Azimuthal Research Articles

Automated Cloud Shadow Detection from Satellite Orthoimages with Uncorrected Cloud Relief Displacements

Clouds and their shadows significantly affect satellite imagery, resulting in a loss of radiometric information in the shadowed areas. This loss reduces the accuracy of land cover classification and object detection. Among various cloud shadow detection methods, the geometric-based method relies on the geometry of the sun and sensor to provide consistent results across diverse environments, ensuring better interpretability and reliability. It is well known that the direction of shadows in raw satellite images depends on the sun’s illumination and sensor viewing direction. Orthoimages are typically corrected for relief displacements caused by oblique sensor viewing, aligning the shadow direction with the sun. However, previous studies lacked an explicit experimental verification of this alignment, particularly for cloud shadows. We observed that this implication may not be realized for cloud shadows, primarily due to the unknown height of clouds. To verify this, we used Rapideye orthoimages acquired in various viewing azimuth and zenith angles and conducted experiments under two different cases: the first where the cloud shadow direction was estimated based only on the sun’s illumination, and the second where both the sun’s illumination and the sensor’s viewing direction were considered. Building on this, we propose an automated approach for cloud shadow detection. Our experiments demonstrated that the second case, which incorporates the sensor’s geometry, calculates a more accurate cloud shadow direction compared to the true angle. Although the angles in nadir images were similar, the second case in high-oblique images showed a difference of less than 4.0° from the true angle, whereas the first case exhibited a much larger difference, up to 21.3°. The accuracy results revealed that shadow detection using the angle from the second case improved the average F1 score by 0.17 and increased the average detection rate by 7.7% compared to the first case. This result confirms that, even if the relief displacement of clouds is not corrected in the orthoimages, the proposed method allows for more accurate cloud shadow detection. Our main contributions are in providing quantitative evidence through experiments for the application of sensor geometry and establishing a solid foundation for handling complex scenarios. This approach has the potential to extend to the detection of shadows in high-resolution satellite imagery or UAV images, as well as objects like high-rise buildings. Future research will focus on this.

Unified analytical theory of nonlinear optical diffraction by nonlinear gratings

When a pump laser shines upon a periodically poled lithium niobate (LN) thin plate nonlinear grating, second-harmonic generation (SHG) and its nonlinear diffraction occurs, with the nonlinear Raman–Nath diffraction (NRND), nonlinear Bragg diffraction (NBD), and nonlinear Cerenkov radiation (NCR) being several prominent examples. In this work we build and present a unified analytical theory to solve SHG for the NRND, NCR, and NBD processes from LN domains, domain walls, and defects. We find that the critical physical entity that governs the nonlinear diffraction is the effective nonlinear coefficient for each Fourier wave component. The analytical theory has a great generality and applicability scope. It allows us to retrieve and analyze everything about the dependence of SHG nonlinear diffraction on a series of physical and geometrical parameters such as the pump laser intensity, polarization, incidence polar and azimuthal angles, the LN thin plate thickness and its crystalline orientation, LN domain size and pitch, domain wall thickness and crystalline configuration, defect size and crystalline configuration, and the SHG diffraction beam angle and polarization. The analytical theory also enables us to analyze deeply the similarities and differences of the three nonlinear diffraction processes NRND, NCR, and NBD, build a smooth and broad connection bridge among these three processes, and construct a unified physical picture to understand, describe, and exploit these three processes of seemingly big difference. Besides, the analytical theory can be applicable to handle nonlinear diffraction by domains, domain walls, and defects in other more complicated 2D and 3D nonlinear gratings made from LN and other nonlinear crystals. Finally, the analytical theory can help to build a bridge connecting the extrinsic SHG nonlinear diffraction properties with the intrinsic domain poling and inversion material and physical properties of LN and other nonlinear crystals and explore novel nonlinear optical devices and technologies.

A position-based method for detecting orbital angular momentum modes

Abstract Due to the inherent limitations of current Orbital Angular Momentum (OAM) mode detection methods and constraints posed by the physical size of receiving antennas, accurately identifying higher-order OAM modes represents a significant challenge. Therefore, there is a pressing necessity to overcome these hurdles. This paper introduces a new approach to OAM mode detection that exploits positional information. Our methodology ascertains the OAM mode by examining the phase and position data of the electric field at any two randomly chosen points within the energy's spatial distribution radiated by vortex electromagnetic waves. This innovation promises not only to precisely detect higher-order OAM modes but also grants greater versatility in the placement of receiving antennas. Moreover, the study delves into the correlation between the electric field phase of vortex electromagnetic waves, the azimuth angle, and the receiving distance. The validity of our approach is confirmed through both simulation outcomes and experimental data derived from physical tests.

