atw - International Journal for Nuclear Power | 10.2020

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atw Vol. 65 (2020) | Issue 10 ı October RESEARCH AND INNOVATION 514 Planned entry for This work is funded by the German Federal Ministry of Economic Affairs and Energy under grant number 1501579 on the basis of a decision by the German Bundestag. The simulations are performed with the code version Open- FOAM-v7 developed by the OpenFOAM Foundation. Water Hammer Simulation in Pipe Systems with Open Source Code OpenFOAM Paul Fuchs and Marco K. Koch Water hammer phenomena can generally be divided into two main parts, the direct and the indirect phenomena. For the direct water hammer phenomena, a shock wave is induced due to the sudden deceleration of a fluid leading to a local rise in pressure. The shock wave then travels through the pipe system and effects like wave reflection, interference, superposition are to be concerned. Furthermore, the valve closure time as well as the deformation of the pipe influences the quality and quantity of the shock wave. On the other hand, the indirect water hammer is induced when a local pressure drop below vapor pressure leads to evaporation and creation of steam bubbles. When the pressure rises again above vapor pressure and especially big steam bubbles implode the surrounding water is rapidly accelerated causing a secondary shock wave once a sudden deceleration occurs at impact. [LUE13] To gain sufficient knowledge of the important physical effects regarding a water hammer phenomena detailed CFD analysis are performed using the open source code OpenFOAM. Effects like propagation of shock waves, cavitation and fluid structure interaction will be included in the code as there is no default capability to model such phenomena. [GRE19] In order to test the applicability of the default code as well as the newly implemented cavitation model two water hammer experiments at the test facility “Heißdampfreaktor” (HDR) will be modelled under simplified conditions. The implementation of the cavitation model basis within the Volume of Fluid (VOF) based, fully compressible, multi fluid solver compressibleMultiphaseInterFoam is described also discussing model strength, restrictions and weaknesses. The simulation results for the two experiments will be compared with and without cavitation model in order Introduction During a loss of coolant accident (LOCA) in certain types of boiling water reactors the continuous undersupply of cooling water eventually leads to the degradation of the reactor core. In order to prevent such an accident, the loss of cooling water is prevented through fast closing valves in the cooling circuit. However, the valve closing process can induce a so called water hammer phenomena in the pipe systems which can damage structures within the cooling circuit. [GIO04] to qualify and quantify the cavitation influence during the water hammer phenomena. At the end potential code improvements and upcoming work is shortly presented. Model basis and cavitation model implementation The Volume of Fluid (VOF) based solver compressibleMultiphaseInter- Foam is fully compressible as density can be computed with multiple accessible equations of state (EOS) also regarding thermal effects. The interface tracking method between multiple non mixable fluids allows for a detailed representation of interface motion including surface tension effects. However, the mesh resolution at the interface needs to be very high in order to give accurate results leading to high computational costs for complex multiphase flows. In general, this method is used for free surface flows or in combination with so called mixture models to model the free surface of bigger bubbles within a continuous fluid. In this study the VOF method is used to model the free surface between water and steam in the upper RDB as well as macroscopic cavitation effects in the check valve region and in the pipe system as mass transfer across the interface is well described for this method. [WAR13] [GRE19] In order to model the water hammer experiments without temperature driven phase change in the upper RPV (Figure 3) a continuous non-condensable steam phase a g (eq. 3) is considered. For the pressure driven phase change a mass transfer term regarding the condensation rate and vaporization rate is added to the continuity equation for water a l (eq. 1) and condensable steam a v (eq. 2) [YU17]: (1) (2) (3) Using the expansion of the convection term and expressing the time plus the advective derivative as the resulting set of equations can be summed to formulate the velocity divergence as [YU17] (4) With equation 4 and an artificial compression Term C to keep interfaces sharp the final set of transport equations can be expressed as [YU17] [GRE19]: (5) (6) (7) Similarly the pressure equation is modified by subtracting the source term from the incompressible part leading to following formulation 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 of the pressure equation with the compressibility Ψ: [YU17] [GRE19] compressible: incompressible: (8) A more detailed description can be found in the paper of Yu et al [YU17]. In order to ensure boundedness of the volume phase fractions (values between 0 and 1) and mass conservation (∑a i=1) the transport equations are solved using “Multidimensional Universal Limiter with Explicit Solution” (MULES) accredited to Henry Weller and well described in San tiagos PhD thesis [SAN13]. MULES requires any source terms S(α i) to be linearized in the form [SAN13] (9) resulting in different formulations for each phase. The mass transfer rates for condensation and vaporization across the respective interface are given with the Kunz cavitation model as follows [KUN99] [YU17] [GRE19]: (10) (11) If vapor pressure p v is smaller than lokal pressure p the vaporization rate is
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atw - International Journal for Nuclear Power | 10.2020

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