Nonuniform Disk Research Articles

Characterizing porous disk wakes in different turbulent inflow conditions with higher-order statistics

The wakes of a uniform and a non-uniform porous disk exposed to two different turbulent flows are investigated experimentally. The disks are representative of static wind turbine models found in literature. Six wake profiles were collected through hot-wire anemometry between three and 30 diameters downstream of the disks. Both one-point and two-point statistics are studied. The results show that higher freestream turbulence affects the wake of the uniform disk more than that of the non-uniform disk, also changing the wake’s shape and recovery rate. Furthermore, we confirm earlier findings that the turbulence at the centerline in the developed part of the wake is independent of both the design of the wake-generating object and the inflow. Similar to findings in the wake of a wind turbine, a ring of high intermittency is found at the very edge of the wakes of both disks and in both inflow conditions. We identify the existence of this ring over a range of scales. The results show that, even for higher-order two-point statistics, the developed wake of different porous disks qualitatively agrees well with the wake of wind turbine models.Graphical abstract

The far wake of porous disks and a model wind turbine: Similarities and differences assessed by hot-wire anemometry

The wakes of two different porous disks have been evaluated experimentally. Such disks are commonly used as physical actuator disk analogs for wind turbines. One disk is made of a uniform wire mesh, while the other has a nonuniform design with radial spars connected by rings. The disks have the same solidity and produce approximately the same drag. The wakes have also been compared to the wake of a model wind turbine and a solid disk. In contrast to earlier studies, the far wake, up to 30 diameters downstream, is included in the comparison. In the near wake, the velocity deficit and turbulence intensity profiles of the disk wakes differ significantly. High levels of turbulence intensity in the wake of the nonuniform disk increase the transverse transport in the wake, which leads to faster spreading and lower velocity deficits in the far wake, compared to the uniform disk and the wind turbine. High velocity gradients in the wake of the uniform disk give rise to turbulence production farther downstream, maintaining higher turbulence levels in the far wake. In addition, coherent vortex shedding is only identified in the wake of the nonuniform disk. None of the disks were able to replicate the asymmetric features of the wind turbine wake. Nonetheless, the results highlight important flow physics that should be considered in the design process of a porous disk used as a wind turbine surrogate.

Validation of actuator disc circulation distribution for unsteady virtual blades model

The actuator disc method is an engineering approach to reduce computer resources in computational fluid dynamics (CFD) simulations of helicopter rotors or aeroplane propellers. Implementation of an actuator disc based on rotor circulation distribution allows for approximations to be made while reproducing the blade tip vortices. Radial circulation distributions can be formulated according to the nonuniform Heyson-Katzoff “typical load” in hover. In forward flight, the nonuniform disk models include “azimuthal” sin and cos terms to reproduce the blade cyclic motion. The azimuthal circulation distribution for a forward flight mode corresponds to trimmed conditions for the disk rolling and pitching moments. The amplitude of the cos harmonic is analysed and compared here with presented in references data and CFD simulations results.

Analytical modeling and experimental verification for linearly gradient thickness disk springs

Even though disk springs with non-uniform thickness have the advantages of improving the load capacity, optimizing the stress distribution, and adjusting the stiffness characteristics, their exploration remains sparse. Prior analytical models for non-uniform disk springs were based on the Almen–Laszlo theory, and the model verifications lacked the support of experiments. A mechanical model of linearly gradient thickness (LGT) disk springs is established in this study in the cylindrical coordinate system based on the theory of plates and shells. A new analytical equation as a function of material and geometric parameters is developed to describe the load–deflection characteristics of LGT disk springs. The load–deflection characteristics of disk springs with different thickness variation parameters are compared through cases with a constant mid-radius thickness and constant flattened load, respectively. Moreover, the stiffness, deformation energy, and stress distribution of the disk springs are also systematically analyzed. To verify the proposed model and characterize the nonlinear load–deflection properties of LGT disk springs, specimens were fabricated, and experimental tests were conducted. Comparisons between the analytical results and experimental data demonstrate the superior effectiveness and accuracy of the developed analytical model in predicting the load–deflection characteristics of disk springs with uniform thickness or LGT. The results from the analytical and finite element methods indicate that the proposed model can describe the load–deflection characteristics of disk springs with different cone angles.

