Axisymmetric Tube Research Articles

Physiological analysis of streamline topologies and their bifurcations for a peristaltic flow of nano fluid

In the present article, the techniques of dynamical systems are utilized to investigate the streamline patterns along their bifurcations for peristaltic flow under mixed convection effect. Here the peristaltic flow is discussed in a vertical channel. The flow is considered in a two-dimensional symmetric channel as well as an axisymmetric tube. We have evaluated the peristaltic flow of blood base nanofluid. The momentum equations are reduced by employing approximation of low Reynolds number and long wavelength. For the discourse of the path of particle in the wave frame, an arrangement of nonlinear independent differential equations are built up and the strategies for dynamical frameworks are utilized to examine the local bifurcations and their topological changes. Critical points classifications were made by scrutiny of the eigenvalues of the Jacobian matrix. This principle are utilized to divulge the local bifurcation of the critical points encountered for different flow situations. Flow situations marked as: backward flow, trapping or augmented flow. The analysis is disclosed that the number and size of trapped bolus increases in planner channel and decline in axisymmetric channel by increasing Grashof number. Moreover, the decreasing behaviour of temperature is depicted, which clarify the nanofluid as a cooling agent. Graphically, a wide range of topological changes of bifurcations are examined. At long last, to outline the bifurcation the diagram of global bifurcation is utilized.

Investigation of base flow for an axisymmetric suddenly expanded nozzle with micro JET

This investigation presents the outcome of the tests conducted to control the pressure in the re-circulation zone. Also, the efficiency of the flow controllers to govern the pressure at the base in a rapidly expanded pipe has been investigated. Tiny jets our in number of 1 mm diameter are positioned at the interval of 90 degrees at 6.5 mm from the central axis of the main jet. The Mach numbers of the abruptly expanded flows studied for base pressure range from 1.1 to 3 and the obtained wall pressure distribution is depicted for Mach number 1.6 and 1.8 respectively. Axi-symmetric round brass tubes were used to join jets; and cross-sectional area of those tubes are 2.56. L/D ratio of the broadened pipe was differed from 1 to 10 and NPR was shifted from 3 to 11. Notwithstanding, the outcomes displayed were for Low L/D values of 4, 3, 2 and 1 individually. Also, when the stream was released to the pipes of the given area ratios, it stayed connected with the channel divider for all the inertial levels and the NPRs tried in the present case. Further it is understood that level of expansion assumes a noteworthy part to choose the pressure at the base and its control adequacy. At whatever point, the stream is over expanded, it leads to the formation of an oblique shock at the nozzle lip, prompting improvement of the pressure in the base locale. Shock waves formation, reflection and recombination proceeded till the pressure winds up noticeably environmental and seen that the stream stays intact for low L/D ratio of 4. Very small scale (micro) jets proved to fit in as controllers for the base pressure.

Two-step forming for improvement of forming limit in rotary nosing with relieved die for fabrication of axisymmetric and eccentric nosed tubes

This paper presents application of two-step forming for improving the forming limit in rotary nosing with a relieved die. Nosing is one method which is used for reducing the diameter of a tube tip. “Two-step nosing” is composed of two stages and different dies are applied for the two stages. The die shapes are determined based on the occurrence tendency of defects in “one-step nosing”, where only one die is used through the whole process. In this research, a series of experiments and numerical analyses of one-step nosing was carried out for investigating the mechanism of the occurrence of defects. As a result, it is revealed that the occurrence of defects was highly relevant with the contact area between the die and tube. Based on the result of one-step nosing, the optimum die shapes were determined for the two stages, and then “two-step nosing” improved the forming limit 9% higher than one-step nosing under the optimum condition. Furthermore, “two-step nosing” was experimentally applied for forming eccentric nosed tubes, and its superiority was verified.

