Unequal Radii Research Articles

Verification experiment of maximum hydraulic diameter in a novel three-dimensional asymmetric oscillating heat pipe

A novel three-dimensional asymmetric oscillating heat pipe (3DAOHP) with unequal curvature radius of upper and lower bends has been designed. Setting the basic factor of diameter from 1.9 mm to 6.2 mm, a verification experiment on the criterion of conventional maximum hydraulic diameter (MHD) has been conducted. The results show that the 3DAOHP can still perform normally and transfer heat effectively, even if the diameter exceeds the MHD by 98.1 %. And the temperature profiles at each end does not show obvious abnormalities. The thermal performance also does not show any deterioration, which still follows the rule that the larger the diameter, the stronger the heat transfer capability. The thermal resistance of the 6.2 mm 3DAOHP can reach 0.07 °C/W at 1300 W without touching the dry-out limit. Moreover, the frequency and amplitude of hot end temperature fluctuation show suppression as the diameter increases. Therefore, the conventional MHD is not a diameter limitation of oscillating heat pipe (OHP) in enhancing heat transfer. Thus, the availability of OHP in high heat loads can be improved by further increasing the tube diameter. These findings are important for the OHP application in higher heat flux.

Study on the Coalescence-Induced Jumping of Droplets with Different Radii on Superhydrophobic Surface

The phenomenon of droplet coalescence and jumping has received increasing attention due to its potential applications in the fields of condensation heat transfer and surface self-cleaning. Basic research on the process and mechanism of coalescence-induced droplet jumping has been carried out, and some universal laws have been established. However, it is found that the focus of these studies is based on two identical droplets, and the coalescence-induced jumping with different radii is rarely investigated, which is commonly encountered in nature. Therefore, it is essential to proceed with the research of coalescence and jumping of droplets with unequal radii. In this paper, molecular dynamics (MD) simulations are performed to reveal the effects of radius ratio and radius of small droplets on jumping velocity. The results show that as the increasing of radius ratio with an unchanged small droplet radius of 8.1 nm, the jumping velocity increases then decreases, which indicates there is an optimal radius ratio to maximize the jumping velocity. Additionally, it is found that if the small droplet radius is changed, the critical radius ratio for characterizing whether the coalesced droplet jumping increases with increasing the small droplet radius. Furthermore, according to energy conservation, the conversion efficiency of energy is discussed. The results show that when the radius ratio is greater than 1.3 with three different small droplet radii, the energy conversion efficiency rapidly decreases to below 1.0%; and the critical radius ratios are consistent with the result obtained from the velocity analysis. This work broadens the understanding of the more general phenomenon of coalescence-induced droplet jumping and can better guide industrial applications.

Design and analysis of a novel Bi-layer curved serpentine chaotic micromixer for efficient mixing

Mixing enhancement at the micro-scale is important in microfluidics applications, including biological and chemical analysis systems. Herein, two new designs of chaotic micromixers named Bi-layer Curved Serpentine (BCS1 and BCS2) micromixers were proposed. The performance analyses were performed by solving the steady equations of conservation of mass and momentum along with the convection-diffusion equation numerically at Reynolds numbers of 0.1–200. These micromixers consisted of curved serpentine channels stacked in two layers with different combinations of curved channel radii in each layer. They exhibited efficient homogenization with a comparatively lower pressure drop and a higher mixing cost. The main mixing processes were Dean vortices, extensional flow, and chaotic advection caused by asymmetrical vortices. The BCS1 micromixer, which has a constant but unequal radius of the serpentine channel in the top and bottom layers, showed the best mixing. BCS1 and BCS2 micromixers showed significantly higher mixing indices than the simple serpentine (SS) micromixer. Furthermore, the BCS1 micromixer provided a higher mixing cost by showing similar mixing at a ∼53% lesser pressure drop than a previously proposed serpentine micromixer. BCS1 and BCS2 micromixers showed mixing index values higher than 0.80 at Re ≥ 40 and Re ≥ 60, respectively.

Instability mechanisms of thermocapillary liquid bridges between disks of unequal radii

In this paper, we explore thermocapillary liquid bridges between two disks of unequal radii with Prandtl numbers Pr of 0.0258 (mercury) and 0.068 (gallium arsenide) to gain insight into the underlying instability mechanism. In the context of Legendre's spectral element method, we determine critical conditions via linear stability analysis and then identify the instability mechanism through energy analysis. For the mercury bridge (Pr = 0.0258), our analysis suggests that the flow instability undergoes an oscillatory bifurcation for radius ratios in the range of 0.5 ≤ Γr ≤ 0.66. In particular, we found three transitions between two-dimensional steady axisymmetric flow and three-dimensional stationary flow by further increasing the radius ratio to 0.73 ≤ Γr ≤ 0.76. For the gallium arsenide liquid bridge (Pr = 0.068), the instability is always an oscillatory bifurcation in the whole computational interval. Furthermore, our observations identify six instability modes with different mechanisms. All instability modes in the mercury bridge (Pr = 0.0258) are purely hydrodynamic, but the thermocapillary mechanism cannot be ignored in the gallium arsenide liquid bridge (Pr = 0.068) because of the enhanced Pr effect.