Vortex shedding modes around oscillating non-uniform double heave plates

Multiple co-axial heave plates of uniform geometry are attached to offshore platforms for inducing damping and added mass. These effects generally decrease the magnitude of the dynamic response of the platform under applied environmental excitation forces. When spacing between heave plates is decreased the damping and added mass performance are altered due to their strong vortex interaction. A new non-uniform plate configuration is proposed that may create different hydrodynamic characteristics. The modes of vortex shedding around plate edges in a non-uniform arrangement under forced harmonic oscillation are investigated via the CFD method. Furthermore, a new simplified formula for the total theoretical added mass of a general non-uniform double disk is proposed when it is in the zone which vortex interaction take places. The results show that a non-uniform double disk has better hydrodynamic performance as compared to the uniform double configuration for a given spacing. It is also observed that the mode and direction of the vortex shedding are different for uniform and non-uniform arrangements in a given spacing and KC value.

A geometric separation method for non-uniform disk packing with prescribed filling ratio and size distribution

This paper proposes an approach to obtain a set of particles with a prescribed filling ratio and size distribution, using only geometric procedures. An essential step in the analysis of discontinuous media using the discrete element method is to obtain an initial set of particles that represents the granular model. Various particle packing approaches are currently employed to achieve a numerical model similar to a real discrete medium. In this context, this paper proposes an alternative particle packing method using the geometric separation procedure. This strategy aims to generate granular models that present particles with desired sizes, without overlapping and that fill a prescribed area of the domain. The method consists of five macro-steps: (a) definition of the initial set of particles; (b) geometric separation; (c) particle reallocation; (d) particle removing, and (e) particle inserting. This work focus on the bi-dimensional approach, where disks represent the particles. An initial set of particles is generated using input data related to the size distribution and filling rate, obtaining random positions for them. The other steps are used to eliminate overlaps between the particles. The packing algorithm provides good performance and approximation to the input parameters filling ration and grain size distribution. Granular models generated from real soil data are presented for validation of the proposed strategy, and practical examples from the literature are reproduced to illustrate its applicability.

Heat transfer from a non-isothermal rotating rough disk subjected to forced flow

This communication aims to report heat transfer characteristics from a non-isothermal wavy disk rotating in a forced flow. The primary objective of this kind of studies is to seek a suitable mechanism for the quick removal of heat energy from a rotating disk surface. The achievement of an efficient mechanism which ensures a further higher rate of heat transfer is a fundamental goal in such studies. In this regard active and passive techniques are of fundamental importance whereby the current study utilizes a combination of both. There are three key elements, namely, the non-uniform disk temperature; surface roughness, and a radial free flow, which are responsible for the augmentation of the heat transfer. The analysis has been carried out for a variety of fluids depicting the increased rate of heat transfer due to a variation of these different elements. In doing so, the local and global heat transfer rates are manipulated in order to obtain a clear picture of the heat transfer process at a corrugated disk. The considered rough non-isothermal disk (with two sinusoids) rotating in the uniform stream of air (Pr = 0.71) leads to a significant (about 263%) enhancement in the overall heat transfer rate compared to that of a flat free rotating disk having surface temperature as quatratic function of the radial coordinate. Moreover, some threshold values (which correspond to seizing the heat transfer process) of the used power-index of the disk temperature (Tw − T∞ = c0rn∗) are also identified which are observed to vary slightly due to the surface irregularities and the relative motion of fluid and disk.

Prediction Model of TBM Disc Cutter Wear During Tunnelling in Heterogeneous Ground

When shield tunnelling is constructed in complex geological conditions using a tunnel boring machine, the disc cutter in the cutterhead easily wears to the failure state, particularly when the ground conditions are heterogeneous. This paper summarises the failure modes of the disc cutter in heterogeneous ground conditions into three categories, based on the observed wear data from field: (1) uniform disc cutter wear, (2) non-uniform disc cutter wear, and (3) breakage of cutter ring. Subsequently, the stress state of a disc cutter in the heterogeneous ground was analysed and the effective factors were investigated. The relationships between friction energy during cutting, working status of the machine and the characteristics of the geological conditions were evaluated. Based on the stress analysis and friction energy, a prediction model was proposed. The proposed model was applied to two field case studies: pertaining to uniform and mixed-face ground conditions, for which the empirical coefficient k for energy transfer was also determined. The preliminary results from this research indicated that the proposed model was valid for both homogeneous and heterogeneous ground conditions. Further case studies provided by co-operators are expected to improve the effectiveness of the proposed model.

