Axisymmetric Vessel Research Articles

Inhomogeneity of the Ideal Gas of a Finite Number of Particles with Angular Momentum Conservation

We continue to study various aspects of the behavior of a classical ideal gas in a stationary axisymmetric container. The symmetry of the vessel leads to the conservation of the gas’s angular momentum and, hence, the state of gas rotation. We consider the case of a nonrotating two-dimensional gas of a finite number of colliding particles. In this case, the gas statistical distributions differ from the classical ones found in the nineteenth century. We will show that the filling of the axisymmetric vessel with a nonrotating gas is not uniform and provide the exact spatial distribution of gas particles. This previously unknown distribution depends on all the particle masses and is found explicitly. The absence of a rotation in gas layers is shown through the investigation of the distributions of the tangential components of particle momenta. We also show that, for any number of particles in a container, the behavior of a massive enough particle may be unusual. The analytic results are confirmed by simple numerical experiments.

Ultrasound elastography to quantify average percent pressure-normalized strain reduction associated with different aortic endografts in 3D-printed hydrogel phantoms

ObjectiveStrain has become a viable index for evaluating abdominal aortic aneurysm stability after endovascular aneurysm repair (EVAR). In addition, literature has shown that healthy aortic tissue requires a degree of strain to maintain homeostasis. This has led to the hypothesis that too much strain reduction conferred by a high degree of graft oversizing is detrimental to the aneurysm neck in the seal zone of abdominal aortic aneurysms after EVAR. We investigated this in a laboratory experiment by examining the effects that graft oversizing has on the pressure-normalized strain (ερ+¯/pulse pressure [PP]) reduction using four different infrarenal EVAR endografts and our ultrasound elastography technique. Approximate graft oversizing percentages were 20% (30 mm phantom-graft combinations), 30% (28 mm phantom-graft combinations), and 50% (24 mm phantom-graft combinations). MethodsAxisymmetric, 10% by mass polyvinyl alcohol phantoms were connected to a flow simulator. Ultrasound elastography was performed before and after implantation with the four different endografts: (1) 36 mm polyester/stainless steel, (2) 36 mm polyester/electropolished nitinol, (3) 35 mm polytetrafluoroethylene (PTFE)/nitinol, and (4) 36 mm nitinol/polyester/platinum-iridium. Five ultrasound cine loops were taken of each phantom-graft combination. They were analyzed over two different cardiac cycles (end-diastole to end-diastole), yielding a total of 10 maximum mean principal strain (ερ+¯) values. ερ+¯ was divided by pulse pressure to yield pressure-normalized strain (ερ+¯/PP). An analysis of variance was performed for graft comparisons. We calculated the average percent ερ+¯/PP reduction by manufacturer and percent oversizing. These values were used for linear regression analysis. ResultsResults from one-way analysis of variance showed a significant difference in ερ+¯/PP between the empty phantom condition and all oversizing conditions for all graft manufacturers (F(3, 56) = 106.7 [graft A], 132.7 [graft B], 106.5 [graft C], 105.7 [graft D], P < .0001 for grafts A-D). There was a significant difference when comparing the 50% condition with the 30% and 20% conditions across all manufacturers by post hoc analysis (P < .0001). No significant difference was found when comparing the 20% and 30% oversizing conditions for any of the manufacturers or when comparing ερ+¯/PP values across the manufacturers according to percent oversize. Linear regression demonstrated a significant positive correlation between the percent graft oversize and the all-graft average percent ερ+¯/PP reduction (R2 = 0.84, P < .0001). ConclusionsThis brief report suggests that a 10% increase in graft oversizing leads to an approximate 5.9% reduction in ερ+¯/PP on average. Applied clinically, this increase may result in increased stiffness in axisymmetric vessels after EVAR. Further research is needed to determine if this is clinically significant.

Analysis of the Shear-Thinning Viscosity Behavior of the Johnson–Segalman Viscoelastic Fluids

This paper presents a numerical comparison of viscoelastic shear-thinning fluid flow using a generalized Oldroyd-B model and Johnson–Segalman model under various settings. Results for the standard shear-thinning generalization of Oldroyd-B model are used as a reference for comparison with those obtained for the same flow cases using Johnson–Segalman model that has specific adjustment of convected derivative to assure shear-thinning behavior. The modeling strategy is first briefly described, pointing out the main differences between the generalized Oldroyd-B model (using the Cross model for shear-thinning viscosity) and the Johnson–Segalman model operating in shear-thinning regime. Then, both models are used for blood flow simulation in an idealized stenosed axisymmetric vessel under different flow rates for various model parameters. The simulations are performed using an in-house numerical code based on finite-volume discretization. The obtained results are mutually compared and discussed in detail, focusing on the qualitative assessment of the most distinct flow field differences. It is shown that despite all models sharing the same asymptotic viscosities, the behavior of the Johnson–Segalman model can be (depending on flow regime) quite different from the predictions of the generalized Oldroyd-B model.

