What you Should know about CFD...  Software packages for fluid flow and heat transfer analysis come in many forms. At the very least, these packages differ greatly in their physical approximations and numerical solution techniques, which makes the selection of a suitable package a challenging proposition. The following discussion covers some important items to consider when choosing simulation software.

Free Surface Modeling Methods  An interface between a gas and liquid is often referred to as a free surface. The reason for the "free" designation arises from the large difference in the densities of the gas and liquid (e.g., the ratio for water and air is 1000). A low gas density means that its inertia can generally be ignored compared to that of the liquid. In this sense the liquid moves independently, or freely, with respect to the gas. The only influence of the gas is the pressure it exerts on the liquid surface. In other words, the gas-liquid surface is not constrained, but free.

FAVOR™ vs Body Fitted Coordinate Systems  The simplicity of the fractional area/volume method FAVOR™ for modeling complex geometric regions is very attractive. But, can it compete in terms of accuracy with deformed grids such as those employed by finite-element or body-fitted coordinate (BFC) methods? A comparison between these methods, which is the subject of the present note, shows that there are only small differences between the capabilities of the two approaches.

Grid Systems  Persons new to computational modeling may be a little bewildered and even intimidated by the process known as "grid generation." This note offers a short introduction to the most common types of three-dimensional grids with comments on their advantages and disadvantages.

Free Gridding Saves Time  Computational fluid dynamic (CFD) algorithms use a grid of small volume elements in which the average values of flow quantities are stored. In many programs the construction of a suitable grid is a formidable task requiring a considerable investment in time and effort.

No Loss with FAVOR™  In a recent paper Mampaey and Xu (see References) showed how Cartesian grid representations of curved flow channels, using a zigzag approximation for the walls, can result in substantial numerical flow losses. There are two sources for these losses. The first source arises from changes in flow direction at a zigzag in the grid boundary. Each abrupt direction change is accompanied by a small loss in kinetic energy. A second type of flow loss may arise from poor approximations of fluid momentum advection near a zigzag boundary. If the finite-difference algorithm uses velocity data located in solid regions outside the channel, these values generally contribute to a slowing down of the flow, i.e., result in a loss of energy.

Relaxation and Convergence Criteria  Numerical methods used to solve the equations for fluid flow and heat transfer most often employ one or more iteration procedures. By their nature, iterative solution methods require a convergence criteria that is used to decide when the iterations can be terminated.

VOF - What's in a Name?  A free surface is an interface between a liquid and a gas in which the gas can only apply a pressure on the liquid. Free surfaces are generally excellent approximations when the ratio of liquid to gas densities is large, e.g., for air and water the ratio is 1000.

Reynolds Number in CFD  What are the highest and lowest Reynolds number flows that can be accurately computed by a given numerical method? This often asked question has a variety of answers and, as with most technical issues, the variety of answers arises from the assumptions involved in giving the answer.

To Conserve or Not  The mathematical formulation of fluid dynamics is based on a conservation of mass, momentum and energy. Because of this fact, there is a strong motivation to preserve these conservation properties when making numerical approximations. In practice, however, there are many situations where adherence to strict conservation principals is not a good idea. An understanding of those situations provides good insight into the subtleties of numerical approximation. Three examples will serve to illustrate this point.

Pressure Boundary Conditions  The ability to specify a pressure condition at one or more boundaries of a computational region is an important and useful computational tool. Pressure boundaries represent such things as confined reservoirs of fluid, ambient laboratory conditions and applied pressures arising from mechanical devices.

Outflow Boundary Conditions  In many simulations there is a need to have fluid flow out one or more boundaries of the computational region. At such "outflow" boundaries there arises the question of what constitutes a good boundary condition.

What are Artificial and Numerical Viscosities?   The earliest, successful, application of computational fluid dynamics (CFD) was in connection with the Manhattan Project during World War II. Researchers used computations to study the propagation and interaction of shock waves, a subject crucial to the success of the Atomic Bomb.

Selecting a Convergence Criteria  No material is truly incompressible, but this assumption is often a good approximation. When using this assumption in connection with a numerical solution scheme it is necessary to devise some way to impose the physical mechanism that is responsible for the incompressible behavior.

Implicit vs. Explicit Methods   Numerical solution schemes are often referred to as being explicit or implicit. When a direct computation of the dependent variables can be made in terms of known quantities, the computation is said to be explicit. In contrast, when the dependent variables are defined by coupled sets of equations, and either a matrix or iterative technique is needed to obtain the solution, the numerical method is said to be implicit.

The Incompressibility Assumption  All materials, whether gas, liquid or solid exhibit some change in volume when subjected to a compressive stress. The degree of compressibility is measured by a bulk modulus of elasticity, E, defined as either

E=dp/ (dr /r ), or E=dp/(-dV/V),

where dp is a change in pressure and dr or dV is the corresponding change in density or specific volume. Since dp/dr =c², where c is the adiabatic speed of sound, another expression for E is

E =rc².

Lagrangian Particles  Can you imagine a computational fluid dynamics program that simulates the behavior of different materials separated by well-defined interfaces that are subject to arbitrarily large deformations? Can you also imagine this program capturing shock waves, tracking rarefactions, slip surfaces and other non-linear hydrodynamic phenomena?