mhd modelingactivities at upc aimed at breeding blanket ... · research groups at upc in tecno_fus...

MHD modeling activities at UPC

aimed at breeding blanket analysis

E. Mas de les Valls, J. Fradera, R. Codina, S. Badia,

R. Planas, L.A. Sedano and L. Batet

IEA International Workshop on Liquid Metal Breeder Blanket, 23-24 September 2010. Madrid, Spain

Contents of the presentation

1. Objective

2. Challenges on LL tritium transfer modeling

3. Modeling activities at CIMNE

4. Modeling activities at T4F, GREENER

5. Conclusions

MHD modelling activities at UPC aimed at breeding blanket analysis

1. Objective


General objective, in the frame of TECNO_FUS National Project:

To obtain predictive tools for MHD and tritium

transfer analysis under breeding blankets

conditions

Predictive tools � numerical tools fully validated

Critical BB aspects to be predicted are:

1) tritium inventories and permeation rates

2) heat extraction and maximum temperatures for material specifications

3) MHD pressure drops

Research groups at UPC in TECNO_FUS MHD task:

CIMNE Int. Center for Num. Methods in Engineering

GREENER RG on Energy and Radiation Studies (Tech for Fusion)

2. Challenges in LL tritium transfer modeling


LL tritium transfer modeling

MHD

Heat transfer

He

tritium

FSI


2. Challenges in LL tritium transfer modeling

turbulence

helium

walls

WF

3D /2D ?

unsteady

B, φφφφ or j ?

buoyancy

MHD

Fe

ρρρρ = ctt?



Structures Department � FEM

At the present status:

- 3D code + j-formulation + inductionless + incompressible

- pure MHD

· 0u∇ =

( ) ( )2

0

1 ·

uu u p u j B f

tν

ρ∂ + ∇ = −∇ + ∇ + × +∂

�

��

· 0j∇ =�

( )0 j u Bσ ϕ= −∇ + ×��

�

Main objective: � algorithm optimization

� implementation of advanced solvers


Approach based on a stabilisation of the finite element method

�solved drawbacks of the standard Galerkin

�based on the variational multiscale framework (FE component + subscale)

�subscale approximation implies stabilisation parameters from the stability and

convergence analysis of the method.

Solver: monolithic

�more effective than partioned approaches

�preconditioner: ILU factorisation + Krylov iterative solver (GMRES)

Note:

the ϕ-formulation has a weak point: the coupling iterations do not involve any

orthogonalisation (minimisation) procedure. So, the convergence of the method is expected

to deteriorate as the coupling becomes more important. As long as the coupling terms

increase, the convergence becomes slower or it simply diverges.

R. Planas, S. Badia, and R. Codina. Approximation of the inductionless MHD problem using a

stabilized finite element method. J. of Comp. Phy., Submitted, 2010



An example of code capabilities: effect of the cooling plates in the HCLL flow

Geometry: system: Lx= 360 mm; Ly = 390 mm (190 + 10 + 190); Lz = 206.5 mm

cooling plates: 280 × 12 × 206.5 mm3

Mesh: 266,072 nodes and 1,417,435 linear tetrahedral elements � 2,128,576 dof

Flow conditions: Haa = 2470, uin = 0.001 m/s, non-slip at walls, free outlet

j·n=0 at external walls; j×n=0 at internal walls


Non homogenelous distribution of the flow among subchannels

Inlet module with ϕ streamlines similar to Shercliff’s case. Different than at the outlet.



OpenFOAM toolbox � FVM

At the present status:

- 3D code + ϕ-formulation + inductionless + incompressible

- MHD + thermal transport (Boussinesq) + passive scalar

· 0u∇ =

( )0 j u Bσ ϕ= −∇ + ×��

�

Main objective: � take profit of present OF tools (PISO, solvers, mesh, …)

� implementation of advanced features (WF, b.c., turb., ... )

( )2

0 · u Bϕ∇ = ∇ ×�

�

( ) ( ) ( ) ( )0 0

1 1 · · T-Td

uu u p u j B g

tν β

ρ ρ∂ + ∇ = − ∇ + ∇ ∇ + × +∂

�

��

( ) ( ) · T · ST

u Tt

α∂ + ∇ = ∇ ∇ +∂

�


Present algorithm:

�partioned approach

�p-u coupling via a PISO-like algorithm

�explicit Lorentz force term but within an inner loop

�for pseudo-transient simulations � time step limitations

�linear wall function


Other algorithms:

�B-formulation

�ϕ-formulation with a sequential p-v coupling

�2D code (SM82)

OpenFOAM:

�unstructured meshes, parallelisation techniques

�several solvers and preconditioners

�turbulence models (RANS, LES) for hydrodynamic flows

�monolithic solvers

�conjugate solvers



Comparison between CIMNE and T4F codes

Shercliff’s case Hunt’s case

�Good accuracy of OpenFOAM

�CIMNE’s code is of higher order � optimised algorithm


An example of code capabilities: effect of buoyancy in the HCLL flow

Geometry:

Mesh: ~ 780,000 nodes (4 nodes at Ha b.l. and 10 nodes at side b.l.)

Flow conditions: Haa = 1740, ReDin = 480, non-slip at walls, free outlet

perfectly (electrically) insulated walls

Grb = 5.21·109, fixed temperature at inlet and walls (723.15 K)


velocity field

temperature field


Tritium analysis:


5. Conclusions


�A first step towards obtaining predictive tools for MHD and

tritium transfer analysis under BB conditions has been done.

�Still some MHD features are missing.

�Algorithm optimisation is of crucial interest for complex flows.

�Multiphysics coupling can be done in parallel.

�Further validation is needed

Thank you for your attention


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