Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic-plastic-damage models. (C) 2007 Elsevier Inc. All rights reserved.

Power Factor Calculation by the Finite Element Method

The use of finite element analysis (FEA) to design electrical motors has increased significantly in the past few years due the increasingly better performance of modern computers. Even though the analytical software remains the most used tool, the FEA is widely used to refine the analysis and gives the final design to be prototyped. The power factor, a standard data of motor manufactures data sheet is important because it shows how much reactive power is consumed by the motor. This data becomes important when the motor is connected to network. However, the calculation of power factor is not an easy task. Due to the saturation phenomena the input motor current has a high level of harmonics that cannot be neglected. In this work the FEA is used to evaluate a proposed (not limitative) methodology to estimate the power factor or displacement factor of a small single-phase induction motor. Results of simulations and test are compared.

Hybrid Method to Assess Sensitive Process Interruption Costs Due to Faults in Electric Power Distribution Networks

This paper shows a new hybrid method for risk assessment regarding interruptions in sensitive processes due to faults in electric power distribution systems. This method determines indices related to long duration interruptions and short duration voltage variations (SDVV), such as voltage sags and swells in each customer supplied by the distribution network. Frequency of such occurrences and their impact on customer processes are determined for each bus and classified according to their corresponding magnitude and duration. The method is based on information regarding network configuration, system parameters and protective devices. It randomly generates a number of fault scenarios in order to assess risk areas regarding long duration interruptions and voltage sags and swells in an especially inventive way, including frequency of events according to their magnitude and duration. Based on sensitivity curves, the method determines frequency indices regarding disruption in customer processes that represent equipment malfunction and possible process interruptions due to voltage sags and swells. Such approach allows for the assessment of the annual costs associated with each one of the evaluated power quality indices.

Analysis of a Three-Phase LSPMM by Numerical Method

Line-start permanent magnet motor (LSPMM) is a very attractive alternative to replace induction motors due to its very high efficiency and constant speed operation with load variations. However, designing this kind of hybrid motor is hard work and requires a good understanding of motor behavior. The calculation of load angle is an important step in motor design and can not be neglected. This paper uses the finite element method to show a simple methodology to calculate the load angle of a three-phase LSPMM combining the dynamic and steady-state simulations. The methodology is used to analyze a three-phase LSPMM.

An Alternative Optical Method for Acoustic Resonance Detection in HID Lamps

Acoustic resonances are observed in high-pressure discharge lamps operated with ac input modulated power frequencies in the kilohertz range. This paper describes an optical resonance detection method for high-intensity discharge lamps using computer-controlled cameras and image processing software. Experimental results showing acoustic resonances in high-pressure sodium lamps are presented.

Buckling and post-buckling of extensible rods revisited: A multiple-scale solution

An exact non-linear formulation of the equilibrium of elastic prismatic rods subjected to compression and planar bending is presented, electing as primary displacement variable the cross-section rotations and taking into account the axis extensibility. Such a formulation proves to be sufficiently general to encompass any boundary condition. The evaluation of critical loads for the five classical Euler buckling cases is pursued, allowing for the assessment of the axis extensibility effect. From the quantitative viewpoint, it is seen that such an influence is negligible for very slender bars, but it dramatically increases as the slenderness ratio decreases. From the qualitative viewpoint, its effect is that there are not infinite critical loads, as foreseen by the classical inextensible theory. The method of multiple (spatial) scales is used to survey the post-buckling regime for the five classical Euler buckling cases, with remarkable success, since very small deviations were observed with respect to results obtained via numerical integration of the exact equation of equilibrium, even when loads much higher than the critical ones were considered. Although known beforehand that such classical Euler buckling cases are imperfection insensitive, the effect of load offsets were also looked at, thus showing that the formulation is sufficiently general to accommodate this sort of analysis. (c) 2008 Elsevier Ltd. All rights reserved.

The natural force density method for the shape finding of taut structures

This work presents, with the aid of the natural approach, an extension of the force density method for the initial shape finding of cable and membrane structures, which leads to the solution of a system of linear equations. This method, here called the natural force density method, preserves the linearity which characterizes the original force density method. At the same time, it overcomes the difficulties that the original procedure presents to cope with irregular triangular finite element meshes. Furthermore, if this method is applied iteratively in the lines prescribed herewith, it leads to a viable initial configuration with a uniform, isotropic plane Cauchy stress state. This means that a minimal surface for the membrane can be achieved through a succession of equilibrated configurations. Several numerical examples illustrate the simplicity and robustness of the method. (C) 2008 Elsevier B.V. All rights reserved.

