Far-field Conditions Research Articles

On the lifetimes of two-dimensional droplets on smooth wetting patterns

We study the evolution and lifetime of droplets evaporating on a smooth chemical pattern, which is characterised by a spatially varying contact angle. We formulate a model that combines the evaporation rate of the droplet for a given volume with the static stability of the droplet as the volume changes in time quasi-statically. We derive an exact equation for the evaporation rate that is studied analytically under the limiting cases of nearly neutral wetting and highly hydrophilic conditions. We find that the evaporation rate of the droplet is highly dependent on the size and shape of the fictitious infinity where a far-field boundary conditions needs to be applied. We also study how the droplet’s lifetime depends on the averaged contact angle and strength varepsilon of the chemical pattern, observing that the lifetime of the droplet is maximised for a droplet with average contact angle pi /2 and with varepsilon lesssim 0.1.

Near-Field Effects on Micrometer Accurate Ranging With Ultra-Wideband mmWave Radar

We investigated near-field effects on free-space ranging with ultra-wideband millimeter-wave (mmWave) radar. In this application, one often assumes far-field conditions. However, with increasing requirements of accuracy, far-field assumptions are not satisfying. The radar measurements are affected by phase variations, leading to erroneous distance estimates. To simulate and approximate these effects, we propose computational methods by means of physical optics. They were validated using a state-of-the-art frequency-modulated continuous-wave radar sensor. Sophisticated experiments show good agreement; thus, in practice, the methods can be used to correct distance estimates to achieve micron accuracy without extensive calibration in advance.

Boundary element method virtual goniometer to predict the diffusion and scattering coefficients

The experimental measurement of the diffusion coefficient according to ISO 17497-2 is very time consuming and requires several sample periods to evaluate the effect of diffraction lobes, an anechoic or large reflection-free volume and far-field conditions. Wave-based BEM methods have predicted diffusion and correlation scattering coefficients very accurately [Hargreaves et al., J. Acoust. Soc. Am. 108 (4), 1710–1720 (2000)]. This presentation will describe a new Python Virtual Goniometer program, called VIRGO, which predicts the free-field and surface-mounted diffusion and correlation scattering coefficients for any shaped surface that can be successfully meshed from a three-dimensional file. The program accurately predicts the periodic diffraction grating lobes of a reference one-dimensional hemicylinder and a two-dimensional hemisphere, both in the free-field and surface mounted on a boundary. The diffusion coefficient and three-dimensional polar responses of additional number-theoretic and optimized profiled and curvilinear shapes will also be compared with scale model boundary-plane goniometer measurements. The results will verify that it is possible to precisely predict the diffusion and correlation scattering coefficients, without having to fabricate or 3D print scale models or full-scale samples.

Nonlinear characteristics and corrections of near-field underwater explosion shock waves

The shock wave characteristics within the near-field are one of the most challenging aspects of understanding an underwater explosion. The latest numerical and experimental techniques were utilized to investigate the near-field pressure distribution and decay features after a shock disturbance. The governing equations in the numerical simulation were discretized with a fifth-order weighted essentially non-oscillatory scheme in space and a third-order Runge–Kutta scheme in time, and multi-medium interactions were defined and resolved via the modified ghost fluid method. The test system consisted of a synchronized high-speed framing camera and polyvinylidene fluoride (PVDF) sensors. Three identical spherical composition B charges were examined under the same test conditions, and the raw data from the high-speed camera were processed with edge detection and circle fitting techniques. The comparison showed that the high-speed camera image data, the PVDF signals, and the numerical computation results were highly consistent with each other. Higher-order correction terms were added to the pressure peak distribution model and the pressure decay model as nonlinear corrections based on further comprehensive and insightful analysis of the verified results. The corrected models not only fit with the near-field data but had better accuracy under the far-field condition as well.

Quasi-anechoic frequency response measurement of underwater acoustic devices using exponential sine sweeps

As part of the development of the MITRE BlueTech Lab, an existing 106 × 40 × 15 ft. underground tank is being repurposed as an underwater acoustic test facility. Here, we report on the development of a procedure to extract anechoic frequency responses from measurements made in the otherwise reverberant environment using exponential sine sweeps. A demonstration of the procedure applied to a small-aperture baffled receiver array is shown, and results are compared to time-gated stepped sine wave measurements. Simple geometric rules to maximize measurement bandwidth while ensuring far-field conditions for both transmitter and receiver array are presented.

