Steady Current Flow Research Articles

Experimental Investigation on Hydrodynamics of a Fish Cage Floater-net System in Oscillatory and Steady Flows by Forced Oscillation Tests

In this article, the hydrodynamic characteristics of a floater-net system in oscillatory and steady flows are investigated through forced oscillation experiments in a towing tank. The effects of Keulegan-Carpenter number, Reynolds number, and reduced velocity are studied. Also, hydrodynamic forces on the floater and net are compared in detail to analyze their respective contributions to the total drag force. The results indicate that in oscillatory flow, the added mass coefficient of the floater is larger than that of the floater-net system, whereas the drag coefficient is smaller. The proportion of the drag force exerted on the floating cylinder reaches its maximum in oscillatory flow and its minimum in steady current flow. In addition, the reduced velocity has a very clear influence on the hydrodynamic performance of the floater-net system; specifically, the drag coefficient in oscillatory flow becomes smaller as reduced velocity increases.

Dynamic Response of a Sphere Immersed in a Shallow Water Flow

This work analyzes the dynamic response of a sphere located close to the floor of a hydraulic channel within steady free-surface current flows. The sphere is free to move in transverse (y) and streamwise (x) directions, and it is characterized by a mass ratio m* equal to 1.34. The oscillation amplitudes and the frequencies of the sphere have been measured by means of the image analysis of a charge coupled device (CCD) camera. The experimental data show a significant influence of the free surface on the sphere movement and highlight a different behavior of the dynamic response to the increasing of the water level on the upper part of the body.

Current blockage experiments: force time histories on obstacle arrays in combined steady and oscillatory motion

AbstractThis paper revisits the problem of forces on obstacle arrays in combined waves and an in-line steady current. The intended application is the design and reassessment of offshore platforms. A series of experiments are performed on planar grids moved in both steady and oscillatory motion through otherwise stationary water. Detailed comparisons are made to a wave-current–structure interaction model recently presented by Taylor, Santo & Choo (Ocean Engng, vol. 57, 2013, pp. 11–24). We present new features of the model and test these against the experimental data. For relatively small current speed (${u}_{c} $) compared with oscillatory velocity amplitude (${u}_{w} $) with phase angle ($\omega t$), the drag force time history on grids with solid area ($A$) and projected frontal area (${A}_{f} $) is well approximated by a summation of the wave drag and the current drag components independently, so there is no ${u}_{w} \times {u}_{c} $ cross-term. The wave drag component is proportional to $\cos \omega t\vert \cos \omega t\vert $, while the current drag component to $\vert \cos \omega t\vert $, i.e. it is phase-locked to the oscillatory wave crests. The form of the predicted time history is new, so much of this paper is occupied in testing the adequacy of this theoretical form both in terms of an improved Morison-type formulation and also in the precise variation of the experimental drag force in time. We show that the measured crest and trough peak values of the drag force are consistent with the force peaks and troughs of the model prediction. The odd frequency harmonics of the measured drag force scale as the square of the oscillatory velocity amplitude $({ u}_{w}^{2} )$ and on the total hydrodynamic area (${C}_{d} A$). The shape of the odd harmonics is very similar to that for a pure oscillatory motion without steady current, but there are also even frequency harmonics associated with the current component. The even harmonics of the force scale as the square of the current speed $({ u}_{c}^{2} )$ and on the ${A}_{f} $, not on the ${C}_{d} A$. All of the above features are identified within the experimental data, and provide considerable support for the new current blockage model.The new model is also shown to fit the entire force time history well for a wide range of individual cases, with different blockage ratio ($A/ {A}_{f} $) and number of grids, requiring only calibration of the Morison-type drag and inertia coefficients. In contrast, the industry-standard form of the Morison equation can only be matched at a single instant of the oscillation cycle, so present practice should be regarded as seriously inadequate for combined steady current and oscillatory flow acting on obstacle arrays.

