Surface Capturing in Droplet Breakup and Wall Interaction

8/9/2019 Surface Capturing in Droplet Breakup and Wall Interaction

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Surface Capturing inDroplet Breakup and

Wall InteractionHrvoje Jasak

[email protected]

Wikki Ltd. United Kingdom

12/Jan/2005

Surface Capturing in Droplet Breakup and Wall Interaction p.1/2


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OutlineObjective

Review surface capturing numerics in CFD

Present Diesel jet breakup and droplet-wall

interaction resultsTopics

Mathematical model and numerics

Preserving sharp interfaces

Jet breakup and droplet-wall interaction



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BackgroundSurface tension-dominated free surface flows

Sometimes difficult to grasp experimentally

Good free surface handling would allow

DNS-like simulations for detailed studiesSurface capturing model

Ideal for flows with breaking waves

Surface denoted by indicator variable

Handles surface tension and wetting angle



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Mathematical ModelTwo-phase incompressible system

t+(u) = 0

u

= 0u

t+(uu) = p + f +

u = u1 + (1 )u2

, = 1 + (1

)2



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Surface CapturingProperties of equation

No diffusion sharp interface

Numerics tends to artificially smear sharp

profiles: unacceptable loss of accuracy In reality, interface is sharp! Do we need

perfect numerics?

Need bounded and sharp discretisation of the(u) in the -equation



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VOF ApproachClassical VOF

For partially filled cells, reconstruct interfacebased on and

Decide on flux depending on flow directionand orientation of interface



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VOF ApproachProblems of classical VOF

Discontinuous reconstructed interface

Works well only on hex-structured meshes

Specifications like mainly parallel andmainly normal imprecise

Potential boundedness problems



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Compressive SchemesRationale

VOF is an interface-compression method

General (better) NVD-based bounded

compression schemes: CICSAM



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Compressive SchemesCICSAM scheme

Combination of Ultimate Quickest andHyper-C using the NVD diagram

Boundedness in is crucial: phaseconservation equation

Simple compressive schemes tend to align

with the mesh: problems with curvature

Seeking balance between good interfaceresolution and parasitic currents



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Parasitic Currents Interface compression = noise in

Worst for no mean flow and high ratio



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Multiphase ModelTwo-phase Eulerian system

t+ u = 0

t

+ u = 0

yields

t+(u) +[(u u)(1 )] = 0



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Multiphase ModelCompression term: [(u u)(1 )]

Term only appears on the interface, contains(unknown) relative velocity

Model ur = u u to compress the interface Both convection terms are bounded and

conservative: discretise with standard

bounded differencing (Gamma scheme)

Interface compression comes from the newterm, not numerics! ur = f()



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Equation CouplingCoupling through surface tension

Surface tension term:

distribution depends on u and u-eqn

depends on

() Highly non-linear, lagged (up coupling),

totally dominant for small bubbles

Wetting angle: fixed gradient condition on atthe wall patch, dependent on near-wall

velocity



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Ligament BreakupCapillary ligament breakup

20m diameter ligament

Initial surface perturbation determines mode

of breakup: large and small droplets No mean flow makes this hard to simulate



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Capillary JetInk-jet printer nozzle, 20m diameter

Pulsating flow, umean = 20m/s

Tuning frequency (50kHz) and amplitude (5%)



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Diesel JetLES of a Diesel Injector

d = 0.2mm, high velocity and surface tension

Mean injection velocity: 460m/s

Diesel fuel injected into air, 5.2MPa, 900K Turbulent and subsonic flow, no cavitation

1-equation LES model with no free surfacecorrection

Fully developed pipe flow inlet



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Diesel InjectorLES of a Diesel injector

Mesh size: 1.2 to 8 million CVs, aggressivelocal refinement, 50k time-steps

6s initiation time, 20s averaging time



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Droplet Impact

Droplet-wall interaction

Series of preliminary calculations fodroplet-wall impact

Two droplet sizes: 0.5mm and 50m

Dry and wet wall (droplet-film interaction)

Normal and oblique impact (900, 45o, 70o)

Slow (10m/s) and fast (100m/s) impact



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Droplet Impact

Dry and wet normal splash



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Further Studies

Experimental comparison

Experimental data required for validation

High-speed photography

Detailed simulation parameters

Multiple droplet impact

Other relevant wall interaction cases



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Summary

Summary

Free surface simulation methodologyimplemented in FOAM

Capable of handling dominant surface tension

Need further experimental validation

Acknowledgements

Spray breakup simulations: Eugene de Villiers, Imperial College

Foam and OpenFOAM are released under GPL: http://www.openfoam.org


Documents

Surface Capturing in Droplet Breakup and Wall Interaction