Impenetrable Cylinder Research Articles

Evaluation of strain-sensitive behavior in elastomeric conductive nanocomposites containing carbon nanotubes-a finite element-percolation model approach

A finite element (FE)-percolation model approach is developed to predict the strain-sensitive response of the three-dimensional (3D) representative volume element (RVE) of carbon nanotube (CNT)-elastomeric nanocomposite. In the simulation model, CNTs are modeled as solid, impenetrable cylinders inside a cubic insulating matrix. FE simulation is performed to evaluate the structural response of the RVE under applied strain. The FE model updates the locations of the CNTs in the deformed RVE. The paths are found using a suitable 3D resistance network associated with different percolation paths involved in the critical distance criterion. The percolation model utilizes the paths found to identify the electrical circuit for predicting tunneling conductivity. The simulating algorithm is used to study the influence of tunneling barrier height, nanotube volume fraction, and geometrical aspects. The lowest critical distance criterion is achieved for higher volume fractions and the most heightened sensitivity is obtained for lower CNT aspect ratios.

Mean square winding angle of Brownian motion around an impenetrable cylinder

An exact formula is derived, as an integral, for the mean square value of the winding angle ϕ (with −∞< ϕ <∞) of Brownian motion (that is, diffusion) after time t, around an infinitely long impenetrable cylinder of radius a, having started at radius R(>a) from the axis. Strikingly, for the simpler problem with a = 0, the mean square winding angle around a straight line, is long known to be instantly infinite however far away the starting point lies. The fractally small, fast, random walk steps of mathematical Brownian motion allow unbounded windings around the zero thickness of the straight line. A remedy, if it is required, is to accord the line non-zero thickness, an impenetrable cylinder, as analysed here. The problem straightaway reduces to a 2D one of winding around a disc in a plane since the axial component of the 3D Brownian motion is independent of the others. After deriving the exact mean square winding angle, the integral is evaluated in the limit of a narrow cylinder a 2 ≪ R 2, highlighting the limits of short and long diffusion times addressed by previous approximate treatments.

Effects of force and moment actuation in active two dimensional VIV control of an elastic circular cylinder in power-law fluid flow

The coupled in-line/crosswise (2-DOF) Vortex-Induced Vibration (VIV) control of a flexibly-supported impenetrable circular cylinder immersed in uniform 2D laminar cross-flow of incompressible non-Newtonian power-law fluids is numerically investigated. Two effective active closed-loop control strategies are separately applied and compared in a real-time collaborative simulation framework that interactively connects the Fluent CFD solver with Matlab/Simulink. Numerical simulations reveal the important effects of power-law rheology and controller configuration on the key cylinder response/aerodynamic parameters and flow structure for a wide range of power-law index parameters (0.4≤n≤1.8). In the absence of the control system, the boundary layer thickness, the attached wake size/strength, and the length/thickness of the associated “shear stretching layer” (vortex shedding frequency) are found to noticeably increase (decrease) with increasing the power law index parameter. As the value of power-law index is largely increased, there is a notable shift of the synchronization (lock-in) region into the higher Reynolds number range besides its marked contraction which can passively complement the cylinder VIV control problem in the highly viscous shear-thickening fluid. When the active control system becomes operative, the superior performance and efficiency of the moment-based controller in effective and rapid mitigation of cylinder VIV and weakening of the vortex intensities through a desynchronization type of action with minimum actuator power requirements is demonstrated.

Acoustic radiation force on a cylindrical particle near a planar rigid boundary II. – Viscous fluid cylinder example and inherent radiation torque

