Fine-mesh multiphysics of LWRs: two-phase flow challenges and opportunities SKC Symposium October 11-12, 2016, Hindås Klas Jareteg Chalmers University of Technology October 12, 2016
Project overview Project overview Two-phase flow in LWRs Motivation for CFD methods Two-fluid solvers Subcooled flow Future outlook 2
FIRE - FIne-mesh deterministic REactor modeling Development of a fine mesh computational tool for nuclear fuel bundles: integrated approach for solving neutronics and thermal-hydraulics single and two-phase flow models based on first principles high-resolution coupling on fine meshes using HPC fuel bundle size calculations, ultimately coupled to coarse mesh solvers Figure: Temperature distribution in moderator and fuel. 3
FIRE - Developments during 2011-2012 September 2012 - June 2013: Master thesis: Development of an integrated deterministic neutronic/thermalhydraulic model using a CFD solver Initiated work on coupled thermal-hydraulics and neutronics Figure: Radial temperature profile, diffusion neutronics Developing basics of a cross-section methodology for fine-mesh simulations Coupling incompressible CFD solver with diffusion solver in OpenFOAM-1.6-ext 4
FIRE - Developments during 2012-2013 Starting as a PhD student September 2013 Implemented and studied coupled formulations for diffusion solver Starting implementation and formulation of transport solver for neutronics Initiating the development of a two-phase solver based on a population balance equation (PBE) Generalizing the geometry and the cross-section algorithms together with meshing techniques Figure: Void fraction, bubble mean diameter and axial velocity 5
FIRE - Developments during 2013-2014 Consolidation of the discrete ordinates solver, benchmarking against Monte Carlo simulations Continued development of subcooled boiling and two-phase flow Extended system size simulations Figure: Moderator temperature 6
FIRE - Developments during 2014-2015 Development of transient multiphysics for single-phase flow with diffusion and S N neutronics Investigations of two-phase flow instabilities for adiabatic bubbly flow Two fluid/pbe approach for heated bubbly flow with condensation (DQMOM/MUSIG) Figure: Emergence of void fraction meso-scale structures 7
FIRE - Developments during 2015-2016 Extension of two fluid/pbe approach for heated bubbly flow with condensation Investigation of phase instabilities in two-fluid solvers for 3D cases Development and implementation of a verification methodology for transient neutronic codes Figure: Mean bubble diameter and void fraction distribution on a heated channel 1 1 K. Jareteg, S. Sasic, P. Vinai, C. Demaziere (2016). A numerical framework for bubble transport in a subcooled fluid flow. Submitted to Journal of Computational Physics 8
Two-phase flow in LWRs Project overview Two-phase flow in LWRs Motivation for CFD methods Two-fluid solvers Subcooled flow Future outlook 9
Motivation i. The curse of simplifications Flow regimes in a BWR: Increasing void fraction Change in characteristic scales Different heat transfer mechanisms Tempting not to work from first principles: Limited mechanistic models, black box approach Enough degrees of freedom to close the equations by experiments Verify and validate for all existing scenarios Figure: Flow regimes (Todreas and Kazimi 1993) Existing typical 1D codes 10
Motivation i. The curse of simplifications Issues: What are the other scenarios? Cost of unresolved physics: Safety margins Influence on other physics Need for fully dimensional, resolved simultions, CFD Figure: Flow regimes (Todreas and Kazimi 1993) 10
