Lund university / Division of Fluid Mechanics / 16.2.2011
Contents
• Spray Regimes
• Numerical Methods and Governing Equations
• VOF – LPT coupling
• Results and Conclusions
Lund university / Division of Fluid Mechanics / 16.2.2011
Spray Regimes
dilute spray
Intact liquid core
dense spray
Lund university / Division of Fluid Mechanics / 16.2.2011
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
Lund university / Division of Fluid Mechanics / 16.2.2011
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
Lund university / Division of Fluid Mechanics / 16.2.2011
Volumes of Fluids
• Gas and liquid described in Eulerian framework :
• Transport equation for the volume fraction :
( α = 1 for liquid, α = 0 for gas )
Lund university / Division of Fluid Mechanics / 16.2.2011
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
Lund university / Division of Fluid Mechanics / 16.2.2011
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.
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet identification
• Spray and coupling layer
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet identification
• Cell ID field initialized with 0
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet identification
• Loop over cells with ID '0'
• If α = 0 → ID = -1
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet identification
• Loop over cells with ID '0'
• If α > 0 → ID = 'new droplet ID'
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet identification
• Loop over neighbour cells
• If α > 0 → ID = 'new droplet ID'
• If α = 0 → ID = -1
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet identification
• Loop over cells with ID '0'
• If α = 0 → ID = -1
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet identification
• Identified droplet area
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet identification
• Identification of droplet volume
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet identification
• Liquid Volume crossing the coupling layer in the current timestep :
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet identification
• Connected liquid volume over several timesteps :
t t + 1
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet identification
• 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
Lund university / Division of Fluid Mechanics / 16.2.2011
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 ???
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet injection
• 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
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet injection
• 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.
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet injection
• Droplet diameter pdf is extracted from the VOF simulation: f(D)
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet injection
• Droplet diameter pdf is extracted from the VOF simulation: f(D)
• f(D) is scaled by the droplet mass:
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet injection
• Droplet diameter pdf is extracted from the VOF simulation: f(D)
• f(D) is scaled by the droplet mass:
• g(D) is integrated andnormalized:
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet injection
• Droplet diameter pdf is extracted from the VOF simulation: f(D)
• f(D) is scaled by the droplet mass:
• g(D) is integrated andnormalized:
• h(D) is inverted and a whitenoise is applied:
Lund university / Division of Fluid Mechanics / 16.2.2011
VOF–LPT coupling - droplet injection
• Injected droplet distribution converges to f(D).
• Same procedure for axialand radial velocity.
Lund university / Division of Fluid Mechanics / 16.2.2011
Results
• Example distribution at the coupling layer :