Far-field approximations to the derivatives of Green\u2019s function for the Ffowcs Williams and Hawkings equation

The surface correction to the quadrupole source term of the Ffowcs Williams and Hawkings integral in the frequency domain suffers from the computation of high-order derivatives of Green’s function. The far-field approximations to the derivatives of Green’s function have been used without derivation and verification in previous work. In this work, we provide the detailed derivations of the far-field approximations to the derivatives of Green’s function. The binomial expansions for the derivatives of Green’s function and the far-field condition are employed during the derivations to circumvent the difficulties in computing the high-order derivatives. The approximations to the derivatives of Green’s function are systemically verified by using the benchmarks two -dimensional convecting vortex and the co-rotating vortex pair. In addition, we provide the derivations of the approximations to the multiple integrals of Green’s function by using the far-field approximations to the derivatives.

Millimeter-Wave New Radio Test Zone Validation for MIMO Over-the-Air Testing

Standardization efforts to define radiated metrics and test methods for verifying millimeter-wave (mmWave) new radio (NR) devices are currently ongoing. Multi-probe anechoic chamber (MPAC) method, which is capable of reproducing spatial fading channels in the test zone, is selected as the reference solution for NR device testing. It is of importance to ensure that the defined testing propagation environment in the test zone is correctly implemented. In this paper, a novel algorithm is proposed to determine the wideband power-angle-delay profile of the reconstructed channels in the test zone for mmWave NR. The proposed algorithm is shown to be generic (applicable for both 2D and 3D testing setup), applicable for both near-field and far-field conditions and robust (i.e. insensitive to measurement distance errors).

Crack field analysis by optical DIC of short cracks in Zircaloy-4

The prediction of fatigue life is most difficult for short cracks, as their local conditions may differ from what is predicted using the remote applied loading and crack geometry. Digital image correlation (DIC) can be utilized to analyze images from an optical microscope (OM), which facilitates the local characterization of the crack field. This paper presents a Finite-Element-based approach that uses DIC-obtained displacement data to retrieve the crack field and quantify the local crack driving force. With the assumption of linear anisotropic elasticity, the change in both the Mode I and Mode II crack intensity factors over a fatigue cycle can be extracted using the interaction integral method. This allows the determination of the local driving force for short crack propagation. The application of this method is demonstrated by the full-field analysis of short fatigue cracks in blocky alpha Zircaloy-4. The sensitivity of the analysis is investigated to factors that include DIC subset size, uncertainties in crack tip position and lower quality data in the crack vicinity. This technique requires no prior knowledge of theoretical solutions or far-field boundary conditions, and it can be applied to the tip of a tortuous crack by defining an appropriate local frame of reference. The analysis is applied here to cracks under similar mode I loading that propagate on the prism plane at different rates in directions that are parallel and perpendicular to the c-axis of the hexagonal unit cell.

Task-Specific Optimization of Virtual Channel Linear Prediction-Based Speech Dereverberation Front-End for Far-Field Speaker Verification

Developing a single-microphone speech denoising or dereverberation front-end for robust automatic speaker verification (ASV) in noisy far-field speaking scenarios is challenging. To address this problem, we present a novel front-end design that involves a recently proposed extension of the weighted prediction error (WPE) speech dereverberation algorithm, the virtual acoustic channel expansion (VACE)-WPE. It is demonstrated experimentally in this study that unlike the conventional WPE algorithm, the VACE-WPE can be explicitly trained to cancel out both late reverberation and background noise. To build the front-end, the VACE-WPE is first independently (pre)trained to produce "noisy" dereverberated signals. Subsequently, given a pretrained speaker embedding model, the VACE-WPE is additionally fine-tuned within a task-specific optimization (TSO) framework, causing the speaker embedding extracted from the processed signal to be similar to that extracted from the "noise-free" target signal. Moreover, to extend the application of the proposed front-end to more general, unconstrained "in-the-wild" ASV scenarios beyond controlled far-field conditions, we propose a distortion regularization method for the VACE-WPE within the TSO framework. The effectiveness of the proposed approach is verified on both far-field and in-the-wild ASV benchmarks, demonstrating its superiority over fully neural front-ends and other TSO methods in various cases.

