Analytic self-similar solutions of the Oberbeck-Boussinesq equations

In this article we will present pure two-dimensional analytic solutions for the coupled non-compressible Newtoniain Navier-Stokes --- with Boussinesq approximation --- and the heat conduction equation. The system was investigated from E.N. Lorenz half a century ago with Fourier series and pioneered the way to the paradigm of chaos. We present a novel analysis of the same system where the key idea is the two-dimensional generalization of the well-known self-similar Ansatz of Barenblatt which will be interpreted in a geometrical way. The results, the pressure, temperature and velocity fields are all analytic and can be expressed with the help of the error functions. The temperature field has a strongly damped oscillating behavior which is an interesting feature.Comment: 13 pages, 4 figure

Hierarchic models for laminated plates

The research conducted in the formulation of hierarchic models for laminated plates is described. The work is an extension of the work done for laminated strips. The use of a single parameter, beta, is investigated that represents the degree to which the equilibrium equations of three dimensional elasticity are satisfied. The powers of beta identify members in the hierarchic sequence. Numerical examples that were analyzed with the proposed sequence of models are included. The results obtained for square plates with uniform loading and homogeneous boundary conditions are very encouraging. Several cross-ply and angle-ply laminates were evaluated and the results compared with those of the fully three dimensional model, computed using MSC/PROBE, and with previously reported work on laminated strips

Modéliser pour prévoir les flux de polluants émis par un dispositif contenant des déchets

Une méthodologie d'étude du comportement en scénario de valorisation de déchets minéraux solidifiés/stabilisés est présentée. La méthodologie est basée sur des outils expérimentaux (des tests paramétriques et des essais de simulation du scénario) et des modèles de comportement. Le cas d'un bassin de stockage d'eau construit avec un matériau contenant des résidus d'épuration des fumées d'incinération d'ordures ménagères est présenté. L'influence de la carbonatation du lixiviat par le CO2 atmosphérique sur le relargage des éléments de constitution du matériau est étudiée. Un modèle de comportement est mis en place pour le cas étudié; il comporte trois niveaux : 1) le matériau (chimie et diffusion), 2) le lixiviat (chimie et convection), 3) l'absorption du CO2 dans le lixiviat. Plusieurs échelles d'expérimentation (tests de laboratoire, pilote de laboratoire, pilote de terrain) ont été mises en place pour l'étude du scénario et pour la validation du modèle de comportement. Le rôle de la modélisation est mis en avant par les résultats prévisionnels des simulations. Ainsi, pour le cas étudié, la carbonatation du système diminue la concentration du plomb dans l'eau du bassin par rapport à un scénario "bassin couvert". La carbonatation ne modifie pas le relargage des éléments solubles (Na, K, Cl) et détermine la spéciation du Ca dans le bassin et à la surface du matériau.The reuse of wastes and industrial residues should only be considered if we can assure that the environmental risks related to the planned use remain acceptable. The assessment and development of methodologies and tools used in evaluating the long-term release of pollutants from materials containing wastes is an area of research that is expanding. These methods depend on not only the characteristics of the materials (especially physical structure and composition) but also contact with both water and the reactive atmosphere.The methodological standard ENV 12 920 is fundamental in the definition of the European approach, which involves the intrinsic and dynamic characterisation of the material/scenario couple in order to model the time-dependent source term. The main steps of the methodology are: 1) definition of the problem and the solution sought; 2) description of the scenario; 3) description of the waste; 4) determination of the influence of parameters on leaching behaviour; 5) modelling of leaching behaviour and 6) behavioural model validation.The reuse scenario considered in the paper was a storage tank open to the atmosphere including material leaching, carbonation and contact with air. The reservoir content was composed of a mixture of hydraulic binders and air pollution control residues from a Municipal Solid Waste Incinerator. Modelling of the source term (the reservoir material) was performed in several steps ranging from the physico-chemical characterisation of the material to the validation of the proposed model by field simulation devices.An experimental "toolbox" consisting of equilibrium dissolution tests and a dynamic leaching test was used. The experimental data supplied by the tests are the necessary input parameters for the behavioural model and give information about the release mechanisms. Identification of the main transfer mechanisms indicates that the release of soluble pollutants is the combined result of diffusional transfer of pollutants in the solution and the physico-chemical specificity of the species.A physico-chemical and transport model has been developed for the long-term prediction of environmental leaching behaviour of porous materials containing inorganic waste solidified with hydraulic binders and placed in a reuse scenario. The model includes the source term, the leachate and the gas/liquid interface. The source term considers the main chemical equilibria (a simplified system) occurring in the interstitial water of the porous material. The consideration of the base content of the material, and the experimental determination of the solubility of heavy metals in the pore water, ensure a good representation of the metal release. The source term also includes diffusion in the porous system, which is considered the main transport phenomenon.The leachate component considers chemical reactions that occur in the leachate. Many competitive dynamic processes (fluxes of mobile species coming from or penetrating into the material, gas absorption) take place in the leachate. Mass transport by convection of the leachate is also considered. Finally, the gas/liquid interface includes absorption with chemical reactions of carbon dioxide.The physico-chemical parameters (initial element content, lead solubility and diffusion coefficient) of the model with respect to the source term were estimated using laboratory leaching tests. The gas/liquid mass transfer coefficient was estimated for each pilot. The simulation results agree with the two scales of experimental data: laboratory scale (volume of reservoir 80 L) and field tests (20 m3). No scale effect was observed as the intensity of the absorption phenomenon was virtually the same.Experimental data and simulations show the main trends for the release of elements contained in the material: 1) The results obtained show that air carbonation of the leachate does not fundamentally change mass transfer mechanisms of easily soluble species (especially for alkaline metals). For these species, the use of the apparent diffusional model is a satisfactory solution for the prediction of long-term leaching behaviour. 2) The release of Ca and Pb was governed by chemical equilibria in pore water and diffusion whereas their speciation in the leachate was determined by pH and the presence of carbonate ions. 3) A carbonation front appears at the leachate/material interface and progresses into the material. 4) The target metal (lead) has a weak release (non-detectable by the analytical method used) for the study period. 5) Simulations of similar scenarios but without carbonation (a closed reservoir) predicts a higher concentration of lead than in the studied scenario.Model estimations may be enhanced by a better knowledge of the source term (particularly the mineralogy and chemistry) and by an exhaustive listing of external factors acting in each scenario. In this study, factors such as the biological activity or temperature fluctuations were not taken into account. The general methodology used is based on several indispensable steps that lead to an environmental assessment of materials containing wastes destined for reuse scenarios. The necessary tools (experimental tests and mathematical models) are however specific for categories of materials (wastes) and types of scenarios.A new generation of decision-making tools, based on modelling and simulation results, can complete, or even replace, the normalised procedures that mainly focus on laboratory experimental data

