Topic

# Couette flow

About: Couette flow is a research topic. Over the lifetime, 5427 publications have been published within this topic receiving 129336 citations.

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TL;DR: In this paper, the authors studied the flow of an idealized granular material consisting of uniform smooth, but nelastic, spherical particles using statistical methods analogous to those used in the kinetic theory of gases.

Abstract: The flow of an idealized granular material consisting of uniform smooth, but nelastic, spherical particles is studied using statistical methods analogous to those used in the kinetic theory of gases. Two theories are developed: one for the Couette flow of particles having arbitrary coefficients of restitution (inelastic particles) and a second for the general flow of particles with coefficients of restitution near 1 (slightly inelastic particles). The study of inelastic particles in Couette flow follows the method of Savage & Jeffrey (1981) and uses an ad hoc distribution function to describe the collisions between particles. The results of this first analysis are compared with other theories of granular flow, with the Chapman-Enskog dense-gas theory, and with experiments. The theory agrees moderately well with experimental data and it is found that the asymptotic analysis of Jenkins & Savage (1983), which was developed for slightly inelastic particles, surprisingly gives results similar to the first theory even for highly inelastic particles. Therefore the ‘nearly elastic’ approximation is pursued as a second theory using an approach that is closer to the established methods of Chapman-Enskog gas theory. The new approach which determines the collisional distribution functions by a rational approximation scheme, is applicable to general flowfields, not just simple shear. It incorporates kinetic as well as collisional contributions to the constitutive equations for stress and energy flux and is thus appropriate for dilute as well as dense concentrations of solids. When the collisional contributions are dominant, it predicts stresses similar to the first analysis for the simple shear case.

2,631 citations

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01 Jan 1995

TL;DR: A Thomas's algorithm for the solution of a tridiagonal system of Equations is described in this paper, as well as a detailed discussion of the future of Computational Fluid Dynamics.

Abstract: Part I*Basic Thoughts and Equations 1 Philosophy of Computational Fluid Dynamics 2 The Governing Equations of Fluid Dynamics Their Derivation, A Discussion of Their Physical Meaning, and A Presentation of Forms Particularly Suitable to CFD 3 Mathematical Behavior of Partial Differential Equations The Impact on Computational Fluid Dynamics Part II*Basics of the Numerics 4 Basic Aspects of Discretization 5 Grids and Meshes, With Appropriate Transformations 6 Some Simple CFD Techniques A Beginning Part III*Some Applications 7 Numerical Solutions of Quasi-One-Dimensional Nozzle Flows 8 Numerical Solution of A Two-Dimensional Supersonic Flow Prandtl-Meyer Expansion Wave 9 Incompressible Couette Flow Numerical Solution by Means of an Implicit Method and the Pressure Correction Method 10 Incompressible, Inviscid Slow Over a Circular Cylinder Solution by the Technique Relaxation Part IV*Other Topics 11 Some Advanced Topics in Modern CFD A Discussion 12 The Future of Computational Fluid Dynamics Appendixes A Thomas's Algorithm for the Solution of A Tridiagonal System of Equations References

1,738 citations

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TL;DR: A novel lattice Boltzmann thermal model is proposed for studying thermohydrodynamics in incompressible limit that can incorporate viscous heat dissipation and compression work done by the pressure, in contrast to the passive-scalar-based thermal latticeboltzmann models.

Abstract: A novel lattice Boltzmann thermal model is proposed for studying thermohydrodynamics in incompressible limit. The new model introduces an internal energy density distribution function to simulate the temperature field. The macroscopic density and velocity fields are still simulated using the density distribution function. Compared with the multispeed thermal lattice Boltzmann models, the current scheme is numerically more stable. In addition, the new model can incorporate viscous heat dissipation and compression work done by the pressure, in contrast to the passive-scalar-based thermal lattice Boltzmann models. Numerical simulations of Couette flow with a temperature gradient and Rayleigh?Benard convection agree well with analytical solutions and benchmark data.

1,243 citations

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TL;DR: In this paper, a complete set of perturbations, ordered by energy growth, is found using variational methods. But the optimal perturbation is not of modal form, and those which grow the most resemble streamwise vortices, which divert the mean flow energy into streaks of streamwise velocity and enable the energy of the perturbance to grow by as much as three orders of magnitude.

Abstract: Transition to turbulence in plane channel flow occurs even for conditions under which modes of the linearized dynamical system associated with the flow are stable. In this paper an attempt is made to understand this phenomena by finding the linear three‐dimensional perturbations that gain the most energy in a given time period. A complete set of perturbations, ordered by energy growth, is found using variational methods. The optimal perturbations are not of modal form, and those which grow the most resemble streamwise vortices, which divert the mean flow energy into streaks of streamwise velocity and enable the energy of the perturbation to grow by as much as three orders of magnitude. It is suggested that excitation of these perturbations facilitates transition from laminar to turbulent flow. The variational method used to find the optimal perturbations in a shear flow also allows construction of tight bounds on growth rate and determination of regions of absolute stability in which no perturbation growth is possible.

1,083 citations

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TL;DR: In this article, the velocity boundary condition for curved boundaries in the lattice Boltzmann equation (LBE) was studied for moving boundaries by combination of the "bounce-back" scheme and spatial interpolations of first or second order.

Abstract: We study the velocity boundary condition for curved boundaries in the lattice Boltzmann equation (LBE). We propose a LBE boundary condition for moving boundaries by combination of the “bounce-back” scheme and spatial interpolations of first or second order. The proposed boundary condition is a simple, robust, efficient, and accurate scheme. Second-order accuracy of the boundary condition is demonstrated for two cases: (1) time-dependent two-dimensional circular Couette flow and (2) two-dimensional steady flow past a periodic array of circular cylinders (flow through the porous media of cylinders). For the former case, the lattice Boltzmann solution is compared with the analytic solution of the Navier–Stokes equation. For the latter case, the lattice Boltzmann solution is compared with a finite-element solution of the Navier–Stokes equation. The lattice Boltzmann solutions for both flows agree very well with the solutions of the Navier–Stokes equations. We also analyze the torque due to the momentum transfer between the fluid and the boundary for two initial conditions: (a) impulsively started cylinder and the fluid at rest, and (b) uniformly rotating fluid and the cylinder at rest.

1,063 citations