Tube Of Variable Cross Section Research Articles

The effects of gravitational and magnetic fields on the propagation of cylindrical strong shock waves in a van der Waals gas

The present study aims to investigate the effects of non-idealness parameter, gravitation and magnetic fields behind the flow of motion for cylindrical hydro-magnetic strong shock waves travelling through a tube of variable cross-section in a self-gravitating van der Waals gas. The analytical expressions of the flow variables for one-dimensional adiabatic flow behind the hydro-magnetic strong shock waves are obtained using Chester-Chisnell-Whitham’s (CCW) Method. The initial density distribution of the medium is assumed to be ρ0=ρ'r−w where ρ' is the density at the axis of symmetry, w is a constant and r is the distance from the axis of symmetry. The magnetic field, on the other hand, is assumed to have only constant axial and variable azimuthal components. Due to the presence of magnetic and gravitational fields, the uniform density distribution of the medium becomes non-uniform and this becomes an interesting fact to study. It is found that, all flow variables except the pressure rises with the shock propagation distance. It is also demonstrated that the gravitational and magnetic fields cause the numerical values of the flow variables to increase behind the shock wave. Further, research shows that even a small increase in the gravitational field increases the pressure behind the shock wave, whereas a small increase in the magnetic field has a little effect on it. Furthermore, it is found that the flow variables get strengthened behind the shock wave in comparison with ahead of the shock. The trends of the current findings are in good agreement with the existing experimental observations and results.

Bistable hybrid symmetric laminates with a clamped-clamped boundary condition: An experimental and numerical investigation

In this work, a clamped-clamped boundary condition is considered for a family of bistable hybrid symmetric laminates in which the direction of curvature does not change during the snap-through process between the two stable configurations. The laminates were modeled using finite element analysis to predict the characteristics of stable configurations, including the distributions of curvatures and out-of-plane displacement in two directions, and then the results were validated by experiments. The snap-through behaviors of the bistable laminates under the clamped-clamped boundary condition were investigated numerically and experimentally and then compared with the preloaded laminates with the same boundary condition. The results showed that the bistable laminates require a lower snap-through load than the preloaded laminates when they have a similar maximum out-of-plane displacement. The loading position, lay-up design, and length of the clamped region were employed as variables to discover the features of snap-through behavior. It was found that the unsymmetric deformation mode was present regardless of the load position during the snap-through behavior of these bistable laminates. At last, a variable cross-section tube consisting of two bistable laminates was proposed, and the area of the cross-section could be increased by 80% after the snap-through of the two bistable laminates

Exponential horn revisited: wave equation, normal modes and experimental measurements

In this work, a theoretical analysis is first presented to find the wave equation corresponding to the propagation of disturbances in the air contained inside a tube of variable cross section. In particular, the case of a tube with a circular cross section whose area varies exponentially as a function of the axial coordinate is studied. The hypotheses of the model used are discussed and the solutions of the wave equation obtained are presented. Secondly, and with the aim of validating the model used, measurements are made on a tube such as the one described, built using a 3D printer.

Use of half-cylinder obstacle for enhancing aeroelastic energy harvesting

ABSTRACT This study aims to improve the performance of the galloping-based piezoelectric energy harvester (GPEH) by benefiting from two half-cylinder obstacles. Two half-cylinder obstacles are employed to construct a variable cross-section tube which changes the airflow characteristics near the GPEH placed inside. The performance of the GPEH in the variable cross-section tube is tested by wind tunnel experiments. The experimental results demonstrate that compared with the traditional GPEH, the cut-in speed of the GPEH with the two half-cylinder obstacles at the downstream position −1.5D is reduced by 43.87%, from 2.23 m/s to 1.55 m/s. For the highest experimental wind speed of 4.29 m/s, the output voltage of the GPEH with the two half-cylinder obstacles is increased by 109.28%, from 4.31 V to 9.02 V. Moreover, the performance of the GPEH with the obstacles can be improved by appropriately increasing the obstacle curvature and reducing the throat width. The computational fluid dynamics (CFD) simulations are conducted to qualitatively interpret the experimental discoveries. The results demonstrated that the downstream area is beneficial to the GPEH, whereas the upstream area degrades the performance.

