Numerical simulation of pressure pulsations in Francis turbines

Transcription

1 IOP Conference Series: Earth and Environmental Science Numerical simulation of pressure pulsations in Francis turbines To cite this article: M V Magnoli and R Schilling 2012 IOP Conf. Ser.: Earth Environ. Sci View the article online for updates and enhancements. Related content - Influence of Hydraulic Design on Stability and on Pressure Pulsations in Francis Turbines at Overload, Part Load and Deep Part Load based on Numerical Simulations and Experimental Model Test Results M V Magnoli and M Maiwald - Challenges in Dynamic Pressure and Stress Predictions at No-Load Operation in Hydraulic Turbines B Nennemann, J F Morissette, J Chamberland-Lauzon et al. - Dynamic loads in Francis runners and their impact on fatigue life U Seidel, C Mende, B Hübner et al. This content was downloaded from IP address on 22/09/2018 at 19:42

2 Numerical simulation of pressure pulsations in Francis turbines M V Magnoli 1 and R Schilling 2 1 Voith Hydro Holding GmbH & Co. KG, Alexanderstr. 11, Heidenheim, Germany 2 Institute of Fluid Mechanics, TU München, Boltzmannstr. 15, Garching, Germany Marcelo.Magnoli@Voith.com Abstract. In the last decades, hydraulic turbines have experienced the increase of their power density and the extension of their operating range, leading the fluid and mechanical dynamic effects to become significantly more pronounced. The understanding of the transient fluid flow and of the associated unsteady effects is essential for the reduction of the pressure pulsation level and improvement of the machine dynamic behaviour. In this study, the instationary fluid flow through the complete turbine was numerically calculated for an existing Francis machine with high specific speed. The hybrid turbulence models DES (detached eddy simulation) and SAS (scale adaptive simulation) allowed the accurate simulation of complex dynamic flow effects, such as the rotor-stator-interaction and the draft tube instabilities. Different operating conditions, as full load, part load, higher part load and deep part load, were successfully simulated and showed very tight agreement with the experimental results from the model tests. The transient pressure field history, obtained from the CFD (computational fluid dynamics) simulation and stored for each time step, was used as input for the full instationary FEA (finite element analysis) of turbine components. The assessment of the machine dynamic motion also offered the possibility to contribute to the understanding of the pressure pulsation effects and to further increase the turbine stability. This research proect was developed at the Institute of Fluid Mechanics of the TU München. 1. Background In the last decades, the international market competition, associated to the technical evolution, drove the hydraulic turbine development to produce more compact designs, with smaller and faster machines than in the past. The current demand for energy and grid regulation services led the energy producers to enlarge the machine operating range, pushing the turbine into operating conditions, which were not experienced in years ago. With the extended operating range and with the increasing power density, several dynamic phenomena, which were not clearly noticeable in the past because of the robust structure construction, became decisive for the smooth and safe operation of modern hydraulic power plants. Among the many transient phenomena, which take place in the generating unit, the pressure oscillations in the fluid flow through the turbine and its impact on the mechanical structure is of main importance, for assuring the a reliable operation of the machine. Published under licence by Ltd 1

