Annulus Thickness Research Articles

Modelling collective invasion with reaction–diffusion equations: When does domain curvature matter?

Real-world cellular invasion processes often take place in curved geometries. Such problems are frequently simplified in models to neglect the curved geometry in favour of computational simplicity, yet doing so risks inaccuracies in any model-based predictions. To quantify the conditions under which neglecting a curved geometry is justifiable, we explore the dynamics of a system of reaction–diffusion equations (RDEs) on a two-dimensional annular geometry analytically. Defining ϵ as the ratio of the annulus thickness δ and radius r0 we derive, through an asymptotic expansion, the conditions under which it is appropriate to ignore the domain curvature for a general system of reaction–diffusion equations. To highlight the consequences of these results, we simulate solutions to the Fisher–Kolmogorov–Petrovsky–Piskunov (Fisher–KPP) model, a paradigm nonlinear RDE typically used to model spatial invasion, on an annular geometry. Thus, we quantify the size of the deviation from an analogous simulation on the rectangle, and how this deviation changes across the width of the annulus. We further characterise the nature of the solutions through numerical simulations for different values of r0 and δ. Our results provide insight into when it is appropriate to neglect the domain curvature in studying travelling wave behaviour in RDEs.

Effect analysis of uneven thickness of resin annulus on anchorage failure of cable bolt and uniformity guarantee device

Resin grouted cable bolts are widely used in the control of surrounding rock in underground engineering such as roadways and tunnels. This study conducted theoretical analysis and laboratory experiments to investigate the influence mechanism and characteristics of the uneven thickness of the resin annulus on the anchorage performance of the cable bolt, and developed an effective method for controlling the uneven thickness. The theoretical analysis of the shear stress distribution in the resin annulus under tension revealed that, when the thickness of the resin annulus is uniform, the shear stress in the resin annulus and interface around the cable bolt has balanced distribution overall. When the resin annulus thickness is uneven, the shear stress level is higher in the thinner area compared with the thicker area of the resin annulus. The pullout test results for cable bolt specimens anchored with different resin annulus thicknesses reveal that, as the thickness uniformity of the resin annulus decreases, the pullout load of the anchored specimen decreases to different degrees. According to the structure of the cable bolt and the resin anchoring construction characteristics, the resin annulus thickness uniformity guarantee device (RATUGD) was designed. The results obtained by a device working effect experiment reveal that the RATUGD can significantly improve the thickness uniformity of the resin annulus, and the pullout resistance of the anchored specimen is also ensured when the device is used. This study elucidated the influence mechanism of an uneven resin annulus on the anchoring performance of a cable bolt to a certain extent. Additionally, technology that ensures the resin annulus uniformity is proposed to further ensure and enhance the support effect of a resin grouted cable bolt on the surrounding rock of underground engineering such as roadways and tunnels.

Ultrasonic pitch-catch measurement wavefield analysis and casing reflection suppression

Ultrasonic pitch-catch measurements are increasingly recognized in cement bond evaluations for their unique ability to discern between light cement and mud within the annulus. They also effectively capture reflections from the annulus-formation interface, also known as the third-interface echo (TIE), in a single-cased hole. The TIE offers valuable insights into the condition of the annulus behind the casing and can be leveraged to calculate casing eccentering, annulus thickness, and image annulus-formation interface. However, the TIE may be obscured by reflections from the casing's inner surface, as well as multiple reflections from the casing and the tool housing. This overlap can lead to complications in data interpretation. Furthermore, the use of only two wave trains at near and far receivers in ultrasonic pitch-catch measurement adds to the difficulty of suppressing casing reflections. To tackle these challenges, we first analyze the wavefield in various models and then develop a phase-shift interpolation (PSI)-based technique to suppress casing reflections. This method initially converts the two waveforms into array waveforms using the PSI approach, then employs a median filter to suppress casing reflections. Finally, we can pick TIE arrival time from the refined data to further estimate the casing eccentering. The effectiveness of proposed technique in suppressing casing reflections and their multiples is verified by numerical simulations and a field example. These breakthroughs are poised to greatly enhance the precision and reliability of cement bond evaluations.

