Individual Grid Elements Research Articles

Conflict defined by global gestalt can modulate binocular rivalry suppression.

Binocular rivalry suppression is thought to necessarily require local interocular conflict: the presence of incompatible image elements, such as orthogonal contours, in retinally corresponding regions of two monocular displays. Whether suppression can also be driven by conflict at the level of spatially nonlocal surface or object representations is unclear. Here, we kept local contour conflict constant while varying global conflict, defined by the gestalt formed by the two monocular displays. Specifically, each eye was presented with a grid of image elements (crosses or plusses), placed such that the two eyes’ individual grid elements did not directly overlap but the grids as a whole did. In a “shared motion” condition, all elements moved in unison, inviting a gestalt made up of all elements across both eyes; in a “different motions” condition, the elements’ trajectories differed between eyes, inviting a gestalt of two overlapping surfaces, each associated with one eye. Perceptual disappearances of image elements occurred more readily in the different motions condition, an observation that could not be explained by any between-condition differences in local contour conflict. In a second experiment, we furthermore established that, whereas perceptual disappearances in the shared motion condition tended to involve a single element at a time, in the different motions condition, multiple elements belonging to the same gestalt often disappeared together. These findings indicate that, even though binocular rivalry may critically rely on inhibition due to locally incompatible image elements, this inhibition also depends on the global gestalt to which these elements contribute.

Increasing the Resilience of Cyber Physical Systems in Smart Grid Environments using Dynamic Cells

Resilience is an important system property that relies on the ability of a system to automatically recover from a degraded state so as to continue providing its services. Resilient systems have the means of detecting faults and failures with the added capability of automatically restoring their normal operations. Mastering resilience in the domain of Cyber-Physical Systems is challenging due to the interdependence of hybrid hardware and software components, along with physical limitations, laws, regulations and standards, among others. In order to overcome these challenges, this paper presents a modeling approach, based on the concept of Dynamic Cells, tailored to the management of Smart Grids. Additionally, a heuristic algorithm that works on top of the proposed modeling approach, to find resilient configurations, has been defined and implemented. More specifically, the model supports a flexible representation of Smart Grids and the algorithm is able to manage, at different abstraction levels, the resource consumption of individual grid elements on the presence of failures and faults. Finally, the proposal is evaluated in a test scenario where the effectiveness of such approach, when dealing with complex scenarios where adequate solutions are difficult to find, is shown.

OPEN GRID BRIDGE NOISE FROM GRID AND TIRE VIBRATIONS

The noise generated during the passage of vehicles on open grid bridge decks has a strong tonal component, which can be a source of annoyance to nearby residents. Potential sources of noise are the vibrations of the grid and the vibrations of the tire. In this paper, the relative contributions from the grid and the tire are investigated by using analytic modelling and field and laboratory measurements. It is shown that the contribution to the overall noise level measured at the curb from the vibrations of the grid is small compared to that from the vibrations of the tire. This is attributed to the fact that the grid has a poor acoustic radiation efficiency because of the large percentage of open area, and the individual grid elements are also very inefficient acoustic radiators in the frequency range of interest. Based on an estimate of the interaction force between the tire and the grid, the radiated noise from the tire alone accounts for the field measured noise level at the curb. To verify that the tire is the dominant source of noise, sound pressure level measurements were performed on a simulated track with the contribution from the grid vibrations removed. The measured sound pressure levels were similar to those measured at the curb. The significance of this result is that mitigation procedures that only reduce the vibration of the grid will not significantly reduce the overall radiated noise, and alternative mitigation procedures must be considered that attempt to reduce the excitation of the tire.

Structural vibration noise from open grid bridge decks

The contribution to the overall tonal component of the noise from the vibration of the grid section of an open grid bridge deck due to excitation by the interaction with the vehicle tires is investigated. Using vibration field measurements of the grid and laboratory measurements of the acoustic radiation efficiency, it is shown that the contribution to the overall noise level measured at the curb from the vibrations of the grid is insignificant. The main reason for this result is the poor acoustic radiation efficiency of the grid. Because of the large percentage of open area, the plate‐like modes of the grid deck have very poor radiation efficiency. Similarly, the individual grid elements, based on their size and the frequency range where the predominant excitation from the tire takes place, are also very inefficient acoustic radiators. The significance of this result is that mitigation procedures that only reduce the vibration of the grid will not significantly reduce the overall radiated noise. [Work sponsored by FDOT.]

GROUND STATE ENERGY ESTIMATION OF JELLIUM SYSTEMS BY SPATIAL GRIDDING

A numerical approach to estimate the ground state energy of jellium systems is explored. In this approach, the space occupied by the system is gridded, with individual grid elements small enough that the electron density within an element is considered constant. The energy of an element is then a function (and not functional) of its electron density in a given environment and the total energy of the system is obtained by summing the contributions from all the elements. A self-consistent field procedure to optimize the grid densities is then carried out resulting in the ground state energy of the system. The method is tested for known atomic and jellium models to show its validity. This approach shows enough flexibility to handle the irregular jellium shapes.

