Circular Annulus Research Articles

Spectral optimization for Robin Laplacian on domains admitting parallel coordinates

AbstractIn this paper we deal with spectral optimization for the Robin Laplacian on a family of planar domains admitting parallel coordinates, namely a fixed‐width strip built over a smooth closed curve and the exterior of a convex set with a smooth boundary. We show that if the curve length is kept fixed, the first eigenvalue referring to the fixed‐width strip is for any value of the Robin parameter maximized by a circular annulus. Furthermore, we prove that the second eigenvalue in the exterior of a convex domain Ω corresponding to a negative Robin parameter does not exceed the analogous quantity for the exterior of a disk whose boundary has a curvature larger than or equal to the maximum of that for .

Investigation of rectangular apertures and their application on speckle imaging

BackgroundAn aperture in the form of four squares arranged symmetrically along the cartesian coordinates with equal distances from the center investigated. Three models are suggested in the computation of the Point Spread Function PSF using the FFT technique. In the 1st model, circular annulus is placed in the center, while in the 2nd model a square annulus is shown, and in the 3rd model, two symmetric squares in the models 1, 2 are replaced by two symmetric rectangles while the center remains of square annulus. In all the models, central obstruction is made seeking to improve the PSF.ResultsAn analytical formula for the PSF for the aperture described in the 1st model is obtained. In addition, the autocorrelation corresponding to these apertures are computed and compared with the known autocorrelation corresponding to the whole square aperture. An application on speckle imaging is given using these apertures combined with the diffuser. All images for the design of the apertures and the speckle images are made using the MATLAB code.ConclusionsThe resolution computed from the FWHM showed an improvement for the suggested square apertures as compared with the uniform square aperture where the total width is kept constant. In addition, the strength of the legs in the PSF for the suggested apertures is much higher than that corresponding the uniform aperture which makes it useful for imaging of extended objects.

Analytical solution of cloaking in creeping flow inside composite porous media with simultaneous heat transfer

ABSTRACT This paper presents a theoretical analysis of steady-state creeping flow in a composite porous domain with coupling heat transfer. The problem arises in thermal cloaking studies in which it is desirable to hide an obstacle from the surrounding hydrodynamic and thermal fields, by suitably covering the obstacle with a cloak having specific material properties. The particular system under investigation consists of a porous composite region, with a thermal-hydro field driven by imposed temperature and pressure difference in the surrounding. Both two dimensional circular and three-dimensional axisymmetric spherical annuli are considered. Under the validity of Darcy law for a porous medium, an exact solution satisfying the continuity, momentum and energy equations at any Péclet number is derived. The analytical results have been numerically verified using the commercial code COMSOL.

Regression modeling for laminar flow of herschel–barkley fluids in the concentric elliptical annulus

Deep fractured formations have poor pressure-bearing capacity and a narrow safety drilling fluids density window, leading to high risk of well control. Accurate prediction of annulus pressure drop is great significance to the safe drilling of deep fractured formations. Conventional annulus pressure drop predictions are mostly based on regular circular annulus but elliptical annulus are easily formed due to the rock structure, mechanical properties and heterogeneity of ground stress. In order to accurately and conveniently predict the pressure drop of the Herschel–Barkley (H–B) fluids laminar flow in the concentric annulus of elliptical wellbore (CAEW), an analytical model based on the assumption of narrow-slot flow was established and solved by considering the flow core in this paper. We found that the flow pattern index, the proportion of inner and outer diameter and the proportion of the major and minor axes were the main influencing factors through analysis. On this basis, a new method for predicting pressure drop of the H-B fluids in the CAEW was established. It was found that the new regression model was in excellent agreement with the analytical and numerical models, with most of the error bars within ± 10%, indicating that the regression model could accurately predict the dimensionless pressure gradient in the CAEW without complex mathematic method.

The use of autorefractors using the image-size principle in determining on-axis and off-axis refraction. Part 2: Theoretical study of peripheral refraction with the Grand Seiko AutoRef/Keratometer WAM-5500.

