Fluid dynamic turbulence is one of the most challenging computational physics problems because of the extremely wide range of time and space scales involved, the strong nonlinearity of the governing equations, and the many practical and important applications. While most linear fluid instabilities are well understood, the nonlinear interactions among them makes even the relatively simple limit of homogeneous isotropic turbulence difficult to treat physically, mathematically, and computationally. Turbulence is modeled computationally by a two-stage bootstrap process. The first stage, direct numerical simulation, attempts to resolve the relevant physical time and space scales but its application is limited to diffusive flows with a relatively small Reynolds number (Re). Using direct numerical simulation to provide a database, in turn, allows calibration of phenomenological turbulence models for engineering applications. Large eddy simulation incorporates a form of turbulence modeling applicable when the large-scale flows of interest are intrinsically time dependent, thus throwing common statistical models into question. A promising approach to large eddy simulation involves the use of high-resolution monotone computational fluid dynamics algorithms such as flux-corrected transport or the piecewise parabolic method which have intrinsic subgrid turbulence models coupled naturally to the resolved scales in the computed flow. The physical considerations underlying and evidence supporting this monotone integrated large eddy simulation approach are discussed.

New insights into large eddy simulation

This review pertains to the body of work dealing with internal recirculating flows generated by the motion of one or more of the containing walls. These flows are not only technologically important, they are of great scientific interest because they display almost all fluid mechanical phenomena in the simplest of geometrical settings. Thus corner eddies, longitudinal vortices, nonuniqueness, transition, and turbulence all occur naturally and can be studied in the same closed geometry. This facilitates the comparison of results from experiment, analysis, and computation over the whole range of Reynolds numbers. Considerable progress has been made in recent years in the understanding of three-dimensional flows and in the study of turbulence. The use of direct numerical simulation appears very promising.

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Fluid mechanics in the driven cavity

Mixed convection in a driven cavity with a stable vertical temperature gradient

The robustness, reliability and efficiency of modern numerical methods for obtaining solutions to flow problems have given rise to the adoption of Computational Fluid Dynamics (CFD) as a widely used analysis tool for membrane separation systems. In the past decade, many two-dimensional (2D) flow studies employing CFD have been published. Three-dimensional (3D) solutions are also slowly emerging. This paper reviews recent research utilizing 3D CFD models to simulate the flow conditions in narrow spacer-filled channels, such as those encountered in Spiral Wound Membrane (SWM) modules. Many of these studies have focused on optimizing spacer geometric parameters, while others have attempted to gain a better understanding of the mechanisms giving rise to mass transfer enhancement. Applications of 3D CFD to complex spacer geometries and multiple ionic component diffusion are also discussed.

Review of 3D CFD modeling of flow and mass transfer in narrow spacer-filled channels in membrane modules

Accurate three-dimensional lid-driven cavity flow

https://iopscience.iop.org/article/10.1016/0169-5983(89)90020-8/pdf

Numerical simulation of three-dimensional flow structure in a driven cavity

Incompressible flows around a yawed circular cylinder at a Reynolds number of 2000 have been calculated by the finite difference method based on the third-order upwind scheme for approximating the nonlinear terms of Navier-Stokes equations. No turbulence model is employed in this study. Computations are carried out for cases with and without end plates in order to investigate the effect of end plates on the flow. The calculated pressure distributions around the cylinder are compared with experimental data and the agreement is satisfactory. The results of this computation show the details of the flow especially in the wake region and it is found that the existence of the end plate greatly affects the location of the separation point.

Computation of flow around a yawed circular cylinder

Simulation of transition to turbulence in a cubic cavity

Transverse dunes and linear dunes are simulated numerically in order to make clear the mechanism of the formation of two kinds of typical sand dunes. The numerical method employed in this study can be divided into three parts: (i) Calculation of the air flow above the sand dunes; (ii) Estimation of the sand transfer caused by the flow through the friction; (iii) Determination of the shape of the sand ground. Since the computational area has been changed due to the last step, these procedures are repeated until typical shapes of the sand dunes are formed. One kind of the simulated dunes, which is formed by one wind direction, becomes essentially parallel straight ridges at right angle to the wind direction with only one slip-face on the lee side, which is known as the transverse dunes; The other one, which is formed by two directional wind, becomes essentially parallel straight ridge at the converging direction with two slip-faces on both sides, which is known as linear dunes.

Numerical Study of the Formation of Transverse Dunes and Linear Dunes

The flow around a circular cylinder standing on the sand is computed numerically and the movement of the sand is investigated. The numerical method employed in this study can be divided into three parts : (1) calculation of the air flow around the cylinder using MAC method with a generalized coordinate system ; (2) estimation of the sand transfer caused by the flow through the friction ; (3) determination of the shape of the ground. Since the computational area changes at step (3), this procedure has to be repeated at each time step. Results show that the horseshoe vortex scoops out the ground in front of the cylinder and the wake makes the sand accumulate in the rear region. The dented region becomes deeper as the cylinder leans windward.

Tetuya Kawamura

Papers

Numerical simulation of three-dimensional flow structure in a driven cavity

Computation of flow around a yawed circular cylinder

Simulation of transition to turbulence in a cubic cavity

Numerical Study of the Formation of Transverse Dunes and Linear Dunes

Numerical Study of the Flow and the Sand Movement around a Circular Cylinder Standing on the Sand