Coupling of a LPT and a VOF Simulation - Strömningsteknik€¦ · Lund university / Division of Fluid Mechanics / 16.2.2011 ... Lund university / Division of Fluid Mechanics / 16.2.2011

Coupling of a LPT and a VOF Simulation

Holger Grosshans16.2.2011

Lund university / Division of Fluid Mechanics / 16.2.2011

Contents

• Spray Regimes

• Numerical Methods and Governing Equations

• VOF – LPT coupling

• Results and Conclusions


Spray Regimes

dilute spray

Intact liquid core

dense spray


Spray Regimes

Intact Liquid core and dense spray :

• low spacing between droplets

• Droplet is influenced by turbulence created by preceding droplets

• Turbulent structures created by droplets need to be resolved

Dilute spray :

• High spacing between droplets

• Flow is consifered to be undisturbed

• Turbulent structures created by spray needs to be resolved


Spray Regimes

Intact Liquid core and dense spray :

• Liquid structures are irregular

• High liquid volume fraction

• Large liquid structures

Dilute spray :

• Droplets can be considered spherical

• neglectable liquid volume fraction

• Small droplets

Volumes of Fluids Lagrangian Particle Tracking


Volumes of Fluids

• Gas and liquid described in Eulerian framework :

• Transport equation for the volume fraction :

( α = 1 for liquid, α = 0 for gas )


Lagrangian Particle Tracking

• Gas described in Eulerian framework :

• Dispersed liquid described in Lagrangian framework– Momentum exchange modeled by two-way coupling– Bag and stripping breakup regime modeled– Evaporation model included


VOF–LPT coupling

• VOF-LPT coupling has been done recently as a one-to-one approach [Tomar et al., Multiscale simulations of primary atomization, 2010] :

• To increase computational efficiency, here a statistical approach is chosen.


VOF–LPT coupling - droplet identification

• Spray and coupling layer



• Cell ID field initialized with 0



• Loop over cells with ID '0'

• If α = 0 → ID = -1




• If α > 0 → ID = 'new droplet ID'



• Loop over neighbour cells

• If α > 0 → ID = 'new droplet ID'

• If α = 0 → ID = -1




• If α = 0 → ID = -1



• Identified droplet area



• Identification of droplet volume



• Liquid Volume crossing the coupling layer in the current timestep :



• Connected liquid volume over several timesteps :

t t + 1



• The same procedure as for V is performed for various other droplet parameters

• A equivalent spherical droplet is determined from the irregular liquid structure

• Statistical distributions of this parameters are created


VOF–LPT coupling - droplet injection

• Four parameters need to be defined at droplet injection :

– Radius– Axial velocity– Radial velocity– Radial position

• Are these parameters independent ???



• Radial position is correlated to axial velocity

• 3 Monte-Carlo Simulations are performed to define

– Radius– Axial velocity– Radial velocity

• Radial position is linearly derived from axial velocity



• LPT simulation uses the stochastical parcel method :One parcel represents a number of droplets of the same characteristics.

• The less droplets a parcel contains, the better is the resolution of the droplet distribution

• Most interesting processes :– Gas-liquid momentum exchange– Droplet evaporation

• Both depending on the droplet mass.

Resolution is chosen to be the best for the droplets that represent the most liquid mass.



• Droplet diameter pdf is extracted from the VOF simulation: f(D)




• f(D) is scaled by the droplet mass:





• g(D) is integrated andnormalized:





• g(D) is integrated andnormalized:

• h(D) is inverted and a whitenoise is applied:



• Injected droplet distribution converges to f(D).

• Same procedure for axialand radial velocity.


Results


Results

• Example distribution at the coupling layer :


Conclusions

accuracy

computational effort

LPT

VOF

LPT-VOFstatistically

LPT-VOF1 to 1

Coupling of a LPT and a VOF Simulation - Strömningsteknik€¦ · Lund university / Division of Fluid Mechanics / 16.2.2011 ... Lund university / Division of Fluid Mechanics / 16.2.2011

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