What is Compressible Flow?
This book deals with an introduction to the flow of compressible substances (gases). 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 effect the flow. Though choking occurs in certain pipe flows in astronomy, there also are situations of choking in general (external) flow. Choking is referred to as the situation where downstream conditions, which are beyond a critical value(s), doesn't affect the flow.
The shock wave and choking are not intuitive for most people. However, one has to realize that intuition is really a condition where one uses his past experiences to predict other situations. Here one has to learn to use his intuition as a tool for future use. Thus, not only aeronautic engineers, but other engineers, and even manufacturing engineers will be able use this ``intuition'' in design and even research.
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 above flows 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 external flow.
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 into account.
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 refrigeration systems 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 kind of 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 greater emphasis 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.
Historical Background
in writing this book it became clear that there is more unknown and unwritten about the history of compressible fluid than known. While there are excellent books about the history of fluid mechanics (hydraulic) see for example book by Rouse. There are numerous sources dealing with the history of flight and airplanes (aeronautic). Aeronautics is an overlapping part of compressible flow, however these two fields are different. For example, the Fanno flow and isothermal flow, which are the core of gas dynamics, are not part of aerodynamics. Possible reasons for the lack of written documentation are one, a large part of this knowledge is relatively new, and two, for many early contributors this topic was a side issue. In fact, only one contributor of the three main models of internal compressible flow (Isothermal, Fanno, Rayleigh) was described by any text book. This was Lord Rayleigh, for whom the Rayleigh flow was named. The other two models were, to the undersigned, unknown. Furthermore, this author did not find any reference to isothermal flow model earlier to Shapiro's book. There is no book that describes the history of these models. For instance, the question, who was Fanno, and when did he live, could not be answered by any of the undersigned's colleagues in University of Minnesota or elsewhere.
At this stage there are more questions about the history of compressible flow needing to be answered. Sometimes, these questions will appear in a section with a title but without text or with only a little text. Sometimes, they will appear in a footnote like this For example, it is obvious that Shapiro published the erroneous conclusion that all the chocking occurred at M=1 in his article which contradicts his isothermal model. Additional example, who was the first to ``conclude'' the ``all'' the chocking occurs at M=1 ? Is it Shapiro?
Originally, there was no idea that there are special effects and phenomena of compressible flow. Some researchers even have suggested that compressibility can be ``swallowed'' into the ideal flow (Euler's equation's flow is sometimes referred to as ideal flow). Even before Prandtl's idea of boundary layer appeared, the significant and importance of compressibility emerged.
In the first half of nineteen century there was little realization that the compressibility is important because there were very little applications (if any) that required the understanding of this phenomenon. As there were no motivations to investigate the shock wave or choked flow both were treated as the same, taking compressible flow as if it were incompressible flow.
It must be noted that researchers were interested in the speed of sound even long before applications and knowledge could demand any utilization. The research and interest in the speed of sound was a purely academic interest. The early application in which compressibility has a major effect was with fire arms. The technological improvements in fire arms led to a gun capable of shooting bullets at speeds approaching to the speed of sound. Thus, researchers were aware that the speed of sound is some kind of limit.
In the second half of the nineteen century, Mach and Fliegner ``stumbled'' over the shock wave and choking, respectively. Mach observed shock and Fliegner measured the choking but theoretical science did not provide explanation for it (or was award that there is an explanation for it.).
In the twentieth century the flight industry became the pushing force. Understandably, aerospace engineering played a significant role in the development of this knowledge. Giants like Prandtl and his students like Van Karman , as well as others like Shapiro , dominated the field. During that time, the modern basic classes became ``solidified.'' Contributions by researchers and educators from other fields were not as dominant and significant, so almost all text books in this field are written from an aerodynamic prospective.
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