Computational thermal-Fluid-Dynamics (CtFD) Issues in Nuclear Fusion Reactors

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Computational thermal-Fluid-Dynamics (CtFD) Issues in Nuclear Fusion Reactors. R. Zanino, S. Giors, L. Savoldi Richard, F. Subba Dipartimento di Energetica, Politecnico, Torino, Italy. Outline. Introduction Selected topics:
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R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006Computational thermal-Fluid-Dynamics (CtFD) Issues in Nuclear Fusion ReactorsR. Zanino, S. Giors, L. Savoldi Richard, F. Subba Dipartimento di Energetica, Politecnico, Torino, ItalyR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006Outline
  • Introduction
  • Selected topics:
  • Physics: Modeling plasma-surface interactions (PSI) in tokamaks CODEDEVELOPMENT only
  • Magnet Technology: Modeling cable-in-conduit conductors (CICC) for the superconducting ITER coils CODEDEVELOPMENT + FLUENT
  • Vacuum Technology: Modeling Turbo-Molecular Pumps (TMP) FLUENT only
  • Conclusions and perspective
  • R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006Introduction (I): Nuclear fusion
  • Conditions: magnetically confine in a volume (~ 102-103 m3), for a sufficiently long time, a mixture (plasma = fully ionized gas) of deuterium (D) and tritium (T) with density ~ 1020-1021 m-3 and temperature ~ 10-20 keV
  • Potential: (almost) clean and unlimitedenergy!!
  • Aim: realize a sufficient amount of nuclear fusion reactions
  • 2D + 3T  n (14.1 MeV) + 4He (3.5 MeV)Heats the blanket  Thermal energy  Electric powerHeats the plasma  IgnitionR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006Components of a tokamak fusion reactor
  • V = vacuum chamber,
  • PI = pellet injector, NBI = neutral beam injector,
  • FW = first wall, DP = divertor plate,
  • A = antenna for auxiliary plasma heating,
  • B = blanket,
  • Magnet system: CS = central solenoid, TF = toroidal field coil, PF = poloidal field coil,
  • C = cryostat,
  • SG = steam generator, T = turbine.
  • Vertical cross section through symmetry axis (sketch)R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006Introduction (II): ITER
  • ITER tokamak construction approved June 2005
  • 10 GEuro project: 50 % EU, 50 % (JA, RF, US, CN, KO, IN)
  • Reactor site Cadarache (F)
  • 10 year construction (start 2007) + 20 year operation
  • R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006Tokamaks: generalitiesToroidal geometryTransformer principlePoloidal magnetic field generated by plasma currentComplex magnetic field assembly for confining and controlling the plasmaR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006Introduction (IV): ITER goals
  • Achieve inductive plasma burn with amplification factor
  • Q = generated/injected power of at least 5-10;
  • Possibility of controlled ignition (Q  ) not precluded
  • Integrate the technologies essential for a fusion reactor (e.g. superconducting magnets, remote maintenance);
  • Test components for a future reactor (e.g. divertor and torus vacuum pumps);
  • Test tritium breeding module concepts for DEMO.
  • R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006PSI in tokamaks: GeometryScrape-off layer (SOL)(“open” magnetic surfaces)Limiter/First WallMain plasma (closed magnetic surfaces)
  • Toroidal symmetry edge plasma problem is 2D :
  • radial r (across magnetic surfaces)
  • poloidal  (around “small” torus circumference)
  • DivertorplatesR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006PSI in tokamaks: PhysicsPlasma confinement is never perfect because of dissipationThe plasma interacts with the solid wallsHeat load peaks up to tens of MW/m2 Possible serious damage of plasma facing components (walls)  Lifetime issueRadiation from the plasma edge in a first-wall/limiter tokamakImmission of impurities from the walls into the plasma (e.g.. C in the case of graphite walls) Erosion of the walls but also radiation from ionized impurities  possible switch-off of fusion reactions.Radiation from the plasma edge in a divertor tokamakR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006Plasma-Boundary electrostatic sheathIons: large mass, low speedWallElectrons: small mass, high speedRandom motion electric wall current charge accumulation electrostatic sheathni profilene profileParticle flux n = ncs (not zero!!!)WallEnergy flux E =  nmain plasma ~ 8 (Ion + Electron contribution)sheathD~ 10-5 mCosine ModelnSOLBwallL = Connection length (distance between walls)MAIN PLASMAFrom continuity: Heat flux on the wall making a finite angle with B: R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006Power balance considerations (Lawson Criterion with impurities)Output (losses):Pout = PL + PRPL = 3nT/E Conduction/convectionPR = n nz (T,Z) Impurity radiation lossesInput:PinPin = n2/4<V>E From fusion reactionsIGNITION (= self-sustained reaction): Pin PoutLimitation on the tolerable radiation from impurities PR ~ nz (T,Z) CHOICE OF MATERIAL!R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006PSI in tokamaks: Modeling issues
  • Fluid vs. kinetic plasma
  • (10-7 < Kn  mfp/L < 101 range achieved in SOL!)
