The year 2007 marks the 50th and 60th anniversaries of two publications in ultrasonics, which probably did not receive much attention when published. One was a doctoral dissertation at the University of Michigan  by a graduate student, J.R. Frederick, who later became a professor there. The other, by a professor in the United Kingdom, was published in Philosophical Magazine . Both publications described ultrasonic pulse methods, new at the time, to measure elastic properties of materials. Neither publication dealt with flow; apparently neither author anticipated flow applications would be derived half a century later from ideas contained in their research. The first paper used pulses in the MHz range. The other used pulses in the 100-kHz range. Some readers will recognize that such frequencies are often used in today’s ultrasonic flowmeters for liquids and gases, respectively. A third paper , published 41 years ago, also should be mentioned, as it too is part of this story.
In brief, these papers described new and improved ways of transmitting ultrasound efficiently in a solid specimen from Point A to Point B, in a way that allows accurate measurement of transit time. In modulus studies, the path is the length of the specimen. In flow applications, which are the focus of our attention here, the path includes the fluid. In contrapropagation flowmeters, time is measured with the flow and against the flow.
Old publications from 1947, 1957, and 1966 might seem unlikely places to search for hints on how to make an ultrasonic flowmeter for accurate measurement of gas or liquid flow, e.g. gas flow at very high temperature and pressure, or liquid flow at cryogenic conditions. However, these three publications could be said to comprise important parts of the scientific and engineering foundation for the buffer waveguide described below and widely used since the late 1990s. By late 2001 more than 1,000 high-temperature ultrasonic gas flowmeters incorporating these buffers had been installed , and the total is likely several thousand today.
Measuring Elastic Moduli via Ultrasonic Pulses
No doubt musicians through the centuries have known that the pitch of their instruments varied with temperature. After this effect was quantitatively associated with elastic moduli, resonance methods evolved for determining moduli as a function of temperature. Resonance methods require measuring resonant frequencies, providing a solution in the frequency domain. (Interference from moisture and other variables needs to be eliminated. This is typically achieved by testing the specimen in a controlled environment, e.g., in vacuum.)
Since no method has all the advantages, it is natural to inquire, what might be the advantages of the corresponding solution in the time domain? For our purposes we can simplify the problem into determining the speed of sound in a short specimen attached to or coupled to a lead-in rod in such a manner that the specimen’s sound speed can be measured at all temperatures of interest, cryogenic, ordinary, or high. Following this line of inquiry in the mid-1940s, Frederick considered the situation depicted in Figure 1. The elastic "lead-in" rod diameter is not small compared to wavelength. This little detail led to problems, which in turn led to solutions that were utilized years later in ultrasonic flowmeters.
Mode Conversion: Longitudinal waves striking the rod’s periphery at grazing incidence generate shear waves by a mode conversion process. Shear waves propagate diagonally at a speed about half that of longitudinal waves towards the opposite side of the rod. Here, they partly reflect as shear and, again due to mode conversion, reflect partly as longitudinal waves. The diagram illustrates the multiple mode conversion process in the lead-in, with the initial longitudinal wave A0 yielding a first reflected longitudinal wave A1 followed by delayed longitudinal waves A2 and A3. Each of the latter two results from shear-to-longitudinal conversions. Angles for the reflected shear wave and the partition of energy between longitudinal and shear depend on incidence conditions, Snell’s Law and σ, analyzed in 1948 by Arenberg . Arenberg’s amplitude ratio graphs are reproduced on pages 226 and 227 in . The net result of the many extra echoes is noise that can obscure the signal. In other words, the reflections, mode conversions, and subsequent reflections create multiple sidewall echoes. These can interfere with timing the signal echoes of interest from a specimen comprising the rightmost portion of this waveguide system, unless, as shown by Frederick , the periphery is altered, for example, by grooving or threading, or properly proportioning the specimen’s dimensions. In  the specimen was sometimes created by notching the lead-in near the end opposite the transducer.
Frederick’s solutions included pressure-coupling using gold foil. Pressure coupling was achieved by clamping the threaded lead-in and specimen together using a nut. In flowmeter parlance we might say he demonstrated by 1947 a high-temperature, clamp-on technique. In many of his experiments the metal specimen temperature reached 815 C. Threaded buffer rods and gold foil coupling reappeared in various high-temperature ultrasonic flowmeter studies in the 1970s. Threaded pressure-coupling, sometimes aided by grease, has been used in thousands of flowmeter applications where a permanent pipe plug is installed in a pipe or spool in a way that accommodates a removable transducer. The "nut" can be part of the plug, adapted to the removable transducer. (Caution must be exercised to safely remove the transducer from the wetted plug, such that the pressure boundary is always maintained leak-tight.)
