CONCEPT OF GAS DYNAMICS

1.1. Introduction

Gas dynamics mainly concerned with the motion of gases and its effects .It differ from fluid dynamics .Gas dynamics considers thermal or chemical effects while fluid dynamics usually does not.

Gas dynamics deals with the study of compressible flow when it is in motion. It analyses the high speed flows of gases and vapors’ with considering its compressibility. The term gas dynamics is very general and alternative names have been suggested e.g.: Supersonic flow, compressible flow and aero thermodynamics etc.,

1.2. Applications

        Gas dynamics is of interest to both mechanical and the aeronautical engineers but particular field of interest of the two different .It may be said that thermodynamicist is concerned with how an object in motion influenced as it flies through still air. In contrast to it the thermodynamicist in more interested in the cases in which the object in stationary and the fluid is in motion .The applications of gas dynamics are given below.

1.      It is used in Steam and Gas turbines

2.      High speed aero dynamics

3.      Jet and Rocket propulsion

4.      High speed turbo compressor

The fluid dynamics of compressible flow problems which involves the relation between forse, density, velocity and mass etc.Therfore the following laws are frequently used for solving the dynamic problems.

1. Steady flow energy equation

2. Entropy relations

3. Continity equation

4. Momentum equation

1.3. One dimensional flow of a compressible fluid

It is meant that flow parameters changing in one direction only, particularly in direction of flow. In gas dynamics analysis it is necessary to satisfy four equations. These are conservation of mass, energy, Momentum along with the equations of the equation of the state of fluid used. In most practical applications the flow of  a fluid   through a pipe or duct can be approximated to be one dimensional flow and thus the properties can be assumed to vary in one direction only (the direction of flow).As a result , all the properties are assumed to have bulk average values over the cross section. However the values of the properties at a cross section may change with time unless the flow is steady.

The one dimensional-flow approximation has little impact on most properties of a fluid flowing in a pipe or duct such as temperature, pressure and density since these properties usually remain over the cross section .this is not the case of velocity, However, whose values varies from zero at the wall to maximum at the center because of the viscous effect (friction between fluid layers)

1.4. The Kinetic Molecular Theory

The kinetic molecular theory describes the properties of molecules in terms of motion (kinetic energy) and of temperature. The theory is most often applied to gases but is helpful in explaining molecular behavior in all states of matter. As applied to gases, the kinetic molecular theory has the following postulates:

1. Gases are composed of very tiny particles (molecules). The actual volume of these molecules is so small as to be negligible compared with the total volume of the gas sample. A gas sample is, then, mostly empty space. This fact explains the compressibility of gases.
2. There are no attractive forces between the molecules of a gas. This postulate explains why, over a period of time, the molecules of a gas do not cluster together at the bottom of its container.
3. The molecules of a gas are in constant, rapid, random, straight-line motion. This postulate explains why a gas spreads so rapidly through the available space - for example, why the smell of hot coffee can spread quickly from the kitchen throughout the house.
4. During their motion, the gas molecules constantly collide with one another and with the walls of the container. (The collision with the walls provides the pressure exerted by a gas.) None of these collisions is accompanied by any loss of energy; instead, they are what is known as elastic collisions. A "new" tennis ball collides more elastically than a "dead" tennis ball.
5. The average kinetic energy of the molecules in a gas sample is proportional to its temperature (Kelvin) and is independent of the composition of the gas. In other words, at the same temperature, all gases have the same average kinetic energy. It also follows from this postulate that at zero Kelvin all molecular motion has ceased.

These postulates and the experimental evidence for them are summarized in Table

The kinetic molecular theory
Postulate	Evidence
1. Gases are tiny molecules in mostly empty space.	The compressibility of gases.
2. There are no attractive forces between molecules.	Gases do not clump.
3. The molecules move in constant, rapid, random, straight-line motion.	Gases mix rapidly.
4. The molecules collide elastically with container walls and one another.	Gases exert pressure that does not diminish over time.
5. The average kinetic energy of the molecules is proportional to the Kelvin temperature of the sample.	Charles' Law

Clearly, the actual properties of individual gases vary somewhat from these postulates, for their molecules do have a real volume and there is some attraction between the molecules. However, our discussion will ignore these variations and concentrate on an ideal gas, one that behaves according to this model.

   

References

1. Compressible fluid flow  - A. H. Shapiro
2. Fundamentals of compressible flow with aircraft and rocket propulsion   - S. M. Yahya