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

# Furthermore it would not be be possible to employ the

• 164

This preview shows page 12 - 13 out of 164 pages.

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

#### You've reached the end of your free preview.

Want to read all 164 pages?

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern