NUMERICAL SIMULATION OF PARTICLE INTERACTIONS WITH WALL TURBULENCE

This paper presents the results of a numerical investigation of the effects of near‐neutral density solid particles on turbulent liquid flow in a channel. Interactions of particles, in a size range about the dissipative length scale, with wall turbulence have been simulated at low volume fractions (average volume fraction less than 4×10−4). Fluid motion is calculated by directly solving the Navier‐Stokes equations by a pseudo‐spectral method and resolving all scales of motion. Particles are moved in a Lagrangian frame through the action of forces imposed by the fluid and gravity. Particle effects on fluid motion are fed back at each time step by calculating the velocity disturbance caused by the particles assuming the flow around them is locally Stokesian. Particle‐particle interactions are not considered. The slightly heavier‐than‐fluid particles of the size range considered are found to preferentially accumulate in the low‐speed streaks, as reported in several other investigations. It is also found that particles smaller than the dissipative length scale reduce turbulence intensities and Reynolds stress, whereas particles that are somewhat larger increase intensities and stress. By examining higher order turbulence statistics and doing a quadrant analysis of the Reynolds stress, it is found that the ejection‐sweep cycle is affected—primarily through suppression of sweeps by the smaller particles and enhancement of sweep activity by the larger particles. A preliminary assessment of the impact of these findings on scalar transfer is made, as enhancement of transfer rate is a motivation of the overall work on this subject. For the case investigated, comparison of the calculations with an existing experiment was possible, and shows good agreement.

[1]  M. Reeks On the dispersion of small particles suspended in an isotropic turbulent fluid , 1977, Journal of Fluid Mechanics.

[2]  S. Pope,et al.  An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence , 1988 .

[3]  Gad Hetsroni,et al.  Heat transfer to a liquid—solid mixture in a flume , 1994 .

[4]  Eckart Meiburg,et al.  TWO-WAY COUPLING IN SHEAR LAYERS WITH DILUTE BUBBLE CONCENTRATIONS , 1994 .

[5]  M. Rashidi,et al.  Turbulence structure in free‐surface channel flows , 1988 .

[6]  M. Rizk,et al.  The motion of a spherical particle suspended in a turbulent flow near a plane wall , 1985 .

[7]  John R. Fessler,et al.  Particle response and turbulence modification in fully developed channel flow , 1994, Journal of Fluid Mechanics.

[8]  D. Kaftori,et al.  Particle behavior in the turbulent boundary layer. I. Motion, deposition, and entrainment , 1995 .

[9]  David Migdal,et al.  A Source Flow Model for Continuum Gas-Particle Flow , 1967 .

[10]  D. Joseph,et al.  ENSEMBLE AVERAGED AND MIXTURE THEORY EQUATIONS FOR INCOMPRESSIBLE FLUID-PARTICLE SUSPENSIONS , 1990 .

[11]  F. Lockwood,et al.  Velocity measurements in a particle laden turbulent free jet , 1981 .

[12]  George Em Karniadakis,et al.  A direct numerical simulation of laminar and turbulent flow over riblet-mounted surfaces , 1993, Journal of Fluid Mechanics.

[13]  S. K. Robinson,et al.  Coherent Motions in the Turbulent Boundary Layer , 1991 .

[14]  T. J. Hanratty,et al.  Measurements of turbulent flow in a channel at low Reynolds numbers , 1990 .

[15]  M. Rashidi,et al.  PARTICLE-TURBULENCE INTERACTION IN A BOUNDARY LAYER , 1990 .

[16]  G. Mariotti,et al.  Direct numerical simulation of particle behaviour in the wall region of turbulent flows in horizontal channels , 1992 .

[17]  J. C. R. Hunt,et al.  The force exerted on a body in inviscid unsteady non-uniform rotational flow , 1988, Journal of Fluid Mechanics.

[18]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[19]  Goodarz Ahmadi,et al.  Direct numerical simulation of particle entrainment in turbulent channel flow , 1995 .

[20]  Parviz Moin,et al.  Direct simulations of turbulent flow using finite-difference schemes , 1991 .

[21]  P. Moin,et al.  The minimal flow unit in near-wall turbulence , 1991, Journal of Fluid Mechanics.

[22]  Parviz Moin,et al.  Direct numerical simulation of turbulent flow over riblets , 1993, Journal of Fluid Mechanics.

[23]  Goodarz Ahmadi,et al.  Brownian particle deposition in a directly simulated turbulent channel flow , 1993 .

[24]  T. J. Hanratty,et al.  Mechanism of turbulent mass transfer at a solid boundary , 1983 .

