Investigation of helix-shaped and transverse crack propagation in rotor shafts based on disk shrunk technology

It is known from international feedback that the rotor shafts of the turbo-generators with disk shrunk technology may have transverse cracks located near the keys which maintain the bond between the core of the shaft and the surrounding disks in case of over speed. It was understood that the cracks were initiated by fretting between the keys and the shaft and that they propagated due to a fatigue mechanism generated by the rotational flexion of the shafts under gravity. The destructive observation now correlated to the service history of the shaft shows different mixed modes propagation phases and a stopped circumferential crack evolution during the last months of service of the shaft. Mechanical studies based on the determination of the stress intensity factors provide the evolution of the stress intensity factors during the crack propagation. They give access to information not available otherwise to explain the observed crack profiles. Finally, experimental investigations are needed to obtain the kinetics as a function of the stress intensity factors. The information provided is helpful in determining the possible crack profiles to be detected by the most suitable vibratory surveillance systems before failure in service of the shaft line.     

Minimizing ordered weighted averaging of rational functions with applications to continuous location

This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are, in general, neither rational functions nor the supremum of rational functions so current results available for the minimization of rational functions cannot be applied to handle these problems. We prove that the problem can be transformed into a new problem embedded in a higher dimensional space where it admits a convenient polynomial optimization representation. This reformulation allows a hierarchy of SDP relaxations that approximates, up to any degree of accuracy, the optimal value of those problems. We apply this general framework to a broad family of continuous location problems showing that some difficult problems (convex and non-convex) that up to date could only be solved on the plane and with Euclidean distance can be reasonably solved with different _?p-norms${?}_p\mathrm{-}\mathrm{norms}$ in finite dimensional spaces. We illustrate this methodology with some extensive computational results on constrained and unconstrained location problems.     

Natural Convection in a Vertical Rectangular Cavity Filled with a Non-Newtonian Power Law Fluid and Subjected to a Horizontal Temperature Gradient

A study of natural convection, in a vertical rectangular cavity filled with a non-Newtonian fluid and subjected to uniform heat flux along the vertical side walls, is carried out numerically by solving the full governing equations. In the limit of a tall enclosure, these equations are considerably reduced by using the parallel flow approximation. Solutions for the flow and temperature fields, and the heat transfer rate, are obtained as functions of the governing parameters. Good agreement is found between the results of the two approaches for a wide range of governing parameters.     

Optimal Natural Convection Heat Transfer Improvement by Combining Periodic Heating Temperature,Cavity Inclination,and Nanofluid

Natural convection within a square inclined cavity filled with Al₂O₃–water nanofluid is investigated numerically. The temperature of the cooled surface is maintained constant, while that of the opposite surface (heating temperature) is varied sinusoidally in time. The remaining walls are considered adiabatic. The parameters governing the problem are the amplitude and the period of the variable temperature, the Rayleigh number, the inclination of the cavity, and the solid volume fraction. A substantial enhancement of heat transfer is obtained by combining the beneficial effects of the variable heating temperature (via its period and amplitude), the inclination of the cavity, and the nanoparticles fraction. In comparison with the constant heating conditions, it is found that both the variable heating temperature and the inclination of the cavity may lead to drastic changes in the flow structure and the corresponding heat transfer. The resonance phenomenon, observed for critical periods of the exciting temperature, is amplified by adding Al₂O₃ nanoparticles to the base fluid.     

Analytical and Numerical Study of Combined Effects of a Magnetic Field and an External Shear Stress on Soret Convection in a Horizontal Porous Enclosure

The fluid flow induced by combined actions of Soret effect and shear stress applied on the top horizontal free surface (the lower one being rigid) in a horizontal porous layer, under an external magnetic field, is studied analytically and numerically. The horizontal walls of the porous layer are subject to uniform heat fluxes. The porous layer is sparsely packed then the flow is governed by the Brinkman model assuming the Boussinesq approximation. The governing parameters are the thermal Rayleigh number, R_T, the Lewis number, Le, the separation parameter, ?, the effective Darcy number, Da, the Hartmann number Ha, the dimensionless shear stress, τ, and the aspect ratio of the enclosure, A_r. An analytical solution is derived on the basis of the parallel flow approximation, assuming enlarge aspect ratio layer, and validated numerically using a finite-difference method. The critical Rayleigh numbers for the onset of stationary, subcritical, and oscillatory convection are determined explicitly as functions of the governing parameters for infinite layers with a zero shear stress, τ = 0. The codimension-2 point is identified and different flow behaviors are observed and discussed. The effects of the governing parameters on the fluid flow intensity and heat and mass transfer characteristics are also discussed.     

Modeling and control of photovoltaic energy conversion connected to the grid

This paper presents modeling and control of a photovoltaic generator (PVG) connected to the grid. The parameters of the PVG have been identified in previous work (series and parallel resistance, reverse saturation current and thermal voltage) using Newton-Raphston and the gradient algorithm. The electrical energy from a PVG is transferred to the grid via two static converters (DC/DC and DC/AC). The objective of the proposed control strategy is to maximize energy captured from the PVG. The adapted control law for extracting maximum power from the PVG is based on the incremental conductance algorithm. The developed algorithm has the capability of searching the maximum photovoltaic power under variable irradiation and temperature. To control the DC/AC inverter, an intelligent system based on two structures is constructed: a current source control structure and a voltage source control structure. The system has been validated by numerical simulation using data obtained from the PVG installed in the laboratory research (INSAT, Tunisia).     

Varying Heating Effect on Mixed Convection of Nanofluids in a Vented Horizontal Cavity with Injection or Suction

The problem of mixed convection heat transfer inside a horizontal vented enclosure through the lower and upper parts, respectively, of its left and right vertical walls is studied numerically using Al₂O₃-water nanofluid as working fluid. The bottom wall is subjected to a linearly varying (increasing or decreasing) heating temperature profiles, while the other boundaries are considered thermally insulated. The fresh fluid is admitted from the bottom part of the left vertical wall by injection or by the suction imposed on the opening of the right vertical wall. Based on numerical predictions, the conjugate effect of the Reynolds number and the nanoparticle concentration on fluid flow and heat transfer characteristics is studied. The obtained results demonstrate clearly the positive role of the nanoparticles addition on the improvement of the heat transfer rate and the mean temperature within the cavity. In addition, the flow structure and the temperature distribution inside the cavity are seen to be very sensitive to the variations of the Reynolds number, the imposed external flow mode, and the heating type. Results presented show that, in general, the decreasing heating mode is more favorable to the heat transfer in comparison with the case of the increasing heating mode. The cooling efficiency is found to be more pronounced by the injection/suction mode by applying the increasing/decreasing heating type.