Falling sheet envelope method for non-destructive testing time-dependent signals

In this work, an algorithm to compute the envelope of non-destructive testing (NDT) signals is proposed. This method allows increasing the speed and reducing the memory in extensive data processing. Also, this procedure presents advantage of preserving the data information for physical modeling applications of time-dependent measurements. The algorithm is conceived to be applied for analyze data from non-destructive testing. The comparison between different envelope methods and the proposed method, applied to Magnetic Bark Signal (MBN), is studied. (C) 2010 Elsevier Ltd. All rights reserved.

A critical reassessment of elastic unloading in sharp instrumented indentation experiments and the extraction of mechanical properties

This work examines the extraction of mechanical properties from instrumented indentation P-h(s) curves via extensive three-dimensional finite element analyses for pyramidal tips in a wide range of solids under frictional and frictionless contact conditions. Since the topography of the imprint changes with the level of pile-up or sink-in, a relationship is identified between correction factor beta in the elastic equation for the unloading indentation stage and the amount of surface deformation effects. It is shown that the presumption of a constant beta significantly affects mechanical property extractions. Consequently, a new best-fit function is found for the correlation between penetration depth ratios h(e)/h(max), h(r)/h(max) and n, circumventing the need for the assumption of a constant value for beta, made in our prior investigation [Acta Mater. 53 (2005) pp. 3545-3561]. Simulations under frictional contact conditions provide sensible boundaries for the influence of friction on both h(e)/h(max) and h(r)/h(max). Friction is essentially found to induce an overestimation in the inferred n. Instrumented indentation experiments are also performed in three archetypal metallic materials exhibiting distinctly different contact responses. Mechanical property extractions are finally demonstrated in each of these materials.

Floquet stability analysis of the flow around an oscillating cylinder

This investigative work is concerned with the flow around a circular cylinder submitted to forced transverse oscillations. The goal is to investigate how the transition to turbulence is initiated in the wake for cases with different Reynolds numbers (Re) and displacement amplitudes (A). For each Re the motion frequency is kept constant, close to the Strouhal number of the flow around a fixed cylinder at the same Re. Stability analysis of two-dimensional periodic flows around a forced-oscillating cylinder is carried out with respect to three-dimensional infinitesimal perturbations. The procedure consists of performing a Floquet type analysis of time-periodic base flows, computed using the spectral/hp element method. With the results of the Floquet calculations, considerations regarding the stability of the system are drawn, and the form of the instability at its onset is obtained. The critical Reynolds number is observed to change with the amplitude of oscillation. With respect to instabilities, unstable modes with the same symmetry as mode A of a fixed cylinder are observed; however, they present different wavelengths. Also, the instabilities observed for the oscillating cylinder are distinctively stronger in the braid shear layers. Other unstable modes similar to mode B are found. Quasi-periodic modes are observed in the 2S wake, and subharmonic mode occurrences are reported in P + S wakes. (C) 2009 Elsevier Ltd. All rights reserved.

Galerkin finite element method for incompressible thermofluid flows framed within the bond graph theory

In this paper a bond graph methodology is used to model incompressible fluid flows with viscous and thermal effects. The distinctive characteristic of these flows is the role of pressure, which does not behave as a state variable but as a function that must act in such a way that the resulting velocity field has divergence zero. Velocity and entropy per unit volume are used as independent variables for a single-phase, single-component flow. Time-dependent nodal values and interpolation functions are introduced to represent the flow field, from which nodal vectors of velocity and entropy are defined as state variables. The system for momentum and continuity equations is coincident with the one obtained by using the Galerkin method for the weak formulation of the problem in finite elements. The integral incompressibility constraint is derived based on the integral conservation of mechanical energy. The weak formulation for thermal energy equation is modeled with true bond graph elements in terms of nodal vectors of temperature and entropy rates, resulting a Petrov-Galerkin method. The resulting bond graph shows the coupling between mechanical and thermal energy domains through the viscous dissipation term. All kind of boundary conditions are handled consistently and can be represented as generalized effort or flow sources. A procedure for causality assignment is derived for the resulting graph, satisfying the Second principle of Thermodynamics. (C) 2007 Elsevier B.V. All rights reserved.

Discrete approximation to the global spectrum of the tangent operator for flow past a circular cylinder

This paper deals with the calculation of the discrete approximation to the full spectrum for the tangent operator for the stability problem of the symmetric flow past a circular cylinder. It is also concerned with the localization of the Hopf bifurcation in laminar flow past a cylinder, when the stationary solution loses stability and often becomes periodic in time. The main problem is to determine the critical Reynolds number for which a pair of eigenvalues crosses the imaginary axis. We thus present a divergence-free method, based on a decoupling of the vector of velocities in the saddle-point system from the vector of pressures, allowing the computation of eigenvalues, from which we can deduce the fundamental frequency of the time-periodic solution. The calculation showed that stability is lost through a symmetry-breaking Hopf bifurcation and that the critical Reynolds number is in agreement with the value presented in reported computations. (c) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

Exergy-based method for analyzing the composition of the electricity cost generated in gas-fired combined cycle plants

The proposed method to analyze the composition of the cost of electricity is based on the energy conversion processes and the destruction of the exergy through the several thermodynamic processes that comprise a combined cycle power plant. The method uses thermoeconomics to evaluate and allocate the cost of exergy throughout the processes, considering costs related to inputs and investment in equipment. Although the concept may be applied to any combined cycle or cogeneration plant, this work develops only the mathematical modeling for three-pressure heat recovery steam generator (HRSG) configurations and total condensation of the produced steam. It is possible to study any n x 1 plant configuration (n sets of gas turbine and HRSGs associated to one steam turbine generator and condenser) with the developed model, assuming that every train operates identically and in steady state. The presented model was conceived from a complex configuration of a real power plant, over which variations may be applied in order to adapt it to a defined configuration under study [Borelli SJS. Method for the analysis of the composition of electricity costs in combined cycle thermoelectric power plants. Master in Energy Dissertation, Interdisciplinary Program of Energy, Institute of Eletro-technical and Energy, University of Sao Paulo, Sao Paulo, Brazil, 2005 (in Portuguese)]. The variations and adaptations include, for instance, use of reheat, supplementary firing and partial load operation. It is also possible to undertake sensitivity analysis on geometrical equipment parameters. (C) 2007 Elsevier Ltd. All rights reserved.

A comparison of the critical impeller speed for solids suspension in a bench-scale and a pilot-scale mechanical flotation cell

This paper compares the critical impeller speed results for 6 L Denver and Wemco bench-scale flotation cells with findings from a study by Van der Westhuizen and Deglon [Van der Westhuizen, A.P., Deglon, D.A., 2007. Evaluation of solids suspension in a pilot-scale mechanical flotation cell: the critical impeller speed. Minerals Engineering 20,233-240; Van der Westhuizen, A.P., Deglon, D.A., 2008. Solids suspension in a pilot scale mechanical flotation cell: a critical impeller speed correlation. Minerals Engineering 21, 621-629] conducted in a 125 L Batequip flotation cell. Understanding solids suspension has become increasingly important due to dramatic increases in flotation cell sizes. The critical impeller speed is commonly used to indicate the effectiveness of solids suspension. The minerals used in this study were apatite, quartz and hematite. The critical impeller speed was found to be strongly dependent on particle size, solids density and air flow rate, with solids concentration having a lesser influence. Liquid viscosity was found to have a negligible effect. The general Zwietering-type critical impeller speed correlation developed by Van der Westhuizen and Deglon [Van der Westhuizen, A.P., Deglon, D.A., 2008. Solids suspension in a pilot scale mechanical flotation cell: a critical impeller speed correlation. Minerals Engineering 21, 621-629] was found to be applicable to all three flotation machines. The exponents for particle size, solids concentration and liquid viscosity were equivalent for all three cells. The exponent for solids density was found to be less significant than that obtained by the previous authors, and to be consistent with values reported in the general literature for stirred tanks. Finally, a new dimensionless critical impeller speed correlation is proposed where the particle size is divided by the impeller diameter. This modified equation generally predicts the experimental measurements well, with most predictions within 10% of the experimental. (C) 2009 Elsevier Ltd. All rights reserved.