Non-uniform Cross-sectional Area Research Articles

LVI analysis on the beams with nonuniform cross-sectional area using exponential shear–strain function

Purpose The study aims to investigate the low-velocity impact (LVI) on the surface of a beam with a changeable cross-sectional area. In the study “LVI on a beam with a changeable cross-sectional area and clamped-free boundary conditions”, the effect of changes in the cross-section are on the contact force, the beam displacement, the impactor displacement and the impactor velocity are investigated. Design/methodology/approach To obtain the motion equations, first, a field of displacements of the beam is written using third-order shear deformation of beams, including the exponential shear–strain function, and then the energy method is used. By combining Hamilton’s approaches and Ritz’s method, finally, the equations of motion are extracted. Using ABAQUS finite element code, validation of the theoretical approach is carried out. In this study, the beam with changeable cross-sectional area is considered in such a way that the height of the beam is constant, but the width of the beam changes linearly. Findings The results show that assuming the width of the beam in the clamped support is constant, an increase in the width of the beam in the free support leads to an increase in the peak contact force and the residual velocity of the impactor, also, the peak displacement of the beam and the impactor are decreased. Originality/value It can be shown from the analysis of LVI on beams with nonuniform cross-sectional area that the important influence on the contact force, impactor residual velocity, beam displacement and impactor displacement is achieved.

Analytical solutions for the acoustic field in thin annular combustion chambers with linear gradients of cross-sectional area and mean temperature

Predictions of thermoacoustic instabilities in annular combustors are essential but difficult. Axial variations of flow and thermal parameters increase the cost of numerical simulations and restrict the application of analytical solutions. This work aims to find approximate analytical solutions for the acoustic field in annular ducts with linear gradients of axially non-uniform cross-sectional area and mean temperature. These solutions can be applied in low-order acoustic network models and enhance the ability of analytical methods to solve thermoacoustic instability problems in real annular chambers. A modified WKB method is used to solve the wave equation for the acoustic field, and an analytical solution with a wide range of applications is derived. The derivation of the equations requires assumptions such as low Mach number, high frequency and small non-uniformity. Cases with arbitrary distributions of cross-sectional surface area and mean temperature can be solved by the piecewise method as long as the assumptions are satisfied along the entire chamber.

Analytical solutions of acoustic field in annular combustion chambers with non-uniform cross-sectional surface area and mean flow

Low-order acoustic network models, treating the complex combustor geometry as a network of simple geometry elements, are typically used to analyse circumferential combustion instabilities in annular combustion chambers. These elements are typically assumed to have uniform cross-sectional surface area and average radius so that the analytical solutions of the acoustic field within them can be directly obtained. However, this may lead to errors in the combustion instability analyses. The present work derives the analytical solutions of the acoustic field in annular combustion chambers with both varying cross-sectional surface area and average radius sustaining a mean flow. A wave equation for the pressure perturbation is firstly derived based on very few assumptions. Analytical solutions of the acoustic field are then derived based on a modified WKB approximation. These solutions are then validated by comparing them to results by numerically resolving the linearised Euler equations. Results show that accurate predictions can always be obtained for a smooth change of the cross-sectional surface area and small-to-moderate subsonic axial Mach numbers as long as the frequency is larger than a certain value.

Synchronization of thermoacoustic quasiperiodic oscillation by periodic external force.

Quasiperiodic oscillations can occur in nonequilibrium systems where two or more frequency components are generated simultaneously. Many studies have explored the synchronization of periodic and chaotic oscillations; however, the synchronization of quasiperiodic oscillations has not received much attention. This study experimentally documents forced synchronization of the quasiperiodic state and the internally locked state of a thermoacoustic oscillator system. This system consists of a gas-filled resonance tube with a nonuniform cross-sectional area. The thermoacoustic oscillator was designed and built in such a way that nonlinear interactions between the fundamental acoustic oscillation mode and the third mode of the gas column are controlled by a temperature difference that is locally created in the resonance tube. Bifurcation diagrams were mapped out by changing the forcing strength and frequency. Separated Arnold tongues were found and both modes were entrained to the external force through complete synchronization. A saddle-node bifurcation was observed in the route from partial to complete synchronization when the forcing strength was relatively weak. However, a Hopf (torus-death) bifurcation was observed when the forcing was relatively strong. In the internally locked state, the bifurcation occurred after the internal locking was broken down by the external force.

