Elliptic Cylinder Research Articles

Two-dimensional dynamics of a mobile elliptical cylinder in an upward flow

The fully resolved dynamics of an elliptical particle suspended in an upward flow in an expanding channel, with successively increasing degrees of freedom of motion from a completely fixed state to an eventually fluidized state, are examined using particle resolved direct numerical simulation. The signed distance function immersed boundary method (sdfibm), implemented in OpenFOAM, is validated against results from COMSOL for the case of a pinned ellipse. The aspect ratio of the ellipse (defined as the ratio of the major to the minor axis (γ=Ra/Rb) is held constant at 2, while the minor axis is kept as Rb=0.15 (with respect to the inlet width, Wi = 1). A particle Reynolds number defined as Rep=(2Ra)Vmax/ν (where Vmax = 1 is the centerline velocity) is varied up to 300. The simulations exhibit rich dynamical behavior with stable, steady solutions up to Rep around 67, above which vortex shedding begins, with the ellipse responding with its oscillatory motion in response to the stresses and torques acting on it by the fluid. For the case of free translation in the x direction, multiple oscillatory states are found, where the particle is confined in the left or right half of the flow domain, depending on the initial placement of the particle. The forces on the particle get progressively complicated as the degree of freedom of movement of the ellipse increases, indicating that traditional drag correlations with fixed particles may not be valid in situations when they have mobility if one desires higher fidelity in coarse-grained models.

Semi-Analytical Solution of Transverse Vibration of Cylinders with Non-Circular Cross-Section Partially Submerged in Water

The free transverse vibration of a surface-piercing, vertical cylinder partially submerged in water was studied. The cylinder had an arbitrary non-circular, but symmetric, cross-section in the vibration direction. The water was assumed to be an incompressible and inviscid fluid. The effect of the surface waves of water was neglected in the analysis. The exact solution of velocity potential of water was derived by the method of separation of variables. The unknown coefficients in the solution of the velocity potential were expressed in the form of integral equations, including the dynamic deformation of the beam. Then, the governing differential equation of bending vibration of the cylinder under the hydrodynamic pressure was obtained. The Galerkin method was used to obtain the eigenvalue equation by expanding the wet modes of the cylinder into a series of dry modes. The elliptical cylinders partially submerged in water were taken as the numerical example. The accuracy of the proposed method was evaluated by the convergence studies. As a consequent result, the non-dimensional added virtual mass incremental (NAVMI) factor solutions were compared to the present Galerkin solutions, which can be used as a benchmark test for more sophisticated numerical simulations of computational fluid dynamics.

Numerical simulation of the natural double-diffusive convection in an elliptical cylinder -Impact of the buoyancy force-

The natural laminar and stable heat and mass convection in an enclosure defined by two horizontal confocal elliptical cylinders with normal and opposite buoyancy forces under uniform concentration and temperature has been numerically explored in this study. The physical Cartesian domain is transformed into an elliptical domain. For the numerical simulation, the equations of conservation of mass, momentum and energy as well as the boundary conditions are discretized by the numerical approach of finite volumes. The algebraic equations obtained were solved by the iterative Gauss-Seidel method. As a function of the effective variables, which are the Rayleigh number, the buoyancy force number N, the Prandtl number, and the Lewis number, the findings are shown as fields of velocities, temperatures, and concentrations as well as the average Nusselt and Sherwood numbers. The results showed that there is a critical buoyancy ratio Ncr = −1, where the mean Sherwood and Nusselt number values are minimal. Their values are decreased by rising values of N when N < Ncr and raised by rising values of N when N > Ncr, and raising the buoyancy ratio N's absolute value results in higher heat and mass transfer characteristics (averages Nusselt and Sherwood numbers).

Flow-induced vibration of an elliptical cylinder and a wake-mounted flat plate

A numerical simulation is carried out to study flow-induced vibration of an elliptical cylinder equipped with a wake-mounted flat plate in a laminar flow regime at Re = 100. The objects are constrained to vibrate independently in the cross-flow direction. The Vortex-induced vibration of an upstream cylinder with four different aspect ratios (AR = 0.25, 0.5, 0.75, 1) is investigated in the presence of a plate mounted in different horizontal spacing of G = 0.5–3. Simulations are performed for a fixed mass ratio of 10 and negligible damping ratio across a range of reduced velocities (Ur = 2–12). The results demonstrate that the presence of the flat plate can amplify the vibration amplitude of the cylinder by altering the shear layers’ structure, particularly at short horizontal distances. Moreover, the phase difference of the objects shows a correlation with both the horizontal distance and the AR. Furthermore, the presence of the plate results in broader lock-in regimes across all aspect ratios by delaying its end to larger reduced velocities. While reducing the AR leads to a higher maximum vibration amplitude of the cylinder, it results to a considerably lower amplitude for the plate due to different wake structures and reduced interaction between the shear layers and the flat plate.