Adapting ideas and techniques from the magnetostrictive delay line art, Bell avoided sidewall echoes by arranging for the lead-in and specimen diameters to be small compared to wavelength . In this thin-rod case the "longitudinal" wave is often referred to as an extensional wave, and the equation relating its speed to Young’s modulus E is simpler than for ultrasonic waves in thick rods [15, 16]. Bell’s work  led first to process control applications other than flow: temperature sensing starting in the 1960s and liquid level measurement in the 1970s . Although a bundle buffer possibility was recognized and demonstrated by Gelles in 1966 , flow applications did not develop on a large-scale basis until the mid-to-late 1990s .
Out of Many Rods, One Bundle
The motto imprinted on U.S. coins, E pluribus unum, means "out of many, one." These words might also be interpreted as a suggestion to make one bundle out of many waveguides. Another principle taught by a close-packed array of pennies (Figure 5) is that when arranged as shown, each penny is contacted by others only at six or fewer points. Most of the perimeter is free.
In 1966, Gelles  demonstrated pulse echo operation of a fiberoptic bundle and suggested several potential applications. But it was not until the mid-1990s that a practical way was found of packing hundreds of rods whose diameters were sufficiently small compared to wavelength to avoid dispersion into rigid metallurgically sealed enclosures [7, 8]. These designs started with simple welded enclosures, such that radiation was from a flat end. The end was perpendicular to the bundle axis. Later enclosures chamfered the radiating face once or twice, achieving radiation oblique to the bundle axis (Figure 6). Motivation was to allow installation in a nozzle normal to the main pipe or spool axis, with the buffer remaining nonintrusive, i.e., not protruding beyond the inside wall, yet radiating obliquely.
There are other ways to avoid the noise associated with unwanted echoes from sidewall reflections and delayed mode conversions. Approximately 10 years ago a clad waveguide solution became available . This solution, which is one of several clad solutions due to C.-K. Jen and colleagues, may be explained in terms of a similarity to the SOFAR channel in the ocean. The sound speed in the ocean initially decreases with depth because the ocean is colder as one goes down. However, the temperature cannot decrease indefinitely. But as one goes deeper, the pressure continues to increase in proportion to depth, and this leads to an increase in sound speed. Therefore, there is a depth, ~1 km below the ocean surface in middle and equatorial latitudes, at which the sound speed is minimum, with higher speeds above and below . Because of refraction, sound waves bend towards the region of minimum sound velocity. Sound launched in the low-speed SOFAR channel is trapped. Similarly, sound in the clad rod’s slow core is trapped and can’t reach the periphery composed of a fast cladding, so the unwanted reflections and mode conversions shown in Figure 1 are avoided. The clad rod, like the bundle, avoids energy losses due to diffraction or beam spread. The threaded or grooved buffer rod does not avoid these losses, which explains why, if the buffer is long, the SNR (signal to noise ratio) is expected to be better for the clad or the bundle solutions.
Returning to the bundle operated in its dispersive region: the normal (perpendicular) installation idea is represented in Figure 7. One design problem is that as the sound speed c3 in the fluid changes, the sound speed c1 in the bundle must be adjusted to maintain a fixed ratio for c3 /c1, or the beam’s refracted angle in the fluid, Θ3, would change. Figure 4(a) suggests how adjusting the frequency (or wavelength within the rods) can be utilized to adjust c1. Of course, if the nozzle is oblique, the simple nondispersive bundle with radiating flat end perpendicular to its axis may suffice despite the small fluid-filled cavity near the inside wall of the pipe or spool.
In November 2001, it was reported in  that over 1,000 gas flow applications at temperature extremes had been solved using bundled waveguides. In some cases, e.g., at a refinery in the Netherlands, the design temperature was about 500 C. It seems reasonable to estimate that since then, BWT™ bundle waveguide technology buffers have been installed in thousands of additional installations worldwide, for measuring flow of fluids such as air, steam, natural gas, and other gases [13, 14]. Liquids have included hydrocarbons, chemicals, and water, and occasionally, two-phase or multi-phase mixtures. Some liquids are of unusually high viscosity. Liquids are often interrogated using ultrasonic frequencies of 0.5 or 1 MHz. For gas or steam the frequency usually is lower, 200 kHz. The wetted material comprising the radiating portion of the buffer’s enclosure, as well as other parts, is most often SS316L, and optionally, commercially pure Ti. Special metals or alloys have been used when necessary for compatibility with particularly aggressive fluids or to meet NACE or other requirements.
