This review concerns recent progress in primary atomization modeling. The numerical approaches based on direct simulation are described first. Although direct numerical simulation (DNS) offers the potential to study the physical processes during primary atomization in detail, thereby supplementing experimental diagnostics, it also introduces severe numerical challenges. We outline these challenges and the numerical methods to address them, highlighting some recent efforts in performing detailed simulation of the primary atomization process. The second part is devoted to phenomenological models of primary atomization. Because earlier conventional models of breakup are well reported in the available literature, we highlight only two recent developments: (a) stochastic simulation of the liquid jet depletion in the framework of fragmentation under scaling symmetry and (b) primary atomization in terms of Reynolds-averaged Navier-Stokes (RANS) mixing with a strong variation of density.

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This paper considers the breakup of liquid drops at the large Weber number within the framework of Kolmogorov’s scenario of breakup. The population balances equation for droplet radius distribution is written to be an invariant under the group of scaling transformations. It is shown that due to this symmetry, the long-time limit solution of this equation is a power function. When the standard deviation of droplet radius strongly increases and, consequently, the characteristic length scale disappears, the power asymptotic solution can be viewed as a further evolution of Kolmogorov’s log-normal distribution. This new universality appears to be consistent with the experimental observation of fractal properties of droplets produced by air-blast breakup. The scaling properties of Kolmogorov’s model at later times are also demonstrated in the case where the breakup frequency is a power function of instantaneous radius. The model completes the Liouville equation for distribution function of liquid particles in the phase space of droplet position, velocity, and radius. The numerical scheme is proposed for stochastic modeling of droplets production. Lagrangian simulation of the spray under air-blast atomization is performed using KIVA II code, which is a frequently used code for computation of turbulent flows with sprays. The qualitative agreement of simulation with measurements is demonstrated.

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Consistently with observations from recent experiments and DNS, we focus on the effects of strong velocity increments at small spatial scales for the simulation of the drag force on particles in high Reynolds number flows. In this paper, we decompose the instantaneous particle acceleration in its systematic and residual parts. The first part is given by the steady-drag force obtained from the large-scale energy-containing motions, explicitly resolved by the simulation, while the second denotes the random contribution due to small unresolved turbulent scales. This is in contrast with standard drag models in which the turbulent microstructures advected by the large-scale eddies are deemed to be filtered by the particle inertia. In our paper, the residual term is introduced as the particle acceleration conditionally averaged on the instantaneous dissipation rate along the particle path. The latter is modeled from a log-normal stochastic process with locally defined parameters obtained from the resolved field. The residual term is supplemented by an orientation model which is given by a random walk on the unit sphere. We propose specific models for particles with diameter smaller and larger size than the Kolmogorov scale. In the case of the small particles, the model is assessed by comparison with direct numerical simulation (DNS). Results showed that by introducing this modeling, the particle acceleration statistics from DNS is predicted fairly well, in contrast with the standard LES approach. For the particles bigger than the Kolmogorov scale, we propose a fluctuating particle response time, based on an eddy viscosity estimated at the particle scale. This model gives stretched tails of the particle acceleration distribution and dependence of its variance consistent with experiments.

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Direct numerical simulations (DNS) are used here to study inertial particle acceleration statistics in the near-wall region of a turbulent channel flow. The study is motivated by observations in homogeneous isotropic turbulence (HIT) suggesting that when particle inertia increases, particle acceleration variance decreases due to both particle preferential accumulation and the filtering effect of inertia. In accordance with these studies, the present DNS shows that for increasing inertia, solid particle acceleration probability density functions (PDFs), scaled by the acceleration root-meansquare (RMS), depart from that of the fluid. The tails of these PDFs become narrower. However, in turbulent channel flow, as the Stokes number increases up to 5, the streamwise acceleration RMS in the near-wall region increases, while further increase of the Stokes number is characterized by the streamwise acceleration RMS decrease. In parallel, contrary to calculations in homogeneous isotropic turbulence, the conditional acceleration statistics of the fluid seen by the solid particle show that while the vertical and transverse acceleration RMS components remain close to the unconditional fluid acceleration, the longitudinal RMS component is remarkably higher in the near wall region. This feature is more pronounced as the Stokes number is increased. Additionally, the conditional acceleration PDFs overlap almost perfectly with the unconditional fluid PDFs, normalized by the acceleration RMS. The enhanced longitudinal acceleration variance of the fluid seen by the particles may be due to the spanwise alternation of high-and-low speed streaks. Depending on inertia, particles may respond to those fluid solicitations (experiencing an increase of the longitudinal acceleration RMS) or ignore the wall turbulent structures (presenting in that case a more homogeneous concentration).