Numerical simulation of wave–current interaction using a RANS solver

A numerical model is developed to study the wave propagation in the presence of a steady current flow. This model is based on Reynolds-Averaged Navier–Stokes (RANS) equations with k−ε turbulence closure scheme. A novel volume of fluid (VOF) method is applied to accurately capture the water free surface. The current flow is initialized by imposing a steady inlet velocity on one domain end and pressure outlet on the other end, while the desired wave is generated by an internal wave-maker from mass source term of mass conservation equation. Simulated water surface profile and velocity distribution agree well with experimental measurements of Umeyama (2011), indicating that this model has a great ability in simulating wave–current interaction. The validated model is then used to investigate the effects of wave period and current velocity on regular wave–current induced water surface profile and velocity distribution. The propagation of a solitary wave traveling with a following/opposing current is also numerically investigated by this model.

Analysis of the temperature field near a corner composed of dissimilar metals subjected to a current flow

The 2D electro-thermal problem near a corner composed of two dissimilar materials in an angled metal line is analyzed. The line is assumed to be of uniform width and subjected to a steady direct current flow. We show the development work leading to the formulation of the current density and temperature distributions. The parameters affecting the singularities concerning the electro-thermal problem are also discussed. The electrical potential and current density distributions near a corner in an arbitrary angled line are determined, and the temperature field in a point symmetric line which is commonly met in metal interconnection structures is analyzed. In addition, we show that the temperature field solution is also valid for a symmetric line and a right angled line.

Influence of fluorination time on surface charge accumulation on epoxy resin insulation

In order to suppress surface charge accumulation on the epoxy resin insulation and to investigate the influence of treatment time on the charge accumulation, epoxy samples are surface fluorinated for the different times of 10 min, 30 min and 60 min in a laboratory vessel using an F2/N2 mixture. Attenuated total reflection infrared analyses and the observations of the cross section and the surface of the samples by SEM indicate the increases in degree of fluorination, thickness and compactness of the fluorinated layer, and the decrease in surface roughness, with treatment time increasing. Compared with the deep surface charge traps and stable surface charge of the unfluorinated (original) sample, as indicated by the open-circuit thermally stimulated discharge current measurement, the fluorinated surface cannot store the charge. The corona charges deposited on the sample surfaces fluorinated for 10 min, 30 min or 60 min rapidly decay to zero in about 2 min, 10 min or 15 mi at room temperature respectively, showing a slowed-down release of charge with fluorination time. The measurements of surface conductivity and contact angle and the calculation of surface energy reveal that fluorination gives rise to dramatic increases in surface conductivity, surface wettability and polarity, while they decrease with treatment time. The significant increase in surface conductivity of the fluorinated sample is attributed to a very likely substantial decrease in trap depth and the adsorbed water on the fluorinated surfac. Surface charging current measurements further show that large steady state current flows along the fluorinated surface during corona charging, in comparison with the almost zero steady state current for the original sample. This implies that the fluorinated sample has much lower surface charge accumulation in the period of charging, than the original sample.

Calculating Hydrodynamic Loads on Pipelines and Risers: Practical Alternative to Morison’s Equation

Hydrodynamic stability analysis is one of the major tasks in the design of subsea pipelines and risers. The analysis is important to ensure stability of pipelines and risers under the action of the hydrodynamic forces produced by waves and currents during construction and operation stages. Morison related these hydrodynamic forces to kinematic wave properties, water particle velocity, and acceleration. However, previous studies show that Morison’s equation does not describe accurately the forces for combined wave and steady current flow. The actual measured forces differ significantly from the forces calculated using Morison’s equation. Though Morison’s equation leads to easy computer application for design purposes, it is a very conservative approach resulting in high cost of construction of offshore structures. In this paper the Wake II Model is incorporated into MathCAD software to practically determine hydrodynamic forces acting on cylindrical offshore structures. The Wake II Model takes into account the vortex shedding effect in the wake of a bluff body resulting in velocity reversal, thus the velocity is modified to include this effect. The modified velocity, time dependent drag and lift coefficients are then used to calculate hydrodynamic forces of lift and drag using MathCAD software. The results showed that the forces predicted using the Wake II Model is significantly less in comparison to the Morison’s equation. The results achieved in this project are consistent with results achieved by Lambrakos in his comparison of the Wake Model predictions with measured forces (actual loads) from the Exxon Pipeline Field Measurement Project (PFMP). The Wake II Model lends itself to easy computer application such as MathCAD so ftware and will also reduce the overall construction cost of cylindrical offshore structures such as pipelines and risers.

