Non-uniform Tube Research Articles

THERMALLY INDUCED DEFORMATIONS OF COMPOSITE TUBES SUBJECTED TO A NONUNIFORM HEAT SOURCE

Analytical solutions are obtained for thermally induced axisymmetric elastic and elastic-plastic deformations in nonuniform heat-generating composite tubes with fixed ends. Thermoelastic solutions are obtained using four different boundary conditions: (i)free, (ii) radially constrained and free, (iii) free and pressurized, (iv) free and radially constrained. Elastic-plastic solutions are obtained for a composite tube having free inner and radially constrained outer boundaries using Tresca's yield condition and its associated flow rule. The first two stages of elastic-plastic deformations are studied considering nonlinearly hardening, linearly hardening, and perfectly plastic material behavior. The theory developed is illustrated in several numerical examples.

Why helicity injection causes coronal flux tubes to develop an axially invariant cross-section

It is shown that electric current flowing along an axially non-uniform magnetic flux tube produces an associated non-linear, non-conservative axial MHD force which pumps plasma from regions where the flux tube diameter is small to regions where it is large. In particular, this force will ingest plasma into the ends of a fat, initially potential flux tube and then pump the ingested plasma towards the middle bulge, thereby causing mass accumulation at the bulge.The ingested plasma convects frozen-in toroidal magnetic flux which accumulates at the middle as well. Flux accumulation at the bulge has the remarkable consequence of causing the bulge to diminish so that the flux tube becomes axially uniform as observed in coronal loops. Stagnation of the convergent plasma flow at the middle heats the plasma. A small number of tail particles bouncing synchronously between approaching fluid elements can be Fermi-accelerated to very high energies. Since driving a current along a flux tube is tantamount to helicity injection into the flux tube, this mass ingestion, heating, and straightening should be ubiquitous to helicity injection processes.

The meaning of the Kelly-Lochbaum acoustic-tube model.

The scattering equations of the Kelly-Lochbaum segmented tube, including the time-varying extension by Strube, are originally based on the assumption of uniform spatial segments and stepwise time update of the acoustic impedances. Here, it is shown that the same equations can be derived without these assumptions for a nonuniform time-varying tube from the discretization of space and time derivatives by the bilinear z transform or by centered differences along the rotated coordinates ct+/-x. Moreover, the same equations also hold for a chain of lattice circuits (or equivalents) with appropriate parameters, if time derivatives are discretized by the bilinear z transform. These circuits can also be extended to simulate uniform segments of varying length.

Peristaltic Transport of a Particle–Fluid Suspension through a Uniform and Non‐Uniform Annulus

This study looks at the influence of an endoscope on the peristaltic flow of a particle–fluid suspension (as blood model) through tubes. A long wavelength approximation through a uniform and non‐uniform infinite annulus filled with an incompressible viscous and Newtonian fluid mixed with rigid spherical particles of identical size is investigated theoretically. The inner tube is uniform, rigid and moving with a constant velocity V0, whereas the outer non‐uniform tube has a sinusoidal wave travelling down its wall. The axial velocity of the fluid phase uf, particulate phase up and the pressure gradients have been obtained in terms of the dimensionless flow rate Q, the amplitude ratio ɸ, particle concentration C, the velocity constant V0 and the radius ratio ϵ (the ratio between the radius of the inner tube and the radius of the outer one at the inlet). Numerical calculations for various values of the physical parameters of interest are carried out for the pressure rise and the friction force on the inner and the outer tubes.

Adaptive changes in the capillary network in the left ventricle of rat heart.

Capillaries are nonuniform thin tubes: The arteriolar and venular capillary portions express alkaline phosphatase (AP) and dipeptidyl peptidase IV (DPPIV), respectively. Differences in enzyme activities between arteriolar and venular capillary portions could be shown by staining sections of cardiac tissues for AP and DPPIV after coronary infusion of microspheres and by staining cultured endothelial cells that had been collected from coronary microvessels. Through use of a double staining method for AP and DPPIV, adaptive changes in the capillary network were studied in rat hearts exposed to cold, exercise, hypertension, chronic coronary occlusion, and transient coronary occlusion followed by reperfusion. Two patterns could be seen in the adaptations of the ventricular capillary network. The increase in the venular capillary portions is accompanied by remarkable increases in capillary density and capillary-to-myocyte ratio. The increase in the arteriolar capillary portion seemed to be accompanied by a decrease or only a limited increase in capillary density in stressed hearts. The increase in the total capillary density improves the capacity for oxygen transport to tissues with a high tissue perfusion and a short diffusion distance for oxygen. The increase in the arteriolar capillaries may also improve oxygen transport by increasing the arterial blood perfusing the tissue. This seems, however, a compensation for the limited angiogenesis: The alleviation of stresses, such as pharmacological treatment of the hypertrophied heart and reperfusion after transient ischemia, increases venular capillary portions and capillary density. These changes are discussed with immunohistochemical observations of rapid and prolonged expressions of angiogenic growth factors.

