Application de l'approximation polytropique à la Simulation Numérique Directe de gaz chaudsApplication of the polytropique approximation to Direct Numerical Simulation of heated gases

As alternative to the usual assumptions of Boussinesq, we propose, for heated gases, a new approximation called polytropic approximation. With this approximation the quantities of corresponding state are related by a polytropic law of exponent χ of which we neglect the variability in space-time derivations in the equations governing the flow considered. As application, we used this new proposition to solve numerically a heated gas flow in an annular cavity of rotor-stator type. We expose here the numerical method and some results of the polytropic approximation with comparison to results of Boussinesq approximations. To cite this article: S. Benjeddou et al., C. R. Mecanique 332 (2003).     

Application de l'approximation polytropique à la turbulence statistique en moyenne de FavreApplication of the polytropic approximation to turbulence statistics using Favre averaging

The application of the polytropic approximation connecting the quantities of corresponding state, to experimental analysis, is clarified. A method of polytropic determination of the exponent χ (variable but non-fluctuating) in each point of the flow is given. This approximation makes it possible the generation of representative signals of fluctuating quantities, like pressure or density. For heated gases, the problem of measurement of the equations terms written with Favre averaging is thus almost solved. Then, measurement of χ allows the determination by the experiment of crucial terms like turbulent fluxes of mass and momentum, and presso correlation. To cite this article: C. Rey, S. Benjeddou, C. R. Mecanique 332 (2004).     

Free vibration analysis of moderately thick asymmetric piezoelectric adaptive cantilever beams using the distributed transfer function approach

A semi-analytical distributed transfer function (DTF) approach is proposed for the free-vibration analysis of moderately thick cantilever beams with a single surface-bonded piezoelectric patch. The asymmetric piezoelectric adaptive structure is decomposed into three segments; the first and third segments are bare beam parts before and after the patch, while the second segment contains the beam part with attached piezoelectric patch bonded to its upper surface. The theoretical formulation assumes first-order shear deformation kinematics and linear electric potential through the patch thickness with an electrode equipotential physical condition, and uses the extended Hamilton?s principle to derive the equations of motion and electromechanical boundary conditions. The latter, together with the continuity and equilibrium conditions at the segments interfaces, are then transformed into a first-order state space equation that is solved using the DTF approach. The electrodes of the piezoelectric patch are considered either in short-circuit (SC) or open-circuit (OC); this leads to two free-vibration problems to be solved for the corresponding SC and OC frequencies, from which the Electro-Mechanical Coupling Coefficient (EMCC) is post-treated. Four benchmarks from the open literature are simulated in order to validate the proposed approach. Very satisfactory correlations are obtained for all examples with maximum errors less thank 5 percent in all results. For future reference, an additional benchmark is proposed to assess the influence of the patch-to-composite host width ratio on the effective modal EMCC. It was found that the latter is mode-dependent (as expected) and decreases with increasing the former.     

Une alternative aux hypothèses de Boussinesq des gaz chauds : L'approximation polytropiqueAn alternative to Boussinesq hypothesis for hot gases,the polytropic approximation

A new approximation is proposed for the balance equations of heated gas flows, taking into account completely the couplings between dynamic and thermal fields, as well as compressibility, stating in a polytropic formulation the relation between the quantities of corresponding state. The polytropic exponent is the new variable that characterises the transfers; it substitutes the temperature for the pressure and the density that are physical quantities difficult to grasp. The method opens interesting prospects for the study of heated gases, for experiments, or for modelling and numerical simulation. To cite this article: C. Rey, S. Benjeddou, C. R. Mecanique 332 (2004).     

A ferroelectric and ferroelastic 3D hexahedral curvilinear finite element

An isoparametric 3D electromechanical hexahedral finite element integrating a 3D phenomenological ferroelectric and ferroelastic constitutive law for domain switching effects is proposed. The model presents two internal variables which are the ferroelectric polarization (related to the electric field) and the ferroelastic strain (related to the mechanical stress). An implicit integration technique of the constitutive equations based on the return-mapping algorithm is developed. The mechanical strain tensor and the electric field vector are expressed in a curvilinear coordinate system in order to handle the transverse isotropy behavior of ferroelectric ceramics. The hexahedral finite element is implemented into the commercial finite element code Abaqus® via the subroutine user element. Some linear (piezoelectric) and non linear (ferroelectric and ferroelastic) benchmarks are considered as validation tests.     

Effect of the coflow stream on a plane wall jet

We propose in this work to study an isothermal and a non-isothermal laminar plane wall jet emerging in a coflow steam. The numerical solution of the governing equations was performed by a finite difference method. In this work, we are interested in the study of the influence of Grashof numbers on the wall jet emerging in a medium at rest. Further, we will examine the effect of the coflow stream on the behavior of the dynamic and thermal properties of the wall jet subjected to a constant temperature. A comparison with a simple wall jet is carried out. The results show that for a buoyant wall jet, two parameters can influence the flow: the inertial and buoyancy forces. The velocity effect indicates that the potential core length increases with the velocity ratio. We are also showed that when using a momentum length scale, the normalized longitudinal maximum velocity can reach an asymptotic curve at different velocity ratios.     

Investigation of a turbulent wall jet in forced convection issuing into a directed coflow stream

In the present paper, we have studied numerically the directed coflow stream effects on mean and turbulent flow properties of a turbulent plane wall jet in forced convection emerging into a directed coflow stream. The system of equations governing the studied configuration is solved with a finite difference scheme using a staggered grid for numerical stability, not uniform in the two directions of the flow. The modified version of the first-order low Reynolds number k–? turbulence model is used and compared to existing experimental findings. It is found that predicted results are in satisfactory agreement with the experimental data and that the wall jet fluid decays faster in presence of a directed coflow stream. Results show also that the increase of coflow deviation angles causes an increase of the growth rates of the dynamic and thermal half-width of the jet and enhances the turbulent mixing. It is found that the longitudinal development of normalised forms of the jet characteristics parameters at different directed coflow velocity ratios can be reasonably well collapsed onto universal trends through the use of momentum length scale.