Uniform Rectangular Cross-section Research Articles

Inertial particle focusing in fluid flow through spiral ducts: dynamics, tipping phenomena and particle separation

Small finite-size particles suspended in fluid flow through an enclosed curved duct can focus to points or periodic orbits in the two-dimensional duct cross-section. This particle focusing is due to a balance between inertial lift forces arising from axial flow and drag forces arising from cross-sectional vortices. The inertial particle focusing phenomenon has been exploited in various industrial and medical applications to passively separate particles by size using purely hydrodynamic effects. A fixed size particle in a circular duct with a uniform rectangular cross-section can have a variety of particle attractors, such as stable nodes/spirals or limit cycles, depending on the radius of curvature of the duct. Bifurcations occur at different radii of curvature, such as pitchfork, saddle-node and saddle-node infinite period (SNIPER), which result in variations in the location, number and nature of these particle attractors. By using a quasi-steady approximation, we extend the theoretical model of Harding et al. (J. Fluid Mech., vol. 875, 2019, pp. 1–43) developed for the particle dynamics in circular ducts to spiral duct geometries with slowly varying curvature, and numerically explore the particle dynamics within. Bifurcations of particle attractors with respect to radius of curvature can be traversed within spiral ducts and give rise to a rich nonlinear particle dynamics and various types of tipping phenomena, such as bifurcation-induced tipping (B-tipping), rate-induced tipping (R-tipping) and a combination of both, which we explore in detail. We discuss implications of these unsteady dynamical behaviours for particle separation and propose novel mechanisms to separate particles by size in a non-equilibrium manner.

Numerical study of turbulent flow and heat transfer in a novel design of serpentine channel coupled with D-shaped jaggedness using hybrid nanofluid

This study aimed to examine numerically the effects of a dimpled surface over a mini-channel heat exchangeron the flow characteristics and heat transfer across a serpentine channel with a uniformrectangular cross-section. The dimples were arranged in parallel with a spanwise (y/d) distance of 3.125 and streamwise (x/d) distance of 11.25 along just one side of the serpentine channel's surface.Turbulent flow regime with Reynolds number ranging from 5 × 103 to 20 × 103 in the channel with the surface modificationwas studied using water and various volume concentrations(φ = 0.1%, 0.33%, 0.75%, 1%) ofAl2O3-Cu/waterhybrid nanofluid as the coolant to achieve a three-step passive heat transfer enhancement. Applying the Finite Volume Method (FVM), RNG k-e turbulence model, and a constant heat flux of 50 kW/m2, simulations were run assuming the mixture of Al2O3-Cunanoparticles homogenous using ANSYS 2020 R1. The second-order upwind approach is used forapproximation of solution and discretizationwith SIMPLE pressure–velocity coupling. Taking heat transfer increment and pressure drop penalty into consideration,the dimpled serpentine channel provides a 1.47-times improvement in thermal efficiency using water as the coolant, andthe dimpled channel with 1% vol.Al2O3-Cu/water nanofluid enhanced thermal efficiency by a remarkable maximumof 2.67-times at Re 5 × 103. The study also indicates that thermal efficiency increased with an increasing volume concentration of the nanofluid and increment in thermal efficiency gradually decreased as the Re increased.

On pure bending in non-linear elasticity: A circular closed-form 2D solution for semi-linear orthotropic material

Large-deformation pure bending of a straight beam of uniform rectangular cross-section in plane strain is re-visited and generalised to an orthotropic linear-elastic material and the case of plane stress. The beam is bent into a completely shearless state by means of normal surface traction of a specific profile. For a linear-elastic material expressed in terms of Biot strain and stress tensors (orthotropic generalisation of the so-called semi-linear material) the solution still exists in closed form and is expressed in terms of the applied cross-sectional traction. As such, it provides a convenient benchmark reference for numerical methods in non-linear elasticity.In agreement with the isotropic case, through-the-thickness stresses develop in the form a hyperbolic cosine, but now with the magnitude actually depending on a measure of orthotropy in the material, while the longitudinal stresses change over the thickness in the form of a hyperbolic sine. In general, the unstrained axis is displaced from the centroidal axis.For an ideal material with infinite yield strength, the theoretical maximum of the magnitude of the longitudinal traction is limited to the amount of the geometric mean of the effective Young's moduli in the longitudinal and the through-the-thickness directions while, for a brittle material, bending strength reduces by approximately 715 of the square of the ratio between the magnitude of the applied traction and this mean value.