Numerical Simulation of CFD and Fluid-Structure-Interaction (FSI) of Steady Flow in a Stenotic Vessel

This paper is concerned with the computational results of two-dimensional axisymmetric rigid and elastic wall formulation. In this paper, steady flow in a stenotic vessel is simulated and compared to available numerical data with COMSOL Multiphysics software. Numerical results for a 2D axisymmetric vessel of 45% area reduction indicate that as the area is reduced with the decreasing of cross-section, the maximum axial velocity at post stenotic decreases until the end of the artery but the radial velocity increases upto 4 mm from the stenosis throat and then decreases. Overall, comparison is carried out on hemodynamics for elastic and rigid wall of steady flow. Our investigated findings may enable risk factor for patients with attacked cardiovascular diseases and can play an important role to detect a solution to such kinds of diseases.

Exact elasticity solutions to rotating pressurized axisymmetric vessels made of functionally graded materials (FGM)

AbstractIn this study the plane elasticity equations of pressurized and rotating structures, generalized analytical closed‐form solutions are presented for hollow cylinders, spheres and thin disks. Three well known material pairs are graded in radial direction by using the power rule for various boundary and load conditions. Stress and displacement solutions are obtained. The effect of a constant rotational velocity is also investigated separately in absence of the internal and external pressures. Crucial results are also presented in tabular form.

Приближенные вычисления собственных значений вращающейся жидкости, вытекающей из произвольной осесимметричной емкости

The paper addresses the problem of proper motions of a rotating fluid that partially fills an axisymmetric vessel in the presence of an outflow through a rigid bottom. The problem is solved in a quasi-stationary setting within the framework of an ideal fluid model, with account for hydraulic losses during fluid flow through the bottom of the vessel. Numerical research was carried out using the finite element method. The study investigates the spectrum of eigenvalues and reveals the characteristics of the wave motions of the fluid. Numerical calculations confirm the possible appearance of wave motions on the drain surface, i.e. drain waves caused by the presence of fluid outflow through the bottom of the vessel. The paper presents the results of calculating the wavenumbers and the complex attenuation coefficient. Findings of the research can be used in practical calculations of dynamic modes at the design stage of promising space-rocket vehicles.

Increasing the strength of welded thin-walled axisymmetric vessels made of corrosion-resistant steel

Structural elements of thin-walled vessels operating under internal pressure are mainly made from sheet blanks using welding operations. To reduce the negative impact of welds in the manufacture of thin-walled vessels, it is proposed to use separate calibration processes by compressing vessel parts with subsequent welding and their joint calibration by distribution and rotary rolling. Compression calibration ensures the accuracy of matching of the abutting annular edges of the vessel parts. During rotary rolling, the welds are simultaneously smoothed and the strength characteristics are improved due to plastic hardening caused by thinning and leveling the wall thickness of the vessel body. Based on the conducted research, technological recommendations have been developed for the manufacture of thin-walled vessels of increased strength from corrosion-resistant steels.

Analytical thickness distribution for minimum compliance axisymmetric vessels

Abstract The paper is devoted to the analytic optimization of the thickness distribution of axisymmetric vessels where the cost functional to minimize is the compliance. The goal is achieved by minimizing the strain energy under mass constraint. The theoretical framework of the mechanics of thin walled membrane shells is recalled at the beginning of the paper. The optimization problem is stated, formulated and solved by means of calculus of variations. Based on the augmented Lagrangian formalism, the Euler-Lagrange equation leads to analytical optimal thickness distributions. Numerical illustrative examples are given and the optimal solutions are obtained for standard and nonstandard meridian shapes and end closures. Finally, the compliance of optimal solutions is compared with its counterpart of constant-thickness vessels of the same mass.

