Non-circular Cross-section Research Articles

On the physics of viscoplastic fluid flow in non-circular tubes

Flow of Bingham plastics through straight, long tubes is studied by means of a versatile analytical method that allows extending the study to a large range of tube geometries. The equation of motion is solved for general non-circular cross-sections obtained via a continuous and one-to-one mapping called the shape factor method. In particular the velocity field and associated plug and stagnant zones in tubes with equilateral triangular and square cross-section are explored. Shear stress normal to equal velocity lines, energy dissipation distribution and rate of flow are determined. Shear-thinning and shear-thickening effects on the flow, which cannot be accounted for with the Bingham model, are investigated using the Hershey-Bulkley constitutive formulation an extension of the Bingham model. The existence and the extent of undeformed regions in the flow field in a tube with equilateral triangular cross-section are predicted in the presence of shear-thinning and shear-thickening as a specific example. The mathematical flexibility of the analytical method allows the formulation of general results related to viscoplastic fluid flow with implications related to the design and optimization of physical systems for viscoplastic material transport and processing.

Segmentation and Visualization of Human Coronary Artery Trees from CTA Datasets

The volume information extracted from computed tomography angiogram is very useful for cardiologists to diagnose various diseases. An approach is presented to segment human coronary artery trees from the volumetric datasets. The coronary arteries’ surfaces are recovered by triangle mesh with the boundary points extracted from the coronary artery voxels segmented. The positions where the calcified plaques occur are identified by mapping the intensities of boundary points of the coronary artery trees on the triangle meshed surfaces. If different values of the computed maximum principle curvatures of boundary points surrounding the lumen cross section are mapped on the triangle meshed surfaces of the segmented coronary artery trees, the cross section structure of the coronary artery lumen segment is noncircular cross section structure.

Experimental Characterization of Magnetorheological Fluids Using a Custom Searle Magnetorheometer: Influence of the Rotor Shape

In this paper, we investigated the behavior of magnetorheological fluids (MRFs) by means of a custom Searle magnetorheometer. The Searle measuring system is composed of an outer stationary cylinder and an inner cylinder driven by a motor. The MRF is placed between the two concentric cylinders. While the bob is rotating, the fluid transmits a torque to the outer cylinder, which is related to the velocity profile through the gap and the magnetic field applied. In particular, we wanted to assess the influence of different bob shapes on the shear stress–shear rate curves. Indeed, a non-circular cross section causes cyclic variations on the gap thickness and, consequently, can squeeze the active MRFs, causing the formation of thicker columns and higher values of shear stresses. This phenomenon known as a squeeze-strengthen effect can be exploited to achieve higher energy absorption on magnetorheological devices like brakes and clutches. Two different cross sections were taken into account and then compared with the cylindrical one: 1) elliptical and 2) quadrilobate. In both cases, the gap size varies from 0.25 to 0.75 mm. The experimental results showed that with the new bob shapes, the squeeze-strengthen effect does not occur. However, using the elliptical and quadrilobate bobs, changes in the slope of the flow curves have been measured. This may suggest that the post-yield viscosity can be influenced by more complex factors like non-uniform magnetic field or hydrodynamic phenomena. Further studies, such as 3-D magnetic simulation and CFD analysis, will be taken into account to explain the new phenomena brought up in this paper.

Magnetohydrodynamic theory of the global structure and magnetic components of the geodesic acoustic continuum modes in tokamaks

Ideal magnetohydrodynamic (MHD) theory is used to investigate some of the fundamental properties of the geodesic acoustic continuum modes (GAMs) in tokamaks, including their global structure, their associated magnetic components both inside and outside the plasma, and effects of a non-circular cross section of the plasma. In addition to the well-known side-bands in the perturbed density and pressure of the (electrostatic) GAM, the MHD continuum GAM also includes a side-band in the perturbed toroidal magnetic field as well as side-bands in the perturbed density, pressure, poloidal flow and in the magnetic components and ( is the poloidal mode number). These side-bands exist within the whole plasma and the magnetic components also outside the plasma, and the magnitudes of these components in the vacuum region are calculated in the paper. It is shown that, for plasmas with a conducting wall not too far from the plasma surface, the perturbed magnetic field in the vacuum region is dominated by its poloidal component , with poloidal dependence , in agreement with experiments. Aspects of the plasma equilibrium that affect the magnitude of the perturbed magnetic field in the vacuum region are discussed in the paper. Furthermore, the influence of a non-circular plasma cross section on the GAM frequency and on the spectrum of the global, perturbed magnetic field is analysed. It is found that the only significant effect of a non-circular cross section on the GAM frequency comes from elongation and its variation across the plasma radius. However, higher-order shaping effects, as well as finite aspect ratio, induce other Fourier components than in the magnetic halo that surrounds the GAM surface.