Analysis of forced response of detuned blade rows

A mathematical model is developed and utilized to demonstrate the enhanced forced response behavior associated with aerodynamic, structural, and combined aerodynamic-structural detuning of a loaded rotor operating in an incompressible flow field. The unsteady aerodynamic gust response and oscillating cascade aerodynamics are determined by developing both a complete first-order unsteady aerodynamic analysis and a locally analytical solution in individual grid elements of a body fitted computational grid. The aerodynamic detuning is accomplished by means of alternate circumferential airfoil spacing, with alternate blade structural detuning also considered. The beneficial forced response effects of these detuning techniques are then demonstrated by applying this model to various detuned rotor configurations.

Analysis of the viscous aerodynamics of a thin airfoil cascade by a locally analytic method

A mathematical model is developed to analyze the steady viscous aerodynamics of a cascade of thin airfoils in an incompressible laminar flow. Solutions for the flow field, described by the nonlinear Navier-Stokes equations, are obtained by developing a locally analytical method. In this technique, the discrete algebraic equations which represent the flow field equations are obtained from analytical solutions in individual grid elements, accomplished by locally linearizing the convective terms. Analytical solutions are then developed by applying these solutions to individual grid elements. The ability of the steady flow model and locally analytical solution to predict flow development, separation, and reattachment at moderate values of the Reynolds numbers is then demonstrated.

Cascade aerodynamic gust response including steady loading effects

AbstractTo predict the unsteady convected gust aerodynamic response of a cascade comprised of arbitrary thick and cambered aerofoils in an incompressible, inviscid, flow field, a complete first‐order model is formulated. The flow is analysed by considering a periodic flow channel. The velocity potential is separated into steady and unsteady harmonic components, each described by a Laplace equation. The strong dependence of the unsteady aerodynamics on the steady effects of aerofoil and cascade geometry and incidence angle is manifested in the coupling of the unsteady and steady flow fields through the unsteady boundary conditions. Analytical solutions in individual grid elements of a body‐fitted computational grid are then determined, with the complete solution obtained by assembly of these local solutions. The validity and capabilities of this model and solution technique are then demonstrated by analysing the steady and unsteady aerodynamics of both theoretical and experimental cascade configurations.

Viscous aerodynamic analysis of an oscillating flat-plate airfoil

CONSIDERABLE progress has been made in the prediction of the unsteady aerodynamics of oscillating airfoils. These analyses are typically limited to inviscid potential flows, with the unsteady flow assumed to be a small perturbation to the mean flow and the Kutta condition imposed. By considering the airfoils to be zero-thickness flat plates at zero mean incidence, the steady and unsteady flowfields are uncoupled, with the steady flow being uniform and parallel. In this paper, an analysis is developed that models the unsteady aerodynamics of an harmonically oscillating flatplate airfoil, including the effects of mean flow incidence angle, in an incompressible laminar flow at moderate values of the Reynolds number. The unsteady viscous flow is assumed to be a small perturbation to the steady viscous flowfield. The nonuniform and nonlinear steady flowfield is described by the Navier-Stokes equations and is independent of the unsteady flow. The small-perturbation unsteady viscous flow is described by a system of linear partial differential equations that are coupled to the steady flowfield, thereby modeling the strong dependence of the unsteady aerodynamics on the steady flow. Solutions for both the steady and unsteady viscous flowfields are obtained by a locally analytical method in which the discrete algebraic equations representing the flowfield equations are obtained from analytical solutions in individual local grid elements. The locally analytical method for steady two-dimensional fluid flow and heat-transfer problems was initially developed by Chen et al. 1*2 They have shown that it has several advantages over finite-difference and finite-element methods, including being less dependent on grid size, with the system of algebraic equations relatively stable. Also, since the solution is analytical, it is differentiable and is a continuous function.

Prediction of oscillating thick cambered aerofoil aerodynamics by a locally analytic method

AbstractA complete first‐order model and locally analytic solution method are developed to analyse the effects of mean flow incidence and aerofoil camber and thickness on the incompressible aerodynamics of an oscillating aerofoil. This method incorporates analytic solutions, with the discrete algebraic equations which represent the differential flow field equations obtained from analytic solutions in individual grid elements. The velocity potential is separated into steady and unsteady harmonic parts, with the unsteady potential further decomposed into circulatory and non‐circulatory components. These velocity potentials are individually described by Laplace equations. The steady velocity potential is independent of the unsteady flow field. However, the unsteady flow is coupled to the steady flow field through the boundary conditions on the oscillating aerofoil. A body‐fitted computational grid is then utilized. Solutions for both the steady and the coupled unsteady flow fields are obtained by a locally analytic numerical method in which locally analytic solutions in individual grid elements are determined. The complete flow field solution is obtained by assembling these locally analytic solutions. This model and solution method are shown to accurately predict the Theodorsen oscillating flat plate classical solution. Locally analytic solutions for a series of Joukowski aerofoils demonstrate the strong coupling between the aerofoil unsteady and steady flow fields, i.e. the strong dependence of the oscillating aerofoil aerodynamics on the steady flow effects of mean flow incidence angle and aerofoil camber and thickness.

