A Computational Study of Multiphase Flows

Deshpande, S. S. A Computational Study of Multiphase Flows. University of Wisconsin-Madison, 2014.

We computationally study two multiphase problems namely (i) atomization leading to a spray of droplets in air, and (ii) air bubble entrainment in a water pool by a plunging water jet. The aim is to identify and investigate in detail the key underlying physical processes. Simulations are based on a volume of fluid approach, which we have thoroughly tested through several validation and verification exercises. Key process in liquid sheet atomization are identified as (i) transient penetration, (ii) quasi-steady breakup, (iii) interfacial instabilities, and (iv) droplet creation. Sheet penetration speed US in the transient period is shown to be smaller than injection speed, and is predicted using potential flow theory. The prediction U_S=U inj/(1+r1/2), where r=?g/?l compares favorably with simulations. Breakup length in quasi-steady period is found to scale with r-1/2. Interfacial waves are explained using Orr-Sommerfeld anlaysis. Preferential amplification of certain wavemodes from an arbitrary spectrum causes discrete waves on the interface, whose wavelength is predicted well with linearized analyses. Latter stages of evolution show generation of slender ligaments, which breakup under capillary effects. This process is studied using Rayleigh-Plateau mechanism. Ohnesorge number, Oh=0.1, is shown to roughly separate viscous and inviscid ligament breakup regimes and this influences droplet sizes and breakup times. Breakup time predictions based on linear theory are in good agreement with simulations.

Next, air bubble entrainment is studied by simulating water jets plunging at different inclinations into the pool. Shallow inclinations (10-12 deg) lead to nearly periodic entrainment of large air cavities and large subsurface air content ? a feature missing in steep configurations. Large cavities are shown to be due to a stagnation flow and their periodicity is due to gravity waves set up in the pool. A scaling study reveals a linear relation between entrainment period and Froude number, which is verified computationally. These features are absent at angles exceeding ?25 deg and entrainment occurs chaotically in the form of small bubbles. Reconciling, the periodicity at shallow angles is a special case of entrainment by highly disturbed jets ? the disturbances are not arbitrary, but instead periodic due to action of gravity waves.