Pressure Losses in Power-Law Fluid Flow through a Tube of Variable Cross-Section

Steady laminar flow of an incompressible power-law fluid is a tube with an obstacle of given shape is numerically simulated. The mathematical description of the process is based on the vortex transport equation and the Poisson equation for the stream function, while the rheological properties of the medium are described by the Ostwald—de Waele power law. The steady solution of the problem is obtained using a time-dependent method based on the finite-difference approximation of the governing equations. The pressure distribution is determined by numerically solving the Poisson equation. A parametric investigation of the kinematic and dynamic flow parameters, as functions of the control parameters of the problem, is performed for non-Newtonian media. The effect of the Reynolds number, the nonlinearity exponent, and the obstacle geometry on the coefficient of the local fluid resistance is demonstrated.

Nonlinear Oscillations of a Chain of Masses in a Liquid

Nonlinear regular and random vibrations of a metamaterial made as a chain of massive elements immersed in a viscous liquid are studied. The nearest neighbors are connected by nonlinear elastic forces. Stokes friction is taken into account. A system of equations for mass oscillations is obtained. In the continuum long-wave approximation, the system is reduced to a simplified partial differential equation with nonlinear and dissipative terms. We find the exact solutions and show that the competition of nonlinearity and absorption can lead to the formation of a steady wave profile shape. For noise waves, the correlation function and intensity spectrum are given. The process of sawtooth wave excitation by distributed external sources is analyzed. The limiting “peak” amplitude is calculated. Waves in tubes of variable cross section filled with metamaterial are considered. Based on the solution of the equation containing coordinate-dependent tube section, an expression is found for the amplitude of the sawtooth wave.

Singularities and spectral asymptotics of a random nonlinear wave in a nondispersive system

In this paper, we study the propagation of high-intensity acoustic noise in free space and in waveguide systems. A mathematical model generalizing the Burgers equation is used. It describes the nonlinear wave evolution inside tubes of variable cross-section, as well as in ray tubes, if the geometric approximation for heterogeneous media is used. The generalized equation transforms to the common Burgers equation with a dissipative parameter, known as the “Reynolds–Goldberg number”. In our model, this number depends on the distance travelled by the wave. With a zero “viscous” dissipative term, the model reduces to the Riemann (or Hopf) equation. Its solution presents the field by an implicit function. The spectral form of this solution makes it possible to derive explicit expressions for both dynamic and statistical characteristics of intense waves. The use of a spectral approach allowed us to describe the high-intensity noise in media with zero and finite viscosity. Applicability conditions of these solutions are defined. Since the phase matching is fulfilled for any triplet of interacting spectral components, there is an avalanche-like increase in the number of harmonics and the formation of shocks. The relationship between these discontinuities and other singularities and the high-frequency asymptotic of intense noise is studied. The possibility is shown to enhance nonlinear effects in waveguide systems during the evolution of noise.

On the Boundary Layer in the Case of Viscous Fluid Flowing Around Confuser with the Ladyzhenskaya Rheological Law

We consider the Prandtl type boundary layer equations for a fluid with the nonlinear Ladyzhenskaya rheological equation. In a nonstandard case of a fluid flow through a confuser (a tube of variable cross-section), we study the behavior of the boundary layer and derive an asymptotic estimate for the solution.

The evolution of resonance: a multiscale approach to the effect of nonlinearity, frequency dispersion and geometry

Nonlinear resonant oscillations in continuous media contain two natural time scales: the travel time in the medium and the ‘slow’ time defined by the small nonlinearity. A multiscale approach is used to describe the evolution to a periodic state. We focus on three basic experiments that define nonlinear resonant oscillations in continuous media: a gas in both a straight tube and a tube of variable cross-section, and shallow water in a tank. The outcomes of these experiments are described and the mathematical techniques that show the evolution to the final periodic states are given in some detail.

