atw - International Journal for Nuclear Power | 10.2020

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atw Vol. 65 (2020) | Issue 10 ı October RESEARCH AND INNOVATION 516 | Fig. 3. HDR test facility modelling approach. Modelling approach with OpenFOAM-v7 During the modelling of the HDR test facility with OpenFOAM-v7 dif ferent aspects concerning initial and boundary conditions, meshing process, equation of state (EOS) and overall simulation parameters where optimized to a point where simulation stability, computation time as well as result quality are in reasonable equilibrium. The meshing process revealed that it is necessary to model the whole cooling circuit as only modelling the part between break nozzle and RPV results in unneglectable deviation of the pressure dynamics. Furthermore, making a well-structured hexahedral mesh with the commercial program ANSYS ICEM (Figure 3) instead an unstructured hexahedral mesh with snappyHexMesh significantly improves simulation stability as well as result quality. In order to model the check valve, the boundary condition activeBaffle Velocity was modified so closure times can be modelled according to the user’s demands. As an alternative a dynamic mesh approach can be implemented using a fixed wall in a rotating area to close off the pipe | Fig. 4. Simulation results for the damped check valve implementation. diameter. However, this approach increases the computation time while lowering the simulation stability without improving the result quality. In terms of boundary conditions, it leads to much better simulation stability to apply saturation pressure at the break nozzle (Figure 3) instead of atmospheric pressure as atmospheric pressure is much lower than vapor pressure for the experiments. This approach also allows for a better comparison between before and after applying a cavitation model. Initial condition wise system pressure is applied to the whole domain while water temperature is set to 220 °C and non-condensable steam at the RPV top is set to saturation temperature at 285 °C (Figure 3). Applying stationary operation state flow conditions does not influence the simulation results compared to a zero velocity initialization. To capture pressure driven density variations of water and steam linear equations of state are used for both phases neglecting non-linear change of state variables. For steam the ideal gas equation [GRE19] (13) is applied with R g as the special gas constant. To compute the density variation for water the stiffened EOS (perfectFluid) [GRE19] (14) is used where p 0 is a reference density and the so called fluid ‘constant’ R f can be evaluated with the relationship [GRE19] (15) where c is the speed of sound. Using real gas equations like the approach from Peng and Robinson is possible in OpenFOAM but results in higher computation times. However, in literature deviation up to 30 % are described when using linear EOS especially for gases at high pressure [SIR17]. In future work the influence of non-linear change of state variables will be conducted. In order to model turbulence, the SST k-ω-model from Wilcox is used. Simulation results The pressure evaluation at measurement position for the damped check valve implementation (Figure 4) shows good results with cavitation modelling (red) while without cavitation modelling larger deviation compared to the experiment data (black) occur. After detonating the burst disk (0.0 s) the reflection behavior of the pressure balance wave between the break nozzle and the RPV (0.0-0.1 s) is in decent agreement to the experimental data for both simulations. While the timing of the pressure peak (0.1 s) is in good comparison to the experimental data the peak is overshot without cavitation modelling (150 bar). Applying cavitation, the pressure peak decreases towards the experimental value at 120 bar improving the results as cavitation effects at the check valve are considered (Figure 5). After the pressure peak the pressure decrease is undershot and the low frequent pressure amplitude is not modelled with either simulation approach leading to deviations to the experimental data. In the report of KIT strong pipe oscillation are mentioned after the pressure peak which can influence fluid properties. For the non-damped check valve implementation (Figure 6), the pressure peak (0.09 s) is overshot Research and Innovation Water Hammer Simulation in Pipe Systems with Open Source Code OpenFOAM ı Paul Fuchs and Marco K. Koch
