Annular Geometry Research Articles

Quantitative three-dimensional echocardiographic analysis of the bicuspid aortic valve and aortic root: A single modality approach.

Patients with bicuspid aortic valves (BAV) are heterogeneous with regard to patterns of root remodeling and valvular dysfunction. Two-dimensional echocardiography is the standard surveillance modality for patients with aortic valve dysfunction. However, ancillary computed tomography or magnetic resonance imaging is often necessary to characterize associated patterns of aortic root pathology. Conversely, the pairing of three-dimensional (3D) echocardiography with novel quantitative modeling techniques allows for a single modality description of the entire root complex. We sought to determine 3D aortic valve and root geometry with this quantitative approach. Transesophageal real-time 3D echocardiography was performed in five patients with tricuspid aortic valves (TAV) and in five patients with BAV. No patient had evidence of valvular dysfunction or aortic root pathology. A customized image analysis protocol was used to assess 3D aortic annular, valvular, and root geometry. Annular, sinus and sinotubular junction diameters and areas were similar in both groups. Coaptation length and area were higher in the TAV group (7.25 ± 0.98 mm and 298 ± 118 mm2 , respectively) compared to the BAV group (5.67 ± 1.33 mm and 177 ± 43 mm2 ; P = .07 and P = .01). Cusp surface area to annular area, coaptation height, and the sub- and supravalvular tenting indices did not differ significantly between groups. Single modality 3D echocardiography-based modeling allows for a quantitative description of the aortic valve and root geometry. This technique together with novel indices will improve our understanding of normal and pathologic geometry in the BAV population and may help to identify geometric predictors of adverse remodeling and guide tailored surgical therapy.

Transcatheter MitraClip repair alters mitral annular geometry \u2013 device induced annular remodeling on three-dimensional echocardiography predicts therapeutic response

BackgroundEchocardiography (echo) is widely used to guide therapeutic decision-making for patients being considered for MitraClip. Relative utility of two- (2D) and three-dimensional (3D) echo predictors of MitraClip response, and impact of MitraClip on mitral annular geometry, are uncertain.MethodsThe study population comprised patients with advanced (> moderate) MR undergoing MitraClip. Mitral annular geometry was quantified on pre-procedural 2D transthoracic echocardiography (TTE) and intra-procedural 3D transesophageal echocardiography (TEE); 3D TEE was used to measure MitraClip induced changes in annular geometry. Optimal MitraClip response was defined as ≤mild MR on follow-up (mean 2.7 ± 2.5 months) post-procedure TTE.ResultsEighty patients with advanced MR underwent MitraClip; 41% had optimal response (≤mild MR). Responders had smaller pre-procedural global left ventricular (LV) end-diastolic size and mitral annular diameter on 2D TTE (both p ≤ 0.01), paralleling smaller annular area and circumference on 3D TEE (both p = 0.001). Mitral annular size yielded good diagnostic performance for optimal MitraClip response (AUC 0.72, p < 0.01). In multivariate analysis, sub-optimal MitraClip response was independently associated with larger pre-procedural mitral annular area on 3D TEE (OR 1.93 per cm2/m2 [CI 1.19–3.13], p = 0.007) and global LV end-diastolic volume on 2D TTE (OR 1.29 per 10 ml/m2 [CI 1.02–1.63], p = 0.03). Substitution of 2D TTE derived mitral annular diameter for 3D TEE data demonstrated a lesser association between pre-procedural annular size (OR 5.36 per cm/m2 [CI 0.95–30.19], p = 0.06) and sub-optimal MitraClip response. Matched pre- and post-procedural TEE analyses demonstrated MitraClip to acutely decrease mitral annular area and circumference (all p < 0.001) as well as mitral tenting height, area, and volume (all p < 0.05): Magnitude of MitraClip induced reductions in mitral annular circumference on intra-procedural 3D TEE was greater among patients with, compared to those without, sub-optimal MitraClip response (>mild MR) on followup TTE (p = 0.017); greater magnitude of device-induced annular reduction remained associated with sub-optimal MitraClip response even when normalized for pre-procedure annular circumference (p = 0.028).ConclusionsMitraClip alters mitral annular geometry as quantified by intra-procedural 3D TEE. Pre-procedural mitral annular dilation and magnitude of device-induced reduction in mitral annular size on 3D TEE are each associated with sub-optimal therapeutic response to MitraClip.