3 In normal operation at full load, the pressure pulsations in Francis turbines arise typically from the rotor-stator-interaction (RSI). At part load they are mainly caused by the vortex rope in the draft tube cone, associated to flow instabilities (DTI). At deep part load, the pressure oscillations are due to draft tube instabilities, runner channel vortices and to the further increasing flow deviation angle at the entrance edge of the runner blades. At extreme operating conditions, the operating stability of the unit might be compromised. The oscillating pressure field over the runner blades leads to dynamic loads on the runner structure, which produces dynamic mechanical stresses. The dynamic structural stresses add up to the static stresses, caused by the mean pressure field. In severe cases, the runner structure might fail. Such cases have been extensively reported, as for example by FISCHER ET AL. [1], COUTU ET AL. [2] and BHAVE, MURTHY AND GOYAL [3]. The current dynamic simulation methods for the Francis runners structure are very limited and do not offer the required accuracy for a reliable and competitive design. They rely basically on extrapolated test data, numerous theoretical assumptions, simplifications and experience. The numerical simulation method proposed here intends to supply an accurate tool to predict the transient flow phenomena and the dynamic mechanical stresses for the fatigue analysis. The main part of the process concentrates on the CFD simulation of the fluid flow through the entire turbine. The numerical model reproduces the complete turbine geometry and counts with e.g. the SAS and DES turbulence models. Turbulence modelling showed up to be decisive for a proper turbine flow simulation. The transient pressure field history, provided by the CFD analysis, constitutes the input for the runner mechanical stress calculation. The structural simulation is carried out with the FEM and the transient load steps are solved with the direct integration method. The calculated dynamic mechanical stresses on the runner could be even used for fatigue life prediction. As an application example, a Francis turbine with high specific speed was simulated. Its hydraulic design was developed about 20 years ago and the corresponding prototype has already been in operation for 15 years. Several operating points were chosen for the calculations, including full load, higher part load, part load and moderate deep part load. These points are representative for different types of dynamic phenomena taking place during machine operation, such as rotor-stator-interaction, vortex rope instabilities in the draft tube cone and channel vortex in the runner. The numerical results were compared to experimental results and achieved very good agreement, showing the accuracy and advantages of the method. 2. Numerical setup for CFD To investigate the pressure pulsations in radial hydraulic machines, a complete Francis turbine, n q 80 min -1, was numerically simulated with CFD. This particular machine, denominated FT 80, was chosen, since Francis machines with high specific speeds are especially affected by the adverse operating conditions at part load. The numerical simulation offered an economic possibility to investigate the nature of pressure pulsations in Francis turbines, with the additional advantage of offering practical visualisation and measuring tools, which otherwise might require complicated and expensive experimental devices. The simulated operating points were taken from real operating conditions from an existing prototype turbine, already in operation and built with exact the same geometry as the turbine model FT 80. The considered operating points comprise the optimum, full load, normal operation, part load at low and high heads and moderate deep part load. For the obective of this study, the last three load conditions are the most interesting and belong to the critical portion of the hill chart in terms of pressure oscillations. The computational model is only suitable for the investigations, if it can accurately reproduce the real behaviour of the physical flow through the turbine, qualitatively as well as quantitatively. Therefore, after the preparation of the numerical model, it was preliminary verified by stationary simulations, whose results were compared to the experimental head, flow, power and efficiency measurements available from the model test. 2

4 Figure 1. Computational mesh for the fluid flow simulation. As the main interest of the simulations was in reproducing the transient phenomena, the instationary calculations were also verified by the observations and pressure oscillation values from the experimental data Steady-state flow simulations The numerical steady-state flow simulations were carried out with the finite volume method (FVM) applied to the complete turbine with all its maor hydraulic components: spiral case, stay vanes, guide vanes, runner and draft tube. The calculations were conducted in a coupled manner, i.e. considering all the turbine components and interfaces between them, since the dynamic effects in the fluid flow through the turbine arise from the interaction between the rotating runner and the stationary parts. Different computational mesh densities were tested and optimized to deliver accurate results with acceptable computation times. The final computational mesh counted with more than 6 million cells and part of it can be seen in Figure 1. The employed FVM made use of second-order interpolation schemes. With the preliminary steady-state flow simulations, different turbulence models were tested: standard k-, k- LCL, k- and k- SST, and no significant influence on the results was noticed. However, the standard k- model achieved the best agreement with the available experimental results. The comparison between the results from the computational simulation and from the model test is reproduced in Table 1. The accuracy provided by the numerical model offers a maximum deviation of less than 2% Transient simulations For the simulation of the instationary effects in the fluid flow through the turbine, like rotor-stator interaction and flow instabilities in the draft tube, adequate time resolution and turbulence models were needed. Approximately 400 time steps were calculated for each runner revolution, in order to not only capture the effects from the draft tube instabilities, but also from the rotor-stator interaction. Concerning the turbulence modelling, the URANS (unsteady averaged Navier-Stokes equations) model introduced excessive artificial dissipation in the flow simulation, as expected by FRÖHLICH AND RODI [4], and turned out to be unable to reproduce the highly transient effects in the turbine, especially in the draft tube. Therefore, more sophisticated turbulence models had to be employed. 3

