MODELING STATUS Presented by Sergey Smolentsev - - PowerPoint PPT Presentation

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MODELING STATUS Presented by Sergey Smolentsev ========================================

• Modeling of low-conductivity fluid flow and heat transfer using

“K-epsilon” model

• “HIMAG”, HyPerComp – UCLA code for simulation LM MHD

flows

• Modeling LM MHD flows using 3-D thin-shear-layer

approximation

• Implementation of different MHD formulations

======================================= Electronic APEX Meeting 20 August 13, 15 2002

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Modeling of low-conductivity fluid flow and heat transfer using “K-epsilon” model

• Calculations have been done for OB FW Flinabe flow, which

take into account poloidal distribution of the heat flux and volumetric heating

2 4 6 8 10

Distance from the inlet, m

20 40 60 80 100

T-Tinlet, K

Average surface heat flux: 1.4 MW/m2 (uniform) Average neutron heating: 0

Surface Temperature Bulk Temperature

2 4 6 8 10

Distance from the inlet, m

40 80 120

T-Tinlet, K

Average surface heat flux: 1.4 MW/m2 (parabolic) Average neutron heating: 7 MW/m2 (parabolic)

Surface Temperature Bulk Temperature

BEFORE AND AFTER

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Modeling of low-conductivity fluid flow and heat transfer using “K-epsilon” model

• Calculations have been done to estimate the effect of turbulence

reduction by a magnetic field in the blanket flows.

10 20 30 40 50

x / h

80 120 160 200 240 280

Nuh

Duct Flibe Flow: Nuh vs. x / h h=1 cm (width); U=5 m/s; B=10 T

Re=7000, Ha=0 Re=7000, Ha=10

Dittus-Boelter formula Calculations have been done to estimate turbulent heat transfer reduction by a magnetic field in a Flibe blanket flow using the “K-epsilon” model. The flow parameters were chosen as follows: U=5 m/s (flow velocity); h=1 cm (channel width); B=10 T (magnetic field). The Nusselt number built through h (the channel width), Nuh, was calculated for two cases: with a magnetic field and without a magnetic field. The difference in the fully developed Nusselt number between these two cases is about 10%. The case without a magnetic field agrees very well with the calculations based on the Dittus-Boelter formula.

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Modeling of low-conductivity fluid flow and heat transfer using “K-epsilon” model

• Special calculations have been done to estimate turbulence

suppression by a magnetic field in the spiral blanket flow (Igor Sviatoslavsky).

ZONE I

Midplane channel: Channel dimension- 14 cm radial poloidal height- 6.7 cm at FW and 4.2 cm at shaft Length along FW 30cm Magnetic field paralel to flow Inboard 7.9 T, outboard 4.7 T Average velocity 3 m/s

ZONE II

Extremities channel: Channel dimension-14 cm radial poloidal height-6.7 cm at FW and 4.2 cm at shaft Length along FW 23 cm Magnetic field as above Average velocity 3.1 m/s

The magnetic field is parallel to the main flow direction. This means that the effect of turbulence suppression by a magnetic field is weak comparatively to the case with the magnetic field perpendicular to the

• flow. The friction factor, f, and fully developed Nusselt number,

Nu_fd, without the field are 0.00451 and 609 respectively. With the field, f=0.00446, and Nu_fd=605. This means that the effect of the magnetic field on the flow and heat transfer is negligible.

ZONE III

Side channels Channel dimension-14 cm in toroidal direction poloidal height same as above length of channel 30 cm Magnetic field perpendicular to flow and varies Inboard from 8.3-7.9 T

• utboard 4.7-4.2 T

Average velocity 3 m/s

The magnetic field is perpendicular to the flow. The effect of the magnetic field on the flow is pronounced. I calculated two cases: with the Hartmann effect (there is a magnetic field component perpendicular to the wall), and without the Hartmann effect (the magnetic field is completely spanwise). The results are the following.

• 1. With the Hartmann effect: f=0.00487, Nu_fd=380. The

higher value of f is explained by the Hartmann effect.

• 2. Without the Hartmann effect: f=0.00223, Nu_fd=365.

In both cases the turbulence suppression is very pronounced and heat transfer reduction is by a factor of almost two. However, there is only neutron heating in Zone III, so that Nu number results are not applicable here.

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Modeling of low-conductivity fluid flow and heat transfer using “K-epsilon

• New data on heat transfer from the FliHy experiment are being

incorporated into the “K-epsilon” model to take into account waviness effect on heat transfer through the turbulent Prandtl number distribution. Preliminary analysis shows the heat transfer enhancement by 1-2 times. The results will be reported at the APEX Meeting in Princeton

SMOOTH INTERFACE (SUBCRITICAL)

Heat transfer reduction due to the blockage effect

WAVY INTERFACE (SUPERCRITICAL)

Heat transfer improvement due to

• reducing the blockage effect
• breaking the surface
• turbulence generation by the waves

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“HIMAG”, HyPerComp – UCLA code for simulation LM MHD flows

• S T A T U S S U M M A R Y

3-D unstructured grid code for simulation free surface MHD flows with Level Set Method for tracking the interface TASK STATUS I: Flow solver development

Has been written and validated against canonical test problems

II: MHD model development

ϕ-formulation, B-formulation have been implemented and tested (Ha up to 103) for closed channel flows.