Integral Solution of Two-Region Solid–Liquid Phase Change in Annular Geometries and Application to Phase Change Materials–Air Heat Exchangers

A mathematical model based on the integral method is developed to solve the problem of conduction-controlled solid–liquid phase change in annular geometries with temperature gradients in both phases. The inner and outer boundaries of the annulus were subject to convective, constant temperature or adiabatic boundary conditions. The developed model was validated by comparison with control volume-based computational results using the temperature-transforming phase change model, and an excellent agreement was achieved. The model was used to conduct parametric studies on the effect of annuli geometry, thermophysical properties of the phase change materials (PCM), and thermal boundary conditions on the dynamics of phase change. For an initially liquid PCM, it was found that increasing the radii ratio increased the total solidification time. Also, increasing the Biot number at the cooled (heated) boundary and Stefan number of the solid (liquid) PCM, decreased (increased) the solidification time and resulted in a greater (smaller) solid volume fraction at steady state. The application of the developed method was demonstrated by design and analysis of a PCM–air heat exchanger for HVAC systems. The model can also be easily employed for design and optimization of annular PCM systems for all associated applications in a fraction of time needed for computational simulations.

Identification of obstacles immersed in a stationary Oseen fluid via boundary measurements

In this paper we consider the interior inverse problem of identifying a rigid boundary of an annular infinitely long cylinder within which there is a stationary Oseen viscous fluid, by measuring various quantities such as the fluid velocity, fluid traction (stress force) and/or the pressure gradient on portions of the outer accessible boundary of the annular geometry. The inverse problems are nonlinear with respect to the variable polar radius parameterizing the unknown star-shaped obstacle. Although for the type of boundary data that we are considering the obstacle can be uniquely identified based on the principle of analytic continuation, its reconstruction is still unstable with respect to small errors in the measured data. In order to deal with this instability, the nonlinear Tikhonov regularization is employed. Obstacles of various shapes are numerically reconstructed using the method of fundamental solutions for approximating the fluid velocity and pressure combined with the MATLAB toolbox routine lsqnonlin for minimizing the nonlinear Tikhonov's regularization functional subject to simple bounds on the variables.

Scaling of heat transfer in stagnant lid convection for the outer shell of icy moons: Influence of rheology

The persistence of subsurface oceans in icy moons primarily depends on the efficiency of heat transfer through the outer ice shell. Scaling laws for heat transfer have already been determined by previous studies. These consider however a simplified rheology assuming a single creep mechanism, often using a linearized version of the temperature-dependent viscosity law (called Frank-Kamenetskii approximation). In the present study, we test the influence of ice rheology on the efficiency of heat transfer by considering a more realistic composite viscosity law, including diffusion creep, grain boundary sliding, basal slip and dislocation creep. We performed a large number of numerical simulations of thermal convection in the stagnant lid regime using a 2-D spherical annulus geometry with different rheology assumptions. Our results show that the dynamics of the ice shell is mainly controlled by the dominant creep mechanism in the rheological sublayer (the unstable lower portion of the cold boundary layer beneath the stagnant lid), which is mostly determined by grain size. For grain sizes lower than 3 mm, diffusion creep is the dominant creep mechanism in the rheological sublayer, while a combination of grain boundary sliding and basal sliding prevails for coarser grains. We derive new simple scaling relationships for the heat transfer suitable for the specific case of thin ice shells that account for the activation energy of the dominant creep mechanisms, thus allowing for a more accurate quantification of the temperature profile in the ice shell and cooling rate of the internal oceans.

Where does subduction initiate and cease? A global scale perspective

The thermo-mechanical evolution of the Earth's mantle is largely controlled by the dynamics of subduction zones, which connect the surface tectonic plates with the interior. However, little is known about the systematics of where subduction initiates and ceases within the framework of global plate motions and evolving continental configurations. Here, we investigate where new subduction zones preferentially form, and where they endure and cease using statistical analysis of large-scale simulations of mantle convection that feature self-consistent plate–like lithospheric behaviour and continental drift in the spherical annulus geometry. We juxtapose the results of numerical modelling with subduction histories retrieved from plate tectonic reconstruction models and from seismic tomography. Numerical models show that subduction initiation is largely controlled by the strength of the lithosphere and by the length of continental margins (for 2D models, the number of continental margins). Strong lithosphere favours subduction inception in the vicinity of the continents while for weak lithosphere the distribution of subduction initiation follows a random process distribution. Reconstructions suggest that subduction initiation and cessation on Earth is also not randomly distributed within the oceans, and more subduction zones cease in the vicinity of continental margins compared to subduction initiation. Our model results also suggest that intra-oceanic subduction initiation is more prevalent during times of supercontinent assembly (e.g. Pangea) compared to more recent continental dispersal, consistent with recent interpretations of relict slabs in seismic tomography.