Viscous Taylor droplets in axisymmetric and planar tubes: from Bretherton’s theory to empirical models

The aim of this study is to derive accurate models for quantities characterizing the dynamics of droplets of non-vanishing viscosity in capillaries. In particular, we propose models for the uniform-film thickness separating the droplet from the tube walls, for the droplet front and rear curvatures and pressure jumps, and for the droplet velocity in a range of capillary numbers, Ca, from $$10^{-4}$$ to 1 and inner-to-outer viscosity ratios, $$\lambda$$ , from 0, i.e. a bubble, to high-viscosity droplets. Theoretical asymptotic results obtained in the limit of small capillary number are combined with accurate numerical simulations at larger Ca. With these models at hand, we can compute the pressure drop induced by the droplet. The film thickness at low capillary numbers ( $$Ca<10^{-3}$$ ) agrees well with Bretherton’s scaling for bubbles as long as $$\lambda <1$$ . For larger viscosity ratios, the film thickness increases monotonically, before saturating for $$\lambda>10^3$$ to a value $$2^{2/3}$$ times larger than the film thickness of a bubble. At larger capillary numbers, the film thickness follows the rational function proposed by Aussillous and Quere (Phys Fluids 12(10):2367–2371, 2000) for bubbles, with a fitting coefficient which is viscosity-ratio dependent. This coefficient modifies the value to which the film thickness saturates at large capillary numbers. The velocity of the droplet is found to be strongly dependent on the capillary number and viscosity ratio. We also show that the normal viscous stresses at the front and rear caps of the droplets cannot be neglected when calculating the pressure drop for $$Ca>10^{-3}$$ .

The Influence of Oscillatory Fractions on Mass Transfer of Non-Newtonian Fluid in Wavy-Walled Tubes for Pulsatile Flow

The shape of pipeline structure, fluid medium and flow state have important influence on the heat transfer and mass effect of fluid. In this paper, we investigated the mass transfer behavior of Non-Newtonian fluid CMC solution with 700ppm concentration in five different-sized axisymmetric wave-walled tubes for pulsatile flow. It is revealed that the effect of mass transfer is enhanced with the increase of oscillatory fractions P based on the PIV measurements. Besides, mass transfer rate was measured by the electrochemical method in the larger oscillatory points rate range. It is observed that mass transfer rate increases with the increase in P and reached the maximum mass transfer rate at the most optimal oscillatory fractions Popt. After reaching the optimal oscillatory fractions Popt, the mass transfer rate decreases with increasing P.

Flux tube model in the solar atmosphere

AbstractWe construct two classes of the magnetohydrostatic equilibria of the axisymmetric flux tubes with twisted magnetic fields in the stratified solar atmosphere that span from the photosphere to the transition region. We built the models by incorporating specific forms of the gas pressure and poloidal current in the Grad-Shafranov equation. This model gives both closed and open field structure of the flux tube. The other open field model we construct is based on the self-similar formulation, where we have incorporated specific forms of the gas pressure, poloidal current and two different shape functions. We study the homology of the parameter space that is consistent with the solar atmosphere and find that the estimation of the magnetic structure inside the flux tubes is consistent with the observation and simulation results of the magnetic bright points.

Steady Displacement of Long Gas Bubbles in Channels and Tubes Filled by a Bingham Fluid.

Bingham fluids behave like solids below a von Mises stress threshold, the yield stress, while above it they behave like Newtonian fluids. They are characterized by a dimensionless parameter, Bingham number (Bn), which is the ratio of the yield stress to a characteristic viscous stress. In this study, the non-inertial steady motion of a finite size gas bubble in both a plane 2D channel and an axi-symmetric tube filled by a Bingham fluid has been studied numerically. The Bingham number, Bn, is in the range 0 ≤ Bn ≤ 3, where Bn=0 is the Newtonian case, while the Capillary number which is the ratio of a characteristic viscous force to the surface tension has values Ca=0.05, 0.10, and 0.25. The volume of all axi-symmetric and 2D bubbles has been chosen to be identical for all parameter choices and large enough for the bubbles to be long compared to the channel/tube width/diameter. The Bingham fluid constitutive equation is approximated by a regularized equation. During the motion, the bubble interface is separated from the wall by a static liquid film. The film thickness scaled by the tube radius (axi-symmetric)/half of the channel height (2D) is the dimensionless film thickness, h. The results show that increasing Bn initially leads to an increase in h, however, the profile h versus Bn can be monotonic or non-monotonic depending on Ca values and 2D/axi-symmetric configurations. The yield stress also alters the shape of the front and rear of the bubble and suppresses the capillary waves at the rear of the bubble. The yield stress increases the magnitude of the wall shear stress and its gradient and therefore increases the potential for epithelial cell injuries in applications to lung airway mucus plugs. The topology of the yield surfaces as well the flow pattern in the bubble frame of reference varies significantly by Ca and Bn.