A Cell Damages Study in Pulsatile Blood Flow through Two- and Three-Dimensional Obstructed Vessels Using the Cosserat Continuum Approach

Pulsatile blood flow through both axisymmetric and asymmetric stenotic vessels has been analyzed numerically using the Cosserat continuum to study the possibility of cell damages in it. Transition to turbulence damages the wall and blood cells by two different mechanisms: high viscous shear stresses near the wall and vorticities with Kolmogorov length scale. In the present work, the model of micropolar fluid flow has been introduced to describe the characteristic length of flow particles, model the laminar, transition and turbulent regimes with Stokes layer formation in pulsatile cycle of blood flow, and calculate the Kolmogorov microscale of eddies and the additional shear stress that is produced by the microrotation viscosity of particles in real flow. The model of pulsatile micropolar fluid flow through axisymmetric (two-dimensional) and asymmetric (three-dimensional) stenosed arteries has been solved numerically using finite difference scheme by exploiting a mesh generation technique with a few transformations that lead to a rectangular grid in the computational plane. The governing equations of the two-dimensional model have been solved with stream function-microrotation method and the high shear stresses have been obtained about 70% smaller than the three-dimensional models with similar obstruction percent.

The Effect of Punching Plates to Suppress the Sloshing in a Gas Liquid Separator

Natural gas is relatively clean and its demand is increasing these days. In most of the case, gas fields are located at the bottom of the sea. Therefore, floating production, storage and offloading (FPSO) system is now attracting big attention. This paper is related to dynamical design of FPSO system, specially focused on the free surface elevation in the horizontal cylindrical and axisymmetric liquid vessel with end caps induced by the wave. In this study, the theory on the wave height and resonant frequency in a horizontal cylinder subjected to longitudinal external excitation is developed. Then, the theory capable of taking account of the effect of punching plates is described. Finally, experimental data of resonant wave height up to 3rd mode are shown in comparison with theoretically derived results.

Non-Newtonian characteristics of peristaltic flow of blood in micro-vessels

Of concern in the paper is a generalized theoretical study of the non-Newtonian characteristics of peristaltic flow of blood through micro-vessels, e.g. arterioles. The vessel is considered to be of variable cross-section and blood to be a Herschel–Bulkley type of fluid. The progressive wave front of the peristaltic flow is supposed sinusoidal/straight section dominated (SSD) (expansion/contraction type); Reynolds number is considered to be small with reference to blood flow in the micro-circulatory system. The equations that govern the non-Newtonian peristaltic flow of blood are considered to be non-linear. The objective of the study has been to examine the effect of amplitude ratio, mean pressure gradient, yield stress and the power law index on the velocity distribution, wall shear stress, streamline pattern and trapping. It is observed that the numerical estimates for the aforesaid quantities in the case of peristaltic transport of blood in a channel are much different from those for flow in an axisymmetric vessel of circular cross-section. The study further shows that peristaltic pumping, flow velocity and wall shear stress are significantly altered due to the non-uniformity of the cross-sectional radius of blood vessels of the micro-circulatory system. Moreover, the magnitude of the amplitude ratio and the value of the fluid index are important parameters that affect the flow behaviour. Novel features of SSD wave propagation that affect the flow behaviour of blood have also been discussed.

Vasomotion does inhibit mass exchange between axisymmetric blood vessels and tissue

Vasomotion, the name given to the physiological phenomenon whereby blood vessel walls exhibit rhythmic oscillations in diameter, is a complex process and very poorly understood. It has been proposed as a mechanism for protecting tissue when perfusion levels are reduced, since it has experimentally been shown to occur more frequently under such conditions. However, no quantitative evidence yet exists for whether the oscillation of the wall actually has any effect on mass transport to tissue. In our previous work, it was shown that the presence of non-linearities in the governing equation could result in a significant change in time-averaged mass transport to tissue: however, it was not possible, due to the limitations of the model, to determine whether time-averaged mass transport increased or decreased. This model is extended in this paper through coupling of the one-dimensional axisymmetric mass transport equations in tissue and blood to quantify the effects of vasomotion on mass transport to tissue. The results show that over a wide parameter range, surrounding those values calculated from experimental data, vasomotion does inhibit mass transport to tissue in a one-dimensional axisymmetric blood vessel by an amount that is predominantly dependent upon the amplitude of oscillation and that increases rapidly at larger oscillation amplitudes.