Subwavelength thermally controlled acoustic topological interface states in split hollow spheres

This article puts forward theory and design approaches for three thermally controlled subwavelength acoustic topological insulators. They are presented by immersing arrays of split hollow spheres (SHSs) or cubes in an air background and performing a study on the band structures and topological interface states. The periodically immersed rhombic shape unit cell comprising of two SHSs is analyzed firstly. A subwavelength local resonance bandgap and a Dirac point at the corner of the irreducible Brillouin zone are observed. After inducing a gap for the Dirac cone with unequal inner radius of spheres, we observe topological phase transition by mode shape and valley Chern-number analysis. Generally, local resonance systems are always limited to narrow and fixed bandgaps, therefore active and passive control of the structure are demonstrated. A strip supercell is constructed to induce topologically protected interface mode and to capture highly localized acoustic energies at the interface. Similar analyses are performed on the enlarged hexagonal model with six SHSs and the rhombic model with two split hollow cubes. This study provides a new degree of freedom for active control of acoustic topological modes and sound wave propagation.

A Computational Study of Hydrodynamic Interactions Between Pairs of Sperm With Planar and Quasi-Planar Beat Forms

Although hydrodynamic interactions and cooperative swimming of mammalian sperm are observed, the key factors that lead to attraction or repulsion in different confined geometries are not well understood. In this study, we simulate the 3-dimensional fluid-structure interaction of pairs of swimmers utilizing the Method of Regularized Stokeslets, accounting for a nearby wall via a regularized image system. To investigate emergent trajectories of swimmers, we look at different preferred beat forms, planar or quasi-planar (helical with unequal radii). We also explored different initializations of swimmers in either the same plane (co-planar) or with centerlines in parallel planes. In free space, swimmers with quasi-planar beat forms and those with planar beat forms that are co-planar exhibit stable attraction. The swimmers reach a maintained minimum distance apart that is smaller than their initial distance apart. In contrast, for swimmers initialized in parallel beat planes with a planar beat form, we observe alternating periods of attraction and repulsion. When the pairs of swimmers are perpendicular to a nearby wall, for all cases considered, they approach the wall and reach a constant distance between swimmers. Interestingly, we observe sperm rolling in the case of swimmers with preferred planar beat forms that are initialized in parallel beat planes and near a wall.

A Novel High Concentration Fresnel Lens as a Solar Concentrator

Abstract This paper describes the design methodology for a novel Fresnel lens. The original Fresnel lens is obtained from a plano-convex lens, whose spherical surface is split into a number of divisions (called facets), collapsed onto the flat base. Thus, all the facets of the original Fresnel lens have the same radius as that of the plano-convex lens. The proposed design aims to achieve better ray concentration and reduced spherical aberration than the original Fresnel lens by constructing spherical facets with unequal radii. The centers and radii of facets are constrained so that the ray refracted from the bottom vertex of each facet on one side of the optical axis and the ray refracted from the outer vertex of the corresponding facet on the other side of the optical axis must intersect at the focal plane. The proposed lens design has resulted in a 275% gain in the concentration ratio and a 72.5% reduction in the spherical aberration compared to the original lens of the same aperture diameter and number of facets. The performance of both novel and original Fresnel lenses when used as solar concentrators with a conical coil receiver is evaluated. The novel Fresnel lens led to increased heat gain and resulted in a compact solar collector design.

DETERMINATION OF THE GEOMETRIC SIZE OF THE COMMUNICATION HOLE OF TWO CYLINDRICAL WAVEGUIDES

It is always relevant to improve performance in electrodynamic systems. When solving problems on the electrodynamic characteristics of hollow coupled systems, the question is often asked about the relationship between them, about the form of the communication hole with a certain orientation of the guide axes in the system elements and its geometric dimensions. Such a system is a generator (small-sized local oscillator8 mmrange). The inclusion of a high-Q stabilizing resonator in the Gunn diode generator significantly improves its characteristics. The use of a low-quality coaxial chamber as a diode section increases the generation stability. However, this complicates the numerical calculations of the electrodynamic system of the generator due to the uncertain configuration of the communication hole, since it arises as a result of the intersection of two cylindrical volumes of a coaxial waveguide and a high-quality cylindrical resonator. In the present work, the task is determination of the shape and size of the intersection figure of two unequal radii of cylindrical volumes with axes orthogonally located in relation to each other at a distance. The resulting shape of the intersection figure in a planar approximation forms a flat ellipse. The larger diameter of the coupling ellipse depends on the diameter of the resonator, the smaller on the inner diameter of the coaxial chamber, depending on the distance between their axes. It is necessary to determine the equivalent rectangular hole of the connection. Its presence simplifies the construction of a tangent electric field at the communication hole, which is necessary for numerical calculations of the electrodynamic characteristics of the system. In this case, with constant diameters of the cylindrical resonators, the geometrical dimensions of the hole depend only on the distance between the axes. It is with this circumstance that they are dealing with the study of the connection between a cylindrical coaxial diode section and a high-Q stabilizing resonator. Unlike other circuits, where the diode is included in the waveguide section, in this case, its inclusion is made in a coaxial line.

