Axisymmetric Tube Research Articles

Characterization of peristaltic flow during the mixing process in a model human stomach

Numerical simulations are performed to investigate the characteristics of peristaltic flow in a model stomach during the mixing and digestion process. The geometrical model for the stomach consists of an axisymmetric tube of varying diameter with a wall at one end, representing the antrum and closed pylorus. The antral contraction waves (ACWs) that produce the peristaltic flow are modeled as traveling waves that deform the boundary and consequently the computational mesh. This geometrical model is implemented into the open source code OpenFOAM. A parametric study is performed in which the fluid viscosity, wave speed, wave width, and maximum relative occlusion are varied. The effect of these parameters on the retropulsive jet induced near the pylorus and the recirculation between pairs of consecutive ACWs is investigated. Both of these flow features contribute to the mixing and digestion process. The retropulsive jet is quantified by its peak velocity and length along the centerline. For each wave geometry, these quantities are found to be independent of the Reynolds number for low Reynolds numbers, while for Reynolds numbers exceeding one, the peak centerline velocity decreases and the jet length increases as the Reynolds number increases. Moreover, the velocity and pressure curves are found to scale with the wave speed at low Reynolds numbers. Between different wave geometries, scaling laws are proposed and tested for the peak centerline velocity and jet length. Particle tracking and vorticity plots show that mixing efficiency increases when the relative occlusion increases, as well as when the viscosity or wave width decreases.

Bifurcation and stability analysis of critical/stagnation points for peristaltic transport of a power-law fluid in a tube

The stability of critical/stagnation points and streamline topologies along with their local and global bifurcations for peristaltic flow of an incompressible power-law model have been investigated. The flow is analyzed in an axisymmetric tube subject to the constraints of long wavelength and low Reynolds number, and an exact analytic solution is found in a moving frame of reference. Nonlinear autonomous differential equations are developed to unveil the particle paths and position of critical points in the flow. Stability of obtained critical points and streamline patterns along with their local bifurcations are inspected by using the theory of dynamical system. Three different flow distributions are found in the flow: backward flow, trapping and augmented flow. The transitions between these flow situations correspond to bifurcations in the flow field where non-hyperbolic degenerate points change their behavior to form heteroclinic connection between saddles. The nature and stability of these bifurcations and corresponding topological changes are explored graphically. A global bifurcation diagram is used to epitomize these bifurcations. The fluid behavior index has a significant impact on the stability of critical points and the ranges of flow regions. The backward flow region and trapping region are observed to shrink and expand, respectively, with an increase in the fluid behavior index. The findings of present article are verified by comparing them with the results already existing in the literature.

Analysis of bifurcation dynamics of streamlines topologies for pseudoplastic shear thinning fluid: Biomechanics application

This analysis comprises the innovative technique to analyze the bifurcation of streamlines by considering the model of shear thinning fluid inside the channel as well as through tube of axisymmetric tube. The set of the equations governing the flow model are transformed into differential equations by approximations prior to pursuing the analytical solutions for particle paths. The methodology of dynamical systems is used to inspect the local bifurcation and change observed in their topologies. When sundry parameters take definite degenerate values the phenomenon of bifurcation occurs. Three distinct flow situations like augmented, trapping and backward appear due to transition. The global bifurcation plots summarized all these bifurcation. The topological changes in plots of bifurcation are inspected via graphs.

Fluid Flow and Solute Transfer in a Tube with Variable Wall Permeability

Abstract We considered a steady flow of viscous incompressible fluid and solute transfer in an axisymmetric tube of uniform cross section with variable wall permeability, which is relevant to the study of movement of solute across the glomerular capillaries. The solutions for the nonlinear governing equations of the fluid flow and solute transfer are obtained by analytical/numerical methods. The combined effect of variable wall permeability and flow parameters on the hydrostatic pressure, osmotic pressure, velocity profiles, concentration profiles, and the total solute clearance are investigated and are presented in this paper. It is found that an increase in the variable permeability parameter increases the solute concentration at the wall.

