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## LM-MHD Simulation Development and Recent Results

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### LM-MHD Simulation Development and Recent Results

Presented by Sergey Smolentsev (UCLA)

with contribution from:

R. Munipalli, P. Huang (HyPerComp)

M. Abdou, N. Morley, K. Messadek, N. Vetcha, D. Sutevski (UCLA)

R. Moreau (SIMAP, France)

Z. Xu (SWIP, China)

MHD and heat/mass transfer considerations are primary drivers of any liquid metal blanket design

- The motion of electrically conducting breeder/coolant in strong, plasma-confining, magnetic field induces electric currents, which in turn interact with the magnetic field, resulting in Lorentz forces that modify the original flow in many ways. This is a subject of magnetohydrodynamics (MHD).
- For decades, blankets were designed using simplified MHD flow models (slug flow, core flow approximation, etc.). The main focus was on MHD pressure drop.
- Recent blanket studies have shown that the MHD phenomena in blankets are much richer and very complex (e.g., turbulence, coupling with heat and mass transfer, etc.) and need much more sophisticated analyses.

MHD Thermofluid issues of LM blankets

*- not applicable or low importance; ** - important; *** - very important

Where we are on MHD modeling for fusion?

- No commercial MHD CFD codes
- Modification of existing CFD codes (Fluent, Flow3D, OpenFoam) – no significant progress yet, results are often obviously wrong
- Many 2D, Q2D and 3D research codes – still limited to simple geometries; other restrictions
- Development of specialized MHD codes for blanket applications(e.g. HIMAG) – good progress but there is a need for further improvement to achieve blanket relevant conditions: Ha~104, Gr~1012

MHD modeling and code development at UCLA/HyPerComp

- HIMAG (along with HYPERCOMP) – ongoing work on development of 3D MHD parallel MHD software for LM blanket applications
- 2D, Q2D and 3D research codesto address particular MHD flows under blanket relevant conditions

In this presentation:

- New modeling results for “mixed convection” in poloidal flows
- Study of hydrodynamic instabilities and transitions in MHD flows with “M-shaped” velocity profile
- 3D modeling of Flow Channel Insert (FCI) experiment in China

OTHER RELATED PRESENTATIONS at THIS MEETING

Mixed Convection (MC)

- In poloidal ducts, volumetric heating
- causes strong Archimedes forces in PbLi,
- resulting in buoyant flows
- Forced flow ~ 10 cm/s
- Buoyant flow ~ 30 cm/s
- MC affects the temperature field in the FCI,
- interfacial temperature, heat losses and
- tritium transport – all IMPORTANT!

In the DCLL blanket conditions,

the poloidal flows are expected

to be hydrodynamically unstable and

eventually turbulent

How we attack the MC problem

- Full 3D computations using HIMAG: limited to Ha~1000, Re~10,000, Gr~10^7; the code does not reproduce turbulence
- Spectral Q2D MHD code (UCLA, Smolentsev): captures MHD turbulence but limited to simplified geometry and periodic BC
- 1D analytical solution for undisturbed flow
- Linear stability analysis to predict transitions in the flow – see poster presentation by N. Vetcha
- Experiment – see presentation by K. Messadek

3D modeling of MC flows

Ha=700

Ha=1000

Ha=400

Ha=100

Re=10,000

Gr=107

a/b=1

B-field

B-field

B-field

g

g

g

Tendency to quasi-two-dimensional state as Ha number is increased has been demonstrated for both velocity and temperature field

3D modeling of MC flows

Velocity

- Pronounced entry/exit effects
- Reverse flow bubble at the entry
- Accelerated flow zone at the entry
- “Hot” spot in the left-top corner
- Reduction of entry/exit effects with B
- Near fully developed flow in the middle

Ha=700

Ha=1000

Ha=400

Temperature

Ha=400

Ha=700

Ha=1000

MC: comparison between 3D and 1D

Full solution

Wall functions BC

Wall functions BC

Ha=700

Ha=1000

Ha=400

- 1D analytical solution
- Flow is Q2D
- Flow is fully developed

Fully developed

Quasi-2D

Major assumptions of the 1D theory

have been verified with 3D modeling.