TRICUSPID VALVE (TV) LEAFLET EXPANSION IS THE MAIN ADAPTIVE CHANGE TO MAINTAIN COMPETENCY: A THREE-DIMENSIONAL ECHOCARDIOGRAPHY (3DE) STUDY IN A NOVEL CHRONIC RIGHT VENTRICULAR (RV) PRESSURE AND VOLUME LOADED PIGLET MODEL

Tricuspid valve regurgitation (TR) develops in 25-35% of children with hypoplastic left heart syndrome (HLHS), a risk factor for morbidity and mortality. Surgical strategies for TR in HLHS are modest in success and durability, therefore warrants improved understanding and innovation. We developed a novel piglet model simulating infant HLHS RV physiology to study TV adaptation to chronic increased preload and afterload. We hypothesize that TV competency is maintained by adaptive rapid leaflet expansion despite annular dilation. Sixteen piglets at 4-5weeks of age (maturity equivalent to infants) underwent left thoracotomy. Intervention piglets (IP, n=8) had their pulmonary valve torn to produce moderate to severe pulmonary regurgitation (volume loading) and pulmonary artery band placed to increase RV pressure. Control piglets (CP, n=8), age and gender matched, had sham surgery. Following a 4-week recovery, all piglets underwent hemodynamic assessment and 3DE of TV. We assessed TV annulus and leaflet geometry in mid-systole using a custom 3DE software (MATLAB). Ex-vivo TV total leaflet area was measured. Comparisons between IP and CP were made using Student t-test with significance at p < 0.05. Values were expressed as mean (standard deviation). IP had significant pulmonary regurgitation (mean PR reverse/forward velocity time integral ratio 0.68 (0.09)) and mean RV systolic pressure 77.9% of systemic pressure, reflected in thicker RV free wall and anterior papillary muscle, consistent with an effective model. IP and CP were similar in weight and TR grade. IP TV annulus were larger (p=0.02), more circular (p=0.03) and leaflets more tethered (p=0.02) with 43% larger total leaflet area (p=0.01) [see Table]. Greatest expansion was seen in the posterior leaflet (p=0.01). 3DE TV total leaflet area correlated with ex-vivo TV pathologic specimen area (r=0.63, p=0.02). Following chronic exposure to increased RV preload and afterload, there is TV annular dilation and likely unchanged sub-valve apparatus, resulting in leaflet tethering. In-vivo 3DE identified rapid leaflet expansion as the main adaptive change to maintain competency from detrimental remodeling. Further research into modulation of TV leaflet growth may be important for understanding TV failure in HLHS.

Sound radiation by a vibrating annular plate using radial polynomials and spectral mapping.

This study deals with sound radiation from a thin clamped annular plate. The fluid loading effect is included. Although it is a classical problem, using direct numerical integration to solve such a problem is usually troublesome and time consuming since the coupling integrals have certain singularities. Therefore, this study applies radial polynomials to improve the time efficiency of numerical calculations with no loss of accuracy. As radial polynomials are usually used for circular geometry, spectral mapping has been proposed to perform the necessary conversion from circular to annular geometry. The conversion is performed in the wavenumber domain. Spectral mapping makes it possible to efficiently obtain a number of numerical results for the acoustic power and acoustic field generated.