Consideration on lateral vibration of automobiles in quasi-planar model with wheel separation and road deformation taken into account

This article considers lateral vibration of an automobile in a so-called quasi-planar model where both the loss of contact and road deformation are taken into account. The automobile with dependent suspension is modeled as a vibration system which has two masses and four degrees of freedom. The deformed road is modeled as an elastic beam which has uniform rectangular cross-section, is simply supported at the two ends and lies on the Kelvin's visco-elastic ground. The loss of contact and the change in dimensions of contact areas are considered. The differential equations of motion of the vehicle-road coupled system which contains a partial differential equation are transformed into a set of all ordinary differential equations by applying the Bubnov-Galerkin’s method. A procedure for numerically solving the transformed differential equations of motion is proposed. Some illustrating results coming from numerical consideration are also presented in the paper.

Modeling Large Spatial Deflections of Slender Beams of Rectangular Cross Sections in Compliant Mechanisms

Abstract Modeling large spatial deflections of flexible beams has been one of the most challenging problems in the research of compliant mechanism. This study presents an approach called chained power series model for modeling large spatial defections of flexible beams with uniform rectangular cross section. This approach is based on the power series model developed in our previous work for modeling spatial deflections of rectangular beams in the intermediate deflection range. The chained power series model splits a rectangular beam into several elements and models each element by the power series model, and then, the deflections of all elements are assembled to form the deflection of the beam through transformations using quaternions. The effectiveness of the approach is demonstrated by comparing with the nonlinear finite element model preformed in ansys and the chained 3D pseudo-rigid-body model. Several examples are demonstrated to show the capability of the chained power series model for solving the deflections of rectangular beams in compliant mechanisms.

A Simulation-Based Method to Detect Mechanical Parameters of I-Beams and Hollow Cylinders

Abstract Impulse excitation technique is a simple, convenient, and standard nondestructive method to detect mechanical parameters (dynamic Young’s modulus and dynamic torsional modulus) that only utilizes the first-order flexural resonant frequency, first-order torsional resonant frequency, and dimensions of structures. However, the mechanical parameter detection formulas are well established only for standard uniform specimens with uniform rectangular and circular cross sections. This study suggests a simulation-based method to detect mechanical parameters. A response surface method (RSM) is introduced to design numerical simulation experiments to build up experimental formulas to detect mechanical parameters. Numerical simulations are performed by the finite element method (FEM) to obtain enough simulation data for RSM analysis. After calculations, the two relationships (experimental formulas) can finally be obtained, i.e., the relationship of the dynamic Young’s modulus and first-order flexural resonant frequency with respect to dimensions of structures and the relationship of the dynamic torsional modulus and first-order torsional resonant frequency associated with dimensions of structures. Numerical simulations and experimental investigations show that the simulation-based method can be used to detect mechanical parameters in I-beams and hollow cylinders. More generally, this method can be further developed to detect the mechanical parameters of more complex structures than standard uniform specimens using a combination of FEM simulation and RSM.

Simple Two Variable Refined Theory for Shear Deformable Isotropic Rectangular Beams

In this paper, a displacement-based, variationally consistent, two variable refined theory for shear deformable beams is presented. The beam is assumed to be of linearly elastic, homogeneous, isotropic material and has a uniform rectangular cross-section. In this theory, the beam axial displacement and beam transverse displacement consist of bending components and shearing components. The assumed displacement field of this theory is such that, bending components do not take part in the cross-sectional shearing force, and shearing components do not take part in the cross-sectional bending moment. This theory utilizes linear strain-displacement relations. The displacement functions give rise to the beam transverse shear strain (and hence to the beam transverse shear stress) which varies quadratically through the beam thickness and maintains transverse shear stress-free beam surface conditions. Hence the shear correction factor is not required. Hamilton’s principle is utilized to derive governing differential equations and variationally consistent boundary conditions. This theory involves only two governing differential equations of fourth-order. These governing equations are only inertially coupled for the case of dynamics and are decoupled for the case of statics. This theory is simple and has a strong resemblance with the Bernoulli-Euler beam theory. To demonstrate the efficacy of the present theory, illustrative examples pertain to the static bending and free vibrations of shear deformable isotropic rectangular beams are presented.

