Lattice Boltzmann models for simulations of drop -drop collisions

Kannan Nandha Premnath, Purdue University


In this work, lattice Boltzmann (LB) models are developed to investigate drop-drop collisions. These collisions are important in sprays where the high number density of drops in the near-field of the spray leads to drop interactions which may lead to binary drop collisions and secondary break-up. Following an evaluation of existing LB models for single-phase and two-phase flows, two new LB models are developed to study head-on and off center collisions. An axisymmetric LB model is developed for multiphase flows to investigate problems which may be approximated as axisymmetric such as head-on binary drop collisions. To develop the axisymmetric model, source terms are added to the standard two-dimensional (2D) Cartesian LB model so that the resulting model represents the equations in axisymmetric cylindrical coordinates. To study fluids with lower viscosities and maintain numerical stability a multi-relaxation time (MRT) model is implemented in the axisymmetric model instead of the standard Bhatnagar-Gross-Krook (BGK) model which is widely employed in LB models. A three-dimensional (3D) MRT LB model is developed for multiphase flows to simulate fluids with lower viscosities. This model is employed to study off-center drop-drop collisions. Both models are evaluated for representative multiphase flow problems prior to studying collisions. Drop collisions are investigated for different Weber numbers ( We) and Ohnesorge numbers (Oh) and for different liquid to gas density and viscosity ratios. Different size ratios for the colliding drops are also considered. In the case of head-on collisions, at low We the drops coalesce. When coalescence with relatively small deformation occurs, it is observed that the coalesced drop entraps a stable microbubble. As the We is increased, the colliding drops separate instead of coalescing. At even higher We, satellite droplets are formed. A further increase in We appears to increase the size of the satellite droplets. The Oh has a modulating influence on the outcome and the transient characteristics of colliding drops. The higher the Oh, the smaller is the tendency for separation and the satellite droplets are smaller in size. An increase in the gas density appears to increase the We where separation occurs. Increase in gas density reduces the size of satellite droplets. Collisions of unequal size drops with a size ratio of 2 favor the formation of a larger stable microbubble when compared to that of equal size drops under the same conditions. It is found that there is considerable shape readjustment during unequal drop size collisions which tends to reduce the tendency for separation. In the case of off-center collisions, the 3D MRT LBE model simulates permanent coalescence and stretching separation at lower and higher impact parameters, respectively, which are consistent with experimental observations.




Abraham, Purdue University.

Subject Area

Mechanical engineering|Fluid dynamics|Gases

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