Interpretation of Morphological Details of Nondegenerated Lumbar Intervertebral Discs on Magnetic Resonance Imaging: Insights From a Comparison Between Computed Tomography Discograms and Magnetic Resonance Imaging.

To gain better insight into the magnetic resonance imaging (MRI) appearance of morphological intervertebral disc (IVD) details, such as annular and nucleus pulposus dimensions, by comparing contemporaneously obtained MRI and postdiscogram computed tomography (CT) scans of nondegenerated IVDs. Axial T2-weighted images and same-day postdiscography CTs, acquired after the MRI, of 26 normal-appearing lumbar IVDs (control IVDs at discography) were compared. The location and extent of central hyperintense zone on MRI and the extent of contrast distribution on CT relative to the IVD width (in anteroposterior [AP] and lateral planes) were assessed, with difference in measures between the modalities used to provide apparent inner annulus thickness and to estimate dimensions of also the outer annulus and location of nucleus pulposus. The mean (SD) extent of contrast distribution on CT discograms (53.1% [6.6%] and 58.1% [8.7%] of AP and lateral IVD width) was smaller than (P < 0.001 for both), and correlated weakly (r = 0.31 and 0.32 for AP and lateral planes) with corresponding measurements (58.4% [5.3%] and 65.7% [5.9%], respectively) for central hyperintense zone at MRI. The center of contrast opacification on CT discograms was located posterior to that of central T2 hyperintense zone on MRI in AP (P < 0.01), without any difference in lateral direction (P = 0.60). Normal-appearing lumbar IVDs are supported by outer annulus of larger relative thickness anteriorly, seen on both modalities. The shown discrepancy between the central T2 hyperintense zone and contrast distribution on CT discogram might reflect the inner annulus or structural changes within the borderzone nucleus and annulus. The exact nucleus size and inner annulus thickness could not be established due to a variable permeation of contrast across the central hyperintense zone on T2-weighted images.

Individualized Glaucoma Change Detection Using Deep Learning Auto Encoder-Based Regions of Interest.

PurposeTo compare change over time in eye-specific optical coherence tomography (OCT) retinal nerve fiber layer (RNFL)-based region-of-interest (ROI) maps developed using unsupervised deep-learning auto-encoders (DL-AE) to circumpapillary RNFL (cpRNFL) thickness for the detection of glaucomatous progression.MethodsForty-four progressing glaucoma eyes (by stereophotograph assessment), 189 nonprogressing glaucoma eyes (by stereophotograph assessment), and 109 healthy eyes were followed for ≥3 years with ≥4 visits using OCT. The San Diego Automated Layer Segmentation Algorithm was used to automatically segment the RNFL layer from raw three-dimensional OCT images. For each longitudinal series, DL-AEs were used to generate individualized eye-based ROI maps by identifying RNFL regions of likely progression and no change. Sensitivities and specificities for detecting change over time and rates of change over time were compared for the DL-AE ROI and global cpRNFL thickness measurements derived from a 2.22-mm to 3.45-mm annulus centered on the optic disc.ResultsThe sensitivity for detecting change in progressing eyes was greater for DL-AE ROIs than for global cpRNFL annulus thicknesses (0.90 and 0.63, respectively). The specificity for detecting not likely progression in nonprogressing eyes was similar (0.92 and 0.93, respectively). The mean rates of change in DL-AE ROI were significantly faster than for cpRNFL annulus thickness in progressing eyes (−1.28 µm/y vs. −0.83 µm/y) and nonprogressing eyes (−1.03 µm/y vs. −0.78 µm/y).ConclusionsEye-specific ROIs identified using DL-AE analysis of OCT images show promise for improving assessment of glaucomatous progression.Translational RelevanceThe detection and monitoring of structural glaucomatous progression can be improved by considering eye-specific regions of likely progression identified using deep learning.

Fast Discrete Finite Hankel Transform for Equations in a Thin Annulus

An algorithm is proposed for a fast discrete finite Hankel transform of a function in a thin annulus. The transform arises in a natural way in the Neumann boundary-value problem for the Poisson equation in an annulus when spectral methods are applied for its numerical solution. The proposed algorithm uses the limiting properties of eigenvalues and eigenfunctions of the Laplace operator as the annulus thickness goes to zero.