Study on weldability window and interface morphology of steel tube and tungsten alloy rod welded by explosive welding

The explosive welding of the axisymmetric 30CrMnSi tube and tungsten alloy rod was studied. Through theoretical analysis, the weldability window of these two metals was obtained, which could enable the prediction of the welding interface morphology under different explosive conditions. The explosive welding tests under different explosive loading conditions were carried out and 30CrMnSi/tungsten alloy composite rods were obtained. Analytical investigations of the microstructure, hardness, and composition of the samples were performed. The results showed that 30CrMnSi steel tubes and tungsten alloy rods could be successfully welded together. The welding interfaces of composite rods obtained under different explosive loads had different morphological characteristics. With the increase in the explosive load, the welding interface transforms from a straight interface to a corrugated one and even forms a melting transition zone at the interface. The chemical compositions of the transition zone showed that the region consists of two kinds of welded materials. It indicated that the temperature at the interface during the welding process exceeded the melting temperature of the tungsten alloy, and both of the welded materials generated melting phenomena.

Blast load simulation using conical shock tube systems

With the increased frequency of accidental and deliberate explosions, evaluating the response of civil infrastructure systems to blast loading has been attracting the interests of the research and regulatory communities. However, with the high cost and complex safety and logistical issues associated with field explosives testing, North American blast-resistant construction standards (e.g. ASCE 59-11 and CSA S850-12) recommend the use of shock tubes to simulate blast loads and evaluate relevant structural response. This study first aims at developing a simplified two-dimensional axisymmetric shock tube model, implemented in ANSYS Fluent, a computational fluid dynamics software, and then validating the model using the classical Sod’s shock tube problem solution, as well as available shock tube experimental test results. Subsequently, the developed model is compared to a more complex three-dimensional model and the results show that there is negligible difference between the two models for axisymmetric shock tube performance simulation; however, the three-dimensional model is necessary to simulate non-axisymmetric shock tubes. Following the model validation, extensive analyses are performed to evaluate the influences of shock tube design parameters (e.g. the driver section pressure and length and the expansion section length) on blast wave characteristics to facilitate a shock tube design that would generate shock waves similar to those experienced by civil infrastructure components under blast loads. The results show that the peak reflected pressure increases as the driver pressure increases, while a decrease in the expansion length increases the peak reflected pressure. In addition, the positive phase duration increases as both the driver length and expansion length are increased. Finally, the developed two-dimensional axisymmetric model is used to optimize the dimensions of a physical large-scale conical shock tube system constructed for civil infrastructure component blast response evaluation applications. The capabilities of such shock tube system are further investigated by correlating its design parameters to a range of explosion threats identified by different hemispherical TNT charge weight and distance scenarios.

Effects of surfactant on propagation and rupture of a liquid plug in a tube.

Surfactant-laden liquid plug propagation and rupture occurring in lower lung airways are studied computationally using a front-tracking method. The plug is driven by an applied constant pressure in a rigid axisymmetric tube whose inner surface is coated by a thin liquid film. The evolution equations of the interfacial and bulk surfactant concentrations coupled with the incompressible Navier-Stokes equations are solved in the front-tracking framework. The numerical method is first validated for a surfactant-free case and the results are found to be in good agreement with the earlier simulations of Fujioka et al. (2008) and Hassan et al. (2011). Then extensive simulations are performed to investigate the effects of surfactant on the mechanical stresses that could be injurious to epithelial cells such as pressure and shear stress. It is found that the liquid plug ruptures violently to induce large pressure and shear stress on airway walls and even a tiny amount of surfactant significantly reduces the pressure and shear stress and thus improves cell survivability. However, addition of surfactant also delays the plug rupture and thus airway reopening.

