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 shock waves 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)
Search results for: “density”
The Invisible Forces Behind a Lighter
This high-speed schlieren video reveals the ignition of a butane lighter. The schlieren optical technique exaggerates differences in refractive index caused by density variations, enabling experimentalists to see thermal eddies, shock waves, and other phenomena invisible to the naked eye. Here a jet of butane shoots upward from the lighter as a valve is released. Then the spark from the lighter ignites the butane gas near the bottom of the jet. A flame front the propagates outward and upward, completing the lighting process. (submitted by @Mark_K_Quinn)
Water Balloon Physics
[original media no longer available]
This video explores some of the physics behind the much-loved bursting water balloon. The first sections show some “canonical” cases–dropping water balloons onto a flat rigid surface. In some cases the balloon will bounce and in others it breaks. The bursting water balloons develop strong capillary waves (like ripples) across the upper surface and have some shear-induced deformation of the water surface as the rubber peals away. Then the authors placed a water balloon underwater and vibrated it before bursting it with a pin. They note that the breakdown of the interface between the balloon water and surrounding water shows evidence of Rayleigh-Taylor and Richtmyer-Meshkov instabilities. The Rayleigh-Taylor instability is the mushroom-like formation observed when stratified fluids of differing densities mix, while the Richtmyer-Meshkov instability is associated with the impulsive acceleration of fluids of differing density.
Underwater Plumes
During 2010’s Deepwater Horizon oil spill there were reports of underwater plumes of oil escaping collection. This video demonstrates how such a plume can form. There are two clips shown here; in both the tank is filled with salt water of varying salinity, with denser saltwater at the bottom. The first jet is a green alcohol/water mixture and the second is a red gauge oil. Both jets have the same density and flow rate, but they vary in their Reynolds number. The first turbulent jet gets trapped at the interface between the denser and lighter saltwater while the less turbulent red jet passes the interface with no difficulty. The researchers suggest that strong turbulence can create an emulsion, a mixture of two normally immiscible fluids–imagine shaking a container of oil and vinegar really well–which can lead to underwater trapping.
Convection Visualization
Here on Earth a fascinating form of convection occurs every time we put a pot of water on the stove. As the fluid near the burner warms up, its density decreases compared to the cooler fluid above it. This triggers an instability, causing the cold fluid to drift downward due to gravity while the warm fluid rises. Once the positions are reversed, the formerly cold fluid is being heated by the burner while the formerly hot fluid loses its heat to the air. The process continues, causing the formation of convection cells. The shapes these cells take depend on the fluid and its boundary conditions. For the pot of water on the stove and in the video above, the surface tension of the air/water interface can also play a role in modifying the shapes formed. The effects caused by the temperature gradient are called Rayleigh-Benard convection. The surface tension effects are sometimes called Benard-Marangoni convection.
2D Convection
This simulation shows 2D Rayleigh-Benard convection in which a fluid of uniform initial temperature is heated from below and cooled from above. This is roughly analogous to the situation of placing a pot of water on a hot stovetop. (In the case of the water on the stove, the upper boundary is the water-air interface, while, in the simulation, the upper boundary is modeled as a no-slip (i.e. solid) interface.) The simulation shows contours of temperature (black = cool, white = hot). In general, the hot fluid rises and the cold fluid sinks due to differences in density, but, as the simulation shows, the actual mixing that occurs is far more complex than that simple axiom indicates.
Tank Shock Waves
High-speed video of a tank firing at 18000 fps shows shock waves made visible due to light distortion. When the air density changes (due to temperature or compression), it’s index of refraction changes, causing the background to appear distorted. Most of the video shows the subsonic development of the turbulent exhaust plume. Note the speed at which the exhaust moves relative to the airborne shrapnel. (submitted by Stephan)
Liquid Rope Coiling
Some liquids, when falling in a stream into a pool, tend to coil into a liquid rope. This video shows honey, but the effect can also be observed in syrups and silicone oil. The rate of coiling is dependent on the height from which the liquid falls. Other factors governing coiling include viscosity, density, and flow rate.
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)
Reader Question: Froude vs. Reynolds
@spooferbarnabas asks: I was wondering what the difference is between Froude’s number and Reynold’s number? they seem very similar
Fluid dynamicists often use nondimensional numbers to characterize different flows because it’s possible to find similarity in their behaviors this way. The Reynolds number is the most common of these dimensionless numbers and is equal to (fluid density)*(mean fluid velocity)*(characteristic length)/(fluid dynamic viscosity). The Reynolds number is considered a ratio of total momentum (or inertial forces) to the molecular momentum (or viscous forces). A small Reynolds number indicates a flow dominated by viscosity; whereas a flow with a large Reynolds number is considered one where viscous forces have little effect.
The Froude number, in contrast, focuses on resistance to flow caused by gravitational effects, not molecular effects. It is defined as (mean fluid velocity)/(characteristic wave propagation velocity). Initially, it was developed to describe the resistance of a model floating in water when towed at a given speed. As the boat’s hull moves through the water, it creates a wave that travels forward (and backward in the form of the wake), carrying information about the boat–much like pressure waves travel before and behind a subsonic aircraft. The speed of the wave created by the boat depends on gravity (see shallow water waves). The closer the boat’s speed comes to the water wave’s speed, the greater the resistance the boat experiences. In this respect, the Froude number is actually analogous to the Mach number in compressible fluids.
I hope that helps explain some of the differences!