Fluid particle model, discrete-particles

To analyze the individual heat transfer kinetics of droplet clusters within the spray of twin-fluid atomizers, the local correlations between the droplet concentration and the heat and flow conditions are evaluated. Numerical simulations of the spray flow analyzed in this paper have been carried out with Large-Eddy-Simulation (LES) models with Lagrangian particle tracking (discrete particle method) for the droplet motion. A synthetic perturbation generator [30] for the inflow conditions for the gas flow and simple perturbations are added to the dispersed phase to induce realistic vortex patterns at the nozzle and in the consequent spray. 

GASFLOW models geometrically complex containments, buildings, and ventilation systems with multiple compartments and internal structures. It calculates gas and aerosol behavior of low-speed buoyancy driven flows, diffusion-dominated flows, and turbulent flows dunng deflagrations. It models condensation in the bulk fluid regions heat transfer to wall and internal stmetures by convection, radiation, and condensation chemical kinetics of combustion of hydrogen or hydrocarbon.s fluid turbulence and the transport, deposition, and entrainment of discrete particles. 

V, ip, x, and t) in the PDF transport equation makes it intractable to solve using standard discretization methods. Instead, Lagrangian PDF methods (Pope 1994a) can be used to express the problem in terms of stochastic differential equations for so-called notional particles. In Chapter 7, we will discuss grid-based Eulerian PDF codes which also use notional particles. However, in the Eulerian context, a notional particle serves only as a discrete representation of the Eulerian PDF and not as a model for a Lagrangian fluid particle. The Lagrangian Monte-Carlo simulation methods discussed in Chapter 7 are based on Lagrangian PDF methods. 

Here we present the derivation of the transport coefficients due to diffusion of discrete particles in a homogeneous turbulent flow. Although the Hinze-Tchen model was developed in a more general form for general particle-fluid multiphase flows, we introduce this model only for the cases of gas-solid flows. Some assumptions for this model are the following ... 

Consider an example from nucleation and growth of thin films. At least three length scales can be identified, namely, (a) the fluid phase where the continuum approximation is often valid (that may not be the case in micro- and nanodevices), (b) the intermediate scale of the fluid/film interface where a discrete, particle model may be needed, and (c) the atomistic/QM scale of relevance to surface processes. Surface processes may include adsorption, desorption, surface reaction, and surface diffusion. Aside from the disparity of length scales, the time scales of various processes differ dramatically, ranging from picosecond chemistry to seconds or hours for slow growth processes (Raimondeau and Vlachos, 2002a, b). 

Fig. 7. Schematic illustrating the coupling of a fluid-phase mass transfer model with a discrete, particle model, such as KMC, through the boundary condition. The continuum model passes the external field and the KMC simulation computes spatial and temporal rates that are needed in the boundary condition of the continuum model.

Similar to the role that DNS and discrete particle models (see Section IV,B,3) might play in the development of improved turbulence models, which can be used in engineering applications, and closure laws for gas-solid continuum models. Brownian dynamics (BD) should be mentioned as a powerful tool to develop closure models for non-Newtonian fluids (Brady and Bossis, 1988). 

There are two main approaches for the numerical simulation of the gas-solid flow 1) Eulerian framework for the gas phase and Lagrangian framework for the dispersed phase (E-L) and 2) Eulerian framework for all phases (E-E). In the E-L approach, trajectories of dispersed phase particles are calculated by solving Newton s second law of motion for each dispersed particle, and the motion of the continuous phase (gas phase) is modeled using an Eulerian framework with the coupling of the particle-gas interaction force. This approach is also referred to as the distinct element method or discrete particle method when applied to a granular system. The fluid forces acting upon particles would include the drag force, lift force, virtual mass force, and Basset history force.Moreover, particle-wall and particle-particle collision models (such as hard sphere model, soft sphere model, or Monte Carlo techniques) are commonly employed for this approach. In the E-E approach, the particle cloud is treated as a continuum. Local mean... 

Keywords Atomization Chemical reactions Craiservation equations Constitutive equations Drop breakup Drop deformation Drop collisions Evaporation LES Newtonian fluids RANS Spray modeling Spray PDF Stochastic discrete particle method Source terms Turbulence... 

At a higher level, the flow field is modeled at a scale much larger than the size of the particles, and the fluid velocity and pressure are obtained by solving the volume-averaged Navier-Stokes equations. The particle particle interactions (particle wall as well) are formulated with the so-called discrete particle models (DPMs), which are based on the schemes that are traditionally used in molecular dynamics simulations, with the addition of dissipation of mechanical energy. 

J. M. Link, C. Zeilstra, N. G. Deen and J. A. M. Kuipers, Validation of a discrete particle model in a 2D spout-fluid bed using non-intrusive optical measuring techniques, Can. J. Chem. Eng., 2004, 82, 30. 

The lattice Boltzmann method is a mesoscopic simulation method for complex fluid systems. The fluid is modeled as fictitious particles, and they propagate and coUide over a discrete lattice domain at discrete time steps. Macroscopic continuum equations can be obtained from this propagation-colhsion dynamics through a mathematical analysis. The particulate nature and local d3mamics also provide advantages for complex boundaries, multiphase/multicomponent flows, and parallel computation. 

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