1. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 1 Fluid-Structure Interaction Calculations of a Large-Break Loss-of-Coolant Accident Antti Timperi Kul-34.4551 Postgraduate Seminar in Fluid Mechanics 3.5.2010

2. 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.

3. 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

4. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 4 HDR test facility vs. PWR (cont.) QuantityHDRPWR Pressure, MPa1112.5 P 0 − P sat, MPa5.57 T core − T downc, °C0…5030 Break diameter, m0.20.5 Break opening time, ms1…2? Core barrel length, m7.68.1 Core barrel thickness, mm2350 Core barrel diameter, m2.663.2 Maximum stress, MPa100230 Maximum displacement, mm24…5

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.

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

7. 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. ~ 78 000 hex cells

8. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 8 ABAQUS structural model t Fully linear model with ~ 15 000 8-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.

9. 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.

10. 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.

11. 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):

12. 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:

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

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

15. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 15 Pressures, experiment vs. CFD-FEM: z = 8.850 m,  = 90°z = 7.780 m,  = 270° z = 5.505 m (core) z = 5.550 m,  = 90°

16. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 16 Displacements of the core barrel, experiment vs. CFD-FEM: z = 7.150 m,  = 90°z = 7.150 m,  = 270° z = 5.550 m,  = 90°z = 2.300 m,  = 90°

17. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 17 Pressures, experiment vs. acoustic model: z = 8.850 m,  = 90°z = 5.550 m,  = 90° z = 5.505 m (core) z = 5.550 m,  = 90°

18. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 18 Displacements of the core barrel, experiment vs. acoustic model: z = 7.150 m,  = 90°z = 7.150 m,  = 270° z = 2.300 m,  = 90°z = 2.300 m,  = 270°

19. 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).

20. 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.

21. 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.