User:Nlhw13/sandbox

Schlieren photograph showing the thermal convection plume rising from an ordinary candle in still air. The plume is initially laminar, but transition to turbulence occurs in the upper 1/3 of the image. The image was made using the 1-meter-diameter schlieren mirror of Floviz Inc. by Dr. Gary Settles

In fluid mechanics and transport phenomena , an eddy is not a property of the fluid, but a violent swirling motion caused by the position, direction, and the overall nature of turbulent flow.

The swirling motion of eddies in turbulent flow of a fluid provides a convenient method for mixing multiple fluid streams together.

Reynolds Number and Turbulence

Reynolds number is a unit-less number used to determine when turbulent flow will occur. Conceptually, the Reynolds number is the ratio between inertial forces and viscous forces.

The general form for the Reynolds number flowing through a tube of radius r:

$Re={2v\rho r \over \eta }$

where: ${v}=velocity$

Water flow observed in a pipe, as drawn by Osborne Reynolds in his best-known experiment on fluid dynamics in pipes. Water flows from left to right in the transparent tube, and dye (represented in black) flows in the middle. The nature of the flow (turbulent, laminar) can be observed easily. These drawings were published in Reynolds’ influential 1883 paper "An experimental investigation of the circumstances which determine whether the motion of water in parallel channels shall be direct or sinuous and of the law of resistance in parallel channels".

$\rho =density$

$r=radius$

$\eta =viscosity$

The transition from laminar to turbulent flow in a fluid is defined by the critical Reynolds number:

$Re_{c}\approx 2000$

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

$v_{c}={R_{c}\eta \over \rho r}$

Research and development

A diagram showing the velocity distribution of a fluid moving through a circular pipe, for laminar flow (left), turbulent flow, time-averaged (center), and turbulent flow, instantaneous depiction (right)

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. 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

Using turbulent flow to improve the properties of a golf ball in-flight

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.

Used to thoroughly mix fluids and increase reaction rates within industrial processes.

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. Eddy formations circulate trash and other pollutants into concentrated areas which researchers are tracking to improve clean-up and pollution prevention.

Mesoscale ocean eddies play crucial rolls in transferring heat poleward, as well as maintaining heat gradients at different depths.

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:

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

where

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

Note that that inclusion of ${2 \over 3}\rho \kappa \delta _{i,j}$  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$\kappa$ .

Peer Review

Hey Nlhw13,

Your article seems off to a good start! I would put in a lead section that gives readers a good grasp of the whole article / what eddies are all about. You could add in research and development in the lead. The headings are in a logical order. I would add more sources for each research and development topic so that the article has balanced info on research that's been done (e.g. on hemodynamics or industrial processes). The tone is encyclopedia/objective, and the spelling/grammar is fine. One last thing I recommend doing is finding another source that backs up the source "Why are golf balls dimpled" (from a textbook or journal article) just to be on a safe side.

MissAndrea (talk) 03:52, 14 February 2017 (UTC)

Thank you for your comments and suggestions! I agree with all of your inputs on what could be improved in the article. Nlhw13 (talk) 03:46, 22 February 2017 (UTC)