5 Table 1. Experimental results obtained at the model test and numerically simulated results. Model Test Simulation Deviation Operating Point n ' 1/n ' 1,opt Q ' 1/Q ' 1,opt T ' 1/T ' 1,opt / opt n ' 1/n ' 1,opt Q ' 1/Q ' 1,opt T ' 1/T ' 1,opt / opt n ' 1 Q ' 1 T ' 1 (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) Optimum Full Load Normal High Head Low Head The detached eddy simulation (DES), for example, attempts to resolve the turbulent eddies, which are larger then the mesh resolution, in the same way as it would be done in a strict large eddy simulation (LES). Eddies smaller than the grid resolution are modelled in the same manner as done in URANS. This hybrid behaviour is achieved by the modification of the turbulence dissipation,, with the limiter F DES, which accounts for the local mesh size. STRELETS [5] modified the k- SST model with the DES approach, coming to the modified turbulence transport equations below. k u k u i * k i kfdes kt (1) t x x x x u t x T ui i x 2 1 T 21 F (2) 1 2 x x x x The influence of the mesh resolution appears in the dissipation term, * k F DES, in the turbulence kinetic energy transport equation. The last term in the transport equation of the specific dissipation rate is the normal SST modification of the original k- model. The interpolation scheme has also to be modified for the application of the DES model. In the regions where DES assumes the LES characteristic, the interpolation function must reproduce the CDS (central difference scheme) scheme. While, in other regions, where the URANS behaviour is dominant, the interpolation function must be second-order UDS (upwind difference scheme). This blend between these two interpolations schemes is based on local flow characteristics and is described by TRAVIN ET AL. [6]. The transient numerical simulation was also verified with experimental data. The calculated and measured pressure fluctuation amplitudes at four measuring points at the draft tube cone were compared and are presented in Table 2. The shape of the vortex rope in the draft tube could also be accurately predicted by the numerical simulation, as seen in Figure 2. The transient simulation required approximately 30 runner revolutions, depending on the operating point and on the prescribed initial solution, until the instationary flow patterns were established. The computation of one revolution took, in average, 15 hours in a Linux cluster with 8 Intel Q6600 processors, each with 4 kernels, 2.4 GHz and 2 GB memory. 4

6 Table 2. Experimental results of pressure oscillation amplitude in the draft tube cone obtained at the model test and numerical results simulated with DES. Model Test Simulation Deviation Operating Point P / g H P / g H P f / f n f / f n f / f n HW 90 TW 270 HW 90 TW 270 HW 90 TW 270 (%) (%) (%) (%) (-) (%) (%) (%) (%) (-) (%) (%) (%) (%) (%) High Head Low Head Figure 2. Comparison of the vortex rope shape observed at the model test and numerically simulated at part load and high head. 3. Application The obective in the development and verification of the numerical model for the simulation of the transient fluid flow through the turbine was to allow an accurate simulation of the pressure fluctuations in the hydraulic machine, especially in the turbine runner. After the extensive verification of the numerical model with experimental data, during the numerical setup, the model accuracy was considered adequate for the extraction of dynamic results, related to the transient fluid flow. The extension of dynamic measurements in the model machine or in the prototype is very limited at present. Therefore, the numerical model developed here was used to obtain more quantitative information about the dynamic behaviour of Francis turbines, with the main purpose to predict how the pressure fluctuations might affect the loads at the runner structure. The pressure oscillations are responsible for the dynamic structural load at the runner and required for an accurate calculation of the dynamic structural stresses. The CFD model allowed the numerical computation of transient effects, providing the dynamic pressure distribution in the complete machine, including the turbine runner. The calculated pressure oscillation amplitude, P / (gh), at full load, higher part load and moderate deep part load can be found in Figure 3, Figure 4 and Figure 5. The pressure oscillation amplitude is shown as contour plot for the pressure and suction sides of the runner blades and guide vanes. The hydraulic surfaces were transformed to the meridional view. The right side of the figure corresponds to the pressure side and the left to the suction side. At full load the plot scale was limited to 3,0% to improve the visualization. 5

7 Figure 3. Pressure oscillation amplitude at the runner at full load. Figure 4. Pressure oscillation amplitude at the runner at higher part load. Figure 5. Pressure oscillation amplitude at the runner at deep part load. 6

