THESIS
2016
xlii, 340 pages : illustrations ; 30 cm
Abstract
Water supply systems (WSS) experience blockages during their life time due to physical
and/or chemical processes (e.g. material deposition, tubercles (rust), scales, plaque, bio-fouling and inadvertently throttled inline valves, and air intrusion). Such blockages result in
wastage of energy and financial resources, reduction in carrying capacity, and increased
potential for contamination. This research investigates the physics of wave-blockage
interaction in WSS by analytical, numerical and experimental means. Both shallow
blockages (i.e., blockages with small radial protrusion) and severe blockages (i.e., blockages
with large radial protrusion) are studied. The principle of action invariance shows that w
m E
m
is conserved for small blockages implying Δw
m / w
m = -ΔE
m / E
m , where...[
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Water supply systems (WSS) experience blockages during their life time due to physical
and/or chemical processes (e.g. material deposition, tubercles (rust), scales, plaque, bio-fouling and inadvertently throttled inline valves, and air intrusion). Such blockages result in
wastage of energy and financial resources, reduction in carrying capacity, and increased
potential for contamination. This research investigates the physics of wave-blockage
interaction in WSS by analytical, numerical and experimental means. Both shallow
blockages (i.e., blockages with small radial protrusion) and severe blockages (i.e., blockages
with large radial protrusion) are studied. The principle of action invariance shows that w
m E
m
is conserved for small blockages implying Δw
m / w
m = -ΔE
m / E
m , where w
m and E
m are the
eigenfrequency and total energy of the m
th mode and Δw
m and ΔE
m its eigenfrequency and
energy shift due to the blockage. The change in energy is shown to be equal to the work of
the radiation pressure during the formation of the blockage. In addition, it is found that a
small blockage reduces the potential energy, but increases the kinetic energy of all modes.
For a severe blockage, the pipe system is decoupled into two independent subsystems: a
subsystem that involves the blockage and another that involves the intact pipe section. The
decoupling is lost when the blockage length is such that the fundamental frequencies of the
two subsystems are close or equal, resulting in resonance which means that waves within the
subsystem involving the blockage are able to penetrate (transmit) to the second subsystem
and vice-versa. It is shown that the assumption of small blockage is applicable when the blockage occupies 30% of the crossectional area. The assumption of severe blockage is
applicable when the blockage occupies 30% of the crossectional area or larger provided that
the decoupling assumption is valid. When the blockage and the remainder of the pipe system
are coupled, perturbation theory is successfully used to derive a simple frequency relation for
the case of a blockage with large radial extent. This study also reveals that Bragg’s resonance
plays a key role where the wave-blockage interaction is minimal for certain frequencies and
maximal for others. The spacing between consecutive Bragg’s resonance frequencies, where
maximal interaction occurs, scales as the wavespeed divided by the blockage length.
Therefore, a wideband frequency of the transient generator is required to capture the
signature of a short blockage. However, the use of high frequency waves (HFW) excites
radial and azimuthal waves and renders the classical one-dimensional water-hammer (WH)
theory invalid. Unlike classical WH theory, the resulting wave field is highly dispersive.
Therefore, this thesis examines and reviews the behaviour of HFW in water-filled pipes and
how they interact with blockages. As a result, a high-order numerical scheme has been
developed and tested. The results show the strong effects of multi-paths on the propagation
of high HFW in WSS and highlight that such waves, althgouh provide the required resolution,
have a low range of detectability. Thus, a double pronged approach, where low frequency
waves are used for reconnaissance and HFW are used for the localization is desirable in the
future.
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