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  • 1
    Electronic Resource
    Electronic Resource
    On the collision rate of small particles in isotropic turbulence. II. Finite inertia case (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 1206-1216 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Numerical experiments have been performed to study the geometric collision rate of heavy particles with finite inertia. The turbulent flow was generated by direct numerical integration of the full Navier-Stokes equations. The collision kernel peaked at a particle response time between the Kolmogorov and the large-eddy turnover times, implying that both the large-scale and small-scale fluid motions contribute, although in very different manners, to the collision rate. Both numerical results for frozen turbulent fields and a stochastic theory show that the collision kernel approaches the kinetic theory of Abrahamson [Chem. Eng. Sci. 30, 1371 (1975)] only at very large τp/Te, where τp is the particle response time and Te is the flow integral time scale. Our results agree with those of Sundaram and Collins [J. Fluid Mech. 335, 75 (1997)] for an evolving flow. A rapid increase of the collision kernel with the particle response time was observed for small τp/τk, where τk is the flow Kolmogorov time scale. A small inertia of τp/τk=0.5 can lead to an order of magnitude increase in the collision kernel relative to the zero-inertia particles. A scaling law for the collision kernel at small τp/τk was proposed and confirmed numerically by varying the particle size, inertial response time, and flow Reynolds number. A leading-order theory for small τp/τk was developed, showing that the enhanced collision is mainly a result of the nonuniform particle concentration that results from the interaction of heavy particles with local flow microstructures. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869644
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  • 2
    Electronic Resource
    Electronic Resource
    Statistical mechanical descriptions of turbulent coagulation (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 2647-2651 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A fundamental tenet of statistical mechanics is that the rate of collision of two objects is related to the expectation value of their relative velocities. In pioneering work by Saffman and Turner [J. Fluid Mech. 1, 16 (1956)], two different formulations of this tenet are used to calculate the collision kernel Γ between two arbitrary particle size groups in a turbulent flow. The first or spherical formulation is based on the radial component wr of the relative velocity w between two particles: Γsph=2πR2〈|wr|〉, where wr=w⋅R/R, R is the separation vector, and R=|R|. The second or cylindrical formulation is based on the vector velocity itself: Γcyl=2πR2〈|w|〉, which is supported by molecular collision statistical mechanics. Saffman and Turner obtained different results from the two formulations and attributed the difference to the form of the probability function of w used in their work. A more careful examination reveals that there is a fundamental difference between the two formulations. An underlying assumption in the second formulation is that the relative velocity at any instant is locally uniform over a spatial scale on the order of the collision radius R, which is certainly not the case in turbulent flow. Therefore, the second formulation is not expected to be rigorously correct. In fact, both our analysis and numerical simulations show that the second formulation leads to a collision kernel about 25% larger than the first formulation in isotropic turbulence. For a simple uniform shear flow, the second formulation is about 20% too large. The two formulations, however, are equivalent for treating the collision rates among random molecules and the gravitational collision rates. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869777
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  • 3
    Electronic Resource
    Electronic Resource
    On the collision rate of small particles in isotropic turbulence. I. Zero-inertia case (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 266-276 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Numerical experiments have been performed to study the geometric collision rate of finite-size particles with zero inertia (i.e., fluid elements) in isotropic turbulence. The turbulent flow was generated by the pseudospectral method. We argue that the formulation of Saffman and Turner [J. Fluid Mech. 1, 16 (1956)] for the average collision kernel is correct only under the assumptions that the particles are kept in the system after collision and allowed to overlap in space. This was confirmed, for the first time, by numerical experiments to within a numerical uncertainty as small as 1%. Finite corrections to the Saffman and Turner result must be made if one applies the theory to actual coagulation process where particles are not allowed to overlap before collision and particles are removed from a given size group after collision. This is due to the fact that Saffman and Turner assumed a uniform, time-independent concentration field in their formulation of the average collision kernel, while in the actual modeling of population evolution the particle number concentration changes in time and may be locally nonuniform as a result of a biased removal process due to spatially nonuniform coagulation rates. However, the quantitative level of the deviations from the Saffman and Turner result remain to be explained. Numerical experiments in simple shear flow were also conducted to elaborate our findings. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869565
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  • 4
    Electronic Resource
    Electronic Resource
