Sébastien Alligné

Cavitation surge modelling in Francis turbine draft tube

Francis turbines may experience cavitation surge phenomenon in the draft tube inducing large pressure fluctuations which can jeopardize the hydraulic system integrity. To predict this phenomenon, a one-dimensional draft tube model is derived from flow momentum and continuity equations including the convective terms that are not considered in the existing models. A parametric analysis of the draft tube model is carried out to investigate the influence of parameters on the cavitation surge onset identified by the hydraulic system stability. It is shown that convective terms have a stabilizing influence modifying stability limit prediction driven by the divergent geometry modelling of the draft tube.

Prediction of a Francis turbine prototype full load instability from investigations on the reduced scale model

The growing development of renewable energies combined with the process of privatization, lead to a change of economical energy market strategies. Instantaneous pricings of electricity as a function of demand or predictions, induces profitable peak productions which are mainly covered by hydroelectric power plants. Therefore, operators harness more hydroelectric facilities at full load operating conditions. However, the Francis Turbine features an axi-symmetric rope leaving the runner which may act under certain conditions as an internal energy source leading to instability. Undesired power and pressure fluctuations are induced which may limit the maximum available power output. BC Hydro experiences such constraints in a hydroelectric power plant consisting of four 435 MW Francis Turbine generating units, which is located in Canadas province of British Columbia. Under specific full load operating conditions, one unit experiences power and pressure fluctuations at 0.46 Hz. The aim of the paper is to present a methodology allowing prediction of this prototypes instability frequency from investigations on the reduced scale model. A new hydro acoustic vortex rope model has been developed in SIMSEN software, taking into account the energy dissipation due to the thermodynamic exchange between the gas and the surrounding liquid. A combination of measurements, CFD simulations and computation of eigenmodes of the reduced scale model installed on test rig, allows the accurate calibration of the vortex rope model parameters at the model scale. Then, transposition of parameters to the prototype according to similitude laws is applied and stability analysis of the power plant is performed. The eigenfrequency of 0.39 Hz related to the first eigenmode of the power plant is determined to be unstable. Predicted frequency of the full load power and pressure fluctuations at the unit unstable operating point is found to be in general agreement with the prototype measurements.

Unstable Operation of Francis Pump-Turbine at Runaway: Rigid and Elastic Water Column Oscillation Modes

This paper presents a numerical simulation study of the transient behavior of a 2x340MW pump-turbine power plant, where the results show an unstable behavior at runaway. First, the modeling of hydraulic components based on equivalent schemes is presented. Then, the 2 pump-turbine test case is presented. The transient behavior of the power plant is simulated for a case of emergency shutdown with servomotor failure on Unit 1. Unstable operation at runaway with a period of 15 seconds is properly simulated using a 1-dimensional approach. The simulation results points out a switch after 200 seconds of the unstable behavior between a period of oscillations initially of 15 seconds to a period of oscillation of 2.16 seconds corresponding to the hydraulic circuit first natural period. The pressure fluctuations related to both the rigid and elastic water column mode are presented for oscillation mode characterization. This phenomenon is described as a switch between a rigid and an elastic water column oscillation mode. The influence of the rotating inertia on the switch phenomenon is investigated through a parametric study.

Hydroacoustic Simulation of Rotor-Stator Interaction in Resonance Conditions in Francis Pump-Turbine

Combined effect of rotating pressure field related to runner blade and wakes of wicket gates leads to rotor stator interactions, RSI, in Francis pump-turbines. These interactions induce pressures waves propagating in the entire hydraulic machine. Superposition of those pressure waves may result in standing wave in the spiral casing and rotating diametrical mode in the guide vanes and can cause strong pressure fluctuations and vibrations. This paper presents the modeling, simulation and analysis of Rotor-Stator Interaction of a scale model of a Francis pump-turbine and related test rig using a one-dimensional approach. The hydroacoustic modeling of the Francis pump-turbine takes into account the spiral casing, the 20 guide vanes, the 9 rotating runner vanes. The connection between stationary and rotating parts is ensured by a valve network driven according to the unsteady flow distribution between guide vanes and runner vanes. Time domain simulations are performed for 2 different runner rotational speeds in turbine mode. The simulation results are analyzed in frequency domain and highlights hydroacoustic resonance between RSI excitations and the spiral case. Rotating diametrical mode in the vaneless gap and standing wave in the spiral case are identified. The influence of the resonance on phase and amplitude of pressure fluctuations obtained for both the spiral case and the vaneless gap is analyzed. The mode shape and frequencies are confirmed using eigenvalues analysis.

A fully modular tool for small-signal stability analysis of hydroelectric systems

In electrical systems, the small-signal stability analysis method is usually applied to synchronous machines by using the Park representation (d, q-components). This paper presents the generalization of a different approach for this method, based on a, b, c phase variables. This approach is essential to software systems using phase variables as state variables and its generalization yields a small-signal stability analysis tool which is fully modular. Two test cases are presented to showcase the application of this approach to elements such as synchronous machines, automatic voltage regulator (AVR), power system stabilizer of type IEEE PSS2B, penstock, Francis turbine and speed regulator.

