Compressibility effects in a turbulent annular mixing layer are studied with direct simulation. The centerline Mach number was varied from M_j = 0.2 to M_j = 3.5 which correspond to convective Mach numbers of M_c = 0.1 to M_c = 1.8. The mixing layer growth rate is suppressed by a factor of four with increasing Mach number. Analysis of the Reynolds stress transport equations shows a strong connection between suppressed growth rate and pressure-strain-rate correlation. A suppressed role of pressure is primarily responsible for this and pressure fluctuations are found to scale well with the gradient Mach number, M_g = \frac\ella \fracd\bar ud r. Mixing of a passive scalar is also studied. The mixture fraction p.d.f.\ switches from `non-marching' at low Mach number to `marching' at high Mach number and the mixing efficiency is found to increase from 0.5 to 0.67 with increasing Mach number. The scalar and axial velocity fields become highly correlated at high Mach numbers and again a suppressed role of pressure is found to be responsible for this.
[Ib.02] A gradient transport model for oceanic eddy fluxes that includes Coriolis and \beta--plane effects
L. Margolin (Los Alamos National Laboratory), A.C. Poje (Brown University), J.R. Ristorcelli (ICASE, NASA Langley)
A heuristic Lagrangian analysis for the eddy flux of a conserved scalar indicates its dependence on the Coriolis and beta parameters. Even in the case of an isotropic Reynolds stress the eddy flux exhibits anisotropic effects that are due to Coriolis and \beta--plane effects. In the mean scalar transport equation conserved scalar only the beta effect remains to contributes to the gradient transport expression. The result is an extremely simple model which clearly reproduces the well documented anisotropy of the eddy diffusion tensor. The \beta--effect prejudices fluctuating particle displacements resulting in zonal advection terms in the mean scalar evolution equation.
[Ib.03] Line Dispersion in Homogenous Turbulence
Eric van Doorn, K.R. Sreenivasan (Yale University)
To gain insight into the turbulent mixing processes at small scales, we study the time evolution of an initially regular passive scalar pattern in three-dimensional homegeneous turbulence. We generate turbulence (R_\lambda \leq 100) by towing a grid (mesh size M=1.27cm, solidity \sigma=0.44) down a 120 cm tall tank of cross-section 30cm\times 30cm containing water. The initial pattern consists of a vertical line of highly concentrated KMnO_4 solution with an approximate initial width w=0.5 mm, and is formed by dropping a small crystal of the dye in the tank after the grid has passed. Using back lighting and a high resolution digital camera, we resolve the integrated concentration field at scales ranging from 40\mu m to 40 mm. We present data on the probability density functions (pdf) of both the concentration and concentration gradient fields. In some range, the pdf for the concentration falls off exponentially and the exponent decreases as the turbulence decays. The concentration gradient along the vertical direction, as well as the concentration gradient along the projected line of highest concentration have approximately exponential pdfs.
[Ib.04] Lagrangian statistics of passive scalars in turbulent mixing.
P.K. Yeung (Georgia Tech)
The development of stochastic mixing models aimed at predicting the evolution of passive scalar fluctuations following the fluid in turbulent flow remains a significant challenge in the probability density function modeling approach, which is otherwise very attractive for use in reacting flows. In this work we study the statistical properties of Lagrangian scalar time series extracted (perhaps for the first time) from direct numerical simulations (DNS). For the case of isotropic turbulence with uniform mean scalar gradients, the scalar time series is found to behave as a process with stationary increments. The autocorrelation of the scalar fluctuation has a time scale larger than that of the fluid velocity. The use of the new DNS data for model testing and development is currently being investigated. As an example, data comparisons show that a standard IEM (Interaction by Exchange with the Mean) model is capable of predicting scalar variances, but performs poorly when predictions of joint statistics of multiple scalars of different molecular diffusivities (as in differential diffusion) are required. Of special interest for Markovian models are the first few moments of the Lagrangian scalar increment conditioned upon the current scalar value.
[Ib.05] Coherent Sturctures and Conditional Statistics in Inhomogeneous Turbulent Mixing
J.E. Wesfreid (ESPCI), G. Stolovitzky (The Rockefeller University), J.L. Aider, E. Gaudin (ESPCI)
We study the statistics of a passive scalar mixed by a turbulent flow that contains coherent structures. The structures under consideration are longitudinal vortices which arise from a centrifugal (Görtler) instability at the concave wall of a curved channel. These structures entrain the passive scalar in such a way that its one-point probability density function (pdf) has a non-standard shape that can be explained as a superposition of a background Gaussian mixing on the one hand, and the action of the Görtler vortices on the other. We propose a ``mean field'' approach to predict this pdf. This study constitutes the first experimental example for which the conditional expectation of the second temporal derivative of the concentration of a passive scalar given the concentration deviates from a linear behavior. Our approach is applicable to a wider class of systems.