Open and Closed Magnetic Configurations of Twisted Flux Tubes

We construct two classes of magnetohydrostatic (MHS) equilibria for an axisymmetric vertical flux tube spanning from the photosphere to the lower part of the transition region within a realistic stratified solar atmosphere subject to solar gravity. We assume a general quadratic expression of the magnetic flux function for the gas pressure and poloidal current and solve the Grad-Shafranov equation analytically. The solution is a combination of a homogeneous and a particular part where the former is separable by a Coulomb function in $r$ and exponential in $z$, while the particular part is an open configuration that has no $z$ dependence. We also present another open field solution by using a self-similar formulation with two different profile functions and incorporating stratified solar gravity to maintain the magnetohydrostatic equilibria, which is a modification of earlier self-similar models with a twist. We study the admitted parameter space that is consistent with the conditions in the solar atmosphere and derive magnetic and the thermodynamic structures inside the flux tube that are reasonably consistent with the photospheric magnetic bright points (MBPs) for both open and closed field Coulomb function and self-similar models as estimated from observations and simulations. The obtained open and closed field flux tube solutions can be used as the background conditions for the numerical simulations for the study of the wave propagation through the flux tubes. The solutions can also be used to construct realistic magnetic canopies.

Erratum to: Mathematical modelling of two-fluid electro-osmotic peristaltic pumping of an Ellis fluid in an axisymmetric tube

Erratum to: Mathematical modelling of two-fluid electro-osmotic peristaltic pumping of an Ellis fluid in an axisymmetric tube

Simultaneous Effects of Heat Transfer and Variable Viscosity on Peristaltic Transport of Casson Fluid Flow in an Inclined Porous Tube

The present study investigates the combined effects of varying viscosity and heat transfer on a Casson fluid through an inclined porous axisymmetric tube in the presence of slip effects. The modeled governing equations are solved analytically by considering the long wavelength and small Reynolds number approximations. The numerical integration is employed to obtain pressure rise and frictional force. A parametric analysis has been presented to study the effects of the Darcy number, angle of inclination, varying viscosity, velocity slip, thermal slip, yield stress, amplitude ratio, Prandtl number and Eckert number on the pressure rise, pressure gradient, streamlines, frictional force and temperature. The study reveals that an increase in the angle of inclination and viscosity parameter has a proportional increase in the pressure rise. Also, an increase in the porosity causes a significant reduction in the pressure rise.

Mathematical modelling of two-fluid electro-osmotic peristaltic pumping of an Ellis fluid in an axisymmetric tube

This article explores analytically the dynamics of two-fluid electro-osmotic peristaltic flow through a cylindrical tube. The rheology of the fluid in the central core (inner region or core region) is captured through the Ellis equation. The region adjacent to the wall (outer region or peripheral region) is occupied by a Newtonian fluid. The equations governing the flow in each region are modeled by using the appropriate suppositions of long wavelength and low Reynolds number. Closed form expressions for the stream function corresponding to each region are obtained and utilized to determine the axial pressure gradient and the interface between the inner and the outer regions. The pumping characteristics, trapping and reflux phenomena are investigated in detail with reference to the Ellis model parameters and the electro-kinetic slip velocity. The present model also generalizes earlier studies from the literature which can be retrieved as special cases. The analysis shows that pressure drop at zero volumetric flow rate is elevated with increasing occlusion parameter. Trapping and reflux phenomena are mitigated with increasing electro-osmotic slip and shear-thinning effects. At larger value of the occlusion parameter an increase in the power-law index reduces the magnitude of the pressure drop. Increasing Ellis rheological parameter reduces the pressure drop over the entire range of occlusion parameters for the case when the peripheral region fluid viscosity exceeds that of the core region fluid. The results obtained may be applicable in the modulation of peristaltic pumping in the efficient operation of various industrial and bio-medical devices.

Computational model of the mechanoelectrophysiological coupling in axons with application to neuromodulation.

