Stabilité de l'écoulement de Hartmann chauffé par le basStability of the Hartmann flow heated from below

A numerical study is conducted in order to determine the influence of a vertical magnetic field, the Reynolds number and a temperature stratification on the instabilities occurring in the Hartmann flow heated from below. For $\mathit{Pr}=0.001$ and $\mathit{Ha}?2.5$, the results show that the vertical magnetic field has a stabilizing effect on both transverse oscillatory travelling waves $(T)$ and longitudinal stationary rolls $(L)$. The temperature stratification is responsible of a destabilization of the transverse $(T)$ modes and the appearance of longitudinal $(L)$ modes non-existent for the isothermal Hartmann flow. Moreover, the extent of the domains of Re where the transverse modes $(T)$ prevail is found to narrow when Ha increases and to widen when Ra increases for a given value of Ha. On the other hand, for the $(L)$ modes, the extent of the domains of Re where they prevail increases when Ha grows. To cite this article: W. Fakhfakh et al., C. R. Mecanique 334 (2006).     

A twofold strength and toughness criterion for the onset of free-edge shear delamination in angle-ply laminates

Free edge delamination in composite structures results from very localised stress fields which induce a stress concentration promoting the nucleation of an interfacial crack. To predict such a delamination onset at the free edge of a $(\pm \theta {)}_s$ laminate in traction, use is made of a strength and toughness criterion which combines a stress condition with an energy analysis. A generalised plane strain model allows to determine the stress distribution near the free edge and the energy released by the nucleation of an interfacial crack. The results show that this approach can predict the delamination onset for $((\pm 10{)}_s\text{,}(\pm 20{)}_s)$ laminates provided the interfacial fracture energy and interlaminar shear strength are known. These characteristic values can be identified with the help of traction tests performed on samples with different thicknesses.     

Scale-by-scale energy budget in a turbulent boundary layer over a rough wall

Hot-wire velocity measurements are carried out in a turbulent boundary layer over a rough wall consisting of transverse circular rods, with a ratio of 8 between the spacing (w) of two consecutive rods and the rod height (k). The pressure distribution around the roughness element is used to accurately measure the mean friction velocity ($U_{\tau }$) and the error in the origin. It is found that $U_{\tau }$ remained practically constant in the streamwise direction suggesting that the boundary layer over this surface is evolving in a self-similar manner. This is further corroborated by the similarity observed at all scales of motion, in the region $0.2⩽y/\delta ⩽0.6$, as reflected in the constancy of Reynolds number ($R_{\lambda }$) based on Taylor’s microscale and the collapse of Kolmogorov normalized velocity spectra at all wavenumbers.A scale-by-scale budget for the second-order structure function $〈{(\delta u)}^2〉$ ($\delta u=u(x+r)-u(x)$, where u is the fluctuating streamwise velocity component and r is the longitudinal separation) is carried out to investigate the energy distribution amongst different scales in the boundary layer. It is found that while the small scales are controlled by the viscosity, intermediate scales over which the transfer of energy (or $〈{(\delta u)}^3〉$) is important are affected by mechanisms induced by the large-scale inhomogeneities in the flow, such as production, advection and turbulent diffusion. For example, there are non-negligible contributions from the large-scale inhomogeneity to the budget at scales of the order of $\lambda$, the Taylor microscale, in the region of the boundary layer extending from $y/\delta =0.2$ to 0.6 ($\delta$ is the boundary layer thickness).     

Estimation of aerodynamic noise generated by forced compressible round jetsEstimation du bruit d'origine aérodynamique rayonné par des jets ronds forcés compressibles

An acoustic numerical code based on Ligthill's analogy is combined with large-eddy simulations techniques in order to evaluate the noise emitted by subsonic $(M=0.7)$ and supersonic $(M=1.4)$ round jets. We show first that, for centerline Mach number $M=0.9$ and Reynolds number $\mathit{Re}=3.6\times {10}^3$, acoustic intensities compare satisfactorily with experimental data of the literature in terms of levels and directivity. Afterwards, high Reynolds number $(\mathit{Re}=3.6\times {10}^4)$ free and forced jets at Mach 0.7 and 1.4 are studied. Numerical results show that the jet noise intensity depends on the nature of the upstream mixing layer. Indeed, the subsonic jet is 4 dB quieter than the free jet when acting on this shear layer by superposing inlet varicose and flapping perturbations at preferred and first subharmonic frequency, respectively. The maximal acoustic level of the supersonic jet is, on the other hand, 3 dB lower than the free one with a flapping upstream perturbation at the second subharmonic. The results reported in this paper confirm previous works presented in the literature demonstrating that jet noise may be modified according to the inlet conditions. To cite this article: M. Maidi, C. R. Mecanique 334 (2006).