Influence of the Francis Turbine location under vortex rope excitation on the Hydraulic System Stability

Hydroelectric power plants are known for their ability to cover variations of the consumption in electrical power networks. In order to follow this changing demand, hydraulic machines are subject to off-design operation. In that case, the swirling flow leaving the runner of a Francis turbine may act under given conditions as an excitation source for the whole hydraulic system. In high load operating conditions, vortex rope behaves as an internal energy source which leads to the self excitation of the system. The aim of this paper is to identify the influence of the full load excitation source location with respect to the eigenmodes shapes on the system stability. For this, a new eigenanalysis tool, based on eigenvalues and eigenvectors computation of the nonlinear set of differential equations in SIMSEN, has been developed. First the modal analysis method and linearization of the set of the nonlinear differential equations are fully described. Then, nonlinear hydro-acoustic models of hydraulic components based on electrical equivalent schemes are presented and linearized. Finally, a hydro-acoustic SIMSEN model of a simple hydraulic power plant, is used to apply the modal analysis and to show the influence of the turbine location on system stability. Through this case study, it brings out that modeling of the pipe viscoelastic damping is decisive to find out stability limits and unstable eigenfrequencies.

Identification of Francis Turbine Helical Vortex Rope Excitation by CFD and Resonance Simulation With the Hydraulic System

Due to the growing development of new renewable energies, which production is difficult to foreseen, power grid is subjected to disturbances. Hydropower plants are one of the solution to restore the grid stability by allowing hydraulic machines, especially Francis turbines, to change quickly of operating points in a very large range of heads and power in order to cover the variation of the electrical demand. In part load conditions, the cavitating vortex rope is an excitation source for the whole hydraulic circuit. The frequency of the excitation may matches with one of the eigenfrequency of the system leading to resonance phenomena. The aim of this paper is to simulate this hydroacoustic resonance by identifying the excitation source with CFD numerical simulations of the cavitating vortex rope and simulating the response of the hydraulic system with a one dimensional compressible model. A one dimensional draft tube model including three key parameters is used: the excitation momentum source corresponding to the force induced by the vortex rope acting on the wall, the excitation mass source induced by the cavitation volume fluctuations and the thermodynamic damping modeling energy dissipation during the phase change between cavitation and liquid. These parameters are computed for the FLINDT reduced scale model with the help of unsteady CFD simulations considering both one phase and two phase simulations. Finally these parameters are injected in the one dimensional hydroacoustic model to simulate the resonance phenomenon. In out of resonance conditions, maximum of pressure fluctuations are found in the draft tube cone with an amplitude of 1% of the turbine head. However, when resonance occurs, maximum amplitude of pressure fluctuations reaches up to 6.8%.© 2011 ASME

Simulation of water column separation in Francis pump-turbine draft tube

The paper presents the modelling, simulation and analysis of the transient behaviour of a 340 MW pump-turbine in case of emergency shutdown in turbine mode with focus on possible draft tube water column separation. The model of a pumped storage power plant with simplified layout is presented. This model includes a penstock feeding one 340MW pump-turbine with the related rotating inertia and a tailrace tunnel. The model of the tailrace tunnel allowing for water column separation simulation is introduced. The simulation results of the transient behaviour of the pump-turbine in case of emergency shutdown in generating mode, with and without downstream water column separation model are presented for different degree of severity triggered by the submergence and the tailrace tunnel length. The amplitudes of the pressure peaks induced by the cavity collapse are analysed with respect to the pressure drop magnitude and tailrace dimensions. The maximum and minimum pressure amplitudes obtained along the tailrace tunnel are analysed for different test case conditions.

Stability study of a complete hydroelectric production site by eigenvalues analysis method based on phase variables

The eigenvalues analysis method is generally applied to synchronous machines by using d,q-components. This paper presents the application of this method on an equivalent model for the synchronous machine based on phase variables a,b,c instead of d,q-components. The advantages of this approach, essential for programs using phase variables as state variables, are presented. The application of this method to a complete hydroelectric production site including hydraulic components (pump-turbine, penstock, gallery, reservoir…), permits the study and analysis of the interactions between the hydraulic, electric and regulation parts of the system. Results coming from the proposed eigenvalues analysis method and the numerical simulations confirm the interest of the presented approach.

Determination of Surge Tank Diaphragm Head Losses by CFD Simulations

At early stage of a hydroelectric project, 1D transient simulations are performed to determine the basic layout of power plant. In this phase, the design of surge tanks is decisive to achieve good dynamic performances of the power plant, with respect to water hammer and mass oscillations induced by the hydraulic machines for normal, exceptional, and accidental operation. As the head losses between the gallery and the surge tank have strong influence on the transient behavior of the hydraulic system, they are usually optimized by means of 1D transient simulation to avoid low pressure in gallery or surge tank overflow. An asymmetric diaphragm is often placed at the surge tank inlet to achieve the optimum inlet and outlet head losses. Thus, the design of such diaphragm is a challenging task usually performed through an iterative process on reduced-scale model. In this context, 3D CFD simulations can significantly improve the design process to select the appropriate geometry of the diaphragm. In this chapter, head losses coefficients of a surge tank scale model are derived from CFD simulations performed with ANSYS CFX. Results are compared with measurements on reduced-scale physical model and analytical approach. The good agreement of CFD computations with measurements demonstrates that a design optimization with 3D flow simulations can be performed preliminary to scale model tests in order to reduce the number of geometries to be tested to achieve the expected head losses.