Interior Fluid Region Research Articles

사각용기의 슬로싱 유동에 관한 연구

The two-dimensional sloshing problem in a rigid rectangular tank with a free surface is considered. The flow is generated by a container in harmonic motion in time along the horizontal axis, i.e., a container excited by u=Asin() where u denotes the container velocity imposed externally, A is the amplitude of the oscillation velocity, and f is the frequency of oscillation. Experimental apparatus is arranged to investigate the large-amplitude sloshing flows in off-resonant conditions, where the large amplitude means that A~O(1), and the distance, S, is comparable to the breadth, L, of the container, i.e., L/S~O(1). Comprehensive particle image velocimetry (PIV) data are obtained, which show that the flow physics of the nonlinear off-resonant sloshing problem can be characterized into three peculiar free surface motions: standing-wave motions similar to those of linear sloshing, a run-up phenomenon along the vertical sidewall at the moment of turn-over of the container, and gradually propagating bore motion from the sidewall to the interior fluid region, like a hydraulic jump.

Dynamic crack propagation in a magneto-electro-elastic solid subjected to mixed loads: Transient Mode-III problem

The transient response of a Mode-III crack propagating in a magneto-electro-elastic solid subjected to mixed loads is investigated through solving the corresponding boundary-initial-value problem in both the cracked solid region and the interior fluid region with treatment of electro-magnetically permeable and impermeable crack face conditions in a unified way. The closed-form results for the dynamic field intensity factors are used to evaluate the dynamic energy release rate through the crack-tip dynamic contour integral. The permeability of the interior fluid region relative to the cracked solid region significantly affects the magneto-electro-mechanical coupling coefficient in the Bleustein–Gulyaev wave function and, consequently, the horizontal shear surface wave speed, the dynamic field intensity factors and the dynamic energy release rate. It is revealed from dynamic fracture mechanics analysis that the dynamic energy release rate thus obtained has an odd dependence on the dynamic electric displacement intensity factor and the dynamic magnetic induction intensity factor. It is also found that the horizontal shear surface wave speed provides the limiting velocity for the propagation of a Mode-III crack in a magneto-electro-elastic solid when there is only applied traction loading.

Wave Trapping by Axisymmetric Concentric Cylinders

It is both a pleasure and privilege to present a paper on the uniqueness of linearized water waves at this mini-symposium in honor of Professor John Wehausen whose classic review article Surface Waves (with E. V. Laitone) has done so much to influence workers in the field in the forty-two years since its publication. The question of the uniqueness of solutions to the linearized water wave equations was settled once and for all in a paper in the Journal of Fluid Mechanics by M. McIver. She constructed a solution for the motion between a pair of fixed rigid surface-piercing cylinders in two dimensions which decayed at large distances from the cylinders. Soon after she was joined by P. McIver in producing an axisymmetric example in the form of a fixed rigid surface-piercing toroid of a special shape which supported an oscillatory motion in its interior fluid region whilst the motion in the exterior region decayed to zero. This wave trapping effect or non-uniqueness occurred for a particular relation between the wave frequency and the toroid geometry. In the present paper we show that such a phenomenon can occur for simple geometries also. In particular we show that wave trapping can occur in the annular region between two partially immersed vertical concentric circular cylindrical shells for particular values of radii and frequencies.

Simplified analytical solutions for wave interaction with absorbing-type caisson breakwaters

Simplified analytical solutions are presented to model the interaction of linear waves with absorbing-type caisson breakwaters, which possess one, or two, perforated or slotted front faces which result in one, or two, interior fluid regions (chambers). The perforated/slotted surfaces are idealized as thin porous plates. Energy dissipation in the interior fluid region(s) inside the breakwater is modelled through a damping function. Under the assumption of potential flow and linear wave theory a boundary-value problem may then be formulated to describe wave interaction with the idealized structure. A solution to this simplified problem may be obtained by an eigenfunction expansion technique and an explicit analytical expression may be obtained for the reflected wave height. Using the experimental work of previous authors, damping coefficients are determined for both single and double chamber absorbing-type caisson breakwaters. Based on the damping for a single perforated-wall breakwater, a methodology is proposed to enable the estimation of the damping coefficients for a breakwater with two chambers. The theoretical predictions of the reflection coefficients for the two-chamber structures using the present model are compared with those obtained from laboratory experiments by other authors. It is found that the inclusion of the damping in the interior fluid region gives rise to improved agreement between theory and experiment.

Water wave interaction with an array of bottom-mounted surface-piercing porous cylinders

The interaction of water waves with arrays of bottom-mounted, surface-piercing circular cylinders is investigated theoretically. The sidewall of each cylinder is porous and thin. Under the assumptions of potential flow and linear wave theory, a semi-analytical solution is obtained by an eigenfunction expansion approach first proposed for impermeable cylinders by Spring and Monkmeyer (1974), and later simplified by Linton and Evans (1990). Analytical expressions are developed for the wave motion in the exterior and all interior fluid regions. Numerical results are presented which illustrate the effects of various wave and structural parameters on the hydrodynamic loads and the diffracted wave field. It is found that the porosity of the structures may result in a significant reduction in both the hydrodynamic loads experienced by the cylinders and the associated wave runup.

Harmonic response of finite cylindrical shells coupled to interior fluid regions.

The effects of internal fluid loading on the harmonic response of finite circular cylindrical shells were investigated. Interior fluid loading on the shell was included via a Green’s function approach for the Newmann boundary value problem. The shells were treated analytically and via finite-element methods. The fluid and structural models were combined and solved using both mobility matrix and eigenfunction expansion approaches. A circular cylindrical shell open at one end (i.e., pressure release) and capped at the opposite end was investigated as a special case. The shell was driven by a force acting on the end cap along the axis of symmetry. A parametric study of this configuration was conducted. An experimental investigation of this configuration was also conducted. Analytical results for the invacuo and fluid-loaded shell response are compared to experimental data. Longitudinal resonances of the interior fluid are clearly evident in the response of the shell.

On the thermal adjustment of an almost-enclosed fluid region with through-flow

The dynamics of a heat-up process in a horizontally enclosed fluid region, with an imposed through-flow and subject to weak thermal forcing, is investigated. Based on a boundary layer approach, a simple one-dimensional model for the interior fluid region is derived. The predicted response of the temperature field agrees well with numerical solutions of the corresponding undegenerate one-dimensional problem. The analytical results are in reasonably close agreement with numerical results presented in a companion paper by Hyun and Hyun ( Int. J. Heat Mass Transfer 29, 1487–1493 (1986)).

A note on the heat-up of an initially isothermal fluid

Let an initially isothermal fluid be subject to an impulsive increase in its ambient temperature with the consequence that the fluid is suddenly heated from its lateral boundaries and flows upwards in thin thermal boundary layers. This flow will start filling up the container and consequently the temperature of the fluid region will increase in time and approach the ambient temperature. A highly idealized model of this process is proposed in this article. The model is based on a separation of the interior fluid region into two regions, each with its own dynamics. One region is isothermal and initially occupies the entire interior. The other region is stratified and expands with time from the top of the container. The position of the interface between the two interior regions is governed by the volume flux in the thermally forced boundary layers. The stratified region fills up the whole container after a certain time whereupon it approaches its new steady-state. The predictions of this model are compared with results from a laboratory experiment and the agreement was found to be fair.