Eddy (dinámica de fluidos)

The swirling of a fluid and the reverse current created when the fluid is in a turbulent flow regime

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Una calle de vórtice alrededor de un cilindro. Esto puede ocurrir alrededor de cilindros y esferas, para cualquier fluido, tamaño de cilindro y velocidad del fluido, siempre que el flujo tenga un número de Reynolds en el rango de ~ 40 a ~ 1000. ^[1]

En dinámica de fluidos , un remolino es el remolino de un fluido y la corriente inversa creada cuando el fluido está en un régimen de flujo turbulento. ^[2] El fluido en movimiento crea un espacio desprovisto de fluido que fluye corriente abajo en el lado corriente abajo del objeto. El líquido detrás del obstáculo fluye hacia el vacío creando un remolino de líquido en cada borde del obstáculo, seguido de un breve flujo inverso de líquido detrás del obstáculo que fluye corriente arriba, hacia la parte posterior del obstáculo. Este fenómeno se observa naturalmente detrás de grandes rocas emergentes en ríos de corrientes rápidas.

Remolinos y remolinos en ingeniería

La propensión de un fluido a girar se utiliza para promover una buena mezcla de aire y combustible en los motores de combustión interna.

En la mecánica de fluidos y los fenómenos de transporte , un remolino no es una propiedad del fluido, sino un movimiento de remolino violento causado por la posición y dirección del flujo turbulento. ^[3]

Un diagrama que muestra la distribución de la velocidad de un fluido que se mueve a través de una tubería circular, para flujo laminar (izquierda), flujo turbulento, promediado en el tiempo (centro) y flujo turbulento, representación instantánea (derecha)

Número de Reynolds y turbulencia

Experimento de Reynolds (1883). Osborne Reynolds de pie junto a su aparato.

En 1883, el científico Osborne Reynolds realizó un experimento de dinámica de fluidos con agua y tinte, donde ajustó las velocidades de los fluidos y observó la transición de flujo laminar a turbulento, caracterizado por la formación de remolinos y vórtices. ^{[4] El} flujo turbulento se define como el flujo en el que las fuerzas inerciales del sistema son dominantes sobre las fuerzas viscosas. Este fenómeno se describe mediante el número de Reynolds , un número sin unidades que se utiliza para determinar cuándo ocurrirá un flujo turbulento. Conceptualmente, el número de Reynolds es la relación entre las fuerzas inerciales y las fuerzas viscosas. ^[5]

Fotografía de Schlieren que muestra la columna de convección térmica que se eleva desde una vela ordinaria en el aire en calma. La pluma es inicialmente laminar, pero la transición a la turbulencia ocurre en el tercio superior de la imagen. La imagen fue hecha usando un espejo schlieren de un metro de diámetro por Gary Settles.

La forma general del número de Reynolds que fluye a través de un tubo de radio r (o diámetro d):

${\displaystyle \mathrm {Re} ={2v\rho r \over \mu }={\rho vd \over \mu }}$

donde v es la velocidad del fluido, ρ es su densidad , r es el radio del tubo y μ es la viscosidad del fluido. Un flujo turbulento en un fluido se define por el número crítico de Reynolds; para una tubería cerrada, esto equivale aproximadamente a

${\displaystyle \mathrm {Re} _{\text{c}}\approx 2000.}$

In terms of the critical Reynolds number, the critical velocity is represented as

${\displaystyle v_{\text{c}}={\frac {\mathrm {Re} _{\text{c}}\mu }{\rho d}}.}$

Research and development

Computational fluid dynamics

These are turbulence models in which the Reynolds stresses, as obtained from a Reynolds averaging of the Navier–Stokes equations, are modelled by a linear constitutive relationship with the mean flow straining field, as:

${\displaystyle -\rho \langle u_{i}u_{j}\rangle =2\mu _{t}S_{i,j}-{2 \over 3}\rho \kappa \delta _{i,j}}$

where

• ${\displaystyle \mu _{t}}$ is the coefficient termed turbulence "viscosity" (also called the eddy viscosity)
• ${\displaystyle \kappa ={\tfrac {1}{2}}(\langle u_{1}u_{1}\rangle +\langle u_{2}u_{2}\rangle +\langle u_{3}u_{3}\rangle )}$ is the mean turbulent kinetic energy
• ${\displaystyle S_{i,j}}$ is the mean strain rate