A $p$-Adaptive Scheme for Scalar Fields, Using High-Order, Singular Finite Elements

For problems with sharp edges, where the electric or magnetic field is singular, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -adaptive finite-element analysis loses some of its effectiveness. This can be remedied by including singular elements which are better able to model the potentials near such edges. The singular elements are hierarchal and the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -adaption takes place over the combined set of singular and regular elements. An energy-based error indicator guides the adaption. Three test cases are considered: an electrostatic problem for finding the capacitance of a stripline gap; a steady current flow problem for finding busbar resistance; and a magnetostatic problem for finding the torque on a prism of permeable material. Results show that, although the use of singular elements does not increase the dimension of the global matrix, more conjugate gradient iterations are needed to solve the matrix equation. Nevertheless, the use of singular elements leads to a greatly improved adaptive convergence, with final accuracies about one order of magnitude higher, for a similar computational cost.

Accuracy Investigations of Boundary Element Methods for the Solution of Laplace Equations

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Boundary element methods (BEMs) are approved methods for an efficient numerical solution of problems, which are based on a Laplace equation. Here, the solution of electrostatic field problems, steady current flow field problems, and magnetostatic field problems is considered. Focus of this paper is on investigations of accuracy of direct formulations, which are based on Green's theorem. Different types of coupling of computational domains are examined with respect to accuracy and convergence behavior of iterative solvers of the linear system of equations. Furthermore, the influence of singular and nearly singular integrals and the influence of matrix compression techniques to the accuracy of the solution are observed. </para>

Electro-Thermal Problems near the Corner of Diamond-Shaped Hole Having Right-Angle in a Plate under a Direct Current Flow

The damage of electronic devices is often due to the generation of heat within the components. When the current is supplied to electronic components, their temperature rises because of the fact of Joule-heating. To evaluate the reliability of components subjected to Joule-heating, it is essential to analyze the associated current density and temperature distributions in the components. In this study, two-dimensional electro-thermal problems concerned with steady current flow near the corner of a hole were treated, where the shape of the hole was assumed to be a right-angled diamond. Distribution of current density near the corner was analyzed theoretically based on the Schwarz-Christoffel transformation. Electrical potential, which was calculated from the current density analyzed, was compared with FE analysis. Temperature near the corner was analyzed based on the electrical potential calculated. For the case when the heat flux related to the gradient of the temperature field associated with the problem without Joule-heating equals to zero, the temperature near the corner was verified to remain constant although current density decreased gradually far from the corner.

Fast multipole method based solution of electrostatic and magnetostatic field problems

Applications of boundary element methods (BEM) to the solution of static field problems in electrical engineering are considered in this paper. The choice of a suitable BEM formulation for electrostatics, steady current flow fields or magnetostatics is discussed from user's point of view. The dense BEM matrix is compressed with an enhanced fast multipole method (FMM) which combines well-known BEM techniques with the FMM approach. An adaptive grouping scheme for problem oriented meshes is presented along with a discussion on the influence of the mesh to the efficiency of the FMM. The computational costs of the FMM algorithm are analyzed for typical problems in practice. Finally, some electrostatic and magnetostatic numerical examples demonstrate the simple usability and the efficiency of the FMM.

Signatures of quantum chaos in complex wavefunctions describing open billiards

We discuss signatures of quantum chaos in open chaotic billiards. Solutions for such a system are given by complex scattering wavefunctions ψ = u + iv when a steady current flows through the billiard. For slightly opened chaotic billiards the current distributions are simple and universal. It is remarkable that the resonant transmission through integrable billiards also gives the universal current distribution. Currents induced by the Rashba spin–orbit interaction can flow even in closed billiards. Wavefunction and current distributions for a chaotic billiard with weak and strong spin–orbit interactions have been derived and compared with numerics. Similarities with classical waves are considered. In particular we propose that the networks of electric resonance RLC circuits may be used to study wave chaos. However, being different from quantum billiards, there is a resistance from the inductors which gives rise to heat power and decoherence.