[Ib.06] Wavelet Analysis of Tropospheric Thermal Fluctuations and Thermal Dissipation
L.F. Rossi (), G. Kaiser (University of Massachusetts Lowell)
The US Air Force and associated Phillips Laboratories have made high-resolution measurements of thermal fluctuations in the atmosphere. Using orthogonal wavelet expansions, we analyze the spectra and structure functions associated with thermal fluctuations as well as thermal dissipation in the stratosphere and troposphere. Applying minimal assumptions about the nature of the underlying turbulent flow, we segment the data into stationary regions of uniform thermal dissipation and recover Kolmogorov statistics in these regions. As a stricter diagnostic, we find that we can recover higher order structure functions. Most importantly, we find that thermal dissipation can provide a means of determining integral scales and calculating spectra or structure functions when intervals are smaller than the associated integral scales. Using wavelet averages, we see that a single atmospheric layer does not have one set of turbulent statistics punctuated by intermittent bursts, but rather has several regions each with its own distinct turbulent statistics in agreement with Kolmogov's universal equilibrium.
[Ib.07] Measurements of the Three-Dimensional Scalar Gradient in Gas-Phase Planar Turbulent Jets
L.K. Su, N.T. Clemens (University of Texas at Austin)
Simultaneous, planar Rayleigh scattering and laser-induced fluorescence yields three-dimensional scalar gradient vector information in a gas-phase, planar turbulent jet. The jet fluid is propane, seeded with acetone for fluorescence. The measurement region extends into the far-field of the jet, with outer-scale Reynolds numbers in excess of 6000. The strain-limited molecular mixing scale is resolved in the three spatial dimensions. The nature of these measurements allows investigation of the structure of the three-dimensional scalar gradient field in low Schmidt number molecular mixing. Application of the results to reacting flows is also discussed. (Supported by NSF.)
[Ib.08] Asymmetric mixing and non-Gaussian statistics of passive scalars in vortices in shear
Diego del-Castillo-Negrete (Scripps Institution of Oceanography, University of California San Diego)
We study passive scalar transport in vortices in shear layers, and jets. Surrounding the vortices there is a stochastic layer where the scalar exhibits Lagrangian turbulence, and alternates randomly between being trapped in the vortices, and moving following the shear flow. Transport is asymmetric: mixing between the vortices and the up-stream flow is different from mixing between the vortices and the down-stream flow. We present two transport models: a streamfunction model based on the potential vorticity equation, and a discrete map model based on the Melnikov function analysis. The passive scalar statistics is non-Gaussian: there is anomalous advection, anomalous (i.e. non-Brownian) diffusion, and the passive scalar probability density function (PDF) relaxes to a self-similar, asymmetric distribution with broad tails. We study the dependence of the skewness and the flatness of the passive scalar PDF on the properties of flow. The PDFs of the duration of flight (motion following the shear flow) events exhibit algebraic scaling with divergent second order moments, and correspond to Lévy flights. The results are compared with experiments in a rotating flow.
[Ib.09] Statistics of fluid particle-pair dispersion in homogeneous turbulent shear flow.
Peiqing Shen, P.K. Yeung (Georgia Tech.)
The dispersion of Lagrangian fluid particle pairs in homogeneous turbulent shear flow is studied by direct numerical simulation using 256\times 128^2 grid points. The effects of both magnitude and orientation of the initial separation vector on two-particle statistics, such as mean-squared relative dispersion and particle-pair velocity correlations, have been examined separately with emphasis on anisotropic behavior due to mean shear. Relative dispersion is found to be most effective in the streamwise direction, especially for particle pairs with initial separation vector in the direction of the mean velocity gradient; similarly the one-time, two-particle velocity correlation is strongest in the streamwise component. We also investigate the behavior of two-time, two-particle velocity correlations (in a tensor form as required by anisotropy), which can be used to compute compute particle-pair dispersion for modeling purposes. Results at different non-dimensional shear rates (comparing shear and turbulence time scales) will be shown.
[Ib.10] Jet Mixing, Verification of CFD with Full-field Velocity Vector Measurements
Yang Zhao (), Robert Brodkey (Chemical Engineering, The Ohio State University), David Unger (), Fernando Muzzio (Chemical Engineering, Rutgers University)
Full-field, time-resolved, velocity vector information was obtained for an opposing jet reactor configuration in which the two jets are along a diameter of a cylinder. The experimental velocities were measured by using stereoscopic particle tracking velocimetry (PTV) and the simulation was done for the same field using FLUENT. The initial conditions for the simulation were fixed by the initial measurements made. The computations were then used to predict the flow for subsequent periods of time. The comparisons are currently limited to short times after the initial conditions because time evolution was not incorporated into the FLUENT computations. In addition, long time averages were obtained and are compared with the same information from the simulations. The results are for an inlet jet Reynolds number of 200, with the two opposing jets (each, 2 cm in diameter) placed 8.7 cm apart (the diameter of cylinder). Additional experimental results are available up to a jet Reynolds number of 5000.