Time reversal (TR) of waves is an intriguing wave property that has been found to successfully
address the inverse problem in other scientific fields, such as physics and medicine, and deliver
ground-breaking applications. Waves contain information about their sources and the media
through which they propagate. Thus, TR of measured wave signals has the potential of
localizing and characterizing wave sources and scatterers, as well as inferring the properties of
the medium. This thesis presents the first-ever experimental proof of the time reversibility of
acoustic waves propagating in water-filled viscoelastic HDPE pipes and develops a TR-based
high-resolution methodology for defect detection in pipes, where the probing pressure waves
with wavelengths comparable to the cross-sectional dimensions are employed (i.e., High
Frequency Waves (HFW)). Despite offering superior resolution by virtue of their short
wavelength, HFW in pipes are dispersed and strongly interact with the pipe wall, thus their
implementation is not straightforward. Wave time reversal provides an elegant way to resolve
these intricacies and permits defect localization with a resolution in the order of the probing
wavelength. The proposed TR-based pipe diagnostic method comprises of two distinct steps:
(i) an experimental or physical step that entails the active probing of the defected pipe system
to extract a useful response, and (ii) a theoretical step where the experimentally obtained response is used as input to an inverse problem to detect and localize the defect. Each of these
two steps, that have never been attempted before using HFW in pipes, present their own set of
challenges that this thesis effectively addresses. For instance, real-world water supply pipes are
largely inaccessible; hence, to execute the experimental step a novel lab setup is assembled
where high-frequency pressure transducers are placed within the pipe cavity. In the theoretical
step, the defects are identified and localized by using TR to match the experimentally obtained
response to the analytical model. However, this is a highly ill-posed problem due to the
modelling uncertainties and measurement noise. To minimize modelling errors, this thesis
proposes an impedance-based model where the elastic pipe wall behaviour is approximated
using shell theory assumptions. This model presents a manageable closed-form dispersion
relationship for the coupled fluid/pipe waveguide that affords intuitive analysis, encapsulates
the essential physics, and can be adjusted to a pressure wave solution. The approximate
impedance-based model is validated experimentally on an elastic thin-walled copper and a
viscoelastic thick-walled High-Density Polyethylene (HDPE). For the purpose, the two water-filled
pipes are subjected to a wideband in-pipe acoustic source, and the response is evaluated
in both the fluid and structure domains. Subsequently, the dispersion relationship of the
approximate impedance-based model is checked against both the experimentally derived
dispersion curves and the predictions of a state-of-the-art general model for the two pipes.
Besides, wall displacement solutions are extracted from the impedance-based model and are
used in conjunction with the accelerometer measurements to explain the frequency intervals
where the pipe wall participates the most. Appropriate simplifications to the characteristic
equation of the impedance-based model yield well-known wave speed relations (e.g.,
Korteweg’s equation) that are accurate only under particular frequency ranges. Furthermore,
analysis shows the water hammer wave to be plane only at frequencies 20% of the pipe ring
frequency f

_{ring}. At frequencies that approach f

_{ring} and beyond, the wavefront is no longer plane.
Instead, the pipe wall resonates and executes a “breathing” motion, giving rise to a surface
wave in the fluid that propagates along a small region adjacent to the pipe wall. Lastly, the
proposed impedance-based model is adapted to a pressure wave solution and successfully
tested against the experimental system response to narrowband probing pulses, hence
substantiating its versatility.

To complete the theoretical step of the inverse problem, wave TR presents as an inversion
technique that, if proven, enables the localization of defects. Water supply pipes, however,
present a challenging environment for TR with considerable damping, instabilities, and irregularities. The two mechanisms that are known to restrict time reversal, namely the stability
of wave paths to perturbations and damping, are investigated analytically. Perturbations are
found to grow slowly in time (~ t

^{1/2}) and are not a limiting factor for the time reversal of waves.
To evaluate the effect of damping, an order of magnitude analysis on the non-reversible terms
of the coupled waveguide momentum equations is performed and a dimensionless time reversal
parameter TR is derived to show that damping develops linearly with time (i.e., TR ~ t). The TR parameter is applied to the presented experiments as well as relevant experimental proofs
from the literature to find that the time reversal of waves only holds for TR ~ 1 or less; hence
providing a general criterion to estimate the range over which time reversal-based wave
techniques and methodologies are valid. A TR-based pulse-echo defect detection technique is
proposed to provide a general inverse solution to the theoretical step. The developed closed-form
high-frequency wave-leak interaction solution is formed on the basis of Neumann series
and is experimentally verified on a real leak and small blockage, both localized with
unprecedented accuracy. In fact, it is shown that the developed TR-based technique identifies
defects with a resolution of the order of the minimum wavelength of the injected signal. To
investigate the robustness of the proposed TR-based defect detection method, experiments are
performed under conditions that fundamentally violate traditional time reversal and include
turbulent flow (Re = 40000), or the introduction of inline junctions in the backpropagation
wave path. It is found that flow causes a shift to the refocusing point that is linearly dependent
on the probing frequency, while inline junctions exert severe damping to the propagating
pressure wave. Finally, HF wave propagation over pipe bends is tested experimentally to reveal
that the dispersion relationship is altered substantially compared to an equivalent straight pipe
segment.

Keywords: Wave time reversal, pipe defect detection, fluid-structure interaction, wave-defect
interaction, pressure transients, wave dispersion

## Post a Comment

Your email address will not be published. Required fields are marked *