ObjectiveThis study extends the scope of a previous analysis on the time-averaged acoustic radiation force on a rigid (sound impenetrable) cylinder near a flat boundary [F.G. Mitri, J. Phys. Commun. 2 (2018) 045019] to the case of a viscous compressible fluid (sound penetrable) particle, and determine the time-averaged acoustic radiation torque as well. Motivation and noveltyPrevious analytical formalisms did not consider the case of a sound penetrable cylindrical particle insonified at an arbitrary angle of incidence (in the polar plane) near a reflecting boundary. This work fills this gap, and provides exact expressions and computations for the acoustic radiation force and torque components. MethodThe partial-wave series expansion method, in conjunction with the method of images and the translational addition theorem of cylindrical wave functions are used to derive the analytical expressions for the longitudinal and transverse acoustic radiation force components. Moreover, the emergence of a radiation torque that causes the particle to rotate around its center of mass is computed using an exact partial-wave series expression. Results, key conclusion and some perspectivesAttractive (pulling), repulsive (pushing) and neutral (zero) forces arise depending on the particle-boundary distance, the cylinder size parameter as well as the angle of incidence (in the polar plane) of the insonifying waves. Emphasis is also given on the emergence of an acoustic radiation torque (that vanishes for a rigid or non-viscous circular cylinder). Computations for the axial radiation torque efficiency anticipate the generation of positive radiation torque, its reversal, in addition to a zero efficiency, leading, respectively, to counter-clockwise, clockwise or lack of particle rotation as the angle of the incident waves deviates from normal incidence with respect to the boundary surface. The extension to the case of an elliptical/oval cylinder near a boundary is mentioned, and replies to some misleading and obtuse comments on the paper [F.G. Mitri, Phys. Fluids 28 (2016) 077104] are provided.

Propagation and scattering of waves by dense arrays of impenetrable cylinders in a waveguide

A coupled numerical scheme, based on modal expansions and boundary integral representations, is developed for treating propagation and scattering by dense arrays of impenetrable cylinders inside a waveguide. Numerical results are presented and discussed concerning reflection and transmission, as well as the wave details both inside and outside the array. The method is applied to water waves propagating over an array of vertical cylinders in constant depth extended all over the water column, operating as a porous breakwater unit in a periodic arrangement (segmented breakwater). Focusing on the reflection and transmission properties, a simplified model is also derived, based on Foldy–Lax theory. The latter provides an equivalent index of refraction of the medium representing the porous structure, modeled as an inclusion in the waveguide. Results obtained by the present fully coupled and approximate models are compared against experimental measurements, collected in wave tank, showing good agreement. The present analysis permits an efficient calculation of the properties of the examined structure, reducing the computational cost and supporting design and optimization studies.

Semi-Active Vortex Induced Vibration Control of an Elastic Elliptical Cylinder with Energy Regeneration Capability

The concept of energy-regenerative damping is adopted in semi-active vortex-induced vibration (VIV) suppression of an elastically supported inclined impenetrable elliptical cylinder modeled as a two degree-of-freedom (DOF) system in laminar cross-flow at low Reynolds numbers (Re = 210). It is based on the intelligent (model free) adaptive fuzzy sliding mode control (AFSMC) strategy in conjunction with switch-based energy regenerating circuit of a tunable electromagnetic (EM) damper. The semi-active damper is linked to the plant model in a multi-field co-simulation framework via MATLAB/Simulink coupled with a user defined function in a CFD package. The AFSM controller initially calculates the desired transverse control force for suppression of the cylinder VIV. Consequently, by smart adjustment of the variable circuit load resistance, the current flow through EM damper circuit is adaptively modulated in such a way that the damping force continually tracks its active counterpart in a semi-active manner. Furthermore, when the damper is operating in the regeneration mode, the mechanical vibration energy that is traditionally dissipated as heat in conventional viscous dampers will be stored as electric charge in a capacitor. Numerical simulations demonstrate that the regenerative semi-active EM-based VIV control system can effectively suppress the cylinder motion while recovering a certain portion of mechanical vibration energy through the cooperative action of two distinct operation modes of the EM damper. Unlike conventional active control systems, the proposed system does not require a large external power supply, and at least part of the required power may be provided by the recovered energy.

