Papers presented in the workshop

The third Francis-99 workshop was held on 28 and 29 May 2019. All the papers were peer-reviewed before the publication and the the are available online in Journal of Physics: Conference Series.

[1] E Tengs, J Einzinger and PT Storli, 2019, "Two-way coupled simulation of the Francis-99 hydrofoil using model order reduction,"

Abstract: The Francis-99 hydrofoil is simulated using a quasi two-way Fluid-Structure Interaction procedure. The structural domain is reduced by the use of modal decomposition, and solved for inside the commercial fluid solver ANSYS CFX. Both the first order Backward Euler and second order Crank-Nicolson time discretization scheme is used in the structural equations, with significantly different results. Several coupled fluid- structure phenomena is observed that would be unobtainable in a normal one-way approach. The most interesting is an "added stiffness" effect, where the eigenfrequency of the foil increases when the flow velocity is increased. This trend corresponds well with available experimental results. The same phenomenon is observed in the hydrodynamic damping on the foil. Self-induced vibration due to vortex shedding is also simulated with good results. The implemented two-way approach allows the different forcing terms to be tracked individually, due to the discretization of the second order structural system. This provides insight into the underlying physics behind the different FSI phenomena seen, and helps us explain why the damping and eigenfrequency characteristics change as the flow velocity passes the lock-in region.

[2] P Cupr, D Stefan, V Haban and P Rudolf, 2019, "FSI analysis of Francis-99 hydrofoil employing SBES model to adequately predict vortex shedding,"

Abstract: The added effects from the fluid on a structure submerged in water significantly affect its dynamic response. Since the hydraulic turbine runner is geometrically complex and involves complicated flow phenomena, the research on simple hydrofoil offers a unique opportunity to investigate added effects and mutual interaction of the elastic structure and vortical flow. For this purpose, the fluid structure interaction of Francis-99 hydrofoil was analysed using the Stress Blended Eddy Simulation (SBES). Advantage of this hybrid RANS-LES turbulence model over RANS models is shown by its enhanced ability to represent vortex shedding. The results of modal sensitivity analysis showed, that fillets of the fixed hydrofoil have negligible influence on the natural frequencies of the hydrofoil and therefore the simplified geometry was used. The modal analysis of fully fixed hydrofoil both in the air and submerged in water were carried out to investigate the added mass effect. Moreover, the hydrodynamic damping for various flow velocities was also investigated for the first bending mode. Overall results are complemented by sensitivity analysis of time step size and mesh for both structural and fluid domains. The results showed that the computed damping ratio above the lock-in and vortex shedding frequency at lock-in are largely underestimated. Therefore, the geometry with blunt trailing edge was additionally tested.

[3] CW Bergan, EO Tengs, BW Solemslie, P Østby and OG Dahlhaug, 2019, "Damping measurements on a multi-blade cascade with multiple degrees of freedom,"

Abstract: Due to thinner blades and higher demands for flexibility, the high-head Francis runners designed today face considerable challenges that severely affect the runners’ expected lifetime. For many high-head Francis runners, the leading cause of fatigue is blade cracking due to Rotor-Stator Interaction, which cause vibrations in the runner blades. Accurate prediction of the vibration magnitudes in a turbine is paramount in designing a reliable Francis runner. The understanding of the interaction between the hydrodynamic forces and the internal stresses in the runner is not yet sufficient to make this prediction. Previous investigations have identified some key parameters that affect dynamic behaviour in water, such as added mass, as well as added stiffness and damping from moving water. These parameters affect the natural frequency and damping of a structure, which in the end will affect what vibrations magnitudes the runner will be subjected to for a given frequency of excitation. The behavior of these parameters have recently been investigated by several researchers, but the effect of neighboring blades is yet not understood. A multi-blade cascade has been tested for four of its different modes of vibration. The results indicate that the slope of the damping with respect to the inverse Strouhal number is constant. This slope was found to be the same as for several single-blade tested performed, both in the same rig and in other works. The implication is that the product of added mass and mode shape does not change significantly.