Load Transfer Characteristics of a Cable Bolt in DEPT

Cable bolts help surrounding rock masses of underground excavations to form internal rock structure and thus self‐stabilize through effective load transfer between rock masses and cable bolts. The load transfer characteristics of cable bolt play the most significant role in cable selection for support design. There are many factors potentially affecting the load transfer characteristics of cable bolt via strengthening or weakening load contributors such as cable bonding, mechanical interlocking, frictional resistance at cable‐grout interface and grout‐rock interface, and shearing of grout anchorage. Double embedment pull test (DEPT) is an effective, reliable, and repeatable test method of investigating the load transfer characteristics of cable bolt and thus was selected in this study. With DEPT, the influence of factors such as cable rotation, grout age, grout anchorage annulus thickness, cable wire profile, and failure mode on the load transfer characteristics of cable bolt were investigated in terms of tensile strength and stiffness in different loading stages. Conclusions drawn from the study can be used to improve cable installation quality and to select appropriate cable bolting technique.

Effects of fins geometries, arrangements, dimensions and numbers on natural convection heat transfer characteristics in finned-horizontal annulus

Natural convection heat transfer in closed enclosure exists in a wide range of engineering applications. Although huge researches were conducted for natural convection in non-circular enclosures, researches for annular enclosures are very limited, especially finned enclosures. In the present results natural convection air flow and heat transfer characteristics in un-finned and finned annulus enclosed between two concentric horizontal cylinders are numerically investigated. The effects of the Rayleigh numbers, annulus width, fins geometrical dimensions, fins numbers, fins shapes and fins arrangements on the heat transfer, fluid flow and effective thermal conductivity of the annulus were investigated. The results show the increase of the heat transfer and the effective thermal conductivity of the annulus with the increase of the annulus thickness, Rayleigh number, number of fins and the fins width. For the same fins areas, the longitudinal fins showed more heat transfer rate and effective thermal conductivities enhancements compared to the annular fins.

A theoretical model for capacitance measurement of liquid films in an annular flow

This paper develops mathematical models for a proposed production logging tool, which uses capacitance sensors to measure liquid annulus thickness and liquid type for a primarily gas-carrying wellbore. A semi-analytical method is devised which uses Fourier analysis to account for the complicated system geometry and reduces the problem to singular integral equations over a sensor electrode. Approximate solutions of these integral equations give expressions for capacitance, which is calculated for different liquids and varying liquid annuli thicknesses and electrode positions. These results are compared with capacitance values found using COMSOL Multiphysics, a finite element package. Good agreement is obtained between these two methods, with a discrepancy range of 1–8 %. Capacitance values obtained range from 32 to 93 pF/m, and sensitivity is estimated to range from 0.8 to 60 %, depending mainly on the proximity of the electrode to the liquid and also on the permittivity and thickness of the liquid layer. Practical implications of the study are also discussed. Realistically useful measurements, where ~0.2 mm of liquid is detectable, can potentially be made using an electrode 4–6 mm away from the inner wellbore wall.

Understanding acoustic methods for cement bond logging.

Well cementation is important for oil/gas production, underground gas storage, and CO2 storage, since it isolates the reservoir layers from aquifers to increase well integrity and reduce environmental footprint. This paper analyzes wave modes of different sonic/ultrasonic methods for cement bonding evaluation. A Two dimensional finite difference method is then used to simulate the wavefield for the ultrasonic methods in the cased-hole models. Waveforms of pulse-echo method from different interfaces in a good bonded well are analyzed. Wavefield of the pitch-catch method for free casing, partial or full bonded models with ultra-low density cement are studied. Based on the studies, the modes in different methods are considered as follows: the zero-order symmetric Leaky-Lamb mode (S0) for sonic method, the first-order symmetric Leaky-Lamb mode (S1) for the pulse-echo method, and the zero-order anti-symmetric Leaky-Lamb mode (A0) for the pitch-catch method. For the sonic method, a directional transmitter in both the azimuth and axial directions can generate energy with a large incidence angle and azimuth resolution, which can effectively generate S0 and break out the azimuth limitation of the conventional sonic method. Although combination of pulse-echo and pitch-catch methods can determine the bonding condition of the third interface for the ultra-low density cement case, the pitch-catch cannot tell the fluid annulus thickness behind casing for the partial bonded cased-hole.