Investigation of two-dimensional nonstationary processes of outflow a gas-saturated liquid from axisymmetric vessels

The two-dimensional and two-phase model of the gas-liquid mixture is constructed. The validity of numerical model realization is justified by using a comparative analysis of test problems solution with one-dimensional calculations. The regularities of gas-saturated liquid outflow from axisymmetric vessels for different geometries are established.

Computational Investigations Into Draining in an Axisymmetric Vessel

Within an aero-engine, bearing chamber oil is provided for components to lubricate and cool. This oil must be efficiently removed (scavenged) from the chamber to ensure that it does not overheat and degrade. Bearing chambers typically contain a sump section with an exit pipe leading to a scavenge pump. In this paper, a simplified physical situation related to bearing chamber scavenge is computationally modeled. The volume of fluid (VOF) model of Hirt and Nichols (1981, “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” J. Comput. Phys., 39, pp. 201–225), implemented within the commercial computational fluid dynamics (CFD) code FLUENT (Fluent, 2006, Fluent 6.3 User’s Guide, 10 Cavendish Court, Lebanon, NH 03766), has been applied to investigate the case of transient draining in an axisymmetric vessel. The model is setup to match the experimental work of Lubin and Springer (1967, “The Formation of a Dip on the Surface of a Liquid Draining From a Tank,” J. Fluid Mech., 29(2), pp. 385–390). First, a comparison of the computational predictions with the experimental results for free draining is presented. Second, a comparison between the free surface positions obtained the developed VOF methodology and the results obtained by Zhou and Graebel (1990, “Axisymmetric Draining of a Cylindrical Tank With a Free Surface,” J. Fluid Mech., 221, pp. 511–532) using a boundary integral method is reported. When comparing the results with the observations of Lubin and Springer some differences are noted. These differences, which relate to the effect of initial height and outflow history, may have arisen due to the experimental procedure used by Lubin and Springer. This paper shows that CFD is a promising approach to analyzing these simple draining situations in terms of predicting bulk quantities, transitions, and free-surface shape and position.

Nonlinear and viscous effects on wave propagation in an elastic axisymmetric vessel

In this paper, a power series and Fourier series approach is used to solve the governing equations of motion in an elastic axisymmetric vessel with the assumption that the fluid is incompressible and Newtonian in a laminar flow. We obtain solutions for the wave speed and attenuation coefficient, analytically where possible, and show how these differ under a number of different conditions. Viscosity is found to reduce the wave speed from that predicted by linear wave theory and the nonlinear terms to increase the wave speed in comparison to the linear solution. For vessels with a wall stiffness in the arterial range, the reduction in the wave speed due to the viscous terms is approximately 10% and the increase due to the nonlinear terms is approximately 5%. This difference between the linear and nonlinear wave speeds was found to be largely constant irrespective of the number of terms considered in the power series for the velocity profile. The linear wave speed was found to vary weakly with stiffness, whilst the nonlinear wave speed was found to vary significantly with the stiffness, especially at low values of stiffness. The 10% variation in the wave speed due to the viscous terms was found to be constant with wall stiffness whilst the 5% variation due to the nonlinear terms was found to vary with wall stiffness. The importance of the number of terms considered in the power series is discussed showing that only a relatively small number is required in the viscous case to obtain accurate results.

Quantification of the effects of vasomotion on mass transport to tissue from axisymmetric blood vessels

The process known as vasomotion, rhythmic oscillations in vessel diameter, has been proposed to act as a protective mechanism for tissue under conditions of reduced perfusion, since it is frequently only observed experimentally when perfusion levels are reduced. This could be due to a resultant increase in oxygen transport from the vasculature to the surrounding tissue, either directly or indirectly. It is thus potentially of significant clinical interest as a warning signal for ischemia. However, there has been little analysis performed to quantify the effects of vessel wall movement on time-averaged mass transport. We thus present a detailed analysis of such mass transport for an axisymmetric vessel with a periodically oscillating wall, by solving the non-linear mass transport equation, and quantify the differences between the time-averaged mass transport under conditions of no oscillation (i.e. the steady-state) and varying wall oscillation amplitude. The results show that if the vessel wall alone is oscillated, with an invariant wall concentration, the time-averaged mass transport is reduced relative to the steady-state, but if the vessel wall concentration is also oscillated, then mass transport is increased, although this is generally only true when these oscillate in phase with each other. The influence of Péclet number and the non-dimensional rate of consumption of oxygen in tissue, as well as the amplitude of oscillations, are fully characterised. We conclude by considering the likely implications of these results in the context of oxygen transport to tissue.

