Compressible Flow

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Compressible Flow The main difference between compressible flow and almost incompressible flow is not the fact that compressibility has to be considered. Rather, the difference is in two phenomena that do not exist in incompressible flow. The first phenomenon is the very sharp discontinuity (jump) in the flow in properties. The second phenomenon is the choking of the flow. Choking is when downstream variations don't affect the flow. Though choking occurs in certain pipe flows in astronomy, there
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  Compressible Flow The main difference between compressible flow and almost incompressible flowis not the fact that compressibility has to be considered. Rather, the difference isin two phenomena that do not exist in incompressible flow. The firstphenomenon is the very sharp discontinuity (jump) in the flow in properties. Thesecond phenomenon is the choking of the flow. Choking is when downstreamvariations don't affect the flow. Though choking occurs in certain pipe flows inastronomy, there also are situations of choking in general (external) flow. Chokingis referred to as the situation where downstream conditions, which are beyond acritical value(s), doesn't affect the flow.The shock wave and choking are not intuitive for most people. However, one hasto realize that intuition is really a condition where one uses his past experiencesto predict other situations. Here one has to learn to use his intuition as a tool forfuture use. Thus, not only aeronautic engineers, but other engineers, and evenmanufacturing engineers will be able use this ``intuition'' in design and evenresearch. Why Compressible Flow is Important? Compressible flow appears in many natural and many technological processes.   Compressible flow deals with more than air, including steam, natural gas, nitrogen   and helium, etc. For instance, the flow of natural gas in a pipe system, a common   method of heating in the U.S., should be considered a compressible flow. These   processes include the flow of gas in the exhaust system of an internal combustion   engine, and also gas turbine, a problem that led to the Fanno flow model. The aboveflows that were mentioned are called internal flows. Compressible flow also includes   flow around bodies such as the wings of an airplane, and is considered an externalflow.These processes include situations not expected to have a compressible flow, such as   manufacturing process such as the die casting, injection molding. The die casting   process is a process in which liquid metal, mostly aluminum, is injected into a mold to   obtain a near final shape. The air is displaced by the liquid metal in a very rapid   manner, in a matter of milliseconds; therefore the compressibility has to be taken intoaccount.Clearly, Aero Engineers are not the only ones who have to deal with some aspect of compressible flow. For manufacturing engineers there are many situations where the  compressibility or compressible flow understating is essential for adequate design. For   instance, the control engineers who are using pneumatic systems use compressed   substances. The cooling of some manufacturing systems and design of refrigerationsystems also utilizes compressed air flow knowledge. Some aspects of these systems   require consideration of the unique phenomena of compressible flow.Traditionally, most gas dynamics (compressible flow) classes deal mostly with shock    waves and external flow and briefly teach Fanno flows and Rayleigh flows (two kindof choking flows). There are very few courses that deal with isothermal flow. In fact,many books on compressible flow ignore the isothermal flow. In this book, a greateremphasis is on the internal flow. This doesn't in any way meant that the important   topics such as shock wave and oblique shock wave should be neglected. This book    contains several chapters which deal with external flow as well. Choking Flow The schematic of deLavel's turbine after Stodola, Steam and Gas Turbine The choking problem is almost unique to gas dynamics and has many differentforms. Choking wasn't clearly to be observed, even when researcher stumbledover it. No one was looking for or expecting the choking to occur, and when it wasfound the significance of the choking phenomenon was not clear. The firstexperimental choking phenomenon was discovered by Fliegner's experimentswhich were conducted sometime in the middle of 186x on air flow through aconverging nozzle. As a result deLavel's nozzle was invented by Carl Gustaf Patrikde Laval in 1882 and first successful operation by another inventor (Curtis) 1896  used in steam turbine. Yet, there was no realization that the flow is choked justthat the flow moves faster than speed of sound.The introduction of the steam engine and other thermodynamics cycles led to thechoking problem. The problem was introduced because people wanted toincrease the output of the Engine by increasing the flames (larger heat transfer orlarger energy) which failed, leading to the study and development of Rayleighflow. According the thermodynamics theory (various cycles) the larger heatsupply for a given temperature difference (larger higher temperature) the largerthe output, but after a certain point it did matter (because the steam waschoked). The first to discover (try to explain) the choking phenomenon wasRayleigh.After the introduction of the deLavel's converging-diverging nozzle theoreticalwork was started by Zeuner. Later continue by Prandtl's group starting 1904. In1908 Meyer has extend this work to make two dimensional calculations.Experimental work by Parenty and others measured the pressure along theconverging-diverging nozzle.It was commonly believed that the choking occurs only at M=1 . The first one toanalyzed that choking occurs at for isothermal flow was Shapiro (195x). It isso strange that a giant like Shapiro did not realize his model on isothermalcontradict his conclusion from his own famous paper. Later Romer at el extendedit to isothermal variable area flow (1955). In this book, this author adaptsE.R.G. Ecert's idea of dimensionless parameters control which determines wherethe reality lay between the two extremes. Recently this concept was proposed(not explicitly) by Dutton and Converdill (1997). Namely, in many cases the realityis somewhere between the adiabatic and the isothermal flow. The actual resultswill be determined by the modified Eckert number to which model they arecloser.    Figure:   The measured pressure in a nozzle taken from Stodola 1927 Steam and Gas Turbines   Fanno flow Fanno flow refers to adiabatic flow through a constant area duct where the effect of  friction is considered. Compressibility effects often come into consideration, although the Fanno flow model certainly also applies to incompressible flow.For this model, the duct area remains constant, the flow is assumed to be steady andone-dimensional, and no mass is added within the duct. The Fanno flow model isconsidered an irreversible process due to viscous effects. The viscous frictioncauses the flow properties to change along the duct. The frictional effect ismodeled as a shear stress at the wall acting on the fluid with uniform propertiesover any cross section of the duct.For a flow with an upstream Mach number greater than 1.0 in a sufficiently long enough duct, deceleration occurs and the flow can become choked.On the other hand, for a flow with an upstream Mach number less than 1.0, acceleration occursand the flow can become choked in a sufficiently long duct. It can be shown that
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