Almost all bundles used in industry have been in contrapropagation flowmeter systems. However, in principle, the bundle buffer may be used with other ultrasonic flow measuring technologies too. Examples: tag , stroboscopic scattering [3, 9], and vortex shedding [9, 14, 18]. Applications in the future might occur with measurands other than flow.
Larry Lynnworth’s work in ultrasonics includes R&D in NDT, elastic moduli measurements at high temperature, and process control, primarily temperature, liquid level, and flow. Mr. Lynnworth has published many papers, seven chapters, and one book . He has 48 U.S. patents, two of which relate to the bundle technology described in this article. After retiring from GE Sensing, Mr. Lynnworth founded Lynnworth Technical Services, a consulting firm. Mr. Lynnworth can be reached at [email protected] or 781 894-2309.
Entire contents of this article are © 2007 Lynnworth Technical Services. This article appeared in the March 2007 print issue of Flow Control magazine, Vol. XIII No. 3, pages 36-43.
1. Arenberg, D.L., Ultrasonic solid delay lines, J Acoust Soc Am 20 (1) 1-26 (1948).
2. J.F.W. Bell, The velocity of sound in metals at high temperatures, Phil. Mag. 2, 1113–1120 (1957).
3. Brown, A.E. and Lynnworth, L., Ultrasonic flowmeters, chap. 20, 515-573 in Spitzer, D.W. (Ed.), Flow Measurement, 2nd Ed., ISA (2001).
4. Frederick, J.R., A Study of the Elastic Properties of Various Solids by Means of Ultrasonic Pulse Techniques, Ph.D. Dissertation, University of Michigan (1947).
5. Gelles, I.L., Optical-fiber ultrasonic delay lines, J Acoust Soc Am 39 (6) 1111–1119 (1966).
6. Jen, C.-K., and Legoux, J.G., Clad ultrasonic waveguides with reduced trailing echoes, US Patent 5,828,274 (1998). (b) —, High performance clad metallic buffer rods, Proc. IEEE Ultrasonics Symp. 771-776 (1996). (c) —, Nguyen, K.T., Ihara, I., and Hébert, H., Novel clad ultrasonic buffer rods for the monitoring of industrial materials processing, Proc. 1st Pan American Conference for Nondestructive Testing (1998) , paper 16 www.ndt.net/article/pac ndt98/16/16.htm.
7. Liu, Y, Lynnworth, L.C. and Zimmerman, M.A. Buffer waveguides for flow measurement in hot fluids, Ultrasonics 36, 305–315 (Feb. 1998).
8. Liu, Y. and Lynnworth, L.C., Ultrasonic path bundle and system, US Patent 5,962,790 (1999); US Patent 6,343,511 (2002).
9. Lynnworth, L.C. Ultrasonic Measurements for Process Control, Academic Press (1989).
10. Lynnworth, L.C., High-temperature flow measurement with wetted and clamp-on ultrasonic sensors, Sensors 16 (10) 36-52 (1999) archives.sen sorsmag.com/articles/1099/36/main.shtml.
11. —, Ultrasonic flow measurement, at ordinary temperatures, using wetted and clamp-on transducers, Flow Control VI (2) 28-37 (2000).
12. —, Measuring flow under tough conditions using ultrasonics, Control Solutions 74 (11) 14-17 (2001).
13. —, Liu, Y., and Umina, J.A., Extensional bundle waveguide techniques for measuring flow of hot fluids, IEEE TUFFC 52 (4) 538-544 (2005); www.david son.com.au/products/flowvelocity/Panametrics/pdf/bwt.pdf; BWT is a trademark of General Electric Co.
14. — and Liu, Y., Ultrasonic flowmeters: Half-century progress report, 1955–2005, Ultrasonics 44 (Supplement 1) e1371-e1378 (22 December 2006); dx.doi.org/10.1016/j.ultras.2006.05.046.
15. —, Waveguides in acoustic sensor systems, Chapter 10, pp. 217-244, in Chen, C.H. (Ed.), Ultrasonic and Advanced Methods for Nondestructive Testing and Material Characterization, World Scientific Publ. Co. (2007 or 2008).
16. Rose, J.L., Ultrasonic Waves in Solid Media, Chapter 11, Cambridge University Press (1999).
17. Spiesberger, J.L. and Metzger, K., Basin-scale ocean monitoring with acoustic thermometers, Oceanography 5 (2) 92-98 (1992).
18. Spitzer, D.W. (Ed.), Flow Measurement, 2nd Edition, ISA (2001), esp. Chapter 20, pp. 530-537.
Professor Joseph L. Rose of Pennsylvania State University supplied the dispersion curve [Fig. 4(a)] for this article.