External Fluid Domain Research Articles

Dynamic Response Analysis of a Subsea Rigid M-Shaped Jumper under Combined Internal and External Flows

To analyze the dynamic response of a rigid M-shaped jumper subjected to combined internal and external flows, a one-way coupled fluid–structure interaction process is applied. First, CFD simulations are conducted separately for the internal and external fluid domains. The pressure histories on the inner and outer walls are exported and loaded into the finite element model using inverse distance interpolation. Then, FEA is performed to determine the dynamic response, followed by a fatigue assessment based on the obtained stress data. The displacement, acceleration, and stress distribution along the M-shaped jumper are obtained. External flow velocity dominates the displacements, while internal flow velocity dominates the vibrations and stresses. The structural response to the combined effect of internal and external flows, plus the response to gravity alone, equals the sum of the structural responses to internal flow alone and external flow alone. Fatigue damage is calculated for the bend exhibiting the most intense vibration and higher stress levels, and the locations with significant damage correspond to areas with high maximum von Mises stress. This paper aims to evaluate multiple flow fields acting simultaneously on subsea pipelines and to identify the main factors that provide valuable information for their design, monitoring, and maintenance.

Design of a one-dimensional underwater acoustic leaky wave antenna using an elastic metamaterial waveguide

Acoustic imaging in water traditionally relies on phased arrays of active electro-acoustic transducers to steer acoustic energy in specific directions. One potential alternative approach to steer acoustic beams is to use a single transducer attached to a dispersive antenna that radiates or receives acoustic energy from different directions as the frequency of operation changes. This is known as a leaky wave antenna (LWA). While LWAs have been proven effective in beam steering for electromagnetic and air-borne acoustic waves, the design of an analog device in water presents a unique challenge due to the low contrast in acoustic impedance between elastic solids and water, which necessitates the consideration of fluid-elastic coupling in the design of the elastic LWA. This work presents an approach to design an elastic metamaterial waveguide coupled to an external fluid domain as one means to create an acoustic LWA for underwater operation. Forward-to-backward radiation is achieved through the design of mass-in-cavity structures that produce simultaneous negative effective mass and modulus by considering fluid-elastic coupling. The design is presented through finite element analysis of individual unit cells and a water-loaded elastic LWA. A design example is presented that steers through backfire to endfire as a function of input frequency.

Analysis of water wave interaction with a submerged quarter-circular breakwater using multipole method

This article studies water wave interaction with a submerged quarter-circular breakwater based on potential theory and multipole expansion method. The obliquely and normally incident waves are independently considered. The series solution of velocity potential in the external fluid domain is expressed through the multipole expansions, while the series solution of velocity potential in the quarter-circular internal fluid domain is obtained through the separation of variables. Then, the unknown coefficients in the series solutions are determined by matching the boundary conditions between external and internal fluid domains. The calculation methods for the reflection and transmission coefficients of the submerged quarter-circular breakwater as well as the horizontal and vertical wave forces on the breakwater are presented. The wave forces acting on the submerged breakwater with a seaside quarter-circular-arc and that with a leeside quarter-circular-arc are compared. The hydrodynamic quantities of the submerged quarter-circular breakwater are also compared with those of the submerged semi-circular breakwater. In addition, the effects of breakwater radius, incident frequency, and incident angle on the hydrodynamic quantities of the quarter-circular breakwater are clarified. Valuable results for practical engineering application are drawn.

Coupling Effects of Sloshing and Barge Motion in Variable Bathymetry

Abstract Two partially filled tanks fixed on rectangular barge floating in variable bathymetry is studied based on the linearized potential theory in the frequency domain. The internal sloshing motion is simulated by linearized superposition of natural sloshing modes. The motion of barge is solved by matching eigenfunctions expansion in the external fluid domain. The computational model is verified by experimental results. Coupling sway and roll motions of floating body with different filling levels are compared. The effects of both inclined bottom with different slopes and hump-shaped bottom with different heights are analyzed. Viewing from the results, coupling sway and roll motions of floating body are significantly affected by the shapes of bottoms.

