The Thermal Wake Function for Rectangular Electronic Modules

1994 ◽  
Vol 116 (1) ◽  
pp. 55-59 ◽  
Author(s):  
S. S. Kang
Keyword(s):  
Turbulent Flows ◽  
Peclet Number ◽  
Present Model ◽  
Source Model ◽  
Length Scale ◽  
Point Heat Source ◽  
Heat Source Model ◽  
Péclet Number ◽  
Thermal Wake ◽  
Flow Stream

A point heat source model is employed to study the thermal wake function for an array of rectangular electronic modules situated in a uniform flow stream. For the particular case of in-line modules, a simple equation for the wake function is developed in terms of a modified Peclet number. The length scale for the Peclet number is the square of the module width divided by the streamwise spacing of the modules. The downstream decay of the wake function is shown to be well represented by a power law. Sample calculations using the present model are shown to compare well with experimental data for laminar as well as turbulent flows.

Minimum state for high Reynolds and Péclet number turbulent flows

2009 ◽  
Vol 373 (31) ◽  
pp. 2746-2749 ◽  
Author(s):  
Ye Zhou ◽  
A.C. Buckingham ◽  
F. Bataille ◽  
L. Mathelin
Keyword(s):  
Turbulent Flows ◽  
Peclet Number ◽  
Péclet Number ◽  
High Reynolds

A Disperse-Phase Dynamic SGS Coupling Model for Particle-Laden Turbulent Flows

2007 ◽  
Author(s):  
Kangbin Lei ◽  
Kiwamu Kase ◽  
Nobuyuki Oshima ◽  
Toshio Kobayashi
Keyword(s):  
Turbulent Flows ◽  
Present Model ◽  
Coupling Model ◽  
Stokes Number ◽  
Particle Diffusion ◽  
Length Scale ◽  
Phase Dynamic ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Lagrangian Motion

In order to study the effects of turbulence sub-grid-scale (SGS) fluctuation on particle Lagrangian motion in turbulent flows, a dynamic random walk (DRW) SGS coupling model based on an Eulerian-Lagrangian approach was developed. The advantage of the new model is that the Gaussian statistical distribution and local isotropic properties of turbulence SGS fluctuation can be parameterized by Germano’s (1991) Eulerian dynamic procedure. Using the present model, large eddy simulation (LES) was performed for downward channel flow at a Reynolds number of 180, as in the direct numerical simulation (DNS) done by Rouson & Eaton in 1997. Through a comparing of the statistical properties of particle diffusion with DNS, the capabilities and limitations of the present DRW SGS model were verified. Moreover, it was found that turbulence SGS fluctuation was strongly associated with particle motion, because preferred particles were affected by the preferred length scale of the eddy structure around. It was also found that turbulence SGS fluctuations are indispensable in calculating particles’ Lagrangian trajectories in LES even when the particle Stokes number is high.

scholarly journals Hydrodynamic Dispersion in Porous Media and the Significance of Lagrangian Time and Space Scales

Fluids ◽  
2020 ◽  
Vol 5 (2) ◽  
pp. 79
Author(s):  
Vi Nguyen ◽  
Dimitrios V. Papavassiliou
Keyword(s):  
Porous Media ◽  
Peclet Number ◽  
Dispersion Coefficient ◽  
Flow In Porous Media ◽  
Hydrodynamic Dispersion ◽  
Length Scale ◽  
Packed Beds ◽  
Péclet Number ◽  
Molecular Diffusivity ◽  
Effective Lagrangian

