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.

Small Péclet-number mass transport to a finite strip: An advection–diffusion–reaction model of surface-based biosensors

2019 ◽  
Vol 31 (5) ◽  
pp. 763-781
Author(s):  
EHUD YARIV
Keyword(s):  
Shear Flow ◽  
Mass Transport ◽  
Sherwood Number ◽  
Peclet Number ◽  
Outer Region ◽  
Diffusion Reaction ◽  
Background Concentration ◽  
Leading Order ◽  
Péclet Number ◽  
Inner Region

AbstractWe consider two-dimensional mass transport to a finite absorbing strip in a uniform shear flow as a model of surface-based biosensors. The quantity of interest is the Sherwood number Sh, namely the dimensionless net flux onto the strip. Considering early-time absorption, it is a function of the Péclet number Pe and the Damköhler number Da, which, respectively, represent the characteristic magnitude of advection and reaction relative to diffusion. With a view towards modelling nanoscale biosensors, we consider the limit Pe«1. This singular limit is handled using matched asymptotic expansions, with an inner region on the scale of the strip, where mass transport is diffusively dominated, and an outer region at distances that scale as Pe-1/2, where advection enters the dominant balance. At the inner region, the mass concentration possesses a point-sink behaviour at large distances, proportional to Sh. A rescaled concentration, normalised using that number, thus possesses a universal logarithmic divergence; its leading-order correction represents a uniform background concentration. At the outer region, where advection by the shear flow enters the leading-order balance, the strip appears as a point singularity. Asymptotic matching with the concentration field in that region provides the Sherwood number as $${\rm{Sh}} = {\pi \over {\ln (2/{\rm{P}}{{\rm{e}}^{1/2}}) + 1.0559 + \beta }},$$ wherein β is the background concentration. The latter is determined by the solution of the canonical problem governing the rescaled inner concentration, and is accordingly a function of Da alone. Using elliptic-cylinder coordinates, we have obtained an exact solution of the canonical problem, valid for arbitrary values of Da. It is supplemented by approximate solutions for both small and large Da values, representing the respective limits of reaction- and transport-limited conditions.

Wall Shear Stress in Turbulent Pipe Flow

2009 ◽  
Author(s):  
Roland Gårdhagen ◽  
Jonas Lantz ◽  
Fredrik Carlsson ◽  
Matts Karlsson
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Flows ◽  
Intima Media Thickness ◽  
Elevated Risk ◽  
Laminar Flows ◽  
Turbulent Pipe Flow ◽  
Mean Flow ◽  
The Mean ◽  
Wall Shear

Low and/or oscillatory Wall Shear Stress (WSS) has been correlated with elevated risk for increased intima media thickness and atherosclerosis in several studies during the last decades [1, 2]. Most of the studies have addressed laminar flows, in which the oscillations mainly are due to the pulsating nature of blood flow. Turbulent flows however show significant spatial and temporal fluctuations although the mean flow is steady.

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

Comparison and Scaling of the Bursting Period in Rough and Smooth Walls Channel Flows

1999 ◽  
Vol 121 (4) ◽  
pp. 735-746 ◽  
Author(s):  
S. Demare ◽  
L. Labraga ◽  
C. Tournier
Keyword(s):  
Turbulent Flows ◽  
Major Part ◽  
Reynolds Numbers ◽  
Channel Flows ◽  
Quadrant Analysis ◽  
Number Range ◽  
Mixed Variables ◽  
Detection Techniques ◽  
Turbulent Channel Flows ◽  
Bursting Process

The Structure of Smooth and k-type rough wall turbulent channel flows was examined over a Reynolds number range of 12,700–55,000 using a few of the most common detection techniques (Modified U_Level (MODUL), TERA, Quadrant analysis) and conditional averages. When grouping time is used and a threshold-independent range could be found, all of the above techniques yield approximately the same time between bursts in the major part of the turbulent flow. In the range of Reynolds numbers studied, the bursting frequency is best scaled on mixed variables. The conditional averaged patterns give a representation of the bursting process and show some differences between turbulent flows which develop on smooth and rough walls, in both inner and outer regions.

scholarly journals Interactions among pressure, density, vorticity and their gradients in compressible turbulent channel flows

