Fine-mesh multiphysics of LWRs: two-phaseflow challenges and opportunities

SKC Symposium October 11-12, 2016, Hindås

Klas Jareteg

Chalmers University of Technology

October 12, 2016

Project overviewProject overviewTwo-phase flow in LWRs

Motivation for CFD methodsTwo-fluid solversSubcooled flow

Future outlook

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FIRE - FIne-mesh deterministic REactor modeling

Development of a fine meshcomputational tool for nuclear fuelbundles:

• integrated approach for solvingneutronics and thermal-hydraulics

• single and two-phase flow models basedon first principles

• high-resolution coupling on fine meshesusing HPC

• fuel bundle size calculations, ultimatelycoupled to coarse mesh solvers

Figure: Temperature distributionin moderator and fuel.

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FIRE - Developments during 2011-2012

Figure: Radial temperatureprofile, diffusion neutronics

• September 2012 - June 2013: Masterthesis: ”Development of an integrateddeterministic neutronic/thermalhydraulicmodel using a CFD solver”

• Initiated work on coupledthermal-hydraulics and neutronics

• Developing basics of a cross-sectionmethodology for fine-mesh simulations

• Coupling incompressible CFD solver withdiffusion solver in OpenFOAM-1.6-ext

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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 velocity5

FIRE - Developments during 2013-2014

• Consolidation of the discreteordinates solver, benchmarkingagainst Monte Carlo simulations

• Continued development ofsubcooled boiling and two-phaseflow

• Extended system size simulations

Figure: Moderator temperature

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FIRE - Developments during 2014-2015

Figure: Emergence of void fractionmeso-scale structures

• Development of transientmultiphysics for single-phase flowwith diffusion and SN neutronics

• Investigations of two-phase flowinstabilities for adiabatic bubblyflow

• Two–fluid/PBE approach forheated bubbly flow withcondensation (DQMOM/MUSIG)

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FIRE - Developments during 2015-2016

• Extension of two–fluid/PBEapproach for heated bubbly flowwith condensation

• Investigation of phase instabilitiesin two-fluid solvers for 3D cases

• Development and implementationof a verification methodology fortransient neutronic codes Figure: Mean bubble diameter and void

fraction distribution on a heated channel 1

1K. Jareteg, S. Sasic, P. Vinai, C. Demaziere (2016). “A numerical framework for bubbletransport in a subcooled fluid flow”. Submitted to Journal of Computational Physics

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Two-phase flow inLWRs Project overview

Two-phase flow in LWRsMotivation for CFD methodsTwo-fluid solversSubcooled flow

Future outlook

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Motivationi. The curse of simplifications

Figure: Flow regimes (Todreas andKazimi 1993)

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

⇒ Existing typical 1D codes

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Motivationi. The curse of simplifications

Figure: Flow regimes (Todreas andKazimi 1993)

Issues:

• What are the other scenarios?• Cost of unresolved physics:

• Safety margins• Influence on other physics

⇒ Need for fully dimensional, resolvedsimultions, CFD

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Motivationii. 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 newmethods

Figure: Bubble jet simulated withtwo–fluid model

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Two–fluid model: The Beauty or the Beast?

Advantages:• Affordable cost for larger systems• Computationally scalable• Resolving (in 3D) phase distributions

Issues:• No phase boundaries resolved• Separation of scales?• Stability issues?

Figure: High-level equation format

Figure: Domain decomposition

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Two-fluid model: Formulation and Implementation

• Mass conservation equation:

∂αiρi

∂t +∇ · (αiρiUi) = 0

• Momentum conservation equation:

∂αiρiUi

∂t +∇ · (αiρiUiUi) = −∇ ·(αi(¯̄τi + ¯̄τ t

i ))−∇(αiP) + αiρig + Mi,

• PISO algorithm, shared pressure

• Interfacial forces including:• drag (Schiller-Naumann)• virtual mass (Cvm = 0.5)

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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 systems2

• limiting the computational burden• instabilities shown (in multiple software)

• In this stage we perform 3D simulations3:• allowing instablities to grow in third direction.

2K. Jareteg, H. Ström, S. Sasic, C. Demazière (2015). “Numerical investigation of instabilitiesin the two-fluid model for CFD simulations of LWRs”. M&C 2015, Nashville, Tennessee.