  • Complicating physics/geometry issues
  • Multi-fluid (1 fluid = 1 ionization stage) for impurities, e.g., 6 fluids for C but, in principle, 74 fluids for W!
  • Presence of non-magnetized, kinetic neutral particles Sources  Monte-Carlo approach typically adopted
  • Treatment of third (diamagnetic) direction (drifts, etc.)
  • Lack of consolidated fundamental knowledge on some issues
  • Radial “anomalous” transport  most often adopt diffusive Ansatz
  • Boundary conditions (Debye sheath, etc)
  • Atomic physics database available (for some materials)
  • R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006PSI in tokamaks: Fluid (Braginskii) plasma modelSources from plasma-neutral interactions
  • j = i, e (pure plasma)
  • Complete Navier-Stokes solved only along magnetic field B
  • R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006PSI in tokamaks: Computational issues
  • Huge transport anisotropy: Vr << V, r << 
  • SOL thickness << SOL length  Stretched grid with very good alignment in  is needed!
  • Strong gradients from localized sources (adaptivity needed, …)
  • Strong nonlinearities (transport coefficients along B  T5/2, radiation/atomic physics rates (exponential), …)
  • Different physical processes involved  Often need to couple intrinsically different numerical approaches (e.g. CFD + Monte Carlo)
  • PROBLEM BEYOND CAPABILITIES OF STANDARD COMMERCIAL CODESDEVELOPMENT NEEDED!R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006PSI in tokamaks: Numerical methods (I) -- FV
  • FV were historically the first method adopted for CFD edge plasma modeling
  • A number of widely used tools exists today
  • 5-point molecule (B2)
  • 9-point molecule (UEDGE and EDGE2D)
  • based on quadrilateral meshes  optimized for divertor
  • Increasingly complex physical/numerical ingredients added by many contributors over more than 20 years
  • Areas of active research development:
  • Other geometries besides divertor  First Wall/Limiter
  • Adaptive grid methods
  • Some physics models are still not validated
  • R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006PSI in tokamaks: Results (I)FV multi-fluid model of ASDEX Upgrade divertorComputed (B2-Eirene) vs. measured radiation intensityTomographic reconstructionProfiles at the targetR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006PSI in tokamaks: Numerical methods (II) -- FE
  • First attempt at dealing with realistic geometries (early-to-mid ’90s)
  • Extended to use adaptive grids (late ’90s)
  • Adaptive triangular grid generator written by INRIA [H. Bourouchaki et al] coupled with model electron heat advection/diffusion/radiation Finite Element solver
  • Mesh size and alignment controlled by locally defining the 2D metric
  • Mesh alignment guaranteed within a few degrees
  • Conservation issue (see below)
  • R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006PSI in tokamaks: Results (II)FE model of ASDEX Upgrade divertorADBCnTeTiRelatively slow convergence likely due to non conservation on finite gridR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006PSI in tokamaks: Results (IIa)FE model of scalar problems in divertor geometryAnisotropic diffusionAdaptive gridsAnisotropic advectionR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006PSI in tokamaks: Numerical methods (III) -- CVFE
  • Most recent attempt at dealing with complex geometries while still guaranteeing conservation
  • Adopt triangular meshes. Force one element side to be always aligned with the B field
  • Employ the Control-Volume Finite-Element technique to guarantee conservation on every finite-size mesh
  • Segregated approach to couple continuity-momentum-energy equations
  • First single-fluid application proved effective on the difficult (= previously untackled) First-Wall/Limiter geometry
