Determination of turbine runner dynamic behaviour under operating condition by a two-way staggered fluid-structureinteraction method

Transcription

1 IOP Conference Series: Earth and Environmental Science Determination of turbine runner dynamic behaviour under operating condition by a two-way staggered fluid-structureinteraction method To cite this article: F Dompierre and M Sabourin 2010 IOP Conf. Ser.: Earth Environ. Sci Related content - Influence of the rotor-stator interaction on the dynamic stresses of Francis runners R Guillaume, J L Deniau, D Scolaro et al. - Challenges in Dynamic Pressure and Stress Predictions at No-Load Operation in Hydraulic Turbines B Nennemann, J F Morissette, J Chamberland-Lauzon et al. - Evaluation of RSI-induced stresses in Francis runners U Seidel, B Hübner, J Löfflad et al. View the article online for updates and enhancements. This content was downloaded from IP address on 29/04/2018 at 06:48

2 Determination of turbine runner dynamic behaviour under operating condition by a two-way staggered fluid-structure interaction method 1. Introduction F Dompierre 1 and M Sabourin 1 1 Alstom Power Systems, Hydro 1350 chemin Saint-Roch, Sorel-Tracy (Québec), Canada, J3R 5P9 frederick.dompierre@power.alstom.com Abstract. This paper presents the application of the two-way fluid-structure interaction method introduced by ANSYS to calculate the dynamic behaviour of a Francis turbine runner under operating condition. This time-dependant calculation directly takes into account characteristics of the flow and particularly the pressure fluctuations caused by the rotor-stator interaction. This formulation allows the calculation of the damping forces of the whole system implicitly. Thereafter, the calculated dynamic stress can be used for a fatigue analysis. A verification of the mechanical and fluid simulations used as input for the fluid-structure interaction calculation is first performed. Subsequently, a connection of these two independent simulations is made. A validation according to the hydraulic conditions is made with the measurements from the scale model testing. Afterwards, the static displacement of the runner under the hydraulic load is compared with the results of a classical static analysis for verification purposes. Finally, the natural frequencies deduced by the post-processing of the dynamic portion of the runner displacement with respect to time are compared with the natural frequencies obtained from a classical acoustic modal analysis. All comparisons show a good agreement with experimental data or results obtained with conventional methods. The failure of hydraulic turbine components under operating condition may cause important losses of production for hydroelectric plant owners. The runner, which is responsible of the conversion of hydraulic energy into mechanical energy, is the most vulnerable component since it is exposed to many sources of dynamic excitation. To avoid its failure, it is therefore of a great importance to predict its dynamic behaviour at the design stage. However, this prediction is not simple because of the system's complexity, which includes the runner itself and the flow passing through it. The fluid-structure interaction (FSI) involved presents a strong coupling. A decade ago, acoustic modal analysis has emerged to allow the prediction of the natural frequencies of turbine runners in still water [1, 2, 3]. Because the excitation frequencies are relatively well known, this method allows to establish if a frequency match exists between a structural vibration mode and a given hydraulic excitation. More recently, harmonic acoustic analysis has been used to quantify the dynamic response of turbine runner taking into account the geometric compatibility between fluid excitation calculated by Computational Fluid Dynamics (CFD) and a single mode calculated in still water [4], [5]. Nevertheless, a parameter of major influence in the vicinity of the resonance remains unknown, namely the damping force contribution. Indeed, the damping factor in still water is usually much lower than when the flow is taken into account [6]. It also depends strongly on the vibration mode considered. For a harmonic acoustic analysis, the damping factor is an input that must be determined empirically. This paper presents the application of the two-way FSI method introduced by ANSYS to predict the dynamic behaviour of a Francis turbine runner under normal operating condition. This method allows the calculation of the runner dynamic response with respect to time taking into account all the characteristics of the flow such as the fluid viscosity and turbulence. The damping contribution is then calculated implicitly. This method has been validated for simple academic test cases of free vibration in still water [7]. c 2010 Ltd 1

3 2. Francis Turbine Analysis The simulated case presented in this paper corresponds to a Francis turbine at industrial scale having 15 runner blades and 20 guide vanes. This particular configuration allows the modeling of one 5 th of the system and the reduction of the mesh size by the use of cyclic symmetry conditions. The distributor is approximated as being axisymmetric and the model includes only the draft tube cone. The computational domain is shown in Fig. 1. Fig. 1 Geometry of the domain used for the Francis turbine simulation Some simplifications have been made to the turbine geometry to facilitate the calculation. First, the balancing pipes have been replaced by balancing holes. Secondly, labyrinth seal clearances have been tripled to avoid excessive local mesh resolution. The computation by the two-way FSI method is made by the union of a classical mechanical simulation and a classical CFD simulation. To ensure proper behaviour of the FSI simulation, each basic simulation must be verified independently before their coupling. 3. Mechanical Simulation The mesh of the mechanical simulation is made of tetrahedral quadratic elements. The resolution is about nodes for one 5 th of the runner. This mesh is presented in Fig. 2. Table 1 Mechanical analysis parameters Parameters Units Time step (s) 2.5 * 10-4 Rotational Speed (RPM) 300 Gravitational (m/s 2 ) 9.81 Acceleration Solver type - Direct Non-linear method - Newton- Raphson Fig. 2 Solid mesh corresponding to one 5 th of the Francis turbine runner 2