To determine, through simulations, the likely validity of Grand-Seiko autorefractors with annular targets in peripheral refraction. Using a physical model eye, the distance inside the eye to which the Grand Seiko AutoRef/Keratometer WAM-5500 beam was converging and the effective size of its outer diameter at the cornea were determined. Grand-Seiko refraction was calculated from Rx =(θ+α)/h1 , where θ is the angle of the ingoing radiation beam, h1 is the height of the beam at the anterior cornea and α is the angle of the beam emerging from the eye following reflection at the retina. Two eye models were used: a Navarro schematic eye and a Navarro schematic eye with a contact lens having a highly positive aspheric front surface. The instrument beam was determined to be converging towards the eye to a distance of 24.4mm behind the corneal vertex, with a 2.46mm effective size outer diameter of the beam at the anterior cornea. The Grand-Seiko refractions provided accurate estimates of peripheral refraction for the model eyes. The results were closer to Zernike refractions than to Zernike paraxial refraction. Spherical aberration influenced refraction by up to 0.5 D, and peripheral coma had limited influence. Grand-Seiko autorefractors in current use, and having a circular annulus with an ingoing effective outer diameter at the front of the eye of about 2.4mm, are likely to give valid peripheral refractions.

Investigating the effects of a non - uniform magnetic field on heat and flow characteristics of a ferrofluid

A numerical study is performed to investigate the effect of a non - uniform magnetic field from a current carrying wire on the ferrofluid flow. The analysis is carried out for a semi circular annulus with three different locations of wire relative to it, by solving coupled set of flow field equations, energy equations and the Maxwell’s magnetostatics equations. Results from the present study offers better insight about the ferrofluid behaviour and heat transfer mechanism. It also explains the dependency of flow distribution on the location of the electric wire and the magnitude of current flowing through it.

Quantification of noncircular stent expansion after TAVR into a pathological annulus and its impact on paravalvular leakage

Abstract Patients undergoing transcatheter aortic valve replacement (TAVR) may suffer severe clinical complications, caused by paravalvular leakage (PVL) which is defined as leakage between TAVR and aortic annulus. PVL is often facilitated by a severely calcified annulus. This limits the expansion of a self-expandable TAVR stent. To assess TAVR performance in terms of leakage, measurement of regurgitation fraction in a pathophysiological annulus is recommended according to ISO 5840. For this purpose, a configuration of a circular annulus with a calcification nodule has been proposed in the recently published ISO 5840. The impact of the proposed pathophysiological annulus model on the expansion of self-expandable TAVR stents and on the regurgitation fraction was investigated in this study. For this purpose, two commercially available selfexpandable TAVRs (Evolut R and Portico) were implanted in a calcified annulus model. Circular expansion of the TAVR stents was investigated based on μCT scans of the implanted TAVR. The calcification-induced area in which retrograde flow can occur during diastole was detected. These results were then compared with the experimentally determined regurgitation fraction obtained from pulse duplicator tests. The results of the μCT scans showed a continuous leakage area in the region of the annulus for the Evolut R compared to a locally larger leakage area of the Portico, which, however, reattaches to the annulus in the distal inflow region. The hydrodynamic measurements confirmed a smaller leakage in the pathological annulus for the Portico. In summary, it can be assumed that a continuous leakage area in the TAVR stent inflow region encourages the PVL of TAVR.

