Sergey Smolentsev,1 Leo Bühler2

1 University of California, Los Angeles, USA

2 Karlsruhe Institute of Technology, Germany

Recent advances and prospects for

further progress in modeling the coupled

MHD thermofluids phenomena of heat,

mass, and momentum transfer

3rd IAEA DEMO Programme Workshop

May 11-14, 2015

Hefei, China

MHD and Heat & Mass Transfer (transport processes), are primary drivers of any liquid metal blanket design

MHD. The motion of electrically conducting breeder/coolant in magnetic field induces electric currents, which interact with the magnetic field, resulting in strong Lorentz forces (4 to 5 orders of magnitude higher than hydrodynamic forces) that modify the flow in many ways.

Heat transfer. The flowing LM and the surrounding structure absorb volumetric and surface heat resulting in high, strong-gradient temperature field in the liquid and the solid.

Mass transfer. (1) Li or PbLi are chemically aggressive, causing corrosion of structural and functional materials. (2) Once generated, Tritium is convected by the flowing LM and diffuses through the liquid and the solid.

B=1.7 T Corrosion of RAFM in PbLi under B-field

Velocity and induced currents in MHD flow in a duct

Temperature field in DCLL (ITER TBM)

Analysis of transport processes in LM MHD flows is based on the SIMILARITY THEORY that involves dimensionless

numbers

These numbers represent ratios between different physical mechanisms or forces

acting on the flowing liquid, such as:

They are used to construct so-called scaling laws in the form S=F(Ha,Re,Gr…) Progress of all the R&D activities can be measured based on how close these

parameters to those in real blanket applications

• Reynolds Number, �� = � �� ��� � � = � � • Hartmann Number, � = � � � �� � ^0.5�� � � ^0.5 = �� �

• Grashof Number, � = � �� �� ��� � � = �∆��

Non-Dimensional Control Parameters

Characteristic values of the dimensionless parameters

for LM blanket concepts under different conditions

DCLL DCLL DCLL HCLL Li/V

Self-cooled

Machine ITER TBM DEMO DEMO ITER TBM DEMO

Location Outboard Outboard Inboard Outboard Inboard

B0, T 4 4 10 4 10

L, m 0.1 0.1 0.1 0.07 0.05

U0, m/s 0.04 0.07 0.15 0.001 0.5

NWL, MW/m2

(average)

0.78 2.13 1.33 0.78 2.0

Ha 6.5 x 103 1.2x104 3.0x104 1.1 x 104 4.5x 104

Re 3.0 x 104 6.0x104 1.2x105 670 3.2 x 104

N 1.4 x 103 2.4x103 7.5x103 1.8 x 105 6.0 x 104

R 4.6 5.0 4.0 0.06 0.7

Gr 7.0 x 109 2.0x1012 1.6x1012 1.0 x 109 6.0 x 108

Reference [46] [46] [47] [26] -

Maximum values: Ha~10^4, Re~10^4, Gr~10^12

In a LM blanket, MHD and Heat & Mass Transfer are non-linearly coupled

Simulation of the coupled transport processes requires I N T E G R A T E D M O D E L I N G T O O L S !

A strong need for full 3-D VALIDATED INTEGRATED MODELING CMHD* TOOLS for blanket applications has been

acknowledged by the fusion community only recently

• For many years blankets were designed

using simplified approaches, such as “slug

flow approximation” and more advanced but still limited “core flow approximation”

• The main research focus was placed on

prediction of MHD pressure drop in purely

MHD flows for various flow configurations

• The MHD pressure drop still remains a

research topic of high practical importance, but there is much

more…MHD instabilities, buoyancy-driven

flows, MHD turbulence, MHD flow-driven

corrosion, which are still uncovered Significant progress in CMHD since

~2007 thanks to consistent and

conservative numerical scheme by Ni *Computational Magnetohydrodynamics

Where are we now in CMHD?

We are still pretty far from the target numbers

What CMHD tools are presently available?

• FLUENT – commercial multi-purpose CFD solver with a built-in MHD module

• CFX – commercial multi-purpose CFD solver with a user-developed MHD module

• SC/TETRA – commercial multi-purpose CFD solver with a built-in MHD module

• OpenFoam – open-source multi-purpose CFD solver with a build-in electrodynamics module or user-developed MHD module

• FLUIDYN - CFD and multi-physics solver with build-in MHD capabilities by TRANSOFT International

• MTC (China) – “home-made” MHD solver with many computational capabilities

• HIMAG (USA) - “home-made” MHD solver with many computational capabilities

• FEMPAR (Spain, Badia et al.) – “home-made” multi-physics solver with MHD capabilities

• 2D, Q2D and 3D research codes, e.g. CoreFlow (L. Bühler, Germany), TRANSMAG (S. Smolentsev, US)

• DNS codes, e.g. by Satake/Kunugi (Japan), Krasnov/Zikanov/Bueck (Germany)

I

II

III

CMHD development in the US, 1

Recent studies (2007- ):

1) MHD mixed convection in poloidal flows

2) Q2D MHD turbulence

3) Instabilities and laminar-turbulent transitions

4) Hydrodynamic slip effect

5) MHD flows in a fringing magnetic field

6) Impact of FCI on MHD flow and heat transfer

7) MHD flow-induced corrosion

8) New MHD computational models (j-formulation, B-formulation)

UCLA in cooperation with HyPerComp have a very

intensive effort on model and code development.

