A Two-Time-Scale Model for Turbulent Mixing Flows Induced by Rayleigh–Taylor and Richtmyer–Meshkov Instabilities

A two-time-scale closure model for compressible flows previously developed is extended to turbulent Rayleigh-Taylor and Richtmyer-Meshkov driven flows where mixing coexists with mean pressure gradients. Two model coefficients are calibrated with the help of Canuto-Goldman's model. For several Rayleigh-Taylor configurations, it is shown that the characteristic lengths scale as t ² while the kinetic energies and spectral transfers behave as t ² and t, respectively. The computed phenomenological coefficients of Youngs' scaling law are compared with experimental data ones. Comparisons with Youngs' three-dimensional numerical simulation (The Physics of Fluids A 3 (1991) 1312) are also performed. Finally three shock tube experiments, where the Richtmyer-Meshkov instability initiates the mixing, are simulated. The mixing thickness evolution is well reproduced while the turbulence levels seem to be overestimated with such first order models. The capability of the two-time-sale model to recover available data for different turbulent flows allows us to conclude to a more universal behavior in comparison with single-time-scale models. This revised version was published online in July 2006 with corrections to the Cover Date.     

Subgrid-modelling in LES of compressible flow

Subgrid-models for Large Eddy Simulation (LES) of compressible turbulent flow are tested for the three-dimensional mixing layer. For the turbulent stress tensor the recently developed dynamic mixed model yields reasonable results.A priori estimates of the subgrid-terms in the filtered energy equation show that the usually neglected pressure-dilatation and turbulent dissipation rate are as large as the commonly retained pressure-velocity subgrid-term. Models for all these terms are proposed: a similarity model for the pressure-dilatation, similarity andk-dependent models for the turbulent dissipation rate and a dynamic mixed model for the pressure-velocity subgrid-term. Actual LES demonstrates that for a low Mach number all subgrid-terms in the energy equation can be neglected, while for a moderate Mach number the effect of the modelled turbulent dissipation rate is larger than the combined effect of the other modelled subgrid-terms in the filtered energy equation.     

Three-dimensional LDA measurements in the impeller region of a turbulently stirred tank

Three-dimensional, angle-resolved LDA measurements of the turbulent flow field (Re = 2.9 × 10⁴) in the vicinity of a Rushton turbine in a baffled mixing tank have been performed. For this goal, a procedure for accurate beam alignment, based on a submerged micro-mirror system, has been developed. Results on the average flow field as well as on the complete set of Reynolds stresses are presented. The anisotropy of the turbulence has been characterized by the invariants of the anisotropy tensor. The trailing vortex structure, which is characteristic for the flow induced by a Rushton turbine, is demonstrated to be associated with strong, anisotropic turbulent activity. Received: 14 September 1998/Accepted: 22 February 1999     

Planar measurements of the full three-dimensional scalar dissipation rate in gas-phase turbulent flows

A simultaneous planar Rayleigh scattering and planar laser-induced fluorescence (PLIF) technique is described which allows planar measurement of the full three-dimensional scalar gradient, ∇C (x, t), and scalar energy dissipation rate, χ≡D ∇C·∇C, in gas-phase turbulent flows. The conserved scalar used is the jet fluid concentration, where the jet consists of propane and seeded acetone. The propane serves as the primary Rayleigh scattering medium, while the acetone is used for fluorescence. For a given amount of available laser energy, this planar Rayleigh scattering/PLIF technique yields much higher signals levels than would, for example, a two-plane Rayleigh scattering technique. By applying the current technique to a single spatial plane, the errors incurred in measuring a spatial derivative across distinct planes are quantified. The errors are found to be well described by a random distribution, and the magnitude of these errors is found to be smaller than the magnitude of significant events in the true scalar gradient fields. Sample results for the fields of the three-dimensional scalar gradient and scalar energy dissipation in a planar turbulent jet, with outer scale Reynolds numbers between 3200 and 8400, are shown, demonstrating the applicability of these measurements to analyses of the fine scale mixing in turbulent flows. The application of these measurements to determination of the scaling properties of the dissipation rate is also discussed. Received: 3 June 1998/Accepted: 12 February 1999     

Modelling of pressure–strain correlation in compressible turbulent flow

Previous studies carried out in the early 1990s conjectured that the main compressible effects could be associated with the dilatational effects of velocity fluctuation. Later, it was shown that the main compressibility effect came from the reduced pressure-strain term due to reduced pressure fluctuations. Although better understanding of the compressible turbulence is generally achieved with the increased DNS and experimental research effort, there are still some discrepancies among these recent findings. Analysis of the DNS and experimental data suggests that some of the discrepancies are apparent if the compressible effect is related to the turbulent Mach number, Mt. From the comparison of two classes of compressible flow, homogenous shear flow and inhomogeneous shear flow （mixing layer）, we found that the effect of compressibility on both classes of shear flow can be characterized in three categories corresponding to three regions of turbulent Mach numbers： the low-Mr, the moderate-Mr and high-Mr regions. In these three regions the effect of compressibility on the growth rate of the turbulent mixing layer thickness is rather different. A simple approach to the reduced pressure-strain effect may not necessarily reduce the mixing-layer growth rate, and may even cause an increase in the growth rate. The present work develops a new second-moment model for the compressible turbulence through the introduction of some blending functions of Mt to account for the compressibility effects on the flow. The model has been successfully applied to the compressible mixing layers.     