4 A static analysis of the runner made at the runaway speed has been compared with a similar analysis for a complete runner. The calculated displacements were compared to check the convergence and the consistency of the model including cyclic symmetry conditions. From the verified static analysis, a time-dependant analysis is built. Since this simulation is used as an input to the simulation including FSI, all surfaces in contact with water are flagged to allow the imposition of pressure fields which will come from the CFD calculation. No structural damping is imposed since the damping contribution of fluid flow is assumed to be much higher. The mechanical analysis parameters are summarized in Table CFD Simulation The turbine operating point used for the calculation has been chosen to maximize the rotor-stator interaction (RSI) intensity. The guide vanes opening angle is then set to maximum in order to reduce the gap between the guide vanes outlet and the runner blade inlet. The meshes used for the static and the rotating parts of the fluid simulation are of unstructured tetrahedral type. An inflate of prismatic elements is applied on all solid walls of the runner. The resolution of the fluid meshes is summarized in Table 2. A cross section of the meshes at the distributor axis elevation is shown in Fig. 3. Table 2 Resolution of the CFD meshes Domain Resolution (Nodes) Distributor Runner Fig. 3 Fluid mesh section of the turbine at the distributor axis elevation As boundary conditions, the flow angle at the inlet section is set to ensure the flow alignment with the stay vanes. A total pressure condition with an average turbulence intensity of 5% and a length scale equal to 10% of the inlet height are imposed at the inlet section. An average static pressure condition is set at the outlet section. The connection between static and rotating meshes is of "transient rotor-stator" type. This connection type allows to fully take into account the fluctuations generated by the RSI. The K-ε turbulence model is selected for this study. A convergence study with respect to the spatial resolution and timestep has been performed to ensure that the pressure fluctuations, the power output and the mass flow corresponding to the considered operation point are well converged. To obtain the mass flow of the chosen operating point from the model test, the net head imposed needs to be corrected by -3.0%. This discrepancy is due to the fact that only a portion of the turbine is modeled. Thus, losses in the spiral case and the draft tube are not computed. The theoretical power output evaluated by the torque on the runner differs by -4.1% from the measured value. This difference can be explained by the application of a reduced net head, the boundary conditions and differences between the geometry used for the simulation and the 3

5 real turbine geometry. Since this study aims at the prediction of the runner dynamic behaviour, emphasis is rather on the pressure fluctuations than the exact prediction of hydraulic conditions related to the model testing operating condition. In this perspective, the CFD calculation is satisfactory. A good way to quantify the RSI intensity is to track the dynamic torque fluctuation applied on the runner blades. Fig. 4 shows the blade torque curves with respect to time coming from the CFD calculation. Fig. 4 Blade torque curves with respect to time Each curve presents a phase shift and alternating peaks of high and low intensity. This phenomenon can be explained by the fact that the turbine has one stay vane for two wicket gates. The maximum fluctuation is about + / - 5.4% of the mean torque and the frequency of the first theoretical harmonic of the RSI is perfectly predicted by the CFD calculation. 5. Fluid-Structure Interaction Simulation The calculation including FSI is based on the connection of the two simulations presented in the previous sections. The bidirectional resolution scheme is presented in Fig. 5. Fig. 5 Bidirectional resolution scheme used for FSI simulations Fig. 6 Comparison between calculated and measured pressure fluctuations in the gap between the wicket gates and the runner blades (horizontal axes not at the same scale) 4