Unsupervised Clustering-based 3D Static Scene Construction Using LiDAR Channel and Azimuth Angle

Abstract. Cameras are typically used at road intersections to collect data to perform object detection but struggle in low-light and harsh weather. On the other hand, Light Detection and Ranging (LiDAR) is used as a key technology in 3D vision systems. It gives the 3D point cloud, which includes accurate depth information, but its resolution is cost-dependent, with higher resolutions being more expensive. Deep learning-based method requires large, labelled dataset which increases the cost, time and accuracy depending on the model trained on labelled dataset. To perform object detection in point cloud data is a challenging task due to the incomplete representations, data sparsity and unavailability of training data. To overcome this by using an unsupervised approach, it is important to identify the static scene and then detect the moving object. This work incorporated a novel approach to construct static scene using azimuth angle and laser channel information using an unsupervised clustering approach. This work incorporates two modules I) data collection using VLP-16 LiDAR, and II) static scene construction using DBSCAN (density-based spatial clustering and noise) clustering-based approach. Data is collected at a 4-legged intersection and pre-processed to extract aggregated distances corresponding to the unique pair of azimuth angle and laser channel. DBSCAN is used to perform clustering on the aggregated distances, based on the highest silhouette score and lowest intra distance between points in cluster, static points are identified, and static scene constructed. The qualitative evaluation of method demonstrates that the algorithm effectively and accurately filters out background points.

An optimal parameterized Newton-type structure-preserving doubling algorithm for impact angle guidance-based 3D pursuer/target interception engagement

The proposed strategy, finite-time state-dependent Riccati equation (FT-SDRE)-based impact angle guidance, is generally employed to solve the 3D pursuer/target interception model with fixed lateral accelerations. This article expands its application to a general scenario where the lateral acceleration of a target may change. To achieve this, we approximate the accelerations of the azimuth and elevation angles of the target in the inertial frame via second-order finite difference schemes and develop a high-performance FT-SDRE algorithm with structure-preserving doubling algorithms (SDAs). As a result, the update frequency of the controller can be increased, and better guidance of the pursuer can be obtained to address the high maneuverability of the target during the entire interception procedure. At every state of the FT-SDRE, a modified Newton–Lyapunov method is employed to solve the continuous algebraic Riccati equation (CARE), and a new simplified SDA with adaptive optimal parameter selection is proposed for solving the associated Lyapunov equation. Our numerical results demonstrate that the FT-SDRE algorithm accelerated by our proposed methods is approximately three times faster than the FT-SDRE algorithm, in which the MATLAB functions icare and lyap are used to solve the CARE and the Lyapunov equation, respectively, throughout the entire interception procedure. In other words, the control frequency can be increased threefold. In our benchmark cases where the target maneuvers with nonlinear lateral acceleration, the target can be intercepted earlier via the proposed FT-SDRE algorithm.

Developing biomimetic PVA/PAA hydrogels with cellulose nanocrystals inspired by tree frog structures for superior wearable sensor functionality

This study developed a wearable sensor device featuring biomimetic structures inspired by tree frog toe pads to measure shoulder joint movements effectively. A PVA/PAA double-network hydrogel was formulated by mixing PVA and PAA in a 3:7 ratio, resulting in a Young's modulus of 7.2 kPa, closely matching human skin's mechanical properties. To enhance moisture retention, the hydrogel was supplemented with 20 mL glycerin, increasing its weight retention rate to 95 % after 28 days, a 5.6-fold improvement over glycerin-free hydrogels. Additionally, the incorporation of 0.2 wt% cellulose nanocrystals (CNC) increased the cross-linking density, reducing the swelling ratio from 124 % to 106 % and minimizing the impact of swelling cycles on mechanical properties from 22 % to 4 %. Treefrog-inspired microstructures were fabricated on the sensor surface using laser cutting and casting techniques, significantly enhancing adhesion under humid conditions, with normal, lateral, and peel-off adhesion forces improving by 500, 700, and 700 %, respectively. The sensor demonstrated accurate measurement of shoulder joint movements with an error margin of 6.3 % for polar angles (45°-135°) and 7.8 % for azimuth angles (0°-45°). The accompanying smartphone application provided real-time feedback, helping to prevent exercise injuries and improve user awareness and control of shoulder movements, making it suitable for both rehabilitation and athletic training.

