Near-field Formulation Research Articles

Semi-analytic solutions to edge singularities of three-dimensional axisymmetric bodies

Axisymmetric geometries, such as cylindrical elements, are widely used in offshore structures. However, the presence of sharp edges in these geometries introduces challenges in numerical simulations due to singularities. To address this issue, one possible solution is to represent the singularities using analytic eigenfunctions. This approach can provide insights into the essence of the problem and has successfully applied to two-dimensional (2D) corner problems. However, finding appropriate eigenfunctions for the three-dimensional (3D) edges remains an open challenge. This paper proposes a semi-analytic scheme for 3D axisymmetric problems utilizing a scaled boundary finite element method (SBFEM). A dimensional reduction is introduced to the 3D Laplace equation, and a 3D edge is handled on the generatrix plane while governed by a complicated equation. The algorithm for resolving the SBFEM fundamental space is improved, and the singularities are approximated using a fractional-order basis. The effectiveness of the proposed method is demonstrated through its application to solve the radiation problem of a heaving cylinder. The method accurately captures the singular velocity field at the edge tip, ensuring that the boundary condition on the body surface is strictly satisfied in the neighborhood of the singularity. Accuracy of the mean drift force is ensured by performing direct pressure integrations over the body surface using a near-field formulation, which becomes as accurate as the middle-field formulation.

Beamforming for NOMA Under Similar Channel Conditions Including Near-Field Formulation

Beamforming for NOMA Under Similar Channel Conditions Including Near-Field Formulation

Transport and dispersion of tracers simulating COVID-19 aerosols in passenger aircraft.

Many laboratory experiments and model development activities have been underway to better estimate the risk of a person indoors becoming infected with COVID-19. The current paper focusses on the near-field (distances<about 5m) transport and dispersion (T&D) of the virons, treating them as inert tracers. The premise is that the T&D process follows widely used basic analytical near-field formulations such as a slab model, a Gaussian plume model, or a diffusivity (K) model. A slab or Gaussian model is more appropriate for cloud sizes less than the distance scale of the turbulence, while a K model is more appropriate for cloud sizes larger than the distance scale. The proposed slab model is evaluated with observations from the TRANSCOM tracer experiment in Boeing 767 and 777 airplanes, which involved multiple release scenarios. Release rates of 1-μm plastic bead inert tracers were constant over 60s from a mannequin's mouth and samplers were placed at about 40 nearby seat locations. A simple basic science near-field slab model is shown to agree with observations of maximum concentration and dose within a factor of two or three.

Salvesen’s Method for Added Resistance Revisited

Abstract Almost 4 years after the appearance of Salvesen–Tuck–Faltinsen (STF) strip theory (Salvesen et al., 1970, “Ship Motions and Sea Loads,” Annual Meeting of the Society of Naval Architecture and Marine Engineers (SNAME), New York, Nov. 12–13), Salvesen in 1974 published his popular method for calculation of added resistance (Salvesen, 1974, “Second-Order Steady State Forces and Moments on Surface Ships in Oblique Regular Waves,” Vol. 22; Salvesen, 1978, “Added Resistance of Ships in Waves,” J. Hydronautics, 12(1), pp. 24–34). His method is based on an exact near-field formulation; however, he applied the long-wave and the weak-scatterer assumptions to present his approximate method using the integrated quantities (hydrodynamic and geometrical coefficients). Considering the available computational powers in the 1970s, both of these assumptions were absolutely justifiable. The intention of this paper is to disseminate the results of a recent study at the Technical University of Denmark, whereby the Salvesen’s formulation has been revisited and the added resistance is computed from the original exact equation without invoking the weak-scatterer or the long-wave assumptions. This is performed using the solutions of the radiation and the scattering problems, obtained by a low-order boundary element method and the two-dimensional free-surface Green function inside our in-house STF theory implementation (Bingham and Amini-Afshar, 2020, DTU_Strip Theory Solver). The weak-scatterer assumption is then removed through a direct calculation of the x-derivatives of the velocity potentials and the normal vectors along the body. Knowing the velocity potentials over each panel, the long-wave assumption is also avoided by a piece-wise analytical integration of sectional Kochin Function (Kochin, 1936, “On the Wave Resistance and Lift of Bodies Submerged in Fluid,” Transactions of the Conference on the Theory of Wave Resistance, Moscow.). The presented results for five ship geometries testify that the correct treatment of the original equation is achieved only after both of the above-mentioned assumptions are removed. Implemented in this manner, Salvesen’s method proves to be relatively more accurate and robust than has been generally perceived during all these years.

