a coupled level set/volume-of-fluid (clsvof) method for target
TRANSCRIPT
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A Coupled Level Set/Volume-of-Fluid(CLSVOF) Method for Target Flow Simulation
Yan Zhan
8-18-2011
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Outline
• What is CLSVOF?
• Why CLSVOF?
• How to implement CLSVOF?
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What is CLSVOF?Volume of Fluid (VOF) Level Set (LS)
• Volumetric phase fraction FPhase 1 F=1Phase 2 F=0Interface 0<F<1
• Transport of F:
• Mass-conservative• Diffusion of the interface
• Level-Set function ФPhase 1 Ф>0Phase 2 Ф<0Interface Ф=0
• Transport of F:
• Robust geometric information (normalsand curvatures); automatic handling of topological changes (merging and pinching);• Not mass-conservative
0)~()( =⋅∇+ FUF t ρρ 0)~()( =⋅∇+ φρρφ Ut
Level SetVolume of Fluid
CLSVOF
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Why CLSVOF?
Sussman, J. Comput. Phys., 162, 2 (2000)Menard, International Journal of Multiphase Flow, 33, 5 (2007)
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Why CLSVOF?
Development of the liquid jet (time step is 2.5 μm) (Menard, 2007)
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Why CLSVOF?
Liquid jet surface and break-up near the jet nozzle
Liquid parcels
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How to implement CLSVOF?
• Couple LS with VOF within the CFD code FLUENT by implementing user defined functions (UDF)
• UDF– User written program that can be linked with FLUENT at
run-time
– Programmed in C and FLUENT defined macros
– User-defined scalar (UDS) transport modeling customize FLUENT for level set equation
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How to implement CLSVOF?
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How to implement CLSVOF?
B. A. Nichita, 2010, PhD thesis, An improved CFD tool to simulate adiabatic and diabatic two-phase flows
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How to implement CLSVOF?
• B.A. Nichita’s test case– A bubble rising in a viscous fluid due to gravity
Level set contour (red) and volume-of-fluid contour (green) without coupling betweenLS and VOF (with large loss of mass).
Level set contour (red) and volume-of-fluid contour (green) after solving the couplingequation between LS and VOF.
(t = 0.2s)
(t = 0.2s)
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How to implement CLSVOF?
• Setup UDS for LS in FLUENT
Scalar ø Transport Equation
– Unsteady term
– Convection term
– Diffusive term
– Source term
Additional term appear for turbulent flow such as
0)~( =⋅∇+∂∂ φρρφ U
t
)~( φρU⋅∇
t∂∂ρφ
0
0
j
tj xu
∂∂
Γ=′′−φφρ
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How to implement CLSVOF?
• Setup UDS for LS in FLUENT– Set number of UDS
– Set UDS terms (Appendix A)• DEFINE_UDS_UNSTEADY
– Get unsteady term for scalar equation
• DEFINE_UDS_FLUX– Returns user specified flux
• DEFINE_DIFFUSIVITY– Returns user diffusion coefficient (Γ)
• DEFINE_SOURCE
– Set UDS boundary conditions• Constant
• UDF: DEFINE_PROFILE
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Appendix Equations• Incompressible two-phase flow
Density ρ(Ф), viscosity μ (Ф), and curvature κ (Ф) are written as,
D is defined as the rate of deformation tensor
0=⋅∇ U
FHDpUUUt +∇−⋅∇+∇
−=∇⋅+ )()()(
1))(2()(
1)(
φφγκφρ
φµφρφρ
0=∇⋅+ φφ Ut
φφφκ
φµφµφµφρφρφρ
∇∇⋅∇=
+−=
+−=
)(
)())(1()()())(1()(
HHHH
lg
lg
TUUD )()( ∇+∇=
0)( =⋅∇+ UFFt
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Appendix Equations• Incompressible two-phase flowThe surface tension force is
where H is the Heaviside function,
F will be initialized in each computational cell Ωij
where Ωij is
)()()(
1 φφγκφρ
H∇
>
=otherwise. 0
0 if 1)(
φφH
∫∆∆
=Ωij
rdrdzzrHzr
Fij ))0,,((1 φ
11 and ),(++
≤≤≤≤=Ω jjiiij zzzrrrzr
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• Re-Initialization– Reinitialize ф
where w is the characteristic velocity pointing outward from the free surface
The sign function is
Appendix Equations