An expression saying that cracks moving above the Rayleigh wave speed need negative energy seems physically impossible, and an expression requiring imaginary energy seems even worse. Once the crack speed exceeds the transverse wave speed, the expression becomes imaginary. The denominator of this expression vanishes when the crack speed v reaches the Rayleigh wave speed, and for slightly higher velocities it becomes negative. Where v is the crack speed, c l and c t are longitudinal and transverse wave speeds, respectively,, , μ is a Lamé constant, and K I, the mode I dynamic stress intensity factor, is the coefficient of a universal singularity that develops outside of cracks that run as they are pulled symmetrically in tension from above and below. This is one reason supersonic cracks in tension had been thought not to exist. Thus, while supersonic cracks are no less physical than subsonic cracks, the connection between microscopic and macroscopic behaviour must be made in a different way. Subsonic cracks are characterized by small-amplitude, high-frequency oscillations in the vertical displacement of an atom along the crack line, while supersonic cracks have large-amplitude, low-frequency oscillations. For supersonic cracks, the stress intensity factor disappears. Subsonic cracks feature displacement fields consistent with a stress intensity factor. Using our analytical methods, we examine in detail the motion of atoms around a crack tip as crack speed changes from subsonic to supersonic. Cracks that propagate faster than the Rayleigh wave speed have been thought to be forbidden in the continuum theory, but clearly exist in lattice systems. ![]() This allows quick numerical evaluation of solutions for very large systems, facilitating comparisons with continuum fracture theory. ![]() 178–188.We present the full analytical solution for steady-state in-plane crack motion in a brittle triangular lattice. (1990), Dilatation Dissipation: The Concept and Application Compressible Mixing Layers, Phys. (1970), The two-dimensional mixing layer, J. (1989), The Analysis and Modeling of Dilatational Terms in Compressible Turbulence, ICASE Report, N ° 89–79. (1990), Application of a Reynolds Stress Turbulence Model to the Compressible Shear Layer, ICASE Report, N° 90–18. (1993), Turbulence measurements in axisymmetric jets of air and helium-Part 1 and 2, J. K (1994), Compressibility Effects on Turbulence, Annual Review of Fluid Me-chanics, Vol. (1993), Three-Dimensional Velocity Field in a Compressible Mixing Layer, AIAA Journal Vol. (1994), Contribution à l’étude expérimentale de jets turbulents axisymétriques à densité variable, Thèse de Doctorat de l’Université de Marseille, juillet 1994. (1994), Couches de mélange turbulentes supersoniques, Rapport final, contrat DGA/DRET N ° 91/172, Août 1994.ĭjeridane T. This process is experimental and the keywords may be updated as the learning algorithm improves.īonnet J.P., Chambres O., Lammari M., Barre S. These keywords were added by machine and not by the authors. Then we compare it to the balance obtained in subsonic jets or mixing layers with and without density gradients. So, we decided to measure with 2D Laser Doppler Velocimetry, a preliminary turbulent kinetic energy budget in a highly compressible mixing layer (convective Mach number close to 1) with assumptions derived from the work of different authors ((Panchapakesan & Lumley, 1993), (Wygnanski & Fiedler, 1970) and (Gruber et al., 1993)). Trying to understand what the real differences are between compressible and incompressible turbulence seems to be an interesting first step to increase our knowledge. Applications of such models to mixing layer computations described qualitatively the flow but the results are not accurate enough to make these models available for practical applications (Sarkar & Balakrishnan, 1990). (1989) both proposed a model based on an extra dissipation due to dilatation to explain the observed decrease of turbulent activity in high speed flows. For example Zeman (1990) and Sarkar et al. Different authors tried to explain this fact in order to be able to take in account these effects in modelling such flows. ![]() It has been observed by many experimentalists that the turbulent intensity is decreased while increasing compressibility. Despite all these efforts it seems that, at this time, nobody knows yet what is the real mechanism which creates the compressiblity effects observed on supersonic free flows like mixing layers or jets. In particular, the supersonic mixing layer was extensively studied (see (Lele, 1994) for a review). In recent years, a lot of experimental and computational work was done to study the effect of compressibility on turbulent free flows.
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