2011 ◽  
Vol 673 ◽  
pp. 1-18 ◽  
Author(s):  
LIANG WEI ◽  
ANDREW POLLARD
Keyword(s):  
Pressure Gradient ◽  
Transport Equation ◽  
Turbulent Flows ◽  
Variable Viscosity ◽  
Correlation Coefficients ◽  
Channel Flows ◽  
Turbulent Channel Flows ◽  
Spanwise Vorticity ◽  
The Difference ◽  
Vorticity Flux

The interactions among pressure, density, vorticity and their gradients in compressible turbulent channel flows (TCF) are studied using direct numerical simulations (DNS). DNS of three isothermal-wall TCF for Mach number Ma = 0.2, 0.7, and 1.5, respectively are performed using a discontinuous Galerkin method (DGM). The Reynolds numbers of these three cases are ≈2800, based on the bulk velocity, bulk density, half channel width and dynamic viscosity at the wall. A high cross-correlation between density and spanwise vorticity occurs at y+≈4, which is coincident with the peak mean spanwise baroclinicity. The relationship between the spanwise baroclinicity and the correlation is analysed. The difference between the evolution of density and spanwise vorticity very near the wall is discussed. The transport equation for the mean product of density and vorticity fluctuations 〈ρ′ω′i〉 is presented and the distributions of terms in the 〈ρ′ω′z〉 transport equation indicate that the minima and maxima of the profiles are located around y+≈5. The connection between pressure gradients and vorticity fluxes for compressible turbulent flows with variable viscosity has been formulated and verified. High correlations (0.7–1.0) between pressure gradient and vorticity flux are found very close to the wall (y+<5). The correlation coefficients are significantly influenced by Ma and viscosity in this region. Turbulence advection plays an important role in destroying the high correlations between pressure gradient and vorticity flux in the region away from the wall (y+ > 5).

Analysis of Complex Flows From Experimental Data and Numerical Experiments

2010 ◽  
Author(s):  
Je´roˆme Ve´tel ◽  
Andre´ Garon ◽  
Dominique Pelletier
Keyword(s):  
Experimental Data ◽  
Turbulent Flows ◽  
Turbulent Transport ◽  
Diagnostic Techniques ◽  
Complex Flows ◽  
Time Resolved ◽  
Taylor Hypothesis ◽  
The Rich ◽  
Passive Tracers ◽  
Advanced Post Processing

Fluid mechanics is considered to be a privileged field in physics because phenomena can be made visible. This is unfortunately not the case in turbulence where diffusion and mixing of passive tracers are enhanced by turbulent transport. Consequently, the analysis of the rich flow physics provided by direct numerical simulations (DNS) and by modern optical diagnostic techniques require advanced post-processing tools to extract fine flow details. In this context, this paper reviews most recent techniques used to reveal coherent structures and their dynamics in turbulent flows. In particular, results obtained with standard Eulerian techniques are compared to those obtained from a more recent Lagrangian technique. Even if this latter technique can provide finer details, it is found that the two methods are complementary. This is illustrated with DNS results and with experimental data including planar measurements as well as time-resolved measurements converted to quasi-instantaneous volumetric data by using the Taylor hypothesis.

On the collision rate of small particles in turbulent flows

1999 ◽  
Vol 391 ◽  
pp. 67-89 ◽  
Author(s):  
RENWEI MEI ◽  
KEVIN C. HU
Keyword(s):  
Shear Flow ◽  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Particle Collision ◽  
Turbulence Structure ◽  
Collision Rate ◽  
Collision Velocity ◽  
Mean Flow ◽  
Laminar Shear Flow ◽  
Laminar Shear

A theoretical framework is developed to predict the rate of geometric collision and the collision velocity of small size inertialess particles in general turbulent flows. The present approach evaluates the collision rate for small size, inertialess particles in a given instantaneous flow field based on the local eigenvalues of the rate-of-strain tensor. An ensemble average is then applied to the instantaneous collision rate to obtain the average collision rate. The collision rates predicted by Smoluchowski (1917) for laminar shear flow and by Saffman & Turner (1956) for isotropic turbulence are recovered. The collision velocities presently predicted in both laminar shear flow and isotropic turbulence agree well with the results from numerical simulations for particle collision in both flows. The present theory for evaluating the collision rate and the collision velocity is also applied to a rapidly sheared homogeneous turbulence to assess the effect of strong anisotropy on the collision rate. Using (ε/v)1/2, in which ε is the average turbulence energy dissipation rate and v is the fluid kinematic viscosity, as the characteristic turbulence shear rate to normalize the collision rate, the effect of the turbulence structure on the collision rate and collision velocity can be reliably described. The combined effects of the mean flow shear and the turbulence shear on the collision rate and collision velocity are elucidated.

