Fuck Yeah Fluid Dynamics

Celebrating the physics of all that flows. Ask a question, submit a post idea or send an email. You can also follow FYFD on Twitter and Google+. FYFD is written by Nicole Sharp, PhD.

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Posts tagged "cylinder"

A simple cylinder in a steady flow creates a beautiful wake pattern known as a von Karman vortex street. The image above shows several examples of this pattern. Flow is from bottom to top, and the Reynolds number is increasing from left to right. In the experiment, this increasing Reynolds number corresponds to increasing the flow velocity because the cylinder size, fluid, and temperature were all fixed. As the Reynolds number first increases, the cylinder begins to shed vortices. The vortices alternate the side of the cylinder from which they are shed as well as alternating in their sense of rotation (clockwise or counterclockwise). Further increasing the Reynolds number increases the complexity of the wake, with more and more vortices being shed. The vortex street is a beautiful example of how fluid behavior is similar across a range of scales from the laboratory to our planet’s atmosphere.  (Image credit: Z. Trávníček et. al)

Flow over blunt bodies produces a series of alternating vortices that are shed behind an object. The image above shows the turbulent wake of a cylinder, with flow from right to left. Red and blue dyes are used to visualize the flow. This flow structure is known as a von Karman vortex street, named for aerodynamicist Theodore von Karman. The meander of the wake is caused by the shed vortices, each of which has a rotational sense opposite its predecessor. The rapid mixing of the two dyes is a result of the flow’s turbulence. In low Reynolds number laminar cases of this flow the structure of individual vortices is more visible. Similar flow structures are seen behind islands and in the wakes of flapping objects. (Photo credit: K. Manhart et al.)

The von Karman vortex street of shed vortices that form the wake of a stationary cylinder are a classic image of fluid dynamics. Here we see a very different wake structure, also made up of vortices shed from a cylindrical body.  This wake is formed by two identical cylinders, each rotating at the same rotational rate. Their directions of rotation are such that the cylinder surfaces in between the two cylinders move opposite the flow direction (i.e. top cylinder clockwise, bottom anti-clockwise). This results in a symmetric wake, but the symmetry can easily be broken by shifting the rotation rates out of phase. (Photo credit: S. Kumar and B. Gonzalez)

David asks: 

I’m taking an undergraduate fluid dynamics course, and I’m having trouble understanding what a Creeping Flow exactly is. The only thing I understand about that is that the Re should be 0 or close to 0 for the flow… Could you post an example of a creeping flow please? Thank you!

Absolutely! Creeping flow, also called Stokes flow, is, like you said, a very low Reynolds number flow. It would be hard to say that the Reynolds number is zero because that would seem to imply no flow at all. Think of it instead as a Reynolds number much, much less than one. When the Reynolds number is very low, it means that viscous forces are dominating the flow. The video above shows creeping flow around a cylinder; notice how the streamlines stay attached all the way around the surface of the cylinder.  There’s no separation, no turbulent wake, no von Karman vortex street. Viscosity is so dominant here that it’s damped out all of that inertial diffusion of momentum.

We’ve posted some other great examples of creeping flow, as well, though not by that name. There are the reversible laminar flow demos and various experiments in Hele-Shaw cells, all of which qualify as creeping flow because of their highly viscous nature. If you have the time, there’s also a great instructional video from the 1960s called “Low Reynolds Number Flow” (Parts 1, 2, 3, 4) starring G. I. Taylor (a famous fluid dynamicist) that is full of one demo after another.

This numerical simulation shows unsteady supersonic flow (Mach 2) around a circular cylinder. On the right are contours of density, and on the left is entropy viscosity, used for stability in the computations. After the flow starts, the bow shock in front of the cylinder and its reflections off the walls and the shockwaves in the cylinder’s wake relax into a steady-state condition. About halfway through the video, you will notice the von Karman vortex street of alternating vortices shed from the cylinder, much like one sees at low speeds. The simulation is inviscid to simplify the equations, which are solved using tools from the FEniCS project. (Video credit: M. Nazarov)

One common simple form of flow visualization is the smoke-wire technique. A thin wire is coated in oil, then heated. The resulting smoke flows over and around the object of study, providing a useful tracer for the flow. While not necessarily helpful as a quantitative measure, smoke-flow visualization helps researchers get a sense of what is going on in the flow. (Photo credits: TAMU Hypersonics Lab)

This numerical simulation shows vortex shedding behind a hot cylinder. The behavior is very similar to what one sees behind an unheated cylinder, until the coefficient of thermal expansion increases and the von Karman vortex street is completely distorted. Describing the particulars of the computation, jessecaps writes (links added):

I wrote an incompressible flow solver to simulate flow past a heated cylinder. The Navier-Stokes equations are discretized on a Cartesian grid and solved explicitly in time. The pressure-Poisson equation is solved implicitly using a bi-conjugate gradient method. The Boussinesq approximation was used (density is constant everywhere except for the gravity term) to account for buoyancy. Reynolds number = 250, Froude number = 1 (gravity is pointing down). The two simulations show the effect of the coefficient of thermal expansion. Each video shows a plot of velocity and temperature.

(submitted by jessecaps)

The von Karman vortex street is a series of vortices shed periodically in the wake of a bluff body. Although they are commonly observed in the lab behind cylinders, they also occur in nature, as seen here in the wake of Juan Fernandez Islands near Chile. The strong equatorward wind creates steady flow over the mountainous island, creating a pattern in the clouds that stretches 10,000 times longer than vortex streets created in a laboratory. (via freshphotons)

A flow visualization behind a cylinder shows the formation of a von Karman vortex street. The frequency of vortex shedding in the wake is directly related to the speed of the airflow—the higher the velocity, the faster vortices will shed from the cylinder. This relationship is expressed in the Strouhal number, which remains constant for any cylinder. (via freshphotons)