The influence of tricuspid annuloplasty prostheses on ovine annular geometry and kinematics

BackgroundSurgical repair of functional tricuspid regurgitation is centered on annular reduction with artificial rings; however, the precise effect of prosthesis implantation on annular geometry, dynamics, and strain is unknown. MethodsForty healthy sheep had sonomicrometry crystals implanted around the tricuspid annulus and onto right ventricle free wall. Ten animals underwent tricuspid annuloplasty with a flexible Duran AnCore ring (Medtronic, Minneapolis, Minn) (28 ± 1 mm), 10 with Contour 3D rigid ring (Medtronic) (29 ± 1 mm), 10 with hybrid Tri-Ad Adams band (Medtronic) (28 ± 1 mm), and 10 had no prosthesis (control group). Pressure sensors were inserted in the left ventricle, right ventricle, and right atrium. Data were acquired with open chest after weaning off cardiopulmonary bypass and hemodynamic stabilization. Annular area, global and regional contraction, height, and strain were calculated based on cubic spline fits to crystal locations. ResultsTricuspid annular area contraction during the cardiac cycle was 11% ± 3% in the control group. The Contour 3D ring significantly impaired annular contraction (2% ± 1%) whereas the Duran AnCore ring and Tri-Ad Adams band (9% ± 3% and 8% ± 4%, respectively) permitted dynamic area change. Global perimeter reduction was 6% ± 1% in the control group and decreased in the Duran AnCore (3% ± 1%), Contour 3D (0.4% ± 0.2%), and Tri-Ad Adams (3% ± 1%) groups (all P values < .001 vs control). Annular height was 6.2 ± 2.0 mm in the control group, unchanged in the Contour 3D (4.9 ± 1.1 mm) but reduced in the Duran AnCore (3.1 ± 1.3 mm) and Tri-Ad Adams (3.1 ± 1.0 mm) groups (P < .001 Duran AnCore and Tri-Ad Adams vs control). Rings perturbed systolic global annular strain (control, 5.3% ± 1.8%; Duran AnCore, 2.3% ± 1.0%; Contour 3D, 0.6% ± 0.2%; and Tri-Ad Adams, –2.6% ± 0.7%) with Contour 3D inducing the biggest change (P < .05 vs other groups). ConclusionsIn healthy ovine hearts, flexible and hybrid rings better preserved annular dynamics and strain, whereas the rigid ring maintained 3-dimensional geometry. These data may aid the design of optimal tricuspid annular prostheses and improve durability of valve repair.

The narrow escape problem in a circular domain with radial piecewise constant diffusivity

The stochastic motion of particles in living cells is often spatially inhomogeneous with a higher effective diffusivity in a region close to the cell boundary due to active transport along actin filaments. As a first step to understand the consequence of the existence of two compartments with different diffusion constant for stochastic search problems we consider here a Brownian particle in a circular domain with different diffusion constants in the inner and the outer shell. We focus on the narrow escape problem and compute the mean first passage time (MFPT) for Brownian particles starting at some pre-defined position to find a small region on the outer reflecting boundary. For the annulus geometry we find that the MFPT can be minimized for a specific value of the width of the outer shell. In contrast for the two-shell geometry we show that the MFPT depends monotonously on all model parameters, in particular on the outer shell width. Moreover we find that the distance between the starting point and the narrow escape region which maximizes the MFPT depends discontinuously on the ratio between inner and outer diffusivity.

H∞ loop-shaping control of azimuthal combustion instabilities in annular combustors

Lean combustion technique and annular geometries are preferred in aero-engines and gas turbines, which however may lead to azimuthal combustion instabilities. Active control can be used to stabilize combustion instabilities. Due to its easy use, linear feedback controllers embedded with linear flame response models under weak perturbation amplitude are typically preferred. However, flame responses to oncoming disturbances are typically nonlinear; such controllers are not guaranteed to stabilize. Model-based control strategies generally focus on axisymmetric cases, even though symmetry breaking of azimuthal thermoacoustic modes often occurs in annular combustors. This work uses an improved thermoacoustic model to simulate combustion instabilities within annular combustors, providing a platform on which control strategies development can be performed. The improved model takes into account the nonlinear flame response and the symmetry breaking of azimuthal modes. Single-input single-output control strategies targeting on these nonlinear instabilities are developed in this work. Such controllers can achieve stability for linear and nonlinear fluctuations as well as in symmetric and non-axisymmetric cases. The controllers adopt the [Formula: see text] loop-shaping control strategy and a satisfactory robust performance is obtained.