Ultra-deep Subwavelength Confinement Palladium-Based Elliptical Cylinder Plasmonic Waveguide in the Near-Infrared Range

Ultra-deep Subwavelength Confinement Palladium-Based Elliptical Cylinder Plasmonic Waveguide in the Near-Infrared Range

Numerical Research of Double‐Diffusive Natural Convection in Elliptical Cylinders: Influence of Internal Eccentricity

The second part study of this paper is to numerically study the double-diffusive natural convection phenomenon inside a space annulus, situated between two horizontal confocal elliptic cylinders filled with a laminar flow, is presented. The elliptical coordinates do utilize to transform the physical domain into one rectangular. The basic equations are discretized using the finite-volume method. Using a developed code, the study covers a wide range for (103 ≤ Rat ≤105), Le = 2, N = 1, e = 0.52, 0.62, 0.72, 0.82.We have made some detailed studies covering the influence of the internal eccentricity parameter e1 on heat and mass transfer. Results do present in the form of isotherms, streamlines, and heat transfer. The local and average numbers for Sherwood and Nesselt are also displayed.Comparison with the published results showed that there is a good agreement. Keywords:double-diffusive, natural convection, elliptic cylinders, Rayleigh number, Lewis number.

An analytical method for the drag force of a thin flat plate in a flow of viscous fluid

In the problem of classical hydrodynamics about a thin finite-length flat plate in a uniform flow of viscous incompressible fluid we propose a new analytical method to develop an explicit representation for the drag force. The approach proposed is based on a certain integral equation of the first kind which is valid in the case of small Reynolds numbers (strong viscosity, or slow stream). The constructed asymptotic solution coincides with the classical Harrison–Filon formula, developed by absolutely different technique, as a particular case of the Oseen slow flow around an elliptical cylinder.

An efficient algorithm for calculating boundary elements in vortex methods

A theorem on the conformal mapping of the flow field with a continuous vorticity distribution is proved. An efficient algorithm of the boundary elements computing based on the theorem is applied in simulation of two-dimensional flow around an elliptic cylinder by the meshless method of Viscous Vortex Domains (VVD). The algorithm makes it possible to significantly reduce (orders of magnitude compared to conventional methods) the time spent on calculating boundary elements and multiply the number of calculation points on the body contour, which is necessary for high resolution of the boundary layer at high values of the Reynolds number. The algorithm can also be used to calculate boundary elements on cylindrical surfaces of arbitrary section and in combination with different vortex methods. The flow around an elliptical cylinder is simulated with a high resolution of the boundary layer for Re numbers from 102 to 105.

Electromagnetic scattering of a plane wave by a perfectly conducting elliptic cylinder near a plane surface

In this paper, we present a rigorous analytical and numerical method to evaluate the scattering of a plane electromagnetic wave by an infinite, perfectly conducting elliptic cylinder parallel to a non-perfectly reflecting plane surface. The analytical solution is based on the spectral domain method and the plane-wave expansion of the elliptic cylindrical waves and is applicable in a broad variety of cases in which the properties of the plane surface may be expressed by means of a reflection coefficient. The proposed approach is suitably implemented in a specific computational code to achieve a numerical solution. Results of validation trials, performed by using finite element method commercial software, are provided.

Carpal Tunnel Anthropometrics Using Acrylic Casts: A Cadaveric Study With Implications for Carpal Tunnel Release.