Oscillatory flow of a Casson fluid in an elastic tube with variable cross section

Abstract The aim of this paper was to study an oscillatory flow of a Casson fluid through an elastic tube of variable cross section. The radial displacement of tube wall is taken into consideration. The problem is modelled under the assumption that the variation of the cross section of the tube is slow in the axial direction. Cylindrical coordinate system is chosen to study the problem. The analytical expressions for axial velocity and mass flux as a function of pressure gradient are obtained. The change in pressure distribution for various pressure****radius relationships is analyzed by considering different geometries. The effects of elastic parameter, Womersley parameter and Casson parameter on excess pressure and pressure gradient along axial direction are discussed through graphs. The results reveal that the elastic parameter plays a key role in the variation of pressure along the tube. Womersley parameter has significant effect on pressure distribution. Another important observation is that the amplitude of pressure increases for growing values of Casson parameter for both tapered and constricted tubes. In addition, the pressure oscillates more for the case of locally constricted tube when compared to other geometries.

Re-Reflection Effect On Shock Waves in Two-Phase Flows through a Tube of Variable Cross-Section

In present paper Re-reflection effect on shock –waves in two-phase flows through a tube of variable cross-section is considered when particle volume fraction appeared as an additional variable .It is concluded that re-reflected effects reduce the cross sectional area .For two-phase flows when equilibrium is eventually established , presence of particle volume fraction , further reduce the cross – sectional area. One dimensional area relation for a non – uniform , steady flow ahead of a shock is obtained and concluded that all the results are valid for the case when direction of the shock motion and the gas flow ahead of the shock is same . In preparation of graphs Mathematica 7 is used .

Re-Reflection Effect On Shock Waves in Two-Phase Flows through a Tube of Variable Cross-Section

In present paper Re-reflection effect on shock –waves in two-phase flows through a tube of variable cross-section is considered when particle volume fraction appeared as an additional variable .It is concluded that re-reflected effects reduce the cross sectional area .For two-phase flows when equilibrium is eventually established , presence of particle volume fraction , further reduce the cross – sectional area. One dimensional area relation for a non – uniform , steady flow ahead of a shock is obtained and concluded that all the results are valid for the case when direction of the shock motion and the gas flow ahead of the shock is same . In preparation of graphs Mathematica 7 is used .

Peristaltic transport of Herschel–Bulkley fluids in tubes of variable cross section induced by dilating peristaltic waves: application to sliding hiatus hernia

The presented formulation deals with the flow of Herschel–Bulkley fluid induced by progressive transverse dilating peristaltic waves in a circular cylindrical tube of non-uniform cross sectional area. This is an intended act to model swallowing of various types of chewed foods in oesophagus which suffers from hiatus hernia. Due to sliding hiatus hernia, the cross section of the lower oesophagus does not remain uniform. The impact of bulging, which is formed by various combinations of divergence and convergence, is examined. Effects of dilating amplitude, the flow behavior index etc. are also investigated. The non-linear governing equations which represent the model are linearized by low Reynolds number and long wavelength approximations and after that computer simulation is used to evaluate the numerical results. Pressure in the oesophagus along its axis and the time averaged volume flow rate over a period for a single wave propagation are also evaluated. It is inferred that pressure drops right from the beginning and lowers further in the lower part even if only the lower portion of the cylindrical tube diverges. Experimental observations confirm this when the oesophagus suffers from sliding hiatus hernia causing the lower oesophagus to bulge towards the end. If the lower part of the tube subsequently converges towards the end after divergence, pressure is found to increase. Pressure is found to increase with the flow behavior index even when the tube changes its cross sectional area. When the bolus is nearing the cardiac sphincter, pressure-rise and pressure-drop are both less in a diverging tube than that in a uniform tube. Therefore, the pressure requirement to deliver bolus in stomach is less if oesophagus diverges. The presented investigation is significant for the patients suffering from sliding hiatus hernia.

