Transport of Heavy Particles in a Three-Dimensional Mixing Layer

1998 ◽  
Vol 120 (3) ◽  
pp. 613-620 ◽  
Author(s):  
Qunzhen Wang ◽  
Kyle D. Squires
Keyword(s):  
Stokes Equations ◽  
Fluid Velocity ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Stokes Number ◽  
Experimental Measurements ◽  
Initial Field ◽  
Heavy Particles ◽  
Velocity Statistics

Particle transport in a three-dimensional, temporally evolving mixing layer has been calculated using large eddy simulation of the incompressible Navier-Stokes equations. The initial fluid velocity field was obtained from a separate simulation of fully developed turbulent channel flow. The momentum thickness Reynolds number ranged from 710 in the initial field to 4460 at the end of the calculation. Following a short development period, the layer evolves nearly self-similarly. Fluid velocity statistics are in good agreement with both the direct numerical simulation results of Rogers and Moser (1994) and experimental measurements of Bell and Mehta (1990). Particles were treated in a Lagrangian manner by solving the equation of motion for an ensemble of 20,000 particles. The particles have the same material properties as in the experiments of Hishida et al. (1992), i.e., glass beads with diameters of 42, 72, and 135 μm. Particle motion is governed by drag and gravity, particle-particle collisions are neglected, and the coupling is from fluid to particles only. In general, the mean and fluctuating particle velocities are in reasonable agreement with the experimental measurements of Hishida et al. (1992). Consistent with previous studies, the Stokes number (St) corresponding to maximum dispersion increases as the flow evolves when defined using a fixed fluid timescale. Definition of the Stokes number using the time-dependent vorticity thickness, however, shows a maximum in dispersion throughout the simulation for St ≈ 1.

scholarly journals Concentration and velocity statistics of inertial particles in upward and downward pipe flow

2017 ◽  
Vol 822 ◽  
pp. 640-663 ◽  
Author(s):  
J. L. G. Oliveira ◽  
C. W. M. van der Geld ◽  
J. G. M. Kuerten
Keyword(s):  
Liquid Velocity ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Stokes Number ◽  
Terminal Velocity ◽  
Point Particle ◽  
Inertial Particles ◽  
Carrier Fluid ◽  
Velocity Statistics ◽  
The Difference

Three-dimensional particle tracking velocimetry is applied to particle-laden turbulent pipe flows at a Reynolds number of 10 300, based on the bulk velocity and the pipe diameter, for developed fluid flow and not fully developed flow of inertial particles, which favours assessment of the radial migration of the inertial particles. Inertial particles with Stokes number ranging from 0.35 to 1.11, based on the particle relaxation time and the radial-dependent Kolmogorov time scale, and a ratio of the root-mean-square fluid velocity to the terminal velocity of order 1 have been used. Core peaking of the concentration of inertial particles in up-flow and wall peaking in down-flow have been found. The difference in mean particle and Eulerian mean liquid velocity is found to decrease to approximately zero near the wall in both flow directions. Although the carrier fluid has all of the characteristics of the corresponding turbulent single-phase flow, the Reynolds stress of the inertial particles is different near the wall in up-flow. These findings are explained from the preferential location of the inertial particles with the aid of direct numerical simulations with the point-particle approach.

scholarly journals A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 756
Author(s):  
Federico Lluesma-Rodríguez ◽  
Francisco Álcantara-Ávila ◽  
María Jezabel Pérez-Quiles ◽  
Sergio Hoyas
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Direct Numerical Simulations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Thermal Flow ◽  
Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

Modeling of the Vortex-Structure in a Particle-Laden Mixing-Layer

2005 ◽  
Author(s):  
Jens A. Melheim ◽  
Stefan Horender ◽  
Martin Sommerfeld
Keyword(s):  
Vortex Structure ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Mixing Layer ◽  
Equation Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Calculated Concentration ◽  
Langevin Model ◽  
Particle Velocities

Numerical calculations of a particle-laden turbulent horizontal mixing-layer based on the Eulerian-Lagrangian approach are presented. Emphasis is given to the determination of the stochastic fluctuating fluid velocity seen by the particles in anisotropic turbulence. The stochastic process for the fluctuating velocity is a “Particle Langevin equation Model”, based on the Simplified Langevin Model. The Reynolds averaged Navier-Stokes equations are closed by the standard k-epsilon turbulence model. The calculated concentration profile and the mean, the root-mean-square (rms) and the cross-correlation terms of the particle velocities are compared with particle image velocimetry (PIV) measurements. The numerical results agree reasonably well with the PIV data for all of the mentioned quantities. The importance of the modeled vortex structure “seen” by the particles is discussed.

Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds

2002 ◽  
Author(s):  
Azita Soleymani ◽  
Eveliina Takasuo ◽  
Piroz Zamankhan ◽  
William Polashenski
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Results ◽  
Transition To Turbulence ◽  
Wide Range

Results are presented from a numerical study examining the flow of a viscous, incompressible fluid through random packing of nonoverlapping spheres at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), spanning a wide range of flow conditions for porous media. By using a laminar model including inertial terms and assuming rough walls, numerical solutions of the Navier-Stokes equations in three-dimensional porous packed beds resulted in dimensionless pressure drops in excellent agreement with those reported in a previous study (Fand et al., 1987). This observation suggests that no transition to turbulence could occur in the range of Reynolds number studied. For flows in the Forchheimer regime, numerical results are presented of the lateral dispersivity of solute continuously injected into a three-dimensional bounded granular bed at moderate Peclet numbers. Lateral fluid dispersion coefficients are calculated by comparing the concentration profiles obtained from numerical and analytical methods. Comparing the present numerical results with data available in the literature, no evidence has been found to support the speculations by others for a transition from laminar to turbulent regimes in porous media at a critical Reynolds number.

scholarly journals Finite Element Analysis of Turbulent Flows Using LES and Dynamic Subgrid-Scale Models in Complex Geometries

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Wang Wenquan ◽  
Zhang Lixiang ◽  
Yan Yan ◽  
Guo Yakun
Keyword(s):  
Finite Element ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Francis Turbine ◽  
Complex Geometries ◽  
Subgrid Scale ◽  
Element Analysis

An innovative computational model is presented for the large eddy simulation (LES) of multidimensional unsteady turbulent flow problems in complex geometries. The main objectives of this research are to know more about the structure of turbulent flows, to identify their three-dimensional characteristic, and to study physical effects due to complex fluid flow. The filtered Navier-Stokes equations are used to simulate large scales; however, they are supplemented by dynamic subgrid-scale (DSGS) models to simulate the energy transfer from large scales toward subgrid-scales, where this energy will be dissipated by molecular viscosity. Based on the Taylor-Galerkin schemes for the convection-diffusion problems, this model is implemented in a three-dimensional finite element code using a three-step finite element method (FEM). Turbulent channel flow and flow over a backward-facing step are considered as a benchmark for validating the methodology by comparing with the direct numerical simulation (DNS) results or experimental data. Also, qualitative and quantitative aspects of three-dimensional complex turbulent flow in a strong 3D blade passage of a Francis turbine are analyzed.

Secondary instability of a temporally growing mixing layer

1987 ◽  
Vol 184 ◽  
pp. 207-243 ◽  
Author(s):  
Ralph W. Metcalfe ◽  
Steven A. Orszag ◽  
Marc E. Brachet ◽  
Suresh Menon ◽  
James J. Riley
Keyword(s):  
Growth Rates ◽  
Stokes Equations ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Mixing Layers ◽  
Navier Stokes ◽  
Small Scale ◽  
Two Dimensional ◽  
Mean Flow ◽  
Direct Numerical Integration

