Finite element analysis of low speed viscous and inviscid aerodynamic flows

A weak interaction solution algorithm was established for aerodynamic flow about an isolated airfoil. Finite element numerical methodology was applied to solution of each of differential equations governing potential flow, and viscous and turbulent boundary layer and wake flow downstream of the sharp trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. Closure for turbulence was accomplished using both first and second order models. The COMOC finite element fluid mechanics computer program was modified to solve the identified equation systems for two dimensional flows. A numerical program was completed to determine factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems. Good accuracy and convergence are demonstrated. Each solution is obtained within the identical finite element framework of COMOC

CAD-based approach for identification of elasto-static parameters of robotic manipulators

The paper presents an approach for the identification of elasto-static parameters of a robotic manipulator using the virtual experiments in a CAD environment. It is based on the numerical processing of the data extracted from the finite element analysis results, which are obtained for isolated manipulator links. This approach allows to obtain the desired stiffness matrices taking into account the complex shape of the links, couplings between rotational/translational deflections and particularities of the joints connecting adjacent links. These matrices are integral parts of the manipulator lumped stiffness model that are widely used in robotics due to its high computational efficiency. To improve the identification accuracy, recommendations for optimal settings of the virtual experiments are given, as well as relevant statistical processing techniques are proposed. Efficiency of the developed approach is confirmed by a simulation study that shows that the accuracy in evaluating the stiffness matrix elements is about 0.1%.Comment: arXiv admin note: substantial text overlap with arXiv:0909.146

Wilson's renormalization group applied to 2D lattice electrons in the presence of van Hove singularities

The weak coupling instabilities of a two dimensional Fermi system are investigated for the case of a square lattice using a Wilson renormalization group scheme to one loop order. We focus on a situation where the Fermi surface passes through two saddle points of the single particle dispersion. In the case of perfect nesting, the dominant instability is a spin density wave but d-wave superconductivity as well as charge or spin flux phases are also obtained in certain regions in the space of coupling parameters. The low energy regime in the vicinity of these instabilities can be studied analytically. Although saddle points play a major role (through their large contribution to the single particle density of states), the presence of low energy excitations along the Fermi surface rather than at isolated points is crucial and leads to an asymptotic decoupling of the various instabilities. This suggests a more mean-field like picture of these instabilities, than the one recently established by numerical studies using discretized Fermi surfaces.Comment: gzipped tar file, 31 pages including 10 figures, minor correction of misprint

Ultrasonic Technique in Determination of Grid-Generated Turbulent Flow Characteristics

The present study utilizes the ultrasonic travel-time technique to diagnose grid-generated turbulence. The statistics of the travel-time variations of ultrasonic wave propagation along a path are used to determine some metrics of the turbulence. The motivation for this work stems from the observation of substantial delta-t variation in ultrasonic measuring devices like flow meters and circulation meters. Typically, averaging can be used to extract mean values from such time series. The corollary is that the fluctuations contain information about the turbulence. Experimental data were obtained for ultrasonic wave propagation downstream of a heated grid in a wind tunnel. Such grid-generated turbulence is well characterized and features a mean flow with superimposed velocity and temperature fluctuations. The ultrasonic path could be perpendicular or oblique to the mean flow direction. Path lengths were of the order of 0.3 m and the transducers were of 100 kHz working frequency. The data acquisition and control system featured a very high-speed analog to digital conversion card that enabled excellent resolution of ultrasonic signals. Experimental data for the travel-time variance were validated using ray acoustic theory along with the Kolmogorov “2/3†law. It is demonstrated that the ultrasonic technique, together with theoretical models, provides a basis for turbulent flow diagnostics. As a result, the structure constant appearing in the Kolmogorov “2/3†law is determined based on the experimental data. The effect of turbulence on acoustic waves, in terms of the travel time, was studied for various mean velocities and for different angular orientations of the acoustic waves with respect to the mean flow. Average travel time in the presence of turbulence was shorter then in the undisturbed media. The effect of the time shift between the travel times in turbulent and undisturbed media is associated with Fermat’s principle. The travel time and log-amplitude variance of acoustic waves were investigated as functions of travel distance and mean velocity over a range of Reynolds number varying from 4000 to 20000. Experimental data are interpreted using classical ray acoustic approach and the parabolic acoustic equation approach together with the perturbation method. It was experimentally demonstrated that there is a strong dependence of the travel time on the mean velocity even in the case where the propagation of acoustic waves is perpendicular to the mean velocity. The effect of thermal fluctuations, which result in fluctuations of sound speed, was studied for two temperatures of the grid: (no grid heating) and . A semi analytical acoustic propagation model that allows determination of the spacial correlation functions of flow field is developed based on the classical flow meter equation and statistics of the travel time of acoustic waves traveling through the velocity and the thermal turbulence. The basic flow meter equation is reconsidered in order to take into account sound speed fluctuations and turbulent velocity. The resulting equation is written in terms of correlation functions of travel time, sound speed fluctuation and turbulent velocity fluctuations. Experimentally measured travel time statistics data with and without grid heating are approximated by Gaussian function and used to solve the integral flow meter equation in terms of correlation functions analytically

Ruelle-Pollicott Resonances of Stochastic Systems in Reduced State Space. Part II: Stochastic Hopf Bifurcation

The spectrum of the generator (Kolmogorov operator) of a diffusion process, referred to as the Ruelle-Pollicott (RP) spectrum, provides a detailed characterization of correlation functions and power spectra of stochastic systems via decomposition formulas in terms of RP resonances. Stochastic analysis techniques relying on the theory of Markov semigroups for the study of the RP spectrum and a rigorous reduction method is presented in Part I. This framework is here applied to study a stochastic Hopf bifurcation in view of characterizing the statistical properties of nonlinear oscillators perturbed by noise, depending on their stability. In light of the H\"ormander theorem, it is first shown that the geometry of the unperturbed limit cycle, in particular its isochrons, is essential to understand the effect of noise and the phenomenon of phase diffusion. In addition, it is shown that the spectrum has a spectral gap, even at the bifurcation point, and that correlations decay exponentially fast. Explicit small-noise expansions of the RP eigenvalues and eigenfunctions are then obtained, away from the bifurcation point, based on the knowledge of the linearized deterministic dynamics and the characteristics of the noise. These formulas allow one to understand how the interaction of the noise with the deterministic dynamics affect the decay of correlations. Numerical results complement the study of the RP spectrum at the bifurcation, revealing useful scaling laws. The analysis of the Markov semigroup for stochastic bifurcations is thus promising in providing a complementary approach to the more geometric random dynamical system approach. This approach is not limited to low-dimensional systems and the reduction method presented in part I is applied to a stochastic model relevant to climate dynamics in part III