Note that that inclusion of ${\displaystyle {\tfrac {2}{3}}\rho \kappa \delta _{i,j}}$ in the linear constitutive relation is required by tensorial algebra purposes when solving for two-equation turbulence models (or any other turbulence model that solves a transport equation for ${\displaystyle \kappa }$ .^[6]

Hemodynamics

Hemodynamics is the study of blood flow in the circulatory system. Blood flow in straight sections of the arterial tree are typically laminar (high, directed wall stress), but branches and curvatures in the system cause turbulent flow.^[2] Turbulent flow in the arterial tree can cause a number of concerning effects, including atherosclerotic lesions, postsurgical neointimal hyperplasia, in-stent restenosis, vein bypass graft failure, transplant vasculopathy, and aortic valve calcification.

Industrial processes

Lift and drag properties of golf balls are customized by the manipulation of dimples along the surface of the ball, allowing for the golf ball to travel further and faster in the air.^[7][8] The data from turbulent-flow phenomena has been used to model different transitions in fluid flow regimes, which are used to thoroughly mix fluids and increase reaction rates within industrial processes.^[9]

Fluid currents and pollution control

Oceanic and atmospheric currents transfer particles, debris, and organisms all across the globe. While the transport of organisms, such as phytoplankton, are essential for the preservation of ecosystems, oil and other pollutants are also mixed in the current flow and can carry pollution far from its origin.^[10][11] Eddy formations circulate trash and other pollutants into concentrated areas which researchers are tracking to improve clean-up and pollution prevention. The distribution and motion of plastics caused by eddy formations in natural water bodies can be predicted using Lagrangian transport models.^[12] Mesoscale ocean eddies play crucial roles in transferring heat poleward, as well as maintaining heat gradients at different depths.^[13]

Environmental flows

Modeling eddy development, as it relates to turbulence and fate transport phenomena, is vital in grasping an understanding of environmental systems. By understanding the transport of both particulate and dissolved solids in environmental flows, scientists and engineers will be able to efficiently formulate remediation strategies for pollution events. Eddy formations play a vital role in the fate and transport of solutes and particles in environmental flows such as in rivers, lakes, oceans, and the atmosphere. Upwelling in stratified coastal estuaries warrant the formation of dynamic eddies which distribute nutrients out from beneath the boundary layer to form plumes.^[14] Shallow waters, such as those along the coast, play a complex role in the transport of nutrients and pollutants due to the proximity of the upper-boundary driven by the wind and the lower-boundary near the bottom of the water body.^[15]

Mesoscale ocean eddies

Downwind of obstacles, in this case, the Madeira and the Canary Islands off the west African coast, eddies create turbulent patterns called vortex streets.

Eddies are common in the ocean, and range in diameter from centimeters to hundreds of kilometers. The smallest scale eddies may last for a matter of seconds, while the larger features may persist for months to years.

Eddies that are between about 10 and 500 km (6.2 and 310.7 miles) in diameter and persist for periods of days to months are known in oceanography as mesoscale eddies.^[16]

Mesoscale eddies can be split into two categories: static eddies, caused by flow around an obstacle (see animation), and transient eddies, caused by baroclinic instability.

When the ocean contains a sea surface height gradient this creates a jet or current, such as the Antarctic Circumpolar Current. This current as part of a baroclinically unstable system meanders and creates eddies (in much the same way as a meandering river forms an ox-bow lake). These types of mesoscale eddies have been observed in many of major ocean currents, including the Gulf Stream, the Agulhas Current, the Kuroshio Current, and the Antarctic Circumpolar Current, amongst others.

Mesoscale ocean eddies are characterized by currents that flow in a roughly circular motion around the center of the eddy. The sense of rotation of these currents may either be cyclonic or anticyclonic (such as Haida Eddies). Oceanic eddies are also usually made of water masses that are different from those outside the eddy. That is, the water within an eddy usually has different temperature and salinity characteristics to the water outside the eddy. There is a direct link between the water mass properties of an eddy and its rotation. Warm eddies rotate anti-cyclonically, while cold eddies rotate cyclonically.