A study on peristaltic flow of micropolar fluids: an application to sliding hiatus hernia

In this paper, we presented a mathematical formulation deals with the flow of micro-polar fluid in a circular cylindrical tube of non-uniform cross-sectional area induced by peristaltic waves of increasing amplitude. This is an intended act to model the swallowing of various types of foods in the oesophagus which suffers from a 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, has been examined. The effects of dilating amplitude, a slope of the tube wall, the coupling number, and micro-polar parameter, have been investigated.

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.

Development of a capillary plasma pump with vapour bubble for water purification: experimental and theoretical investigation

This paper describes the development of a small-sized reactive plasma pump driven by capillary bubble discharge for the purification of treated water. The apparatus we developed decomposes the pollutants in the water by using chemical species generated by the plasma discharge. The resulting stream of bubbles obviates the need for an external gas supply or pump to transport the water. A high-speed camera was used to investigate the bubble dynamics responsible for the pumping effect, which is achieved by selecting the shape of the capillary such that the bubble ejections within enhance the ‘self-repetition’ action required for the pumping motion. Our experiments showed that optimal bubble generation requires a consumed power of 17.8 W. A theoretical model was developed to investigate the pumping mechanism. We solve the problems associated with liquid oscillations in the U-shaped water reservoir by employing a non-uniform cross-sectional area in our model. The chemical reactivity of the device was confirmed by using emission spectroscopy of OH radical and by measuring the decomposition of methylene blue.

Collision-free path planning of a novel reconfigurable mobile parallel mechanism

This paper initially deals with the design of a new customized reconfigurable mobile parallel mechanism. This mechanism is called the ‘Taar Reconfigurable ParaMobile’ (TRPM), consisting of three mobile robots as the main actuators. Then, the kinematics and path planning for this mechanism are presented. The newly proposed mechanism is expected to circumvent some shortcomings of inspection operation in unknown environments with unexpected changes in their workspace, for example, in a water pipe with a non-uniform cross-sectional area. In this paper, ‘Artificial Potential Field’ (APF) has been assumed to be the path planning algorithm and its resulting attractive and repulsive forces are only applied to the end-effector to generate the desired path. It is worth mentioning that the obstacle considered in this paper is a wedge which models an environment with non-uniform cross-sectional area along the path travelled by the end-effector. The inverse kinematics of the TRPM is then solved by resorting to the Resultant method as well as the Homotopy continuation method. The objective of utilizing these two well-known methods is to verify the correctness of the upper bound of solutions. It should be mentioned that solving the inverse kinematic problem obtained from both above-mentioned methods, leads to 12 solutions: eight real and four complex solutions. As a novel parallel mechanism, the TRPM yields a three-degrees-of-freedom kinematic redundancy. Despite the fact that the redundancy is sometimes beneficial for the control procedure, solving the inverse kinematics of the TRPM would be feasible only by adding some constraints. As a result, there will be a system of equations consisting of three kinematic equations and three auxiliary equations. Results from this study reveal that, by applying APF as the path planning algorithm to the TRPM, it is possible to track proper paths to reach the target.

Finite Volume Solution of a 1-D Hyperbolic Conduction Equation

A one-dimensional hyperbolic conduction equation written in primitive variables is solved by a numerical method based on a finite volume formulation. Accuracy of the proposed formulation is verified by exact solutions for homogeneous medium and then applied to composite materials with different conductivity, specific heat, and heat flux lagging constant. Results show quite distinct wave penetration through and reflection at interfaces of dissimilar materials even though the wave speed in the second medium remains identical in all cases. Effect of non-uniform cross-sectional area on wave propagation is also examined. The formulation is straightforward and can be easily extended to multidimensional problems for heterogeneous media with temperature-dependent properties since no special treatments are needed at the interfaces.