  • R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006PSI in tokamaks: Numerical methods (IIIa) -- CVFEBBR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006V// [m/s] @ Top regionZ [m]0.906.4e40.880.863.2e40.840.823.2e20.800.78-3.1e40.767.85-6.3e40.747.800.721.050.951.10R [m]1.007.75Particles [1020´s-1]7.70Mesh-independent value, estimated by Richardson extrapolation7.657.60200400600800100012001400Number of nodesPSI in tokamaks: Results (III)CVFE model of IGNITOR first wall/limiterSpatial convergence tests on simple model problems were satisfactoryCVFE show good performance in regions where quadrilateral meshes would be too distortedR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006ITER superconducting magnet system (I)R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006Current lead 80kACurrent lead 80kACryostatExtensionBus bar type1Bus bar type2TF-model coil (TFMC)Inter-coil structure (ICS)Vacuum vesselMagnet windingsPANCAKE WOUNDLAYER WOUNDR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER superconducting coilsSC coils for fusion applications (e.g., ITER) carry high currents (up to ~ 70-80 kA) to generate high magnetic fields (up to ~ 13 T)Low critical temperature SC (e.g., Nb3Sn or NbTi) are used inmulti-stage cable-in-conduit conductors (CICC) cooled by supercritical He @ ~ 5 K and 0.5 MPaR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006Thermophysical Properties of Materials in Cryogenic Conditions·Solids
  • Super-conductors (e.g., Nb3Sn, NbTi)
  • Conductors (Cu)
  • Structural (SS, Incoloy, Ti)
  • ·Fluids
  • He
  • R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER: Modeling issues
  • Conductor must be kept below critical temperature  capability to reproduce/predict thermal-hydraulic transient:
  • Heat slug propagation
  • Stability
  • Quench propagation
  • Absence of diagnostics inside the conductors/magnets  the conductor performance must be reliably extract from “global” (=inlet, outlet) measurements (T, dm/dt, p, V, I,…)
  • The level of detail needed in the TH analysis (global vs. local analysis, …) is function of the nature of the problem (slow vs. fast transient, …) and of the SC type (Nb3Sn vs. NbTi)
  • R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER: Computational issues
  • Multi-physics (TH + EM + ME) nature of the problem
  • Timescales: 10-3 s  102 s
  • Length scales: 10-6 m  102 m
  • Complex structure of the cable bundle
  • Complex interaction between cable constituents
  • R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER : Models (I) – Global 1D thermal-hydraulics
  • Length ~ 102 m >> Diameter ~ 10-1-10-2 m 1D model
  • Compressible Euler-like flow ofat least two fluid components: supercritical He (~ 5 K, 0.5 MPa) in annulus voids and in central channel
  • Heat conduction along at least two solid components: strands (SC + Cu)andjacket /conduit (SS, Incoloy, Ti, ...)
  • External (cryogenic) circuit model to provide “boundary conditions” in predictive simulations
  • Transverse coupling inside or between CICC, possibly through structures, requires Multi-conductor and/or Multi-dimensional model
  • R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER : Single-conductor model(Mithrandir code)RHS sources/sinks ( interaction with solids and other channels) include constitutive relations which require transport coefficients (friction factors, heat transfer coefficients)  Local 3D modelsR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER : Models (II) – Local thermal-hydraulics
  • Recent idea: derive from local 3D models the constitutive relations for the radial transport fluxes to be used in global 1D models
  • The commercial FLUENT code is used for 3D analysis
  • Different issues could be addressed:
  • Friction in the central channel
  • Friction in the annular region (?)
