This paper presents a variety of modeling and simulation methods for complex multiphase flow at microscopic, mesoscopic and macroscopic scales. Each method is discussed in terms of its scale-resolving capability and its relationship with other approaches. Examples of application are provided using a liquid-gas system, in which complex multiscale interactions exist among flow, turbulence, combustion and droplet dynamics. Large eddy simulation (LES) is employed to study the effects of a very large number of droplets on turbulent combustion in two configurations in a fixed laboratory frame. Direct numerical simulation (DNS) in a moving frame is then deployed to reveal detailed dynamic interactions between droplets and reaction zones. In both the LES and the DNS, evaporating droplets are modeled in a Lagrangian macroscopic approach, and have twoway couplings with the carrier gas phase. Finally, droplet collisions are studied using a multiple-relaxation-time lattice Boltzmann method (LBM). The LBM treats multiphase flow with real-fluid equations of state, which are stable and can cope with high density ratios. Examples of successful simulations of droplet coalescence and off-center separation are given. The paper ends with a summary of results and a discussion on hybrid multiscale approaches. Boltzmann method. the complexity of the subject. In this paper, we focus on the interaction of flow, turbulence, combustion and droplets, each of which introduces a separate set of spatial and temporal scales as follows. Note that to facilitate discussions, all the dimensional quantities and variables in Secs. 1-4 are indicated by the superscript *. Those without this superscript are normalized quantities. Section 5 has a set of self-contained notations.Flow. The full spectrum of scales in flow ranges from nanometers (e.g., in nanofluids) to kilometers (e.g., clouds). The various flow regimes are classified according to the Knudsen number, Kn, which is the ratio of the mean free path of molecules to a characteristic flow length (λ * /L * ). As Kn goes from zero to infinity, the flow exhibits four regimes: continuum (Kn < 0.01), slip flow (0.01 < Kn < 0.1), transitional flow (0.1 < Kn < 10) and free molecular flow (Kn > 10).Turbulence. Turbulence is characterized by the presence of a very wide range of time and length scales associated with various turbulent eddies, which form a turbulence cascade. The length scale associated with the large eddies is the integral length scale, l * t , which is of the order of the size of the flow configuration. The smallest length scale in turbulence, the Kolmogorov length scale, l * k , is imposed by the molecular viscosity. The range of the length scale in turbulence is indicated by l * t /l * k ∼(Re t ) 3/4 , where Re t is the turbulent Reynolds number defined using the integral length scale. Considering that the Reynolds number of a practical system (e.g., an aircraft engine exhaust) can reach millions, the range of scales in turbulence can be very large. Similarly, the range of turbulent time...