Factors Influencing the Quality of Encapsulation in Rock Bolting

Bolt installation quality is influenced by various factors, some are well known and others are less recognised. A programme of field and laboratory studies was undertaken to examine various factors of relevance to the load transfer mechanism between the bolt, resin and rock to ensure test methods truly represent field performance. Short encapsulation tests were undertaken as part of the Australian Coal Association Research Program (ACARP) funded project (C21011) with the ultimate aim of developing standard test methods for assessing bolt encapsulation with chemical resin anchor installations. The field study consisted of a series of Short Encapsulation Pull Tests (SEPT) carried out in three mines with different geological conditions to determine the most representative and practical method of SEPT. Additional field work included installation of bolts into threaded steel tubes for subsequent removal and laboratory evaluation. A series of pull tests was carried out by installing bolts in overhead rig mounted sandstone block, cast in concrete with controlled encapsulation length. Factors of importance considered included; borehole diameter, resin annulus thickness, installation time (including bolt spin to the back and ‘‘spin at back’’), the effect of gloving and hole over drill. It was found that the borehole diameter had a detrimental effect on the encapsulation bonding strength. Bolt installation time of approximately 10 s constituted an acceptable time for effective bolt installation and within the resin manufacturers recommended time of 14 s. Maintaining constant length of encapsulation was paramount for obtaining consistency and repeatability of the test results. Finally, a numerical simulation study was carried out to assess the capabilities of FLAC 2D software in simulating the pull testing of rock bolts.

The Voidage in a CFB Riser as Function of Solids Flux and Gas Velocity

Circulating Fluidised Beds (CFBs) are widely applied in the process industry, for mostly gas-solid and gas-catalytic reactions. The riser is the key component of the CFB being the process reactor. The important design parameters are the operating gas velocity (U) and the solids concentration flux (G). The CFB operation starts at moderate to high superficial gas velocities. Its voidage exceeds ∼ 0.9 and is a function of the solids circulation flux. Different flow modes have been presented in literature, and result in an operation diagram where G and U delineate specific operations, from dilute riser flow, through core-annulus flow, to dense riser upflow (mostly at any U, G exceeding 80 to 120 kg m-2s-1). Increasing G whilst maintaining the gas velocity will cause an increase in suspension concentration. The riser flow can hence be characterized by its apparent voidage, ɛ. In the core-annulus operation, clusters of particles reflux near the wall, thus influencing the local radial voidage in the cross section of the riser, and also extending over a given distance, δ, from the wall to the core .Through measurements in CFBs of 0.1 and 0.14 m I.D., the research has been able to determine the average axial and radial voidages of the dense phase within the different regimes, whilst also determining the thickness of the annulus (in CAF-mode). Experimental results will be illustrated and compared with previous empirical equations, shown to have a limited accuracy only both for ɛ, and for the thickness of the annulus in CAF operation. Within the operating conditions tested, results demonstrate that the annulus thickness is about 15 to 20% of the riser diameter in CAF, and that the voidage in the riser is a function of U and G, with riser diameter and distance along the riser length as secondary parameters.

Numerical Simulation of Oil‐Water Core Annular Flow in a U‐Bend Based on the Eulerian Model

AbstractThe oil‐water core annular flow through a U‐bend is simulated by computational fluid dynamics based on the Eulerian model. More flow parameters and the effect of annulus thickness on core annular flow are discussed. Conformity between the simulated and experimental data is observed. The development of oil‐water core annular flow in the U‐bend is analyzed, and the distributions of pressure and velocity are discussed. Results of the Eulerian model and volume‐of‐fluid (VOF) model are compared and the influence of oil properties on total pressure gradient is investigated. The suitable range of annulus thickness is identified. The results provide suitable operation conditions for designing the U‐bend pipefitting.