Active closed-loop vortex-induced vibration control of an elastically mounted circular cylinder at low Reynolds number using feedback rotary oscillations

An active rotary oscillation feedback control methodology is adopted to suppress the flow-induced transverse vibration (VIV) of an elastically supported impenetrable circular cylinder in a uniform low Reynolds number flow (\(\textit{Re} = 100\)). The coupled fluid–structure interaction is replicated by applying the moving mesh technique via a user-defined function (UDF) in the main code of a commercial CFD solver. The closed-loop VIV control action is realized by active forced rotational oscillations of the circular cylinder about its axis based on the feedback signal of the lift coefficient. This prevents the occurrence of resonance by shifting the vortex shedding frequency away from the natural oscillator frequency. Three different active closed-loop proportional controllers are implemented, and their superior performance in cylinder VIV suppression is demonstrated against that of a representative open-loop control system with pre-specified rotational oscillations. It is shown that, in comparison with the open-loop system, the selected closed-loop controller achieves a better cylinder VIV response suppression with a much lower control effort along with considerable reductions in the associated lift/drag coefficients. Furthermore, the closed-loop controller is very effective in a wide range of reduced velocities and does not need to find the “lock-on” forcing frequency for proper de-synchronization. Moreover, the imposed feedback cylinder rotary oscillation is found to considerably affect the spatial characteristics of the wake flow structure by changing the 2S-Coalescent wake pattern (C-2S-mode) of an uncontrolled cylinder into the classical von Karman vortex street (2S-mode), very similar to that of a stationary obstacle. Lastly, when the system is in the fully developed condition, the proportional controller can be complemented by a fuzzy logic inference system for intelligent tuning of gain parameter in order to suppress the impulsive upsurge observed in the cylinder force coefficients of the proportional controller at the start of the control action.

Calculation of spiral turbine cases according to the equations of flow caused by vortex discharge - circle

The authors considered the issues of spiral turbine cases calculation with the help of the equations of fluid flow line of a potential flow induced by vortex discharge-circle situated on an infinite impenetrable cylinder in infinite space filled with ideal (nonviscous) fluid and the characteristics of the flow in spiral cases. It was established that: 1) the stated equations allow calculating the spiral cases, which differ in constructive parameters and the direction of the flow at the entry to the stator of the turbine; 2) slope angle of spiral cones and the direction of the flow at the entry into the stator significantly influence the dimensions of the spiral case; 3) the shape of the cross-sections of the spiral differs from the T-shaped and circle ones usually applied today; 4) the height of the cross-sections is greater than their width. This difference grows in the direction from the entry section to the tooth of the spiral case; 5) the dimensions of the calculated spiral cases are smaller than the dimensions of the cases with round cross sections and bigger than the ones with T shape. It was stated that the theoretical characteristics of the floe formed by spiral case calculated according to the equations of the potential flow induced by vortex discharge-circle situated on an infinite impenetrable cylinder are in good agreement with the experimental characteristics and are favourable for flow-around of stay vanes and guide vanes of turbines.

Coupling of parabolic equation method with the scattering of sound

The problem of sound scattering by an infinitely long penetrable and impenetrable cylinder suspended over a realistic impedance ground is investigated. The analytical approach using the image source method in the scattering of sound involves expressing the total sound field at any receiver point (over a locally reacting ground) as the sum total of the direct field, the ground reflection from the source, scattered field by the actual cylinder and finally by its image. The exact solutions can then be expressed as an infinite series, containing Bessel and Hankel functions of increasing order. The coefficients of the scattered field are determined by matching the desired boundary condition (for a rigid circular cylinder, for example, the normal component of velocity is zero on the boundary). Although the preceding approach is commonly used in theoretical treatments of sound scattering, to the best of our knowledge this is the first time it has been attempted numerically with coupling to the Parabolic Equation (PE) method. Presented is a Two-dimensional case of sound scattering of PE generated acoustic field by an impenetrable (soft or rigid) and penetrable cylindrical obstacle over a finite impedance ground in a non-refractive atmosphere.

Effect of Ionic Size on the Structure of Cylindrical Electric Double Layers: A Systematic Study by Monte Carlo Simulations and Density Functional Theory