Analytical Solutions for Cusp Resonance in Dissipative MHD

The present paper considers resonant slow waves in 1D non-uniform magnetic flux tubes in dissipative MHD. Analytical solutions are obtained for the Lagrangian displacement and the Eulerian perturbation of the total pressure for both static and stationary equilibrium states. From these analytical solutions we obtain the fundamental conservation law and the jump conditions for resonant slow waves in dissipative MHD. The validity of the ideal conservation law and jump conditions obtained by Sakurai, Goossens, and Hollweg (1991) for static equilibria and Goossens, Hollweg, and Sakurai (1992) for stationary equilibria is justified in dissipative MHD.

Vortex solitons in a rotating fluid within a non-uniform tube

For analyzing forced axisymmetric flow of a non-uniformly rotating, inviscid and incompressible fluid within a long tube of slowly varying radius, a theoretical model called the forced Korteweg-de Vries (fKdV) equation with variable coefficients is derived to calculate the amplitude function of the Stokes stream function. When the fluid system is placed under forcing by axisymmetric disturbance steadily moving with a transcritical velocity, new numerical results of flow streamlines are presented to show that well-defined axisymmetrical recirculating eddies can be periodically produced and sequentially emitted to radiate upstream of the disturbance, becoming permanent in form as a procession of vortex solitons. The Rankine vortex and the Burgers vortex are adopted as two primary flows to exemplify this phenomenon and it is shown that flow with a highly centralized axial vorticity is more effective in producing upstream-radiating vortex solitons.

On the wave excitation and the formation of recirculation eddies in an axisymmetric flow of uniformly rotating fluids

The inertial waves excited in a uniformly rotating fluid passing through a long circular tube are studied numerically. The waves are excited either by a local deformation of the tube wall or by an obstacle located on the tube axis. When the flow is subcritical, i.e. when the phase and group velocity of the fastest wave mode in their long-wave limit are larger than the incoming axial flow velocity, the excited waves propagate upstream of the excited position. The non-resonant waves have many linear aspects, including the upstream-advancing speed of the wave and the coexisting lee wavelength. When the flow is critical (resonant), i.e. when the long-wave velocity is nearly equal to the axial flow velocity, the large-amplitude waves are resonantly excited. The time development of these waves is described well by the equation derived by Grimshaw & Yi (1993). The integro-differential equation, which describes the strongly nonlinear waves until the axial flow reversal occurs, can predict the onset time and position of the recirculation eddies observed in the solutions of the Navier-Stokes equations. The numerical results and the theory both show that the flow reversal most probably occurs on the tube axis and also when the waves are excited by a contraction of the tube wall. The structure of the recirculation eddies obtained in the solutions of the Navier-Stokes equations at Re = 105 is similar to the axisymmetric or ‘bubble-type’ breakdown observed in the experiments of the vortex-breakdown which used a different non-uniform (Burgers-type) rotation. In uniformly rotating fluids the formation of the recirculation eddies has not been observed in the previous numerical studies of vortex breakdown where a straight tube was used and thus the inertial waves were not excited. This shows that the generation of the recirculation eddies in this study is genuinely explained by the topographically excited large-amplitude inertial ‘waves’ and not by other ‘instability’ mechanisms. Since the wave cannot be excited in a straight tube even in the non-uniformly rotating flows, the generation mechanism of the recirculation eddies in this study is different from the previous numerical studies for the vortex breakdown. The occurrence of the recirculation eddies depends not only on the Froude number and the strength of the excitation source but also on the Reynolds number since the wave amplitude generally decreases by the viscous effects. Some relations to the experiments of vortex breakdown, which have been exclusively done for non-uniformly rotating fluids but done in a ‘non-uniform tube’, are discussed. The flow states, which are classified as supercritical, subcritical or critical in hydraulic terminology, changes along the flow when the upstream flow is near resonant conditions and a non-uniform tube is used.