Investigation of a turbulent spot using multi-plane stereo particle image velocimetry

The multi-plane stereo particle image velocimetry (MSPIV) technique has been applied to an investigation of the spatial and temporal development of turbulent spots in a laminar flat-plate boundary-layer flow with a slight adverse pressure gradient. On the basis of a large number of evaluated instantaneous 3- and 2-component velocity-vector fields, measured synchronously and separated in space, or with different time separations in one or two planes, the technique enabled the determination of several statistical quantities of fluid mechanical significance. The shape and role of coherent substructures for the growth and turbulent mixing of the spot were the focus of this investigation.List of symbols x, y, z stream-, normal-, and spanwise coordinate - U freestream velocity (U=7 m/s) - Re Reynolds number, =Re_x^1/2 - u, v, w instantaneous velocity components - u, v, w fluctuation velocity components - Q-1,...,4 quadrants of Reynolds stress uv' - PDF probability density function - R_ii space–(time)-correlation function - wavelength of laser light - TE trailing edge of turbulent spot - LE leading edge of turbulent spot     

K-ε-T model of dense liquid-solid two-phase turbulent flow and its application to the pipe flow

To predict the characteristics of dense liquid-solid two-phase flow, K-ε-T model is established, in which the turbulent flow of fluid phase is described with fluid turbulent kinetic energy K_f and its dissipation rate ε_f, and the particles random motion is described with particle turbulent energy K_p and its dissipation rate ε_p and pseudothermal temperature T_p. The governing equations are also derived. With K-ε-T model, numerical study of dense liquid-solid two-phase turbulent up-flow in a pipe is performed. The calculated results are in good agreement with experimental data of Alajbegovic et al. (1994), and some flow features are captured.     

The propagation mechanism of high speed turbulent deflagrations

The propagation regimes of combustion waves in a 30 cm by 30 cm square cross–sectioned tube with an obstacle array of staggered vertical cylindrical rods (with BR=0.41 and BR=0.19) are investigated. Mixtures of hydrogen, ethylene, propane, and methane with air at ambient conditions over a range of equivalence ratios are used. In contrast to the previous results obtained in circular cross–sectioned tubes, it is found that only the quasi–detonation regime and the slow turbulent deflagration regimes are observed for ethylene–air and for propane–air. The transition from the quasi–detonation regime to the slow turbulent deflagration regime occurs at (where D is the tube “diameter” and is the detonation cell size). When , the quasi–detonation velocities that are observed are similar to those in unobstructed smooth tubes. For hydrogen–air mixtures, it is found that there is a gradual transition from the quasi–detonation regime to the high speed turbulent deflagration regime. The high speed turbulent deflagration regime is also observed for methane–air mixtures near stoichiometric composition. This regime was previously interpreted as the “choking” regime in circular tubes with orifice plate obstacles. Presently, it is proposed that the propagation mechanism of these high speed turbulent deflagrations is similar to that of Chapman–Jouguet detonations and quasi-detonations. As well, it is observed that there exists unstable flame propagation at the lean limit where . The local velocity fluctuates significantly about an averaged velocity for hydrogen–air, ethylene–air, and propane–air mixtures. Unstable flame propagation is also observed for the entire range of high speed turbulent deflagrations in methane–air mixtures. It is proposed that these fluctuations are due to quenching of the combustion front due to turbulent mixing. Quenched pockets of unburned reactants are swept downstream, and the subsequent explosion serves to overdrive the combustion front. The present study indicates that the dependence on the propagation mechanisms on obstacle geometry can be exploited to elucidate the different complex mechanisms of supersonic combustion waves. Received 5 November 2001 / Accepted 12 June 2002 / Published online 4 November 2002 Correspondence to: J. Chao (e-mail: jenny.chao@mail.mcgill.ca) An abridged version of this paper was presented at the 18th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Seattle, USA, from July 29 to August 3, 2001.     

Large Eddy Simulation of a plane impinging jet

Large Eddy Simulations of a plane turbulent impinging jet have been carried out using the dynamic Smagorinsky model. The statistical results are first validated with the measurements from the literature: mean and turbulent quantities along the jet axis and at different vertical locations are presented. This study is completed by the analysis of the wall shear stress at the impingement wall. The effect of the jet Reynolds number (3000Re13500) on the kinematic development of the jet is also discussed. To cite this article: F. Beaubert, S. Viazzo, C. R. Mecanique 330 (2002) 803–810.