Modelling electro-active polymers with a dispersion-type anisotropy

We propose a novel constitutive framework for electro-active polymers (EAPs) that can take into account anisotropy with a chain dispersion. To enhance actuation behaviour, particle-filled EAPs become promising candidates nowadays. Recent studies suggest that particle-filled EAPs, which can be cured under an electric field during the manufacturing time, do not necessarily form perfect anisotropic composites, rather they create composites with dispersed chains. Hence in this contribution, an electro-mechanically coupled constitutive model is devised that considers the chain dispersion with a probability distribution function in an integral form. To obtain relevant quantities in discrete form, numerical integration over the unit sphere is utilized. Necessary constitutive equations are derived exploiting the basic laws of thermodynamics that result in a thermodynamically consistent formulation. To demonstrate the performance of the proposed electro-mechanically coupled framework, we analytically solve a non-homogeneous boundary value problem, the extension and inflation of an axisymmetric cylindrical tube under electro-mechanically coupled load. The results capture various electro-mechanical couplings with the formulation proposed for EAP composites.

Peristaltic transport of two-layered blood flow using Herschel–Bulkley Model

The present article investigates the peristaltic transport of a Herschel–Bulkley fluid in an axisymmetric tube. The governing equations are solved using the long wavelength and small Reynolds numbe...

The Computational Fluid Dynamics Analyses on Hemodynamic Characteristics in Stenosed Arterial Models.

Arterial stenosis plays an important role in the progressions of thrombosis and stroke. In the present study, a standard axisymmetric tube model of the stenotic artery is introduced and the degree of stenosis η is evaluated by the area ratio of the blockage to the normal vessel. A normal case (η = 0) and four stenotic cases of η = 0.25, 0.5, 0.625, and 0.75 with a constant Reynolds number of 300 are simulated by computational fluid dynamics (CFD), respectively, with the Newtonian and Carreau models for comparison. Results show that for both models, the poststenotic separation vortex length increases exponentially with the growth of stenosis degree. However, the vortex length of the Carreau model is shorter than that of the Newtonian model. The artery narrowing accelerates blood flow, which causes high blood pressure and wall shear stress (WSS). The pressure drop of the η = 0.75 case is nearly 8 times that of the normal value, while the WSS peak at the stenosis region of η = 0.75 case even reaches up to 15 times that of the normal value. The present conclusions are of generality and contribute to the understanding of the dynamic mechanisms of artery stenosis diseases.

On the preservation of fibre direction during axisymmetric hyperelastic mass-growth of a finite fibre-reinforced tube

Several types of tube-like fibre-reinforced tissue, including arteries and veins, different kinds of muscles, biological tubes as well as plants and trees, grow in an axially symmetric manner that preserves their own shape as well as the direction and, hence, the shape of their embedded fibres. This study considers the general, three-dimensional, axisymmetric mass-growth pattern of a finite tube reinforced by a single family of fibres growing with and within the tube, and investigates the influence that the preservation of fibre direction exerts on relevant mathematical modelling, as well on the physical behaviour of the tube. Accordingly, complete sets of necessary conditions that enable such axisymmetric tube patterns to take place are initially developed, not only for fibres preserving a general direction, but also for all six particular cases in which fibres grow normal to either one or two of the cylindrical polar coordinate directions. The implied conditions are of kinematic character but independent of the constitutive behaviour of the growing tube material. Because they hold in addition to and simultaneously with standard kinematic relations and equilibrium equations, they describe growth by an overdetermined system of equations. In cases of hyperelastic mass-growth, the additional information they thus provide enables identification of specific classes of strain energy densities for growth that are admissible and, therefore, suitable for the implied type of axisymmetric tube mass-growth to take place. The presented analysis is applicable to many different particular cases of axisymmetric mass-growth of tube-like tissue, though admissible classes of relevant strain energy densities for growth are identified only for a few example applications. These consider and discuss cases of relevant hyperelastic mass-growth which (i) is of purely dilatational nature, (ii) combines dilatational and torsional deformation, (iii) enables preservation of shape and direction of helically growing fibres, as well as (iv) plane fibres growing on the cross section of an infinitely long fibre-reinforced tube. The analysis can be extended towards mass-growth modelling of tube-like tissue that contains two or more families of fibres. Potential combination of the outlined theoretical process with suitable data obtained from relevant experimental observations could lead to realistic forms of much sought strain energy functions for growth.

