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

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

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

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

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

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

Mathematical model


Characteristic scales

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

Droplet Break-up in the vicinity of a second droplet


Numerical 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 1


Godunov projection method algorithm 2

Godunov Projection Method: Algorithm 2


Marker particle tracking

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

Droplet test configurations

  • Single configuration

  • Shielded configuration

  • Diagonal configuration


We g 7

WeG = 7

Series B

Lx/Dd = 2

Series A


We g 71

WeG = 7

Series C

Lx/Dd = 2, Ly/Dd = 1

Series C

Lx/Dd = 2, Ly/Dd = 1

Series A


We g 62

WeG = 62

Series B

Lx/Dd = 2

Series B

Lx/Dd = 2

Series A


We g 621

WeG = 62

Series C

Lx/Dd = 2, Ly/Dd = 1

Series C

Lx/Dd = 2, Ly/Dd = 1

Series A


Conclusions

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

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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