Drill cuttings transport and deposition in complex annular geometries of deviated oil and gas wells: A multiphase flow analysis of positional variability

In this study, the two-fluid Eulerian–Eulerian multiphase flow model in ANSYS Fluent (v17.1) is adopted for the simulation of cuttings transport in a deviated annular geometry using two different non-Newtonian drilling fluids (described using the power law and Herschel–Bulkley models). The Syamlal-O'Brien interphase momentum exchange coefficient is implemented to capture non-spherical effects of the drill cuttings. The analysis conducted is based on the hypothesis that a position-dependent profile evaluation is expected to yield more insight into the transport process compared to a volume-averaged analysis over the entire flow domain. This is because the adopted simulation approach takes into account the microscopic particle properties which significantly affect the overall particle transport mechanism. However, this requires the application of robust postprocessing functionalities for data extraction from desired annular regions. Particle sizes considered are in the range of 0.002m–0.008m with a sphericity range of 0.5 to 1.0. A rotational effect is incorporated in our model to describe the drillpipe motion in an annular wellbore with a vertical eccentricity of 0.6. The considered geometry contains a vertical, inclined and horizontal section with interconnecting upper and lower bends. The analysis of the particle velocity and concentration profiles revealed that the mud rheology, particle sphericity and particle sizes play vital roles in determining the cuttings removal process. It is also particularly observed that the lower annular region of the upper bend is the most susceptible to particle deposition with the lowest transport velocities observed. Our positional variability analysis has shown that the variable dominance of non-spherical and spherical particles’ velocities significantly depends on the nature of the flow (i.e. dense granular flow or dilute annular flow in the upper and lower sections, respectively).

Effects of the Compositional Viscosity Ratio on the Long‐Term Evolution of Thermochemical Reservoirs in the Deep Mantle

AbstractNumerical experiments of thermochemical mantle convection in 2‐D spherical annulus geometry are performed to investigate the effects of compositional viscosity ratio (ΔηC) on the long‐term evolution of reservoirs of dense, primordial material in the lowermost mantle of the Earth. The internal heating rate in the primordial material is larger than in the ambient mantle by a factor of 10, accounting for the fact that this material may be enriched in radiogenic elements. We find that if the chemical density contrast is large (128 kg/m3), ΔηC plays only a second‐order role on the long‐term stability of these reservoirs. As the chemical density contrast decreases to smaller values (90 kg/m3), ΔηC plays a more significant role. More specifically, when ΔηC is large, around 10 or larger, convection within the reservoirs of primordial material is less vigorous, which increases the temperature and thermal buoyancy of these structures. This, in turn, can eventually lead them to become unstable, with the majority of the primordial material being advected into the large‐scale mantle circulation.

Entire mitral reconstruction with porcine extracellular matrix in an acute porcine model

ObjectiveThe objective of our study was to investigate the feasibility of reconstructing the entire mitral valvular and subvalvular apparatus in pigs using a modified tube graft design made of 2-ply small intestinal submucosa extracellular matrix. MethodsThe reconstructions were performed in an acute 80-kg porcine model with 8 pigs, each acting as its own control. A modified tube graft was designed from a sheet of 2-ply small intestinal submucosa extracellular matrix. Before and after mitral valve reconstruction, echocardiography was used to assess mitral regurgitation, left ventricular outflow tract obstruction due to systolic anterior motion, mitral stenosis, leaflet mobility, and leaflet geometry. ResultsThe reconstructed mitral valves were fully functional without any observable echocardiographic signs of regurgitation. We did not observe any left ventricular outflow tract obstruction due to systolic anterior motion nor any mitral valve stenosis, despite a diminished septal-lateral distance after reconstruction. The reconstruction had a reduced tenting area, a reduced coaptation length (9.6 ± 1.7 mm vs 7.9 ± 1.0 mm, P = .010, diff = −1.7 mm, 95% confidence interval, −3.1 to −0.4 mm), and atrial bending of both leaflets. ConclusionsIn this acute porcine study, entire mitral valvular and subvalvular apparatus reconstruction using a modified tube graft design made from 2-ply small intestinal submucosal extracellular matrix was feasible. The 2-ply small intestinal submucosa extracellular matrix could withstand the pressure exerted by the left ventricle without any signs of tearing or rupture. These promising results warrant further assessment of both the annular geometry and the long-term durability.