    Quantification of chaotic dynamics for heavy particle dispersion in ABC flow (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 1073-1080 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A six-dimensional nonlinear dynamic system describing the Lagrangian motion of a heavy particle in the Arnold–Beltrami–Childress (ABC) flow was numerically studied. Lyapunov exponents and fractal dimension were used to quantify the chaotic motion. A single set of ABC flow parameters and a limited set of initial conditions were used. Given these restrictions, the following were found. (1) Attractor fractal dimension varies significantly with Stokes number, and, depending on inertia, periodic, quasiperiodic, and chaotic attractors may exist. (2) Particle drift reduces the fractal dimension when the drift is small. It can also cause irregular jumps when the drift parameter is close to one. (3) Quasiperiodic orbits on smooth two-dimensional manifolds were shown to be the most common ultimate solutions of the system when either the inertia or the drift is relatively large. (4) Different initial conditions can lead to different attracting sets; however, most of them have the same dimension. (5) A direct measure of dispersion based on mean square displacement was defined, but no relation between this dispersion measure and fractal dimension was found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858088
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  • 5
    Electronic Resource
    Electronic Resource
    EDQNM model of a passive scalar with a uniform mean gradient (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 1588-1608 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Dynamic equations for the scalar autocorrelation and scalar-velocity cross correlation spectra have been derived for a passive scalar with a uniform mean gradient using the Eddy Damped Quasi Normal Markovian (EDQNM) theory. The presence of a mean gradient in the scalar field makes all correlations involving the scalar axisymmetric with respect to the axis pointing in the direction of the mean gradient. Equivalently, all scalar spectra will be functions of the wave number k and the cosine of the azimuthal angle designated as μ. In spite of this complication, it is shown that the cross correlation vector can be completely characterized by a single scalar function Q(k). The scalar autocorrelation spectrum, in contrast, has an unknown dependence on μ. However, this dependency can be expressed as an infinite sum of Legendre polynomials of μ, as first suggested by Herring [Phys. Fluids 17, 859 (1974)]. Furthermore, since the scalar field is initially zero, terms beyond the second order of the Legendre expansion are shown to be exactly zero. The energy, scalar autocorrelation, and scalar-velocity cross correlation were solved numerically from the EDQNM equations and compared to results from direct numerical simulations. The results show that the EDQNM theory is effective in describing single-point and spectral statistics of a passive scalar in the presence of a mean gradient. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868933
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  • 6
    Electronic Resource
    Electronic Resource
    Dispersion of particles injected nonuniformly in a mixing layer (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 1599-1601 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The dispersion of fluid elements distributed nonuniformly at the interface of a two-dimensional, temporally evolving mixing layer was studied. The average transverse dispersion of fluid elements was found to be either enhanced or reduced markedly by simply varying the initial number density distribution along the interface. The increase in dispersion is due to the nonuniform stretching of the interface during the growth of the vortical structure. This naturally leads to a conclusion that the dispersion rate of particles in a spatially evolving mixing layer can be controlled by injecting particles nonuniformly in time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858433
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  • 7
    Electronic Resource
    Electronic Resource
    Chaotic dynamics of heavy particle dispersion: Fractal dimension versus dispersion coefficients (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 1305-1308 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The chaotic dynamics of Lagrangian motion of particles in a steady Arnold–Beltrami–Childress (ABC) flow and a pseudoturbulence are investigated and the Lyapunov exponents and fractal dimensions of particle trajectories for different particle inertia and particle drift velocity are computed. The dispersion process of particles could be characterized by the fractal dimension and dispersion coefficients. The interesting behavior of fractal dimension of particle motion in ABC flow suggested the similarity of particle motion in ABC flow and in a mixing layer. The relationship between particle dispersion coefficient and fractal dimension was nearly linear for the pseudoturbulence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857579
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  • 8
    Electronic Resource
    Electronic Resource
    The motion of microbubbles in a forced isotropic and homogeneous turbulence (1993)
    Springer
    Flow, turbulence and combustion 51 (1993), S. 291-296 
    Details
    ISSN: 1573-1987
    Keywords: microbubble transport ; local accumulation ; turbulence structures ; inertial bias
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract We have studied the concentration distribution of microbubbles in forced isotropic turbulence. An initially uniform concentration field is shown to evolve to a highlyintermittent orspotty concentration distribution at long time due to the interactions of microbubbles with small-scale, intense, and coherent flow vortical structures. The maximum bubble concentration can be as large as 3,000 times the mean concentration and the local accumulations occur preferentially in the regions of high flow vorticity and low flow pressure. A quantitative measure of global nonuniformity in the concentration field is used to confirm that the preferential accumulation does follow Kolmogorov scaling, as opposed to the large-scale scaling commonly used for dispersion quantification.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01082551
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