Lock exchange simulation
Instructors: |
Professor
Randall J. LeVeque Guggenheim 408A tel: 685-3037 rjl@amath.washington.edu |
Professor Peter Schmid
Guggenheim 408K tel: 543-2584 pjs@amath.washington.edu |
Some topics we plan to cover, and other pointers:
Turn on the kitchen faucet and hold a plate in the water stream,
a few inches below the faucet. You should see a roughly circular region on
the surface of the plate where the water flows very rapidly outwards away
from the stream in a very thin layer. This region is bounded by a "hydraulic
jump", where the depth of the water suddenly increases and its speed
abruptly decreases. This is an example of a
shock wave. Note that the location of the jump changes if
you adjust the water volume. This behavior can be predicted by fluid
dynamics. The image shows a computer simulation of such a flow.
Put a thin layer of water in a 9x9 baking pan, add some food coloring, and slosh it back and forth slowly. This gives a nice illustration of wave motion and hydraulic jumps.
Why study sloshing water? While the examples shown here are mostly to illustrate some simple fluid motion, studies of exactly this type of motion are important in designing "Tuned Liquid Dampers". These are simply tanks of water placed on the top of tall buildings or towers to damp vibrations in the structure induced by earthquakes or high winds. The sloshing water exerts a force that damps these vibrations if the size of the container and depth of the water are properly tuned to the expected frequency of vibration.
Research on this topic is being caried out here in the Civil Engineering Department by Professors Dorothy Reed and Harry Yeh and their students, using computational fluid dynamics as well as experiments.
Here's one list of some structues which have such dampers (tuned liquid dampers are at the bottom of the list).
The simplest example of a shock wave can be observed when a traffic light turns red on a road with lots of traffic, particularly if it's foggy out so that drivers can't see beyond the car in front of them. They won't see that traffic has stopped until they come to a sudden stop themselves. The edge of this pileup moves up the highway, against traffic, and marks a sharp jump in the velocity (and also the density) of cars.
Shock waves are an important phenomenon in many types of fluid flow, especially in rapidly moving gases. Think of air molecules as being like cars on a foggy highway. If we shoot air at high speed into a brick wall then a shock wave will result, separating the rapidly moving air from stationary denser air adjacent to the wall. Conversely, if the air is stationary but the wall is moving (or some other object, such as an airplane, is moving through the air), then a shock wave can also arise. An airplane moving at supersonic speed gives rise to a shock wave which propagates far away from the airplane and is known as a sonic boom.
An airplane stays in the air because of the net upward force exerted by the air on the lower surface of the wing (the lift). An airplane flying through the air at several hundred miles per hour has a major impact on the air, and it is not at all easy to predict exactly what forces will result. Small changes in the shape of the wings or body can cause large changes in the lift, and other characteristics which determine how well the plane flies and how much fuel it requires. Although wind tunnels are still essential, computational fluid dynamics is a fundamental tool that is heavily used in designing new airplanes.
A billion flops is called a gigaflop and a trillion is called a teraflop. Note that the fastest machine in the table does about 1.3 teraflops at peak performance.
