3d modelling of edge parallel flow asymmetries

1/1318th PSI conference – Toledo, May 2008 P. TamainAssociationEURATOM-CEA

3D modelling of edge 3D modelling of edge parallel flow asymmetriesparallel flow asymmetries

P. Tamainab, Ph. Ghendriha, E. Tsitronea, Y. Sarazina, X. Garbeta, V. Grandgirarda, J. Gunna, E. Serrec,

G. Ciraoloc, G. Chiavassac

aAssociation Euratom-CEA, CEA Cadarache, FrancebEuratom-UKAEA Fusion Association, Culham Science Centre, UK

cUniversity of Provence/CNRS, France


Strong poloidal asymmetries in parallel Mach Strong poloidal asymmetries in parallel Mach number measured on all machinesnumber measured on all machines

Expected situation:

symmetrical parallel flow

parallel Mach number at the top: M = u// /cs ~ 0

Experimental results:

asymmetrical flow

M~0.5 at the top universal phenomenon

(X-point and limiter)

[Asakura, JNM (2007)]

expected M measured M

[courtesy J. Gunn]

M~0

M=+1 M=-1


Hard to reproduce with transport codes Hard to reproduce with transport codes without any ad-hoc hypothesiswithout any ad-hoc hypothesis

[Zagorski et al., 2007]

DLFS / D

HFS ~ 200

Modelling attempts with 2D transport codes [Erents, Pitts et al., 2004]

[Gunn & al., JNM (2007)]

M=+1 M=-1

M~0.5

HFS LFS

ad-hoc strong ballooning of radial transport necessary to recover experimental amplitudes:

evidence for influence of drifts (ExB and diamagnetic)


TOKAM-3D: a new numerical tool able to TOKAM-3D: a new numerical tool able to tackle consistently this kind of issuetackle consistently this kind of issue

centre

edgeSOL

limiter

simulated region

3D - full torus

closed + open field lines

3D fluid drift equations [B. Scott, IPP 5/92, 2001]

density, potential, parallel current and Mach number M Bohm boundary conditions in the SOL flux driven, no scale separation => Turbulence + Transport


3D drift fluid equations3D drift fluid equations

continuity

charge

parallel momentum

parallel current

vorticity definition

ExB advection

curvature

parallel dynamics

diffusive transport


““Neoclassical” vs turbulent regime Neoclassical” vs turbulent regime

D/DBohm ~ *

t

1

8.10-2

high D: “neoclassical” equilibrium with drifts => only large scale effects

low D: turbulent regime => impact of small scales


neoclassical equilibrium with ExB and diamagnetic drifts

non-zero Mach number at the top: M~0.25

uniform D not linked to poloidal distribution of radial transport

LFSHFS

Parallel Mach number M

M=0

M>0

M<0

0.5

0

-0.5

1

-1

Neoclassical regime: growth of poloidal Neoclassical regime: growth of poloidal asymmetries even without turbulenceasymmetries even without turbulence

mechanism: combination of global ExB drift and curvature


Par

alle

l Mac

h nu

mbe

r

θ

1

0

LFSHFS Top

-1P

aral

lel M

ach

num

ber

0.25

0

Minor radius r/ρL

10040 160

LCFS

Is that enough to recover experimental Is that enough to recover experimental results?results?

larger amplitude than that found in previous studies but still lower than experiments

radial extension in the SOL not deep enough

The answer seems to be NO: there must be something else…

θ = π/2 (top)

r/a = 1.07


Edge turbulent transport can generate large Edge turbulent transport can generate large amplitude poloidal asymmetriesamplitude poloidal asymmetries

low diffusion: D /DBohm=0.02

=> turbulent transport

poloidal up/down (m=1,n=0) asymmetry in spite of strongly aligned structures

M<r

turb >t,,

<rdiff

>t,,

r0

1

Density n no limiter => previous large scale drifts effect not included


0

0.4

-0.4

HFS LFS

90% of the flux at the LFS90% of the flux at the LFS

Mach number at the top: Mtop~0.35

LFS r / tot r ~ 0.9

M

<r>

HFS LFS

asymmetry due to ballooned transport:

90% of total flux


turbulent regime in closed + open flux surfaces

filament-like structures generated in the vicinity of the LCFS

and propagate in the SOL

How do these two mechanisms overlap in a How do these two mechanisms overlap in a complete edge simulation?complete edge simulation?

N

HFS LFS

M

HFS LFS


experimental large amplitudes Mtop~0.5 recovered even in far SOL

The superposition of both mechanisms The superposition of both mechanisms allows a recovery of experimental featuresallows a recovery of experimental features

good qualitative and quantitative agreement with experimental data


SUMMARY / CONCLUSIONSUMMARY / CONCLUSION

Parallel flows poloidal asymmetries: confirmation of the existence of 2 distinct mechanisms:

- large scale drifts => coupling between ExB, curvature and the limiter

- ballooning of turbulent radial transport => coupling between turbulent scales and curvature

superposition of both mechanisms leads to good agreement with experimental data without requiring ad-hoc hypotheses

TOKAM-3D: new generation of edge codes: 3D transport & turbulence across LCFS success of fully consistent approach on-going development for model and code improvements


The TOKAM-3D ModelThe TOKAM-3D Model

Fluid modeling with no scale separation 3D fluid drift equations : matter, charge, parallel momentum,

parallel current (generalized Ohm’s law) [Scott, IPP 5/92, 2001]

isothermal closure in current version

periodic

buffer zone

buffer zone


3D drift fluid equations3D drift fluid equations

continuity

charge

parallel momentum

parallel current

vorticity definition

ExB advection

curvature

parallel dynamics

diffusive transport


Geometrical dependancesGeometrical dependances

3 identical cases: limiter poloidal shift and B reversal (B drift sign)

Impact of field inversion and of limiter position

Bottom, normal B

LFSHFS

M=0

(BxB)ions

Equatorial, normal B

LFSHFS

M=0

(BxB)ions

Bottom, reverse B

LFSHFS

M=0(BxB)ions


‘‘Return parallel flow’ mechanism driven by Return parallel flow’ mechanism driven by ExB and curvatureExB and curvature

r

LCFS

step 1: establishment of large poloidal ExB drift at LCFS

LFSHFS

step 2: curvature effects trigger symmetric inhomogeneities

step 3: ExB drift advects the density and breaks the symmetry

M//ExB

N

top LFS

N ExB

LFStop


Origin of the Mach number asymmetryOrigin of the Mach number asymmetry

ExB drift + curvature plays a major role step 1: establishment of large poloidal ExB drift at LCFS

Bottom, normal B

Bottom, reverse B Equatorial, normal B

r r r

LCFS

r sign changes => drift direction does not change with field direction



ExB drift + curvature plays a major role

Bottom, normal B Bottom, reverse B Equatorial, normal B

N N N

top LFS

step 1: establishment of large poloidal ExB drift at LCFS step 2: curvature effects trigger symmetric inhomogeneities

No curvature effect at equatorial plane



ExB drift + curvature plays a major role

Bottom, normal B Bottom, reverse B Equatorial, normal B

N N N

top LFS

step 1: establishment of large poloidal ExB drift at LCFS step 2: curvature effects trigger symmetric inhomogeneities step 3: ExB drift advects the density and breaks the symmetry

ExBExB

3d modelling of edge parallel flow asymmetries

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