Pulsatile flow of non-Newtonian blood fluid inside stenosed arteries: Investigating the effects of viscoelastic and elastic walls, arteriosclerosis, and polycythemia diseases

Background and objectiveIn this study, the interaction of pulsatile blood flow with the viscoelastic walls of the axisymmetric artery is numerically investigated for different severities of stenosis. The geometry of artery is modeled by an axisymmetric cylindrical tube with a symmetric stenosis in a two-dimensional case. The effects of stenosis severity on the axial velocity profile, pressure distribution, streamlines, wall shear stress, and wall radial displacement for the viscoelastic artery are also compared to the elastics artery. Furthermore, the effects of atherosclerosis and polycythemia diseases on the hemodynamics and the mechanical behavior of arterial walls are investigated. MethodsThe pulsatile flow of non-Newtonian blood is simulated inside the viscoelastic artery using the COMSOL Multiphysics software (version 5) and by employing the fluid-structure interaction (FSI) method and the arbitrary Lagrangian-Eulerian (ALE) method. Moreover, finite element method (FEM) is used to solve the governing equations on the unstructured grids. For modeling the non-Newtonian blood fluid and the viscoelastic arterial wall, the modified Casson model, and generalized Maxwell model are used, respectively. ResultsAccording to the results, with stenosis severity increasing from 25% to 75% at the time of maximum volumetric flow rate, the maximum value of axial velocity and its gradient increase 7.9 and 19.6 times, and the maximum wall shear stress of viscoelastic wall increases 24.2 times in the constriction zone. With the progression of the atherosclerosis disease (fivefold growth of arterial elastic modulus), the wall radial displacement of viscoelastic arterial walls decreases nearly 40%. ConclusionsIn this study, axial velocity profile, pressure distribution, streamlines, wall radial displacement, and wall shear stress were examined for different percentages of stenosis (25%, 50%, and 75%). The atherosclerosis disease was investigated by the fivefold growth of viscoelastic arterial elastic modulus and polycythemia disease was examined by the 21-fold increase in the yield stress of the blood fluid. Furthermore, the comparison of results between the elastic and viscoelastic arterial walls shows that the wall radial displacement for viscoelastic artery is lower than that for the elastic artery as much as 21.7% for the severe stenosis of 75%.

Resonant oscillations in open axisymmetric tubes

We study the behaviour of the isentropic flow of a gas in both a straight tube of constant cross section and a cone, open at one end and forced at or near resonance at the other. A continuous transition between these configurations is provided through the introduction of a geometric parameter k associated with the opening angle of the cone where the tube corresponds to \(k=0\). The primary objective is to find long-time resonant and near-resonant approximate solutions for the open tube, i.e. \(k\rightarrow 0\). Detailed analysis for both the tube and cone in the limit of small forcing \((O(\varepsilon ^{3}))\) is carried out, where \(\varepsilon ^{3}\) is the Mach number of the forcing function and the resulting flow has Mach number \(O(\varepsilon )\). The resulting approximate solutions are compared with full numerical simulations. Interesting distinctions between the cone and the tube emerge. Depending on the damping and detuning, the responses for the tube are continuous and of \(O(\varepsilon )\). In the case of the cone, the resonant response involves an amplification of the fundamental resonant mode, usually called the dominant first-mode approximation. However, higher modes must be included for the tube to account for the nonlinear generation of higher-order resonances. Bridging these distinct solution behaviours is a transition layer of \(O(\varepsilon ^{2})\) in k. It is found that an appropriately truncated set of modes provides the requisite modal approximation, again comparing well to numerical simulations.