atw Vol. 65 (2020) | Issue 10 ı October | Fig. 5. Cavitation effects at the check valve. without (green) and with cavitation modelling (red) at around 320 bar compared to 250 bar measured during the experiment (black). This overestimation is caused by deviation between real density and computed density according to the perfectFluid EOS. It is therefore necessary to implement either a better EOS for high pressure ranges at high temperatures or use a fitting polynomial based on material properties to improve the peak quantity. After the initial pressure peak vapor pressure is reached at measurement point resulting in evaporation between check valve and RPV (Figure 7) leading to a delayed second pressure peak at 0.2 s. If no cavitation model is used the delay is not captured accordingly leading to an earlier second peak at 0.15 s while pressure drops near 0 bar. Applying the Kunz cavitation model the timing of the second peak fits the experimental data very well while the peak amplitude is underestimated at 160 bar compared to 190 bar. This further leads to a different frequency and amplitude of the following cavitation influenced three pressure peaks (0.25 to 0.4 s). A scaling of the empirical condensation and vaporization constants (eq. 10, 11) will probably improve the results in this regard. Looking at the well captured fifth pressure increase (0.45 s, red) as well as the upcoming reflection behavior (0.45 to 0.9 s) an overestimation of the frequency occurs. This deviation can be explained with either missing fluid structure interaction effects or from inaccuracies resulting from the perfectFluid EOS. Conclusion The implementation of the Kunz cavitation model for a multi fluid, fully compressible VOF approach improves the simulation results of the HDR test facility showing that cavi tation effects influence the water hammer phenomena significantly. Especially for the non-damped check valve implementation the dynamic pressure changes are in much better agreement to the experimental data as macro cavitation in the pipe section between check valve and RPV is considered. However, deviations of pressure amplitude still persist for high pressure peaks suggesting an improvement of the density calculation. As the perfectFluid EOS assumes a constant sonic speed pressure dependent compressibility changes are neglected. In order to capture effects of fluid structure interaction during the water hammer phenomena further development concerning the coupling interface preCICE [BUN16] between OpenFOAM-v7 and CalculiX [DHO18] will be done. The goal is to develop an OpenFOAM-v7 solver specialized to accurately model water hammer phenomena regarding high pressure changes, cavitation effects as well as fluid structure interaction for different systems. References [BRA19] Bratfisch, C.; Stahlberg, G.; Koch, M.K.: Simulation von Druckstoßphänomenen in kerntechnischen Anlagen mit ATHLET, Technical report regarding BMWi research project 1501522, January 2019, PSS-TR-6. [BUN16] Bungartz, H.J. et Al.: preCICE – A fully parallel library for multiphysics surface coupling, Research article, Computer & Fluids Volume 141 p. 250-258, December 2016. [DHO18] Dhondt, G.: CalculiX CrunchiX USER’S MANUAL version 2.14, April 2018. [GIO04] Giot, M. et al.: TWO-PHASE FLOW WATER HAMMER TRANSIENTS AND INDUCED LOADS ON MATERIALS AND STRUCTURES OF NUCLEAR POWER PLANTS (WAHALoads). Technical report, 2004. [GRE19] Greenshields, C. J.: OpenFOAM User Guide version 7. The OpenFOAM Foundation, 2019. [HDR81] KIT: HDR Sicherheitsprogramm – Untersuchungen an einem Speisewasserrückschlagventil NW 350 bei Bruch einer Reaktorkühlmittelleitung. Kernforschungszentrum Karlsruhe (KIT), 1981. | Fig. 6. Simulation results for the non-damped check valve implementation. [KUN99] Kunz, R.F. et. Al.: A Preconditioned Navier-Stokes Method for Two-Phase Flows with Application to Cavitation Prediction, American Institute of Aeronautics and Astronautics (AIAA), 1999. [LUE13] Lüdecke, H. J. et al.: KSB Know-how, Band 1 Der Druckstoß. KSB Aktiengesellschaft, Halle (Saale), 2013. [SAN13] Santiago, M.D.: An Extended Mixture Model for the Simultaneous Treatment of Short and Long Scale Interfaces, PhD thesis, Universidad Nacional del Litoral, 2013. [SIR17] Sirignano, W.A.: Compressible flow at high pressure with linear equation of state, research article, Cambridge University Press, December 2017. [VAL99] Valencia, L.; Bacher, H. P.: Rückbau des Heißdampfreaktors in Kahl am Main bei Aschaffenburg, Kernforschungszentrum Karlsruhe (KIT), 1999. [WAR13] Wardle, K.E.; Weller, H.G.: Hybrid Multiphase CFD Solver for Coupled Dispersed/Segregated Flows in Liquid-Liquid Extraction, International Journal of Chemical Engineering, Research Article, 2013. [YU17] | Fig. 7. Cavitation effects at the pipe section between check valve and RPV. Authors Yu, H.; Goldsworthy, L.; Brandner, P. A.; Garaniya, V.: Applied Mathematical Modelling 45 – Development of a compressible multiphase cavitation approach for diesel spray modelling p. 705-727. ELSEVIER, 2017. Paul Fuchs paul.fuchs@pss.rub.de Prof. Marco K. Koch Ruhr-Universität Bochum Plant Simulation and Safety Group Universitätsstraße 150 44801 Bochum, Germany RESEARCH AND INNOVATION 517 Research and Innovation Water Hammer Simulation in Pipe Systems with Open Source Code OpenFOAM ı Paul Fuchs and Marco K. Koch
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