We all encounter the flow of liquids and gasses often in our everyday lives. Here at Los
Alamos National Laboratory we are interested in fluid flow for many different reasons.
The Telluride project hopes to answer questions the laboratory has about manufacturing
processes such as metal casting and welding, both of which involve the flow of liquids.

Over 100 years ago the equations that describe the flow of liquids were formulated by
physicists, including Reynolds, Stokes, Euler, and Navier. These equations have
generally become known as the Navier-Stokes Equations. The Truchas code that is being
developed by the Telluride Project uses large computers to find solutions to these
equations using what are know as finite-volume approximations to the Navier-Stokes
equations. Our implementation of these methods allows us to follow the way that fluids
move and change with time, a technique that is called time-dependent simulation.

One of the most interesting aspects of fluid flow that occurs in both casting and welding
processes is that there are sharp fluid interfaces that separate different fluids from one
another. A fluid interface that may be familiar also occurs in the decorative “lava lamps”
that have been popular in homes since the 1960s. These lamps contain two materials,
clear water and a colored waxy material that do not easily mix together. A small bulb sits
in the bottom of the lamp and shines up through the water. The bulb also heats the water
and wax and causes a phenomenon called natural convection due to the change in fluid
density that occurs when it is heated. This natural convection flow causes the water and
wax to change positions in an always varying way that makes watching a lava lamp fun
and interesting. The Truchas computer program uses its finite volume approximations
(and a method called Volume of Fluid) to follow the way that a lava lamp behaves. You
can see an animation of this in our Examples section.

Another phenomena that is important both in the lava lamp and in welding is called
surface tension. This is the physical effect that causes the melted wax to form
approximately spherical blobs as it floats around the interior of the lamp, and for those
blobs to slowly oscillate as they move. Truchas includes special models that help it to
include these kinds of effects in its simulations of welding. Surface tension is greatly
influenced by the temperature of the fluid at the interface. This is seen in the Marangoni
effect that drags fluid parallel to any interface with varying temperatures. This effect is
included in Truchas simulations of welding, for which it can be very important.

When fluid flows there is usually internal friction (called viscosity) that eventually brings
the fluid to rest, unless it is being pushed by some kind of force. This is important in
deciding how quickly fluid sloshing dies out and is included in Truchas simulations of
both welding and metal casting. Viscosity is particularly important in welding because it
resists the acceleration of the metal that is pushed by the heat applied, and therefore
determines the steady speed at which the fluid flows as the weld progresses.

These same fluid flow equations describe many other interesting phenomena, and
Truchas is used by researchers both here at Los Alamos and at Universities and research
laboratories around North America to study such flows as waves breaking on shore
during storms and flows through the cracks in the ground.