Towards a thermo-magneto-mechanical coupling framework for magneto-rheological elastomers

Magnetorheological elastomers (MREs) are a relatively new class of smart materials that can undergo large deformations resulting from external magnetic excitation. These are promising candidates in producing sensors and actuators. Due to their inherent chemical compositions, most polymeric materials are highly susceptible to temperature. While performing experiments on MREs that are exposed to magneto-mechanically coupled loads, maintaining a constant temperature profile is a non-trivial task for various reasons, e.g., i) experiments need to be performed in a temperature chamber that can maintain a prescribed temperature throughout a test, and ii) additional temperature gradients can be generated internally. In this paper, a thermo-magneto-mechanically coupled constitutive model is devised that is based on the total energy approach frequently used in MREs modelling and computation. Relevant constitutive equations are derived exploiting basic laws of thermodynamics that result in a thermodynamically consistent formulation. We demonstrate the performance of the proposed thermo-magneto-mechanically coupled framework with the help of two non-homogeneous boundary value problems. In both problems an axisymmetric cylindrical tube is deformed under thermo-magneto-mechanically coupled loads. In the first example the mechanical deformation is a combination of axial stretch and radial inflation whereas in the second example the cylinder is put under a mechanical load of torsion around the cylinder axis combined with an axial stretch. In both examples a circumferential magnetic field and a radial temperature gradient are applied. The results capture various thermo-magneto-mechanical couplings with the formulation proposed for MRE.

A new model for calculating the transient displacement field within a linear elastic isotropic solid with a through hole under dynamic impact: A 3D model is developed and a 2D case study is examined

Abstract This paper presents an exact analytical solution in tensor notation for solving the elastic wave propagation for any 3-dimensional shape objects with a hole (from infinitesimal to finite). For validating the proposed model, a case study of an axisymmetric thick walled cylindrical metallic tube with finite length under a dynamic impact, was modeled and computed. The case study was also computed and validated by using an explicit time integration finite element method, LS-Dyna, for comparison purpose. The LS-Dyna simulation results were used to calculate the boundary conditions for the proposed model for obtaining the analytical solution because in the real world applications these boundary conditions can be obtained through measurement data or the signals of sensors. Based on the virtual boundary conditions obtained from simulation, the proposed model can compute the displacement field (transient response) of the object under dynamic impact. Once the displacement field is available, all transient stress, strain, rotation etc. can be computed as needed. The obtained analytical displacement fields as a function of time and coordinates were compared with the simulation results from LS-Dyna. It has been proven in this paper that the efficiency, accuracy and robustness of the proposed model meet the needs of any potential applications.

Numerical investigation on flow and heat transfer characteristics of corrugated tubes with non-uniform corrugation in turbulent flow

Abstract Based on finite volume method, the pressure drop and heat transfer characteristics of one smooth tube and ten different axisymmetric corrugated tubes, including two with uniform corrugation and eight with non-uniform corrugation, have been studied. A physical model of the corrugated tube was built, then the numerical simulation of the model was carried out and the numerical simulation results were compared with the empirical formula. The results show that: the friction factor decreases with the increase of Reynolds number ranging from 6000 to 57000, the value of which in the corrugated tubes with non-uniform corrugation (tube 03–10) are smaller than those with uniform corrugation (tube 01–02). The geometry parameters of tube (01) have advantages on the heat transfer enhancement in low Reynolds number flow region (from 6000 to 13000) and tube (07–08) have advantages on the heat transfer enhancement in high Reynolds number flow region (from 13000 to 57000). The vortex, existed in each area between two adjacent corrugations called second flow region, is the root of the enhancement on heat transfer in the corrugated tubes. The effectiveness factor decreases with the increasing of Reynolds number and the performances of the corrugated tubes with pitch of 12.5 mm have advantages than these of 10 mm under the same corrugation geometric parameter.