Abundant literature exists on the morphology of the carpal tunnel. Despite this, the shape of the carpal tunnel has been reported erratically, and most studies did not attempt to correlate findings with measurements taken from cadavers. The objective of this study was to perform a morphological analysis, determine the shape and mean dimensions of the carpal tunnel, determine the level of the narrowest area of the tunnel, and establish a set of values capable of serving as a reference for carpal tunnel release. The carpal tunnels of 20 fresh cadaveric hands were dissected, and acrylic casts were created and measured using industrial computed tomography. Of the 20 casts, 19 were shaped like elliptic cylinders, with little variation in their measurements along the length. The location of the narrowest section of the carpal tunnel is very different among casts, and the length of the roof of the carpal tunnel ranged from 21.26 to 29.86 mm. The most common shape of the carpal tunnel is an elliptic cylinder. Because of the unpredictability of the location of the narrowest area of the carpal tunnel, carpal tunnel release must continue through all extension of its roof. We advise that the release should rarely be extended distally more than 30 mm from the distal palmar wrist crease, which corresponds, in most cases, to the middle of the pisiform.

Investigation of film boiling over tandem arrangement of elliptical cylinders in vertical cross-flow of saturated liquid

The present study investigates the phenomenon of film boiling heat transfer for the tandem arrangement of elliptical heaters placed in cross-flow of saturated liquid (water) at near critical pressure conditions (P/Pc = 0.99), using the Eulerian approach-based volume of the fluid framework. The effect of vertical spacing between the heaters (pd = 7.5a to 12.5a), their aspect ratio (ψ = 0.4 to 1), degree of wall superheat (Jav/Prv = 0.6 to 1.8) and Reynolds number for liquid flow (Rel = 10 to 40) is investigated on the bubble departure dynamics and heat transfer characteristics. It is observed that the bubble departure size from the bottom heater has remained almost unchanged for all the situations whereas its departure frequency has increased upon an increase of Reynolds number and degree of superheat. The bubble size has varied significantly for the top elliptical heater and its departure frequency has increased with the decrease of aspect ratio and increase of pitch, Reynolds number and degree of superheat. The time-averaged heat transfer coefficient has increased upon an increase in pitch distance, aspect ratio, Reynolds number and degree of superheat, however, the rate of increase has diminished at a high degree of superheat.

Dynamic response of an elliptic cylinder inclusion with imperfect interfaces subjected to plane SH wave

Underground chambers or tunnels often contain inclusions, the interface between the inclusion and the surrounding rock is not always perfect, which influences stress wave propagation. In this study, the imperfect interface and transient seismic wave were represented using the spring model and Ricker wavelet. Based on the wave function expansion method and Fourier transform, an analytical formula for the dynamic stress concentration factor (DSCF) for an elliptical inclusion with imperfect interfaces subjected to a plane SH-wave was determined. The theoretical solution was verified via numerical simulations using the LS-DYNA software, and the results were analyzed. The effects of the wave number (k), radial coordinate (ξ), stiffness parameter (β), and differences in material properties on the dynamic response were evaluated. The numerical results revealed that the maximum DSCF always occurred at both ends of the elliptical minor axis, and the transient DSCF was generally a factor of 2–3 greater than the steady-state DSCF. Changes in k and ξ led to variations in the DSCF value and spatial distribution, changes in β resulted only in variations in the DSCF value, and lower values of ωp and β led to a greater DSCF under the same parameter conditions. In addition, the differences in material properties between the medium and inclusion significantly affected the variation characteristics of the DSCF with k and ξ.

Equivalent Dynamic of Liquid Sloshing Coupled with Mass Transfer During On-Orbit Refueling

During an on-orbit refueling mission, the liquid fuel partially filling in the tanks will slosh and produce coupled motion with the servicer-to-client transfer, which may bring dangers to the spacecraft and even lead to attitude divergence. To effectively simulate the motion and the inertia of liquid fuel in a cylindrical tank during refueling, equivalent dynamic modeling of liquid fuel sloshing coupled with mass transfer is developed in this paper. A spring–mass–damper model with time-varying elastic and damping coefficients is implemented in the axial direction to equal the motion of the liquid mass center, while a pendulum model with time-varying pendulum length is adopted in the radial direction. An equivalent liquid elliptical cylinder is developed to approximate the inertia of dispersed liquid while sloshing. A series of computational fluid dynamics simulations are carried out to observe the liquid behaviors in the fuel tanks and to verify the proposed equivalent dynamic model. Finally, three-dimensional sloshing is theoretically and numerically analyzed.