Numerical studies on the swaging process of tubes with variable wall thickness for monobloc driving shafts

This study analyzed thickening trends of the variable cross-section tube in relation to swaging process variables to present an effective design for the tube manufacturing process. The extent of thickening was evaluated through a finite element analysis of the swaging process with varying process variables such as die shape and initial tube thickness. As a result, the amount of thickening was found to improve with decreasing diameter reduction, taper angle, and initial tube thickness.

Passive time-domain numerical models of viscothermal wave propagation in acoustic tubes of variable cross section.

Numerical modeling of wave propagation in acoustic tubes is a subject of longstanding interest, particularly for enclosures of varying cross section, and especially when viscothermal losses due to boundary layer effects are taken into consideration. Though steady-state, or frequency domain methods, are a common avenue of approach, recursive time domain methods are an alternative, allowing for the generation of wideband responses, and offer a point of departure for more general modeling of nonlinear wave propagation. The design of time-domain methods is complicated by numerical stability considerations, and to this end, a passive representation is a useful design principle leading to simple stable and explicit numerical schemes, particularly in the case of viscothermal loss modeling. Such schemes and the accompanying energy and stability analysis are presented here. Numerical examples are presented for a variety of duct profiles, illustrating strict energy dissipation, and for comparison of computed input impedances against frequency-domain results.

Dodecapod’s movement algorithm within a linear cylindrical tube of variable cross-section

Dodecapod’s movement algorithm within a linear cylindrical tube of variable cross-section

Stability Analysis and Numerical Simulation of the Conical Tower of the Wind Turbine

In the light of the structural features of the wind turbine tower and force characteristics, the mechanical model of the variable cross-section tube tower is established. Based on the elastic stability theory, the buckling of tower is studied, and the critical force formula of the tower under the concerted action of concentrated force and gravity is deduced. Calculation models are numerically simulated for the stability of the tower by using the finite element software ANSYS, and corresponding critical load is obtained. The results show that the finite element models are feasible in engineering application, and the analysis provides a theoretical basis for structural design of wind turbine.

Residual Wall Thickness Study of Variable Cross-section Tube in Water-assisted Injection Molding

Abstract Residual wall thickness is an important measure of the quality of water-assisted injection molding (WAIM) parts. Based on the traditional injection molding model, Reynolds stress was introduced into the WAIM model for the turbulent characteristics of high pressure water. In addition, residual wall thickness was computed by a computational fluid dynamics (CFD) method, and the results matched well with experimental data. The results show that the hollowed core ratio changes from small to large in the first half of water penetration, while in the latter half it is just the opposite. Difference of the residual wall thickness is larger at the large-diameter position of a part than other position. Residual wall thickness is mainly affected by water injection pressure, delay time, melt temperature, mold temperature and amount of short shot, in which the amount of short shot is the most obvious.

FEM Simulation and Optimization of Process Parameters for Tube Hydroforming

The finite element software DYNAFORM was applied to simulate the whole tube hydroforming process. Two main failure types in the process of hydroforming are wrinkling and bursting. The strain distribution and thickness distribution at different process parameters were presented. Not only friction coefficient but also the effect of different matching of internal pressure and axial force was simulated and analyzed. In addition, the velocity of punch was considered too. The result has reference value for the variable cross-section tube hydroforming process research.

Optimization of Process Parameters of Tube Hydroforming Based on Orthogonal Experiment

Numerical simulation was made on parameters like internal pressure and axial force as well as friction coefficient of tube that affect the formation of variable cross-section tube. Through numerical simulation and orthogonal optimization, the most thickness reduction ratio and thickness uniformity on different conditions were contrasted and analyzed. An optimum scheme was obtained and it could improve the formability of variable cross-section tube. The result indicates that the axial force plays the most important role on thickness reduction ratio. The result provides technical support for the variable cross-section tube hydroforming research.