Secondary atomisation in disturbed flow fields
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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

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Secondary Atomisation in Disturbed Flow Fields

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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 = 1×10-5kg/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


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

Lx/Dd = 2, Ly/Dd = 1

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

Lx/Dd = 2, Ly/Dd = 1

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


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