Forest Inventory with Terrestrial LiDAR: A Comparison of Static and Hand-Held Mobile Laser Scanning

The application of static terrestrial laser scanning (TLS) in forest inventories is becoming more effective. Nevertheless, the occlusion effect is still limiting the processing efficiency to extract forest attributes. The use of a mobile laser scanner (MLS) would reduce this occlusion. In this study, we assessed and compared a hand-held mobile laser scanner (HMLS) with two TLS approaches (single scan: SS, and multi scan: MS) for the estimation of several forest parameters in a wide range of forest types and structures. We found that SS is competitive to extract the ground surface of forest plots, while MS gives the best result to describe the upper part of the canopy. The whole cross-section at 1.3 m height is scanned for 91% of the trees (DBH > 10 cm) with the HMLS leading to the best results for DBH estimates (bias of −0.08 cm and RMSE of 1.11 cm), compared to no fully-scanned trees for SS and 42% fully-scanned trees for MS. Irregularities, such as bark roughness and non-circular cross-section may explain the negative bias encountered for all of the scanning approaches. The success of using MLS in forests will allow for 3D structure acquisition on a larger scale and in a time-efficient manner.

Analytical Solution of Laplace and Poisson Equations Using Conformal Mapping and Kronecker Products

In this paper, using the eigenvalues and eigenvectors of symmetric block diagonal matrices with infinite dimension and numerical method of finite difference, a closed-form solution for exact solution of Laplace equation is presented. The method of this paper has applications in different states of boundary conditions like Neumann, Dirichlet, and other mixed boundary conditions. Using the method of this paper, a mathematical model for the exact solution of the Poisson equation is derived. Since these equations have many applications in engineering problems, in each part of this paper, examples, like water seepage problem through the soil and torsion of prismatic bars, are presented. Finally, a method is provided for torsion problem of prismatic bars with non-circular and non-rectangular cross-sections utilizing conformal mapping.

Shape effect of nanochannels on water mobility

Confinement can induce unusual behaviors of water. Inspired by the fabrication of carbon nanotubes with noncircular cross sections, we performed molecular dynamics simulations to investigate the mobilities of water confined in carbon nanochannels with circular, square, and equilateral triangular cross sections over a variety of dimensions. We find that water exhibits disparate mobilities across different types of channels below 0.796 nm2. Notably, compared with the other two channels, water in equilateral triangular channels displays the greatest mobilities. Moreover, at 0.425 nm2, different ordered structures are found in the three channels, and water inside the square channel exhibits an extremely low mobility. It is also found that above 0.796 nm2, the mobilities along the tube axis of water converge to that of the bulk. These phenomena are understood by analyzing the structure, dynamics, and hydrogen bonding of water. Our work explores the mobilities of water across noncircular carbon nanochannels, which may expand the prospect of noncircular nanochannels in scientific studies and practical applications, such as desalination and drug delivery.

Application of MFS–MPS to the current-hole simulation in a Tokamak

A meshless method based on fundamental and particular solutions (MFS–MPS) has been implemented for the current-hole simulation in cylindrical tokamaks. We first benchmark the method by solving the Grad–Shafranov (GS) equation for zero as well as nonzero inverse aspect ratios and noncircular cross-sections. Thereafter, the method is implemented to solve the time-dependent reduced resistive MHD equations for the current-hole simulation. The initial current density profile with a negative current density near the center is chosen and the corresponding equilibrium magnetic flux profile is first computed using the GS equation. These profiles are then used to solve the coupled nonlinear system of MHD equations using MFS–MPS and a semi-implicit time differencing scheme. After an initial linear phase extending up to a few thousand Alfvén times, the nonlinear oscillations are observed which continue for several Alfvén times. This oscillating behavior is in agreement with the previous simulations using other numerical methods. It is also found that these oscillations are damped out at higher resistivity.