THE IMPORTANCE OF GEOMETRIC EFFECTS IN CORONAL LOOP MODELS

We systematically investigate the effects of geometrical assumptions in one-dimensional (1D) models of coronal loops. Many investigations of coronal loops have been based on restrictive assumptions, including symmetry in the loop shape and heating profile, and a uniform cross-sectional area. Starting with a solution for a symmetric uniform-area loop with uniform heating, we gradually relax these restrictive assumptions to consider the effects of nonuniform area, nonuniform heating, a nonsymmetric loop shape, and nonsymmetric heating, to show that the character of the solutions can change in important ways. We find that loops with nonuniform cross-sectional area are more likely to experience thermal nonequilibrium, and that they produce significantly enhanced coronal emission, compared with their uniform-area counterparts. We identify a process of incomplete condensation in loops experiencing thermal nonequilibrium during which the coronal parts of loops never fully cool to chromospheric temperatures. These solutions are characterized by persistent siphon flows. Their properties agree with observations (Lionello et al.) and may not suffer from the drawbacks that led Klimchuk et al. to conclude that thermal nonequilibrium is not consistent with observations. We show that our 1D results are qualitatively similar to those seen in a three-dimensional model of an active region. Our results suggest that thermal nonequilibrium may play an important role in the behavior of coronal loops, and that its dismissal by Klimchuk et al., whose model suffered from some of the restrictive assumptions we described, may have been premature.

Robust and high‐resolution simulations of nonlinear electrokinetic processes in variable cross‐section channels

We present a model and an associated numerical scheme to simulate complex electrokinetic processes in channels with nonuniform cross-sectional area. We develop a quasi-1D model based on local cross-sectional area averaging of the equations describing unsteady, multispecies, electromigration-diffusion transport. Our approach uses techniques of lubrication theory to approximate electrokinetic flows in channels with arbitrary variations in cross-section; and we include chemical equilibrium calculations for weak electrolytes, Taylor-Aris type dispersion due of nonuniform bulk flow, and the effects of ionic strength on species mobility and on acid-base equilibrium constants. To solve the quasi-1D governing equations, we provide a dissipative finite volume scheme that adds numerical dissipation at selective locations to ensure both unconditional stability and high accuracy. We couple the numerical scheme with a novel adaptive grid refinement algorithm that further improves the accuracy of simulations by minimizing numerical dissipation. We benchmark our numerical scheme with existing numerical schemes by simulating nonlinear electrokinetic problems, including ITP and electromigration dispersion in CZE. Simulation results show that our approach yields fast, stable, and high-resolution solutions using an order of magnitude less grid points compared to the existing dissipative schemes. To highlight our model's capabilities, we demonstrate simulations that predict increase in detection sensitivity of ITP in converging cross-sectional area channels. We also show that our simulations of ITP in variable cross-sectional area channels have very good quantitative agreement with published experimental data.

On the crushing response of random open-cell foams

This study examines the effect of randomness of the cellular microstructure on the calculated compressive response of a class of open-cell aluminum alloy foams. The foams are modeled using realistic random soap froth with N3 cells generated using the Surface Evolver software. The ligaments are made straight but with non-uniform cross sectional area distributions that mimic those of the physical foams. The models are also assigned the density and anisotropy measured. The ligaments are modeled as shear deformable beams with the elasto-plastic material behavior of the Al-alloy. The microstructure is discretized with finite elements using LS-DYNA, which allows for beam-to-beam contact on the outer surface of the ligaments. 103 cell domains compressed between rigid planes are shown to reproduce the measured compressive responses in both the rise and transverse directions. This includes the complete response from the initial elastic regime, through “yielding,” the extended stress plateau, to densification. More importantly, localized bands of crushed cells that develop and gradually spread throughout the domain resemble closely experimental observations made using X-ray tomography. This is a major improvement over previous models that idealized monodispersed foams as periodic Kelvin cells, and should allow modeling of polydisperse foams. The contact algorithm, friction between ligaments, and generally the discretization play crucial roles in the accuracy of the calculation as well as their numerical stability.