The three-dimensional stability of two-dimensional vortical states of planar mixing layers is studied by direct numerical integration of the Navier-Stokes equations. Small-scale instabilities are shown to exist for spanwise scales at which classical linear modes are stable. These modes grow on convective timescales, extract their energy from the mean flow and exist at moderately low Reynolds numbers. Their growth rates are comparable with the most rapidly growing inviscid instability and with the growth rates of two-dimensional subharmonic (pairing) modes. At high amplitudes, they can evolve into pairs of counter-rotating, streamwise vortices, connecting the primary spanwise vortices, which are very similar to the structures observed in laboratory experiments. The three-dimensional modes do not appear to saturate in quasi-steady states as do the purely two-dimensional fundamental and subharmonic modes in the absence of pairing. The subsequent evolution of the flow depends on the relative amplitudes of the pairing modes. Persistent pairings can inhibit three-dimensional instability and, hence, keep the flow predominantly two-dimensional. Conversely, suppression of the pairing process can drive the three-dimensional modes to more chaotic, turbulent-like states. An analysis of high-resolution simulations of fully turbulent mixing layers confirms the existence of rib-like structures and that their coherence depends strongly on the presence of the two-dimensional pairing modes.

Simulation of Fluid Flow Through a Granular Bed

2006 ◽  
Author(s):  
Arezou Jafari ◽  
S. Mohammad Mousavi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Packed Bed ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Duct Geometry ◽  
Flow Through

Numerical study of flow through random packing of non-overlapping spheres in a cylindrical geometry is investigated. Dimensionless pressure drop has been studied for a fluid through the porous media at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), and numerical solution of Navier-Stokes equations in three dimensional porous packed bed illustrated in excellent agreement with those reported by Macdonald [1979] in the range of Reynolds number studied. The results compare to the previous work (Soleymani et al., 2002) show more accurate conclusion because the problem of channeling in a duct geometry. By injection of solute into the system, the dispersivity over a wide range of flow rate has been investigated. It is shown that the lateral fluid dispersion coefficients can be calculated by comparing the concentration profiles of solute obtained by numerical simulations and those derived analytically by solving the macroscopic dispersion equation for the present geometry.

Direct numerical simulation of a three-dimensional spatially developing bubble-laden mixing layer with two-way coupling

2001 ◽  
Vol 429 ◽  
pp. 23-61 ◽  
Author(s):  
O. A. DRUZHININ ◽  
S. E. ELGHOBASHI
Keyword(s):  
Strain Rate ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Velocity Fluctuations ◽  
Vortex Pairing ◽  
Preferential Accumulation ◽  
Principal Axes ◽  
Bubble Phase

Direct numerical simulations (DNS) of a three-dimensional spatially-developing mixing layer (ML) laden with spherical gaseous bubbles are performed, with both one-way and two-way coupling between the two phases. Forcing is used to initialize the spanwise vortex roll-up and to create a pair of counter-rotating streamwise vortices, rendering the carrier flow three-dimensional. The characteristics of the resulting ML flow field are similar to those reported in numerous experimental and numerical studies. The volume fraction (or concentration) of the bubble phase is considered small enough to neglect bubble–bubble interactions. The no-slip fluid velocity condition is assumed at the bubble surface, and the bubble Reynolds number is less than 1 throughout the simulation time. The two-fluid formulation (TF) is used to compute the bubble-phase velocity and concentration and the two-way coupling source term in the fluid momentum equation. A Lagrangian–Eulerian mapping (LEM) solver is employed to solve the equations for the bubble velocity and concentration. LEM is capable of resolving the gradients of concentration created by the bubble preferential accumulation without numerical instabilities. Two different inflow profiles (Cref(z)) of bubble-phase concentration are considered: a uniform profile and a tanh-profile. In the latter case, the high-speed (upper) stream is devoid of bubbles, and the low-speed (lower) stream is uniformly laden with bubbles at the inflow plane.The DNS results show that in addition to the well-known preferential accumulation of bubbles in the vortex centres, sheets of increased bubble concentration (C-sheets) develop in the rollers created by the vortex pairing in the ML core, with two local maxima of vorticity and an enhanced strain-rate field. The development of C-sheets is governed by the stretching and contraction along the principal axes of the local strain rate.In the case of uniform Cref, the two-way coupling reduces the average ML vorticity thickness and the entrainment of the irrotational fluid into the ML core, as compared to the bubble-free case, upstream of the location of the first vortex pairing. However, both ML vorticity thickness is increased and entrainment is enhanced by the bubbles farther downstream, after the pairing. The fluid velocity fluctuations are reduced by the bubbles throughout the ML, as compared to the one-way coupling case.In the case of the tanh-profile of Cref, the velocity fluctuations and the ML vorticity thickness are increased by the bubbles upstream the location of the first vortex pairing owing to the ‘unstable’ inflow bubble stratification (Druzhinin & Elghobashi 1998). On the other hand, the velocity fluctuations are reduced by the bubbles, and the ML vorticity thickness oscillates with the streamwise distance farther downstream.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 1. Velocity and acceleration distributions

