MODELING AT UCLA. CURRENT STATUS By Sergey Smolentsev and UCLA - - PowerPoint PPT Presentation

MODELING AT UCLA. CURRENT STATUS By Sergey Smolentsev and UCLA Modeling Group

APEX e-Meeting 22 February 4, 6 2003

CONTENT Benchmark case. Lid-driven cavity flow 3-D MHD flows in non-uniform magnetic fields with j- and B-formulations First steps towards stability analysis for jet flows in a magnetic field

Benchmark case. Lid-driven cavity flow

Classic test for 2-D, 3-D CFD codes Not extended to 3-D MHD flows yet UCLA code 1 (Ni), FLUENT (Morley), UCLA code 2 (Smolentsev), HIMAG (Ni, Munipalli)

Lid moves in X-direction B applied in Z-direction

Ha=45 Re=100

• 1
• 0.5

0.5 1 Z-coordinate

• 1
• 0.5

0.5 1 Y-coordinate

Benchmark case. Lid-driven cavity flow

UCLA code 1 (Ni) FLUENT (Morley) UCLA code 2 (Smolentsev) HIMAG (Ni, Munipalli)

• Collocated grid
• B-formulation
• Commercial code
• Unstructured grid
• B- or ϕ-formulation
• Fully staggered grid
• B- or ϕ-formulation
• Unstructured grid
• B-formulation

Benchmark case. Lid-driven cavity flow

UCLA code 1 (Ni) FLUENT (Morley) UCLA code 2 (Smolentsev) HIMAG (Ni, Munipalli) BC: B=0 at Γ1 BC 1: B=0 at Γ2 BC 2: Bτ=0, ∂Bn/∂n=0 at Γ1 BC: jn=0 at Γ1 BC: B=0 at Γ1 Note: UCLA code 1 and FLUENT use physically incorrect BC

Benchmark case. Lid-driven cavity flow

u y

• 0.25

0.25 0.5 0.75 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

From Mingjiu using a projection method for B From Neil using FLUENT to solve B From Sergey by solving B formulation From HIMAG by solving electrical potential formulation NonMHD flow

UCLA code 1 FLUENT (B-formulation) UCLA code 2 (B-formulation) HIMAG Non-MHD flow

U(Y) at X=0.5, Z=0.5

Benchmark case. Lid-driven cavity flow

z u

0.2 0.4 0.6 0.8 1

• 0.2
• 0.175
• 0.15
• 0.125
• 0.1
• 0.075
• 0.05
• 0.025

From Mingjiu using a projection method for B From Sergey by solving B formulation From HIMAG by solving electrical potential formulation NonMHD flow

UCLA code 1 UCLA code 2 (B-formulation) HIMAG Non-MHD flow

U(Z) at X=0.5, Y=0.5

Benchmark case. Lid-driven cavity flow V(X) at Y=0.5, Z=0.5

x v

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

• 0.3
• 0.25
• 0.2
• 0.15
• 0.1
• 0.05

0.05 0.1 0.15 0.2

From Mingjiu using projection method for B From Neil using FLUENT to solve B From Sergey by solving B formulation From HIMAG by solving electrical potential formulation NonMHD Result

V

UCLA code 1 FLUENT (B-formulation) UCLA code 2 (B-formulation) HIMAG Non-MHD flow

Benchmark case. Lid-driven cavity flow

All codes demonstrated excellent agreement in non-MHD case. The velocity field is almost insensitive to the BCs on B even though they are not quite correct. Fluent with ϕ-formulation had no convergence. UCLA code 2 with ϕ-formulation converged but the result was very different from other calculations. HIMAG with ϕ-formulation converged and the result agreed well with other calculations. In MHD case all calculations demonstrated reasonable agreement. Higher discrepancy in U(Z) can be explained by a strong impact

• f the Hartmann layers on the flow, which were probably resolved

differently by different codes.

3-D MHD flows in non-uniform magnetic fields with j- and B-formulations

Z X

Y

S N

GOALS Implementation of different MHD formulations Comparisons with other codes Application to APEX Construction of divB=0, rotB=0 applied magnetic fields

3-D MHD flows in non-uniform magnetic fields with j- and B-formulations

Analytical solution for a 3-D magnetic field in the gap between the magnetized plates was used to describe the applied magnetic field B-formulation J-formulation is being tested

Computations by Sergio Cuevas. More results will be presented at the next APEX Meeting.

First steps towards stability analysis for jet flows in a magnetic field

Rayley-Weber classic theory of capillary jet disintegration

) 3 1 ( 2 2 1 La + = ω ) 3 1 ( 2 1 La k + = We La C d L ) 3 1 ( / + =

Similar approach is used to study capillary jet break up in a magnetic field (radial). Preliminary analysis showed significant increase in L/d0 as the magnetic field grows.

B-field

L