Dynamic analysis of helicoidal bars with non-circular cross-sections via mixed FEM

One of the objectives of this study is to implement the direct calculation of the torsional moment of inertia for non-circular cross-sections, which is based on the St. Venant torsion formulation and the finite element method. Recently the proposed method provides a unique calculation of the torsional rigidity of simply and multiply connected cross-sections. Next, free vibration analyses of cylindrical and non-cylindrical helices with non-circular cross-sections are solved by a curved two-nodded mixed finite element based on the Timoshenko beam theory. Some thin-thick closed or open sections are handled and the natural frequencies of cylindrical and non-cylindrical helices are compared with the literature and the commercial finite element program SAP2000.

Free Torsion of Viscoelastic Rod with Non-circular Cross-section

The problem of determining the stress-strain state of the rod with non-circular cross-section in torsion considering creep was solved. The solution is based on the hypothesis of Saint-Venant used in the theory of elastic torsion of rods. In contrast to the elastic problem, warping function in creep is not a harmonic function. The problem has reduced to the Poisson differential equation for the stress function. The solution is made numerically by using the finite difference method. An example of the calculation for the polymeric rod from recycled PVC is given. It was found that the shear stresses during creep virtually unchanged, and the relative twist angle increased by 14%.

The influence of secondary flow in a two-phase gas-solid system in straight channels with a non-circular cross-section

The paper considers two-phase gas-solid turbulent flow of pneumatic transport in straight horizontal channels with a non-circular cross-section. During turbulent flow, a specific flow phenomenon, known as secondary flow, occurs in these channels in the cross-sectional plane. The existence of strong temperature gradients in the cross-sectional plane of the channel or the cases of curved channels result in the appearance of the secondary flow of the first kind. However, in straight channels with a non-circular cross-section, in the developed turbulent flow mode, a secondary flow, known as Prandtl?s secondary flow of the second kind, is induced. The paper presents a numerical simulation of a developed two-phase turbulent flow by using the PHOENICS 3.3.1 software package. Reynolds stress model was used to model the turbulence. The paper provides the data on the changes in turbulent stresses in the channel cross-section as well as the velocities of solid particles transported along the channel.

Viscoelastic fluid flow in a prismatic channel of square cross-section with reference to the example of rubber mixtures

Flow in a prismatic channel of the melts of the SKI-3 and SKMS30-ARKM-15-based rubber mixtures widely used in the chemical industry is numerically investigated. The description of these media, which exhibit viscoelstic properties when being processed, requires a particular approach that would take their rheological behavior and various anomalies into account. Amidst many rheological equations governing flows of rheologically complex media the equation that would ensure not only the good reliability of the results but also the feasibility in its practical use should be selected. The special features of viscoelastic fluids clearly manifest themselves in the flow in a prismatic channel of a noncircular cross-section. Secondary flows characteristic of the viscoelastic flows in such channels force the fluid particles to move in spiral trajectories along the channel. In the numerical calculations the Phan-Thien–Tanner (PTT) rheological model is used; its parameters are obtained on the basis of experimental data. The calculations are performed using the COSMOL Multiphysics software complex. the method of solution was tested against the analytical solution of the PTT fluid flow in a round tube which was compared with the numerical solution.

Buckling failures in insect exoskeletons

Thin walled tubes are often used for load-bearing structures, in nature and in engineering, because they offer good resistance to bending and torsion at relatively low weight. However, when loaded in bending they are prone to failure by buckling. It is difficult to predict the loading conditions which cause buckling, especially for tubes whose cross sections are not simple shapes. Insights into buckling prevention might be gained by studying this phenomenon in the exoskeletons of insects and other arthropods. We investigated the leg segments (tibiae) of five different insects: the locust (Schistocerca gergaria), American cockroach (Periplaneta americana), death’s head cockroach (Blaberus discoidalis), stick insect (Parapachymorpha zomproi) and bumblebee (Bombus terrestris audax). These were tested to failure in cantilever bending and modelled using finite element analysis (FEA). The tibiae of the locust and the cockroaches were found to be approximately circular in shape. Their buckling loads were well predicted by linear elastic FEA, and also by one of the analytical solutions available in the literature for elastic buckling. The legs of the stick insect are also circular in cross section but have several prominent longitudinal ridges. We hypothesised that these ridges might protect the legs against buckling but we found that this was not the case: the loads necessary for elastic buckling were not reached in practice because yield occurred in the material, causing plastic buckling. The legs of bees have a non-circular cross section due to a pollen-carrying feature (the corbicula). We found that this did not significantly affect their resistance to buckling. Our results imply that buckling is the dominant failure mode in the tibia of insects; it likely to be a significant consideration for other arthropods and any organisms with stiff exoskeletons. The interactions displayed here between material properties and cross sectional geometry may provide insights for the biomimetic design of engineering structures using thin walled tubes.