Added resistance using Salvesen–Tuck–Faltinsen strip theory and the Kochin function

It is now more than half a century since the development of the renowned and well-established strip theory of Salvesen–Tuck–Faltinsen (STF), Salvesen et al. (1970). One of the existing, and widely used, methods for calculating the wave drift force (zero-speed case), or added resistance (forward-speed case), within this strip theory, is a near-field formulation which was developed by Salvesen himself in Salvesen (1974), Salvesen (1978). This method invokes a weak-scatterer assumption to drop one term, and also approximates the exponential terms as constant in the integrals over each two-dimensional ship section. These approximations are essentially a long-wave assumption Salvesen (1974). The main objective of this paper, which has been entirely inspired by the method of Kashiwagi et al. (2010), is to apply a far-field formulation, in the context of STF strip theory, without the above-mentioned assumptions. This far-field method is implemented following Maruo (1960b), Maruo (1963) and employs the Kochin function Kochin (1936) to express the wave kinematics in the far field. The necessary ingredients for this method are obtained by an implementation of STF theory using a low-order Boundary Element Method (BEM) and the two-dimensional free-surface Green function. No weak-scatterer assumption is required as the Kochin function explicitly includes the interaction of the disturbance potentials. Sectional integrals of the Kochin function are calculated analytically, assuming piecewise-constant variation of the potentials. Within this far-field framework all three integrals from Maruo’s relation are treated, and the line integral along the vessel’s length is calculated exactly assuming either a linear or a Fourier-mode decomposition of the non-exponential terms. The outcome is a far-field calculation procedure inside STF theory which compares very well with experimental measurements and relevant reference solutions. This is verified by the calculation of wave drift force and added resistance for six different ship hulls. One notable advantage of the presented framework, in comparison to Salvesen’s method (and also to that of Gerritsma and Beukelman (1972)), is its ability to accurately predict the zero-speed wave drift force. In addition, the long-wave approximate form of the Kochin function method is also discussed. Similar to Salvesen’s method, the wave drift force using this approximation, is expressed in terms of the body motion, the hydrodynamic coefficients and the sectional geometric constants. The approximate form performs well at zero-speed, but deteriorates quickly as the speed increases.

Local Enhancements of the Mean Drift Wave Force on a Vertical Column Shielded by an Exterior Thin Porous Shell

The wave interaction with a vertical column shielded by an exterior porous shell is studied within the framework of potential flow theory. The structures are fixed rigidly at the sea bottom. The interior cylinder is impermeable, and the exterior shell is slightly porous and thin. Additionally, the exterior shell is assumed to have fine pores, and a linear pressure drop is adopted at the porous geometry. The mean drift wave force on the system is thereby formulated by two alternative ways, based respectively on the direct pressure integration, i.e., the near-field formulation, and the application of the momentum conservation theorem in the fluid domain, i.e., the far-field formulation. The consistency of the two formulations in calculating the mean drift wave force is assessed for the present problem. Numerical results illustrate that the existence of the porous shell can substantially reduce the mean drift wave force on the interior column. It also appears that the far-field formulation consists of a conventional part as well as an additional part caused by the energy dissipation through the porous geometry. The mean drift wave force on the system is dominated by the first part, which resembles that on an impermeable body. Local enhancements of the mean drift wave force are found at some specific wave frequencies at which certain propagation modes of the fluid satisfy a no-flow condition at the porous shell.

Notice of Retraction: Exact Near-Field Formulation for Shielding Evaluation: The Werner's Equations Revised

After having studied and implemented the original Werner's equations for the evaluation in closed form of the near-field components produced by an electric dipole, there have been identified a number of them that can be transformed by analytical manipulation in a more convenient form for a quick and accurate computation. In this study, the new forms are derived and presented and their performances in terms of accuracy and computing time compared versus the original formulation.

Increase of Ship Fuel Consumption Due to the Added Resistance in Waves

Added resistance in waves is the second-order steady force dependant on the ship motions. It significantly affects ship operability and causes speed loss. Therefore the required power and fuel consumption of a ship advancing in a seaway increase. In this paper, additional fuel consumption is approximated in relation to the increased resistance, i.e. the difference between the ship resistance in calm water and resistance while operating in waves. Ship advancing in regular head waves with different speeds is examined. Calm water resistance is calculated according to the potential flow theory and ITTC 1957 model-ship correlation line. The added resistance in waves is calculated using three-dimensional boundary element method based on the potential flow theory. Motion induced resistance due to heave and pitch motions as well as reflection induced resistance are taken into account. Therefore, overall assessment of added resistance in regular waves is achieved through evaluation of the ship drift forces and quadratic transfer function. The so-called near-field formulation is used to determine wave loads acting on the ship hull. Evaluation of increased fuel consumption is made on the basis of estimated added resistance for different speeds and wave frequencies. Correlation of fuel consumption with various wave frequencies that the ship may encounter in its voyage is obtained.

