure, the resonance frequency is determined. Then, the pressure amplitude and the resonance frequency are used as two objectives functions for the optimization process aiming to derive the 1-D model parameters.

International Association For Hydraulic Research2016