Kinked and forked crack arrays in anisotropic elastic bimaterials

The fracture problem of multiple branched crack arrays in anisotropic bimaterials is formulated by use of the Stroh formalism to the linear elasticity theory of dislocations. The general full-field solutions are obtained from the standard technique of continuously distributed dislocations along finite-sized cracks of arbitrary shapes, which are embedded in dissimilar anisotropic half-spaces under far-field stress loading conditions. The bimaterial boundary-value problem leads to a set of coupled integral equations of Cauchy-type that is numerically solved by using the Gauss–Chebyshev quadrature scheme with appropriate boundary conditions for kinked and forked crack arrays. The path-independent Jk-integrals as crack propagation criterion are therefore evaluated for equally-spaced cracks, while the limiting configuration of individual cracks is theoretically described by means of explicit expressions of the local stress intensity factors K for validation and comparison purposes on several crack geometries. The short-range interactions resulting from the idealized configurations of infinitely periodic cracks are investigated as well as various size- and heterogeneity-effects on the mixed-mode cracks in complex stress-state environments. The influences of anisotropic elasticity, elastic mismatch, applied stress direction, inter-crack spacings and crack length ratios on the predictions from the Jk- and K-based fracture criteria are examined in the light of different configurations from the single kinked crack case in homogeneous media to the network of closely-spaced forked cracks in presence of bimaterial interfaces.

Photonic topological transition in dimerized chains with the joint modulation of near-field and far-field couplings

Topological systems containing near-field or far-field couplings between unit cells have been widely investigated in quantum and classic systems. Their band structures are well explained with theories based on tight-binding or multiple scattering formalism. However, characteristics of the topology of the bulk bands based on the joint modulation of near-field and far-field couplings are rarely studied. Such hybrid systems are hardly realized in real systems and cannot be described by neither tight-binding nor multiple scattering theories. Here, we propose a hybrid-coupling photonic topological insulator based on a quasi-1D dimerized chain with the coexistence of near-field coupling within the unit cell and far-field coupling among all sites. Both theoretical and experimental results show that topological transition is realized by introducing near-field coupling for given far-field coupling conditions. In addition to closing and reopening the bandgap, the change in near-field coupling modulates the effective mass of photonics in the upper band from positive to negative, leading to an indirect bandgap, which cannot be achieved in conventional dimerized chains with either far-field or near-field coupling only.

Inerter-added transmissibility to control base displacement in isolated structures

A solution to the large base displacement problem in isolated structures under seismic loads is proposed; it is based on a displacement transmissibility formulation that includes the inerter device. The solution is also based on a novel spectral characterization of ground displacement; it should be clear that if the problem is displacement, the focus must be on displacements, both, as the excitation: ground displacement (rather than acceleration which is the norm) and as isolator displacement, through a transmissibility that relates both input and output displacements, all of which is a new approach. The proposal can serve as a passive-control design procedure, either under near-field or far-field conditions, when an inerter at the base level is chosen to solve the large isolator displacement problem. An isolated structural model commonly used in the subject literature is employed to show that the base displacement level can be reduced to under the ground displacement level, which implies a positive comparison with previous passive and active control solutions, including inerter solutions; in fact, the design aim is a competitive 0.95 ratio for both displacements.

On the Determination of Thermal Conductivity From Frequency Domain Thermoreflectance Experiments

Abstract The Fourier and the hyperbolic heat conduction equations were solved numerically to simulate a frequency-domain thermoreflectance (FDTR) experiment. Numerical solutions enable isolation of pump and probe laser spot size effects and use of realistic boundary conditions. The equations were solved in time domain and the phase lag between the temperature of the transducer (averaged over the probe laser spot) and the modulated pump laser signal was computed for a modulation frequency range of 200 kHz–200 MHz. Numerical calculations showed that extracted values of the thermal conductivity are sensitive to both the pump and probe laser spot sizes, while analytical solutions (based on Hankel transform) cannot isolate the two effects. However, for the same effective (combined) spot size, the two solutions are found to be in excellent agreement. If the substrate (computational domain) is sufficiently large, the far-field boundary conditions were found to have no effect on the computed phase lag. The interface conductance between the transducer and the substrate was found to have some effect on the extracted thermal conductivity. The hyperbolic heat conduction equation yielded almost the same results as the Fourier heat conduction equation for the particular case studied. The numerically extracted thermal conductivity value (best fit) for the silicon substrate considered in this study was found to be about 82–108 W/m/K, depending on the pump and probe laser spot sizes used.

