Numerical simulation of Fluid-Structure Interaction in high head Francis turbines
Abstract
Renewable energy sources are becoming an integral part of the global energy mix. As hydropower can be used to stabilize the new energy market, this calls for increased demands from Francis turbines. Accurate calculation of the dynamic loads, as well as estimation of the deflection and stresses in the turbine materials, is essential for safe and reliable operation of modern turbines.
The primary objective of this work has been to investigate the phenomenon of resonance in Francis turbines. A procedure for numerically simulating this is presented, a three-step procedure consisting of calculating a fluid pressure, a damping ratio, and finally performing a coupled structural-acoustic simulation. The pressure in the runner channel is shown to be the sum of the viscous and acoustic pressure contributions, and this corresponds well with experiments.
Included in structural- acoustic simulations is the effect of added mass. This effect will lower the natural frequency of the turbine runner from the frequency of freevibration in a vacuum. Added mass is crucial to include, as one of the critical points in a design process is to ensure that the load frequency is not equal to the natural frequency of the runner.
Obtaining accurate viscous load from CFD was shown to be straightforward. Both full turbine models and reduced geometry models predicted pressure fluctuations within a couple of percent of experimental results. The damping ratio can be obtained by a modal work approach, a one-way CFD simulation using the mode shape and frequency of the structure as input. On a simplified blade cascade this was shown to be a very successful procedure, and easy to apply to turbine-like structures as well. Another interesting finding was a nearly linear relationship between the damping and a reduced velocity parameter. This relation could be used as a rough estimate for damping if CFD analysis is not performed.
As the computational expense of performing accurate fluid and mechanical simulations are high, several model order reduction procedures have been tested. Depending on the physical domain, and solver method, different methods are used. In fluid simulations, it is seen that the most efficient way of reducing simulation time is to solve in the frequency domain. These methods are under development; however, there exist similar strategies today that can be used to reduce the geometrical domain as well.
In the structural domain, the goal is to reduce the coefficient matrices in the governing second order equations. This is done in two different ways, using a modal decomposition method, and Krylov vectors as vector space. The modal decomposition method provides a way of solving a quasi-two-way coupled fluid-structure simulation. Here an interesting added stiffness effect was observed when the flow across a hydrofoil was increased. The Krylov vector approach was shown to provide almost identical results as solving the full structural model.
Has parts
Paper 1: Tengs, Erik Os; Fevåg, Live Salvesen; Storli, Pål-Tore Selbo. Francis-99: Coupled simulation of the resonance effects in runner channels. Journal of Physics: Conference Series 2019 ;Volum 1296.(1) s. 1-16 - Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. (CC BY 3.0) https://doi.org/10.1088/1742-6596/1296/1/012005Paper 2: Effects of passage modelling in high head Francis turbines Tengs, E. , Storli, P. T. , Holst, M. A. Hydropower and Dams, E-Proceedings Hydro 2017 International Journal of Applied Mechanics and Engineering
Paper 3: Numerical simulation of the hydrodynamic damping of a vibrating hydrofoil Tengs, E., Bergan, C.W. , Jakobsen, KR. , Storli, P. T. IOP Conference Series: Earth and Environmental Science, 240 062002, 2019 Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. (CC BY 3.0) https://doi.org/10.1088/1755-1315/240/6/062002
Paper 4: Tengs, Erik Os; Charrassier, Flora; Holst, Martin; Storli, Pål-Tore Selbo. Model Order Reduction Technique Applied on Harmonic Analysis of a Submerged Vibrating Blade. International Journal of Applied Mechanics and Engineering 2019 ;Volum 24.(1) s. 131-142 - Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) https://doi.org/10.2478/ijame-2019-0009
Paper 5: Tengs, Erik Os; Einzinger, Johannes; Storli, Pål-Tore Selbo. Two-way coupled simulation of the Francis-99 hydrofoil using model order reduction. Journal of Physics: Conference Series 2019 ;Volum 1296 Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. (CC BY 3.0) https://doi.org/10.1088/1742-6596/1296/1/012001
Paper 6: Tengs, Erik Os; Storli, Pål-Tore Selbo; Holst, Martin. Numerical Generation of Hill-Diagrams; Validation on the Francis99 Model Turbine. International Journal of Fluid Machinery and Systems 2018 ;Volum 11.(3) s. 294-303 https://doi.org/10.5293/IJFMS.2018.11.3.294
Paper 7: Tengs, Erik Os; Storli, Pål-Tore Selbo; Holst, Martin. Optimization procedure for variable speed turbine design. Engineering Applications of Computational Fluid Mechanics 2018 ;Volum 12.(1) s. 652-661 This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), (CC BY 4.0) https://doi.org/10.1080/19942060.2018.1507950
Paper 8: Reducing computational effort of high head Francis turbines Jakobsen, KR., Tengs, E., Holst, M. A. IOP Conference Series: Earth and Environmental Science, 240 072001, 2019 - Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. CC BY 3.0 Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd https://doi.org/10.1088/1755-1315/240/7/072001
Paper 9: High Efficiency CFD Simulations of High Head Francis Turbines Jakobsen, KR., Tengs, E., Holst, M. A. International Journal of Fluid Machinery and Systems, Accepted for publication, 2019
Paper 10: Bergan, Carl Werdelin; Tengs, Erik Os; Solemslie, Bjørn Winther; Dahlhaug, Ole Gunnar. An Experimental Investigation of the Hydroynamic Damping of Vibrating Hydrofoils. IOP Conference Series: Earth and Environmental Science (EES) 2019 ;Volum 240.(6) s. 1-10 - Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. CC BY 3.0 Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd. https://doi.org/10.1088/1755-1315/240/6/062008
Paper 11: Bergan, Carl Werdelin; Tengs, Erik Os; Solemslie, Bjørn Winther; Østby, Petter Thorvald Krogh; Dahlhaug, Ole Gunnar. Damping Measurements on a Multi-Blade Cascade with Multiple Degrees of Freedom: A Francis-99 Test Case. Journal of Physics: Conference Series 2019 ;Volum 1296.(1) s. 1-12 - - Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. CC BY 3.0 Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd. https://doi.org/10.1088/1742-6596/1296/1/012003