Technology & Engineering
Compressible Fluid
A compressible fluid is a substance, such as gas or vapor, that can be compressed or expanded. Unlike incompressible fluids like water, compressible fluids change in density when subjected to pressure variations. This property is important in various engineering applications, such as in the design of gas turbines, aircraft engines, and pneumatic systems.
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11 Key excerpts on "Compressible Fluid"
eBook - PDF- Patrick H. Oosthuizen, William E. Carscallen(Authors)
- 2013(Publication Date)
- CRC Press(Publisher)
In such cases, it is necessary to study the thermodynam-ics of the flow simultaneously with its dynamics. The study of these flows in which the changes in density and temperature are important is basically what is known as compress-ible fluid flow or gas dynamics , it usually only being in gas flows that compressibility effects are important. The fact that compressibility effects can have a large influence on a fluid flow can be seen by considering the three aircraft shown in Figure 1.1. The first of the aircraft shown in Figure 1.1 is designed for relatively low speed flight. It has straight wings, it is propel-ler driven, and the fuselage (the body of the aircraft) has a “rounded” nose. The second aircraft is designed for higher speeds. It has swept wings and tail surfaces and is powered by turbojet engines. However, the fuselage still has a “rounded” nose and the intakes to the engines also have rounded edges, which are approximately at right angles to the direc-tion of flight. The third aircraft is designed for very-high-speed flight. It has highly swept wings and a sharp nose, and the air intakes to the engines have sharp edges and are of complex shape. These differences between the aircraft are mainly because compressibility effects become increasingly important as the flight speed increases. Although the most obvious applications of Compressible Fluid flow theory are in the design of high speed aircraft, and this remains an important application of the subject, a 2 Introduction to Compressible Fluid Flow (a) (b ) (c) FIGURE 1.1 Aircraft designed to operate at different speeds: (a) De Havilland Canada Dash 8; (b) Canadair CL-600 Regional Jet; (c) Aerospatiale-BAC Concorde. (Courtesy of Eduard Marmet. Airliners.net.) 3 Introduction knowledge of Compressible Fluid flow theory is required in the design and operation of many devices commonly encountered in engineering practice.
- Andrew L. Gerhart, John I. Hochstein, Philip M. Gerhart(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
Fluid compressibility is very important in numerous engineering applications of fluid mechanics. For example, the measurement of high-speed flow velocities requires compressible flow theory. The flows in gas turbine engine components are generally compressible. Many aircraft fly fast enough to encounter compressible flow. The variation of fluid density for compressible flows requires a relationship between density and other fluid properties, especially pressure and temperature. This relationship, the fluid equation of state, often unimportant for incompressible flows, is vital in the anal- ysis of compressible flows. Also, temperature variations for compressible flows are usually significant, and thus the energy equation is necessary. Curious phenomena can occur with compressible flows. For example, we can have fluid acceleration because of friction, fluid deceleration in a converging duct, fluid temperature decrease with heating, and the formation of abrupt discontinuities in flows across which fluid properties change appreciably. For simplicity, in this introductory study of compressibility effects we mainly consider the steady, one-dimensional, constant (including zero) viscosity, compressible flow of an ideal gas. We limit our study to compressibility due to high-speed flow. In this chapter, one- dimensional flow refers to flow involving uniform distributions of fluid properties over any flow cross-sectional area. Both frictionless ( μ = 0 ) and frictional ( μ ≠ 0 ) compressible flows are considered. If the change in density associated with a change of pressure is considered a measure of compressibility, our experience suggests that gases and vapors are much more 582 CHAPTER 11 | Compressible Flow compressible than liquids. We focus our attention on the compressible flow of a gas because such flows occur often.
- Andrew L. Gerhart, John I. Hochstein, Philip M. Gerhart(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
Fluid compressibility is very important in numerous engineering applications of fluid mechanics. For example, the measurement of high-speed flow velocities requires compressible flow theory. The flows in gas turbine engine components are generally compressible. Many aircraft fly fast enough to encounter compressible flow. The variation of fluid density for compressible flows requires a relationship between density and other fluid properties, especially pressure and temperature. This relationship, the fluid equation of state, often unimportant for incompressible flows, is vital in the anal- ysis of compressible flows. Also, temperature variations for compressible flows are usually significant, and thus the energy equation is necessary. Curious phenomena can occur with compressible flows. For example, we can have fluid acceleration because of friction, fluid deceleration in a converging duct, fluid temperature decrease with heating, and the formation of abrupt discontinuities in flows across which fluid properties change appreciably. For simplicity, in this introductory study of compressibility effects we mainly consider the steady, one-dimensional, constant (including zero) viscosity, compressible flow of an ideal gas. We limit our study to compressibility due to high-speed flow. In this chapter, one- dimensional flow refers to flow involving uniform distributions of fluid properties over any flow cross-sectional area. Both frictionless ( μ = 0 ) and frictional ( μ ≠ 0 ) compressible flows are considered. If the change in density associated with a change of pressure is considered a measure of compressibility, our experience suggests that gases and vapors are much more 474 CHAPTER 11 Compressible Flow compressible than liquids. We focus our attention on the compressible flow of a gas because such flows occur often.
- Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
604 11 Most first courses in fluid mechanics concentrate on constant density (incompressible) flows. In earlier chapters of this book, we mainly considered incompressible flow behavior. The model of an inCompressible Fluid is convenient because when constant density and constant (including zero) viscosity are assumed, problem solutions are greatly simplified. Also, fluid incompressibility allows us to build on the Bernoulli equation as was done, for example, in Chapter 5. Examples in Chapters 5–10 should have convinced you that nearly incompressible flows are common in every-day experiences. Any study of fluid mechanics would, however, be incomplete without a brief introduction to compressible flow. Fluid compressibility is very important in numerous engineering applications of fluid mechanics. For example, the measurement of high-speed flow velocities requires compress-ible flow theory. The flows in gas turbine engine components are generally compressible. Many aircraft fly fast enough to encounter compressible flow. The variation of fluid density for compressible flows requires a relationship between density and other fluid properties, especially pressure and temperature. This relationship, the fluid equation of state, often unimportant for incompressible flows, is vital in the analysis of compressible flows. Also, temperature variations for compressible flows are usually significant, and thus the energy equation is necessary. Curious phenomena can occur with compressible flows. For example, we can have fluid acceleration because of friction, fluid deceleration in a converging duct, fluid tempera-ture decrease with heating, and the formation of abrupt discontinuities in flows across which fluid properties change appreciably. After completing this chapter, you should be able to: ■ explain speed of sound and Mach number and their practical significance.
eBook - PDF- Ronald K. McLaughlin, R. Craig McLean, W. John Bonthron(Authors)
- 2016(Publication Date)
- Butterworth-Heinemann(Publisher)
In addition, vaporisa-tion effects are displayed in liquids which have a free surface. These three important characteristics will now be reviewed briefly. 1.2.2 Compressibility All fluids may be compressed by the application of pressure forces. The degree of compressibility of a fluid is characterised by 1 1 2 The Fundamentals of Fluid Flow defining the bulk modulus V K E = -Ap — ΔΙ/' (1.1) Here Ap represents the increase in pressure necessary to decrease a given volume V' by the amount-ΔΙ/'. All liquids have a high value of bulk modulus and are compressible only to a small extent. For example, the bulk modulus of water is quoted as 20.085 x 10 5 kN/m 2 , and thus a decrease of only 0.2% in a given volume requires a pressure increase of In the study of fluid mechanics it is necessary to make the dis-tinction between flows in which compressibility effects may be ignored and flows in which they require to be taken into account. As the change in the density of a liquid with an increase in pres-sure is small even for very large pressure changes, the density of a liquid is consequently taken as constant in most flow situations. The analysis of problems involving liquids is thereby greatly sim-plified. Some exceptions to this general simplification do exist however, and in certain special flow problems the compressibility of liquids is an important factor—as in the case of water-hammer, where the fluid is subjected to a very high rate of velocity change. Unlike liquids, gases are highly compressible. However, in flows where a gas is subjected to relatively small changes in pres-sure (e.g. ventilation and air conditioning systems), the corres-pondingly small density variations are generally ignored and the gas is treated as an inCompressible Fluid. On the other hand, in high-speed flows, where the fluid velocity approaches that at which sound is propagated through the medium, compressibility effects become important and must be taken into account.