A peridynamic model for crevice corrosion damage

A new peridynamic (PD) model for crevice corrosion damage is introduced and cross-validated with experimental results from the literature. Electrochemical mechanisms are reduced to a simple metal-ion concentration-dependent corrosion rate. Computations over domains with extreme aspect ratios like those seen in crevices are efficiently performed by modifying the PD formulation to accommodate arbitrary-shape horizons. The model is validated against experimental results on bolted washers. Simulations predict both the location and the depth of deep corrosion trenches that form at a distance from the crevice mouth. Far-field boundary conditions are used to autonomously reproduce the experimentally observed progression of crevice corrosion. The PD model results also show that the two factors considered here (diffusion-driven transport of dissolved metal ions, and dissolution being dependent on their concentration) are sufficient to predict the evolution of crevice corrosion.

Development and assessment of an intrusive polynomial chaos expansion‐based continuous adjoint method for shape optimization under uncertainties

AbstractThis article contributes to the development of methods for shape optimization under uncertainties, associated with the flow conditions, based on intrusive Polynomial Chaos Expansion (iPCE) and continuous adjoint. The iPCE to the Navier–Stokes equations for laminar flows of incompressible fluids is developed to compute statistical moments of the Quantity of Interest which are, then, compared with those obtained through the Monte Carlo method. The optimization is carried out using a continuous adjoint‐enabled, gradient‐based loop. Two different formulations for the continuous adjoint to the iPCE PDEs are derived, programmed, and verified. Intrusive PCE methods for the computation of the statistical moments require mathematical development, derivation of a new system of governing equations and their numerical solution. The development is presented for a chaos order of two and two uncertain variables and can be used as a guide to those willing to extend this development to a different set of uncertain variables or chaos order. The developed method and software, programmed in OpenFOAM, is applied to two optimization problems pertaining to the flow around isolated airfoils with uncertain farfield conditions.

Analytical Stress Solution and Numerical Mechanical Behavior of Rock Mass Containing an Opening under Different Confining Stress Conditions

In this study, the triangle interpolation method for the calculation of mapping functions of plates containing an opening with arbitrary shapes is investigated with an improved method for point adjudgment during iterations. Afterwards, four kinds of openings with typical shapes are considered and the mapping functions for them are calculated, based on which the influence of calculation parameters such as iteration time and the number of terms on the accuracy of mapping function is discussed. Finally, the stress around an inverted U-shaped opening and around an arched opening under different far-field stress conditions is calculated and the effect of opening shape and lateral pressure coefficient on stress distribution and rock mechanical behaviors is further analyzed combined with the discrete element method (DEM) numerical simulation. The result shows that the stability and failure pattern of the rock mass is correlated with the stress around the opening, which is affected by the opening shape. The existence of opening also greatly reduces the enhancing influence of confining stress on rock specimen.

Stress field analysis of an infinite plate with a central closed inclined crack under uniaxial compression

In view of the shortcomings of existing studies, the mechanical behavior of the closed crack under uniaxial compression is studied. Based on the far-field and the crack surface stress boundary conditions, Kolossoff-Muskhelishvili stress function of an infinite plate with a central closed inclined crack is derived with Muskhelishvili complex theory. Then the calculation methods of the stress components, stress intensity factors and T-stress at the crack tip are proposed. The mainly findings are as follows. First of all, the crack surface stress boundary conditions vary with variation of the far-field stress condition from tension to compression, so it’s false to directly introduce the theory for the crack under tension to that for the closed crack under compression. Next, it is found that there is no KI singular term at the crack tip and meanwhile KII and T-stress are influenced by the effective shear stress on the crack surface. When the effective shear stress is zero, there are two T-stress components (i.e. Tx and Ty, which are parallel and perpendicular to the crack surface respectively). While the effective shear stress is greater than zero, the third T-stress component (namely Txy which is along the xy direction) also exists. Finally, the theoretical predictions with the proposed method are verified with the isochromatic fringe patterns of photoelasticity experiment near the crack tip under uniaxial compression. Meanwhile the distribution of each stress component around the crack is effected obviously by the friction coefficient of the crack surface and the dip angle of crack, but the distribution tendency of these stress components is similar.