3K. Jareteg, H. Ström, S. Sasic, C. Demazière (2016). “On the dynamics of instabilities intwo-fluid models for bubbly flows”. Submitted to Chemical Engineering Science.

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Computational setupFormulation and parameter variations

Case geometry• Domain size: 10 cm × 40 cm × 10 cm• Mesh size: 32× 64× 32

Boundary conditions• Vapor velocity Ug = (0, 0, 0) m/s,

• Fully periodic• Liquid velocity Ul = (0, 0, 0) m/s

• Fully periodic• Pressure p:

• Axially: jump condition• Horizontally: periodic

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ResultsVoid fraction, time-resolved uniformity index and velocity4

0.048

0.050

0.052

0.055α

[-]

10−4

10−3

10−2

10−1

100

Φ[-]

0 50 100 150 200Time [s]

0.025

0.050

0.075

0.100

Velo

city

[m/s

]

Ug

Ul

(a) With virtual mass

0.040

0.080

0.120

α[-]

10−5

10−4

10−3

10−2

10−1

100

101

Φ[-]

0 50 100 150 200Time [s]

0.08

0.16

0.24

0.32

Velo

city

[m/s

]

Ug

Ul

(b) Without virtual mass

3K. Jareteg, H. Ström, S. Sasic, C. Demazière (2016). “On the dynamics of instabilities intwo-fluid models for bubbly flows”. Submitted to Chemical Engineering Science

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ResultsHorizontal effects5

Horizontaldiscontinuity duringgrowth of Φ

Cell-wise discontinuityin void fraction

Meso-scaleheterogeneities largerthan cell size

Horizontaldiscontinuity duringgrowth of Φ

Cell-wise discontinuityin void fraction

Meso-scaleheterogeneities largerthan cell size

Horizontaldiscontinuity duringgrowth of Φ

Cell-wise discontinuityin void fraction

Meso-scaleheterogeneities largerthan cell size

Horizontaldiscontinuity duringgrowth of Φ

Cell-wise discontinuityin void fraction

Meso-scaleheterogeneities largerthan cell size

4K. Jareteg, H. Ström, S. Sasic, C. Demazière (2016). “On the dynamics of instabilities intwo-fluid models for bubbly flows”. Submitted to Chemical Engineering Science

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ResultsMagnitude of virtual mass force?

-1.50.01.5

F vm,x/F

d,x

[-]

-2.00.02.04.0

F vm,y/F

d,y

[-]

0 50 100 150 200Time [s]

-3.0-1.50.01.5

F vm,z/F

d,z

[-]

Figure: Magnitude of virtual mass force relative to the drag force, presented for eachCartesian component.

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Extension of two–fluid model: Subcooled flow

Problem: Two–fluid methodology treating vapor and liquid phases asinterpenetrating continua - separate bubbles not resolved

Remedy: PBM• Retrieve bubble size distribution• Size-dependent formulations of

particle forces and condensation

Bubble size

Nu

mb

er

den

sity

Population balance equation:

∂n(x, r, t)∂t +∇x ·

(∂x(x, r, t)

∂t n(x, r, t))

+∇r · (U(x, r, t)n(x, r, t)) = S(x, r, t)

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Efficient tracking of bubble size distribution

Figure: Mean bubble diameter and void fraction distribution on aheated channel 6

6K. Jareteg, S. Sasic, P. Vinai, C. Demaziere (2016). “A numerical framework for bubbletransport in a subcooled fluid flow”. Submitted to Journal of Computational Physics

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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

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Future outlookProject overviewTwo-phase flow in LWRs

Motivation for CFD methodsTwo-fluid solversSubcooled flow

Future outlook

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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)

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Publications and conferences

Publications2016 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 bubbletransport 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-meshLWR multiphysics solver in a CFD framework”. M&C 2015, Nashville, Tennessee

K. Jareteg, H. Ström, S. Sasic, C. Demazière (2015). “Numerical investigation of instabilitiesin 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). “Developmentof 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-FluidModel for Fine-Scale Simulations of Bubbly Flow in Nuclear Reactors”. International Journal ofChemical Reactor Engineering 13.4, pp. 449–459