III: Graphical interface

Preliminary GUIs have been developed for pre- and postprocessing.

IV: Solution acceleration technique

Conjugate gradient method for PPE has been

• implemented. Parallelization will be started soon.

V: Free surface models

Level Set Method is being debugged.

VI: Validation and accuracy

Has been validated against closed channel flow

• cases. Benchmarks for free surface flows have

been chosen.

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“HIMAG”, HyPerComp – UCLA code for simulation LM MHD flows

• Near-future plans
• 1. Jet flows under NSTX conditions
• 2. Chute-type flow in a 3-component B-field with the normal

component varying in space

• 3. ARIES RS FW flows without penetrations
• 4. ARIES RS FW flows with penetrations

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Modeling LM MHD flows using 3-D thin-shear-layer approximation

• Model description and its applications

3-D thin-shear-layer equations for flows of conducting fluids in a magnetic field have been derived in orthogonal body-oriented coordinates. Unlike the classic boundary-layer-type equations, present ones permit information to be propagated upstream through the induced magnetic field. Another departure from the classic theory is that the normal momentum equation keeps the balance between the pressure gradient term, and those related to gravity, centrifugal forces, and Lorentz force. Thus, the normal pressure variations are allowed. The model describes basic 3-D effects due to the wall curvature and spatial variations of the applied magnetic field. The model can be applied to the following open-surface MHD flows:

• flows with rotational symmetry;
• chute-type flows in a gradient magnetic field (some restrictions);
• flows around penetrations (some restrictions).

At present, the model is being modified to include turbulence effects (NSTX case).

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Modeling LM MHD flows using 3-D thin-shear-layer approximation

• UCLA-HyPerComp benchmark case for 3-D open surface flow

y / h0

5 10 15 20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x / h0 Flow without a magnetic field. Velocity vector plot in the x-y plane. Changes are due to the gravity force and geometrical variations.

23500 / Re = = ν h U

,

. 5 ) /(

2

= = gh U Fr 8500 )] /( [

5 .

= = νρ σ h B Ha 07 . Re = = σ µ h U

m

Liquid flows down over a “bottle- neck” surface of revolution

5 10 15 20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

y / h0 x / h0

5 10 15 20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

y / h0 x / h0 Flow with a magnetic field. Left: velocity vector plot. Right: induced magnetic field counter lines.

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Modeling LM MHD flows using 3-D thin-shear-layer approximation

• MHD flows around penetrations: problem formulation
• Boundary conditions at the

inlet/outlet, free surface and at the solid wall are as usual

• Boundary conditions at Z=±∞

correspond to the undisturbed flow

• Kinematic free surface condition

is used for tracking the free surface

h x h x h x

V x h V x h V t h

= = =

= ∂ ∂ + ∂ ∂ + ∂ ∂

2 2 2

| | |

2 3 3 1 1

x

flow Magnetic field

y

The approach can be used as an alternative to the HIMAG code or as a benchmark case.

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Modeling LM MHD flows using 3-D thin-shear-layer approximation

• MHD flows around penetrations: governing equations in

boundary fitted coordinates

1 2 2 1 2 1 1 1 2 3 1 3 3 1 3 1 3 1 3 1 3 3 2 1 2 1 1 1 1 1

) ( 1 1 1 1 B j× + ∂ ∂ + + ∂ ∂ − =         ∂ ∂ − ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ ρ ν ρ x V g x p H V x H V V x H H H x V H V x V V x V H V t V

2 2 2 2 3 2 3 3 1 3 1 2 1 2 1

1 ) ( 1 2 x p g V H N V V H H M V H L ∂ ∂ − = × − − + + ρ ρ B j

3 2 2 3 2 3 3 3 2 3 3 1 3 1 1 3 3 1 3 3 3 3 2 3 2 1 3 1 1 3

) ( 1 1 1 1 B j× + ∂ ∂ + + ∂ ∂ − =         ∂ ∂ − ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ ρ ν ρ x V g x p H V x H V V x H H H x V H V x V V x V H V t V

H1, H2, and H3 are the components of the metric tensor, which allow straightforward implementation of the complex geometry

• The induced electric current is calculated using Ohm’s low.
• The electric potential is calculated using the equation for the potential also written

in the boundary fitted coordinates.

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Implementation of different MHD formulations

• B-formulation

How large is the error from imposing the BCs on the magnetic field at the boundaries of the flow domain ? At what distance from the flow domain should the BCs on the magnetic field be imposed ? To answer these two questions, a 3-D lid-driven cavity flow in a magnetic field is considered for different orientations of the field and for different Ha S.Smolentsev and S.Cuevas

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Implementation of different MHD formulations

• j-formulation
• Since the electric current does not exist in the vacuum exterior, the equations for

the electric current are solved only within the flow (wall) domain.

• The boundary conditions at the boundaries of the flow domain can be formulated

in terms of the “thin conducting wall approximation”. This means that the current entering the wall creates a potential distribution in the wall. Since the wall is thin, this distribution can be calculated using a 2-D potential equation based on the continuity equation for the electric current.

• With this formulation, it is easy to calculate the Lorentz force (just jxB). Curl or

grad operations are not required to calculate j.

• A problem can arise with providing div j=0. Good results were achieved for 2-D

closed channel flows. The approach will be tested using the same problem for 3-D lid driven cavity flow in a magnetic field. S.Smolentsev and S.Cuevas