For more than half a century, the action potential (AP) has been considered a purely electrical phenomenon. However, experimental observations of membrane deformations occurring during APs have revealed that this process also involves mechanical features. This discovery has recently fuelled a controversy on the real nature of APs: whether they are mechanical or electrical. In order to examine some of the modern hypotheses regarding APs, we propose here a coupled mechanoelectrophysiological membrane finite-element model for neuronal axons. The axon is modeled as an axisymmetric thin-wall cylindrical tube. The electrophysiology of the membrane is modeled using the classic Hodgkin-Huxley (H-H) equations for the Nodes of Ranvier or unmyelinated axons and the cable theory for the internodal regions, whereas the axonal mechanics is modeled by means of viscoelasticity theory. Membrane potential changes induce a strain gradient field via reverse flexoelectricity, whereas mechanical pulses result in an electrical self-polarization field following the direct flexoelectric effect, in turn influencing the membrane potential. Moreover, membrane deformation also alters the values of membrane capacitance and resistance in the H-H equation. These three effects serve as the fundamental coupling mechanisms between the APs and mechanical pulses in the model. A series of numerical studies was systematically conducted to investigate the consequences of interaction between the APs and mechanical waves on both myelinated and unmyelinated axons. Simulation results illustrate that the AP is always accompanied by an in-phase propagating membrane displacement of ≈1nm, whereas mechanical pulses with enough magnitude can also trigger APs. The model demonstrates that mechanical vibrations, such as the ones arising from ultrasound stimulations, can either annihilate or enhance axonal electrophysiology depending on their respective directionality and frequency. It also shows that frequency of pulse repetition can also enhance signal propagation independently of the amplitude of the signal. This result not only reconciles the mechanical and electrical natures of the APs but also provides an explanation for the experimentally observed mechanoelectrophysiological phenomena in axons, especially in the context of ultrasound neuromodulation.

Numerical study of peristaltic motion of non-Newtonian fluid at high Reynolds number in an axisymmetric tube

In the present investigation, we have studied numerically the peristaltic motion of micropolar fluid through a circular tube without imposing low Reynolds number and long wave length assumption. Galerkin’s finite element method has been used on the governing Navier–Stokes equation in the form of $$\psi - \omega$$ . The current study obtained the microrotation and streamline line directly from governing equations. The graphs of computed longitudinal velocity and pressure are plotted against different value of emerging parameter using stream function and vorticity. We observed that for small value of coupling number and microrotation parameter, the rotation of fluid particles is much faster than that for large value of coupling number and microrotation parameter.

Origin of the synchronous pressure fluctuations in the draft tube of Francis turbines operating at part load conditions

The synchronous pressure surge effect is a critical phenomenon occurring in Francis turbines operating at part load conditions. In this regime, pressure fluctuations are predominantly coming from the temporal rotation of a single helical vortex inside the turbine draft tube, called the part load vortex rope. However the combination of multi-physics interactions, geometry, cavitation, swirling flow and acoustic waves leads to a pressure amplification, called the synchronous pressure surge effect, which is more dangerous than the fluctuations resulting from the precessing vortex rope. While this subsequent amplification mechanism has been unraveled, the physical mechanism originating in the synchronous pressure wave remains poorly understood. We have therefore investigated the birth and the growth of the synchronous pressure wave in Francis turbines. By energy consideration of an azimuthal–temporal Fourier decomposition of the three dimensional numerical flow solutions in an axisymmetric draft tube geometry that is slightly disturbed at the wall, the source of the synchronous pressure and its amplification region are identified. In addition, the origin of this wave as the interaction of a wall disturbance with the part load vortex rope, is investigated using an asymptotic analysis and brings deeper comprehension of the synchronous wave generation mechanism.