K. Jareteg, P. Vinai, S. Sasic, C. Demazière (2015). “Coupled fine-mesh neutronics andthermal-hydraulics - modeling and implementation for PWR fuel assemblies”. Annals of NuclearEnergy, 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

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2014 K. Jareteg, P. Vinai, C. Demazière (2014). “Fine-mesh deterministic modeling of PWR fuelassemblies: Proof-of-principle of coupled neutronic/thermal–hydraulic calculations”. Annals ofNuclear Energy 68.0, pp. 247 –256

K. Jareteg, P. Vinai, S. Sasic, C. Demazière (2014). “Influence of an SN solver in a fine-meshneutronics/thermal-hydraulics framework”. PHYSOR 2014, September 28 - October 3, Japan

C. Demazière, K. Jareteg (2014). “Developing a course in nuclear reactor modelling and goingfrom 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 modelfor simulations of bubbly flow in nuclear reactors”. 13th International Conference on MultiphaseFlow in Industrial Plants (MFIP)

2013 K. Jareteg, P. Vinai, C. Demazière (2013). “Investigation of the possibility to use a fine-meshsolver for resolving coupled neutronics and thermal-hydraulics”. M&C 2013, Sun Valley, Idaho

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Workshops and conferences

2016 International Conference on Multiphase Flow (ICMF), May 2015 (Presentation title:Numerical simulations of subcooled boiling using a two-fluid/DQMOM methodol-ogy)

2015 Gothenburg Region OpenFOAM User Group Meeting, November 2015 (Presenta-tion titles: ”Increasing performance and cutting computational time - examplesand thoughts on acceleration at different code levels” and ”A Two-Fluid/DQMOMMethodology For Condensation In Bubbly Flow”)

SKC Symposium, Uppsala, October 2015 (Presentation title: ”Transient fine-meshsimulations 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 opensource computational framework in research”)

RPNC 2015, Chalmers, Gothenburg, April 2015 (Presentation title: ”Fine-meshmultiphysics modeling within FIRE - Challenges and opportunities with CFDmethodologies in reactor physics calculations”)

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2014 Gothenburg Region OpenFOAM User Group Meeting, November 2014 (Presenta-tion 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: ”To-wards fine-mesh multiphysics simulations of BWR fuel assemblies”)

PHYSOR 2014, Kyoto, Japan, September 2014 (Presentation title: ”Influence ofan SN 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 forfine-mesh simulations”

9th OpenFOAM Workshop, Zagreb Croatia, June 2014 (Presentation and abstracttitles: pUCoupledFoam - an open source coupled incompressible pressure-velocitysolver based on foam-extend and Multiphysics simulations of Light Water Reactorsusing OpenFOAM®

NAFEMS Nordic, Göteborg, May 2014 (Presentation and abstract title: Multi-physics 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

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2013 SIAMUF Fall meeting, ABB, Västerås, November 2013 (Presentation title: ”Mul-tiphase flow simulations for multiphysics simulations for BWRs within FIRE”

Gothenburg Region OpenFOAM User Group Meeting, November 2013 (Presenta-tion title: ”Coupled calculations in OpenFOAM - Multiphysics handling, structuresand solvers”)

SKC Symposium 2013, Gimo, Östhammar, October 2013 (Presentation title: ”FIRE- Status presentation”)

RPNC 2013, Kjeller, Norway (Presentation title: Deterministic fine-mesh coupledneutronics 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 thepossibility to use a fine-mesh solver for resolving coupled neutronics and thermal-hydraulics”

2012 Participation to SIAMUF Fall meeting, Varberg, October 2012

SKC Symposium 2012, Chalmers, Göteborg, October 2012 (Presentation title: De-velopment of an integrated deterministic neutron/thermal-hydraulic model using aCFD solver

SIAMUF Spring meeting, Sundsvall, May 2012 (Presentation title: Development ofan integrated deterministic neutronic/thermal-hydraulic model using a CFD solver

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Thank you! Questions?

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References:N. Todreas, M. Kazimi (1993). Nuclear systems I: Thermal hydraulicfundamentals. Taylor & Francis, Levittown, USA

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