1. Secondary Atomisation in Disturbed Flow Fields
Simulation of droplet flow in dense sprays
Frank Bierbrauer and Tim Phillips
Cardiff University, UK

2. Initial stages of spray Break-up
Spray break-up: Liquid sheet → ligaments → droplets
Dispersed Phase: individual droplets of varying size and shape

3. Droplet break-up within the dispersed phase
Aerodynamic break-up: relative velocity enough to fragment the droplet through Rayleigh-Taylor and Kelvin-Helmholtz instabilities
Collision induced break-up: droplets may coalesce/merge and/or cause further disruption of the droplets

4. Single Droplet Break-Up regimes
Vibrational: WeG ≤ 12
Bag: 12 < WeG ≤ 50
Bag/stamen: 50 < WeG ≤ 100
Sheet stripping: 100 < WeG ≤ 350
Catastrophic: WeG > 350
With the gas Weber number:
Bag break-up

5. Break-up in dense sprays
In the case of dense sprays neighbouring droplets may influence each other through
Collision, coalescence
The gas phase can gain significant momentum from the droplets causing a disturbance within the gas which can effect other nearby droplets
This gives rise to gas-phase turbulence and turbulent eddies which can collide with other droplets and cause break-up
(T.G. Theofanus, G.J. Li, T.N. Linh, C.-H. Chang, J.Fluid Mech.,
593 (2007), )

6. Mathematical model

7. Characteristic scales
Characteristic parameters for the droplet (d) and the ambient gas (g)
Dd = m, rd = 1000 kg/m3, md = kg/ms, sgd = N/m, rg = 1 kg/m3, mg = 1×10-5 kg/ms
Low speed inflow: Ui = 10 m/s, WeG = 7
High speed inflow: Ui = 30 m/s, WeG = 62

8. Droplet Break-up in the vicinity of a second droplet

9. Multiphase flow: One-Field model
Numerical model
Multiphase flow: One-Field model
Solution Type: Eulerian-Lagrangian, mesh-particle method
Incompressibility: Godunov projection method
Interface Tracking
Algorithm: Marker-Particle Method
(F. Bierbrauer, S.-P. Zhu, Comput. Fluids, 36 (2007), ,
F. Bierbrauer, T.N. Phillips, Int. J. Numer. Fluids, 56 (2008), )

10. Godunov Projection Method: Algorithm 1

11. Godunov Projection Method: Algorithm 2

12. Marker-Particle Tracking
Initial particle configuration (e.g. 4 particles per cell)
Allocation of fluid colour C within a computational cell containing two fluid phases: 1 and 2. Two sets of marker particles are required, one for each fluid involved
Use Lagrangian tracking of particles by solving dxp/dt = up where up is a particle velocity interpolated from nearby grid velocities
Interpolate particle colour data back to grid
Particles permanently maintain fluid identity throughout the simulation

13. Droplet test configurations
Single configuration
Shielded configuration
Diagonal configuration

14. WeG = 7
Series B
Lx/Dd = 2
Series A

15. WeG = 7 Series C Lx/Dd = 2, Ly/Dd = 1 Series C Series A

16. WeG = 62
Series B
Lx/Dd = 2
Series B
Lx/Dd = 2
Series A

17. WeG = 62 Series C Lx/Dd = 2, Ly/Dd = 1 Series C Series A

18. Conclusions
Significant difference between the results of Series A and B-C
Series A
Break-up proceeds through a downstream filament which also breaks up followed by two internal vortices creating a concavity inside the droplet on the downstream side
Series B
Downstream droplet is sheltered by the upstream droplet
The downstream droplet is severely deformed by the filament ejected from the upstream droplet
Series C
filament generated by the upstream droplet is oscillatory interfering with the break-up of the downstream droplet
Stronger downstream filaments generated by the
We = 62 case

19. Future Work
The current work is only a qualitative study of the effect of neighbouring droplets on break-up behaviour. This involves
Disturbed flow fields: flow past single or multiple droplets disturb the initial flow field
Direct Influence: the break-up of one droplet directly effects another neighbouring droplet
Future work will involve a detailed quantitative study taking into account, for example:
The initiation time of break-up and how this changes from one droplet to two neighbouring droplets
How the stress generated by a neighbouring droplet changes the stability at the interface of the neighbour
How these characteristics depend on orientation, distance and droplet size
Further improvements are required for the implementation of proper outflow boundary conditions