The Stationary Thermal Field in a Multilayer Elliptic Cylinder

An analytical–numerical method for determining the two-dimensional (2D) thermal field in a layer-inhomogeneous elliptic cylinder (elliptical roller) was developed in the article. A mathematical model was formulated in the form of a boundary problem for Poisson equations with an external boundary condition of the third kind (Hankel’s). The conditions of continuity of temperature and heat flux increment were assumed at the inner boundaries of material layers. The eigenfunctions of the boundary problem were determined analytically. Hankel’s condition was subjected to appropriate mathematical transformations. As a result, a system of algebraic equations with respect to the unknown coefficients of the eigenfunctions was obtained. The above-mentioned system of equations was solved numerically (iteratively). As an example of an application of the aforementioned method, an analysis of the thermal field in an elliptical electric wire was presented. The system consists of an aluminum core and two layers of insulation (PVC and rubber). In addition to the field distribution, the steady-state current rating was also determined. The thermal conductivities of PVC and rubber are very similar to each other. For this reason, apart from the real model, a test system was also considered. Significantly different values of thermal conductivity were assumed in individual layers of the test model. The temperature distributions were presented graphically. The graphs showed that the temperature drop is almost linear in the insulation of an electrical conductor. On the other hand, in the analogous area of the test model, a broken line was observed. It was also found that the elliptical layer boundaries are not isothermal. The results obtained by the method presented in this paper were verified numerically.

Flow-Permeable and Tunable Metalens for Subdiffraction Waterborne-Sound Focusing

Metalenses with high-efficiency focusing functionality and a water-flow-permeable structure are desired in various acoustic applications, such as medical imaging and underwater navigation. Here, we propose a design paradigm for a metalens for waterborne sound with a compact and simple configuration. The metalens is composed of an open central region reserved as a steady water-flow channel, and a metagrating-based peripheral region consisting of a grating of meta-atoms. Each meta-atom containing two elliptical iron cylinders is smartly designed according to the grating diffraction theory and intelligent optimization algorithm, so that it can deflect a normally incident wave along the desired direction toward the focal spot. In this way, subdiffraction focusing with a high energy concentration ratio is achieved, which breaks the conventional Rayleigh-Abbe diffraction limit in the focal plane. Here the subdiffraction focusing is due to the coherent interference in the far field of the \ifmmode\pm\else\textpm\fi{}first-order diffracted waves from each meta-atom, and is attributed to the superoscillation phenomenon. Interestingly, the focal depth of the metalens can be conveniently tuned by applying a background water flow with different velocities and directions, and the superresolution focusing effect is sustained regardless of whether there is a water flow or not. Since the magnitude and direction of the water-flow velocity can be electrically controlled, the compact and open configuration of the metalens not only provides a flexible and practical solution for sharp and controllable sound focusing, but also has potential applications in metagrating-based planar acoustic devices.

The effect of the vibrissa shaped cylinder on the aeolian tone mitigation

This paper studies vibrissa shaped cylinder as a passive control method for reducing the aerodynamic noise of the flow past a cylinder. One elliptical cylinder is also investigated for comparison. The far-field noise results show that compared with the cylinder case, the tonal peak almost disappears in the vibrissa shaped cylinder case and the sound pressure level (SPL) could be reduced by up to 30dB within the velocity range from 8m/s to 35m/s. The elliptical cylinder only shows a slight SPL reduction by about 4 dB with a shift in the tonal peak frequency from St=0.2 to St=0.39. Furthermore, some noticeable variations occur in the noise directivity pattern for the vibrissa shaped cylinder case. The shift in the tonal peak frequency, the reduction in noise and modifications in the noise directivity is related to the changing and breakdown of the vortex shedding caused by the interference with the elliptical and vibrissa shaped cylinder surfaces. The LES is conducted to the elliptical and vibrissa cylinder case for the fluid field information to further understand the mechanism of the noise reduction due to the vibrissa shaped cylinder and elliptical cylinder.

Intrinsic-crack modelling of the notch fatigue limit of a solid with an elliptical-cylindrical or a spheroidal cavity

Based on an approximate stress-intensity factor for a crack emanating from an elliptical-cylindrical or spheroidal cavity, the El Haddad intrinsic-crack method for modelling the notch fatigue limit of a solid containing a cavity has been extended from a straight through-crack or a circular crack to a wider range of cavity shapes. Thus, predictions of the notch fatigue limit have been presented for elliptical cylinders, ranging from a through-crack to a circular cylinder, and for limiting cases of spheroids, viz. the circular crack and the sphere. These predictions have been shown to be in good to excellent agreement with those based on the theory of critical distances.

