Spray Modelling

The model is based on the Eulerian-Lagrangian approach, by which air/vapour mixture is modelled as  continuous phase and the liquid droplets as the dispersed one. Many of the fundamental physical processes assumed to take place during the spray development are incorporated in the model. These include link with the internal nozzle flow conditions, fuel atomization, liquid droplet aerodynamic break-up, turbulent dispersion, vaporization, droplet-to-droplet interaction and wall impingement. A novel approach accounting for droplet motion in Eulerian grids with cell size comparable to that of the droplets is available.

The liquid initial properties are determined by solving for the flow conditions inside and at the exit of the injector nozzle from which the necessary transient flow rate is obtained. Fuel atomisation strongly depends on the design of the injector.

Multi-component evaporation is available while effects such as internal droplet circulation, temperature variation within the droplet, diffusion between the different compounds and gas solubility are considered. High pressure and superheating effects at the critical point as well as droplet deformation are critical for injection into high pressure/temperature environment.

Droplet aerodynamic break-up plays an important role on the predictions of the droplet size population. The models available combine correlations from various literature findings in order to predict the mean diameter, the droplet deformation and the break-up time over a wide range of Weber numbers. The vibrational, bag-chaotic, stripping and catastrophic break-up regimes are distinguished. Then, droplet size is randomly sampled from various distribution function available.

Droplet drag coefficient is also important since it determines to a large extend the momentum exchange between the gas and the liquid phases. For spherical solid particles or liquid droplets the well-known Stokes law holds only for flows that are entirely dominated by viscous forces (creeping flows), that is, for low Reynolds numbers. For higher Reynolds numbers, various experimental correlation factors for Stokes’ drag law are available. Effects such as movement in an evaporating environment, presence of other droplets and internal flow circulation are included.

Another important aspect taken into account in the model is related to the numerical treatment of the source terms expressing the mass, momentum and energy exchange between the liquid and the gas phases and the interpolation of the continuous phase variables at the parcel location. This is based on the assumption that the region of influence between the two phases should be independent of the cell size and it is defined according to some physical criteria. The cells found within this region of interest are identified while a combination of distance, cell volume and internal energy-based weighting factor is used for the distribution of the source terms to those cells. The void fraction is integrated during the sub-cycles of the droplet parcels according to the residence time of a parcel within a computational cell. Additionally, the excess volume that may result computationally if a cell is fully filled by liquid droplets is again distributed to the surrounding cell.

Examples and validation cases of the spray model can be found in the following links.

    Spray Sample Cases

    Spray Validation Cases

Top of page

Send mail to info@fluid-research.com with questions or comments about this web site.
Copyright © 2005 Fluid Research