Heat transport into a shear flow at high Peclet number

1990 ◽  
Vol 427 (1872) ◽  
pp. 25-30
Keyword(s):  
Thermal Diffusivity ◽  
Temperature Distribution ◽  
Shear Flow ◽  
Heat Transport ◽  
Peclet Number ◽  
Asymptotic Form ◽  
Convex Region ◽  
Heated Region ◽  
Péclet Number ◽  
Special Case

Heat transport from a heated convex region on an otherwise insulating plane, into a fluid in shear flow along the plane, is considered. The asymptotic form of the temperature distribution is determined for large values of the Peclet number sL 2 / k where s is the shear rate of the flow, L is a typical dimension of the heated region and k is the thermal diffusivity of the fluid. From it the asymptotic form of the total heat transport is obtained. Although the shape of the region is arbitrary, the solution is constructed by using previous results for the special case of a heated strip with its edges normal to the flow.

Eddy Viscosity and Reynolds Stress Models of Entropy Generation in Turbulent Channel Flows

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
J. Sun ◽  
D. Kuhn ◽  
G. Naterer
Keyword(s):  
Shear Stress ◽  
Entropy Production ◽  
Eddy Viscosity ◽  
Reynolds Shear Stress ◽  
Channel Flows ◽  
Alternative Formulation ◽  
Mean Flow ◽  
Turbulent Channel Flows ◽  
Entropy Transport ◽  
New Models

This paper presents new models of entropy production for incompressible turbulent channel flows. A turbulence model is formulated and analyzed with direct numerical simulation (DNS) data. A Reynolds-averaged Navier–Stokes (RANS) approach is used and applied to the turbulence closure of mean and fluctuating variables and entropy production. The expression of the mean entropy production in terms of other mean flow quantities is developed. This paper presents new models of entropy production by incorporating the eddy viscosity into the total shear stress. Also, the Reynolds shear stress is used as an alternative formulation. Solutions of the entropy transport equations are presented and discussed for both laminar and turbulent channel flows.

scholarly journals Compressible turbulent channel flows: DNS results and modelling

1995 ◽  
Vol 305 ◽  
pp. 185-218 ◽  
Author(s):  
P. G. Huang ◽  
G. N. Coleman ◽  
P. Bradshaw
Keyword(s):  
Turbulent Flows ◽  
Pressure Fluctuations ◽  
Channel Flows ◽  
Compressible Turbulence ◽  
Turbulent Shear ◽  
Turbulence Energy ◽  
Mean Flow ◽  
Reynolds Analogy ◽  
The Mean ◽  
Compressibility Effects

The present paper addresses some topical issues in modelling compressible turbulent shear flows. The work is based on direct numerical simulation (DNS) of two supersonic fully developed channel flows between very cold isothermal walls. Detailed decomposition and analysis of terms appearing in the mean momentum and energy equations are presented. The simulation results are used to provide insights into differences between conventional Reynolds and Favre averaging of the mean-flow and turbulent quantities. Study of the turbulence energy budget for the two cases shows that compressibility effects due to turbulent density and pressure fluctuations are insignificant. In particular, the dilatational dissipation and the mean product of the pressure and dilatation fluctuations are very small, contrary to the results of simulations for sheared homogeneous compressible turbulence and to recent proposals for models for general compressible turbulent flows. This provides a possible explanation of why the Van Driest density-weighted transformation (which ignores any true turbulent compressibility effects) is so successful in correlating compressible boundary-layer data. Finally, it is found that the DNS data do not support the strong Reynolds analogy. A more general representation of the analogy is analysed and shown to match the DNS data very well.

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