A hyperbolic system of conservation laws for fluid flows through compliant axisymmetric vessels

We are concerned with the derivation and analysis of one-dimensional hyperbolic systems of conservation laws modelling uid ows such as the blood ow through compliant axisymmetric vessels. Early models derived are nonconservative and/or nonhomogeneous with measure source terms, which are endowed with infinitely many Riemann solutions for some Riemann data. In this paper, we derive a one-dimensional hyperbolic system that is conservative and homogeneous. Moreover, there exists a unique global Riemann solution for the Riemann problem for two vessels with arbitrarily large Riemann data, under a natural stability entropy criterion. The Riemann solutions may consist of four waves for some cases. The system can also be written as a 3×3 system for which strict hyperbolicity fails and the standing waves can be regarded as the contact discontinuities corresponding to the second family with zero eigenvalue.

Material strain hardening in pressure vessel design by analysis

The effect of including material strain hardening on the gross plastic deformation (GPD) load of four sample problems from the EPERC Design by Analysis manual is investigated. The models considered are two axisymmetric vessels with flat heads under pressure, a nozzle/knuckle intersection under pressure, and a cylinder-cylinder intersection under combined pressure and moment loading. The results of limit analysis, large deformation elastic-perfectly plastic analysis, and small and large deformation bilinear hardening analysis are presented. Plastic loads are calculated using the ASME twice elastic slope (TES) criterion and the plastic work curvature (PWC) criterion. It is found that the plastic pressures given by the ASME TES criterion are inconsistent with respect to the limit load. The PWC criterion is found to represent strain hardening more consistently and lead to enhanced plastic loads. Von Mises equivalent plastic strain plots show that the form and extent of plastic deformation at the limit load in a perfectly plastic analysis and at the plastic load in a strain hardening analysis are similar, indicating a common definition of GPD.

Pressure and pressure gradient in an axisymmetric rigid vessel with stenosis

Based on an improvement of the Karman-Pohlhausen's method, using nonlinear polynomial fitting and integral integral, the axial distributions of pressure and its gradient in an axisymmetric rigid vessel with stenosis were obtained, and the distributions related to Reynolds number and the geometry of stenotic vessel were discussed. It shows that with the increasing of stenotic degree or Reynolds number, the fluctuation of pressure and its gradient in stenotic area is intense rapidly, and negative pressure occurs subsequently in the diverging part of stenotic area. Especially when the axial range of stenosis extends, the flow of blood in the diverging part will he more obviously changed. In higher Reynolds number or heavy stenosis, theoretical calculation is mainly in accordance with past experiments.

Analysis of the effects of gravity and wall thickness in a model of blood flow through axisymmetric vessels

The effects of gravitational forces and wall thickness on the behaviour of a model of blood flow through axisymmetric vessels were studied. The governing fluid dynamic equations were derived from the Navier-Stokes equations for an incompressible fluid and linked to a simple model of the vessel wall. A closed form of the hyperbolic partial differential equations was found, including a significant source term from the gravitational forces. The inclination of the vessel is modelled using a slope parameter that varied between -1 and 1. The wave speed was shown to be related to the wall thickness, and the time to first shock formation was shown to be directly proportional to this thickness. Two non-dimensional parameters were derived for the ratio of gravitational forces to viscous and momentum forces, respectively, and their values were calculated for the different types of vessel found in the human vasculature, showing that gravitational forces were significant in comparison with either viscous or momentum forces for every type of vessel. The steady-state solution of the governing equations showed that gravitational forces cause an increase in area of approximately 5% per metre per unit slope. Numerical simulations of the flow field in the aorta showed that a positive slope causes a velocity pulse to change in amplitude approximately linearly with distance: -4% per metre and +5% per metre for vessels inclined vertically upwards and downwards, respectively, in comparison with only +0.5% for a horizontal vessel. These simulations also showed that the change relative to the zero slope condition in the maximum rate of change of area with distance, which was taken to be a measure of the rate of shock formation, is proportional to both the slope and the wall thickness-to-inner radius ratio, with a constant of proportionality of 1.2. At a ratio of 0.25, typical of that found in human arteries, the distance to shock formation is thus decreased and increased by 30% for vessels inclined vertically downwards and upwards, respectively. Gravity and wall thickness thus have a significant impact on a number of aspects of the fluid and wall behaviour, despite conventionally being neglected.