EVALUATION OF THE ADDED RESISTANCE AND SHIP MOTIONS COUPLED WITH SLOSHING USING POTENTIAL FLOW THEORY

Ship added resistance is a steady force of the second order which depends on the ship motions and wave diffraction in short waves. To predict the impact of liquid motions inside the ship hull, a flooded tank in the midship area is generated and the ship response to regular waves is calculated. Currently available mathematical models and numerical tools are used to enable new insights into the sloshing effects of a relatively large free surface of flooded water inside the ship hull. The liquid inside the tank is first considered as a solid body in order to make a distinction between the hydrostatic and the hydrodynamic effect on global ship motions. Source formulation panel method is used and wave loads acting on the ship hull are determined using the near-field formulation. Based on the potential flow theory, the influence of sloshing on the ship motions and added resistance is evaluated to get an insight into this complex hydrodynamic problem. The calculated results are compared with the available experimental data from the literature.

Aeroacoustic Scattering Using a Particle Accelerated Computational Fluid Dynamics/Boundary Element Technique

A particle accelerated computational fluid dynamics/boundary element method technique to predict the sound pressure field produced by low Mach number flow past a rigid body is presented. An incompressible computational fluid dynamics solver is used to calculate the transient hydrodynamic flowfield. A near-field formulation based on Lighthill’s analogy is coupled with a particle condensation technique to predict the incident acoustic field and its normal derivative on the body. The near-field formulation involves singular surface and volume integrals, which are regularized via singularity subtraction. A particle condensation technique is applied to accelerate the incident field computations and reduce the amount of data that must be stored during the computational fluid dynamics analysis. The incident field is then combined with a boundary element method model of the body, and the scattered sound pressure field is obtained by solving the Burton–Miller boundary integral equations. The accuracy and computational cost of the particle accelerated computational fluid dynamics/boundary element method approach is demonstrated by calculating the incident acoustic field on a cylinder in crossflow under laminar and turbulent flow conditions as well as predicting the scattered and far-field sound pressures.

Broadband Scattering of the Turbulence-Interaction Noise of a Stationary Airfoil: Experimental Validation of a Semi-Analytical Model

A novel semi-analytical model based on Amiet's theory is proposed to predict the scattered acoustic field related to turbulence-interaction noise. The simulated scattered acoustic field is compared to the corresponding measurements of a stationary airfoil in a turbulent stream for validation purposes. The paper is composed of three main parts, where improvements and extensions of this semi-analytical model are presented. In the first part of the paper, a new formulation taking an intermediate level of geometrical near-field correction into account is derived. The second part provides an implementation of a strip method accounting for spanwise varying incoming flow conditions. The acoustic free-field response of the airfoil is computed using the geometrical near-field formulation with the strip method. In the third part, an innovative Boundary Element Method (BEM) approach is proposed in order to compute the scattered acoustic field of the airfoil by an obstacle. Finally, the scattered acoustic field resulting from the presence of a flat screen is computed by the semi-analytical method combined with the new BEM approach. A good agreement is obtained comparing with the measurements performed in an anechoic room.

Application of the Inhomogeneous Lippmann--Schwinger Equation to Inverse Scattering Problems

In this paper we present a hybrid approach to numerically solving two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is “hybrid” in that it merges a qualitative and a quantitative method to optimize the way of exploiting the a priori information on the background within the inversion procedure, thus improving the quality of the reconstruction and reducing the data amount necessary for a satisfactory result. In the qualitative step, this a priori knowledge is utilized to implement the linear sampling method in its near-field formulation for an inhomogeneous background, in order to identify the region where the scatterer is located. On the other hand, the same a priori information is also encoded in the quantitative step by extending and applying the contrast source inversion method to what we call the “inhomogeneous Lippmann--Schwinger equation''; the latter is a generalization of the classical Lippmann--Schwinger equation to the case of an inhomogeneous background, and in our paper is deduced from the differential formulation of the direct scattering problem to provide the reconstruction algorithm with an appropriate theoretical basis. Then the point values of the refractive index are computed only in the region identified by the linear sampling method at the previous step. The effectiveness of this hybrid approach is supported by numerical simulations presented at the end of the paper.

Attenuation correction factors for cylindrical, disc and box geometry

In the present study, attenuation correction factors have been experimentally determined for samples having cylindrical, disc and box geometry and compared with the attenuation correction factors calculated by Hybrid Monte Carlo (HMC) method [ C. Agarwal, S. Poi, A. Goswami, M. Gathibandhe, R.A. Agrawal, Nucl. Instr. and. Meth. A 597 (2008) 198] and with the near-field and far-field formulations available in literature. It has been observed that the near-field formulae, although said to be applicable at close sample-detector geometry, does not work at very close sample-detector configuration. The advantage of the HMC method is that it is found to be valid for all sample-detector geometries.