Current status of research on heat transfer in forced convection of fluids at supercritical pressures

Investigation of heat transfer at supercritical pressures began as early as the 1930s with the study of free-convection heat transfer to fluids at a near-critical point. In the 1950s, the concept of using supercritical “steam” to increase thermal efficiency of fossil-fired thermal power plants became an attractive option. Germany, USA, the former USSR, and some other countries extensively studied supercritical heat transfer during the 1950s till the 1980s. This research was primarily focused on bare circular tubes cooled with SuperCritical Water (SCW). However, some studies were performed with modeling fluids such as SC carbon dioxide and refrigerants instead of SCW. Currently, the use of supercritical “steam” in fossil-fired thermal power plants is the largest industrial application of fluids at supercritical pressures.Near the end of the 1950s and at the beginning of the 1960s, several studies were conducted to investigate a potential of using SCW as a coolant in nuclear reactors. However, these activities were abandoned for some time and regain momentum in 1990s. In support of development of SuperCritical Water-cooled nuclear-Reactor (SCWR) concepts, first experiments have been started in annular and various bundle-flow geometries. At the same time, more numerical and CFD studies have been performed in support of our limited knowledge on specifics of heat transfer at SC Pressures (SCPs) in various flow geometries.As the first step in this process, heat transfer to SCW in vertical bare tubes can be investigated as a conservative approach (in general, heat transfer in fuel bundles will be enhanced with various types of appendages, i.e., grids, end plates, spacers, bearing pads, fins, ribs, etc.). New experiments in 1990s–2000s were triggered by several reasons: 1) thermophysical properties of SCW have been updated from 1950s to 1970s, e.g., a peak in thermal conductivity in the critical/pseudocritical points was “officially” introduced in 1990s; 2) experimental techniques have been improved; 3) in SCWRs various bundle flow geometries will be used instead of bare-tube geometry; and 4) in SC steam generators of thermal power plants larger diameter tubes/pipes (20–40 mm) are used, however, in SCWRs hydraulic-equivalent diameters of proposed bundles will be within 5–12 mm.A comparison of selected SCW heat-transfer correlations has shown that their results may differ from one to another by more than 200%. Based on these comparisons, it became evident that there is a need for a reliable, accurate and wide-range SCW heat-transfer correlation to be used. Therefore, the objective of this paper is to summarise in concise form the work performed concerning with the heat transfer at SCPs, based mainly on examples of water, carbon dioxide, and R-12.

Procedural and Anatomical Determinants of Multielectrode Renal Denervation Efficacy.

Radiofrequency renal denervation is under investigation for treatment of hypertension with variable success. We developed preclinical models to examine the dependence of ablation biomarkers on renal denervation treatment parameters and anatomic variables. One hundred twenty-nine porcine renal arteries were denervated with an irrigated radiofrequency catheter with multiple helically arrayed electrodes. Nerve effects and ablation geometries at 7 days were characterized histomorphometrically and correlated with associated renal norepinephrine levels. Norepinephrine exhibited a threshold dependence on the percentage of affected nerves across the range of treatment durations (30-60 s) and power set points (6-20 W). For 15 W/30 s treatments, norepinephrine reduction and percentage of affected nerves tracked with number of electrode treatments, confirming additive effects of helically staggered ablations. Threshold effects were only attained when ≥4 electrodes were powered. Histomorphometry and computational modeling both illustrated that radiofrequency treatments directed at large neighboring veins resulted in subaverage ablation areas and, therefore, contributed suboptimally to efficacy. Account for measured nerve distribution patterns and the annular geometry of the artery revealed that, regardless of treatment variables, total ablation area and circumferential coverage were the prime determinants of renal denervation efficacy, with increased efficacy at smaller diameters.

Holdup and frequency characteristics of slug flow in concentric and fully eccentric annuli pipes