Prediction of loaded airfoil unsteady aerodynamic gust response by a locally analytical method

A complete first-order model is formulated to analyze the effects of steady loading on the incompressible unsteady aerodynamics generated by a two-dimensional gust convected with the steady mean flow past an arbitrary airfoil at finite nonzero angle of attack. A locally analytical solution is then developed in which the discrete algebraic equations which represent the flow field equations are obtained from analytical solutions in individual grid elements. The unsteady flow field is rotational and is linearized about the full potential steady flow past the airfoil. Thus, the effects of airfoil geometry and angle of attack are completely accounted for through the mean potential flow field. The steady flow is independent of the unsteady flow. However, the strong dependence of the unsteady flow on the steady effects of airfoil geometry and finite angle of attack are manifested in the unsteady boundary conditions which are coupled to the steady flow. A body-fitted computational grid is utilized. Analytical solutions to the transformed flow equations in individual grid elements are then developed, with the complete solution obtained by assembling these locally analytical solutions. This model and locally analytical solution are then applied to a series of airfoil and flow configurations. The results demonstrate that accurate predictions for the unsteady aerodynamic gust response are obtained only by including the coupled steady flow effects on the unsteady aerodynamics. Thus for cambered, or cambered and thick airfoils at zero or finite angle of attack, or a thin flat plate airfoil at a nonzero angle of attack, the model and solution developed herein accurately predict the gust response. It was also demonstrated that the classical small perturbation combined transverse and chordwise gust models yield accurate predictions only for the special case of a thin flat plate airfoil at zero angle of attack, i.e. only when the chordwise gust is zero.

Prediction of loaded airfoil unsteady aerodynamic gust response by a locally analytical method

A complete first order model is formulated to analyze the effects of steady loading on the incompressible unsteady aerodynamics generated by a two-dimensional gust convected with the steady mean flow past an arbitrary airfoil at finite nonzero angle of attack. A locally analytical solution is developed in which the discrete algebraic equations which represent the flow field equations are obtained from analytical solutions in individual grid elements. This model and locally analytical solution are then applied to a series of airfoil and flow configurations.

Locally analytic numerical method and application to viscous internal and external flows

A locally analytic numerical method is developed to predict the two-dimensional internal and external steady laminar flow of an incompressible viscous fluid. In this method, analytic solutions of locally linearized partial differential equations are incorporated into the numerical solution. This is accomplished by dividing the flow field into computational grid elements. In each individual element, the nonlinear convective terms of the Navier-Stokes equations are locally linearized, with analytic solutions then determined. The solution for the complete flow field is obtained by the assembly of these locally analytic solutions. The nonlinear character of the complete flow field is preserved as the flow is only locally linearized, i.e. independently linearized solutions are obtained in individual grid elements. This locally analytic numerical solution method is used to analyze the viscous flow in several internal and external flow configurations, with the prediction of flow development, reversal, separation, and reattachment demonstrated over a range of moderate values of the Reynolds number. In particular, three internal and one external flow configurations are investigated, with predictions obtained for entrance flow development in a straight channel, the flow through a sudden expansion, i.e. over a backward step, the flow in a diffuser, and the flow past a flat plate airfoil over a range of mean flow incidence angle values.

Locally analytical prediction of the steady inviscid incompressible flow through an airfoil cascade

A mathematical model and locally analytical solution technique are developed to analyze the steady, inviscid, incompressible, flow through a two-dimensional turbomachinery cascade comprised of cambered, thick, airfoils. The cascade is analyzed by considering a single flow channel. The boundary conditions require a zero velocity normal to the airfoil surfaces, the Kutta condition to be satisfied, and the inlet and exit flow from the cascade to be periodic. The flow field velocity potential is separated into circulatory and noncirculatory components, each individually described by a Laplace equation. A body fitted computational grid is utilized which permits grid points to be specified along the entire computational boundary and results in a smoothly spaced, nonoverlapping grid. General analytic solutions to the Laplace equations in the transformed computational plane are determined by separation of variables. Locally analytical solutions are then developed by applying these solutions to individual grid elements, i.e. the integration and separation constants are determined from the boundary conditions in each grid element. The complete flow field solution is then obtained by assembling these locally analytical solutions. The validity of this locally analytical solution and the flow modelling are then demonstrated by correlation predictions with data from various cascade experiments.