VTT TECHNICAL RESEARCH CENTRE OF FINLAND 1 Fluid-Structure Interaction Calculations of a Large-Break Loss-of-Coolant Accident Antti Timperi Kul Postgraduate Seminar in Fluid Mechanics

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 2 Introduction t Aim of the work has been to find practical tools for analyzing Fluid- Structure Interaction (FSI) problems found in nuclear and also other industries. t Large-Break Loss-Of-Coolant Accident (LBLOCA) is an important Design Basis Accident (DBA) situation. Rapid depressurization of the primary circuit causes loads on the reactor internals. t The motivation for studying more advanced simulation methods for analysis of DBA situations is to get more accurate, so-called ”best estimate”, analysis results. t LBLOCA in the VVER-440 type Pressurized Water Reactor (PWR) was used as a test case in earlier calculations. t Validation of LBLOCA calculations against the German HDR experiments is presented in the following.

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 3 HDR (Heißdampfreaktor) test facility vs. PWR p = 110bar T core = 308ºC T downcomer = 240ºC p = 125bar T hot leg = 295ºC T cold leg = 265ºC

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 4 HDR test facility vs. PWR (cont.) QuantityHDRPWR Pressure, MPa P 0 − P sat, MPa5.57 T core − T downc, °C0…5030 Break diameter, m Break opening time, ms1…2? Core barrel length, m Core barrel thickness, mm2350 Core barrel diameter, m Maximum stress, MPa Maximum displacement, mm24…5

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 5 Overview of the calculations Apros Boundary condition Star-CD Propagation of pressure transient MpCCI Wall position MpCCI Pressure loads Abaqus Stresses and deformation of structures t MpCCI (Mesh-based parallel Code Coupling Interface) is middleware that has been developed at the Fraunhofer Institute t Motion of the core barrel is taken into account in the CFD calculation of pressure.

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 6 Pressure at the break location, measured data and APROS calculations:

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 7 Star-CD CFD model t PISO (“Pressure Implicit with Splitting of Operators”) pressure correction algorithm. t Water is treated as compressible: t Crank-Nicholson method for temporal discretization and MARS/central/central- upwind differencing for spatial discretization. t Standard k-ε model and standard wall functions for modeling turbulence. ~ hex cells

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 8 ABAQUS structural model t Fully linear model with ~ node hexahedral elements. t Continuum shell and solid elements are used for matching geometry between CFD and FEM. t Implicit Newmark direct time integration. t Small amount of stiffness proportional damping was included to the RPV wall: 2 % of critical damping at frequency 1000 Hz.

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 9 CFD-FEM calculation t Explicit, sequential solution strategy, i.e. loose numerical coupling. Stable (usually) in LBLOCA calculations, but has been found unstable in certain other applications. t Interpolation is used for transferring the coupling quantities between the CFD and FEM meshes. t Coupling quantities local fluid pressure (CFD → FEM) and nodal coordinates (FEM → CFD). Data is exchanged in each time step (∆t = 10 μs). t Star-CD analysis has a moving mesh, internal CFD mesh is smoothed by mesh morpher of MpCCI.

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 10 CFD-FEM calculation (cont.) 1. Star-CD sends pressure load corresponding to initial conditions to ABAQUS. 2. ABAQUS simulation advances one time step. 3. ABAQUS sends new nodal coordinates to Star-CD. 4. Star-CD simulation advances one time step. 5. Star-CD sends new pressure load to ABAQUS. The sequence 2-5 is repeated for the duration of the simulation.

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 11 Acoustic-structural calculation t Models sound wave propagation and added mass effects, but effects of bulk flow, e.g. dynamic pressure, are neglected. Assumes small displacements. t Fluid is described as an acoustic medium (three-dimensional wave equation for pressure): t Linear constitutive behavior for the fluid (K is bulk modulus): t Reduces to Laplace equation for incompressible fluid (low- frequency structural motion):

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 12 Acoustic-structural calculation (cont.) t ”Volumetric drag” γ can be added to model bulk viscosity or resistive porous material: t Fluid pressure and structural displacement are coupled on the fluid-structure interface: t A single system of equations is solved, i.e. the fluid and structure domains are solved simultaneously:

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 13 Pressure in the reactor, CFD-FEM calculation: p [Pa] t = 5 ms10 ms15 ms20 ms25 ms

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 14 Stresses and deformations (x200), CFD-FEM calculation: s [Pa] t = 0 ms5 ms20 ms40 ms115 ms

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 15 Pressures, experiment vs. CFD-FEM: z = m,  = 90°z = m,  = 270° z = m (core) z = m,  = 90°

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 16 Displacements of the core barrel, experiment vs. CFD-FEM: z = m,  = 90°z = m,  = 270° z = m,  = 90°z = m,  = 90°

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 17 Pressures, experiment vs. acoustic model: z = m,  = 90°z = m,  = 90° z = m (core) z = m,  = 90°

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 18 Displacements of the core barrel, experiment vs. acoustic model: z = m,  = 90°z = m,  = 270° z = m,  = 90°z = m,  = 270°

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 19 Conclusions on CFD-FEM calculations t The calculated fluid and structural quantities were in fairly good agreement with the experiment. Especially the overall structural behavior of the core barrel was predicted well. t The most significant phenomena of the LBLOCA were well captured by the calculation during the first 100 ms, when the largest loads occurred. t Strong boiling increased pressure significantly after 120 ms, which caused deviation of measured and calculated pressures (single- phase CFD model was used).

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 20 Conclusions on acoustic-structural calculations t The results were in good agreement with the experiment and with the CFD-FEM calculation during the early phase of the simulation when the flow velocity was negligible. t Loads and structural effects were highly over-predicted in the later phase when the effect of bulk flow of water became significant. t The method is considerably more efficient and more robust compared to the CFD-FEM method. t May be considered as an alternative tool for comparison calculations in future work.

VTT TECHNICAL RESEARCH CENTRE OF FINLAND 21 General conclusions t Fairly coarse numerical meshes were sufficient for capturing the most important fluid transient and FSI phenomena. t The single-phase assumption used in the FSI calculations was adequate during the phase when the largest structural effects occurred, i.e. until ~ 100 ms. t The experiment had probably an unrealistically short break opening time, i.e. ~ 1 ms. Opening times of 15 ms and longer have been proposed in the literature.