Radiative heating and the buoyant rise of magnetic flux tubes in the solar interior

We study the effect of radiative heating on the evolution of thin magnetic flux tubes in the solar interior and on the eruption of magnetic flux loops to the surface. Magnetic flux tubes experience radiative heating because (1) the mean temperature gradient in the lower convection zone and the overshoot region deviates substantially from that of radiative equilibrium, and hence there is a non-zero divergence of radiative heat flux; and (2) the magnetic pressure of the flux tube causes a small change of the thermodynamic properties within the tube relative to the surrounding field-free fluid, resulting in an additional divergence of radiative heat flux. Our calculations show that the former constitutes the dominant source of radiative heating experienced by the flux tube. In the overshoot region, the radiative heating is found to cause a quasi-static rising of the toroidal flux tubes with an upward drift velocity ∼ 10-3|δ| cm s-1, where δ ≡ ∇e − ∇ad < 0 describes the subadiabaticity in the overshoot layer. The upward drift velocity does not depend sensitively on the field strength of the flux tubes. Thus in order to store toroidal flux tubes in the overshoot region for a period comparable to the length of the solar cycle, the magnitude of the subadiabaticity δ(< 0) in the overshoot region must be as large as ∼ 3 × 10−4. We discuss the possibilities for increasing the magnitude of δ and for reducing the rate of radiative heating of the flux tubes in the overshoot region. Using numerical simulations we study the formation of ‘Ω’-shaped emerging loops from toroidal flux tubes in the overshoot region as a result of radiative heating. The initial toroidal tube is assumed to be non-uniform in its thermodynamic properties along the tube and lies at varying depths beneath the base of the convection zone. The tube is initially in a state of neutral buoyancy with the internal density of the tube plasma equal to the local external density. We find from our numerical simulations that such a toroidal tube rises quasi-statically due to radiative heating. The top portion of the nonuniform tube first enters the convection zone and may be brought to an unstable configuration which eventually leads to the eruption of an anchored flux loop to the surface. Assuming reasonable initial parameters, our numerical calculations yield fairly short rise times (2–4 months) for the development of the emerging flux loops. This suggests that radiative heating is an effective way of causing the eruption of magnetic flux loops, leading to the formation of active regions at the surface.

Analytic solutions for resonant Alfv�n waves in 1D magnetic flux tubes in dissipative stationary MHD

Resonantly driven Alfven waves are studied in non-uniform stationary magnetic flux tubes. Analytic dissipative MHD solutions are obtained for the Lagrangian displacement and the Eulerian perturbation of the total pressure. These analytic solutions are valid in the dissipative layer and in the two overlap regions to the left and the right of the dissipative layer. From these analytic solutions we obtain the fundamental conservation law and the jump conditions for resonantly driven Alfven waves in magnetic flux tubes with an equilibriun flow. The fundamental conservation law and the jump conditions depend on the equilibrium flow in a more complicated way than just a Doppler shift. The effects of an equlibrium flow are not to be predicted easily in general terms with the exception that the polarization of the driven Alfven waves is still in the magnetic surfaces and perpendicular to the magnetic field lines as it is in a static flux tube.

A simple numerical scheme for the computation of resonant Alfv�n waves

The present paper discusses the implementation of the SGHR method (Sakurai, Goossens, and Hollweg, 1991; Goossens, Ruderman, and Hollweg, 1995) in a numerical scheme for determining resonantly driven Alfven waves in nonuniform magnetic flux tubes. This method is based on jump conditions over the dissipative layer which are obtained from an asymptotic analysis of analytical solutions to simplified versions of the linear non-ideal MHD equations in this dissipative layer. The emphasis is on the computational simplicity and the accuracy of the method. The method derives its computational simplicity from the fact that it circumvents the numerical integration of the non-ideal MHD equations. The implementation only requires the numerical integration of the ideal MHD equations away from the resonant position. There is no need for a special integration scheme and a PC suffices as a hardware tool. The accuracy of the method is verified by means of test computations. These test computations deal with the loss of power of acoustic waves in sunspots by resonant absorption of Alfven waves. Results for the absorption coefficients obtained with the SGHR method are compared with known results in the literature obtained by integration of the full set of the linearized non-ideal MHD equations. The agreement is excellent and identifies the SGHR method as a powerful and extremely easy to use tool for studying resonant Alfven waves.