On the Shift of the Maximum of the Polar Angular Distribution of Sputtered Atoms in the MD Model of the (001) Ni Face Sputtering

Using an up-to-date full molecular dynamics model of sputtering of single crystals, taking into account the incidence of ions on the surface, the peculiarities and mechanisms of atom sputtering during bombardment of the (001) Ni face with 200 eV Ar ions are studied for two target temperatures. It is shown for the first time that with an increase in the energy of sputtered atoms, not only the maximum of their polar angular distribution in the azimuthal direction toward the Wehner spots, but also the maximum of the polar angular distribution integrated over the azimuthal angles shifts first toward the normal to the surface, and then in the opposite direction. The polar distribution integrated over the azimuthal angle is formed by atoms ejecting from the surface at much larger polar angles than in the final (observed) distribution. Both effects are explained in terms of the surface mechanism of single crystal sputtering.

Wall Shading Losses of Photovoltaic Systems

The deployment of photovoltaic (PV) systems on rooftops in urban environments may encounter shading on the PV collectors from surrounding walls, acting adversely on the generated electricity of the PV systems. Most studies on the shading of PV systems do not deal analytically with the shading losses of PV collectors affected by walls, fences, and obscuring objects. The present article mathematically formulates shadow expressions for wall and inter-row shading on PV collectors and calculates the percentage of annual shading losses affected by wall heights and azimuth angles, the distances of walls to collectors, and the length and azimuth angles of collectors. This study indicates that the shading losses increase for shorter distances from the collector to the walls and for higher walls. Shading losses may reach 7 percent for wall heights of 4 m and at a distance of 2 m from the collectors to a wall. The results indicate that wall shading dominates inter-row shading.

Evolution mechanism of deviated well fiber-optic strain induced by single-fracture propagation during fracturing in horizontal wells

Considering the high construction cost of horizontal adjacent well monitoring and the lack of vertical adjacent well fiber optic for obtaining fracturing information, this paper proposes the use of deviated wells with fiber optics for monitoring purposes. To demonstrate the advantages of deviated well fiber optics and the feasibility of their deployment, this paper constructs a forward model based on the finite element coupled with cohesive element approach to simulate the strain induced by the propagation of a single hydraulic fracture in horizontal wells on deviated well fiber optics, and conducts a numerical simulation analysis of the strain induced by the propagation of a single hydraulic fracture on deviated well fiber optics. The results show that the strain evolution induced by single-fracture propagation in deviated well fiber optics can be divided into four stages: strain-enhancing, strain-converging, tensile strain-expanding, and linear strain-converging. The strain evolution characteristics of deviated well fiber optics are manifested as follows: a “heart-shaped” tensile strain convergence zone with a certain deviation appears in the middle, which subsequently converges into a tensile strain convergence band, with compressive strain convergence zones on both sides, and an expanding tensile strain convergence zone on the outer side of the compressive strain convergence band. The analysis finds that when the well inclination angle is greater than 45°, the strain response characteristics of deviated well fiber optics are mainly governed by the width expansion of the fracture, and when less than 45°, they are mainly governed by the height expansion of the fracture. Changes in the azimuth angle can cause a deviation of the “heart-shaped” tensile strain area and the compressive strain convergence zone in the fiber-optic strain waterfall plot, with larger deviations corresponding to smaller azimuth angles. The depth at which the deviated well fiber optics are deployed, reaching the depth of the horizontal section of the horizontal well, can reflect the upward expansion of the fracture height. The results of the analysis illustrate the advantages of deviated well fiber optics in obtaining both fracture width and height expansion information simultaneously and propose a method for selecting suitable deviated well fiber-optic construction parameters based on fracturing monitoring needs. This research can reduce the construction cost of deploying fiber optics in adjacent wells and has significant implications for guiding the layout of adjacent well fiber optics.

Impact of hardware impairments and BS antenna tilt on 3D drone localization and tracking

Today, GPS-free drone localization is increasingly gaining attention in various applications, but it faces significant accuracy challenges in three-dimensional (3D) space due to various impairments. This study investigates the effects of carrier frequency offset (CFO), phase noise (PN), and down-tilted base station (BS) antennas on drone positioning and tracking. Additionally, we explore the impact of inter-site distance (ISD) and BS density on drone position estimation accuracy. In our methodology, we consider a flying drone equipped with a single transmission antenna and BSs configured with 4 × 4 antennas under specific impairments. We first analyze the effects of these impairments on the signal’s covariance matrix. Then, using the MUSIC algorithm, we estimate the azimuth and elevation angles, which serve as the basis for drone localization using the Least Squares (LS) method across all BSs. Finally, the estimated positions feed into an Extended Kalman Filter (EKF) for tracking. Our results present a sequential analysis of the impact of all impairments on the off-diagonal covariance matrix, on the Angle of Arrival (AOA) estimation and 3D drone localization. We use simulations to demonstrate how hardware impairments affect 3D drone localization accuracy under varying ISD and BS densities.