The effect of ionic size on the diffuse layer characteristics of a cylindrical electric double layer is studied using density functional theory and Monte Carlo simulations for the restricted primitive model and solvent primitive model. The double layer is comprised of an infinitely long, rigid, impenetrable charged cylinder also referred to as the polyion, located at the center of a cylindrical cell containing the electrolyte, which is composed of charged hard spheres and the solvent molecules as neutral hard spheres (in the case of the solvent primitive model). The diameters of all the hard spheres are taken to be the same. The theory is based on a partially perturbative scheme, where perturbation is used to approximate the ionic interactions and the hard sphere contribution is treated within the weighted density approach. The Monte Carlo simulations are performed in the canonical ensemble. The zeta potential profiles as a function of the polyion surface charge density are presented for cylindrical double layers at different ionic concentrations, ionic valences, and different hard sphere (ionic and the solvent) diameters of 2, 3, and 4 Å. The theory agrees quite well with the simulation results for a wide range of system parametric conditions and is capable of showing the maximum and minimum in the zeta potential value for systems having divalent counterions. The steric effects due to the presence of solvent molecules play a major role in characterizing the zeta potential and the ionic density profiles. A noticeable change in the concavity of the zeta potential plots with increasing particle size at very low concentrations of monovalent electrolytes is suggestive of the occurrence of infinite differential capacitance for such systems.

Permeability of media composed of impenetrable cylinders covered with porous layer

The liquid flow through a set of nonuniform porous cylinders with a impenetrable core are studied by the Happel—Brenner cell method. Different orientations of cylinders relative to the liquid flow, such as transverse, longitudinal, and random, are considered. Brinkman equations are used to describe the flow of liquid in the porous layer. All known boundary conditions on the cell surface (Happel, Kuwabara, Kvashnin, and Cunningham conditions) are considered. The models proposed can be used to describe the processes of reverse osmosis, as well as nano-and ultrafiltration.

Cell models for flows in concentrated media composed of rigid impenetrable cylinders covered with a porous layer

The hydrodynamic permeability of a membrane simulated by a set of identical impenetrable cylinders covered with a porous layer is calculated by the Happel-Brenner cell method. Both transverse and longitudinal flows of filtering liquid with respect to the cylindrical fibers that compose the membrane are studied. Boundary conditions on the cell surface that correspond to the Happel, Kuwabara, Kvashnin, and Cunningham models are considered. Brinkman equations are used to describe the flow of liquid in the porous layer. Results that correspond to previously published data are obtained for the limiting cases. Theoretical values of Kozeny constants are calculated. The models proposed can be used to describe the processes of reverse osmosis, as well as nano- and ultrafiltration.

Structure of cylindrical electric double layers: A systematic study by Monte Carlo simulations and density functional theory

We present a systematic study of the structure of cylindrical double layers to envisage the distribution of small ions around a cylindrical polyion through canonical Monte Carlo simulation and density functional theory. The polyion is modeled as an infinite, rigid, and impenetrable charged cylinder surrounded by charged hard spheres of equal diameter modeled for small ions of the electrolyte. The solvent is considered as dielectric continuum. The theory is partially perturbative where the hard sphere contribution to the total excess free energy is evaluated using weighted density approximation, and the ionic interactions are calculated using quadratic Taylor expansion with respect to a uniform fluid. The system is studied over a wide range of parameters, viz., ionic concentrations, valences, and ionic sizes as well as for varying axial charge densities of the polyion. The theoretical predictions are observed to be in good agreement with that of simulation results. Some interesting phenomena relating to the width of the diffuse layer, mean electrostatic potential, and charge inversion have been observed to be dependent on different parametric conditions.

Transverse permeability of woven fabrics

transverse permeability is an essential input in describing the consolidation process of CETEX® laminates. A two-dimensional, finite difference based, Stokes flow solver has been developed to determine the mesoscopic permeability of arbitrary fabric structures. The use of a multigrid solver dramatically decreases the cpu time required (less than one minute on a 5122 grid). The permeability of a square packed bed of impenetrable cylinders is calculated and shows excellent agreement with values found in literature.

Acoustic scattering by a rigid elliptic cylinder in a slightly viscous medium

A complete solution is obtained for the two-dimensional diffraction of a time-harmonic acoustic plane wave by an impenetrable elliptic cylinder in a viscous fluid. Arbitrary size, ellipticity, and angle of incidence are considered. The linearized equations of viscous flow are used to write down expressions for the dilatation and vorticity in terms of products of radially and angular dependent Mathieu functions. The no-slip condition on the rigid boundary then determines the coefficients. The resulting computations are facilitated by recently developed library routines for complex input parameters. The solution for the circular cylinder serves as a guide and a differently constructed solution for the strip is also given. Typical results in the "resonant" range of dimensionless wave number, displaying the surface vorticity and the far-field scattering pattern are included, with the latter allowing comparison with the inviscid case.