Dissipative MHD solutions for resonant Alfv�n waves in 1-dimensional magnetic flux tubes

The present paper extends the analysis by Sakurai, Goossens, and Hollweg (1991) on resonant Alfven waves in nonuniform magnetic flux tubes. It proves that the fundamental conservation law for resonant Alfven waves found in ideal MHD by Sakurai, Goossens, and Hollweg remains valid in dissipative MHD. This guarantees that the jump conditions of Sakurai, Goossens, and Hollweg, that connect the ideal MHD solutions forξr, andP′ across the dissipative layer, are correct. In addition, the present paper replaces the complicated dissipative MHD solutions obtained by Sakurai, Goossens, and Hollweg forξr, andP′ in terms of double integrals of Hankel functions of complex argument of order\(\frac{1}{3}\) with compact analytical solutions that allow a straightforward mathematical and physical interpretation. Finally, it presents an analytical dissipative MHD solution for the component of the Lagrangian displacement in the magnetic surfaces perpendicular to the magnetic field linesξ⊥ which enables us to determine the dominant dynamics of resonant Alfven waves in dissipative MHD.

Exponentially tapered t-tube model of systemic arterial system in dogs

This study determines the role of an asymmetric T-tube model as a representation of arterial mechanical properties. The model consists of two non-uniform tubes connected in parallel. The non-uniform properties of each tube include geometric and elastic tapering and each tube terminates in a complex load. Pulsatile pressure and flow velocity of the ascending aorta were measured in 10 closed-chest, anaesthetized dogs. An exponentially tapered transmission line is used to describe the non-uniform properties of the vasculature. The phase constant is a function of position along the path length due to geometric and elastic tapers. This non-uniform T-tube model makes it possible to fit the measured pressure waveform in the ascending aorta. Model parameters could be estimated and used to interpret the physical properties of the arterial system. The mathematical and experimental model impedance spectra are similar. There is a close correspondence between the impedance parameters derived from the non-uniform T-tube model and values computed from measurements on dogs. The results suggest that inclusion of tube tapering improves the mathematical model so that it closely represents the experimentally derived arterial impedance in closed-chest dogs. We conclude that the non-uniform properties of wave-transmission paths may play an important role in governing the behaviour of an asymmetric T-tube for the description of the arterial system.

Particle deposition and plugging in tubes and cracks (with special reference to fission product retention)

The main function of a containment structure enclosing a nuclear reactor is to retain any accidental release of radioactive materials. However, if the containment has leak paths due, for example, to cracks or failed seals, then there is the possibility of particulate matter and gas passing through the opening due to the pressure difference. The work presented in this paper describes in some detail the three main steps reqired to assess the amount of gas and particulate matter that pass into the environment. Step one involves calculation of the gas flow through a tube of non-uniform cross sectional area, step two is concerned with the deposition of small solid particles suspended in the host gas, onto the walls of the tube and, in step three, the rate of buildup of deposit on the tube wall is calculated with the aim of determining the rapidity with which the tube is plugged. We recast the gas dynamics equation into a form suitable for calculating gas flow in non-uniform tubes in the laminar and turbulent flow regimes, from low speed up to critical flow conditions. The results of these calculations are compared with an extensive set of experiments and excellent agreement is found. We briefly outline the various deposition processes that particles can undergo on surfaces and show how the particle concentration in the tube may be calculated. Finally, an equation that determines the shape and rate of formation of a plug is developed. This equation is non-linear and integro-differential in nature, and in order to solve it we develope a method which involves prescibing a geometrical plug shape but allowing the parameters within it to be time dependent. Plugging times and the amounts of particulate and gas that have escaped prior to plugging are calculated. Comparison with experiment is made and reasonable agreement found. A general discussion of the shortcomings of the approach is given together with suggestions for further work.

Resonant behaviour of MHD waves on magnetic flux tubes

Resonant absorption of MHD waves on a nonuniform flux tube is investigated as a driven problem for a 1D cylindrical equilibrium. The variation of the fractional absorption is studied as a function of the frequency and its relation to the eigenvalue problem of the MHD radiating eigenmodes of the nonuniform flux tube is established. The optimal frequencies producing maximal fractional absorption are determined and the condition for total absorption is obtained. This condition defines an impedance matching and is fulfilled for an equilibrium that is fine tuned with respect to the incoming wave. The variation of the spatial wave solutions with respect to the frequency is explained as due to the variation of the real and imaginary parts of the dispersion relation of the MHD radiating eigenmodes with respect to the real driving frequency.