Radial vibration analysis of heterogeneous and non-uniform disks via complementary functions method

Free vibration analysis of heterogeneous (functionally graded) and non-uniform (variable thickness) disks using plane elasticity results in a two-point boundary value problem. Spatially varying mechanical and thickness properties yield variable coefficient governing differential equations where obtaining closed-form solutions are not possible except for certain simple grading and thickness functions. This article uses complementary functions method as a novel approach to determine natural frequencies of functionally graded non-uniform disks. The validation and observation of converges are done using analytical and ANSYS results for a simple power law model uniform disk. The proposed solution method can be applied for disks with any continuous thickness and material grading functions.

Stress and deformation of rocket gas turbine disc under different loads using finite element modelling

Gas turbine discs have numerous applications in the aerospace industry, such as in liquid rocket engines. In this study, the stresses and deformations of a turbine disc were studied. The goal was to highlight the stress and deformation distribution to assist in the design of a disc as well as to demonstrate the importance of using finite element (FE) analysis in simulating an actual design case. Then, to present the real model, a two-dimensional (2D) axisymmetric model for a non-uniform disc was analysed using FE analysis. The stresses and deformations developed as a result of the disc operating conditions at high rotational speeds and thermal gradients were evaluated using two types of heat transfer modes—conduction and convection, taking into consideration the material behaviour at elevated temperatures. The FE model revealed that the weight of the disc should be reduced optimally by using a non-uniform thickness because this results in a huge increase in the applied stresses. The greatest stresses in the disc result from the thermal load caused by conduction, and they are located at the centre of the disc. In addition, an analytical method was used to evaluate and predict the stresses along the disc, and it gave a good estimate of the stress values compared to the FE model. Based on this estimate, a parametric study was conducted for a range of rotational velocities under high temperature loads for a series of disc radii. Finally, it was found that this method can be used for the preliminary design of different turbines.

DISK-SATELLITE INTERACTION IN DISKS WITH DENSITY GAPS

Gravitational coupling between a gaseous disk and an orbiting perturber leads to angular momentum exchange between them which can result in gap opening by planets in protoplanetary disks and clearing of gas by binary supermassive black holes (SMBHs) embedded in accretion disks. Understanding the co-evolution of the disk and the orbit of the perturber in these circumstances requires knowledge of the spatial distribution of the torque exerted by the latter on a highly nonuniform disk. Here we explore disk-satellite interaction in disks with gaps in linear approximation both in Fourier and in physical space, explicitly incorporating the disk non-uniformity in the fluid equations. Density gradients strongly displace the positions of Lindblad resonances in the disk (which often occur at multiple locations), and the waveforms of modes excited close to the gap edge get modified compared to the uniform disk case. The spatial distribution of the excitation torque density is found to be quite different from the existing prescriptions: most of the torque is exerted in a rather narrow region near the gap edge where Lindblad resonances accumulate, followed by an exponential fall-off with the distance from the perturber. Despite these differences, for a given gap profile the full integrated torque exerted on the disk agrees with the conventional uniform disk theory prediction at the level of ~10%. The nonlinearity of the density wave excited by the perturber is shown to decrease as the wave travels out of the gap, slowing down its nonlinear evolution and damping. Our results suggest that gap opening in protoplanetary disks and gas clearing around SMBH binaries can be more efficient than the existing theories predict. They pave the way for self-consistent calculations of the gap structure and the orbital evolution of the perturber using accurate prescription for the torque density behavior.

