Slow flow past periodic arrays of cylinders with application to heat transfer
TL;DR: In this article, the average temperature difference between the bulk and the cylinders which are heated uniformly under conditions of small Reynolds and Peclet numbers is calculated for the slow flow past a square and a hexagonal array of cylinders using a somewhat nonconventional numerical method.
About: This article is published in International Journal of Multiphase Flow.The article was published on 1982-06-01. It has received 626 citations till now. The article focuses on the topics: Volume fraction & Cylinder (engine).
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Abstract: We present a novel method for simulating hydrodynamic phenomena. This particle-based method combines features from molecular dynamics and lattice-gas automata. It is shown theoretically as well as in simulations that a quantitative description of isothermal Navier-Stokes flow is obtained with relatively few particles. Computationally, the method is much faster than molecular dynamics, and the at same time it is much more flexible than lattice-gas automata schemes.
3,338 citations
TL;DR: In this article, a general technique for simulating solid-fluid suspensions is described, which combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the fluid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping flow regime and at higher Reynolds numbers.
Abstract: A new and very general technique for simulating solid–fluid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the fluid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping-flow regime and at higher Reynolds numbers. Brownian motion of the solid particles arises spontaneously from stochastic fluctuations in the fluid stress tensor, rather than from random forces or displacements applied directly to the particles. In this paper, the theoretical foundations of the technique are laid out, illustrated by simple analytical and numerical examples; in a companion paper (Part 2), extensive numerical tests of the method, for stationary flows, time-dependent flows, and finite-Reynolds-number flows, are reported.
2,073 citations
Cites result from "Slow flow past periodic arrays of c..."
...In general the lattice-Boltzmann and finite-difference simulations are in quite good agreement with one another and with the results of Sangani and Acrivos (Table 4). Quantitatively, the lattice-Boltzmann code performs significantly better at high volume fractions. Since the drag force varies rapidly at high concentrations it is necessary to make a precise determination of the hydrodynamic radius, as in section IIIA. At φ = 0.1, the reduced drag force FD/ηUA is given almost exactly (to 1 part in 10 (4)) by the asymptotic expression (Sangani & Acrivos (1982)),...
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TL;DR: In this paper, extensive numerical tests of the method are described; results are presented for creeping flows, both with and without Brownian motion, and at finite Reynolds numbers, and the short-time dynamics of random dispersions of up to 1024 colloidal particles have been simulated.
Abstract: A new and very general technique for simulating solid–fluid suspensions has been described in a previous paper (Part 1); the most important feature of the new method is that the computational cost scales linearly with the number of particles. In this paper (Part 2), extensive numerical tests of the method are described; results are presented for creeping flows, both with and without Brownian motion, and at finite Reynolds numbers. Hydrodynamic interactions, transport coefficients, and the short-time dynamics of random dispersions of up to 1024 colloidal particles have been simulated.
1,331 citations
TL;DR: It is proposed that the osteocytes, although not responsive to substantial fluid pressures, can be stimulated by relatively small fluid shear stresses acting on the membranes of their osteocytic processes.
1,218 citations
TL;DR: In this paper, a review of applications of the lattice-Boltzmann method to simulations of particle-fluid suspensions is presented, together with some of the important applications of these methods.
Abstract: This paper reviews applications of the lattice-Boltzmann method to simulations of particle-fluid suspensions. We first summarize the available simulation methods for colloidal suspensions together with some of the important applications of these methods, and then describe results from lattice-gas and lattice-Boltzmann simulations in more detail. The remainder of the paper is an update of previously published work,(69, 70) taking into account recent research by ourselves and other groups. We describe a lattice-Boltzmann model that can take proper account of density fluctuations in the fluid, which may be important in describing the short-time dynamics of colloidal particles. We then derive macro-dynamical equations for a collision operator with separate shear and bulk viscosities, via the usual multi-time-scale expansion. A careful examination of the second-order equations shows that inclusion of an external force, such as a pressure gradient, requires terms that depend on the eigenvalues of the collision operator. Alternatively, the momentum density must be redefined to include a contribution from the external force. Next, we summarize recent innovations and give a few numerical examples to illustrate critical issues. Finally, we derive the equations for a lattice-Boltzmann model that includes transverse and longitudinal fluctuations in momentum. The model leads to a discrete version of the Green–Kubo relations for the shear and bulk viscosity, which agree with the viscosities obtained from the macro-dynamical analysis. We believe that inclusion of longitudinal fluctuations will improve the equipartition of energy in lattice-Boltzmann simulations of colloidal suspensions.
1,117 citations
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TL;DR: The influence of obstacles arranged in rectangular order upon the properties of a medium was discussed in this article, where it was shown that obstacles can be arranged in a rectangular order to improve the performance of the medium.
Abstract: (1892). LVI. On the influence of obstacles arranged in rectangular order upon the properties of a medium. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 34, No. 211, pp. 481-502.
1,590 citations
TL;DR: In this article, the Fourier series is used to obtain fundamental solutions of the Stokes equations of motion for a viscous fluid past a periodic array of obstacles, and it is shown that the divergence of the lattice sums pointed out by Burgers may be rescued by taking into account the presence of the mean pressure gradient.
Abstract: Spatially periodic fundamental solutions of the Stokes equations of motion for a viscous fluid past a periodic array of obstacles are obtained by use of Fourier series. It is made clear that the divergence of the lattice sums pointed out by Burgers may be rescued by taking into account the presence of the mean pressure gradient. As an application of these solutions the force acting on any one of the small spheres forming a periodic array is considered. Cases for three special types of cubic lattice are investigated in detail. It is found that the ratios of the values of this force to that given by the Stokes formula for an isolated sphere are larger than 1 and do not differ so much among these three types provided that the volume concentration of the spheres is the same and small. The method is also applied to the two-dimensional flow past a square array of circular cylinders, and the drag on one of the cylinders is found to agree with that calculated by the use of elliptic functions.
908 citations
TL;DR: In this article, a modification of the method developed by Hashimoto (1959) was used to calculate the drag force by the fluid on a sphere forming the periodic array of spheres.
402 citations
TL;DR: In this article, a method devised by Lord Rayleigh to enable the calculation of the transport properties of circular cylinders in square and hexagonal arrays is described, and the theory is confirmed by measurements on arrays of perfectly conducting cylinders, and also is compared with asymptotic formulae due to Keller (1963) and O'Brien (1977).
Abstract: We extend a method devised by Lord Rayleigh to enable the calculation of the transport properties of circular cylinders in square and hexagonal arrays. The theory is confirmed by measurements on arrays of perfectly conducting cylinders, and also is compared with asymptotic formulae due to Keller (1963) and O’Brien (1977). It is used to furnish plots of equipotential lines within the array. It is also applied to the calculation of the optical properties of films with columnar structure. Detailed studies for copper films show both the good solar selectivity possible with voided structures and the transition from a good reflector to a metal black consequent upon structural changes.
390 citations