Straight Circular Cylinder Research Articles

Physical origin of vortex stretching and twisting: Viscous or inertial forces

In this paper, the physical origin of vortex stretching and twisting is theoretically investigated. The effects of inertial and viscous forces are mainly considered and discussed. Two key conditions, i.e., solid walls and three-dimensional (3D) disturbances, are adopted in three typical cases. Among them, the first two cases are straight and curved vortex lines at the initial time without any kind of disturbance. The third case is a straight vortex line at the initial time with introduced 3D natural disturbances. Through experimental observations, numerical simulations, and theoretical analysis in these cases, the first two cases illustrate that the straight or curved vortex lines are still straight or curved at the next time, respectively, regardless of whether solid walls are introduced. However, the third case clearly shows that once natural disturbances are introduced, the straight vortex lines near and at solid walls at the initial time are stretched and twisted mainly by viscous forces, instead of inertial forces, typically demonstrated by the 3D wake transition of a straight circular cylinder and the transition of the laminar boundary layer at a flat plate. Accordingly, based on definitions of generation and enhancement in vortex stretching and twisting, it is confirmed that the viscous forces with two key conditions are the generation mechanism, while the inertial forces alone are the enhancement mechanism.

Modeling and simulation of creep response of sorghum stems: Towards an understanding of stem geometrical and material variations

Sorghum [ Sorghum bicolor (L.) ] is a tropical grass that often suffers from structural failure (lodging) when subjected to wind, rain, and hail. During lodging, excessive lateral deflection occurs, which inherently correlates with the biomechanical properties of the stem. As such, a fundamental understanding of sorghum's biomechanical behavior is required to mitigate its propensity for lodging. Herein, we perform creep tests to characterize the mechanical behavior of Della genotype sorghum stems and their constituents, i.e., their rind and pith. This study also examines the influence of various testing geometries and boundary conditions on mechanical property characterization. We determine that small geometric irregularities typical of sorghum stems (e.g., from straight circular cylinders) do not affect their mechanical response in an overall engineering strain sense. However, these typical geometric irregularities do lead to nonuniform (localized) stresses and strains, thereby influencing the quantification of certain properties during mechanical testing. We also implement a viscoelastic constitutive model to describe the creep responses of the individual constituents (rind and pith), as to predict the overall biomechanical response of the stems. We find that even though the rind carries most of the load in the stem and itself does not show a significant time-dependent response, an overall time-dependent response of the stem still occurs, arising from viscoelastic effects in the pith.

Pulsatile Flow of Copper Suspended Nanofluid Venture Through a Bifurcated Artery

With an aim to investigate the pulsatile flow of blood through a bifurcated artery with mild stenosis in the parent lumen in the manifestation of heat transmission. The blood is treated to be copper suspended nanofluid. The arteries forming bifurcation are assumed to be symmetric about the axis of the parent artery and straight circular cylinders of limited length. The highly nonlinear momentum and energy equations of nanofluid model are simplified by considering the mild stenosis case and a radial coordinate transformation is initiated to map irregular geometry into a rectangular grid. The solution for flow rate, impedance, shear stress are found by using the finite difference scheme in a cylindrical coordinate system. An extensive quantitative analysis has been performed based on numerical computations in order to estimate the effects of pertinent parameters on various physical quantities near the apex by means of their graphical representations so as to validate the applicability of the proposed mathematical model.

Peristaltic flow of a magnetohydrodynamic nanofluid through a bifurcated channel

A mathematical model with peristalsis for blood flow through a bifurcated artery is presented by taking blood as a nanofluid with magnetic field effects. The arteries pattern of bifurcation is treated to be symmetric about the axis of the parent artery and straight circular cylinders of limited length. The equations governing the flow are made non-dimensional, and coordinate transformation is employed to convert the irregular boundary to a regular boundary. The resulting system of equations is solved by Cauchy Euler’s method. The influence of model parameters on blood velocity, pressure difference, pressure gradient, and trapping is investigated, and results are represented graphically.