The whipping response of a fluid filled cylindrical shell subjected to an underwater explosion

Fluid filled structure widely exists in the field of ship and ocean engineering, but the investigation concerned with the whipping response of a fluid filled structure subjected to an underwater explosion is very less. A numerical model considering the effect of an internal fluid is established in this paper. In the implementation of the numerical model, the doubly asymptotic approximation for the external fluid is used to model the external fluid domain, the doubly asymptotic approximation for the internal fluid is used to model the internal fluid domain, and the dynamic response of the structure is simulated by the finite element method. After that, the numerical model is validated against the analytical solution. The numerical result agrees well with the analytical result. Finally, the whipping response of a fluid filled cylindrical shell subjected to an underwater explosion is investigated and the influence of the internal fluid on the whipping response is analyzed. The main results are as follows. The existence of the internal fluid makes the maximum relative displacement decrease, as the density of the internal fluid and the sound speed within the internal fluid increase, the maximum of the maximum relative displacement decreases.

Three dimensional non-axisymmetric transient acoustic radiation from an eccentric hollow cylinder

Theoretical analysis and detailed numerical simulations are presented for three-dimensional non-stationary vibroacoustic response of a doubly fluid-loaded infinitely long eccentric hollow elastic circular cylinder of arbitrary wall thickness, under arbitrary non-axisymmetric time-dependent on-surface mechanical drives. The formulation is based on the Navier equations of linear elasticity for the solid material, the wave equation for the internal and external fluid domains, the classical method of separation of variables, and the translational addition theorem for cylindrical wave functions. Laplace transform with respect to the time coordinate, Fourier transform with respect to the axial coordinate, and Fourier series expansion in the circumferential direction, are employed to obtain the transformed solutions in the form of partial-wave expansions of transcendental functions. A set of equally spaced virtual sources are assumed along the axial direction, and semi-analytical solutions are obtained in the Laplace domain as discrete summations of simple two dimensional solutions with different axial wave numbers. Time domain solutions are subsequently calculated by using Durbin’s numerical inverse Laplace transform scheme. The analytical results are illustrated with numerical examples in which air- or water-filled concentric and eccentric steel cylinders, submerged in water, are driven by a pair of equal and opposite external radial point loads of finite duration described by a Ricker pulse. Some interesting features of the transient fluid–solid interaction problem such as the generation of shell-induced circumnavigating waves, appearance of multiple high/low amplitude pressure spots in the internal fluid, and formation of non-propagating evanescent waves in the external fluid are noted using appropriate 2D images of the three dimensional sound fields. Limiting cases are considered and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature.

Electrokinetic Effects on the Transport of Charged Analytes in Biporous Media with Discrete Ion-Permselective Regions

The influence of external electrical fields on local concentration distributions and the mass transport of ionic background (buffer) species, as well as eluting co- and counterionic tracer molecules, was investigated in a fixed bed of native glass beads by confocal laser scanning microscopy and numerical simulations. Due to the negative surface charge of the porous glass beads and significant electrical double layer overlap, the intraparticle mesopore space becomes ion-permselective. This cation selectivity and the externally superimposed electrical fields induce concentration polarization in the bulk electrolyte solution adjacent to the particles. At the anodic hemisphere of a bead, the actual interplay of convection, diffusion, and electromigration leads to the formation of a convective-diffusion boundary layer with reduced ion concentrations relative to the bulk solution. At the opposite, cathodic hemisphere where counterions leave a bead in the direction of the applied field, electrolyte concentrations increase generating an enriched concentration polarization zone. Complementary data from quantitative confocal laser scanning microscopy and numerical simulations provide insight into the spatial variations of chemical and electrical potential gradients in the hierarchically structured material, including molar flux densities of the background ionic species, and reveal the elution dynamics of co- and counterionic analytes. These results demonstrate that concentration polarization in the external fluid domain, as well as the magnitude and sign of electrophoretic with respect to electroosmotic mobility in the ion-permselective domain, are major local contributions to coupled mass and charge transport, reflecting analyte retention, migration, and dispersion on a macroscopic scale.

Finite element modeling of single periodic curved gratings

The analysis of the scattering of a plane acoustic wave by an in-plane periodic, active, or passive structure has been previously performed with the help of the finite element method [A. C. Hladky-Hennion etal., J. Acoust. Soc. Am. 94, 621–635 (1993)]. In that case, the compliant tubes grating is a single periodic structure that is periodic in one direction and infinite in the other one. The method previously described has been extended to take into account the effect of the curvature of the grating, periodic along the symmetry axis. Within this approach, only a bidimensional mesh is needed because the structure is axisymmetrical. Moreover, only one unit cell of the periodic structure, including a small part of the surrounding fluid domain, has to be meshed, due to the use of a classical Block-type relation between the displacement components of points that are separated by the grating spacing. Finally, the effect of the external fluid domain is accounted for by matching the pressure field in the finite element domain to plane waves expressed in terms of a series of Bessel or Hankel functions. This paper describes the general mathematical model and then provides the results obtained for the scattering of a plane wave form simple axisymmetrical structures, this validating the method. Next, the method is applied to the case of curved compliant tubes gratings, thus showing the influence of the curvature.