Study of the effects of flow channel with non-uniform cross-sectional area on PEMFC species and heat transfer

In this study it is investigated the performance of a proton exchange membrane fuel cell. The results show that an inclination of 0.75° in the flow channel can effectively increase the current density generated by almost 9.5% and the maximum power density by 8%. With the use of more tapered channels the distribution of the reactants in the porous media leads to a better effective oxygen distribution, affecting directly the heat transfer inside the cell. In contrast, the pressure drop in the flow channel increase by factors of approximately 2 and 3.5 for angles of 0.5° and 0.75°, respectively.

On the compressive strength of open-cell metal foams with Kelvin and random cell structures

Two families of finite element models of anisotropic, aluminum alloy, open-cell foams are developed and their predictions of elastic properties and compressive strength are evaluated by direct comparison to experimental results. In the first family of models, the foams are idealized as anisotropic Kelvin cells loaded in the <100> direction and in the second family more realistic models, based on Surface Evolver simulations of random soap froth with N3 cells are constructed. In both cases the ligaments are straight but have nonuniform cross sectional area distributions that resemble those of the foams tested. The ligaments are modeled as shear deformable beams with elasto-plastic material behavior. The calculated compressive response starts with a linearly elastic regime. At higher stress levels, inelastic action causes a gradual reduction of the stiffness that eventually leads to a stress maximum, which represents the strength of the material. The periodicity of the Kelvin cell enables calculation of the compressive response up to the limit stress with just a single fully periodic characteristic cell. Beyond the limit stress, deformation localizes along the principal diagonals of the microstructure. Consequently beyond the limit stress the response is evaluated using finite size 3-D domains that allow the localization to develop. The random models consist of 3-D domains of 216, 512 or 1000 cells with periodicity conditions on the compressed ends but free on the sides. The compressive response is also characterized by a limit load instability but now the localization is disorganized resembling that observed in experiments. The foam elastic moduli and strengths obtained from both families of models are generally in very good agreement with the corresponding measurements. The random foam models yield 5–10% stiffer elastic moduli and slightly higher strengths than the Kelvin cell models. Necessary requirements for this high performance of the models are accurate representation of the material distribution in the ligaments and correct modeling of the nonlinear stress–strain response of the aluminum base material.

Equations describing molecular-motor-assisted transport in dendrites with a non-uniform cross-sectional area

The purpose of this paper is to develop new transport equations describing transport of intracellular organelles by a combined effect of diffusion and molecular-motor-driven transport in dendrites of neuron cells that have a non-uniform cross-sectional area which depends on the distance from the neuron soma. The obtained equations are solved numerically for two types of microtubule (MT) orientations that are experimentally found in dendrites. In one type of dendrites, which is found in cultured rat hippocampal neurons, MTs have a mixed polarity orientation while in the second type, which is found in Drosophila neurons, MTs have the minus-end-out polarity orientation. Simulations show important differences in organelle transport in these two types of dendrites. The conclusion is that the MT orientation has a profound effect on the total rate of organelle transfer toward the growth cone of a dendrite and consequently determines its growth potential and its growth rate.

Modeling organelle transport in branching dendrites with a variable cross-sectional area

The purpose of this paper is to develop a method for calculating organelle transport in dendrites with a non-uniform cross-sectional area that depends on the distance from the neuron soma. The model is based on modified Smith-Simmons equations governing molecular motor-assisted organelle transport. The developed method is then applied to simulating organelle transport in branching dendrites with two particular microtubule (MT) orientations reported from experiments. It is found that the rate of organelle transport toward a dendrite's growth cone heavily depends on the MT orientation, and since there is experimental evidence that the MT orientation in a particular region of a dendrite may depend on the dendrite's developmental stage, the obtained results suggest that a rearrangement of the MT structure may depend on the amount of organelles needed at the growth cone.