Thermally driven pumps and diodes in multistage assemblies consisting of microchannels with converging, diverging and uniform rectangular cross sections

Thermal transpiration pumping in multistage assemblies is computationally investigated. Each stage is formed by combining in series-long microchannels with (a) uniform–uniform (“uni–uni”), (b) converging–uniform (“con–uni”), (c) diverging–uniform (“div–uni”) and (d) converging–diverging (“con–div”) rectangular cross sections. In all four investigated assemblies the generated pressure difference with the associated mass flow rate is fully assessed, in terms of inlet pressure, inclination parameter and number of stages. The analysis is based on linear kinetic modeling and is valid in the whole range of gas rarefaction. It is concluded that the “con–uni” and “div–uni” assemblies provide higher pressure differences and lower mass flow rates than the “uni–uni” assembly and they may be more suitable for specific pumping applications. The characteristics of the “con–uni” and “div–uni” assemblies are very close to each other. The multistage “uni–uni”, “con–uni” and “div–uni” assemblies are more stable when operating at small inlet pressures, where the pressure difference remains almost constant in wide ranges of mass flow rate. It is advisable to add as many stages as possible to increase, depending on the application, either the pressure difference or mass flow rate or both. Furthermore, the “con–div” assembly provides smaller pressure differences and mass flow rates than the other three, but it is suitable for diode applications. It is characterized by the so-called blocking inlet pressure, where the deduced pressure difference in the converging and diverging channels is the same. A detailed parametrization of the blocking inlet pressure in terms of inclination ratio, mean height, temperature difference and gas species, has been performed. It is concluded that multistage “con–div” assemblies may be ideally applied as thermally driven microfluidic diodes to control or block the flow, as well as to separate the species in multicomponent gas mixtures.

Exact analytical solution to the 3D Navier-Lame equation for a curved beam of constant curvature subject to arbitrary dynamic loading

This paper presents an exact analytical solution to the 3D transient dynamics of a linear elastic, isotropic homogeneous, curved beam, with uniform rectangular cross-section. The solution technique uses vector identities to decouple the governing equations. The decoupled equations are then solved by method of separation of variables. The solutions to the decoupled equations can be recombined to form a new equation. Solving this new equation yields the displacement field. To demonstrate the capabilities of the proposed solution technique, a generic case study was modeled and computed. A curved beam is subjected to a longitudinal impulse loading and the transient displacement field is calculated. This solution technique is valid for any curvature so long as the curvature is the same throughout the beam. This includes the limiting case where the inner radius of the beam goes to zero and the curved beam becomes a section of a disk. The presented solution results were compared with an approximate solution from the literature and experimental data from the literature. The solution is also compared with an explicit FEM solution conducted by the Authors. The presented solution agrees with the results from the literature and from the FEM solutions conducted by the Authors. This paper demonstrates that the accuracy and robustness of the proposed solution technique meets the needs of many potential applications.

A modeling method for vibration analysis of cracked laminated composite beam of uniform rectangular cross-section with arbitrary boundary condition

This paper establishes an analysis model to study the vibration behavior of a cracked laminated composite beam with uniform rectangular cross-section based on the Jacobi-Ritz method and the first-order shear deformation theory (FSDT). The boundary conditions of both ends of the cracked laminated beam are modeled as the elastic spring and the beam is divided into two parts by the crack section. The continuous conditions at the connecting face are modeled by the inverse of the flexibility coefficients of the fracture mechanics theory. Ignoring the influence of boundary conditions, displacements admissible functions of cracked laminated beam can be set up as Jacobi orthogonal polynomials. The accuracy and robustness of the present method are evidenced through comparison with previous literature and the results achieved by the finite element method (FEM). Numerical examples are given for free vibration analysis of cracked laminated composite beams with various boundary conditions, which may be provided as reference data for future study.

An improved study on Gardiner's work based on elastoplastic analysis considering deformation history

The springback phenomenon plays a significant role in precision sheet metal bending. In an early attempt, Gardiner proposed an analytical solution for springback under pure bending with perfect elastoplasticity. Several studies expanded on Gardiner's research to provide improved solutions of springback. However, the fore-mentioned studies did not account for mechanicalanalysis considering deformation history in their improved solutions. Thus, the present study divides the deformation history of metal material bend-forming intothreestages, namely a loading stage, a free unloading stage, and a non-free unloading stage. An elastoplastic analysis was performed by considering deformation history based on uniaxial stress state and plane section assumptions. The study also investigated the springback rule of bilinear kinematic hardening elastoplastic metal materials with uniform rectangular cross-section under pure bending. With respect to common metal materials, the study obtained an improved springback prediction solution in which the hardening component was considered, and its prediction results indicated a degree of agreement with the experimental data that exceeded those of the prediction results obtained by Gardiner's approximate solution when applied to the springback prediction of sheet metals.