Motivation ii. The need for different models One Method to rule them all...? Lagrangian particle tracking? Immersed boundary method? Volume of fluid? Two-fluid model in 3D? No! Constraints due to computational cost Constraints inherent to the methods Need for combinations or new methods Figure: Bubble jet simulated with two fluid model 11
Two fluid model: The Beauty or the Beast? Advantages: Affordable cost for larger systems Computationally scalable Resolving (in 3D) phase distributions Figure: High-level equation format Issues: No phase boundaries resolved Separation of scales? Stability issues? Figure: Domain decomposition 12
Two-fluid model: Formulation and Implementation Mass conservation equation: α i ρ i t Momentum conservation equation: α i ρ i U i t + (α i ρ i U i ) = 0 + (α i ρ i U i U i ) = (α i ( τ i + τ t i ) ) (α i P) + α i ρ i g + M i, PISO algorithm, shared pressure Interfacial forces including: drag (Schiller-Naumann) virtual mass (C vm = 0.5) 13
Two fluid model: Stablitiy issues? Theoretical literature restricted to 1D models due to: complexity in mathematical formulation relevance for the nuclear system codes in 1D Previous simulations performed in 2D systems 2 limiting the computational burden instabilities shown (in multiple software) In this stage we perform 3D simulations 3 : allowing instablities to grow in third direction. 2 K. Jareteg, H. Ström, S. Sasic, C. Demazière (2015). Numerical investigation of instabilities in the two-fluid model for CFD simulations of LWRs. M&C 2015, Nashville, Tennessee. 3 K. Jareteg, H. Ström, S. Sasic, C. Demazière (2016). On the dynamics of instabilities in two-fluid models for bubbly flows. Submitted to Chemical Engineering Science. 14
Computational setup Formulation and parameter variations Case geometry Domain size: 10 cm 40 cm 10 cm Mesh size: 32 64 32 Boundary conditions Vapor velocity U g = (0, 0, 0) m/s, Fully periodic Liquid velocity U l = (0, 0, 0) m/s Fully periodic Pressure p: Axially: jump condition Horizontally: periodic 15
Results Void fraction, time-resolved uniformity index and velocity 4 0.055 α [-] 0.052 0.050 0.048 10 0 10 1 α [-] 0.120 0.080 0.040 10 1 10 0 10 1 Φ [-] 10 2 Φ [-] 10 2 10 3 10 3 10 4 10 4 10 5 Velocity [m/s] 0.100 0.075 0.050 0.025 U g U l Velocity [m/s] 0.32 0.24 0.16 0.08 U g U l 0 50 100 150 200 Time [s] 0 50 100 150 200 Time [s] (a) With virtual mass (b) Without virtual mass 3 K. Jareteg, H. Ström, S. Sasic, C. Demazière (2016). On the dynamics of instabilities in two-fluid models for bubbly flows. Submitted to Chemical Engineering Science 16
Results Horizontal effects 5 Horizontal discontinuity during growth of Φ Cell-wise discontinuity in void fraction Meso-scale heterogeneities larger than cell size 4 K. Jareteg, H. Ström, S. Sasic, C. Demazière (2016). On the dynamics of instabilities in two-fluid models for bubbly flows. Submitted to Chemical Engineering Science 17
Results Magnitude of virtual mass force? Fvm,x/Fd,x [-] Fvm,y/Fd,y [-] Fvm,z/Fd,z [-] 1.5 0.0-1.5 4.0 2.0 0.0-2.0 1.5 0.0-1.5-3.0 0 50 100 150 200 Time [s] Figure: Magnitude of virtual mass force relative to the drag force, presented for each Cartesian component. 18
Extension of two fluid model: Subcooled flow Problem: Two fluid methodology treating vapor and liquid phases as interpenetrating continua - separate bubbles not resolved Remedy: PBM Retrieve bubble size distribution Size-dependent formulations of particle forces and condensation Number density Bubble size Population balance equation: ( ) n(x, r, t) x(x, r, t) + x n(x, r, t) t t + r (U(x, r, t)n(x, r, t)) = S(x, r, t) 19
Efficient tracking of bubble size distribution Figure: Mean bubble diameter and void fraction distribution on a heated channel 6 6 K. Jareteg, S. Sasic, P. Vinai, C. Demaziere (2016). A numerical framework for bubble transport in a subcooled fluid flow. Submitted to Journal of Computational Physics 20