On the microstructure of open-cell foams and its effect on elastic properties

Synthetic open-cell foams have a complex microstructure consisting of an interconnected network of cells resulting from the foaming process. The cells are irregular polyhedra with anywhere from 9 to 17 faces in nearly monodisperse foams. The material is concentrated in the nearly straight ligaments and in the nodes where they intersect. The mechanical properties of such foams are governed by their microstructure and by the properties of the base material. In this study micro-computed X-ray tomography is used to develop 3D images of the morphology of polyester urethane and Duocel aluminum foams with different average cell sizes. The images are used to establish statistically the cell size and ligament length distributions, material distributions along the ligaments, the geometry of the nodes and cell anisotropy. The measurements are then used to build finite element foam models of increasing complexity that are used to estimate the elastic moduli. In the most idealized model the microstructure is represented as a regular Kelvin cell. The most realistic models are based on Surface Evolver simulations of random soap froth with N 3 cells in spatially periodic domains. In all models the cells are elongated in one direction, the ligaments are straight but have a nonuniform cross sectional area distribution and are modeled as shear deformable beams. With this input both the Kelvin cell models and the larger random foam models are shown to predict the elastic moduli with good accuracy but the random foams are 5–10% stiffer.

On the stability of Kelvin cell foams under compressive loads

It has been previously shown that the nonlinearity exhibited in the compressive response of open cell foams is governed by cell ligament buckling. Significant insight into this behavior can be gained by idealizing such foams as periodic, space-filling Kelvin cells assigned several of the geometric characteristics of actual foams. The cells are elongated in the rise direction; the ligaments are assumed to be straight, to have Plateau border cross sections, and nonuniform cross sectional area distribution. The mechanical response of such foams can be established using models of a characteristic cell assigned appropriate periodicity conditions. The ligaments are modeled as shear deformable beams. The periodicity of this microstructure allows the use of Bloch wave theory to conduct the search for the critical state efficiently. The method tailored to the present microstructure is outlined. It is subsequently used to establish the critical states for uniaxial and a set of triaxial loadings. A rich variety of buckling modes are identified which are affected by the anisotropy and the mutliaxiality of the applied loads. Under some loadings the critical modes have long wavelengths which are shown to lead to unstable postbuckling behavior involving localization. Under other loading conditions the modes are either local to the characteristic cell or involve an assemblage of a few such cells. For the cases analyzed local modes were found to have a stable postbuckling response.

Compressive response of open-cell foams. Part I: Morphology and elastic properties

This study is concerned with the understanding and modeling of the compressive response of open cell foams. The response starts with a nearly linear elastic regime which terminates into a limit load followed by an extensive load plateau. The plateau, which is responsible for the excellent energy absorption capacity of foams, is followed by a second stiff branch. Results from polyester urethane open cell foams with relative densities of about 0.025 are used to illustrate this behavior using experiments coupled with several levels of modeling. The experiments include characterization of the microstructure and the properties of the base material and measurement of the compressive response of the foams of various cell sizes. A sequence of models for predicting the complete response of such foam is developed. The foam is idealized to be periodic using the space-filling Kelvin cell assigned the major geometric characteristics found in the foams tested. The cells are elongated in the rise direction, the ligaments are assumed to be straight, to have Plateau border cross-sections and nonuniform cross-sectional area distribution. The ligaments are modeled as shear-deformable extensional beams and the base material is assumed to be linearly elastic. Prediction of the initial elastic moduli are addressed in Part I. Closed form expressions for the material constants are presented as well as results using a FE model of the characteristic cell. Comparison between measurements and predictions is very favorable. The paper finishes with results from a limited parametric study of the elastic moduli. The results demonstrate that inclusion of the geometric complexities mentioned above is essential for successful prediction of the moduli of such foams. The nonlinear parts of the response including the foam crushing behavior are addressed in Part II.

Spin relaxation caused by thermal excitations of high-frequency modes of cantilever vibrations

We consider the process of spin relaxation in the oscillating cantilever-driven adiabatic reversals technique in magnetic-resonance force microscopy. We simulated the spin relaxation caused by thermal excitations of the high-frequency cantilever modes in the region of the Rabi frequency of the spin subsystem. The minimum relaxation time obtained in our simulations is greater than but of the same order of magnitude as one measured in recent experiments. We demonstrated that using a cantilever with nonuniform cross-sectional area may significantly increase spin-relaxation time.