Capillary bridges between spherical particles under suction control: Rupture distances and capillary forces

This study focuses on properties of axisymmetric capillary bridges between spherical particles in the pendular regime under suction control. Using the toroidal approximation in combination with the governing Young-Laplace equation, analytical expressions for the rupture distance (dependent on the suction) and for the capillary force (dependent on the suction and the interparticle separation distance) have been obtained that do not involve any calibrated coefficient. The developed analytical expressions are effective for values of the dimensionless suction larger than 104. To predict capillary forces and rupture distances for a wider range of values of the dimensionless suction, closed-form expressions for rupture distances and capillary forces have been obtained by curve-fitting to a large dataset of numerical solutions of the Young-Laplace equation. It is shown that these expressions can also be employed for capillary bridges between spheres with unequal radii when the Derjaguin radius is employed.

Robust cylinder fitting in laser scanning point cloud data

Cylinders play a vital role in representing geometry of environmental and man-made structures. Most existing cylinder fitting methods perform well for outlier free data sampling a full cylinder, but are not reliable in the presence of outliers or incomplete data. Point Cloud Data (PCD) are typically outlier contaminated and incomplete. This paper presents two robust cylinder fitting algorithms for PCD that use robust Principal Component Analysis (PCA) and robust regression. Experiments with simulated and real data show that the new methods are efficient (i) in the presence of outliers, (ii) for partially and fully sampled cylinders, (iii) for small and large numbers of points, (iv) for various sizes: radii and lengths, and (v) for cylinders with unequal radii at their ends. A simulation study consisting of 1000 cylinders of 1 m radius with 20% clustered outliers, reveals that a PCA based method fits cylinders with an average radius of 2.84 m and with a principal axis biased by outliers of 9.65° on average, whereas the proposed robust method correctly estimates the average radius of 1 m with only 0.27° bias angle in the principal axis.

An Energy Aware Adaptive Kernel Density Estimation Approach to Unequal Clustering in Wireless Sensor Networks

Energy conservation is one of the most important challenges in wireless sensor networks (WSNs). Therefore, compared with the traditional networks, the WSNs not only need high-quality services with high throughput or low transmission delay, but also pay greater attention to energy utilization to extend network lifetime. The clustering routing algorithm is considered to be among the effective ways to collect and transmit data in WSNs. Cluster head (CH) plays a vital role in the cluster which is in charge of data aggregation and data transmission, so their energy consumption is higher than non-CH nodes. The traditional clustering algorithm tends to have the same size in each cluster. However, due to the randomness of the node distribution, the equal clustering mechanism obviously cannot reduce energy consumption. In order to solve this problem, this paper contributes a new unequal clustering algorithm, an energy-aware adaptive kernel density estimation algorithm (EAKDE), which aims to balance the energy dissipation among the CHs. EAKDE utilizes fuzzy logic to determine the priority of nodes competing for CH. In order to adapt the dynamic change of node conditions, adaptive kernel density estimation algorithm is utilized to assign the appropriate unequal cluster radius to sensor nodes. The simulation results demonstrate that, in different scenarios, EAKDE outperforms the other well-known algorithms in terms of network stability, network lifetime, and energy efficiency.

Simulation and experiments on the capillary forces between two continuously fully wet circular disks

The capillary force of the axisymmetric liquid bridge between two continuously fully wet disks is investigated. The energy minimization method shows excellent consistency with the method based on the Young–Laplace equation. The capillary force between two disks is typically repulsive at small distances, and becomes attractive with increasing separation distance for a fixed liquid volume. In addition, the radius ratio of the two disks has a crucial effect on the capillary forces. The mean curvature, pinned contact angles, and rupture distance of the liquid bridge between two disks of various sizes are characterized. The mean curvature of the liquid bridge first decreases; after a minimum value is achieved, it gradually increases. When the two disks are of equal size, the pinned contact angles are identical. When the two disks have unequal radii, the pinning angles of the liquid at the upper and lower disks tend to coincide with the increase in separation distance. The rupture distance decreases with the increase in the ratio of the radii of the bottom disk to the top one. Finally, the force-distance curves for fully wet circular disks have been experimentally verified, and good consistency has been found.