Axisymmetric lattice Boltzmann model with slip boundary conditions for liquid flows in microtube

Lattice Boltzmann (LB) method, which is a mesoscopic numerical method, has been considered as a powerful tool to study microscale gas and liquid flows. Boundary slip phenomenon, which is a significant feature of both microscale gas and liquid flows, has been extensively studied by the LB method in the past decade. However, most of the previous works have focused on the microchannel flows and studies on the microtube flows are very rare. In this paper, we investigate the widely used slip boundary conditions, i.e., combined bounce-back and specular-reflection (BS) scheme, combined Maxwell-diffusion and specular-reflection (MS) scheme, and combined Maxwell-diffusion and bounce-back (MB) scheme, for the axisymmetric LB model with multi-relaxation-time (MRT) in detail. In order to realize the Navier slip boundary condition for liquid flows, we put forward to a reasonable strategy for determining the combination coefficients and the relaxation time. The proposed boundary schemes are validated by some numerical tests including the Hagen–Poiseuille flow, axisymmetric Womersley flow, Poiseuille flow in a circular annulus, and Womersley flow in a circular annulus. Numerical results are consistent with the analytical solutions, which demonstrate that the proposed boundary schemes are suitable for microscale liquid flows in microtube.

Effect of internal heat generation or absorption on conjugate thermal-free convection of a suspension of hybrid nanofluid in a partitioned circular annulus

This study aims to explain the impact of the presence of a solid conductive partition on the thermal-free convective motion mechanism and heat transmission process within a concentric circular annulus filled with a water-based hybrid nanoliquid containing Copper (Cu) and Alumina (Al2O3) nanoparticles. The thermal natural convective flow is formed within the annulus due to the temperature difference which is externally imposed between the internal heated cylinder and the external cooled one and internally generated by the interior heat generation/absorption (IHG/A) phenomenon. The technique of finite volume is applied to discretize and approximately solve the non-dimensional conservation equations. The influence of selected factors such as the nanoparticles concentration, Rayleigh number, fluid/solid heat conductivity ratio, and the IHG/A parameter on the thermo-hydrodynamic behavior and heat exchange rate is interpreted. The findings show that, in the presence of a conductive solid partition, the combined effects of the IHG/A phenomenon and the combined nanoparticles considerably modify the flow and heat exchange behaviors within the annulus. We also employed a new correlation to predict the mean heat exchange rate in the defined input parameter range.

Consolidated theoretical/empirical predictive method for subcooled flow boiling in annuli with reference to thermal management of ultra-fast electric vehicle charging cables

Ability to deliver very high electrical current through a charging cable is key to successful proliferation of electric vehicles (EVs). Associated with high current delivery is a host of thermal problems stemming from the need to remove enormous amounts of heat from the cable. This study seeks to develop a highly effective thermal management scheme based on subcooled flow boiling principles. The main objective is to develop a consolidated theoretical/empirical method for predicting the heat transfer and pressure drop characteristics of both laminar and turbulent flows though concentric circular annuli with uniformly heated inner wall and adiabatic outer wall. Although maintaining subcooled boiling along the entire cable is a key practical objective, this consolidated method is shown to be capable of tackling multiple flow regimes (single-phase liquid, subcooling boiling, saturated boiling, and single-phase vapor) and highly effective at predicting local surface and fluid temperatures. This method is then adopted to design and optimization of very high current EV charging cable cooling system using dielectric fluid HFE-7100 as coolant. Effects of various parameters, including electrical current, both wire and conduit sizes, inlet fluid temperature, and flow rate are carefully addressed and recommendations made for effective and robust overall system design.

Peristaltic pumping in thin non-axisymmetric annular tubes.