Two-Phase Flow Pressure Drop in Corrugated Tubes Used in an Aero-engine Oil System

In modern aero-engines, the lubrication system holds a key role due to the demand for high reliability standards. An aero-engine bearing chamber contains components like bearings and gears. Oil is used for lubrication and for heat removal. In order to retain the oil in a bearing chamber, pressurized seals are used. These are pressurized using air from the compressor. In order to avoid overpressurization of the bearing chamber, air/oil passages are provided in the bearing chamber. At the top, a vent pipe discharges most of the sealing air and at the bottom, a scavenge pipe is used for discharging the oil by means of a pump (scavenge pump). The scavenge pipe is setup in most cases by tubes of circular or noncircular cross sections. When the scavenge pipe has to be routed in a way that sharp bends or elbows are unavoidable, flexible (corrugated) pipes can be used. Because of the corrugation, considerable flow resistance with high-pressure drop can result. This may cause overpressurization of the bearing compartment with oil loss into the turbomachinery with possibility of ignition, coking (carbon formation), or contamination of the aircraft’s air conditioning system. It is therefore important for the designer to be capable to predict the system’s pressure balance behavior. A real engine bearing chamber sealed by brush seals was used for generating different air/oil mixtures thus corresponding to different engine operating conditions. The mixtures were discharged through a scavenge pipe which was partly setup by corrugated tubes. Instead of a mechanical pump, an ejector was used for evacuating the bearing chamber. An extensive survey covering the existing technical literature on corrugated tube pressure drop was performed and is presented in this paper. The survey has covered both single-phase and multiphase flows. Existing methods were checked against the test results. The method which was most accurately predicting lean air test results from the rig was benchmarked and was used as the basis for extending into a two-phase flow pressure drop correlation by applying two-phase flow multiplier techniques similar to Lockhart and Martinelli. Comparisons of the new two-phase flow pressure drop correlation with an existing correlation by Shannak are presented for mixtures like air/oil, air/water, air/diesel, and air/kerosene. Finally, numerical analysis results using ansys cfx version 15 are presented.

Analytical expression for velocity profiles and flow resistance in channels with a general class of noncircular cross sections

This article discusses how to derive a closed-form analytical solution describing the profile of unidirectional flow through a class of noncircular tubes. The cross sections of the conduits are a slightly distorted version of regular shapes, like triangles or trapeziums or rectangles, that are commonly seen in microfluidic or heat pipe applications. Hence, the study leads to approximate but useful expression for velocity profiles as well as resistivity for the aforementioned channels. Moreover, the paper shows how to extend the fundamental idea to other arbitrary geometries, providing simple expressions for flow fields that can be used subsequently in various hydrodynamic calculations. The analysis also gives an estimate of error in such a mathematical treatment that is found to be adequately accurate. Thus, the findings will be especially relevant in a number of fields, including microfluidic separation, heat pipe design, and capillary transport optimization.

The influences of geometric shape of cross section on equilibrium configuration of DNA in elastic rod model

The equilibrium configuration equations of DNA chain with elastic rod model are derived in detail by the variation of the free energy functional, which depends on the curvature, torsion, twisting angle and its derivative with respect to the arc-length of central axis curve of rod. With the different shapes of rod, we obtain the equilibrium equations of DNA with circular and noncircular cross sections, which provide an approach to describe the physical behaviors of A-, B-, Z-DNA. The results show that the elastic rod model with circular cross section can accurately characterize the equilibrium configurations of A-, B-DNA, while the model with elliptical cross sections is more suitable for Z-DNA.

Neuron anatomy structure reconstruction based on a sliding filter.