Vortex-Induced Vibration of a Cable-Stayed Bridge

The dynamic response of a cable-stayed bridge that consists of a simply supported four-cable-stayed deck beam and two rigid towers, subjected to a distributed vortex shedding force on the deck beam with a uniform rectangular cross section, is studied in this work. The cable-stayed bridge is modeled as a continuous system, and the distributed vortex shedding force on the deck beam is modeled using Ehsan-Scanlan’s model. Orthogonality conditions of exact mode shapes of the linearized undamped cable-stayed bridge model are employed to convert coupled governing partial differential equations of the original cable-stayed bridge model with damping to a set of ordinary differential equations by using Galerkin method. The dynamic response of the cable-stayed bridge is calculated using Runge-Kutta-Felhberg method in MATLAB for two cases with and without geometric nonlinear terms. Convergence of the dynamic response from Galerkin method is investigated. Numerical results show that the geometric nonlinearities of stay cables have significant influence on vortex-induced vibration of the cable-stayed bridge. There are different limit cycles in the case of neglecting the geometric nonlinear terms, and there are only one limit cycle and chaotic responses in the case of considering the geometric nonlinear terms.

Design, fabrication, and testing of a DC MHD micropump fabricated on photosensitive glass

A theoretical and experimental investigation of the performance of a magnetohydrodynamic (MHD) micropump fabricated on photosensitive glass for circulating liquid metal is presented. A one-dimensional design and analysis tool has been developed and employed to design the pump, which has a uniform rectangular cross section of 5mm × 0.8mm and a length of 20mm; perpendicular magnetic fluxes and an axial electric current are generated in the pump. Experimental results are presented for the circulation of liquid Ga using NdFeB permanent magnets that produce 0.375T. The maximum pressure increase generated is 2.82kPa at 6A DC; the maximum efficiency is 0.46% at 2A DC, where the flow rate is 40ml/min.

Preparation and characterization of In2O3/ZnO heterostructured microbelts by sol–gel combined with electrospinning method

Long and thin In2O3/ZnO heterostructured microbelts were synthesized by sol–gel combined with electrospinning process. The as-prepared microbelts show the well defined one-dimensional belt structures with 1–5 μm in width and tens of millimeters in length. The polycrystalline microbelts calcined at 973 K for 1 h are still continuous and have the uniform rectangular cross sections and the thickness to width ratio is around 1:10. The crystalline phases of samples are investigated by X-ray diffraction and the morphology is examined using transmission electron microscope and scanning electron microscope. In2O3/ZnO heterostructured microbelts exhibit the excellent visible photocatalytic property in the photodegradation of methyl orange (MO), and over 94 % of MO was degraded within 3 h.

Features of phonon transport in silicon rods and thin plates in the boundary scattering regime. The effect of phonon focusing at low temperatures

The effect of phonon focusing on the phonon relaxation characteristics in the boundary scattering regime is studied in cubic crystals. The phonon relaxation times due to diffusive scattering at boundaries are calculated for rod-shaped samples and thin plates of finite lengths having uniform rectangular cross-sections. It is shown that relaxation times can be represented by piecewise smooth functions for different intervals of angles defined by the relation between components of the phonon group velocity and geometrical parameters of samples. Thermal conductivity and phonon free paths have been calculated for silicon samples with different orientation of the temperature gradient and side faces in the anisotropic continuum model. Anisotropies of thermal conductivity and phonon free paths for silicon change strongly with the width-to-thickness (aspect) ratio in the range from 1 to 1000, demonstrating steep dependence on the orientation of temperature gradient and the wide face of thin plates with high values of aspect ratio.