The two-dimensional laminar flow of a viscous fluid induced by peristalsis due to a moving wall wave has been studied previously for a rectangular channel, a circular tube and a concentric circular annulus. Here, we study peristaltic flow in a non-axisymmetric annular tube: in this case, the flow is three-dimensional, with motions in the azimuthal direction. This type of geometry is motivated by experimental observations of the pulsatile flow of cerebrospinal fluid along perivascular spaces surrounding arteries in the brain, which is at least partially driven by peristaltic pumping due to pulsations of the artery. These annular perivascular spaces are often eccentric and the outer boundary is seldom circular: their cross-sections can be well matched by a simple, adjustable model consisting of an inner circle (the outer wall of the artery) and an outer ellipse (the outer edge of the perivascular space), not necessarily concentric. We use this geometric model as a basis for numerical simulations of peristaltic flow: the adjustability of the model makes it suitable for other applications. We concentrate on the general effects of the non-axisymmetric configuration on the flow and do not attempt to specifically model perivascular pumping. We use a finite-element scheme to compute the flow in the annulus driven by a propagating sinusoidal radial displacement of the inner wall. Unlike the peristaltic flow in a concentric circular annulus, the flow is fully three-dimensional: azimuthal pressure variations drive an oscillatory flow in and out of the narrower gaps, inducing an azimuthal wiggle in the streamlines. We examine the dependence of the flow on the elongation of the outer elliptical wall and the eccentricity of the configuration. We find that the time-averaged volumetric flow is always in the same direction as the peristaltic wave and decreases with increasing ellipticity or eccentricity. The additional shearing motion in the azimuthal direction will increase mixing and enhance Taylor dispersion in these flows, effects that might have practical applications.

Mixed boundary value problems in power-law functionally graded circular annulus

The present work proposes a semi-analytical technique for solution of mixed boundary value problem in functionally graded circular annulus wherein shear modulus varies radially in power-law form while Poisson’s ratio is constant. The technique relies on two main steps. In the first step, corresponding to terms in periodic Fourier series applied individually as traction along the annulus surface, stress and displacement field in the annulus is computed harnessing Airy stress functions approach. In the second step, leveraging the strain–displacement relations in polar co-ordinates, mixed boundary conditions are rendered in terms of displacement all along the annulus surface. Assuming the unknown traction along the annulus surface in terms of periodic Fourier series with finite terms, the modified displacement boundary condition, family of solution from the first step and orthogonality of sine and cosine functions is used to generate a system of simultaneous linear equations for the series coefficients. Knowing the coefficients of periodic Fourier series, stress and displacement field can be computed everywhere in the annulus. The first step is digitized in terms of MAPLE functions, exhaustively validated through traction distribution comprising of normal, shear traction on part of the boundary and pair of equal and diametrically opposite point load along the boundary. The second step is corroborated through a problem where the inner surface is subjected to a specified traction distribution and mixed boundary conditions exist along the outer surface in the form of complete constraint along a part and traction-free condition elsewhere.

Effect of wall-slip on natural convection in a circular annulus

Two-dimensional natural convection in an annulus enclosed by a hot inner cylinder and cold outer cylinder with air (Prandtl number, Pr=0.71) as the fluid is numerically investigated for Rayleigh number (Ra)= 5 × 104 using OpenFOAM. For a gap width to radius ratio (L/Ri ) of 1.6, the slip configurations are imposed by varying the Slip factor (SF) from 0 (no-slip) to 1 (full-slip) in steps of 0.2. The flow patterns and thermal fields for each slip factor are visualised using streamlines and isotherms and heat transfer is quantified by Nusselt number (Nu). It is observed that the natural convection patterns at full-slip boundary condition (SF=1) exhibit unique phenomena like vortex splitting, shrinkage in the thermally stagnant regions, and reduction in thermal boundary layer thickness. The heat transfer characteristics, in general, get enhanced with the increase in SF.

Experimental investigation of subcooled flow boiling in annuli with reference to thermal management of ultra-fast electric vehicle charging cables