Ultrasound mammography

We introduce a near-field formulation of the acoustic field scattered by a soft tissue organ. This derivation is based on the Huygens–Fresnel principle that describes the scattered field as the result of the interferential scheme of all the secondary spherical waves. This leads us to define a new Fourier transform which yields a spectrum whose harmonic components have an elliptical spatial support. Based on these projections, we define an Elliptical Radon transform that enables us to reconstruct either the impedance or the celerity maps of an acoustical model characterized in terms of impedance and celerity fluctuations. The formulation is very similar to that developed in the far-field domain where the Radon transform pair is derived from an harmonic plane wave decomposition. This formulation allows us to introduce the Ductal Tomography, following the example of the Ductal Echography, that provides a systematic inspection of each mammary lobe, in order to reveal breast lesions at an early stage. In order to review the performances obtained with current echographs in view of specific experiment (numerical simulations), we develop a computer phantom that gains in realism. This 2-D anatomical phantom is an axial cut of the ductolobular structure corresponding to a daisy-like internal arrangement with petals (lobes) radiating around the nipple, for healthy and pathological situations. The different constitutive tissues and ducts are characterized in terms of density and celerity parameters whose spatial distributions are defined with specific random density laws. The use of a velocity–pressure formulation permits us to model time domain acoustic wave propagation. Broadband US pulses are transmitted and measured in diffraction around the breast with a ring antenna, the images are reconstructed using the elliptical back-projection-based procedure mentioned above.

Middle-field formulation for the computation of wave-drift loads

New formulations of second-order wave loads contributed by a first-order wave field are developed by applying two variants of Stokes’s theorem and Gauss’s theorem to a formulation consisting of direct pressure integrations on a body’s hull which is called the near-field formulation. In addition to this direct formulation and the formulation derived from the momentum theorem called the far-field formulation, for the computation of drift (surge/sway) forces in horizontal directions and drift (yaw) moment around the vertical axis, one of new formulations is defined on the control surfaces surrounding the body and called the middle-field formulation. After a brief summary of both pressure-integration (near-field) and momentum (far-field) formulations, the development of the middle-field formulation involving control surfaces is described and complemented in detail in the appendices. The application of the new formulation shows that the near-field and far-field formulations are mathematically equivalent for wall-sided, as well as non-wall-sided bodies and under the condition that the mean yaw moments are expressed with respect to a space-fixed reference point. It is shown that the middle-field formulation is as robust as the far-field formulation and as general as the near-field formulation of second-order loads on a single body as well as on multiple bodies. Furthermore, the extension to the computation of a second-order oscillatory load, which is so far accessed only by the near-field formulation, is envisioned.

Antenna designer's notebook-design of pyramidal horns for fixed phase center as well as optimum gain

A method for designing a pyramidal horn with optimum gain and a phase center that is insensitive to horn rotation over a wide frequency band is presented. The optimum gain comes out to be about 14 dB; ways to increase the optimum gain are suggested. The design is based on a far-field formulation and is useful for common applications. However, a parallel procedure based on a near-field formulation and using more exact gain expressions can be developed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A study of multimode fibre attenuation measurement using a precision spectral radiometer and the near-field filtration technique

Based on the near-field filtration formulation, the paper identifies and quantifies the most important sources of interlaboratory error in multimode fibre attenuation measurements. Measures are proposed for the reduction of these errors, and it is estimated that a lower bound of about 0.04 dB should be possible under certain assumptions.

High-frequency fields excited by a line source located on a perfectly conducting concave cylindrical surface

Alternative representations are obtained for the high-frequency surface field excited on a perfectly conducting concave circular cylinder by an axial magnetic line current located on the surface. Included are ray-optical, canonical integral, whispering gallery mode, and near-field formulations, and various combinations of these. Asymptotic evaluations in different parameter ranges lead to results with varying accuracy and physical content. Their utility is assessed by extensive numerical calculations and comparisons. Most intriguing is a form of the asymptotic solution that involves only a number of geometric optical rays and a number of whispering gallery modes.

New plane wave spectrum formulations for the near-fields of circular and strip apertures

The plane wave spectrum (PWS) method has previously been applied to analyze the near-field of planar apertures. The main goal of this paper is to present new PWS formulations for the near-fields of strip and circular apertures. Only special cases are developed in detail. For example, the uniform and parabolic aperture distributions are developed for the circular aperture. These new formulations are expressed in terms of either elementary functions or Fresnel integrals. Consequently, they permit considerably more rapid and efficient calculations than previous near-field formulations, by either the PWS or the aperture integration approach. The new formulations are especially advantageous for large circularly symmetric apertures (on the order of 100\lambda and larger) in that computational efficiencies are improved by an order of magnitude or two over the original PWS formulation. The improvement over aperture integration techniques is more than a factor of 1000 for the 100\lambda aperture.