Mathematical Modeling of Change in Plasma’s Specific Electrical Conductivity and Noncylindrical Channel Resistance during the Process of Electrical Discharge in Water

This work formulated and solved the problem of determining the specific electrical conductivity of plasma in the channel of the electrical discharge in water as well as that of the discharge channel resistance taking into account the deviation in its shape from that of a straight circular cylinder. The closing ratios and empirical functions whose parameters agree with the experimental data are obtained. The use of the empirical functions necessary for the calculation of the specific electrical conductivity of plasma is justified in connection with its high nonideality and relatively low degree of ionization. The obtained relations allowed for substantially increasing the adequacy of the mathematical model developed earlier for the physical processes of the discharge in water and expanding the range of parameters in which it can be applied.

The analytic solutions for the unsteady rotating flows of the generalized Maxwell fluid between coaxial cylinders

In this paper, we consider the unsteady rotating flow of the generalized Maxwell fluid with fractional derivative model between two infinite straight circular cylinders, where the flow is due to an infinite straight circular cylinder rotating and oscillating pressure gradient. The velocity field is determined by means of the combine of the Laplace and finite Hankel transforms. The analytic solutions of the velocity and the shear stress are presented by series form in terms of the generalized G and R functions. The similar solutions can be also obtained for ordinary Maxwell and Newtonian fluids as limiting cases.

Vibrations of Elastic Shells of Revolution Partially Filled with Ideal Liquid

We propose an algorithm for the numerical analyses of vibrations of elastic shells of revolution partially filled with ideal incompressible liquids. In the solution of this problem, the wave motions of liquid on its free surface are taken into account. The solution of the problem of hydroelasticity is based on the application of the method of decomposition of the domain of integration of equations of the theory of shells with the use of the variational statement of the problem and on the approximate construction of the operator inverse to the operator of the hydrodynamic part of the problem. We construct a generalized functional of displacements of the shell for which the role of conditions of matching for the solutions in different subdomains is played by the natural boundary conditions. The obtained numerical results are compared with the existing exact solutions of the analyzed problem for a shell in the form of a straight circular cylinder.

On some rotational flows of non-integer order rate type fluids with shear stress on the boundary

Abstract This article presents rotational flows of some rate type fluids with non-integer order derivatives. The fluid fills an infinite straight circular cylinder and its motion is generated by a time dependent torsion, applied to the surface of the cylinder. As novelty, the dimensionless governing equation related to the non-trivial shear tension is used and the first exact solutions analogous to a ramped shear stress on the surface are obtained using integral transforms. The results that have been obtained allow us to provide solutions for ordinary Oldroyd-B, non-integer order Maxwell and ordinary Maxwell fluids performing similar motions. In addition, the control of non-integer order framework on shear stress and velocity profiles is analyzed by numerical simulations and graphical interpretations.

Unsteady Helical Flows of a Size-Dependent Couple-Stress Fluid

The helical flows of couple-stress fluids in a straight circular cylinder are studied in the framework of the newly developed, fully determinate linear couple-stress theory. The fluid flow is generated by the helical motion of the cylinder with time-dependent velocity. Also, the couple-stress vector is given on the cylindrical surface and the nonslip condition is considered. Using the integral transform method, analytical solutions to the axial velocity, azimuthal velocity, nonsymmetric force-stress tensor, and couple-stress vector are obtained. The obtained solutions incorporate the characteristic material length scale, which is essential to understand the fluid behavior at microscales. If characteristic length of the couple-stress fluid is zero, the results to the classical fluid are recovered. The influence of the scale parameter on the fluid velocity, axial flow rate, force-stress tensor, and couple-stress vector is analyzed by numerical calculus and graphical illustrations. It is found that the small values of the scale parameter have a significant influence on the flow parameters.