[4] KF Sagmo and PT Storli, 2019, "A test of the v2-f k-ε turbulence model for the prediction of vortex shedding in the Francis-99 hydrofoil test case,"

Abstract: A test of the v2-f k-ε turbulence model for the flow around the Francis-99 hydrofoil geometry is conducted in order to assess it's accuracy of trailing edge vortex shedding prediction. The model is based on the k-ε turbulence model, but needs no wall damping function, and also allows near-wall turbulence anisotropy. For reference, the model results are compared with the SST k-ω, in addition to preliminary experimental results previously published. It is indicated that the v2-f k-ε model gives at least as good, or better results than the more commonly used SST k-ω model for the present case, though further measurements are needed in order to make a proper conclusion.

[5] E Tengs, LS Fevåg and PT Storli, 2019, "Francis-99: Coupled simulation of the resonance effects in runner channels,"

Abstract: A resonance phenomenon is observed experimentally in the runner channels of the Francis-99 model turbine runner. An incompressible CFD simulation is unable to simulate this. Two different coupled physics schemes are therefore presented to investigate if such effects can be replicated through simulations. The first procedure is a fully coupled acoustic-structural simulation, where the surrounding fluid is modelled using acoustic theory. This includes added mass effects and pressure propagation, but not advective and viscous effects. The second procedure is a quasi two-way coupled Fluid-Structure approach based on modal decomposition of the structural domain. In this procedure, the incompressible Navier-Stokes equations are solved along with the structural deformation. The fully coupled acoustic-structural approach does successfully exhibit a magnification of the pressure through the runner channels, indicating a resonance effect. The exact values of the acoustic pressure amplitudes are highly sensitive to the damping, the blade connection to the shroud close to the trailing edge, and more. The second procedure manages to simulate the structural deformation with the correct nodal diameters excited by the Rotor Stator Interaction, all inside the fluid solver. The pressure amplitudes however, does not exhibit the desired resonance effect, likely due to the assumption of incompressible fluid.

[6] P Østby, E Agnalt, B Haugen, JT Billdal and OG Dahlhaug, 2019, "Fluid structure interaction of Francis-99 turbine and experimental validation,"

Abstract: The ability to predict a Francis runners dynamic response to the exciting forces is paramount to avoid unwanted disintegration of the turbines components. In this article, each of the principal factors contributing to the dynamic response of the runner; eigenfrequency, mode shape, damping and pressure force, is individually examined and compared to the measured values from the Francis-99 runner. Even though the runner is made with a bolted connection between the blades and crown/band, and thus severely increasing the complexity, quite accurate predictions are possible using methods previously validated for massive and symmetric runners. All calculations are conducted on the best efficiency point and with eigenmodes corresponding to Nodal Diameter 4 as excited by the second harmonic of the guide vane passing frequency. The calculated natural frequency for the first two ND4 eigenmodes are within ±5% of the measured values. Further are the calculated eigenmodes, forcing pressure field and hydrodynamic damping all within measurement tolerances with some minor exceptions.

[7] P Foti and F Berto, 2019, "Francis 99: Evaluation of the strain energy density value for welded joints typical of turbine runner blades,"

Abstract: The main aim of this work is to investigate the fatigue behaviour of welded joints through an energetic approach based on the Strain Energy Density failure criteria. The geometries, taken from the literature, are typical of turbine runner blades. The results of the fatigue tests on these details were summarised through the Strain Energy Density approach. The application of this method to these geometries is the first step of a wider research with the aim to provide a suitable tool in FEM code for the lifetime estimation of components characterised by complex geometries.

