This image, taken from a direct numerical simulation, shows turbulence in a stably stratified flow in which lighter fluid sits atop a denser fluid. In the image lighter colors represent denser fluid. Turbulence is created by the shear forces caused when the lighter fluid on top moves faster than the denser fluid on the bottom; however the stable stratification will tend to counteract or stabilize the turbulence. Note the vast variety and detail of the scales involved in turbulence; this is what makes it such a difficult process to simulate and model. (Image credit: G. Matheou and D. Chung, NASA/JPL-Caltech)
Tag: CFD
Simulating Turbulence
Turbulent flows are complicated to simulate because of their many scales. The largest eddies in a flow, where energy is generated, can be of the order of meters, while the smallest scales, where energy is dissipated, are of the order of fractions of a millimeter. In Direct Numerical Simulation (DNS), the exact equations governing the flow are solved at all of those scales for every time step–requiring hundreds or thousands of computational hours on supercomputers to solve even a small domain’s worth of flow, as on the airplane wing in the video. Large Eddy Simulation (LES) is another technique that is less computationally expensive; it calculates the larger scales exactly and models the smaller ones. The video shows just how complicated the flow field can look. The red-orange curls seen in much of the flow are hairpin vortices, named for their shape, and commonly found in turbulent boundary layers.
Vortex Shedding from a Hot Cylinder
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)
Supersonic Bullet
[original media no longer available]
This video shows a CFD simulation of a bullet passing through a parallel channel at Mach 2. The simulation captures 3 milliseconds of real-time and shows the Mach number in the top view and the temperature in the bottom view. Note how the bow shock near the front of the bullet and the trailing shock behind it reflect off the walls of the channel and interact. Even though the calculation is inviscid, the shock waves cause intense heating (white) in front of and behind the bullet.
Leapfrogging Vortices
This numerical simulation shows two pairs of vortices interacting in a leap-frogging motion. Another version shows the same situation but with a small perturbation in the rotational alignment that causes even more interesting interactions. Both simulations are of potential flow–an idealized flow without viscosity where velocity can be described as the gradient of a scalar function. The mathematics governing potential flow are notably easier than the full Navier-Stokes equations that govern fluid mechanics. (submitted by jessecaps)
Computational Vortex Rings
Computational fluid dynamics (CFD) sometimes gets a bad rep as “colorful fluid dynamics”, but as computers get faster and faster, more complicated and physically accurate simulations are possible. Shown here are simulations of vortex rings and wingtip vortices in stunningly gorgeous detail. Understanding the evolution of these vortices from a fundamental level helps fluid mechanicians design better methods of controlling them. As mentioned in the video, wingtip vortices are a particularly hazardous everyday example; the time it takes for one plane’s wingtip vortices to disperse determines how quickly the next airplane can take-off or land on that same runway. Being able to break down these vortices faster would allow more frequent use of existing facilities.
Godspeed, Discovery!
The space shuttle, despite three decades of service, remains a triumph of engineering. Although it is nominally a space vehicle, fluid dynamics are vital throughout its operation. From the combustion in the engine to the overexpansion of the exhaust gases; from the turbulent plume of the shuttle’s wake to the life support and waste management systems on orbit, fluid mechanics cannot be escaped. Countless simulations and experiments have helped determine the forces, temperatures, and flight profiles for the vehicle during ascent and re-entry. Experiments have flown as payloads and hundreds of astronauts have “performed experiments in fluid mechanics” in microgravity. Since STS-114, flow transition experiments have even been mounted on the orbiter wing. The effort and love put into making these machines fly is staggering, but all things end. Godspeed to Discovery and her crew on this, her final mission!
Swimming Sandfish Lizards
Sandfish lizards can “swim” through granular flows like sand using an undulating, sinusoidal motion. Having studied this motion, engineers have built a robot that swims similarly through large glass beads and have now created a numerical simulation of the physics that matches the measured forces on the swimmer to within 8%. This type of flow is, in some respects, tougher than actual fluids because individual particles have to followed, while in most of fluid mechanics, we can use the continuum assumption to treat a liquid or gas as a continuous medium. #
Volcanic Turbulence
One of the characteristics of turbulence is its large range of lengthscales. Consider the ash plume from this Japanese volcano. Some of the eddy structures are tens, if not hundreds, of meters in size, yet there is also coherence down to the scale of centimeters. In turbulence, energy cascades from these very large scales to scales small enough that viscosity can dissipate it. This is one of the great challenges in directly calculating or even simply modeling turbulence because no lengthscale can be ignore without affecting the accuracy of the results. #
Colorful Computational Combustion
Many fluid dynamics problems are so complicated that they require supercomputers to calculate the mathematical and physical details. This image shows a computer simulation of a cold ethylene jet combusting in hot air. Different colors indicate different combustion by-products. Researchers use simulations like this one to investigate ideal flames that improve efficiency in applications like cars or jet engines. #