Transportation industry is presently in fast track to transition from Internal Combustion Engine Vehicles (ICEVs) to Electrical Vehicles (EVs). One of the most pressing challenges to full adoption of EVs is very slow charging at the networks of charging stations proposed worldwide. Despite many recent so-called ‘ultra-fast’ charging methods, which capitalize on a variety of single-phase liquid schemes to cool the charging cable, thermal constraints limit the electrical current carrying capacity of the fastest commercial chargers to about 500 A. Achieving the faster charging time required for the anticipated proliferation of EVs will require increasing this current capacity to at least 2000 A, which poses formidable thermal challenges in design of the charging cable. This study explores the development of a vastly more powerful charging cable thermal management scheme to achieve this higher current threshold. Subcooled flow boiling is proposed as the primary means to dissipating the larger amounts of heat generated at higher currents. Experiments are performed by pumping highly subcooled dielectric liquid HFE-7100 though a concentric circular annulus mimicking a segment of an actual cable, with a uniformly heated 6.35-mm-diameter inner surface representing the electrical conductor and adiabatic 23.62-mm-diameter outer surface the external conduit. All experimental cases considered are conFig.d to ensure subcooled fluid conditions throughout the test module. It is shown the proposed cooling scheme is capable of tackling currents up to 2438 A, around four times higher than the present-day commercial maximum. With appropriate batteries and other ancillary components, this technology is expected to bring EV charging times down to less than 5 minutes. Aside from demonstrating this potential, an assessment of available subcooled boiling heat transfer coefficient correlations identified Moles and Shaw's to predict the new experimental data with an overall mean absolute error of only 11.68%. The flow and heat transfer physics are also explained in detail.

Dispersion as a waste-clearance mechanism in flow through penetrating perivascular spaces in the brain

Accumulation of metabolic wastes in the brain is correlated with several neurodegenerative disorders, including Alzheimer’s disease. Waste transport and clearance occur via dispersion, the combined effect of diffusion and advection by flow of fluid. We examine the relative contributions of diffusion and advection in the perivascular spaces (PVSs) that surround penetrating cortical blood vessels and are filled with cerebrospinal fluid (CSF). To do so, we adapt prior analytic predictions of dispersion to the context of PVSs. We also perform advection-diffusion simulations in PVS-like geometries with parameters relevant to transport of amyloid-beta (associated with Alzheimer’s) in a variety of flows, motivated by in vivo measurements. Specifically, we examine solute transport in steady and unsteady Poiseuille flows in an open (not porous) concentric circular annulus. We find that a purely oscillatory flow enhances dispersion only weakly and does not produce significant transport, whereas a steady flow component, even if slow, clears waste more effectively.

DIFFERENTIAL WEATHERING OF DIAGENETIC CONCRETIONS AND THE FORMATION OF NEOPROTEROZOIC ANNULATED DISCOIDAL STRUCTURES

ABSTRACTAnnulated discoidal structures are common in many Neoproterozoic and particularly Ediacaran successions. Their interpretations, especially their biogenicity, are often contentious. Some of them (e.g., Aspidella and related forms) are demonstrably biological structures and may represent holdfasts of frondose Ediacara-type organisms. Others may represent fluid escape structures or tool marks produced by the rotation of tethered organisms. Here we show that differential chemical weathering of diagenetic dolomite concretions can also produce annulated discoidal structures that could be mistaken as Ediacara-type discoidal fossils. Using transmitted-light and cathodoluminescence microscopy in conjunction with Raman and energy dispersive spectroscopy, we analyzed dolomitized discoidal concretions embedded in a phosphorite matrix from the Ediacaran Miaohe Member of South China. Our observations reveal that pervasive and displacive syn-compactional dolomitization of the concretions and differential compaction of surrounding sediment led to the formation of biconvex or upward-convex primary laminae within the concretions. When exposed along parting surfaces and/or bedding planes, disparities in the weatherability of the warped primary laminae within the concretions resulted in the formation of circular annuli that mimic Neoproterozoic discoidal structures, some of which have been contentiously interpreted as discoidal fossils. These findings emphasize the importance of thin-section petrographic observations in the study of discoidal dubiofossils in order to assess their origin as diagenetic concretions or as discoidal macrofossils.