6 At the initial time, the runner is at rest and pressure fields coming from CFD calculation of the turbine under normal operating condition are applied impulsively. This starting condition is obviously not physical but allows the excitation of many modes in the vibration transient response of the runner such as the torsion and uprising modes. The identification of natural frequencies associated to these modes allows to validate the two-way FSI method by comparing the results with those calculated by a classical acoustic modal analysis. The hydraulic conditions of the FSI calculation are strictly the same as those corresponding to the CFD only calculation. The pressure fluctuations taken in the gap between the wicket gates and the runner blades are compared to those measured during the model testing. This comparison is shown in Fig. 6. The amplitude of calculated pressure fluctuations shows good agreement with measured ones. To validate the simulation including FSI, the displacement signals with respect to time are recorded at several material points attached to the runner. The positioning of these points is presented in Fig. 7. The displacement signals can be split into a static contribution and a dynamic contribution. The static contribution is first compared with a typical static analysis. A comparison of normalized static displacements according to the power output can be used in order to validate that the magnitude of the results given by the two-way FSI calculation are consistent. The differences between the displacements given by the two methods are presented in Table 3. Table 3 Comparison between static displacements obtained by the two-way FSI calculation and by a conventional static analysis Fig. 7 Location of material points where displacement signals are recorded Location Radial Displacement Tangential Displacement (%) (%) Crown N/D 7.1 Leading Edge Trailing Edge Band Given the assumptions outlined in Section 2, the differences obtained show that the FSI method is coherent considering the static displacements. The analysis of the dynamic contribution of the displacement signals recorded at the different material points allows the determination of natural frequencies. These signals are presented in Fig. 8 and 9. Fig. 8 Displacement signals recorded at the material points attached to the runner at the begin of simulation 5

7 The entire signals simulated are divided into four sub-sections for analysis purpose. Here is a description of the first three ones: I: Portion of the signals where the runner is subjected to the initial impulsive loading. The torsion modes are clearly involved (first and second orders) by the imposition of the full torque on the runner blades. Also, the resultant force generates a hydraulic axial thrust exciting the uprising mode. The higher order modes are quickly damped, leaving only the first order torsion mode. II: Portion of the signal where the first order torsion mode is basically dominant. All signals have the same phase during the first moments of portion II. For the last moments of this signal portion, a phase shift between the trailing edges due to RSI begins to settle. III: Portion of the signal where the runner is in transient vibration due to the RSI excitation. The phase shift of the blades begins to adjust. The leading edges have essentially zero phase shift between each other ones, while the trailing edges tend to have a phase shift of 120 degrees between them. Portion III corresponds to an adjustment time period where the entire runner structure acquires energy and synchronizes with the RSI excitation. Also, in portion III, the contribution of the torsion mode disappears since there is no compatible excitation coming from the flow. Fig. 9 shows the steady state portion of the displacement signals. Fig. 9 Displacement signals recorded at the material points on the runner after the reaching of the steady state In portion IV of the signals, the vibration is stationary. Not surprisingly, the points which experience the largest dynamic amplitude are those associated to the trailing edges, followed by those associated to the band and the leading edges. The signals recorded from the points attached to the crown do not show any significant variation. All signals have contributions from two frequencies: the frequency of the first harmonic provided by the RSI theory and the natural frequency corresponding to the 5-nodal-diameter mode which is 55% higher (see Table 4 for a summary of the natural frequencies identified). The excitation has the same 5-nodal-diameter configuration than the excited mode. Despite an important frequency mismatch, the geometric compatibility between the excitation and the mode exists. This compatibility explains the presence of 5-nodal-diameter mode contribution in the steady state signals. It can be seen from Fig. 9 that the signals recorded at the trailing edges are out of phase with each other ones. The maximum amplitude is found at point TE2 followed by point TE3. The minimum amplitude is found at point TE1. Analysis of band deformation amplitude can help to understand the causes of this phenomenon. Fig. 10 shows the radial dynamic amplitude of the points located at the bottom of the band with respect to time. According to Fig. 7, points BAND1 to BAND6 are distributed uniformly in azimuth on one 5 th of the runner. The radial amplitude of these points with respect to time shows a quasi-sinusoidal shape of the band which corresponds to the complete runner to a 5-nodal-diameter deformation. The variations to the perfect sine shape are related to the rigidity discontinuities caused by the presence of the blades. A nodal point where the amplitude does not vary with respect to time is located between points BAND6 and BAND1. From Fig. 7, it can be seen that this point corresponds to the junction of blade 1 to the band. This observation explains why point TE1 shows a smaller displacement than the homologous points which are amplified by the radial displacement of the band. 6

8 Fig. 10 Radial dynamic amplitude of the band with respect to time Table 4 presents a comparison between the natural frequencies obtained by the analysis of the dynamic portion of the displacement signals calculated by the two-way FSI method and a classical acoustic modal analysis. Table 4 Comparison of natural frequencies calculated by the two-way FSI method and the acoustic method Modal Analysis Acoustic Modal Analysis FSI Analysis Mode Shapes Nat. Freq. (Vaccum) Nat. Freq. (Water) Nat. Freq. (Water) (Hz) (Hz) (Hz) Torsion ND Uprising ND The natural frequencies predicted by the two-way FSI calculation and the acoustic calculation are very similar for all modes except for the torsion mode. Apart from this mode, the difference between the predictions does not exceed 3%. This error is of the same order as the typical error with measurements. For torsion mode, the difference reaches nearly 17%. A reduction in the torsion mode is due to the presence of balancing holes integrated to the geometry used in two-way FSI simulation. These holes are nonexistent for the geometry used with the acoustic simulation. This geometric difference, however, can not alone explain the difference obtained. It is possible that the presence of flow in the simulation using the two-way FSI method produces a significant increase in the fluid added mass when compared with the same runner in still water as modeled by the acoustic method. An extra fluid added mass tends to lower the related natural frequency. Fig. 11 shows the comparison of the 5-nodal-diameter mode calculated by the acoustic method and by the two-way FSI method. The results are very similar, which shows good consistency. Fig. 11 Amplitude contours of the 5-nodal-diameter mode calculated by the acoustic method and by the twoway FSI method 7