A correlation for natural convection heat transfer from inclined plate-finned heat sinks

Steady-state natural convection heat transfer from inclined plate-finned heat sinks to air is numerically investigated by using an experimentally validated model. The heat sinks with parallel arrangement of uniform rectangular cross section plate fins are inclined from the vertical in both forward and backward directions in order to investigate the effect of inclination on convection. Our previously validated numerical model for vertically oriented heat sinks is directly used without changing any model parameters, but only by varying the direction of the gravitational acceleration to create the effect of inclination. The flow and temperature fields are resolved using a finite volume computational fluid dynamics code. Performing a large number of simulations for the heat sink base inclination angles of ±4°, ±10°, ±20°, ±30°, ±45°, ±60°, −65°, −70°, ±75°, ±80°, ±85°, ±90° from the vertical, the dependence of the convective heat-transfer rate to the inclination angle and Rayleigh number is investigated. Scale analyses are performed in order to generalize estimates for the convection heat-transfer rates. A single correlation is suggested and shown to be valid for a very wide range of angles from −60° (upward) to +80° (downward) in a wide range of Rayleigh numbers from 0 to 2 × 108.

Post‐buckling of simply supported column made of nonlinear elastic materials obeying the generalized Ludwick constitutive law

AbstractIn this article, the post‐buckling behavior of a simply supported column made of nonlinear elastic materials subjected to an end axial force is investigated. The column has a uniform rectangular cross‐section in which the stress–strain relationship of such materials is represented by the generalized Ludwick constitutive law. To derive the governing equations, both geometrical and material nonlinearities have been considered. Further, a set of highly nonlinear simultaneous first‐order differential equations with boundary conditions is established and numerically solved by the shooting method. Several numerical results are carried out and discussed highlighting the significant influences of the material nonlinearity parameter n on the equilibrium configurations and the equilibrium paths. From the results, there are many interesting features associated with the nonlinear hardening column such as a non‐monotonic bifurcation curve, the limit load point, snap‐through phenomenon, and hysteresis loop. Furthermore, the numerical results are compared with previous studies in order to test the validity and accuracy of the present method.

Laminated thin-film Teflon chips for petrochemical applications

We present Teflon-based microfluidic chips fabricated by laminating multiple layers of laser-cut Teflon film. In addition to being solvent-resistant, these chips enable simple multilayer fabrication, have uniform rectangular cross-section and are sufficiently thin to (1) reduce cost, (2) enable rapid temperature control, and (3) provide optical transparency. The chips can be fabricated without a cleanroom from start to finish in less than 2 h. We demonstrate the potential of this approach by measuring the displacement of an oil solution by carbon dioxide in a nine-layer thin-film Teflon chip modelling porous media. Optical transparency through the 9-layers enables the determination of an oil recovery rate. We also demonstrate a thin-film chip measurement of the viscosity of heavy oil/toluene mixtures.

MAGNETIC FORCE CALCULATION BETWEEN CIRCULAR COILS OF RECTANGULAR CROSS SECTION WITH PARALLEL AXES FOR SUPERCONDUCTING MAGNET

The electromagnetic force between two misaligned coils (coils with parallel axes) with uniform current density distribution and rectangular cross section based on the derived semi-analytical expressions was presented. Using the semi-analytical expressions for magnetic force between fllamentary misalignment circular coils we calculate the propulsive and the transverse magnetic force. In order to verify the validity of the expressions, we use the fllament method with Grover's formula to calculate the magnetic force for two coils with parallel axes. The results obtained by two methods are in a very good agreement. In this paper, the derivation of the semi- analytical expressions and the calculation results of the magnetic force are introduced.

Calculation of Coherent Synchrotron Radiation Impedance for a Beam Moving in a Curved Trajectory

Coherent synchrotron radiation (CSR) fields are generated when a bunched beam moves along a curved trajectory. A new code, named CSRZ, was developed using finite difference method to calculate the longitudinal CSR impedance for a beam moving along a curved chamber. The method adopted in the code was originated by Agoh and Yokoya [Phys. Rev. ST Accel. Beams 7 (2004) 054403]. It solves the parabolic equation in the frequency domain in a curvilinear coordinate system. The chamber considered has uniform rectangular cross-section along the beam trajectory. The code was used to investigate the properties of CSR impedance of a single or a series of bending magnets. The calculation results indicate that the shielding effect due to outer chamber wall can be well explained by a simple optical approximation model at high frequencies. The CSR fields reflected by the outer wall may interfere with each other along a series of bending magnets and lead to sharp narrow peaks in the CSR impedance. In a small storage ring, such interference effect can be significant and may cause microwave instability, according to a simple estimate of instability threshold.