Chapter 1

Kinematics, thermodynamics and fluid transport properties

Compressible fluid flows have long been a topic of study in the fluid dynamics community. Whether in engineering or geophysical flows, there is probably some mass density change in any physical flow. Many flow situations do exist, however, where such changes can be neglected and the flow considered incompressible. In naturally occurring atmospheric and oceanographic flows, that is geophysical flows, mass density changes are neglected in the mass conservation equation and the velocity field is taken as solenoidal, but are accounted for in the momentum and energy balances. In engineering flows, mass density changes are not neglected in the mass balance and, in addition, are Compressible flow kept in the momentum and energy balances. Underlying the discussion of the fluid dynamics of compressible flows is the need to invoke the concepts of thermodynamics and exploit the relations between such quantities as mass density, pressure and temperature. Such relations, though strictly valid under mechanical and thermal equilibrium conditions, have been found to apply equally well in moving fluids apparently far from the equilibrium state.

Turbulence and turbulent fluid flows have been the focus of research for over 100 years, and whose complete solution still eludes engineers and scientists. In the earlier part of the last century, many theoretical and experimental studies were made involving incompressible turbulence and flows; however, the understanding of even the incompressible problem was incomplete, and the analyses constrained by the techniques available at the time. The study of compressible turbulence and compressible turbulent flows thus merge together two topical areas of fluid dynamics that have been thoroughly investigated but yet remain elusive to complete prediction and control.

Since an important focus of the material will be on engineering aerodynamic flows, it is useful to provide some historical background on the research trends to date. In the 1930s research groups became focused on the study of compressible, high-speed boundary layer flows. This appears to have been motivated by the extensive experimentation with rockets in the late 1920s and 1930s in Europe, Russia and the USA. While such experimentation had been going for about a decade prior to this, much of the fundamental theoretical work was primarily interested in incompressible flows. Prandtl’s lecture notes of the time (see Prandtl and Tietjens, 1934) include a brief section on compressibility, but were predominantly spent on minimizing its effects in practical instances. By the late 1930s and throughout the 1940s extensive work was done on compressible turbulent flows (Frössel, 1938; Frankl and Voishel, 1943). In the 1950s, research in compressible flows was an active topic from both an experimental and a theoretical standpoint, and the fundamental work of this period is of relevance in today’s analysis of turbulent flows.

With the development of high-speed aircraft and the development of manned and unmanned space programs in the second half of the last century, compressible, turbulent flows became a topic for study with wide-ranging international significance. An illustrative example of Crew Exploration Vehicle (CEV) the complexity of the flow fields around manned space vehicles is shown in Fig. 1.1. The shadowgraph figure of an Apollo-like capsule in a Mach 2.2 flow, and Crew Exploration Vehicle-like (CEV-like) capsule in a Mach 1.2, contains the essential ingredients of these flows including: presence of multiple shock waves, separated zones, turbulent boundary layers and wakes, and large-scale structures.

Figure 1.1 Shadowgraph of supersonic flow around space crew modules: (a) Mach 2.2 flow around an Apollo-like capsule at 25 angle-of-attack (sideview Kruse, 1968; Schneider, 2006); (b) Mach 1.2 flow around a CEV-like capsule at −33 angle-of-attack (top view–heat shield pitched down to flow (Brown, Bogdanoff, Yates, and Chapman, 2008, with permission)).

Although aeronautics and space may now be the primary areas where compressible, turbulent flows are relevant, there exists a diverse range of several industrial applications where supersonic flows can be encountered that are not related to aerospace or aeronautics. These applications follow in the same spirit as the first application of the supersonic nozzle to steam turbines by Gustaf de Laval in the 1890s. As another example, in a Recovery boiler recovery boiler where heat is used to produce high-pressure steam, such as in the conversion of wood into wood pulp, Sootblowers sootblowers are used to remove fireside deposits from tube surfaces by blasting the deposits with high-pressure steam jets (Jameel, Cormack, Tran, and Moskal, 1994; Tran, Tandra, and Jones, 2007). Since the steam flow through the sootblower nozzle is compressible and supersonic (see Fig. 1.2(a)), the nozzle characteristics can be optimized to increase the penetration depth (potential core length) of the jet flow while minimizing the use of high-pressure steam in the process. Another example is in the metal processing industry such as in steel production. Supersonic jets inject oxygen gas into the molten bath of electric arc furnaces (EAF) Electric Arc Furnace (EAF) in order to optimize the carbon oxidation. Once again optimized penetration depth (increase of potential core length) of the jet is desired. While both these examples fully exploit all the underlying physics associated with supsersonic jets and nozzle optimization, their introduction into the industrial process is far less intricate than applications associated with aircraft engine designs. Figure 1.2(b)) shows the oxygen injector of an EAF protruding from the wall of the furnace. Sootblowers While crude in appearance it has an important effect on the manufacturing of no less value than the operational characteristics of more sophisticated applications. Supersonic jets In both these examples, fundamental knowledge and use of compressible fluid dynamics significantly improved the operating efficiency of the processes and reduced the associated costs.

Figure 1.2 (a) Schematic use of supersonic jets in sootblower cleaning process (Tran, private communication; Jameel et al., 1994, with permission); (b) nozzle exit of supersonic oxygen jet installed in Electric Arc Furnace (Allemand, Bruchet, Champinot, Melen, and Porzucek, 2001, with permission).