Numerical studies of a steady state axisymmetric co-axial helicity injection plasma

Steady state current profile, plasma potential, and plasma flow of an electrostatically driven co-axial helicity injection (CHI) plasma with axisymmetry are numerically investigated using both an open field line Grad–Shafranov equilibrium model and self-consistent initial value magnetohydrodynamic (MHD) simulations. For CHI plasmas, the Grad–Shafranov model ignores plasma inertia but not a perpendicular, or Grad–Shafranov, flow. The Grad–Shafranov flow is the result of the gradient of Grad–Shafranov potential across magnetic field lines, and is responsible for toroidal current drive. Numerical Grad–Shafranov solutions show that as the characteristic CHI discharge parameter, the normalized voltage V̂≡μ0V/ηB0q0, becomes order of unity, CHI plasma develops kink-unstable hollow current profile. Here 𝒱 is the imposed voltage, η the plasma resistivity, q0 the toroidal and injector poloidal flux ratio, and B0≡4χ0/ab a nominal poloidal field defined by the injector poloidal flux χ0, plasma minor radius a, and plasma elongation b/a. When a small plasma inertia is included in the equation of motion, such as that in a time dependent MHD calculation, the modification on the perpendicular current is small, but its impact on parallel current distribution and hence the spatial dependence of magnetic flux can be great through the Pfirsch–Schlüter-like effects.

Dynamo and Electrical Jet in Hall Plasmas, Application to Astrophysics

The magnetic field in Hall plasmas is frozen in the electron component and is advected not only with the plasma motion but also with the electrical current flow. Its coupling with the plasma may be not as strong as characteristic of the MHD approximation. The rotation and slipping of the magnetic field result in a very different and less efficient magnetic field generation by dynamo-rotating plasma disk in magnetic field. We found some exact analytical solutions of nonlinear equations describing the dynamo. In particular, the dynamo may not dissipate the energy in the steady state limit. The 3-component magnetic field and magnetic energy are generated and accumulated during the transition time only. An electrical jet is another unusual phenomenon for MHD. It was investigated theoretically and experimentally for laboratory plasmas during the last 15 years and now is used for fast current switching. We found periodical or shock-like nonlinear wave traveling along a Hall plasma column and not associated with plasma motion. A nonlinear equation describing a possible steady state magnetic field distribution and current flow in a Hall plasma conductor is derived, which differs from the Grad-Shafranov equation. In conclusion we discuss how transfer our results onto astrophysical plasmas. This physics could be important for understanding the evolution of dusty plasma disks and jets around new stars.

Modeling of Conductivity Versus Density Behavior in Green-State Powder Metallurgy Compacts

Ongoing research at Worcester Polytechnic Institute (WPI) has recently resulted in the development of an electrostatic multipin instrument capable of testing green-state compacts directly after compaction. By monitoring a steady electric current flow through the sample and recording the voltages over the surface valuable information is gathered, leading to the prediction of the structural health of the green-state parts. Whereas our prior work concentrated on the detection of surface-breaking and subsurface defects, which requires the determination of large differences in material properties over small flaw sizes, the results presented in this paper aim at the density prediction throughout the volume of the sample. This requires the detection of small changes in material properties over large regions. A physical model and a mathematical formulation are reported, which are capable of relating green-state density changes to electric conductivity in the presence of various lubricant concentrations. Preliminary electrostatic measurements of cylindrical compacts have thus far confirmed the theoretical model assumptions, showing that the electric conductivity follows a complex graphical behavior that is determined by the type and concentration of the lubricant. Specifically, the green state conductivity increases as the sample density increases up to values of approximately 6.9 to 7.0 g/cm3. Any further density increase, however, results in a decrease in conductivity.

Performance evaluation of a permanent magnet brushless DC linear drive for high-speed machining using finite element analysis

Linear motor performance under large cutting forces at varying air-gap sizes and voltages is investigated. Under certain loading conditions, electromagnetic, thermal, and static analysis of the secondary elements is determined using EMRC-NISA software. Electric and magnetic field distribution is also determined for generated force by varying voltages and gap sizes. Due to the presence of conduction currents in electromechanical devices such as permanent magnet brushless DC linear motors (PMBDCLM), power losses in the form of heat dissipation are produced which alters the temperature distribution in the device. Change in temperature effects the generated force, electric and magnetic fields, thus overall performance. In this paper, single-sided linear motor geometry is presented. An overall rating based on performance and cost is determined. Post processing is performed in conjunction with steady current flow analysis, magnetic field analysis, electric field analysis, electromagnetic sub-analysis, and static analysis. A case study and result implications are also discussed.