eBook - PDF- John Ward-Smith(Author)
- 2018(Publication Date)
- CRC Press(Publisher)
Compressible flow of gases 11 11.1 INTRODUCTION Although all fluids are to some extent compressible, only gases show a marked change of density with a change of pressure or temperature. Even so, there are many examples of the flow of gases in which the density does not change appreciably, and theory relating to constant-density fluids may then adequately describe the phenomena of flow. In this chapter, however, we turn our attention to the flow of gases in which changes of pressure and velocity are associated with significant changes of density. In general, significant changes of density are those greater than a few per cent, although there is no sharp dividing line between flows in which the density changes are important and those in which they are unimportant. Significant density changes in a gas may be expected if the velocity (either of the gas itself or of a body moving through it) approaches or exceeds the speed of propagation of sound through the gas, if the gas is subject to sudden accelerations or if there are very large changes in elevation. This last condition is rarely encountered except in meteorology and so (apart from the references in Chapter 2 to the equilibrium of the atmosphere) is not considered in this book. Because the density of a gas is related to both the pressure and the tem-perature all changes of density involve thermodynamic effects. Account therefore must be taken of changes in internal energy of the gas, and ther-modynamic relations must be satisfied in addition to the laws of motion and continuity. Furthermore, new physical phenomena are encountered. The study of flow in which density varies is thus a good deal more complex than that with constant density. At this stage it is assumed that the reader knows something of thermodynamics, but in the next section a few brief reminders of thermodynamic concepts are provided.
- Xi Jiang, Choi-Hong Lai(Authors)
- 2016(Publication Date)
- CRC Press(Publisher)
185 7 C H A P T E R LES of Compressible Flows A s discussed in chapter 5, compressible flows represent a broad range of fluid flows of relatively high speeds. Although compressibil-ity in liquid fluids is often negligible, there is a situation where the pressure variation in the flow field is large enough to cause substantial changes in the density of the fluid. This is known as the cavitation phenomenon, where the pressure variations in the flow are large enough to cause a phase change. For liquids, whether the incompressible assumption is valid depends on the fluid properties, particularly the pressure and temperature of the fluid and how close they are to the critical pressure and temperature. However, the majority of the practical compressible flows are gas flows. For flow of gases, the compressibility needs to be taken into account at Mach numbers above approximately 0.3. Such compressible flows are of great importance to aerospace engineering and many other high-speed flow applications. Many high-speed flows have Reynolds numbers too high for DNS to be a viable option, given the state of computational power for the next few decades. In many aeronautical applications, DNS remains impossible for practical applications. For instance, the complete aerodynamic computa-tion of transport aircraft wings such as those on an Airbus A300 or Boeing 747 having nominal Reynolds numbers of 40 million (based on the wing chord) at flight conditions are well beyond the limit of DNS. Even for a small aircraft with a dimension greater than 3 meters, moving faster than 72 km/h or 20 m/s with a nominal Reynolds number of the flow above 4 million is out of reach for DNS. In order to solve the entire domain of these real-life flow problems or even if only a small part of the flow, RANS, LES, and detached eddy simulation (DES) as a combination of RANS and LES 186 Numerical Techniques for Direct and Large-Eddy Simulations are a necessity for the foreseeable future.
- Hugh L. Dryden, Theodore Von Karman, Kalinske Anton Adam(Authors)
- 2016(Publication Date)
UNIVERSITY OF PENNSYLVANIA BICENTENNIAL CONFERENCE Problems of Flow in Compressible Fluids By T H E O D O R E V O N K A R M Ä N , PH.D., DR. ING., SC.D.* IN MANY applications of fluid mechanics the assumption of incom-pressibility or constant density of the fluid yields results of sufficient accuracy for practical purposes. In general it is assumed that this approximation is justified if the velocity, density, and pressure changes are relatively small, as, for example, in most problems of practical hydraulics and aeronautics. Often it is stated that the dynamics of inCompressible Fluids will give satisfactory results if the velocities involved in the problem are small in comparison with the velocity of sound. However, if we look over the entire field of fluid mechanics somewhat more carefully, we find that besides the high-speed phenomena there are other cases in which density variation or elasticity of the fluid cannot be neglected. In all, the problems in which compressibility enters as a governing factor can be classified in the following groups: a) Pressure propagation. In an inCompressible Fluid the pressure changes propagate with infinite velocity. Hence, if we are con-cerned with pressure oscillations in fluids, we have to consider the elasticity of the fluid as the factor governing the phenomena, irre-spectively of the magnitude of the velocities or the pressure changes involved. Problems of acoustics, water hammer in pipes, oscilla-tions in gas conduits, engine manifolds, etc., belong in this class of problems. b) Density currents. In the problems belonging in this group we are concerned with a stratified fluid medium, as the atmosphere or water carrying silt. In such problems the velocities and pressure changes caused by the motion may be small, but the phenomena are governed by the gravity field produced by density differences. c) Slow motion of fluids with large density changes.