Damping of coronal loop kink oscillations due to mode conversion

The damping of kink oscillations of a thin magnetic tube due to mode conversion, also called resonant absorption, is studied. The tube consists of a homogeneous core region and an inhomogeneous annulus, where the density monotonically decreases from its value in the core region to the value in the surrounding plasma. The annulus is assumed to be thin, so the study is carried out in the thin tube thin boundary approximation. The equation governing the amplitude variation of kink oscillations is derived. The initial value problem for this equation is solved to study the resonant damping. This means that, in particular, we study the transient state before the loop oscillates with the stationary or nearly stationary state. The results are compared with those of the direct numerical modelling, and the agreement is found to be fairly good. On the basis of the solution to the initial value problem for the governing equation, the damping time is calculated and compared with that given by the classical theory of resonant absorption. It is found that the classical theory underestimates the damping time, with the error increasing with the increase of the annulus thickness. However, the error is not large, so the damping time given by the classical theory of resonant absorption can be taken as a sufficiently good approximation.

Vortex dynamics in an annular Bose-Einstein condensate

We theoretically show that the topology of a nonsimply connected annular atomic Bose-Einstein condensate enforces the inner surface waves to be always excited with outer surface excitations and that the inner surface modes are associated with induced vortex dipoles unlike the surface waves of a simply connected one with vortex monopoles. Consequently, under stirring to drive an inner surface wave, a peculiar population oscillation between the inner and outer surface is generated regardless of annulus thickness. Moreover, a vortex nucleation process by stirring is observed that can merge the inner vortex dipoles and outer vortex into a single vortex inside the annulus. The energy spectrum for a rotating annular condensate with a vortex at the center also reveals the distinct connection of the Tkachenko modes of a vortex lattice to its inner surface excitations.

In-Situ Tests and Numerical Simulation about the Effect of Annulus Thickness on the Resin Mixture for Fully Grouted Resin Bolt

The main purpose of this paper is to study the effect of annulus thickness on the quality of resin mixture for fully grouted resin bolt. Pullout and mixture tests were made in underground coal mines for the following arrangements: (a) 29 mm borehole diameter, and 19 mm roof bolt diameter with steel wire around the roof bolt; (b) 29 mm borehole diameter, and 19 mm roof bolt diameter with no wire around the roof bolt; and (c) 24 mm borehole diameter, and 19 mm roof bolt diameter with no wire around the roof bolt. The mixture test in steel pipe showed that the best resin mixture is for the 24 mm borehole diameter. The arrangement (b) produced big voids around the bolt. But for the 24 mm hole, arrangement (c), the mixture showed the best results. This was corroborated with the pullout tests results where there was a difference in grout stiffness: in the 24 mm borehole diameter is was about 10 times higher than in the 29 mm borehole diameter. On the other hand, as far as the cohesive strength is concerned, the difference is not significant. Numerical models were built to simulate the pullout tests, and also to simulate the roof support at an intersection. Convergence at two underground intersections, consisting of an immediate roof with laminated sandstone, was monitored to evaluate the performance of the roof supports, using the 29 and 24 mm diameter boreholes (i.e. arrangements ‘a’ and ‘b’). The readings showed that the 24 mm borehole diameter resulted in a slightly smaller convergence.

Analytical investigation of steady convection of a near-critical Van der Waals gas in a porous thin annular cylinder embedded in a heat-conducting medium

Natural convection of a near-critical Van der Waals gas in a horizontal porous thin annular cylinder embedded in a heat-conducting space with a temperature gradient given at infinity is considered. The two-dimensional problem in a plane orthogonal to the cylinder axis is investigated using analytical methods, accurate to quantities of the order of the annulus thickness. A criterion of the onset of an annulus-section-average flow is obtained. The critical Rayleigh-Darcy number is determined for the general case in which the physical properties of the gas can considerably vary throughout the medium. Several limiting cases are considered and the ranges of their applicability are discussed. It is shown that, as the thermodynamic critical point is approached, the asymptotics of the critical Rayleigh-Darcy number depend on the relation between non-Boussinesq parameters, such as hydrostatic compressibility criteria, the temperature difference, and the nearness to the critical point. In the case of steady convection, an analytical solution is also derived in the case in which the above-mentioned stability threshold is exceeded and the physical properties of the gas vary throughout space only slightly. A comparison with the case of a perfect gas is made.

