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Derivations of Two-Phase Flow Modeling Equations
Published in Clement Kleinstreuer, Theory and Applications, 2017
A second category of separated flow model application is Lagrangian particle tracking. Examples include multiple noninteracting particles, i.e., solid spheres, droplets and bubbles, clouds of particles, and dense particle suspension flows. As previously stated, the third and most difficult member of the separated flow group is the two-fluid model. Next, basic sample applications may illustrate salient features of separated flow models.
Influence of the quiescent core on tracer spheroidal particle dynamics in turbulent channel flow
Published in Journal of Turbulence, 2019
Yucheng Jie, Chunxiao Xu, James R. Dawson, Helge I. Andersson, Lihao Zhao
Ten sets of particles are chosen with aspect ratio λ ranging from 0.01 to 100. Initially 300,000 particles of each type are randomly released in the turbulent channel flow at and tracked individually along Lagrangian trajectories. The statistics shown in the following section are obtained over a time-window from to 1235. It should be noted that the trajectories of particles were obtained through a built-in Lagrangian particle tracking method [43]. These particles were tracked using sixth-order Lagrange interpolation in space and the second-order predictor-corrector method with cubic Hermite interpolation in time [44,45]. The velocity gradients along each trajectory are interpolated every 1/5 time step, namely the DNS time step , and then recorded so as to calculate the orientation and rotation every DNS time step.
Assessment of Mixture and Eulerian Multiphase Models in Predicting the Thermo-Fluidic Transport Characteristics for Fly Ash-Water Slurry Flow in Straight Horizontal Pipeline
Published in Heat Transfer Engineering, 2019
Bibhuti Bhusan Nayak, Dipankar Chatterjee
Although it is observed from the above stated works that the ASM model provides good (<5% deviation) prediction for the pressure gradients at low to moderate values of particle concentration and inflow velocity provided the secondary phase is considered as granular particle, it fails to predict the pressure drops, volume fraction distributions and heat transfer accurately at higher concentrations and mean velocities. In general, tracking the trajectories of each individual particle (via Lagrangian particle tracking) is the most physically accurate approach and requires minimal modeling. However, this approach becomes expensive at high volume fractions. On the other hand, the Eulerian approach provides the best compromise between the cost and the accuracy; hence one can therefore choose the granular-Eulerian model, in most cases.
Numerical simulation of parallel-plate particle separator for estimation of charge distribution of PM2.5
Published in Aerosol Science and Technology, 2019
Takuto Yonemichi, Koji Fukagata, Kentaro Fujioka, Tomoaki Okuda
Particle trajectories are computed by Lagrangian particle tracking. The equations of motion of a charged particle including Brownian diffusion and the electrostatic force (Ounis, Ahmadi, and McLaughlin 1991) are given by where and denote the position and velocity of the particle, τp is the particle relaxation time, is a pair of Gaussian random numbers with zero mean and unit variance, is the Schmidt number, is the computational time step, q is the charge of the particle, and m is the mass of the particle. Again, these equations of motion are non-dimensionalized by , , and .