2010 ◽  
Vol 646 ◽  
pp. 59-90 ◽  
Author(s):  
PARTHA S. GOSWAMI ◽  
V. KUMARAN
Keyword(s):  
Particle Velocity ◽  
Stokes Equations ◽  
Hard Spheres ◽  
Flow Direction ◽  
Fluid Velocity ◽  
Gaussian White Noise ◽  
Stokes Number ◽  
Navier Stokes ◽  
Velocity Fluctuations ◽  
Non Gaussian

The effect of fluid velocity fluctuations on the dynamics of the particles in a turbulent gas–solid suspension is analysed in the low-Reynolds-number and high Stokes number limits, where the particle relaxation time is long compared with the correlation time for the fluid velocity fluctuations, and the drag force on the particles due to the fluid can be expressed by the modified Stokes law. The direct numerical simulation procedure is used for solving the Navier–Stokes equations for the fluid, the particles are modelled as hard spheres which undergo elastic collisions and a one-way coupling algorithm is used where the force exerted by the fluid on the particles is incorporated, but not the reverse force exerted by the particles on the fluid. The particle mean and root-mean-square (RMS) fluctuating velocities, as well as the probability distribution function for the particle velocity fluctuations and the distribution of acceleration of the particles in the central region of the Couette (where the velocity profile is linear and the RMS velocities are nearly constant), are examined. It is found that the distribution of particle velocities is very different from a Gaussian, especially in the spanwise and wall-normal directions. However, the distribution of the acceleration fluctuation on the particles is found to be close to a Gaussian, though the distribution is highly anisotropic and there is a correlation between the fluctuations in the flow and gradient directions. The non-Gaussian nature of the particle velocity fluctuations is found to be due to inter-particle collisions induced by the large particle velocity fluctuations in the flow direction. It is also found that the acceleration distribution on the particles is in very good agreement with the distribution that is calculated from the velocity fluctuations in the fluid, using the Stokes drag law, indicating that there is very little correlation between the fluid velocity fluctuations and the particle velocity fluctuations in the presence of one-way coupling. All of these results indicate that the effect of the turbulent fluid velocity fluctuations can be accurately represented by an anisotropic Gaussian white noise.

scholarly journals The Modelling of Flow in the Volute and Vanes of a High Pressure Radial Inflow Turbine

1993 ◽  
Author(s):  
M. Lobo ◽  
R. L. Elder
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
General Description ◽  
Navier Stokes Equations ◽  
Flow Modelling ◽  
Comparison With Experiment ◽  
Flow Features ◽  
Radial Inflow Turbine

The flow in a vaned volute of a radial inflow turbine is analysed using PHOENICS, a very general three-dimensional viscous CFD code based on finite-volume pressure-correction techniques for solving the Navier-Stokes equations. The study involves two physically complementary but mathematically very different problems — flow modelling in the vaneless section of the volute and flow modelling in the vanes. Each of these problems is considered in turn — and each presents characteristic hurdles. Particular attention is paid to grid-generation and the process is carried out alongside the flow computation, the grids being modified in such a way so as to facilitate convergence and accuracy. Numerical results are presented in the form of vector plots for purposes of general description and tables for comparison with experiment. Agreement with experiment is good. However experimental results, for comparison are available only in the vanes. In the vaneless section of the volute, the converged solution depicts some interesting secondary flow features — in regions inaccesible to the current experimental measurements.

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