The computational suite includes two big codes

HIMAG (MHD, Heat Transfer) and CATRIS (Mass

Transfer) and many specialized research codes,

e.g. TRANSMAG (RAFM /PbLi corrosion).

CMHD development in the US, 2

• A parallel, 3D, unstructured mesh based code with graphical utilities for meshing, domain decomposition, parallel execution and solution post-processing.

• Ability to obtain solutions for high Ha-number flows (up to 10,000) even on nonrectangular domains. Typical meshes include ~106 elements.

• Ability of HIMAG to resolve accurately unsteady flows has not been verified yet.

Comparison between HIMAG and experiment for

MHD flow in a rectangular duct (left) and circular pipe

(right) in a fringing magnetic field.

N. B. Morley, M. J. Ni, R. Munipalli, P.A. Huang, and M. A. Abdou,

“MHD simulations of liquid metal flow through a toroidally oriented manifold,” Fusion Eng. Des. 83, 1335 (2008).

HIMAG - HyPerComp Incompressible MHD solver for Arbitrary Geometries

CMHD development at KIT,* 1

*Prepared by Leo Bühler and Chiara Mistrangelo

CMHD development at KIT, 2

UCLA studies of vertical MHD flows with reactor-type volumetric heating suggest that in DCLL, Q2D turbulence will appear either as “weak” or “strong”

• In poloidal flows, buoyancy forces are caused by radial temperature gradients due to exponentially varying volumetric heat. The buoyant flows superimpose on the forced flow. Such mixed-convection flows are foreseen to be hydrodynamically unstable and eventually turbulent.

• For DCLL, our DNS studies and stability analysis suggest two types of instability: (1) primary inflectional instability and (2) secondary instability due to vortex-wall interactions

• Two turbulence regimes have been identified. In “weak turbulence,” eddies remain localized near the inflection point. In “strong turbulence,” bulk eddies interact with the side-wall boundary layer causing its instability and formation of secondary vortices.

Vorticity snapshots in a turbulent mixed-

convection flow at Re = 5000 and Gr = 108.

Strong turbulence: (a) Ha = 50, and (b) Ha = 60.

Weak turbulence: (c) Ha = 100, and (d) Ha = 120.

B

V

g

N. Vetcha, S. Smolentsev, M. Abdou, R. Moreau, Study of instabilities and quasi-two-dimensional turbulence in volumetrically heated MHD flows in a vertical rectangular duct, Phys. Fluids 25,024102 (2013).

HCLL (EU): Importance of buoyancy effects has been demonstrated

recently for 3D magneto-convection in coupled channels

z

y

x

B

g

First wall (FW)

Gr = 1.2 108

= 1.4MW/m3 Q

Back Plate

(BP)

Iso-surfaces of electric potential

Complex flow patterns

Convection rolls are elongated along B

with their axes II to B

Significant differences in flow pattern

and temperature distribution in different

sub-channels

Convection with non-uniform heating Typical convective flow patterns

2000Ha

Radial distribution of heat source according to a

neutronic calculation, Villari et al. 2010

Investigations of the influence of magnetic field and non-uniform heat source on convective flow patterns

Effect of B-field on corrosion of RAFM in the flowing PbLi is one of the least known

• Riga experiment (2009): corrosion at Hartmann walls is doubled due to the B-field effect.

• No corrosion data for the side walls.

• COMPUTATIONS with TRANSMAG: Side walls

experience 2-3 times

higher corrosion rate compared to Hartmann

walls due to velocity jets.

Hartmann wall

(⊥ to B-field)

Side wall

II to B-field)

Hartmann wall

Side wall

VALIDATION & VERIFICATION of CMHD codes is in progress under ongoing blanket studies

between IPR (India) and UCLA (US)

- UCLA: HIMAG

- IPR: FLUIDYN

Case 1 – fully developed MHD flows

Case 2 – flows in a fringing magnetic field

Case 3 – complex geometry flows

IPR-UCLA: Code-to-code and code-to-experiment comparisons for a complex geometry flow are

promising but still not satisfactory

Ha = 514, Re = 82000, Cw = 0.15 Ha = 2059, Re = 66000, Cw = 0.15

- Complex flow experiment, IPUL, Riga, 2012

- Electric potential measurements

- Pressure drop measurements

Major international effort on MHD code V&V started in 2013 involves 12 teams from all over the World

The effort on MHD code V&V is ongoing

A new initiative on Verification and Validation (V&V) of available MHD codes for LM fusion applications was proposed by a group of experts lead by Dr. Sergey Smolentsev, UCLA

First discussed at IEA LB workshop in Barcelona, 2013

A database of 5 benchmark problems for laminar and turbulent MHD flows has been established

12 teams from the US, EU, China, Korea, Russia and India

A paper summarizing the V&V approach has been published in Fusion Engineering and Design, 2014

The 1st benchmark case has been accomplished. The 2nd one is in progress.

CONCLUSIONS

In spite of significant progress in computations of coupled MHD thermofluids phenomena of heat, mass, and momentum transfer there is a strong need for full 3-D VALIDATED INTEGRATED MODELING CMHD TOOLS

The main goal is development of CMHD tools capable of addressing high Ha (~10^4), high Re (10^4), high Gr (10^12) flows in complex geometries

We are still far from the target blanket values of Ha,Re~10^4, Gr~10^12

V&V of major existing CMHD codes is in progress