Enlarged Curvature, Torsion and Torque in Helical Conformations and the Stability and Growth of α-Peptide under the Isochoric and Isobaric Conditions: Variatonal Optimization

The torsional deformation behavior of an elastic bar with a circular cross-section was investigated by applying invariant dyadic analysis, where the small finite displacement functions advocated by Saint-Venant (1855) were fully employed. It was found that the previously overlooked circumferential shear force field generated by pure torsion on the side walls of a bar produces an unusual torque term induced by the skew-symmetric part of the deformation tensor and exhibits quadratic length dependence along the z-axis of the bar. The adaptation of this torque term for a helical conformation of α-peptides creates moments acting on the circular cross-sections and is directed along the surface normal of circular cross-sections, which coincides with the tangent vector of the helix. The projection of this torque along the z-axis of the helix varies quadratically with the azimuthal angle. The radial component of the unusual torque, which also lies along the principal normal vector of the helix, starts to perform a precession motion by tracking a spiral orbit around the z-axis, whereas its apex angle decreases asymptotically with the azimuthal angle and finally reaches a finite value depending on the height of the helix along the z-axis. The ordinary torque terms, which are also deduced from the self- and anti-self-conjugate parts of the deformation tensor, have magnitudes half that of the full torque term reported in the literature. The present results were applied to the helical conformation of α-peptides designated by {3.611} to show that the mechanical stability of strained open-ended helical conformations can be successfully achieved by spontaneous readjustments of the surface and bulk Helmholtz free energies under isothermal isochoric conditions. It has been demonstrated that the main contribution to the mechanical stability of α-peptide 3.611 cannot come alone from the electrostatic dipole-dipole interaction potential of the anti-align excess dipole pairs but also from the surface Helmholtz free energy, which is characterized by a binding free energy of -15.5 eV/molecule (-32.56 Kcal/mole) for an alpha-peptide composed of 11 amino acid residues with a critical arc length of approximately 10 nm, assuming that the shear modulus is G = 1GPa and the surface Helmholtz specific free energy density is fs = 800 erg/cm2. This result was in excellent agreement with the experimental observations of the AH-1 conformation of (Glu)n Cys at pH 8. The present theory indicates that only two excess permanent anti-align dipole pairs for one α-Helical peptide molecule is requirement to stabilize the whole secondary structure of the protein that is exposed to heavy torsional deformation during the folding processes which amounts to 7.75 eV/molecule stored electrostatic energy compared to the interfacial Helmholtz free energy of -23.25 eV/molecule, which is exposed to hydrophobic environments.

Acoustic measurement around the pinna in the VHF region using a dummy head

We investigated the azimuth and vertical angle characteristics of head related transfer function (HRTF) at very high frequency region using head and torso simulator (HATS). The VHF sounds contain potential hazards for young people who can hear such sounds. Therefore, the relationship between hearing thresholds in very-high frequency (VHF) region and intensity of VHF sounds are very important for considering human impact. The former means sound pressure level (SPL) at eardrum, and the latter is SPL at center of two ears without a head. The difference between two SPLs means head-related transform function (HRTF). In this paper, we reported the HRTFs measured in VHF region for the azimuth and vertical angles by using a HATS. The complicated contour maps of HRTFs for angle and frequency show that the SPLs at eardrum in VHF region depend on among material, size and figure of a pinna.

