Propagation of weak shocks through a random medium

The propagation of weak shock waves (M_s = 1.007, 1.03 and 1.1) through a statistically uniform random medium has been investigated experimentally in a shock tube. The wave-from geometry, rise time and amplitude of initially plane shocks which have propagated through a random mixture of helium and refrigerant 12 are measured. The effect of shock propagation on the properties of the random medium is visualized with schlieren and shadow photography. The pressure histories of the distorted shock waves reflecting from a normal end wall are observed to be both peaked and rounded. In the rounded case the perturbed shock is found to be made up of a succession of weak, slightly curved fronts with a total effective rise time orders of magnitude greater than the classical Taylor thickness. The radius of curvature of the weakest shocks after propagating through the random medium is inferred from observations at two downstream stations to be about 7 times the integral scale of the gas inhomogeneities. It is concluded that the observed distortions of the wave fronts can best be explained in terms of random focusing and defocusing of the front by the inhomogeneities in the medium. A ray-tracing calculation has been used to interpret the experimental observations. It is found that geometrical considerations are sufficient to account for many of the effects observed on the shocks

Vorticity alignment results for the three-dimensional Euler and Navier-Stokes equations

We address the problem in Navier-Stokes isotropic turbulence of why the vorticity accumulates on thin sets such as quasi-one-dimensional tubes and quasi-two-dimensional sheets. Taking our motivation from the work of Ashurst, Kerstein, Kerr and Gibson, who observed that the vorticity vector {\boldmath\omega} aligns with the intermediate eigenvector of the strain matrix $S$, we study this problem in the context of both the three-dimensional Euler and Navier-Stokes equations using the variables \alpha = \hat{{\boldmath\xi}}\cdot S\hat{{\boldmath\xi}} and {\boldmath\chi} = \hat{{\boldmath\xi}}\times S\hat{{\boldmath\xi}} where \hat{{\boldmath\xi}} = {\boldmath\omega}/\omega. This introduces the dynamic angle $\phi (x,t) = \arctan(\frac{\chi}{\alpha})$, which lies between {\boldmath\omega} and S{\boldmath\omega}. For the Euler equations a closed set of differential equations for $\alpha$ and {\boldmath\chi} is derived in terms of the Hessian matrix of the pressure $P = \{p_{,ij}\}$. For the Navier-Stokes equations, the Burgers vortex and shear layer solutions turn out to be the Lagrangian fixed point solutions of the equivalent (\alpha,{\boldmath\chi}) equations with a corresponding angle $\phi = 0$. Under certain assumptions for more general flows it is shown that there is an attracting fixed point of the (\alpha,\bchi) equations which corresponds to positive vortex stretching and for which the cosine of the corresponding angle is close to unity. This indicates that near alignment is an attracting state of the system and is consistent with the formation of Burgers-like structures.Comment: To appear in Nonlinearity Nov. 199

Detection of Coherent Vorticity Structures using Time-Scale Resolved Acoustic Spectroscopy

We describe here an experimental technique based on the acoustic scattering phenomenon allowing the direct probing of the vorticity field in a turbulent flow. Using time-frequency distributions, recently introduced in signal analysis theory, for the analysis of the scattered acoustic signals, we show how the legibility of these signals is significantly improved (time resolved spectroscopy). The method is illustrated on data extracted from a highly turbulent jet flow : discrete vorticity events are clearly evidenced. We claim that the recourse to time-frequency distributions lead to an operational definition of coherent structures associated with phase stationarity in the time-frequency plane.Comment: 26 pages, 6 figures. Latex2e format Revised version : Added references, figures and Changed conten

Efficient prediction of broadband trailing edge noise and application to porous edge treatment

Trailing edge noise generated by turbulent flow traveling past an edge of an airfoil is one of the most essential aeroacoustic sound generation mechanisms. It is of great interest for noise problems in various areas of industrial application. First principle based CAA with short response time are needed in the industrial design process for reliable prediction of spectral differences in turbulent-boundary-layer trailing-edge noise due to design modifications. In this paper, an aeroacoustic method is studied, resting on a hybrid CFD/CAA procedure. In a first step RANS simulation provides a time-averaged solution, including the mean-flow and turbulence statistics such as length-scale, time-scale and turbulence kinetic energy. Based on these, fluctuating sound sources are then stochastically generated by the Fast Random Particle-Mesh Method to simulate in a second CAA step broadband aeroacoustic sound. From experimental findings it is well known that porous trailing edges significantly lower trailing edge noise level over a large range of frequencies reaching up to 8dB reduction. Furthermore, sound reduction depends on the porous material parameters, e.g. geometry, porosity, permeability and pore size. The paper presents first results for an extended hybrid CFD/CAA method including porous materials with prescribed parameters. To incorporate the effect of porosity, an extended formulation of the Acoustic Perturbation Equations with source terms is derived based on a reformulation of the volume averaged Navier-Stokes equations into perturbation form. Proper implementation of the Darcy and Forchheimer terms is verified for sound propagation in homogeneous and anisotropic porous medium. Sound generation is studied for a generic symmetric NACA0012 airfoil without lift to separate secondary effects of lift and camber on sound from those of the basic edge noise treatments.Comment: 37 page

Optical propagation through a homogeneous turbulent shear flow

Effects of organized turbulent structures on the propagation of an optical beam in a homogeneous shear flow were studied. A passive-scalar field in a computed turbulent shear flow is used to represent index-of-refraction fluctuations, and phase errors induced in a coherent optical beam by turbulent fluctuations are computed. The organized vortical structures produce a scalar distribution with elongated regions of intense fluctuations which have an inclination with respect to the mean flow similar to that of the characteristic hairpin eddies. It is found that r.m.s. phase error is minimized by propagating approximately normal to the inclined vortical structures. Two-point correlations of vorticity and scalar fluctuation suggest that the regions of intense scalar fluctuation are produced primarily by the hairpin eddies