Analysis of Hartmann boundary layer peristaltic flow of Jeffrey fluid: Quantitative and qualitative approaches

Peristalsis of Jeffrey fluid in axisymmetric tube is studied when the fluid is subject to strong magnetic field. Mathematical analysis is made under the assumption of small Reynolds number and long wave length approximations. An alternate assumption of lubrication theory can also be applied to the peristalsis problem. Both the approaches lead to same mathematical expressions. The effects of magnetic field are investigated in the boundary layer (Hartman boundary layer) and on the boundary layer thickness. The effects of strong magnetic field, in the boundary layer, are explored using asymptotic analysis to find analytical solution. We notice that this approach facilitates to unveil the effects of strong magnetic field explicitly and determines the boundary layer thickness mathematically. The objective behind this study is: how to control the boundary layer thickness through the application of strong magnetic field. This phenomenon is central from theoretical and applied points of view. While going for the asymptotic analysis of large magnetic field; the mathematical model leads to singular perturbation problem which is an apparent diversion to most of the peristalsis problems– attempted by regular perturbation method.The boundary value problem is solved analytically using singular perturbation approach together with higher order matching technique. The important features of peristalsis like stream function, velocity, and pressure rise are calculated. In addition to the analytical solution, we explore the qualitative behavior of the flow using the theory of dynamical systems. The velocity field is determined by the phase plane analysis and the stability of the solution is found through bifurcation diagrams. Qualitative analysis of the solution has been carried out for magnetic parameter, amplitude ratio, flow rate and the Jeffrey fluid parameter. The concomitant change of stability is given through topological flow patterns. Equilibrium plots (bifurcation diagrams) give a complete description of the various flow patterns developed for the complete range of a flow parameters in contrast to most of the studies that describe the flow patterns at some particular value of a parameter. The study helps to analyze the behavior of the fluid at the critical points that represent steady solution. The mix of the analytical and qualitative approach will help to broaden the scope and understanding of peristaltic transport of fluid in channels, tubes and curved tubes (this study).

Mass-growth of a finite tube reinforced by a pair of helical fibres

Several types of tube-like fibre-reinforced tissue, including the layers of arteries and veins, different kinds of muscle, biological tubes as well as plants and trees, are reinforced by a pair of helical fibres wound symmetrically around the tube axis in opposite directions. In many cases, this kind of biological structures grow in an axially symmetric manner that preserves their own shape as well as the direction and shape of their embedded pair of helical fibres. This study considers and investigates the influence that preservation of fibre direction exerts on pseudo-elastic (elastic-like) mass-growth modelling of the described fibre-reinforced structure. Complete sets of necessary conditions that enable the implied axisymmetric tube mass-growth to take place are sought, found and presented. These hold in addition to, and simultaneously with standard kinematic relations and equilibrium equations met in conventional hyperelasticity. They thus render this mass-growth mathematical model the properties of an apparently overdetermined boundary value problem. However, the additional information they provide leads to identification of admissible classes of strain energy densities for growth that enable realisation of the implied type of tube mass-growth. The analysis is applicable to several different types of mass-growth of tube-like tissue reinforced by a pair of symmetrically wound helical fibres. This is demonstrated with an application which considers that mass-growth of the fibre-reinforced tube takes place in an incompressible manner; namely, in a non-isochoric manner that along with fibre direction, it also preserves the material density of the growing tube.

Parameter study and multi-objective optimisation of an axisymmetric rectangular tube with diaphragms for subways

This study proposes a new axisymmetric rectangular tube (ART) with diaphragms. Unlike a uniform thickness tube (UTT), the thicknesses of adjacent ART walls are defined to be independent, with the thicknesses of the opposite walls remaining identical. The finite element model of ART with diaphragms was developed and validated by experiments; moreover, we found this structure exhibited acceptable values of crashworthiness indexes with a controllable and stable collapse pattern. To explore coupling influences of the three types of thicknesses on crashworthiness indexes and obtain optimal designs, we conducted a design of experiment (DOE) and employed polynomial response surface method (PRSM) for parameter study and optimisation. It was found that the ART with diaphragms achieved superior crash performance compared with the UTT with diaphragms, because of lower peak force and higher specific energy-absorption. When configurations of the ART wall thickness changed, the sensitivity of the two tube-wall thicknesses on crashworthiness indexes also changed and diaphragm thickness had different influences on crashworthiness indexes. Moreover, the distribution of design parameters of the thicknesses of ART was helpful in developing a crashworthiness design strategy. Therefore, we introduced this ART with diaphragms into crashworthy subways and recommended optimal designs as excellent energy-absorbing structures in practical engineering.