The effects of insoluble surfactants on the linear stability of a core–annular flow

The effects of an insoluble surfactant on the linear stability of a two-fluid core–annular flow in the thin annulus limit, for axisymmetric disturbances with wavelengths large compared to the annulus thickness, and, consequently, reduces the marginal wavelength below that typical of the capillary instability. However a further increase in Ma eventually reverses these trends. A very large value for Ma stiffens the interface, which opposes any local variation of the tangential velocity along the interface, and this is true whether or not there is a base flow. In the limit of infinite Ma, the growth rate of the instability is 1/4 of that of the clean interface and the marginal wavenumber, non-dimensionalized by the undisturbed core circumference, returns to its clean interface (capillary) value of 1. All trends are explained physically.

Dispersion in core–annular flow with a solid annulus

AbstractThe Taylor dispersion of a solute is studied in a core–annular geometry. The fluid flows only through the core, but the solute can diffuse into the solid annulus. The long time limit of the dispersion coefficient D* is derived by a regular expansion in the aspect ratio for two different scalings of the Biot number (Bi), which is the dimensionless interfacial mass‐transfer resistance. The results for the case of O(1) Bi match those obtained by Aris and a number of other researchers. In the case of O(ε) Bi, where ε is the aspect ratio, the average mass‐transfer equations for the core and the annulus are coupled and do not simplify to a simple convection–dispersion form. The average mass‐transfer equations are derived for two velocity profiles: Poiseuille flow and plug flow. The dispersion coefficient for the limiting case when both the core and the annulus are radially well mixed at all times is also determined for the case of O(1) Bi. For O(1) Bi, the dispersion of the solute arises as a result of molecular diffusion, interfacial mass‐transfer resistance, and convective flow, and the contribution from interfacial mass‐transfer resistance is independent of the velocity profile. This dispersion coefficient reduces to the classical result of fluid flow through a tube in the limit of vanishing annulus thickness and also for the case when the solute has zero solubility in the solid. The core–annular geometry mimics the Krogh cylinder, which is a model used for analyzing mass transfer from capillaries into surrounding tissue. The model predictions for the dispersion coefficients in different tissues agree reasonably with the experimentally reported values, and the agreement is the best for muscles, where the Krogh cylinder model is expected to most closely resemble the actual physiology. © 2005 American Institute of Chemical Engineers AIChE J, 2005

Morphological cervical disc analysis applied to traumatic and degenerative lesions

Trauma and degenerative pathologies at the lower cervical spine are different from lumbar spine pathologies. However, the description of cervical discs is classically taught similarly to that of the lumbar discs. Recent studies have raised this issue, and in 1999, Mercer and Bogduk described ventral annulus fibrosus as a crescent-shaped interosseous ligament. We propose a metric analysis of the different components of the cervical disc to examine this description. We analyzed 140 sagittal and coronal transections of 35 discs. These discs were taken from seven cervical spines at the five lower levels, C2-C3, C3-C4, C4-C5, C5-C6 and C6-C7. We measured quantitative parameters on sagittal, para-sagittal, ventral coronal and dorsal coronal colored transections: disc length (L), ventral annulus thickness (VAF), lateral annulus thickness (LAF), dorsal annulus thickness (DAF), length of the fibrocartilaginous tissue (FC), sagittal and coronal fibrocartilaginous core ratio (% Core) and intra-disc cleft length (Cleft). We also measured two qualitative parameters: degenerative disease of cartilaginous end plates and total intra-disc cleft. Finally, we examined 114 transections, and 18.5% were ruled out. The results showed thick ventral annulus fibrosus, thin lateral annulus and a very thin dorsal annulus. Fibrocartilaginous tissue filled the dorsal sagittal half of the disc. Intra-disc cleft split the fibrocartilaginous tissue and spread through the ventral annulus only six times. The shape of the ventral annulus at the lower cervical spine is compared to a pivot-hinge device. The aspect is functionally discussed in regard to teardrop fractures, unilateral locked facet syndrome and degenerative changes in the unco-vertebral area.