Competitive Electrowetting of Polymer Surfaces by Water and Decane

The present study deals with electrocapillarity effects in the three-phase system water−decane−polymer. This system consists of a decane droplet which adheres under water on a polymer surface. We applied an electric potential between an electrode beneath the polymer film and a platinum electrode immersed in the water. The polymer film acts as insulator: no steady electrical current flows between the electrodes. When the voltage is increased, the contact angle of decane and water changes, in some cases by up to 100°. The shape of the electrowetting curve (contact-angle cosine versus voltage plot) strongly depends on the type of the polymer. A saturation at higher voltages, connected with a hysteresis, is interpreted in terms of charge carrier injection into the polymer surface. Other deviations of the experimental results from the Lippmann−Young parabola concern a broadening with the polyolefins, a strong shift, and apparent reduction to one branch with two fluoropolymers, and for PET and a heavily oxidiz...

Quantum energy flow in mesoscopic dielectric structures

We investigate the phononic energy transport properties of mesoscopic, suspended dielectric wires. The Landauer formula for the thermal conductance is derived and its universal aspects discussed. We then determine the variance of the energy current in the presence of a steady state current flow. In the final part, some initial results are presented concerning the nature of the temperature fluctuations of a mesoscopic electron gas thermometer due to the absorption and emission of wire phonons.

Plasma waves in the sheath of the TSS‐1R satellite

The current flow in the Tethered Satellite System (TSS) induces a strong excitation of electric and magnetic fluctuations in the potential sheath surrounding the subsatellite. The wave sensors of the experiment RETE (Research on Electrodynamic Tether Effects) have measured power spectra of electromagnetic fields from 180 Hz to 12 MHz, providing information on the physical processes taking place around highly charged bodies in the ionosphere and, in particular, the role of wave‐particle interactions and anomalous collisionality. We report on the observations during three events of almost steady current flow at 50, 190 and 55 mA, taking place at positive satellite potentials of about 9, 200 and 2 V. The largest power spectral density occurs at frequencies between 2 and 4 kHz, close to the lower hybrid frequency, where electric field fluctuations up to 12 V/m have been observed. In this frequency band the fields are electrostatic and radially polarized, with a marked ram‐wake signature.

Luminosity characteristics of dart leaders and return strokes in natural lightning

Streak‐camera photographs were obtained in daylight for 23 subsequent strokes in five Florida negative cloud‐to‐ground flashes. Out of the 23 return‐stroke streaked images, only 11 were accompanied by leader streaked images, while all 23 leaders were identified in corresponding electric field records. Thus, 12 subsequent leaders (one of which created a new channel to ground) failed to produce luminosity above the daylight background level. The brightest three dart‐leader/return‐stroke sequences from two flashes have been examined for relative light intensity as a function of time and height. Dartleader light waveforms appear as sharp pulses with 20‐to‐80% risetimes of about 0.5–1 μs and widths of 2–6 μs followed by a more or less constant light level (plateau). The plateau continues until it is overridden by the return‐stroke light waveform, suggesting that a steady leader current flows through any channel section behind the downward moving leader tip before the return‐stroke front has passed that channel section. Return‐stroke light pulses near ground have 20‐to‐80% risetimes of about 1–2 μs and amplitudes a factor of 2 to 3 greater than those of the dart‐leader light pulses. As opposed to the return‐stroke light pulses that suffer appreciable degradation during the upward propagation of the return‐stroke front, the dart‐leader light pulses preserve their shape, and the pulse amplitude is either more or less constant or increases as the leader approaches ground. The average electric field intensity across the dart‐leader front, whose length is inferred from measured light‐pulse risetimes and propagation speed to be of the order of 10 m, should be at least an order of magnitude greater than the average electric field intensity across the return‐stroke front, whose length is inferred to be of the order of 100 m.