Sea surface wind retrieval from CFOSAT Rotating fan-beam scatterometer in ocean cyclones

ABSTRACT Rotating fan-beam scatterometer (RFSCAT) is a radar scatterometer system for sea surface wind vector measurement. Compared with other available scatterometers, RFSCAT can provide more combination of azimuth angles and incidence angles for a single WVC (wind vector cell), this observation mechanism is more conducive to the sea surface wind direction retrieval. In this paper, the NSCAT-4DS GMF (geophysical model function) with SST (sea surface temperature) correction, and the MSS (Multiple Solution Scheme) combination with a 2DVAR (2-dimensional variational analysis) are adopted to retrieve the sea surface winds from RFSCAT on the CFOSAT (Chinese-French Oceanography Satellite). The retrieved RFSCAT sea surface winds and ASCAT (advanced scatterometer) sea surface winds are compared and tested, and the feasibility of the RFSCAT measuring sea surface winds under high wind speeds is analysed. The results show that the RMSE of the RFSCAT sea surface wind speed using improved algorithm has decreased by 0.292 m s−1, the correlation coefficient has increased by 0.032, and the residual standard deviation has decreased by 0.194 m s−1. The RMSE of RFSCAT sea surface wind direction has decreased by 5.950°, the correlation coefficient has increased by 0.002, and the residual standard deviation has decreased by 5.567°. It is shown that the changes in winds RMSE using pre-improved and improved algorithms have statistical significance. In a word, the spaceborne Ku-band rotating fan-beam scatterometer can capture the winds structure of ocean cyclones. Although there may be high wind speeds saturation phenomena, the detecting sea surface winds at high wind speeds show preferable performance.

Steering high-Q intrinsic chiral quasi-bound states in the continuum via engineered 2.5D phase-change metasurfaces.

High-Q intrinsic quasi-bound states in the continuum (QBICs) require three-dimensional (3D) geometries with both in-plane and out-of-plane mirror symmetry breakings, hindering practical implementations due to the complex architectures. Here we demonstrate that high-Q intrinsic QBICs can be flexibly controlled by using the engineered 2.5D phase-change metasurfaces of Ge2Sb2Te5 (GST). By introducing the additional out-of-plane perturbations of slant angle θ and azimuthal angle φ, highly efficient and high-Q intrinsic circular dichroism (CD) for both reflection and transmission can be realized. The spinning-selected magnetic dipole (MD) is responsible for the high-Q intrinsic chirality. The high-Q intrinsic CD is robust to the variation of structural parameters, and its Q-factor and resonance location can be tuned through the phase transition of GST.

Strong and wide-angle nonreciprocal radiation in modified distributed Bragg reflector-Weyl semimetal heterostructure

An approach to obtain easy-to-fabricate and spectrally selective nonreciprocal thermal emitter (NTE) has been proposed. The presented hybrid structure is composed of Weyl semimetal (WSM) film sandwiched by Ge/BaF2/Ge tri-layer and metal substrate. It has been shown that structural parameters hold tolerance on the order of hundreds of nanometers, which are highly favorable for fabricating with low cost and high performance. Multiband responses of the device can be realized through controlling the thickness of last Ge layer, which boosts the flexibility of preparation and potential applications. The giant nonreciprocity can be maintained with broad polar and azimuthal angle ranges. By manipulating the structural parameters, a remarkable result of nonreciprocal radiation is realized under both the transverse electric (TE) and transverse magnetic (TM) wave incidence. By changing the azimuthal angle (ϕi) of incidence, the nonreciprocity (η) can be effectively manipulated. The simulated η spectra is symmetric along the azimuthal angle ϕi=90°, and η=0 when ϕi=90°. Our results provide a much simpler way to achieve the multi-channel nonreciprocity and could lead to the advancement of power scavenging and conversion devices.

The MUSE Ultra Deep Field (MUDF). VI. The Relationship between Galaxy Properties and Metals in the Circumgalactic Medium

We present initial results associating galaxies in the Multi-Unit Spectroscopic Explorer (MUSE) Ultra Deep Field (MUDF) with gas seen in absorption along the line of sight to two bright quasars in this field to explore the dependence of metals in the circumgalactic medium (CGM) on galaxy properties. The MUDF includes ∼140 hr of Very Large Telescope (VLT)/MUSE data and 90 orbits of Hubble Space Telescope (HST)/G141M grism observations alongside VLT/Ultraviolet and Visual Echelle Spectrograph spectroscopy of the two quasars and several bands of HST imaging. We compare the metal absorption around galaxies in this field as a function of impact parameter, azimuthal angle, and galaxy metallicity across redshifts 0.5 < z < 3.2. Due to the depth of our data and a large field of view, our analysis extends to low stellar masses (<107 M ⊙) and high impact parameters (>600 kpc). We find a correlation between the absorber equivalent width and the number of nearby galaxies, but do not detect a significant anticorrelation with the impact parameter. Our full sample does not show any significant change in absorber incidence as a function of azimuthal angle. However, we do find a bimodality in the azimuthal angle distribution of absorption at small impact parameters (<2 r vir) and around highly star-forming galaxies, possibly indicating disk-like accretion and biconical outflows. Finally, we do not detect any systematic deviation from the fundamental metallicity relation among galaxies with detected absorption. This work is limited by gaps in the wavelength coverage of our current data; broader-wavelength observations with the James Webb Space Telescope will allow us to unlock the full potential of the MUDF for studying the CGM.

