We know that fluids are classified as Incompressible and Compressible fluids. Incompressible fluids do not undergo significant changes in density as they flow. In general, liquids are incompressible;water being an excellent example. In contrast compressible fluids do undergo density changes. Gases are generally compressible;air being the most common compressible fluid we can find. Compressibility of gases leads to many interesting features such as shocks, which are absent for incompressible fluids. Gasdynamics is the discipline that studies the flow of compressible fluids and forms an important branch of Fluid Mechanics. In this book we give a broad introduction to the basics of compressible fluid flow.
Though gases are compressible, the density changes they undergo at low speeds may not be considerable. Take air for instance. Fig. 1.2 shows the density changes plotted as a function of Mach Number. Density change is represented as where is the air density at zero speed (i.e., Zero Mach Number).
We observe that for Mach numbers up to 0.3, density changes are within about 5% of . So for all practical purposes one can ignore density changes in this region. But as the Mach Number increases beyond 0.3, changes do become appreciable and at a Mach Number of 1, it is 36.5% . it is interesting to note that at a Mach Number of 2, the density changes are as high as 77%. It follows that air flow can be considered incompressible for Mach Numbers below 0.3.
Another important difference between incompressible and
compressible flows is due to temperature changes. For an
incompressible flow temperature is generally constant. But in a
compressible flow one will see a significant change in temperature
and an exchange between the modes of energy. Consider a flow at a
Mach Number of 2. It has two important modes of energy-Kinetic and
Internal. At this Mach Number, these are of magnitudes 2.3 x
10
A direct consequence of these facts is that while calculating compressible flows energy equation has to be considered (not done for incompressible flows). Further, to handle the exchange in modes of energy one has to understand the thermodynamics of the flow. Accordingly we begin with a review of the concepts in thermodynamics. Thermodynamics is a vast subject. Many great books have been written describing the concepts in it and their application. It is not the intention here to give a detailed treatise than it is to review the basic concepts which hep us understand gasdynamics. Reader is referred to exclusive books on thermodynamics for details.
Subsections
- Compressible Flow
- Equations of Motion for a Compressible Flow
- Isentropic Relations
© Aerospace, Mechanical & Mechatronic
Engg. 2006
University of Sydney |