Excitation of trapped water waves by the forced motion of structures

A numerical and analytical investigation is made into the response of a fluid when a two-dimensional structure is forced to move in a prescribed fashion. The structure is constructed in such a way that it supports a trapped mode at one particular frequency. The fluid motion is assumed to be small and the time-domain equations for linear water-wave theory are solved numerically. In addition, the asymptotic behaviour of the resulting velocity potential is determined analytically from the relationship between the time- and frequency-domain solutions. The trapping structure has two distinct surface-piercing elements and the trapped mode exhibits a vertical ‘pumping’ motion of the fluid between the elements. When the structure is forced to oscillate at the trapped-mode frequency an oscillation which grows in time but decays in space is observed. An oscillatory forcing at a frequency different from that of the trapped mode produces bounded oscillations at both the forcing and the trappedmode frequency. A transient forcing also gives rise to a localized oscillation at the trapped-mode frequency which does not decay with time. Where possible, comparisons are made between the numerical and asymptotic solutions and good agreement is observed. The calculations described above are contrasted with the results from a similar forcing of a pair of semicircular cylinders which intersect the free surface at the same points as the trapping structure. For this second geometry no localized or unbounded oscillations are observed. The trapping structure is then given a sequence of perturbations which transform it into the two semicircular cylinders and the timedomain equations solved for a transient forcing of each structural geometry in the sequence. For small perturbations of the trapping structure, localized oscillations are produced which have a frequency close to that of the trapped mode but with amplitude that decays slowly with time. Estimates of the frequency and the rate of decay of the oscillation are made from the time-domain calculations. These values correspond to the real and imaginary parts of a pole in the complex force coefficient associated with a frequency-domain potential. An estimate of the position of this pole is obtained from calculations of the added mass and damping for the structure and shows good agreement with the time-domain results. Further time-domain calculations for a different trapping structure with more widely spaced elements show a number of interesting features. In particular, a transient forcing leads to persistent oscillations at two distinct frequencies, suggesting that there is either a second trapped mode, or a very lightly damped near-trapped mode. In addition a highly damped pumping mode is identified

The branch structure of embedded trapped modes in two-dimensional waveguides

In this paper we investigate the existence of branches of embedded trapped modes in the vicinity of symmetric obstacles which are placed on the centreline of a twodimensional acoustic waveguide. Modes are sought which are antisymmetric about the centreline of the channel and which have frequencies that are above the first cut-off for antisymmetric wave propagation down the guide. In previous work [1], a procedure for finding such modes was developed and it was shown numerically that a branch of trapped modes exists for an ellipse which starts from a flat plate on the centreline of the guide and terminates with a flat plate perpendicular to the guide walls. In this work we show that further branches of such modes exist for both ellipses and rectangular blocks, each of which starts with a plate of different length on the centreline of the guide. Approximations to the trapped mode wave numbers for rectangular blocks are derived from a two-term matched eigenfunction expansion and these are compared to the results from the numerical scheme described in [1]. The transition from trapped mode to standing wave which occurs at one end of each of the branches is investigated in detail

Trapped modes for off-centre structures in guides

The existence of trapped modes near obstacles in two-dimensional waveguides is well established when the centre-line of the guide is a line of symmetry for the geometry. In this paper we examine cases where no such line of symmetry exists. The boundary condition on the obstacle is of Neumann type and both Neumann and Dirichlet conditions on the guide walls are treated. A variety of techniques (variational methods, boundary integral equations, slender-body theory, modified residue calculus theory) are used to investigate trapped mode phenomena in a number of different frequency bands

Studying the impact of monitoring strategy on disinfection performance evaluation with computational fluid dynamics

Disinfection is a critical process component of drinking water treatment to protect human health. The disinfection performance is highly dependent on the hydraulic efficiency of the disinfection contactor. Accurately evaluating the contactor hydraulic efficiency is important to water treatment plant designers and operators. Tracer analysis is the most used approach for evaluating hydraulic efficiency. Many factors that can impact tracer analysis have been well studied, while the monitoring strategy is not. This study investigates the impact of different monitoring strategies, including single-point, multiple-point, and surface-average monitoring, for hydraulic efficiency evaluation. It is found that: residence time distribution and characteristic times could vary significantly when monitoring two points near to each other, especially at a location with an uneven velocity distribution; the multi-point matrix monitoring approaches proposed in this study could be an alternative to accurately evaluate the contactor hydraulic performance even at the places with an uneven velocity distribution.</p

Deflection curves of buried pipelines under different diameter-thickness ratios.

<p>The deflection curve comes from the displacement of the nodes in the neutral surface for the buried pipeline.</p

Schematic diagram of strata subsidence and pipeline bending deformation.

<p>The red line DC represents the buried pipeline, and it is divided into four sections according to the strata deformation.</p

Out of roundness, longitudinal strain and equivalent plastic strain curves under different subsidence.

<p>Out of roundness <i>k</i>, longitudinal strain <i>ε</i>_x and equivalent plastic strain <i>ε</i>_p change with the increasing of strata subsidence.</p

Cross section shapes of the pipeline before and after failure.

<p>(a) Circular cross section of the new pipeline. (b) Elliptical cross section. (c) Crescent cross section.</p

Bending deformation of buried pipelines under different buried depths.

<p>Deformation of buried pipeline decreases with the increasing of buried depths.</p

Stress-strain curves of X65 and X80.

<p>Relationship of stress and strain of the two buried pipeline materials.</p