Base Pressure Behaviour in a Suddenly Expanded Duct at Supersonic Mach Number Regimes using Taguchi Design of Experiments

Abstract Experimental investigations are carried out to study the control of base pressure without and with the use of micro-jets through suddenly expanded axi-symmetric passage in the supersonic regime. Four micro jets having an orifice diameter of 1mm were located at 90° intervals. In the base area, active controls jets have been placed on a pitch of a circle diameter that is 1.3 times the exit diameter of the nozzle. The jets were dispensed abruptly into the axi-symmetric tube maintained at a cross-sectional area of 4.84 times the exit nozzle area. The variation of base pressure as a function of flow control parameters namely Mach number, nozzle pressure ratio (NPR) and length to diameter) ratio (L/D) are evaluated experimentally. This study also assesses the impact of flow control variables on base pressure for two cases viz. with control and without control respectively. An L 9 orthogonal array of Taguchi and the analysis of variance were employed to investigate the percentage of contribution of these parameters and their interactions affecting the base pressure. The correlations between the various factors affecting the base pressure were obtained by using multiple linear regression equations. Confirmation tests were conducted in order to test the developed linear regression equations for their practical significance. Both the regression models were found to be significant and reliable with a percentage deviation lying in the range of − 6.12% to 10.26% for base pressure without control and −13.92% to 6.58% for base pressure with control. Analysis of variance was also performed in order to determine the statistical significance of each parameter on the total variability of base pressure. The study concluded that Mach number is the most influential parameter affecting base pressure followed by NPR and L/D.

An incremental deformation model of arterial dissection

We develop a mathematical model for a small axisymmetric tear in a residually stressed and axially pre-stretched cylindrical tube. The residual stress is modelled by an opening angle when the load-free tube is sliced along a generator. This has application to the study of an aortic dissection, in which a tear develops in the wall of the artery. The artery is idealised as a single-layer thick-walled axisymmetric hyperelastic tube with collagen fibres using a Holzapfel–Gasser–Ogden strain-energy function, and the tear is treated as an incremental deformation of this tube. The lumen of the cylinder and the interior of the dissection are subject to the same constant (blood) pressure. The equilibrium equations for the incremental deformation are derived from the strain energy function. We develop numerical methods to study the opening of the tear for a range of material parameters and boundary conditions. We find that decreasing the fibre angle, decreasing the axial pre-stretch and increasing the opening angle all tend to widen the dissection, as does an incremental increase in lumen and dissection pressure.

From Wire to Seamless Flow-Formed Tube: Leveraging the Combination of Wire Arc Additive Manufacturing and Metal Forming

Flow forming is a metal-forming process for producing axisymmetric hollowed tubes starting from cylindrical workpieces. In cases where the preformed tube includes defects, impurities or inconsistencies, the final product may not withstand the required standard. In this work, the preformed tubes were produced by metal wires melted into the desired geometry using a gas-metal arc-welding robot. Two geometries were built to allow either forward or backward tube spinning of parts from ER-70S-6 and AWS ER316L welding wires. Following the building process, the parts were machined to fit a flow-forming operation. The mechanical and metallurgical properties of the wires, preformed cylinders and final tubes were compared with conventionally manufactured material. Results indicate that the mechanical properties of the products of the proposed process were superior to those of conventional processing. Applying flow forming to wire-arc additive manufacturing yields a deeper understanding of the material qualities over a large building envelope and can be used as valid quality criteria for the additive manufacturing process qualification.