Furthermore it would not be be possible to employ the level of mathematics used

Furthermore it would not be be possible to employ the

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Furthermore, it would not be be possible to employ the level of mathematics used by research mathematicians in their studies of the N.–S. equations. This is generally too difficult, even for graduate students. 1.2.2 Experimental fluid dynamics In a sense, experimental studies in fluid dynamics must be viewed as beginning when our earliest an- cestors began learning to swim, to use logs for trans- portation on rivers and later to develop a myriad as- sortment of containers, vessels, pottery, etc. , for stor- ing liquids and later pouring and using them. Rather obviously, fluid experiments performed today in first- class fluids laboratories are far more sophisticated. Nevertheless, until only very recently the outcome of most fluids experiments was mainly a qualitative (and not quantitative) understanding of fluid motion. An indication of this is provided by the adjacent pictures of wind tunnel experiments. In each of these we are able to discern quite de- tailed qualitative aspects of the flow over different prolate spheroids. Basic flow patterns are evident from colored streaks, even to the point of indications of flow “separation” and transition to turbulence. However, such diagnostics provide no information on actual flow velocity or pressure—the main quantities appearing in the theoretical equations, and needed for engineering analyses. There have long been methods for measuring pressure in a flow field, and these could be used simultaneously with the flow visualization of the above figures to gain some quantitative data. On the other hand, it has been possible to accurately measure flow velocity simultaneously over large areas of a flow field only recently. If point measurements are sufficient, then hot-wire anemometry (HWA) or laser-doppler velocimetry (LDV) can be used; but for field measurements it is necessary to employ some form of particle image velocimetry (PIV). The following figure shows an example of such a measurement for fluid between two co-axial cylinders with the inner one rotating. This corresponds to a two-dimensional slice through a long row of toroidally-shaped (donut- like) flow structures going into and coming out of the plane of the page, i.e. , wrapping around the circumference of the inner cylinder. The arrows indicate flow direction in the plane; the red asterisks show the center of the “vortex,” and the white pluses are locations at which detailed time series of flow velocity also have been recorded. It is clear that this quantitative detail is far superior to the simple visualizations shown in the previous figures, and as a consequence PIV is rapidly becoming the preferred diagnostic in many flow situations. 1.2.3 Computational fluid dynamics We have already noted that CFD is rapidly becoming the dominant flow analysis technique, es- pecially in industrial environments. The reader need only enter “CFD” in the search tool of any web browser to discover its prevalence. CFD codes are available from many commercial vendors
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