A physics-based model for frost buildup under turbulent flow using direct numerical simulations

We present a new model for frost buildup under turbulent (and laminar) flow using direct numerical simulations. The physical model consists of two layers, the air and the frost. The air layer is fully resolved and consists of solving for the velocity, temperature, and vapor mass fraction fields. The frost layer thickness is resolved using conservation of mass and energy. Both phases are dynamically coupled using the immersed boundary method. Three-dimensional simulations are conducted in an open-channel configuration. A number of challenges need to be overcome to make these simulations feasible. First, to enforce far-field conditions of zero gradient and prescribed mean temperature and humidity, a source term is added to the energy and transport equations in the flow solver. Second, the mean frost thickness is subtracted after each time step to ensure a constant mean flow thickness and level of turbulence in the numerical domain. Third, a slow-time acceleration approach, which accelerates the frost buildup by a predetermined factor, is employed to bridge the gap between the fast turbulent and slow frost buildup time scales. Finally, a frost densification scheme is used to overcome the difficulties of vertically varying frost properties. The model is validated by comparing the frost thickness and frost thickness buildup rate over a period of one hour from a cooled flat plate experiment. Both quantities compare favorably with experiments.

Study on the maximum tangential strain criterion for the initiation of the wing-crack under uniaxial compression

The global stress field function of an infinite plate with a closed inclined crack under uniaxial compression is presented, then the stress field at the crack tip is obtained, namely the formulae of KI, KII and T-stress are obtained. A new maximum tangential strain (MTSN) criterion is proposed to predict the initiation of the crack under compression by considering singular and non-singular terms based on the classical MTSN criterion. The influence factors on KII are analyzed and the effects of T-stress on the tangential strain at the crack tip under different critical plastic zones (rc), dip angel of crack (β), friction coefficients of crack surface (f) and Poisson’s ratio (ν) are studied. The comparison of the wing-crack initiation angle measured from the experimental results and predicted by the proposed criterion and other researchers’ models are made. The following findings are obtained. First of all, the proposed global stress field function satisfies the far-field and crack surface stress boundary conditions. The singular term of KII and non-singular term of T-stress vary with the effective shear stress along the crack surface. When the effective shear stress is zero, there is still singularity at the crack tip, which is completely opposite to the classical theory, and there are two components of T-stress (i.e. Tx and Ty, which is parallel and perpendicular to the crack surface respectively). While there is a third component of T-stress (i.e. Txy, which along the xy direction) when the effective shear stress is greater than zero. Next, the comparison of the wing-crack initiation angle measured from the experimental results and predicted by the proposed criterion and other researchers’ models are made. The results of the proposed method are consistent with the experiments very well, especially when the effective shear stress decreases to zero with the increase of friction coefficient (f). Finally, the tangential strain field at the crack tip are effected significantly by the critical plastic zones (rc), dip angel of crack (β), friction coefficients of crack surface (f) and Poisson’s ratio (ν).

Acoustic field effect on encapsulated spherical drop located in liquid filled cylindrical vessel

The acoustical problem dealing with the interaction of a plane wave propagating along the liquid-filled cylindrical cavity with an elastic spherical shell filled, in turn, with the compressible liquid is solved. An axisymmetric case is studied. The boundary problem for simultaneous solution of the wave equations describing the motion in the fluid filling the vessel as well as in the fluid contained within the shell together with equations of motion of the thin elastic shell is formulated. The problem statement contains the boundary conditions for both fluid–shell interfaces, the condition at the vessel surface and far-field radiation conditions. The incident wave propagating along the vessel axis is expanded into a normal mode series. In order to meet all boundary conditions, the variable separation method along with the spherical wave function representations in terms of the cylindrical ones and vice versa are used. This approach yields exact solution of the boundary problem and enables one to analyze the scattered fields in the low and medium frequency ranges. The problem is reduced to an infinite system of algebraic equations that is solved by the truncation method. The goal of the study is to determine the interaction features between the shell and the vessel surfaces. Obtained numerical results describe scattered field of pressure and velocity in the neighborhood of the shell as functions of frequency, the internal liquid characteristics, and the elastic characteristics of the shell. It is ascertained, that peculiarities of the resonance behavior of the liquid-filled shell can be essentially amplified by the acoustical interaction with the vessel surface.