MHD natural convection of a CNT-based nanofluid-filled annular circular enclosure with inner heat-generating solid cylinder

The present work is dedicated to understanding the natural convective flow mechanism and heat exchange under magnetic field within a concentric circular annulus between a heat-generating conductive internal cylinder and an isothermally cold external cylinder filled with a CNTs-water-based nanoliquid. The free convective flow is generated by the temperature gradient created between the inner heat-generating solid cylinder and the outer cold cylinder. The flow equations in their dimensionless form are numerically solved via the technique of finite volume. The dependency of various factors and their interrelationships affecting the thermo-hydrodynamic behavior and heat exchange rate within the system has been delineated. The findings of this study emphasize the role of the considered control parameters with regards to the hydro-thermal characteristics and the heat exchange rate within the annulus.

Some applications of extended calculus to non-Newtonian flow in pipes

Fractional and non-Newtonian calculus are an extension of classical calculus, usually known for providing new mathematical tools useful in science, developed from alternative approaches. Among fractional calculus, Riemann-Liouville and Caputo fractional derivatives have been the most popular operators employed in spite of their complexity. In this work, two novel and compact methods are presented as an alternative to the fractional calculation options. To test the feasibility of proposed methods, three classical fluid mechanic problems are studied: the flow through circular pipe, parallel plates and annulus, by modifying the constitutive equations into their fractional equivalent. On the other hand, a new weighted non-Newtonian derivative is proposed to extend the possibilities to model fluid viscosity based on the influence of nonadjacent layers, using the pipe flow as an example. Results show that proposed fractional models can describe shear-thinning and shear-thickening behaviors depending on the fractional order of the derivative, while the weighted derivative allows to expand the way viscosity is modeled, demonstrating the suitability of these approaches to describe physical problems.

Thermal Accelerometer Simulation by the R‑Functions Method

As well as many modern devices, thermal accelerometers (TAs) need a sophisticated mathematical simulation to find the ways for their performance optimization. In the paper, a novel approach for solving computational fluid dynamics (CFD) problems in the TA’s cavity is proposed (MQ-RFM), which is based on the combined use of Rvachev’s R-functions method (RFM) and the Galerkin technique with multiquadric (MQ) radial basis functions (RBFs). The semi-analytical RFM takes an intermediate position between traditional analytical approaches and numerical methods, such as the finite-element method (FEM), belonging to the family of the so-called meshless techniques which became popular in the last decades in solving various CFD problems in complex-shaped cavities. Mathematical simulation of TA by using the MQ-RFM was carried out with the purpose to simulate the temperature response of the device and to study and improve its performance. The results of numerical experiments were compared with well-known analytical and numerical benchmark solutions for the circular annulus geometry and it demonstrated the effectiveness of the MQ-RFM for solving the convective heat-transfer problem in the TA’s cavity. The use of solution structures allows one to take a relatively small number of expansion terms to achieve an appropriate accuracy of the approximate solution satisfying at the same time the given boundary conditions exactly. The application of the MQ-RFM gives the possibility to obtain semi-analytical solutions to the diffusion-convection problems and to identify the main thermal characteristics of the TA, that allows one to improve the device performance.

Thermal stresses in a functionally graded rotating disk: An approximate closed form solution

The purpose of this study is to analyze a circular annulus made of a functionally graded material (FGM) subjected to thermomechanical loading. The governing nonlinear differential equation for heat transfer, comprising of all the modes of heat transfer, such as conduction, convection, radiation, and internal heat generation, was formulated and then solved using the homotopy perturbation method (HPM). The stress field in the circular annulus due to thermomechanical loading was obtained using a HPM based approximate closed-form solution for a steady-state nonhomogeneous temperature field coupled with the solution of the classical theory of elasticity. The present work considered both Dirichlet and Neumann boundary conditions. A rigorous study on the effect of various thermomechanical parameters and grading parameters on temperature as well as the stress field is presented. The present approximate closed-form solution was validated with the finite element method (FEM) based solution. The close agreement between HPM based solutions of this work with the results of the ANSYS based FEM confirms the effectiveness and the viability of the present solution method for a FGM rotating disk with multiple variable nonlinearities. The present closed-form solution is more rational and computationally efficient over FEM and other numerical solutions.