Analysis of snake rolling force and torque with changes of thickness depending on unequal roll radii based on pure aluminum experiments

An analytical model, in which unequal radii are replaced with an equivalent radius, is creatively proposed to predict the rolling force and roll torque in general case of snake rolling. With the model, the effects of roll radius ratio, roll speed ratio, offset distance between rolls, reduction and friction coefficient on rolling forces in hot snake rolling of aluminum alloy are obtained. Also, the thicknesses of slab are investigated in different zones, which firstly propose the changes of thickness during snake rolling. Owing to the good agreement with the results measured in experiments and calculated by finite element method and other traditional models, those calculated by the proposed model are verified. The proposed model can be used to predict more accurate theoretical results for snake rolling force and torque.

Stresses in a Spherical Shell Loaded Through Rigid Inclusions

The stress state of a shallow isotropic spherical shell with circular rigid inclusions subject to a force or a moment is determined. The case of two inclusions of unequal radii is analyzed numerically. It is established that the stresses in the shell increase substantially with decrease in the inclusion radius and the distance between the two inclusions

Stresses in a Shallow Spherical Shell Loaded by Two Tangential Forces Via Rigid Circular Inclusions

We obtain the analytic solution of the problem of stressed state for an isotropic shallow spherical shell with two circular perfectly rigid inclusions loaded by shear forces. The cases of two inclusions of equal or unequal radii are investigated numerically. It is shown that the stresses acting in the shell significantly increase as the radii of the inclusions or the distance between them decrease.

Slab analysis of large cylindrical shell rolling considering mixed friction

Large cylindrical shell rolling is an advanced plastic-forming technique that has unequal speed and radius of both its upper and lower rolls. A theoretical model for a large cylindrical shell rolling that is based on the slab method is proposed, in which the non-uniform normal and shear stresses that act on the vertical sides are considered. A mixed friction model of combined Coulomb and sticking friction is used to present interface friction, to improve the accuracy of the proposed model. The rolling pressure, rolling force, and torque as well as friction stress can be rapidly and easily calculated through the proposed model at different rolling conditions. The predicted rolling force is consistent with the experimental result. The research results provide valuable guidelines for both the design and optimization of rolling product, process, and equipment.

Correction of astigmatism and coma using analytic theory of aberrations in imaging spectrometer based on concentric off-axis dual reflector system

A specific imaging spectrometer based on a concentric off-axis dual reflector system is proposed, free of astigmatism and coma. The described imaging spectrometer consists of four spherical mirrors and a plane grating. The analytic theory of aberrations and the optical path-length concept are used to derive the astigmatism elimination and coma removal. It is shown that the astigmatism in these imaging spectrometers is eliminated by characterizing three angles, and the coma is corrected when unequal mirror radii are configured in collimating and condensing optics. The developed aberration principle is verified by comparing the performance of the astigmatism-eliminated spectrometer with the spectrometer which has neither astigmatism nor coma.

Oscillatory flow about a cylinder pair with unequal radii

We consider the oscillating flow about a pair of circular cylinders of unequal diameter. In addition to the relative size of the cylinders, the distance between them can be varied, as can the angle that the undisturbed oscillatory flow makes with the line joining the cylinder centres. For small-amplitude vibrations a time-independent, or steady streaming, motion develops that persists beyond the Stokes layer that forms at the solid boundary. This persistent streaming is considered for large values of a suitably defined streaming Reynolds number.

Stress concentration in a spherical shell with two neighboring circular holes

UDC 539.3 We have solved analytically the problem of the stressed state in an isotropic shallow spherical shell with two circular holes. The cases of the close location of holes of both equal and unequal radii in the shell under the action of internal pressure have been investigated numerically. We have detected a considerable increase in stresses on the bulkhead between the holes at their approach. Stress concentration in plates and shells with several holes has been investigated since long ago [2], but, nevertheless, these data remain important for engineering practice [3–8], especially in the case of close location of the holes between themselves [7]. Numerical results for an isotropic shallow spherical shell with two equal circular holes under the action of internal pressure are described in [1, 2]. Here, the minimal bulkhead width constituted 0.7 of the hole radius. As shown in [7] for a stretched plate with two holes, a significant increase in stress concentration takes place if the holes are located closely. Therefore, in the present work, we study the cases of close location of two circular holes (including unequal) in a spherical shell.

On the mutual influence of closely located circular holes with rigid contours in a spherical shell

We consider a problem of the stressed state of a shallow isotropic spherical shell containing two circular holes with rigid undeformable contours. The cases of rather close location of contours with both equal and unequal radii in the shell under an internal pressure are numerically investigated. It is established that stresses in the bridge between the contours increase substantially as the distance between them decreases.