Excitation of a fluid-filled, submerged spherical shell by a transient acoustic wave

A mathematical formulation and method of solution for the title problem are developed, and numerical results are presented for excitation by a plane step wave. The formulation is based on the familiar equations of motion for a thin spherical shell and the wave equation for the internal and external fluid domains. The Laplace transform is invoked, and the usual separation of variables method produces modal equations for each component of the Fourier–Legendre series solution. The modal equations are then restructured to facilitate transform inversion, yielding delayed differential equations in time for each response mode of the shell-fluid system, which are integrated numerically in time. Complete response solutions then follow by modal superposition, with special techniques being employed to improve modal convergence. Transient response histories are shown for a step-wave-excited steel shell containing water and submerged in water. Also, these results are compared with their counterparts for an empty submerged steel shell.

Modelling of heat transfer by conduction in a transition region between a porous medium and an external fluid

We study the modelling of purely conductive heat transfer between a porous medium and an external fluid within the framework of the volume averaging method. When the temperature field for such a system is classically determined by coupling the macroscopic heat conduction equation in the porous medium domain to the heat conduction equation in the external fluid domain, it is shown that the phase average temperature cannot be predicted without a generally negligible error due to the fact that the boundary conditions at the interface between the two media are specified at the macroscopic level. Afterwards, it is presented an alternative modelling by means of a single equation involving an effective thermal conductivity which is a function of point inside the interfacial region. The theoretical results are illustrated by means of some numerical simulations for a model porous medium. In particular, temperature fields at the microscopic level are presented.

Response of a fluid‐filled spherical shell submerged in an infinite fluid medium to a transient acoustic wave

Transient response problems involving fluid‐filled shell structures submerged in infinite fluid media arise in various fields, including medicine, defense, and materials engineering. A canonical problem of this class possesses a spherical geometry, for which no solutions apparently exist. This paper delineates a relatively simple formulation and method of solution for this canonical problem and presents solutions for excitation by an incident step wave. The formulation begins with the familiar equations of motion for a thin spherical shell and the wave equation for the internal and external fluid domains. The Laplace transform is invoked, and the usual separation of variables method yields modal expressions involving Legendre polynomials and modified spherical Bessel functions. The explicit expressions for the latter are then manipulated to yield, after transform inversion, delayed differential equations in time for each response mode of the shell‐fluid system, which are integrated numerically in time. Complete response solutions then follow by modal superposition, with special techniques being employed to improve modal convergence. To validate the methodology, numerical results are first presented for an incident step wave exciting a shell with mass density and acoustic velocity identical to the corresponding properties characterizing the same internal and external fluid. Results are then shown for a step‐wave‐excited steel shell containing water and submerged in water. [Work supported by DNA.]

Application of the finite element method to the modeling of plane wave scattering from compliant tube gratings at oblique incidence

The modeling of compliant tube gratings has been performed with the help of the finite element method, using the ATILA code [Decarpigny et al., J. Acoust. Soc. Am. 78, 1499–1507 (1985)]. To do this, only the unit cell of the periodic structure, including a small part of the surrounding fluid domain, has to be meshed, due to the use of a classical Bloch‐type relation between the displacement components of points that are separated by the grating spacing. Then, the effect of the external fluid domain is accounted for by matching the pressure field in the finite element domain to simple ingoing and outgoing plane‐wave expressions. This paper describes results obtained for the scattering of a plane wave from different compliant tube gratings, including internal losses, at oblique incidence. First, it shows that a nice agreement has been found between predictions from an analytical model and finite element results for the insertion loss of an infinite elastic plate, thus validating the method. Then it describes the case of cylindrical tube gratings embedded or not in a viscoelastic layer, and shows the effects of low‐stiffness encapsulant on insertion loss curves. Finally, double‐layer gratings with different separations are also considered.