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

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

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

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

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), 131-170)

Mathematical model

Characteristic scales Characteristic parameters for the droplet (d) and the ambient gas (g) Dd = 0.0049 m, rd = 1000 kg/m3, md = 0.001 kg/ms, sgd = 0.072 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

Droplet Break-up in the vicinity of a second droplet

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), 1199-1212, F. Bierbrauer, T.N. Phillips, Int. J. Numer. Fluids, 56 (2008), 1155-1160)

Godunov Projection Method: Algorithm 1

Godunov Projection Method: Algorithm 2

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

Droplet test configurations Single configuration Shielded configuration Diagonal configuration

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

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

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

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

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

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