Finite element based large eddy simulation of flow over bluff bodies

Large eddy simulation (LES) of bluff body flows is performed using a finite element based formulation which employs a combined subgrid-scale model. The combined model uses the residual based variational multiscale (RBVMS) approach along with the dynamic Smagorinsky eddy viscosity model. Specifically, the RBVMS model is used to represent the cross-stress terms while the dynamic eddy viscosity model is used for the Reynolds stresses. The dynamic procedure is based on a localized version of the variational Germano identity. Two sets of cases are considered: flow over straight and wavy circular cylinders at ReDm=3000, and flow over a straight square cylinder at ReD=22,000. For the straight circular cylinder case, we compare LES predictions based on the RBVMS model and the combined subgrid-scale model against the experimental data. The combined model provides better predictions (for both force data and centerline profiles in the wake) and we select it in the rest of the cases. For the wavy circular cylinder case, LES predictions (based on the combined model) shows a good agreement with the experimental data including mean velocity profiles in the wake. It accurately captures the elongation of the recirculation region. In the square cylinder case too, LES predictions (based on the combined model) show a very good agreement with the direct numerical simulation and multiple experimental datasets.

Pulsatile flow of couple stress fluid through a bifurcated artery

Abstract In the present paper, the pulsatile flow of blood through a bifurcated artery with mild stenosis in parent artery is investigated by taking blood as couple stress fluid. The arteries pattern of bifurcation is treated to be symmetric about the axis of the parent artery and straight circular cylinders of limited length. The governing equations are made dimensionless and suitable coordinate transformation is used to convert the irregular boundary to a well designed boundary. The resulting system of equations is solved numerically using the finite difference method. The influence of physical parameters on the velocity, shear stress, flow rate and impedance near the apex is studied graphically. Further, the oscillatory nature of impedance, flow rate and shear stress against time near the apex in both parent and daughter arteries is presented.

GS0533 テーパ円柱から放射されるエオルス音の特性と後流構造に関する研究

In order to clarify Aeolian tone characteristics generated from a tapered circular cylinder and relationship between the Aeolian tone and flow field around the tapered circular cylinder, correlation in terms of far field sound and velocity fluctuations are measured by using a low noise wind tunnel and three types of tapered cylinder. Reynolds number based on the cylinder diameter and the uniform-flow velocity is 2.65 × 10^5. Also, the flow field around the cylinder are calculated by RANS simulation with tetrahedral mesh and prism mesh. As a result, it is observed that the cylinders with taper ratios of 0.05 and 0.025 have different peaks corresponding to the aerodynamic noise in the span wise location. The peaks of aerodynamic noise seems to depend on the upper wake and the lower wake in the span wise location of the model. However, the peaks of the Aeolian tone is not found and aerodynamic noise is drastically reduced with the cylinder with the taper ratio of 0.1. Also, von Karman vortices behind the tapered cylinder are away to downstream of the model compared to for the straight circular cylinder.

Unsteady rotational flows of an Oldroyd-B fluid due to tension on the boundary

Unsteady Taylor–Couette flows of an Oldroyd-B fluid, which fills a straight circular cylinder of radius R, are studied. Flows are generated by the oscillating azimuthal tension which is given on the cylinder surface. As a novelty, authors used in this paper the governing equation related to the tension field. The closed forms of the shear stress and velocity fields corresponding to the flow problems are obtained by means of the integral transforms method. Expressions for the azimuthal tension and fluid velocity were written as sums between the “permanent component” (the steady-state component) and the transient component. By customizing values of parameters from the mathematical model were obtained the corresponding solutions of other types of fluids, namely, Maxwell fluids. By using numerical simulations and diagrams of the azimuthal stress, the fluid behavior has been analyzed. The necessary time to achieve the “steady-state” was, also, determined.

Balance Layout Problem for 3D-Objects: Mathematical Model and Solution Methods

The paper introduces a general mathematical model of the optimal layout of 3D-objects (full-spheres, right circular cylinders, right regular prisms, and right rectangular parallelepipeds) in a container (straight circular cylinder, paraboloid of revolution, truncated circular cone) with circular racks. The model takes into account the minimum and maximum admissible distances between objects as well as the behavior constraints of the mechanical system (equilibrium, moments of inertia, and stability constraints). We propose solution methods based on Shor's r-algorithm, multistart algorithm, and accelerated search of terminal vertices of the decision tree.