Transport in porous media is critical for many applications in the environment and in the chemical process industry. A key parameter for modeling this transport is the hydrodynamic dispersion coefficient for particles and scalars in a porous medium, which has been found to depend on properties of the medium structure, on the dispersing compound, and on the flow field characteristics. Previous studies have resulted in suggestions of different equation forms, showing the relationship between the hydrodynamic dispersion coefficient for various types of porous media in various flow regimes and the Peclet number. The Peclet number is calculated based on a Eulerian length scale, such as the diameter of the spheres in packed beds, or the pore diameter. However, the nature of hydrodynamic dispersion is Lagrangian, and it should take the molecular diffusion effects, as well as the convection effects, into account. This work shifts attention to the Lagrangian time and length scales for the definition of the Peclet number. It is focused on the dependence of the longitudinal hydrodynamic dispersion coefficient on the effective Lagrangian Peclet number by using a Lagrangian length scale and the effective molecular diffusivity. The lattice Boltzmann method (LBM) was employed to simulate flow in porous media that were constituted by packed spheres, and Lagrangian particle tracking (LPT) was used to track the movement of individual dispersing particles. It was found that the hydrodynamic dispersion coefficient linearly depends on the effective Lagrangian Peclet number for packed beds with different types of packing. This linear equation describing the dependence of the dispersion coefficient on the effective Lagrangian Peclet number is both simpler and more accurate than the one formed using the effective Eulerian Peclet number. In addition, the slope of the line is a characteristic coefficient for a given medium.

scholarly journals Dispersion of swimming algae in laminar and turbulent channel flows: consequences for photobioreactors

2013 ◽  
Vol 10 (81) ◽  
pp. 20121041 ◽  
Author(s):  
Ottavio A. Croze ◽  
Gaetano Sardina ◽  
Mansoor Ahmed ◽  
Martin A. Bees ◽  
Luca Brandt
Keyword(s):  
Shear Flow ◽  
Turbulent Flows ◽  
Peclet Number ◽  
Laminar Flows ◽  
Channel Flows ◽  
Mean Flow ◽  
Time Resolved ◽  
Péclet Number ◽  
Turbulent Channel Flows ◽  
Passive Tracers

Shear flow significantly affects the transport of swimming algae in suspension. For example, viscous and gravitational torques bias bottom-heavy cells to swim towards regions of downwelling fluid (gyrotaxis). It is necessary to understand how such biases affect algal dispersion in natural and industrial flows, especially in view of growing interest in algal photobioreactors. Motivated by this, we here study the dispersion of gyrotactic algae in laminar and turbulent channel flows using direct numerical simulation (DNS) and a previously published analytical swimming dispersion theory. Time-resolved dispersion measures are evaluated as functions of the Péclet and Reynolds numbers in upwelling and downwelling flows. For laminar flows, DNS results are compared with theory using competing descriptions of biased swimming cells in shear flow. Excellent agreement is found for predictions that employ generalized Taylor dispersion. The results highlight peculiarities of gyrotactic swimmer dispersion relative to passive tracers. In laminar downwelling flow the cell distribution drifts in excess of the mean flow, increasing in magnitude with Péclet number. The cell effective axial diffusivity increases and decreases with Péclet number (for tracers it merely increases). In turbulent flows, gyrotactic effects are weaker, but discernable and manifested as non-zero drift. These results should have a significant impact on photobioreactor design.

Approximate analysis of the containment of contaminated sites prior to remediation

2000 ◽  
Vol 42 (1-2) ◽  
pp. 319-324 ◽  
Author(s):  
H. Rubin ◽  
A. Rabideau
Keyword(s):  
Steady State ◽  
Peclet Number ◽  
Dimensionless Parameter ◽  
Contaminated Sites ◽  
Unsteady State ◽  
Péclet Number ◽  
Vertical Barrier ◽  
Time Period ◽  
Barrier Performance ◽  
Vertical Barriers

This study presents an approximate analytical model, which can be useful for the prediction and requirement of vertical barrier efficiencies. A previous study by the authors has indicated that a single dimensionless parameter determines the performance of a vertical barrier. This parameter is termed the barrier Peclet number. The evaluation of barrier performance concerns operation under steady state conditions, as well as estimates of unsteady state conditions and calculation of the time period requires arriving at steady state conditions. This study refers to high values of the barrier Peclet number. The modeling approach refers to the development of several types of boundary layers. Comparisons were made between simulation results of the present study and some analytical and numerical results. These comparisons indicate that the models developed in this study could be useful in the design and prediction of the performance of vertical barriers operating under conditions of high values of the barrier Peclet number.

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