Greenwood Margaret Stautberg
Pacific Northwest National Laboratory, P. O. Box 999, Richland, Washington 99352, USA.
Rev Sci Instrum. 2012 Sep;83(9):095101. doi: 10.1063/1.4748520.
The pivotal experiment was performed with a setup in which a plastic cylinder was mounted on the top of a horizontal Rexolite plate and a transducer mounted directly below the cylinder; a single layer of stationary 1588-μm acrylic spheres was placed in the cylinder filled with water. Two well-separated signals were received by the transducer operating in the pulse-echo mode: (1) a signal due to the reflection from water at the interface and (2) a time-delayed signal resulting from the backscattering from the spheres of diameter D. The important observation was that the time delay was equal to 2 D/c using standard notation. A method was developed to use the FFT phase difference between the incident and scattered signals at the interface to determine the time-delay as a function of frequency, the backscattering coefficient M versus frequency, a particle size distribution, and an average value of the diameter. Experimental average diameter results are shown in the square brackets for nominal particle sizes: (1) 1588-μm acrylic spheres [1564 μm], (2) polystyrene spheres for diameters from 200 μm to 500 μm [260 μm-536 μm], (3) suspended slurry of 250-300 μm polystyrene spheres at 2.25 MHz [253 μm], (4) 794 μm [759 μm] and 1588-μm [1623 μm] Teflon spheres, (5) 1588-μm stainless steel spheres [1674 μm], and (6) suspended slurry of 250-300 μm polystyrene spheres [275 μm] at 3.5 MHz for seven volume fractions. Density and particle size measurements were obtained for the latter. For the density measurement, the FFT amplitude of the scattered signal was summed from 2 to 4 MHz for each slurry. A plot of the square root of the FFT-amplitude-sum versus the volume fraction yields a straight line, passing through the origin. A calibration of the experimental setup is obtained by fitting a straight line through the data with error bars. Thus, the volume fraction for a slurry of unknown concentration can be determined by measuring the FFT-amplitude-sum. The density of the slurry is obtained from the volume fraction. These results make it feasible to develop an online and real-time pipeline sensor to measure particle size and slurry density.
一个塑料圆柱体安装在水平的雷索莱特板顶部，一个换能器直接安装在圆柱体下方；在装满水的圆柱体内放置单层静止的1588微米丙烯酸球。换能器以脉冲回波模式工作时接收到两个明显分开的信号：（1）由于界面处水的反射产生的信号，以及（2）由直径为D的球体后向散射产生的延迟信号。重要的观察结果是，使用标准符号时，延迟时间等于2D/c。开发了一种方法，利用界面处入射信号和散射信号之间的快速傅里叶变换（FFT）相位差来确定作为频率函数的延迟时间、后向散射系数M与频率的关系、粒径分布以及直径的平均值。对于标称粒径，实验平均直径结果显示在方括号内：（1）1588微米丙烯酸球[1564微米]，（2）直径为200微米至500微米的聚苯乙烯球[260微米 - 536微米]，（3）2.25兆赫兹下250 - 300微米聚苯乙烯球的悬浮浆料[253微米]，（4）794微米[759微米]和1588微米[1623微米]的聚四氟乙烯球，（5）1588微米不锈钢球[1674微米]，以及（6）3.5兆赫兹下250 - 300微米聚苯乙烯球的悬浮浆料[275微米]，共七种体积分数。对后者进行了密度和粒径测量。对于密度测量，对每种浆料在2至4兆赫兹范围内对散射信号的FFT幅度进行求和。将FFT幅度和的平方根与体积分数作图得到一条过原点的直线。通过用带有误差条的数据拟合一条直线来获得实验装置的校准。因此，通过测量FFT幅度和可以确定未知浓度浆料的体积分数。浆料的密度由体积分数得出。这些结果使得开发一种在线实时管道传感器来测量粒径和浆料密度成为可能。