New methods in potential theory

A theory of equigravitating bodies by which external force fields of volumetric axially symmetric figures can be represented by unitary integrals is developed. This theory is being developed in three directions. The first is connected with the proof of the existence of equigravitating line segments. Such line segments can have both real and imaginary distributions of density; however, the mass and external potential remain real values. The ends of line segments coincide with special points (these are cusp points on the surfaces or special points of the analytical continuation of the external potential inside the body). At two special points, the body has only one line equigravitating segment, otherwise the line segments are compound or form equigravitating “skeletons.” At the isolated special points, external gravitational fields can be presented by a set of line segments and mass points. The second direction is based on a representation of the external gravitational field of volumetric axially symmetric figures with an equator plane by means of potentials of flat round disks. Such disks are obtained on the line segments with symmetric density distributions. The return is always true: for homogeneous or any nonuniform round disk, it is possible to find an equigravitating line segment. It manages to construct chains of “spheroid-disk-line segment” equigravitating bodies. The third direction of this theory is connected with the development and expansion on the scope of the method of confocal transformations. This method is modified and applied not only to continuous homogeneous ellipsoids, but also to non-uniform stratified ellipsoids with a stratification of the general type, as well as to homogeneous and nonuniform shells. Any elementary or thick ellipsoidal shells (and continuous nonuniform stratified ellipsoids) connected by special confocal transformations equigravitate each other.

Thermal effects on film development during spin coating

This study is an extended version of a previous analysis of thermal effects on the free-surface liquid film flow on a flat, heated rotating disk [A. Kitamura, “Thermal effects of liquid film flow during spin coating,” Phys. Fluids 13, 2788 (2001)]. The assumption of a constant disk temperature is extended to a nonuniform disk temperature, and the restriction on small radial distance used in the previous analysis is removed. The evolution equation for the transient film thickness is obtained and solved by the method of characteristics [B. S. Dandapat, P. Daripa, and P. C. Ray, “Asymptotic study of film thinning process on a spinning annular disk,” J. Appl. Phys. 94, 4144 (2003)]. The effect of both thermocapillary forces and variable viscosity on the flow is revealed. A physical explanation is provided to justify the results.

Approximation Algorithms for the Mobile Piercing Set Problem with Applications to Clustering in Ad-Hoc Networks

The main contributions of this paper are two-fold. First, we present a simple, general framework for obtaining efficient constant-factor approximation algorithms for the mobile piercing set (MPS) problem on unit-disks for standard metrics in fixed dimension vector spaces. More specifically, we provide low constant approximations for L1 and L∞ norms on a d-dimensional space, for any fixed d > 0, and for the L2 norm on two- and three-dimensional spaces. Our framework provides a family of fully-distributed and decentralized algorithms, which adapt (asymptotically) optimally to the mobility of disks, at the expense of a low degradation on the best known approximation factors of the respective centralized algorithms: Our algorithms take O(1) time to update the piercing set maintained, per movement of a disk. We also present a family of fully-distributed algorithms for the MPS problem which either match or improve the best known approximation bounds of centralized algorithms for the respective norms and space dimensions.Second, we show how the proposed algorithms can be directly applied to provide theoretical performance analyses for two popular 1-hop clustering algorithms in ad-hoc networks: the lowest-id algorithm and the Least Cluster Change (LCC) algorithm. More specifically, we formally prove that the LCC algorithm adapts in constant time to the mobility of the network nodes, and minimizes (up to low constant factors) the number of 1-hop clusters maintained. While there is a vast literature on simulation results for the LCC and the lowest-id algorithms, these had not been formally analyzed prior to this work.We also present an O(log n)-approximation algorithm for the mobile piercing set problem for nonuniform disks (i.e., disks that may have different radii), with constant update time.

Planetesimal Disk Evolution Driven by Planetesimal-Planetesimal Gravitational Scattering

We investigate the process of inhomogeneous planetesimal disk evolution caused by planetesimal-planetesimal gravitational scattering. We develop a rather general approach based on kinetic theory that self-consistently describes the evolution in time and space of both the disk's surface density and its kinematic properties—dispersions of eccentricity and inclination. The gravitational scattering of planetesimals is assumed to be in the dispersion-dominated regime, which considerably simplifies the analytical treatment. The resultant equations are of the advection-diffusion type. Distance-dependent scattering coefficients entering these equations are calculated analytically under the assumption of two-body scattering to leading order in the Coulomb logarithm. They are essentially nonlocal in nature. Our approach allows one to explore the dynamics of nonuniform planetesimal disks with arbitrary mass and random-velocity distributions. It can also naturally include other physical mechanisms that are important for the evolution of such disks—gas drag, migration, and so on.