BackgroundReconstruction of neuron anatomy structure is a challenging and important task in neuroscience. However, few algorithms can automatically reconstruct the full structure well without manual assistance, making it essential to develop new methods for this task.MethodsThis paper introduces a new pipeline for reconstructing neuron anatomy structure from 3-D microscopy image stacks. This pipeline is initialized with a set of seeds that were detected by our proposed Sliding Volume Filter (SVF), given a non-circular cross-section of a neuron cell. Then, an improved open curve snake model combined with a SVF external force is applied to trace the full skeleton of the neuron cell. A radius estimation method based on a 2D sliding band filter is developed to fit the real edge of the cross-section of the neuron cell. Finally, a surface reconstruction method based on non-parallel curve networks is used to generate the neuron cell surface to finish this pipeline.ResultsThe proposed pipeline has been evaluated using publicly available datasets. The results show that the proposed method achieves promising results in some datasets from the DIgital reconstruction of Axonal and DEndritic Morphology (DIADEM) challenge and new BigNeuron project.ConclusionThe new pipeline works well in neuron tracing and reconstruction. It can achieve higher efficiency, stability and robustness in neuron skeleton tracing. Furthermore, the proposed radius estimation method and applied surface reconstruction method can obtain more accurate neuron anatomy structures.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0780-0) contains supplementary material, which is available to authorized users.

A one-dimensional modeling approach for dual-layer monolithic catalysts

This paper presents a model extension to dual-layer monolithic catalysts from a one-dimensional (1D) (Balakotaiah, 2008; Joshi et al., 2009) mathematical model used for single-layer monolithic catalysts. The novel transient non-isothermal model computes average concentrations inside the bulk flow and in each layer of washcoat at every computational grid point along the monolith channel. The model has the capability that physical (e.g. diffusivity, pore radius, and thickness) and chemical (reaction kinetics) properties of the two layers of the washcoat can be different from each other. The relatively low computational cost offers real-time simulations of multi-layer monolithic catalysts. Analytically derived expressions for transverse mass transfer coefficients between the bulk flow and washcoat layers are presented for single-layer and dual-layer catalysts with circular cross-section, which can be easily extended for multi-layer catalysts. In addition, three expressions are presented for calculation of three internal Sherwood numbers, which are used in the dual-layer model, based on the values of Thiele moduli of the washcoat layers. These expressions are especially useful for calculation of the mass transfer coefficients for dual-layer catalysts with non-circular cross-sections. Application limitations of the 1D multi-layer model with respect to physical and chemical operating conditions are discussed. The derived model is applied for an automotive aftertreatment catalyst and the results of this model are compared with the results of a detailed 2D model (selective catalytic reduction/platinum group metals dual-layer catalysts).

Study on equivalent confinement coefficient of composite CFST column based on unified theory

ABSTRACTThis article introduces the Unified Theory of Concrete Filled Steel Tube (CFST) into counting strength of composite CFST columns subjected to axial compression. There were four types of composite CFST columns listed, and one equivalent confinement coefficient was proposed with consideration of different sections of confining materials, so the whole cross section can be taken as one new composite material to research axial compressive behaviors of the composite CFST column. One unified design formula was derived from the Unified Theory, which was suitable for solid or hollow, circular or non-circular various cross sections of the composite CFST columns. The ultimate compressive bearing capacity was calculated in comparison with corresponding test results. The results show that the equivalent confinement coefficient can be used to calculate the compressive strength of the composite CFST column, and it has a linear relation with the enhanced coefficient of composite strength. Thus, the equivalent confinement coefficient was one important parameter to analyze the mechanical behavior and it can clearly reflect the confinement between concrete and confining material. This method is one more convenient and simpler approach for design work of composite CFST structures.

Input impedance of sheng pipes augmented with resonators

The sheng is a free reed mouth organ constructed of bamboo pipes with a free reed in each pipe near one end. A version commonly available today has 17 pipes in a circular arrangement with the reeds enclosed in a wind chamber. The pipes are nearly cylindrical over a significant portion of their length, but the bore near the reed end becomes approximately conical. A traditional instrument of China, the sheng, has a long recorded history, but a number of enlarged and modernized versions were created in the twentieth century, some featuring keys and additional pipes. The sheng in the current study is a standard 17-pipe configuration, with cylindrical metal pipe resonators attached to most of the pipes. These resonators amplify the radiated sound and also alter the tone quality. Calculations of input impedance have been made for the pipes, with and without the resonators attached, taking into account the position of the reed along the pipe, tuning slots, finger holes, and non-circular pipe cross sections. These calculations are compared with the measured pipe impedances as well as the measured sounding frequencies and sound spectra. [Research supported by NSF REU grant PHY-1004860.]