eBook - PDF- William Graebel(Author)
- 2018(Publication Date)
- CRC Press(Publisher)
447 chapter 9 Compressible Flows Chapter Overview and Goals Compressibility of the fluid in the high-speed flow of gases and liquids introduces a new class of flow effects differing from those we so far have seen. We first introduce the speed of sound and the Mach number. The Mach number is the dimensionless parameter that appears repeatedly throughout this chapter. Compressibility effects in liquids are next studied, including the effect of dissolved gases on the sonic speed and compressibility effects in pipe flow. The thermodynamics of ideal gases is briefly reviewed, and the isentropic flows of these gases is then considered. The possibility of nonisentropic flow regions such as shock waves is introduced, and compressible flow in a nozzle is studied. Nozzle flow offers the possibilities of subsonic, sonic, and supersonic flow existing in the same device, along with the possibility of isolated shock waves. Compressible gas flow in a pipe, where wall friction and/or external heating can be important, is also presented as an illustration of how mechanisms other than area changes can affect the direction in which the Mach number changes. The previous chapters have dealt almost exclusively with constant density flows. Compressibility effects in high-speed flows can cause a dramatically different range of phenomena to appear. These phenomena are important in many physical processes, both in gases and in liquids. In the case of gases we will restrict our attention largely to the flow of ideal gases, for besides being of engineering importance, these flows illustrate with a minimum of mathematics most of the important physics involved with compressible flows. Another feature of compressible flow prompts a note of caution to the student. In incompressible flows we usually deal with pressure differences, and gage pressures can be used.
eBook - PDF- John J. Bertin, Russell M. Cummings(Authors)
- 2021(Publication Date)
- Cambridge University Press(Publisher)
431 8 DYNAMICS OF A COMPRESSIBLE FLOW FIELD Chapter Objectives • Understand the basic thermodynamic concepts that form the basis of high-speed flow theory • Develop a basic physical understanding of the second law of thermodynamics • Be able to use the isentropic flow relationships in analyzing the properties of a flow field • Develop the ability to analyze flow in a stream tube, and understand how a converging-diverging nozzle works • Be able to analyze flow fields using shock and expansion calculation methods • Be able to calculate the local skin-friction coefficient for a compressible boundary layer • Understand the cause and effect of shock/boundary layer and shock/shock interactions • Determine how flight vehicles are tested in wind tunnels, and understand why it is difficult to fully model full-scale flight characteristics So far we have studied the aerodynamic forces for incompressible (constant density) flows past an airplane. At low flight Mach numbers (e.g., below a free-stream Mach number M of approximately 0.3), Bernoulli’s equation [equation (3.10)] provides the 432 Chap. 8 / Dynamics of a Compressible Flow Field relation between the pressure distribution about an aircraft and the local velocity chang- es of the air as it flows around the various components of the vehicle. However, as the flight Mach number increases, changes in the local air density also affect the magnitude of the local static pressure. This leads to discrepancies between the actual aerodynamic forces and those predicted by incompressible flow theory. For our purposes, the Mach number is the parameter that determines the extent to which compressibility effects are important. The purpose of this chapter is to introduce those aspects of compressible flows (i.e., flows in which the density is not constant) that have applications to aerodynamics.
eBook - PDFFlow of Industrial Fluids
Theory and Equations
- Raymond Mulley(Author)
- 2004(Publication Date)
- CRC Press(Publisher)
Acceleration requires energy, and this energy is obtained from the available static energy of the fluid. The result of continued acceleration is more and more energy is required from the available static energy and less and less is available for the conversion process - to overcome the irreversibilities, the losses, the fluid friction. Major difference between compressible and incompressible flow A major difference between compressible and incompressible flow is, with incompressible flow, the pressure at one extreme of the system is always known. The problem resolves itself to computing forward or backward from the known pressure.With compressible flow, it frequently happens that neither the upstream nor the downstream pressure is known.That is to say, the source pressure and the sink pressure may be known, but nei- ther the pressure inside the inlet of a conduit nor inside the discharge are known. A solution to this problem will be given in this chapter. F l o w o f I n d u s t r i a l F l u i d s -T h e o r y a n d E q u a t i o n s 153 I V -3 : USING MODELS C H A P T E R F O U R Models are useful conceptual tools for simplifying analysis and as an aid for performing computations. Ideally, in the industrial situation, the use of a model will produce a reasonable worst-case estimate of the real situa- tion. There are many kinds of models. Some large-scale computer models make use of many simpler smaller-scale models. C o m p r e s s i b l e F l u i d F l o w Equations-of-state Equations-of-state are the primary models relating pressure, temperature, volume and composition of Compressible Fluids. A grasp must be had of the limitations of each equation-of-state. The ideal gas model is the easiest to use, but it is the most inaccurate. It is fair to say that the more accurate the equation-of-state, the more complicated it becomes. Also, the more complicated, the greater the number of parameters needed for its solution.
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