Because eddies may have a vigorous circulation associated with them, they are of concern to naval and commercial operations at sea. Further, because eddies transport anomalously warm or cold water as they move, they have an important influence on heat transport in certain parts of the ocean.

See also

• Eddy diffusion
• Haida Eddies
• Reynolds number - a dimensionless constant used to predict the onset of turbulent flow
• Reynolds experiment
• Kármán vortex street
• Whirlpool
• Whirlwind
• River Eddies in Whitewater
• Wake turbulence
• Computational Fluid Dynamics
• Laminar flow
• Hemodynamics
• Modons, or dipole eddy pairs.

References

1. Tansley, Claire E.; Marshall, David P. (2001). "Flow past a Cylinder on a Plane, with Application to Gulf Stream Separation and the Antarctic Circumpolar Current" (PDF). Journal of Physical Oceanography. 31 (11): 3274–3283. Bibcode:2001JPO....31.3274T. doi:10.1175/1520-0485(2001)031<3274:FPACOA>2.0.CO;2. Archived from the original (PDF) on 2011-04-01.
2. Chiu, Jeng-Jiann; Chien, Shu (2011-01-01). "Effects of Disturbed Flow on Vascular Endothelium: Pathophysiological Basis and Clinical Perspectives". Physiological Reviews. 91 (1): 327–387. doi:10.1152/physrev.00047.2009. ISSN 0031-9333. PMC 3844671. PMID 21248169.
3. Lightfoot, R. Byron Bird ; Warren E. Stewart ; Edwin N. (2002). Transport phenomena (2. ed.). New York, NY [u.a.]: Wiley. ISBN 0-471-41077-2.
4. Kambe, Tsutomu (2007). Elementary Fluid Mechanics. World Scientific Publishing Co. Pte. Ltd. pp. 240. ISBN 978-981-256-416-0.
5. "Pressure". hyperphysics.phy-astr.gsu.edu. Retrieved 2017-02-12.
6. "Linear eddy viscosity models -- CFD-Wiki, the free CFD reference". www.cfd-online.com. Retrieved 2017-02-12.
7. Arnold, Douglas. "The Flight of a Golf Ball" (PDF).
8. "Why are Golf Balls Dimpled?". math.ucr.edu. Retrieved 2017-02-12.
9. Dimotakis, Paul. "The Mixing Transition in Turbulent Flows" (PDF). California Institute of Technology Information Tech Services.
10. "Ocean currents push phytoplankton, and pollution, around the globe faster than thought". Science Daily. 16 April 2016. Retrieved 2017-02-12.
11. "Ocean Pollution". National Oceanic and Atmospheric Administration.
12. Daily, Juliette; Hoffman, Matthew J. (2020-05-01). "Modeling the three-dimensional transport and distribution of multiple microplastic polymer types in Lake Erie". Marine Pollution Bulletin. 154: 111024. doi:10.1016/j.marpolbul.2020.111024. ISSN 0025-326X. PMID 32319887.
13. "Ocean Mesoscale Eddies – Geophysical Fluid Dynamics Laboratory". www.gfdl.noaa.gov. Retrieved 2017-02-12.
14. Chen, Zhaoyun; Jiang, Yuwu; Wang, Jia; Gong, Wenping (2019-07-23). "Influence of a River Plume on Coastal Upwelling Dynamics: Importance of Stratification". Journal of Physical Oceanography. 49 (9): 2345–2363. doi:10.1175/JPO-D-18-0215.1. ISSN 0022-3670.
15. Roman, F.; Stipcich, G.; Armenio, V.; Inghilesi, R.; Corsini, S. (2010-06-01). "Large eddy simulation of mixing in coastal areas". International Journal of Heat and Fluid Flow. Sixth International Symposium on Turbulence and Shear Flow Phenomena. 31 (3): 327–341. doi:10.1016/j.ijheatfluidflow.2010.02.006. ISSN 0142-727X.
16. Tansley, Claire E.; Marshall, David P. (2001). "Flow past a Cylinder on a β Plane, with Application to Gulf Stream Separation and the Antarctic Circumpolar Current". Journal of Physical Oceanography. 31 (11): 3274–3283. Bibcode:2001JPO....31.3274T. doi:10.1175/1520-0485(2001)031<3274:FPACOA>2.0.CO;2. ISSN 1520-0485. S2CID 130455873.