Summary of work on the two fluid model Numerical stability investigations of two fluid model: Lack of hyperbolicity also for 3D cases Virtual mass has a stabilizing effect Results from two fluid model trustworthy? Two fluid model with PBM: Retrieve bubble size information from Eulerian approach Compared PBMs for stability, performance and accuracy 21
Future outlook Project overview Two-phase flow in LWRs Motivation for CFD methods Two-fluid solvers Subcooled flow Future outlook 22
Future outlook Project outlook: Continued development of multiphase flow methodologies Coupled, transient neutronics/thermal-hydraulics with multiphase flow Fine-mesh multiphysics outlook: Large scale simulations with highly resolved physics growing Computer science growing in importance (data structures, parallelism, heterogeneous architecture) 23
Publications and conferences Publications 2016 K. Jareteg, H. Ström, S. Sasic, C. Demazière (2016). On the dynamics of instabilities in two-fluid models for bubbly flows. Submitted to Chemical Engineering Science K. Jareteg, S. Sasic, P. Vinai, C. Demaziere (2016). A numerical framework for bubble transport in a subcooled fluid flow. Submitted to Journal of Computational Physics 2015 K. Jareteg, S. Sasic, P. Vinai, C. Demazière (2015). Development of a Coupled Two- Fluid/DQMOM Methodology for Heated Bubbly Flows. CMFF2015, Budapest, Hungary K. Jareteg, R. Andersson, C. Demazière (2015). Development and test of a transient fine-mesh LWR multiphysics solver in a CFD framework. M&C 2015, Nashville, Tennessee K. Jareteg, H. Ström, S. Sasic, C. Demazière (2015). Numerical investigation of instabilities in the two-fluid model for CFD simulations of LWRs. M&C 2015, Nashville, Tennessee E. Pettersen, C. Demazière, K. Jareteg, E. Schönfeldt T, B. Lauritzen (2015). Development of a Monte-Carlo based method for calculating the effect of stationary fluctuations. M&C 2015, Nashville, Tennessee H. Ström, S. Sasic, K. Jareteg, C. Demazière (2015). Behaviour and Stability of the Two-Fluid Model for Fine-Scale Simulations of Bubbly Flow in Nuclear Reactors. International Journal of Chemical Reactor Engineering 13.4, pp. 449 459 K. Jareteg, P. Vinai, S. Sasic, C. Demazière (2015). Coupled fine-mesh neutronics and thermal-hydraulics - modeling and implementation for PWR fuel assemblies. Annals of Nuclear Energy, Special Issue: Multi-Physics Modeling of LWR Static and Transient Behavior A. Jareteg, K. Jareteg, S. Sasic (2015). Formulation of stresses in dry granular flows. CMFF2015, Budapest, Hungary 24
2014 K. Jareteg, P. Vinai, C. Demazière (2014). Fine-mesh deterministic modeling of PWR fuel assemblies: Proof-of-principle of coupled neutronic/thermal hydraulic calculations. Annals of Nuclear Energy 68.0, pp. 247 256 K. Jareteg, P. Vinai, S. Sasic, C. Demazière (2014). Influence of an S N solver in a fine-mesh neutronics/thermal-hydraulics framework. PHYSOR 2014, September 28 - October 3, Japan C. Demazière, K. Jareteg (2014). Developing a course in nuclear reactor modelling and going from campus-based to web-based teaching. PHYSOR 2014, September 28 - October 3, Japan H. Ström, S. Sasic, K. Jareteg, C. Demazière (2014). On the validity of the Two-fluid model for simulations of bubbly flow in nuclear reactors. 13th International Conference on Multiphase Flow in Industrial Plants (MFIP) 2013 K. Jareteg, P. Vinai, C. Demazière (2013). Investigation of the possibility to use a fine-mesh solver for resolving coupled neutronics and thermal-hydraulics. M&C 2013, Sun Valley, Idaho 25
