Main effects on the accuracy of Pulsed-Ultrasound-Doppler-Velocimetry in the presence of rigid impermeable walls

Abstract

Walls bounding the flow applications under consideration influence the accuracy of Pulsed-Ultrasound-Doppler-Velocimetry (PUDV) by changing the shape of the acoustic beam, the propagation of the ultrasonic burst and the intensity distribution of the returning echo. Based on measurements of the acoustic beam shape and echo intensity distribution, the main effects on the accuracy of PUDV are identified and analyzed in the presence of rigid impermeable walls. Reviewing the main effects of (i) system control parameters and (ii) beam propagation on the accuracy of velocity field measurements using PUDV, we focus on investigating the main effects of (iii) shape of the beam and (iv) echo intensity. Finally, the main effects on the accuracy of PUDV in the presence of rigid impermeable walls are discussed and summarized.

Introduction

Ultrasound Doppler Velocimetry (UDV) has originally been applied in the medical field and dates back to more than 60 years. The use of pulsed emissions in Pulsed Ultrasound Doppler Velocimetry (PUDV) has extended UDV to other fields and has opened the way to new measuring techniques in fluid dynamics. More recently, PUDV was applied to study fluid flow by various investigators, such as Alfonsi et al. [1], Brito et al. [2], Eckert and Gerbeth [3], Garbini et al. [5], Kikura et al. [9], [10], Takeda [14], [15], [16], Wells [17], as well as Xu and Aidun [19]. In the majority of these studies, the emitted acoustic field and the returning echo propagate through a wall.

For example, to non-intrusively measure flow of fiber suspension through a channel, Xu and Aidun [19] place the PUDV transducer at the outside surface of the Plexiglas wall, as shown in Fig. 1. In this typical setup, several factors related to the presence of a wall influence the measurements. Some have been identified and reported by Brito et al. [2], Kagivama et al. [8], Kikura et al. [10], Wunderlich and Brunn [18], as well as Xu and Aidun [19]. However, comprehensive analysis of the interference of the beam with the wall and the impact on the accuracy of the results are missing from past studies.

Compared to Laser Doppler Velocimetry (LDV), a well-known and accepted non-invasive flow velocity measurement device, the main advantage of PUDV is to offer spatial information associated with velocity values instantaneously in opaque liquids where LDV or any other optical method can not be applied. Since LDV makes velocity measurements when particles seeded in the flow pass through an interference pattern created by the intersection of a pair of laser beams, a wall may refract the beam but it does not affect the spatial resolution of LDV. In PUDV on the other hand, a wall not only refracts the beam but it also influences the ultrasonic beam shape and therefore the spatial resolution of the system.

Therefore, the accuracy of the measured velocity field using PUDV not only depends on the system’s control parameters but also on the propagation and shape of the acoustic beam through the flow field as well as the intensity of the echo from the incident particles in the sample volume where velocity is being measured, which have not been discussed in the literature. The propagation and shape of the beam as well as the echo intensity of the beam vary depending on the frequency and diameter of the emitter as well as the characteristics of the acoustic interfaces encountered by the beam.

Reviewing the effect of (i) system control parameters, in Section 3.1, and (ii) beam propagation, in Section 3.2, on the accuracy of velocity field measurements using PUDV, we focus on investigating the (iii) shape of the beam, in Section 3.3, and (iv) echo intensity, in Section 3.4. Thereby, we examine main effects on the accuracy of velocity field measurements with PUDV in the presence of rigid impermeable walls. Based on ultrasonic beam shape and echo intensity measurements described in Section 2, we provide a thorough examination and analysis of errors introduced by system control factors and wall effects in Section 3. Since application of PUDV for velocity measurements almost always involves the propagation of the emitted acoustic field and the returning echo through a wall, the aim of this study is to identify the main effects on the accuracy of the velocity field measurements with PUDV in the presence of rigid impermeable walls.