  • Friction/heat transfer coupling in the central channel
  • Mass transfer between central channel and annular region
  • R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER: Local CtFD model equations (1)
  • Water and Air simulated @ 104 < Re < 106, hydrodynamic similarity envisaged for supercritical Helium
  • Incompressible Reynolds-Averaged Navier-Stokes (RANS) equations, with constant temperature and transport properties are used:
  • Linear energy equation, based on Reynolds analogy between turb. conduction and turbulent momentum transfer, solved for heat transfer problem:
  • 2-layer k- model [Chen&Patel, AIAA J. (1988)] established as best choice closure for flow with separation in 2D [Arman&Rabas, NHTA (1994)], and confirmed in 3D [RZ, SG & RM, ACE (2006)]
  • CLOSURE REQUIRED!R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006yIf y+ > 1  enhanced wall functionsIf y+ < 1  2-layer k- modelyCWALLCICC for ITER: Local CtFD model equation (2):FLUENT Enhanced Wall treatment:For Rey> 200  standard k- model (fully turb. region)2-layer k-model:For Rey < 200  one-equation model of Wolfstein (Viscosity-affected region)t and  are smoothly blended between turbulent and viscosity affected regions, to avoid discontinuity across Rey=200In the viscosity affected region only Mass, Momentum, k and (if needed) Energy conservation eqs. are solved for.Then t and  follow (after Wolfstein):R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006WALLINOUTzLAXISCICC for ITER : Local CtFD model equation (3)BOUNDARY CONDITIONS:WALL:IN-OUT: Periodicity on: Given Tbulk,in Given   dm/dt (or viceversa)AXIS (2D only):
  • SOLUTION
  • Finite Volume discretization, with second order upwind convective fluxes and SIMPLE linearization of pressure-momentum-turbulence equations (solution by FLUENT commercial code)
  • Incompressible, constant properties fluid  linear energy equation is solved after the flow field solution is converged
  • R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER: Results (IIa)Friction in the central channel resultsUnstructured hybrid mesh
  • hexahedral in the gap and wall boundary layer
  • tetrahedral in the core
  • CFD-based predictive correlation derivedValidationExperimental validationReR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER: Results (IIb)Shear stress wg/h = 4  RECIRCULATIONCfMain/core flowg/h = 8  RE-ATTACHMENT2D effect [Webb et al., IJHMT (1971)] recovered in 3D!R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006SIMPLE convergence exampleDin =6 mm, g=8 mm, Re=8104, fields pre-initialized with a coarser mesh solutionEvolution of , for a given dm/dtCONVERGENCE CRITERIA:Variation of  relative to asymptotic value < 2%In this case, ~ 2000 SIMPLE iterations would have been enoughR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER: Results (IIc)Friction in the cable bundle33x19Axial flow contours33x733x7ValidationITER TFMC3x3x5x4x6Compute permeability of complex cable patterns?!R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006Friction in porous mediaDarcyForchheimer3D Seepage velocity1D flow velocityPermeability (m2)Inertial constantFriction factorReynolds numberR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006Dphp/h=10h/D=0.04CICC for ITER: Results (IId)Heat exchange in 2D rib roughened tube: ValidationSt = Nu/Re Pr
  • Presented numerical results are grid independent
  • Very good agreement of friction factor
  • Acceptable agreement of St, slightly better for air (Pr=0.71) than for water (Pr=5.1)
  • R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER: (local) results (IIe)Pr=5.1 (water)Re=105ReattachmentStreamlinesTemperature contours (K)R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006Pr=5.1Re=105CICC for ITER: (local) results (IIf)Colburn-like analogy between global f and St, is not verified owing to the strong contribution to f of form drag vs. friction drag, which does not have any analogy in heat transferComputed Reynolds/Colburn local analogy between momentum and heat transfer is not verifiedCICC for ITER: Heat slug propagation (I)Nb3Sn conductor TH test&analysis (1997)2-fluid code needed to reproduce T evolution @ different sensors  bundle-hole heat diffusion For the average temperature, under suitable assumptions:Taylor-Aris dispersionR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER: Quench propagation (I)Quench propagationCryogenic circuitNb3Sn conductor test&analysis (1997)R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006ITER : Model coils – CSMC & TFMCR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006ITER : Insert coils – CSIC & TFCIR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER: StabilityStability tests on the CS Insert Coil (JAERI Naka, Japan, 2000)Nb3Sn conductor test&analysis (2000)Stability margin vs dm/dtStability margin vs T marginR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER: Quench propagation (II)Nb3Sn conductor test&analysis (2000, 2001)CS Insert Coil tests(JAERI Naka, Japan, 2000)TF Conductor Insert tests(JAERI Naka, Japan, 2002)Propagation of quench frontR. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER : Multi-conductor model(M&M code)Time scale separation along and across CICC  solve 3D problem as several coupled 1D problems.Use Mithrandir model for each CICCTransverse coupling is explicit in timeLongitudinal coupling with circuit code Very general coil topology can be simulated with this strategy!R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006CICC for ITER: Performance assessment (I)(Nb3Sn)Central Solenoid Model Coil test&analysis (2000-2002)TCS testCoil topologyCryogenic circuitR. Zanino, et al
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