[8] M Lazarevikj, F Stojkovski, I Iliev and Z Markov, 2019, "Influence of the guide vanes design on stress parameters of Francis-99 turbine,"

Abstract: The frequencies with predominant amplitudes in low specific speed Francis turbines are related to rotor-stator interaction and they are calculated on the basis of the runner speed and the number of guide vanes and runner blades. Pressure pulsations in the blade channels can be a reason for noise and vibration in the turbine above allowed level. High pressure pulsations can be caused by certain combination of runner blades and guide vanes number and and/or resonance with one of the runner's natural frequencies. The stress parameters of the Francis-99 turbine guide vanes and their modifications are analysed in this paper. The main aim is to determine the impact of the geometry modification (thinner for increased efficiency) of the guide vanes on the Francis turbine stresses by performing numerical simulations. The original Francis-99 turbine guide vane geometry and three modifications consisting of new guide vane shapes are being considered. The numerical investigation of the flow field is based on the k-ω SST turbulence model with 'frozen rotor' approach selected, constituting a quasi-steady state analysis, without taking into account the physical rotation of the runner to obtain Rotor-Stator-Interaction (RSI). Pressure distribution on one guide vane determined by a Computational Fluid Dynamics (CFD) simulation of the turbine is coupled to a Finite Element Method (FEM) simulation in order to analyse the stresses. The results from the one-way fluid-structure interaction analysis give the stresses distribution and deformations of the guide vanes. Moreover, modal-acoustics analysis is conducted to obtain the natural frequencies of the guide vanes in water and comparison is made with the calculated vortex shedding frequencies to estimate the risk of resonance.

[9] D Platonov, A Minakov and A Sentyabov, 2019, "Numerical investigation of pressure pulsations related to rotor-stator interaction in the Francis-99 turbine,"

Abstract: The paper deals with the numerical simulation of the flow in the Francis-99 hydraulic turbine at three different problem formulations, namely, the application of the method of rotating coordinate system, sliding mesh model, and consideration of a compressible fluid. The pulsations intensity and pressure pulsation spectra obtained by numerical simulation and experimentally are compared. It is shown that the simulation of a problem considering compressible fluid, and that conducted by the sliding mesh method gives significantly greater pressure amplitudes. It is also shown that the precessing vortex core is a source of pressure waves in the entire turbine flow path.

[10] G Cvijetic, L Culic and H Jasak, 2019, "Application of the harmonic balance method for regime change prediction using Francis-99 test case,"

Abstract: An efficient method for predicting the turbine start-up and shut-down flow parameters is presented in this paper. Due to start-up or shut-down usually lasting a large number of periods, simulations of such processes are highly demanding and long lasting. To alleviate this, a modified Harmonic Balance method is used, thus casting a problem into spectral space and solving start-up and shut-down simultaneously, as a complete period. By doing this, the results are obtained in a fraction of time required by time-accurate simulation. Furthermore, the same approach could be used for any change of regime from operating point OP1 to operating point OP2 and back to OP1. The method is implemented in foam-extend and suitable for solving incompressible turbulent Navier-Stokes equations. Validation is performed on two test cases: a simple 2D pump case for initial validation, followed by a Francis turbine. Francis turbine test case and experimental data are provided by the Francis-99 Workshop. For Francis turbine the power curve is assembled and compared with experiment.

[11] C Trieu, X Long and B Ji, 2019, "Vortical structures in cavitating flow on the Francis-99 draft tube cone at off-design conditions with the new omega vortex identification method,"

Abstract: The Francis turbine that operates at an off-design load exhibits a strong twist flow near the runner outlet, which causes a cavitating vortex rope on the draft tube cone. The purpose of this study is to apply the new omega vortex identification method (Ω method) and analyze and compare it with traditional methods in regard to its ability to capture the vortex rope in a Francis-99 draft tube cone under an off-design load. The advances of the Ω method for vortex identification on the cavitating flow are elaborated and analyzed. The significance of parameter ε in the Ω method is also highlighted. The determination of ε is further examined and adjusted in this study. Finally, this study demonstrates that the Ω method can be successfully applied to capture vortex structures in the cavitating flow of Francis turbines.

Go to top