Understanding Layer Promotion and Its Relationship to Melting in Krypton on Graphite Using Artificial Constraints

Constant particle number, density and temperature (N, ρ, T) Molecular-Dynamics simulations are used to study second layer promotion and melting in a complete monolayer of krypton deposited onto a graphite substrate. In order to study the vertical behavior of the system and its relationship to melting, artificial horizontal constraints are introduced and their effects are systematically monitored. We find that horizontally confining each atom within an impenetrable cylinder increases the melting temperature Tm and causes melting to be less dramatic. The results also suggest that there is a limiting case of there being no transition for a sufficiently small confining cylinder. Vertical excursions of the adsorbate atoms increase at the onset of melting. The system subsequently goes through a vertical transition with increasing temperature, including second layer promotion followed by extinction of the partial second layer and the presence of a sparsely populated first layer and a large population of desorbed atoms. Horizontal confinement stifles true second layer promotion, causing the atoms to spend less time in the second layer at a given temperature and resulting in a thermal blurring of the adlayer, suggesting that in-plane fluctuations are a necessary part of the layer promotion mechanism. Horizontal confinement also raises the temperature where the vertical transition occurs but does not affect its sharpness or temperature extent.

On the space-time curvature experienced by quasiparticle excitations in the Painlevé–Gullstrand effective geometry

We consider quasiparticle propagation in constant-speed-of-sound (iso-tachic) and almost incompressible (iso-pycnal) hydrodynamic flows, using the technical machinery of general relativity to investigate the “effective space-time geometry” that is probed by the quasiparticles. This effective geometry, described for the quasiparticles of condensed matter systems by the Painlevé–Gullstrand metric, generally exhibits curvature (in the sense of Riemann) and many features of quasiparticle propagation can be re-phrased in terms of null geodesics, Killing vectors, and Jacobi fields. As particular examples of hydrodynamic flow we consider shear flow, a constant-circulation vortex, flow past an impenetrable cylinder, and rigid rotation.

Multiple scattering by two impenetrable cylinders: semiclassical theory.

Scattering of waves and particles by two identical, impenetrable, and parallel cylinders is studied here. The characteristic determinant of the scattering matrices is expanded in terms of simple traces that are semiclassically evaluated in order to extract the periodic orbits. Generalized formulas are derived for all the contributions that are purely geometrical or composite (including a creeping section). All the scattering resonances, interpreted as periodic orbits, are in excellent agreement with the exact results. The scalar problem of scattering by two impenetrable cylinders can be considered as a canonical problem.

Acoustic scattering by a circular cylinder parallel with another of small radius.

The scattering of a plane acoustic wave by an infinite penetrable or impenetrable circular cylinder, parallel with another one, also penetrable or impenetrable, of acoustically small radius, is considered. The method of separation of variables, in conjunction with translational addition theorems for cylindrical wave functions, is used. Analytical expressions are obtained for the scattered pressure field and the various scattering cross sections, for normal incidence. Numerical results are given for penetrable and impenetrable cylinders.

Force and impulse from an Aharonov-Bohm flux line

We calculate the force and impulse operators for a charged particle in the field of an Aharonov-Bohm flux line. The force operator is formally the Lorentz force, with the magnetic field operator modified to include quantum corrections due to anomolous commutation relations. Expectation values for stationary states are calculated. Nonstationary states are treated by integrating the force operator in time to obtain the impulse operator. Expectation values of the impulse are calculated for slow wavepackets (which spread faster than they move) and for fast wavepackets (which spread only negligibly before their closest approach to the flux line). We give two derivations of the force and impulse operators, the first a simple derivation based on formal arguments, and the second a rigorous calculation of wavepacket expectation values. We also show that the same expressions for the force and impulse are obtained if the flux line is enclosed in an impenetrable cylinder,or distributed uniformly over a flux cylinder, in the limit that the radius of the cylinder goes to zero.