It can be seen that at higher gain settings (G7-9) the delay line transducer produces a more distorted profile. Profiles measured using the standard transducer did not show any distortion at high gain settings and are therefore not included here. Based on these results the delay line material seems to influence measurements close to the wall interface when too much amplification is employed (e.g. G7-9 setting). This could be due to multiple ultrasonic reflections inside the delay line material, which if amplified, could cause distortion close to the material surface (pipe wall interface). However, the distortion is very noticeable at the wall region and can easily be corrected for by adjusting the amplification gain settings.
4.3. Velocity profiles before and after deconvolution
Since the setup with standard transducers distorts the measured velocity profile physically due to the large cavities present at the wall interfaces, the deconvolution procedure will not be useful for correction of erroneous data at the pipe walls. Therefore all the results obtained using the standard transducer were not deconvolved. Velocity profiles obtained using the delay line transducers are presented before and after implementing the deconvolution procedure. Three different non-Newtonian fluids (CMC, bentonite and kaolin solutions/suspensions) were tested, which yielded a wide range of rheological properties and thus different velocity profile shapes, i.e. power-law and plug flow profiles.
Fig. 11 shows profiles measured in a 16 mm diameter pipe using a standard and delay line transducer for CMC 7% w/w (K = 1.43, n = 0.67) at a bulk flow rate of 0.141 l/s (Re2 = 988). Note the significant distortion of the measured velocity profile (crosses) due to averaging effects across the finite sample volume in the flowing liquid medium (see Section 2.2). A major improvement between the results obtained using the delay line transducer after deconvolution (circles) can be observed. A theoretical velocity profile (Eq. (2), Section 2.1) was also plotted for comparison (using the pipe viscometer data, Section 3.3). The difference in magnitude between the profiles measured using the standard and delay line transducer was due to slight variations in flow during the measurements. Also, note from Fig. 8 that the Doppler angle had to be corrected due the angle refraction caused by the delay line material. After correcting the beam angle variation found with the delay line transducer, the profiles agreed well with that measured using standard transducers with no angle refraction. The most important observation here is the increase in velocity at the pipe wall for the profile measured using the standard transducer (shown by diamonds). Here the effect of the cavity is more pronounced even for a power-law fluid with no yield stress as the diameter of the transducer (8 mm) is half of the pipe diameter (16 mm).