Lissajous curves with a finite sum of prime number frequencies

The Ulam spiral inspired us to calculate and present Lissajous curves where the orthogonally added functions are a finite sum of sinus and cosines functions with consecutive prime number frequencies.Comment: 5 pages and 4 figure

Apparatus for measuring the temperature of a piston in an internal combustion engine

An apparatus for measuring the temperature of a piston in an internal combustion engine. The apparatus includes a thermistor to sense the temperature of the piston and generate an electrical signal representative of that temperature, a transmission unit connected to the thermistor for receiving the electrical signal and for converting the signal to an infrared beam for transmission to a point remote from the piston, and a receiver to receive the beam and convert the beam to an electrical signal corresponding to the electrical signal generated by the thermistor. The first mentioned electrical signal is converted to a rectangular wave form prior to transmission of the infrared beam.https://digitalcommons.mtu.edu/patents/1082/thumbnail.jp

Elastic-plastic models for multi-site damage

This paper presents recent developments in advanced analysis methods for the computation of stress site damage. The method of solution is based on the p-version of the finite element method. Its implementation was designed to permit extraction of linear stress intensity factors using a superconvergent extraction method (known as the contour integral method) and evaluation of the J-integral following an elastic-plastic analysis. Coarse meshes are adequate for obtaining accurate results supported by p-convergence data. The elastic-plastic analysis is based on the deformation theory of plasticity and the von Mises yield criterion. The model problem consists of an aluminum plate with six equally spaced holes and a crack emanating from each hole. The cracks are of different sizes. The panel is subjected to a remote tensile load. Experimental results are available for the panel. The plasticity analysis provided the same limit load as the experimentally determined load. The results of elastic-plastic analysis were compared with the results of linear elastic analysis in an effort to evaluate how plastic zone sizes influence the crack growth rates. The onset of net-section yielding was determined also. The results show that crack growth rate is accelerated by the presence of adjacent damage, and the critical crack size is shorter when the effects of plasticity are taken into consideration. This work also addresses the effects of alternative stress-strain laws: The elastic-ideally-plastic material model is compared against the Ramberg-Osgood model

Microwave telemetry for sensing conditions in enclosed rotating and/or reciprocating machinery

An apparatus for measuring the pressure within the torque converter of an automatic transmission. The apparatus includes a sensor to sense the interior pressure of the torque converter and generate an electrical signal representative of that pressure. That signal is converted to microwave energy which is radiated into the interior of the torque converter housing from a microwave transmitter located within the torque converter. Receiving microwave antennae exposed to the housing interior receive the microwaves and transmit an electrical signal corresponding to the microwave energy to a remote readout external of the torque converter. The receiving antenna are preferably in the form of resonant slots in the torque converter housing and the slots have a length related to the wavelength of the generated microwaves.https://digitalcommons.mtu.edu/patents/1069/thumbnail.jp

Rotational torque measurement device

A device for measuring torque applied through a rotating member. A first torsion reference member is fixedly coupled to the rotating member at a first axial position and a second torsion reference member is fixedly coupled to the rotating member at a second axial position. A first detector detects the passage of the first torsion reference member past the first detector upon each full rotation of the rotating member and to generate a first signal upon each passage of the first torsion reference member. A second detector detects the passage of the second torsion reference member past the second detector upon each full rotation of the rotating member and to generate a second signal upon each passage of the second torsion reference member. A controller calculates a phase difference between the first signal and the second signal relative during rotation of the rotating member under a torsional load.https://digitalcommons.mtu.edu/patents/1003/thumbnail.jp