NUMERICAL INVESTIGATION OF FORCED CONVECTION HEAT TRANSFER AROUND AND THROUGH AN ELLIPTICAL POROUS CYLINDER

Convection heat transfer from a heated elliptical porous cylinder in the incompressible and laminar cross-flow is studied numerically. The effects of Darcy number (10&lt;sup&gt;-6&lt;/sup&gt; &amp;le; Da &amp;le; 10&lt;sup&gt;-2&lt;/sup&gt;), aspect ratio (0.2 &amp;le; AR &amp;le; 5), Prandtl number (0.7 &amp;le; Pr &amp;le; 70), Reynolds number (10 &amp;le; Re &amp;le; 40), on the average Nusselt number (Nu), as well as the lift and the drag coefficients are investigated. Two types of thermal boundary conditions for porous cylinder are investigated: uniformly distributed heat source and constant temperature. The fluid flow in the porous medium is numerically simulated by the superficial velocity model. Additionally, the energy equation in the porous medium is simplified by the local thermal equilibrium (LTE) hypothesis. It is concluded that the aspect ratio of the elliptical cylinder has a great influence on the heat transfer and fluid flow characteristics of this problem. Results show that increasing the Darcy number increases the Nusselt number and decreases the drag coefficient of the porous cylinder. Moreover, values of Da smaller than 10&lt;sup&gt;-4&lt;/sup&gt; resemble the fluid flow and heat transfer characteristics of the impermeable solid cylinder.

NUMERICAL INVESTIGATION OF LAMINAR NATURAL CONVECTION HEAT TRANSFER IN SQUARE ENCLOSURE WITH TWO HOT INNER CYLINDERS: THE EFFECT OF ONE ELLIPTICAL CYLINDER WITH VARIOUS ASPECT RATIOS

This study conducted two-dimensional numerical simulations of the natural convection in a square enclosure with two inner hot cylinders: one is circular and the other is elliptical at Rayleigh numbers (Ra) of 10&lt;sup&gt;4&lt;/sup&gt; &amp;le; Ra &amp;le; 10&lt;sup&gt;6&lt;/sup&gt; and a Prandtl number (Pr) of Pr &amp;#61; 0.7 (air). The aspect ratio (AR) of the elliptical cylinder ranging from 0.25 &amp;le; AR &amp;le; 4. The flow structures and heat transfer mechanism within a square enclosure were investigated with respect to the transition of the flow regime from steady to unsteady state. The thermal and flow fields reached steady state in the Rayleigh number range of 10&lt;sup&gt;4&lt;/sup&gt; &amp;le; Ra &amp;le; 10&lt;sup&gt;5&lt;/sup&gt;, regardless of the variation in aspect ratio. However, at Ra &amp;#61; 10&lt;sup&gt;6&lt;/sup&gt;, the numerical solutions show time-dependent characteristics in the case of the lower and upper elliptical cylinders except at AR &amp;#61; 4. Thus, the steady or unsteady flow regime is strongly dependent on the Rayleigh number and aspect ratio of the elliptical cylinder. Thus, the variation of the aspect ratio has a significant effect on the heat transfer characteristics at the walls of the enclosure and the surface cylinders.

Differential method for determining the specific absorption rate coefficient of electromagnetic energy for a liquid phantom

The wide use of small-sized wearable electronic devices in various practical human activities makes it relevant to measure the proportion of electromagnetic energy absorbed by the human body. One of the most important parameters that determines it is the specific absorption rate. In this article we propose a method for determining this coefficient for a liquid phantom, with the use of computer simulation and experimental measurement of the microstrip patch antenna parameters.The antenna is located on an elliptical cylinder and operates in the medical body area network. The method is based on measuring the rise in temperature of the liquid phantom exposed to electromagnetic waves generated by a microstrip antenna over a given time. Homogeneous liquid phantom was created by changing the percentage of salt and sugar in 250 g of water, skin phantom – by changing the percentage of water in 200 g of glycerol. The proposed specific absorption rate measurement method eliminates the need to purchase an expensive set of dielectric probes, which demonstrates its cost-effectiveness. The obtained results of experimental measurements are in good agreement with the results of the performed computer simulation.