The study of gases in motion. In general, matter exists in any of three states: solid, liquid, or gas. Liquids are incompressible under normal conditions; water is a typical example. In contrast, gases are compressible fluids; that is, their density varies depending on the pressure and temperature. The air surrounding a high-speed aircraft is an example.
Gas dynamics can be treated in a variety of ways. One such way deals with gases as a continuum. The structure of gases on the particle level is called rarefied gas dynamics. See Aerothermodynamics, Compressible flow, Fluid flow
Gases in motion are subject to certain fundamental laws. These are the laws of the conservation of mass, momentum, and energy. In the case of the dynamics of incompressible fluids, it is usually sufficient to satisfy only the laws of conservation of mass and momentum. This distinction constitutes the fundamental difference between high-speed gas dynamics and hydrodynamics. If irreversibilities are involved, a fourth equation called the entropy balance equation may be considered. Whereas mass, momentum, and energy are conserved, the entropy is not. Real problems are irreversible; that is, losses such as friction are involved. However, as a first approximation such effects are generally not considered. See Conservation laws (physics), Conservation of energy, Conservation of mass, Conservation of momentum
The mass, momentum, and energy equations are higher-order, nonlinear equations that have no general solution, and only a limited number of special cases can be solved. Another approach is to resort to numerical solutions using high-speed digital computers. While this approach has proven to be very useful, it limits the degree to which flow phenomena can be conceptualized. Accordingly, it is frequently permissible to write the equations in one-dimensional form. By one-dimensional flow is meant that the properties of gas such as its velocity and density are assumed to be constant in the direction perpendicular to the direction of the gas flow. Generally, the one-dimensional approach gives excellent insights into understanding the physical behavior of the flow. It is also very useful in setting up the computer algorithm for numerical solutions. See Computational fluid dynamics
One other matter must be considered, namely whether the flow is steady or unsteady. In steady flow, the flow characteristics do not vary with time, whereas unsteady flow implies that the flow assumes different configurations over time. Thus, unsteady flow is broader in scope. In this case the continuity equations for conservation of mass may be written as Eq. (1).
If the flow is steady, there is no time-dependent term, and hence the continuity equation can be written in integrated form as Eq. (2), where A denotes the area in the direction perpendicular to the flow direction.
The momentum equation is the mathematical representation of the law of conservation of momentum. It is a statement of the forces acting on the gas. Different types of forces must be recognized. Body forces, such as gravitation and electromagnetic forces, act at a distance. The so-called surface forces may assume different forms, such as normal stresses and viscosity. The simple form of the momentum equation is Eq. (3),
The energy equation expresses the first law of thermodynamics and accounts for the changes in energy as the gas moves about its path. It can also take into consideration energy exchanges between the gas and its environment, such as radiation. Its simplest form is Eq. (4), where cp denotes the specific heat at constant pressure.
The speed of sound or the acoustic velocity is a very important term in gas dynamics because it serves as a criterion to identify flow regimes. Being able to do so is crucial because the designer must know the conditions that the gas will generate or, conversely, experience. In prescribing flow regimes, the flow velocity of the gas is compared with the acoustic velocity. This ratio, called the Mach number (M), is defined by Eq. (5). (5) 
Using the Mach number the following flow regimes are described: 
High-speed aircraft are categorized by the Mach number. See Mach number, Sound
Flows can be classified as internal flow and external flow. Internal flow refers to the cases where the gas is constrained by a duct of some sort. Characteristically external flow is flow over an airplane or missile. Internal flows are conveniently characterized by (1) the shape of the duct and its variation, (2) the heat transfer through the walls of the duct and internal heat sources, and (3) frictional effects. By varying one of these characteristics at a time, the essential features of internal flow can be discussed most simply.
Boundary layers and wakes are the centers of interest in external flows. Here the effects of compressibility are substantially more difficult to analyze than in internal flows, if for no other reason than the inapplicability of a one-dimensional approach. See Boundary-layer flow, Wake flow
Rarefied gas dynamics is that branch of gas dynamics dealing with the flow of gases under conditions where the molecular mean free path is not negligibly small compared to some characteristic dimension of the flow field. Rarefied flows occur when the gas density is extremely low, as in the cases of vacuum systems and high-altitude flight, but also when gases are at normal densities if the characteristic dimension is sufficiently small, as in the case of very small particles suspended in the atmosphere.
The dimensionless parameter which describes the degree of rarefaction existing in a flow is the Knudsen number, Kn = λ/L, defined as the ratio of the mean free path λ to some characteristic dimension L of the flow field. Depending on the situation, L might be chosen, for example, as the diameter of a duct in a vacuum system, the wavelength of a high-frequency sound wave, the diameter of a suspended submicrometer-size particle, the length of a high-altitude rocket, or the thickness of a boundary layer or a shock wave. The mean free path λ, which is the average distance traveled by a gas molecule between successive collisions with other molecules, is equal to the molecular mean speed, given by Eq. (6)
It is convenient to divide rarefied flows into three flow regimes, according to the range of values of the appropriate Knudsen numbers. The regime of highly rarefied flow, which obtains for Kn much greater than 1 (typically greater than 10), is called collisionless or free-molecule flow, while the regime of slight rarefaction, where Kn is much less than 1 (typically less than 0.1), is called slip flow. Flows at Knudsen numbers intermediate to these limiting values are termed transition flows. The phenomena and methods of analysis associated with the three regimes are in general quite dissimilar.
How to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit webmaster's page for free fun content.
| ?Page tools | ||
|---|---|---|
|