Numerical study of Hall effects on counter-helicity spheromak merging by two-dimensional Hall-MHD simulations

Hall effects on counter-helicity spheromak merging were investigated by two-dimensional MHD and Hall-MHD simulations of merging two axisymmetric toroidal flux tubes. In Hall-MHD cases, the structure of the reconnection current sheet and reconnection outflow are modified from the MHD case due to the Hall effect. We compared two cases (called “case-O” and “case-I”) of counter-helicity merging, which are distinguished by the polarity of toroidal magnetic fluxes. Radial motion of the reconnection X-point is controlled by poloidal electron flow accompanying the toroidal flux of the merging two spheromaks, and this creates a large difference in the current sheet and flow structure between the two cases of the Hall-MHD regime. The radial shift of the reconnection X-point depending on the polarity of toroidal magnetic flux of the spheromaks breaks the symmetry between the two cases. It was also found that there widely exists separation of ion and electron flow which are affected by the modification of the current sheet structure due to the radial shift of the X-point in the downstream side of the merging, and its spatial scale of the distribution of the Hall electric field is larger than the ion skin depth.

Numerical Simulations of Torsional Alfv\xe9n Waves in Axisymmetric Solar Magnetic Flux Tubes

We numerically investigate Alfvén waves propagating along an axisymmetric and non-isothermal solar flux tube embedded in the solar atmosphere. The tube magnetic field is current-free and diverges with height, and the waves are excited by a periodic driver along the tube magnetic field lines. The main results are that the two wave variables, the velocity and magnetic field perturbations in the azimuthal direction, behave differently as a result of gradients of the physical parameters along the tube. To explain these differences in the wave behavior, the time evolution of the wave variables and the resulting cutoff period for each wave variable are calculated and used to determine regions in the solar chromosphere where strong wave reflection may occur.

Rheological fluid motion in tube by metachronal waves of cilia

This paper presents a theoretical study of a non-linear rheological fluid transport in an axisymmetric tube by cilia. An attempt has been made to explain the role of cilia motion in the transport of fluid through the ductus efferent of the male reproductive tract. The Ostwald-de Waele power-law viscous fluid is considered to represent the rheological fluid. We analyze pumping by means of a sequence of cilia beats from row-to-row of cilia in a given row of cells and from one row of cells to the next (metachronal wave movement). For this purpose, we consider the conditions that the corresponding Reynolds number is small enough for inertial effects to be negligible, and the wavelength-to-diameter ratio is large enough so that the pressure can be considered uniform over the cross section. Analyses and computations of the fluid motion reveal that the time-average flow rate depends on ϵ, a non-dimensional measure involving the mean radius a of the tube and the cilia length. Thus, the flow rate significantly varies with the cilia length. Moreover, the flow rate has been reported to be close to the estimated value 6×10−3 ml/h for human efferent ducts if ϵ is near 0.4. The estimated value was suggested by Lardner and Shack (Lardner, T. J. and Shack, W. J. Cilia transport. Bulletin of Mathematical Biology, 34, 325–335 (1972)) for human based on the experimental observations of flow rates in efferent ducts of other animals, e.g., rat, ram, and bull. In addition, the nature of the rheological fluid, i.e., the value of the fluid index n strongly influences various flow-governed characteristics. An interesting feature of this paper is that the pumping improves the thickening behavior for small values of ϵ or in free pumping (ΔP = 0) and pumping (ΔP > 0) regions.

Axisymmetric irrotational potential flows of an ideal fluid in doubly connected domains

Amethod of constructing the model of ideal incompressible unbounded flow past an axisymmetric tube is developed; the tube shape and dimensions are determined in the process of the problem solution. The problem is solved using the method of spatial annular sources and sinks. It is shown that under certain conditions the resulting flow corresponds to that past a round finite-length tube, whose wall has a finite thickness. It is established that near the tunnel entry the flow is considerably restructured.