Slug liquid holdup and frequency for gas-liquid flows in horizontal and upward low-inclination annuli are investigated. The annulus consists of an outer pipe of 99 mm inside diameter and an inner pipe of 50 mm outside diameter. Two annulus configurations are studied, namely, concentric and fully eccentric with the inner pipe at the bottom of the outer pipe. The test fluids are water and Exxsol D60 as the liquid phases and sulphur hexafluoride (SF6) as the gas phase. The slug characteristics are obtained from time-traces of the cross-sectional average liquid holdup from broad-beam gamma densitometers. Results show that the eccentricity of the annulus has limited effect on the slug liquid holdup and slug frequency. For a given superficial liquid velocity, the slug frequency has a parabolic profile as function of the mixture velocity with a minimum value at UM ≈ 3 m/s. Once UM is greater than 3 m/s, the slug frequency sharply increases. Experimental results are compared with predictions calculated using existing correlations and models developed for full pipe systems in the literature. These models fail to capture the slug characteristics in annulus configurations. One of the existing models for predictions of slug liquid holdup has been modified in this paper to account for the effect of the annulus geometry. In addition, the paper documents a new correlation development for slug frequency using the Taylor bubble (or translational velocity) and the slug liquid holdup in an annulus geometry. The proposed models, for both slug liquid holdup and frequency, perform better than the existing models in literature when tested against experimentally obtained annulus flow data.

Gas–liquid slug flow in a horizontal concentric annulus, a comparison of numerical simulations and experimental data

Multiphase flow simulations were run in OpenFOAM utilizing InterFoam, a volume of fluid type solver. A concentric annulus geometry was constructed and periodic boundary conditions were applied to alleviate the requirement for a longer domain. The simulations were run in 3, 5 and 7 m long domains with the annulus dimensioned such that the outer and inner cylinder diameter were 0.1 and 0.05 m respectively. The 4 individual mesh designs were constructed such that the coarsest mesh consists of 102k cells/m while the finest mesh was generated with 400k cells/m. Each mesh was significantly refined within 0.005 m of both the inner and outer cylinder wall. The simulation data was compared with experimental pressure and holdup data collected at Institute for Energy Technology in Norway. The 3 and 7 m domains reproduced slug frequencies to within 9% of the experiment results of 1.43 Hz for all mesh densities. Comparatively, the 5 m domain has larger errors with respect to slugging frequency (22–27%). The 5 m case performs poorly, probably due to an artificial restraint introduced by the limitation of available liquid which is set as αoil=0.53 for all cases. The αoil restriction combined with the domain length determines the amount of liquid in the system. This interaction of factors means that the domain length is an important parameter when preparing the simulation. The pressure data display a stronger dependence on the mesh quality in comparison to the slug frequency analysis. The 3 m domain with a 400k cells/m mesh resulted in a maximum and minimum pressure gradient of 1783.5 and 803.9 Pa/m, compared to the experiment values of 1785 and 822 Pa/m, which are within 3% of the expected results.

Double-wave reentry in excitable media.

A monolayer of chick embryo cardiac cells grown in an annular geometry supports two simultaneous reentrant excitation waves that circulate as a doublet. We propose a mechanism that can lead to such behavior. The velocity restitution gives the instantaneous velocity of a wave as a function of the time since the passage of the previous wave at a given point in space. Nonmonotonic restitution relationships will lead to situations in which various spacings between circulating waves are possible. In cardiology, the situation in which two waves travel in an anatomically defined circuit is referred to as double-wave reentry. Since double-wave reentry may arise as a consequence of pacing during cardiac arrhythmias, understanding the dynamic features of double-wave reentry may be helpful in understanding the physiological properties of cardiac tissue and in the design of therapy.

Immiscible and miscible states in binary condensates in the ring geometry

We report detailed investigation of the existence and stability of mixed and demixed modes in binary atomic Bose–Einstein condensates with repulsive interactions in a ring-trap geometry. The stability of such states is examined through eigenvalue spectra for small perturbations, produced by the Bogoliubov–de Gennes equations, and directly verified by simulations based on the coupled Gross–Pitaevskii equations, varying inter- and intra-species scattering lengths so as to probe the entire range of miscibility–immiscibility transitions. In the limit of the one-dimensional (1D) ring, i.e. a very narrow one, stability of mixed states is studied analytically, including hidden-vorticity (HV) modes, i.e. those with opposite vorticities of the two components and zero total angular momentum. The consideration of demixed 1D states reveals, in addition to stable composite single-peak structures, double- and triple-peak ones, above a certain particle-number threshold. In the 2D annular geometry, stable demixed states exist both in radial and azimuthal configurations. We find that stable radially-demixed states can carry arbitrary vorticity and, counter-intuitively, the increase of the vorticity enhances stability of such states, while unstable ones evolve into randomly oscillating angular demixed modes. The consideration of HV states in the 2D geometry expands the stability range of radially-demixed states.