Effect of steady rotation on low Reynolds number vortex shedding behind a circular cylinder

In this paper control of oblique vortex shedding in the wake behind a straight circular cylinder is explored experimentally and computationally. Towards this, steady rotation of the cylinder about its axis is used as a control device. Some limited studies are also performed with a stepped circular cylinder, where at the step the flow is inevitably three-dimensional irrespective of the rotation rate. When there is no rotation, the vortex shedding pattern is three dimensional as described in many previous studies. With a non-zero rotation rate, it is demonstrated experimentally as well as numerically that the shedding pattern becomes more and more two-dimensional. At sufficiently high rotation rates, the vortex shedding is completely suppressed.

Mathematical modeling of motion of a fluid partially filling a rotating cylinder with radially aligned edges

A boundary-value problem of unsteady vortex motion of a viscous incompressible fluid with a free surface in a cavity rotating with a variable angular velocity and shaped as a straight circular cylinder with equidistant radial ribs is solved in a two-dimensional formulation by finite-difference methods. The drag coefficient of the rib is obtained as a function of its depth relative to the free surface.

Dispersion Characteristics of a Plasma Column in a Toroidal Waveguide

The dispersion characteristics of a toroidal waveguide in the presence of a plasma column are considered. The solution of the wave equation in a toroidal waveguide is presented using an analytical approximation method. In this method, the curvature of the axis of the waveguide is considered as a disturbance parameter to the straight circular cylinder approximation. The perturbed torus field for both the plasma and the vacuum regions is expanded in terms of the eigenfunctions of the unperturbed quantities. The effect of the plasma column in the toroidal waveguide is considered as the second perturbation factor in MHD equations. The perturbed Maxwell's equations along with the perturbed momentum transverse and the continuity equations lead to dispersion relation.

Exact solutions for the unsteady rotating flows of a generalized Maxwell fluid with oscillating pressure gradient between coaxial cylinders

This paper deals with the unsteady rotating flow of a generalized Maxwell fluid with fractional derivative model between two infinite straight circular cylinders, where the flow is due to an infinite straight circular cylinder rotating and oscillating pressure gradient. The velocity field and the adequate shear stress are determined by means of the combine of the sequential fractional derivatives Laplace transform and finite Hankel transform. The exact solutions are presented by integral and series form in terms of the generalized G and Mittag-Leffler functions. The similar solutions can be easily obtained for ordinary Maxwell and Newtonian fluids as limiting cases. Finally, the influence of the relaxation time and the fractional parameter on the fluid dynamic characteristics, as well as a comparison between models, is shown by graphical illustrations.

A note on the unsteady flow of a generalized second-grade fluid through a circular cylinder subject to a time dependent shear stress

The unsteady flow of a generalized second-grade fluid through an infinite straight circular cylinder is considered. The flow of the fluid is due to the longitudinal time dependent shear stress that is prescribed on the boundary of the cylinder. The fractional calculus approach in the governing equation corresponding to a second-grade fluid is introduced. The velocity field and the resulting shear stress are obtained by means of the finite Hankel and Laplace transforms. In order to avoid lengthy calculations of residues and contour integrals, the discrete inverse Laplace transform method is used. The corresponding solutions for ordinary second-grade and Newtonian fluids, performing the same motion, are obtained as limiting cases of our general solutions. Finally, the influence of the material constants and of the fractional parameter on the velocity and shear stress variations is underlined by graphical illustrations.

Computer simulation of plain woven fabric appearance from yarn photographs

This article proposes a method for simulating plain woven fabric appearance based on photographs taken by still camera of actual yarns along their lengths. The survey mathematically models the transformation of yarns from a straight circular cylinder to a flattened and crimped form in the fabric structure. The simulation is performed by yarn images that are obtained by image processing techniques and resized according to mathematical models developed by means of the software prepared. Transforming circular yarn cross-section to elliptical one for simulating yarn flattening and modelling the crimped shape of yarn by an elastica curve are both convenient and realistic. The simulation of plain woven fabric can be performed by a method based on raster graphics. This article provides a model for yarn shape in fabric structure as well as a method for simulating plain woven fabric appearance. This method may be used in textile industry for design and quality control.