Workshops and conferences 2016 International Conference on Multiphase Flow (ICMF), May 2015 (Presentation title: Numerical simulations of subcooled boiling using a two-fluid/dqmom methodology) 2015 Gothenburg Region OpenFOAM User Group Meeting, November 2015 (Presentation titles: Increasing performance and cutting computational time - examples and thoughts on acceleration at different code levels and A Two-Fluid/DQMOM Methodology For Condensation In Bubbly Flow ) SKC Symposium, Uppsala, October 2015 (Presentation title: Transient fine-mesh simulations in LWR fuel assemblies: phenomena and methodologies ) CMFF 2015, Budapest, Hungary, September 2015 (Presentation title: A Two- Fluid/DQMOM Methodology For Condensation In Bubbly Flow ) SIAMUF Spring meeting, Lund, May 2015 (Presentation title: Using an open source computational framework in research ) RPNC 2015, Chalmers, Gothenburg, April 2015 (Presentation title: Fine-mesh multiphysics modeling within FIRE - Challenges and opportunities with CFD methodologies in reactor physics calculations ) 26
2014 Gothenburg Region OpenFOAM User Group Meeting, November 2014 (Presentation title: Multiphysics simulations of nuclear reactors and more ) Participation to SIAMUF Meeting, Gothenburg, November 2014 Mid-term presentation of project, Chalmers, November 2014 (Presentation title: Towards fine-mesh multiphysics simulations of LWR fuel assemblies ) SKC Symposium 2014, KTH, Stockholm, October 2014 (Presentation title: Towards fine-mesh multiphysics simulations of BWR fuel assemblies ) PHYSOR 2014, Kyoto, Japan, September 2014 (Presentation title: Influence of an S N solver in a fine-mesh neutronics/thermal-hydraulics framework Gathering MSc/PhD students - industry, Chalmers, June 2014 (Presentation title: Multiphysics simulatios of nuclear reactors - Modeling and implementation for fine-mesh simulations 9th OpenFOAM Workshop, Zagreb Croatia, June 2014 (Presentation and abstract titles: pucoupledfoam - an open source coupled incompressible pressure-velocity solver based on foam-extend and Multiphysics simulations of Light Water Reactors using OpenFOAM NAFEMS Nordic, Göteborg, May 2014 (Presentation and abstract title: Multiphysics simulations of Light Water Reactors using a CFD approach) Westinghous Electric Sweden, Västerås, April 2014 (Presentation title: FIRE Project presentation at Westinghouse Sweden, Västerås Participation to Konferens om lärande och undervisning, Chalmers, January 2014 27
2013 SIAMUF Fall meeting, ABB, Västerås, November 2013 (Presentation title: Multiphase flow simulations for multiphysics simulations for BWRs within FIRE Gothenburg Region OpenFOAM User Group Meeting, November 2013 (Presentation title: Coupled calculations in OpenFOAM - Multiphysics handling, structures and solvers ) SKC Symposium 2013, Gimo, Östhammar, October 2013 (Presentation title: FIRE - Status presentation ) RPNC 2013, Kjeller, Norway (Presentation title: Deterministic fine-mesh coupled neutronics and thermal-hydraulics within FIRE ) Participation to SIAMUF Spring meeting, Ekerö, Stockholm, June 2013 M&C 2013, Sun Valley, Idaho, May 2013 (Presentation title: Investigation of the possibility to use a fine-mesh solver for resolving coupled neutronics and thermalhydraulics 2012 Participation to SIAMUF Fall meeting, Varberg, October 2012 SKC Symposium 2012, Chalmers, Göteborg, October 2012 (Presentation title: Development of an integrated deterministic neutron/thermal-hydraulic model using a CFD solver SIAMUF Spring meeting, Sundsvall, May 2012 (Presentation title: Development of an integrated deterministic neutronic/thermal-hydraulic model using a CFD solver 28
Thank you! Questions? 29
References: N. Todreas, M. Kazimi (1993). Nuclear systems I: Thermal hydraulic fundamentals. Taylor & Francis, Levittown, USA 30