Variability of the H2O maser emission in S255

The paper reports the results of observations of the H2O maser in S255 carried out in 1982–1985 and 1990–2000 on the 22-meter telescope of the Pushchino Radio Astronomy Observatory. The H2O maser emission extends from −2 to 14 km/s and is mainly concentrated in three radial-velocity intervals. The velocity of the central group of emission features coincides with that of the molecular cloud, while the two lateral groups (blueshifted and redshifted) are positioned in the spectrum more or less symmetrically relative to the central feature. During the monitoring of S255, two phenomena were observed. First, the integrated flux of the H2O maser emission varied in a cyclic manner with a period of two to four years; this may be connected with activity of the protostar. Second, the fluxes of emission features (or groups of features) were anticorrelated. The emission of the three groups of features noted above dominated in succession. In some time intervals, a triplet spectral structure with anticorrelation between the fluxes of the lateral components and of the central and lateral components was observed. The flux anticorrelation between groups of features and individual features could be due to competition between spatial emission pumping modes in a nonuniform Keplerian disk.

Influence of Nonuniformity of ZnO Varistors on Their Energy Absorption Capability

A simple thermo-mechanical model is applied to evaluate the influence of the nonuniformity of ZnO varistor disks used in surge arresters on their energy handling capability. Puncture is the dominating failure mode for slightly nonuniform disks, but cracking becomes more likely as the degree of nonuniformities increases. It is shown that minimization of the chance of a failure of varistor disks at high-current pulses can be achieved by adjusting their resistivity in the upturn region of the I-V characteristic. Simulation of the behavior of varistor disks under high-current 4/10 /spl mu/s pulses required by the ANSI standard tests shows that these tests provide very little information about the actual energy handling capability of the disks. This conclusion suggests that alternate test methods should be developed and included in the relevant standards.

Influence of nonuniformity of ZnO varistors on their energy absorption capability

A simple thermo-mechanical model is applied to evaluate the influence of the nonuniformity of ZnO varistor disks used in surge arresters on their energy handling capability. Puncture is the dominating failure mode for slightly nonuniform disks, but cracking becomes more likely as the degree of nonuniformities increases. It is shown that minimization of the chance of a failure of varistor disks at high-current pulses can be achieved by adjusting their resistivity in the upturn region of the I-V characteristic. Simulation of the behavior of varistor disks under high-current 4/10 /spl mu/s pulses required by the ANSI standard tests shows that these tests provide very little information about the actual energy handling capability of the disks. This conclusion suggests that alternate test methods should be developed and included in the relevant standards.

Ultraviolet and Optical Spectroscopy of AL Comae 1 Year after Superoutburst

We present Hubble Space Telescope (HST) ultraviolet spectra of AL Com obtained with the Faint Object Spectrograph (FOS) during four epochs 10-14 months following its 1995 April superoutburst. During our 1996 observations, the continuum fluxes underwent a slow decline of 20%, while the spectrum showed Lyα and Si II absorption features indicative of a 20,000 K white dwarf. The cooling sequence in AL Com is found to be about half as long as that of WZ Sge. This timescale is what is predicted for an outburst that was half the duration of WZ Sge, if shear mixing and angular momentum result in nonspherical accretion into an equatorial belt. Our longest data set (1996 June) showed spectral line variations on the orbital period with C IV in emission for about one-third of the orbit but revealed no orbital variability in the continuum. Ground-based optical spectra obtained close in time to our February HST data also show stronger line emission for one-third of an orbit and highly variable broad absorption from the secondary star. The spectral variations may be due to the changing visibility of a nonuniform disk or of a secondary star irradiated by the hot white dwarf.

Viscosity and mass transport in nonuniform Keplerian disks

A new quantitative formalism describing the dynamics of a Keplerian particulate disk, based on a heuristic description of viscous transport, permits study of rings with a wide range of ensemble and individual particle properties. Here the formalism is developed and applied to the case of a ring with a radial gradient in optical thickness. A steady-state solution for the velocity distribution directly gives the radial mass transport, as well as the viscosity. The formula for viscosity is identical to that derived a decade earlier by Goldreich and Tremaine for a uniform disk, thus validating the assumption by various workers that it could be applied to nonuniform disks, for example in consideration of ringlet instabilities. Our analytical method involves solving a novel form of the Krook equation by separating the distribution of collisional products in phase space into a symmetrical component and a remainder that can be approximated by delta functions. Unlike most past approaches, a Gaussian form for the solution is not assumed. In the case described here, the model is simplified in common with past work (e.g., small, uniform particles and Krook-type treatment of collisions), but the general approach is extendable to less artificially restricted cases.