8 Table 3. Pressure oscillation amplitudes and dynamic stresses at the runner. Pressure Oscillation Amplitude Maximum Dynamic Structural Stresses Operating Point P / (gh) Leading Edge Blade Body e,a,max / e,m,max (%) (%) (-) Full Load 13,7 2,7 0,04 Higher Part Load 8,6 6,0 0,10 Deep Part Load 14,5 7,7 0,25 At full load, the pressure oscillations were dominated by rotor-stator-interaction effects. Figure 3 shows that the distance to the guide vane trailing edges was an important parameter for the intensity of the pressure oscillations. As expected, the pressure variations were much higher at the runner blades inlet edges than at the rest of the blades bodies. The pressure oscillations decayed considerably from the blade inlet edge to the middle of the blade. The calculated values of P / (gh) were 13,7%, at the blade leading edge and 2,7% at the blade body. In opposition to full load, at higher part load, the higher pressure pulsation amplitudes were distributed at the blade body and not only at the leading edge, as seen in Figure 4. The pressure pulsation amplitudes at the blade body were higher at the suction than at the pressure side because of the vortex rope position below the runner. The maximum numerically predicted pressure oscillation amplitude was 6,0% at the blade body and 8,6% at the blade leading edge. At moderate deep part load, the pressure oscillation amplitudes were induced by the rotating vortex rope in the draft tube cone and by the channel vortex in the runner. The flow along the runner blades lost its smooth characteristic and caused higher pressure pulsation amplitudes, as observed in Figure 5. At the blade leading edge, P / (gh) reached 14,5% and at the blade body 7,7%. The transient pressure field history, calculated with the CFD model, was stored for each simulated time step and for the complete runner geometry. The pressure distribution at each time step was used as input for the instationary FEM simulation of the turbine runner, at each considered operating condition, i.e. full load, higher part load and deep part load. The transient structural simulation was solved with the direct integration method. The calculated dynamic mechanical stresses are presented in Table 3. The calculated dynamic mechanical stresses on the runner could be used for fatigue life prediction. The calculated maximum dynamic von Mises stresses, e,a,max, were normalized with the values of the maximum static von Mises stresses, e,m,max. The values presented in Table 3 came exclusively from the numerical simulations. No prototype measurements of the dynamic stresses were available for comparison with the numerically calculated stresses. The distribution of the pressure oscillation amplitude at the runner surfaces, at higher part load and deep part load, suggests that this range of the turbine hill chart results in less stable operating conditions as full load, for example. The analysis of the dynamic structural stresses in Table 3 also show that the extreme operating conditions, i.e. higher part load and deep part load, lead to higher dynamic loading of the runner structure. The ability to predict the dynamic pressure field and the associated dynamic stresses, as presented here, offers the possibility to improve the design of the hydraulic turbines, with the obective to increase the operating stability and the operating life of the equipment. 7

9 4. Conclusions The developed numerical model allowed a quite good calculation of the pressure pulsation amplitudes in the Francis turbine. The numerical results were verified with available experimental data and they presented very good agreement. With the ability to numerically predict the pressure oscillations in the complete machine, the calculated transient pressure field in the runner was used for the dynamic structural simulation of the runner structure. The analysis of different operating points showed how different operating conditions, as full load, part load, higher part load and deep part load, influenced the machine stability and the dynamic mechanical stresses in the runner. As expected, extreme operating conditions, as deep part load, were the most demanding for the machine structure. With the application of the method developed here for an accurate prediction of the pressure oscillations and dynamic mechanical loads, it is possible to assure more safe design and smoother operation of Francis machines. The further step in the investigation of the dynamic behaviour of Francis turbines, especially of the runner, will be to analyse how the predicted dynamic stresses affect the fatigue life of the machine. This will allow estimating how much each operating condition contributes to the fatigue damage of the unit. References [1] Fischer R, Seidel U, Grosse G, Gfeller W and Klinger R A Case study in resonant hydroelastic vibration: the causes of runner cracks and the solutions implemented for the xiaolangdi hydroelectric proect Proc. of the 21st IAHR Symp. (Lausanne, Switzerland, 2002) [2] Coutu A, Proulx D, Coulson S and Demers A Dynamic assessment of hydraulic turbines Proc. of HydroVision 2004 (Quebec, Canada, 2004) [3] Bhave S K, Murthy C B and Goyal S K 1986 International Water Power and Dam Construction 38(1) [4] Fröhlich J and Rodi W 2000 Introduction to Large-Eddy Simulation of Turbulent Flows (Cambridge: Cambridge University Press) [5] Strelets M Detached eddy simulation of massively separated flows 39th Aerospace Sciences Meeting and Exhibit (Reno, USA, 2001) [6] Travin A, Shur M, Strelets M and Spalart P R Physical and numerical upgrades in the detachededdy simulation of complex turbulent flows EUROMECH Colloquium on LES of Complex transitional and turbulent flows (München, Germany, 2000) 8