[25]  Yannis Hardalupas,et al.  Velocity and particle-flux characteristics of turbulent particle-laden jets , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[26]  Gerard M. Faeth,et al.  Turbulent dispersion of particles in self-generated homogeneous turbulence , 1990, Journal of Fluid Mechanics.

[27]  Gad Hetsroni,et al.  Particles-turbulence interaction , 1989 .

[28]  F. Williams Spray combustion theory , 1959 .

[29]  John B. McLaughlin,et al.  An algorithm for tracking fluid particles in a spectral simulation of turbulent channel flow , 1992 .

[30]  Douglas K. Lilly,et al.  ON THE COMPUTATIONAL STABILITY OF NUMERICAL SOLUTIONS OF TIME-DEPENDENT NON-LINEAR GEOPHYSICAL FLUID DYNAMICS PROBLEMS , 1965 .

[31]  Clayton T. Crowe,et al.  PARTICLE DISPERSION BY COHERENT STRUCTURES IN FREE SHEAR FLOWS , 1985 .

[32]  S. Elghobashi,et al.  On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification , 1993 .

[33]  J. Eaton,et al.  The effect of small particles on fluid turbulence in a flat‐plate, turbulent boundary layer in air , 1991 .

[34]  M. Sokolov,et al.  Distribution of Mass, Velocity, and Intensity of Turbulence in a Two-Phase Turbulent Jet , 1971 .

[35]  Steven A. Orszag,et al.  Transition to turbulence in plane Poiseuille and plane Couette flow , 1980, Journal of Fluid Mechanics.

[36]  J. McLaughlin Aerosol particle deposition in numerically simulated channel flow , 1989 .

[37]  T. J. Hanratty,et al.  Turbulent deposition and trapping of aerosols at a wall , 1992 .

[38]  C. Crowe,et al.  The Particle-Source-In Cell (PSI-CELL) Model for Gas-Droplet Flows , 1977 .

[39]  Sanjoy Banerjee,et al.  A numerical study of free-surface turbulence in channel flow , 1995 .

[40]  Douglas S. Finnicum,et al.  Turbulent normal velocity fluctuations close to a wall , 1985 .

[41]  K. Squires,et al.  Measurements of particle dispersion obtained from direct numerical simulations of isotropic turbulence , 1991, Journal of Fluid Mechanics.

[42]  Sanjoy Banerjee,et al.  On the condition of streak formation in a bounded turbulent flow , 1992 .

[43]  Clayton T. Crowe,et al.  Effect of particle size on modulating turbulent intensity , 1989 .

[44]  J. Chung,et al.  Simulation of particle dispersion in a two‐dimensional mixing layer , 1988 .

[45]  M. Maxey,et al.  Methods for evaluating fluid velocities in spectral simulations of turbulence , 1989 .

[46]  Sangtae Kim,et al.  Microhydrodynamics: Principles and Selected Applications , 1991 .

[47]  D. Kaftori,et al.  Funnel‐shaped vortical structures in wall turbulence , 1994 .

[48]  J. Riley,et al.  Equation of motion for a small rigid sphere in a nonuniform flow , 1983 .

[49]  O. Molerus,et al.  Investigation of solid—liquid pipe flow with regard to turbulence modification , 1979 .

[50]  D. Drew Mathematical Modeling of Two-Phase Flow , 1983 .

[51]  J. Eaton,et al.  The behavior of solid particles in a vertical turbulent boundary layer in air , 1990 .

[52]  M. Maxey,et al.  Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence , 1993, Journal of Fluid Mechanics.

[53]  N. Abuaf,et al.  Velocity measurements in a two-phase turbulent jet , 1974 .

[54]  K. Squires,et al.  Particle response and turbulence modification in isotropic turbulence , 1990 .

[55]  S. Elghobashi,et al.  Direct simulation of particle dispersion in a decaying isotropic turbulence , 1992, Journal of Fluid Mechanics.

[56]  B. Mutlu Sumer,et al.  Particle motions near the bottom in turbulent flow in an open channel. Part 2 , 1978 .

[57]  C. R. Smith,et al.  The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer , 1983, Journal of Fluid Mechanics.

[58]  C. Tchen,et al.  Mean Value and Correlation Problems connected with the Motion of Small Particles suspended in a turbulent fluid , 1947 .

[59]  P. Moin,et al.  Turbulence statistics in fully developed channel flow at low Reynolds number , 1987, Journal of Fluid Mechanics.

[60]  K. Squires,et al.  Preferential concentration of particles by turbulence , 1991 .