1D/3D comparison is fair

MHD turbulence, instability and transitions

- All liquid metal blankets fall on the sub-region below the line Re/Ha~200 associated with the turbulization of the Hartmann layer. Here, MHD turbulence exists in a very specific quasi-two-dimensional (Q2D) form.
- The Q2D turbulent structures appear as large columnar-like vortices aligned with the field direction. This Q2D MHD turbulence is mostly foreseen in long poloidal ducts resulting in a strong modification of heat and mass transfer.
- We do some analysis for MHD instability and laminar-turbulent transitions for flows with “M-shaped” velocity profiles, which are typical to blanket conditions

Type II

Side layer

Internal shear layers

MHD turbulence, instability and transitionsDirect Numerical Simulation of Q2D MHD turbulence

The next few movies will illustrate major findings, namely:

- How the instability starts
- Two types of instability
- Primarily instability (Type I):
- inflectional instability
- Secondary instability (Type II):
- bulk eddy/wall interaction
- How MHD turbulence eventually evolves

MHD turbulence, instability and transitions

Type I (primarily) instability (Re=2500, Ha=200)

Transition from Type I to Type II instability and evolvement of MHD turbulence

Modeling FCI experiment in China

M.S. TILLACK, S. MALANG, “High Performance PbLi Blanket,” Proc.17th IEE/NPSS Symposium on Fusion Engineering, Vol.2, 1000-1004, San Diego, California, Oct.6-10, 1997.

Poloidal duct of the DCLL blanket

with FCI and helium channels

- Sic/SiC FCI is used inside the DCLL blanket and also in the feeding ducts as electrical and thermal insulator allowing for ΔP<2 MPa, T~700 C, >40%
- Possible thermal deformations and small FCI displacements are accommodated with a ~ 2-mm gap also filled with PbLi
- Tritium and corrosion products in the gap are removed with the slowly flowing PbLi
- There are pressure equalization openings in the FCI, either in the form of holes (PEH) or a single slot (PES), to equalize the pressure between the gap and the bulk flow
- The FCI surfaces are sealed with CVD-SiC to prevent “soaking” PbLi. The sealing layer can also serve as a tritium permeation barrier
- The FCI is subdivided into sections, each about 0.25-0.5 m long. Two FCI sections are loosely overlapped at the junction, similar to roof tiles
- The FCI is thought as a purely functional (not a structural) element experiencing only secondary stresses, which can be tolerated

Picture of experimental MHD facilities in the Southerstern Institute of Physics (SWIP), China.

Modeling FCI experiment in ChinaFlow of InGaSn in a SS rectangular duct with ideally insulating FCI made of epoxy

subject to a strong (2 T) transverse magnetic field

Courtesy of Prof. Zengyu XU, SWIP

Modeling FCI experiment in China

- 2 mm FCI made of epoxy provides ideal electrical insulation
- Maximum magnetic field is 2 T (Ha=2400)
- Uniform B-field: 740 mm (length) x 170 mm (width) x 80 mm (height)
- Outer SS rectangular duct: 1500 mm long
- FCI box: 1000 mm long
- Pressure equalization openings: slot (PES) or holes (PES)
- Measurements: pressure drop, velocity (LEVI)

Modeling was performed under the experimental conditions

using the fully developed flow model first (2009) and then in 3D (2010) using HIMAG

1

2D modeling, previous

2

Modeling FCI experiment in China- Previous 2D computations show
- MHD pressure drop much smaller
- than that in the experiment

S. SMOLENTSEV, Z.XU, C.PAN, M.ABDOU, Numerical and Experimental Studies of MHD flow in a Rectangular Duct with a Non-Conducting Flow Insert, Magnetohydrodynamics, 46, 99-111 (2010).

Pressure drop coefficient

- Current 3D computations demonstrate
- good match with the experiment

- These suggest 3D axial currents

In this figure jx (axial current) is plotted:

1 – axial current in the gap, just above the slot

2 – return current

Concluding remarks

- In the recent past, the main focus of MHD studies for fusion applications was placed mostly on MHD pressure drop.
- Although MHD pressure drop still remains one of the most important issues, current studies are more focusing on the detailed structure of MHD flows in the blanket, including various 3D and unsteady effects.
- These phenomena are not fully understood yet. For example, the mass transport (e.g. tritium permeation, corrosion) is closely coupled with MHD flows and heat transfer, requiring much better knowledge compared to relatively simple pressure drop predictions.
- Therefore, the key to the development of advanced liquid metal blankets for future power plants lies in a better understanding of complex MHD flows, both laminar and turbulent, via developing validated numerical tools and physical experiments.

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