9 6. Consideration on the computational resources needed The FSI simulation presented in this paper requires a high amount of computation time before reaching the steady state for the dynamic response of the runner. Tables 5 and 6 show the characteristics of the computer used and the resources needed by the two-way FSI calculation respectively. Table 5 Characteristics of the computer used for FSI calculation Processor nb - Intel Core i7 920 Core nb - 4 RAM memory type - DDR3 RAM memory (Gig) 12 Table 6 Resources used by the two-way FSI calculation Solid Mesh (Node) Fluid Mesh (Node) Timestep (s) Simulation time (s) Computation time (Day) 95 RAM memory used (Gig) 10 The calculation time is excessive to allow the use of the two-way FSI method as standard analysis at the design stage of turbine runners. Nevertheless, improvements of computing time is possible for reaching the steady state. The injection of the runner static displacement under time-averaged hydraulic load can reduce the transient response time. Obviously, the use of a more powerful computer could further reduce the computation time. 7. Conclusion This paper aimed to assess the capability of the two-way FSI method introduced by ANSYS to provide an accurate prediction of the dynamic behaviour of a Francis turbine runner under operating condition. This method offers the advantage of taking into account the strong coupling between the solid and the fluid medium, conserving all the characteristics of fluid flow such as viscosity and turbulence. This feature may be of primary importance when the structure vibrates in the vicinity of resonance. For this condition, the dynamic amplification is very sensitive to the damping forces. The hydraulic portion of the simulation showed good agreement with measurements realized during the model testing. Without target values coming from prototype structural measurements, a comparison of the results obtained by the two-way FSI method can still be made with the results coming from conventional validated methods. This comparison has shown quite good agreement. The static displacements obtained by the two-way FSI method were similar to those obtained by a classical static analysis. Moreover, the natural frequencies obtained were very close to those obtained by conventional acoustic analysis. Although the method calculates the damping factor implicitly, no comparison measurement is currently available to allow the validation of this aspect. The prediction of the damping ratio will be the subject of future investigations. Despite the advantages of the two-way FSI method, the computation time remains currently excessive for its use in a standard design procedure. However, improvements in computation time can be achieved. Finally, it would be of interest to test the two-way FSI method for the prediction of the dynamic behaviour of turbine runners subjected to other hydraulic excitations than RSI, such as the release of von Karman vortices and the partial load vortex rope. Acknowledgments The authors would like to thank École Polytechnique de Montréal, Natural Sciences and Engineering Research Council of Canada and Alstom Hydro Canada Inc. for their contribution to this project. References [1] Jacquet-Richardet G. and Dal-Ferro C 1996 Reduction Method for Finite Element Dynamic Analysis of Submerged Turbomachinery Wheels Computers and Structures 61(6) [2] Sena M, Reynaud G and Kueny J L 1999 Dynamic Behaviour Improvement of Francis Turbine Runners Hydropower and Dams (1) 90-5 [3] Liang Q W, Rodriguez C G, Egusquiza E, Escaler X and Avellan F 2006 Modal Response of Hydraulic Turbine 8

10 Runners Proc. of 23 rd IAHR Symp. on Hydr. Machin. and Syst.(Yokohama, Japan) [4] Coutu A, Velagandula O and Nennemann B 2005 Francis Runner Forced Response Technology Waterpower XIV (Austin, US) [5] Lais S, Liang Q, Henggeler U and Weiss T 2008 Dynamic Analysis of Francis Runners - Experiment and Numerical Simulation Proc. of 24 th IAHR Symp. on Hydr. Machin. and Syst. (Foz de Iguassu, Brasil) [6] Roth S, Calmon M, Farhat M, Muench C, Huebner B and Avellan F 2009 Hydrodynamic Damping Identification from an Impulse Response of a Vibrating Blade Proc. of 3 rd Int. Meet. of the Workg. on Cavit. and Dyn. Probl. in Hydr. Machin. and Syst. (Brno, Czech Republic) [7] Dompierre F, Sabourin M and Pelletier D 2008 Simulation of Structure Vibration in Water Proc. of 24 th IAHR Symp. on Hydr. Machin. and Syst. (Foz de Iguassu, Brasil) 9