Assessment of solar energy potential for Bahir Dar city, Ethiopia.

The world's energy consumption is being replaced by renewable energies in large part because of the depletion of fossil fuels and the acceleration of environmental change. This study reports the amount of inward solar radiation in the date range from January 2018 to December 2022 in the Gregorian Calendar for certain areas in Bahir Dar, Ethiopia: 37°E and 11.6°N. On the horizontal surface of the case area, the month with the highest global radiation (monthly average daily) is March, at approximately 42.56 MJ/m2. day; June has the lowest diffuse radiation, at 16.2 MJ/m2.day. Furthermore, April had the most global radiation (monthly average hourly) on the horizontal surface, measuring 9.09MJ/m2.hour, while June had the lowest diffuse radiation, measuring 2.3MJ/m2.hour. In addition, this study predicts the beam, diffuse, and total radiation on the tilted collector using the total available horizontal radiation on a monthly and hourly basis. According to the research, the output of the radiation on the tilted surface towards the equator in the northern hemisphere, azimuth angle, γ = 0°, shows that the highest possible total radiation (monthly average daily) is 48.3 MJ/m2. day (January) and the highest possible total radiation (monthly average hourly) in February, 9.14 MJ/m2.hour at 1:00 p.m.

Rotational Risley prisms: Fast and high-accuracy inverse solution and application based on back propagation neural networks

In the application of rotational Risley prism systems, there is a conflict between inverse solution time and accuracy. This paper proposes an inverse solution method based on back propagation neural networks to solve this problem. The training set data for prism rotation, azimuth, and elevation angles are produced based on the beam deflection model of the actual application. After that, two independent networks are trained individually. One network is used to calculate the angular difference, while the other network calculates the synchronous rotation angle to satisfy the solutions of elevation and azimuth angles of target. The azimuth and elevation root mean square errors for the inverse solution of the spiral trajectory using the trained network were 8.04e-04 arcsec and 2.60e-3 arcsec, respectively. At a solution time of 80 µs, the pointing accuracy in the experiment was less than 1 arcsec. The experimental results demonstrate that the proposed inverse solution method can obtain high-accuracy analytical solutions with low time consumption.

A Method to Estimate Solar Panel Orientation Effectivity

Abstract In the past years, new photovoltage (solar panel) systems have been installed rapidly, for instance, in regular households. Investment decisions have often been made without knowing all technical facts and information, which are affecting total energy production of photovoltage systems. In this work, we have made a simple model, which shows solar panels energy production with the different orientation angles of solar panel. Our results show that if panels are installed more than 30 degrees from the optimal orientation, the energy production drops drastically. This result applies to both azimuth and tilt angles. The developed model is very adaptive, and it can use any locations and all orientation angles. We confirm our calculation result by making a measurement with a small (30 W) test solar panel. The model and measurement results have a good relationship (correlation coefficient, R 2 = 0.7). The obtained result is satisfactory by taking into account the fact that measurements were made during the variable weather conditions and over long period of time (six months).

Hydrodynamic force coefficients for spherical triangle shell fragments: Dependence on the aspect ratio and flatness

Euler–Lagrange simulations of particle-laden flow require hydrodynamic models of drag and lift forces for individual particles. Our goal is to develop models that can prescribe these forces for arbitrarily orientated shell objects. Here, we use computational fluid dynamics simulations of steady bottom-boundary layer flow over a series of spherical triangle shell fragments to calculate the hydrodynamic forces. The simulations explicitly resolve the wall boundary layers using grid resolution on the order of y+=1 at the shell fragment surface and use the SST k-omega turbulence closure model. These fragments cover a range of aspect ratio and flatness characteristics. The shell fragments are generated as triangular selections of a spherical shell with azimuthal and longitudinal angles proscribed based on elongation and flatness parameters (varying between 1 to 5, and 0.02 to 0.2 respectively), while characteristic length of the fragment is held constant to define the overall fragment size. Fragment orientations are considered with independently varying pitch, roll, and yaw each ranging from 0 to 180 degrees. The numerical estimates for the forces from all simulations were used to develop robust parameterizations of the drag and lift as a function of aspect ratio and flatness characteristics, as well as orientation of the shell fragments.