The mercury-in-glass thermometer of non-uniform capillary tube

The mercury-in-glass thermometer of non-uniform capillary tube

Flow of Newtonian fluid in non-uniform tubes with variable wall permeability with application to flow in renal tubules

The hydrodynamical aspects of flow through proximal renal tubule have been investigated. Assuming renal fluid as Newtonian fluid, flow through diverging/converging tubes with variable wall permeability has been considered. Solutions have been obtained for approximate Navier-Stokes equations with boundary conditions which include a dynamic condition, i.e., leakage flux at the wall depends on variable wall permeability and transboundary pressure drop. Numerical solutions, using fourth order Runge-Kutta method, and approximate analytic solutions, using perturbation method, have been obtained. A comparison of the numerical solution with approximate analytic solution, shows a good agreement (difference less than 4%) between the two solutions for small values of |e|, a tube non-uniformity parameter. The velocity profiles at different positions along the axis, the axial distribution of wall shear stress, flow rate and leakage flux have been obtained. For a given value of wall permeability, in diverging (converging) tubes the fractional reabsorption FR is more (less) than its corresponding value in uniform tubes. Further, FR increases (decreases) as the wall permeability increases (decreases) as a linear function of axial distance. The results for flow with constant/variable permeability through uniform tubes and for flow through diverging/converging tubes with constant permeability can be obtained as special cases of this analysis. It is shown that by considering the divergent tube model with linear increase of wall permeability along the axis, an improvement of about 20% in total reabsorption can be achieved over the uniform tube model with constant wall permeability. It is concluded that the approach of using a dynamic boundary condition for leakage flux at the wall has an advantage over the method of prescribing the leakage flux at the wall for this physical problem. Using a set of data, relevant to a physiological situation, implications of the results on glomerular tubular balance have been briefly discussed.

A method to measure the area function from distribution of complex sound pressure in the nonuniform acoustic tube

AbstractDetermination of the area function of the vocal tract is an important problem for the speech production model. This paper proposes a method to measure the area function from the distribution of complex sound pressure in the nonuniform acoustic tube. The area is obtained with the calculation procedure of the cascade matrix at each measuring point under the assumptions of plane‐wave propagation and the losslessness of the non‐uniform tube. Discussions are also presented on the experiments for axially symmetric tubes and replicas of oral cavities. The proposed method is useful in investigating the influence from the complicated shapes of the oral cavities by using their replicas.

Vascular resistance of arterioles with nonuniform diameters

Arterioles in various vascular beds have been often observed to have nonuniform diameters along the vessel axis. The effect of nonuniformity of arteriolar diameter on vascular resistance was investigated using a theoretical model of blood flow in arterioles. Viscous flow of a Newtonian fluid in tubes with periodically changing diameters along the tube axis was analyzed by a finite element method based on the Stokes equations. Vascular resistance for the nonuniform tube was computed over a spatial period of the variation in diameter and was compared to resistance for a uniform tube with a constant diameter equal to the mean diameter of the nonuniform tube. In all cases, resistance for a tube with a nonuniform diameter was larger than resistance for a uniform tube with a diameter equal to the mean diameter of the nonuniform tube. Increases in the amplitude of the variation in diameter resulted in a rapid increase in resistance when the period of the variation remained constant. On the other hand, as the period of the diameter variation increased when amplitude remained constant, resistance decreased and approached the values obtained under the assumption of a Poiseuille flow at each cross section of the tube in the limit of an infinite period. Our theoretical model was applied to our previous in vivo studies of vessel diameter nonuniformity for rabbit mesentery arterioles in a contracted state. It was shown that vascular resistance calculated by our model was 2 to 11% higher than resistance obtained for a uniform tube with a diameter equal to the mean diameter of the arteriole.

Flow of urine through the ureter: a collapsible, muscular tube undergoing peristalsis.

In steady flow through nonuniform collapsible tubes a key concept is the compressive zone, at which flow limitation can occur at both high and low Reynolds numbers. Ureteral peristalsis can be considered as a series of compressive zones, corresponding to waves of active muscular contraction, that move at near-constant speed along the ureter towards the bladder. One-dimensional, lubrication-theory analysis shows that peristalsis can pump urine from kidney into the bladder only at relatively low mean rates of urine flow. Under these circumstances isolated boluses of urine are propelled steadily through the ureter (assumed uniform) by the contraction waves. At higher mean rates of flow the behavior depends on whether the frequency of peristalsis is higher or lower than a critical value. For frequencies above the critical value steady propagation of boluses that are in contact with contraction waves at both ends is possible. As the flow rate rises the urine begins to leak through the contraction waves and steady peristaltic flow breaks down. There is an upper limit to the mean flow rate that can be carried by steady peristalsis, which depends on the mechanical properties of the ureter. At high flow rates the peristaltic contractions do not pump but hinder the flow of urine through the ureter.