Turbulent Free Shear Flows Research Articles

Modulation on flow field by solid particles in gas-solid two-phase turbulent free shear flows*

Abstract In order to understand the interaction between fluid and particles, a two-way coupled three-dimensional mixing layer laden with particles at a Stokes number of 5 with different mass loadings is numerically studied. The pseudospectral method is used for the flow fluid and the Lagrangian approach is used to trace particles. The concept of computational particles is introduced to vary the mass loading of particles. The momentum coupling effect introduced by a particle is approximated to the point force. The simulation results show that the coherent structures are still dominant in the mixing layer, but the flow field is modulated by particles. The addition of the particles enhances the energy of all the Fourier modes with non-zero spanwise wavenumber, and the enhancement increases with the augment of the mass loading. A higher mass loading results in a lower energy at fundamental wavenumber and streamwise subharmonic Fourier mode of the fluidin the phase of Kelvin-Helmholtz rolling up. but for large...

804 自由せん断乱流の混合遷移とコヒーレント微細渦

804 自由せん断乱流の混合遷移とコヒーレント微細渦

Modulation on flow field by solid particles in gas-solid two-phase turbulent free shear flows

Modulation on flow field by solid particles in gas-solid two-phase turbulent free shear flows

Further characterization of large-scale coherent structure signatures in a turbulent-plane mixing layer

In order to complement a previous collaborative testing of eddy structure identification methods in free turbulent shear flows, a study about the influence of the transverse location of these large-scale vortical structures on their signatures for the same referenced data base is carried out. Using vorticity-based conditional sampling, events which are located on the same transverse locations are selected and averaged. Results show that a coherent structure has its proper identity contained in its core and keeps it whatever its trajectory. In this way, only its signature in comparison with the surrounding environment changes. The comparison with vorticity-based conditional sampling without this transverse selection brings to the fore a bias on the signature of coherent structures. This result throws back into question previous conclusions about the morphology of structures and related energy transfer scenarios.

Two-way coupled bubble laden mixing layer

A discrete vortex model is used to approximate adequately large eddy features in turbulent free shear flows and the effects of two-way mass and momentum coupling on Lagrangian bubble trajectories and dispersion in such eddy structures are investigated. The number of bubbles introduced into the flow is sufficiently large enough for cumulative effects of bubbles to influence the flow but is still small enough so that bubble–bubble interactions can be neglected. It is demonstrated that for two-way coupling case, a reduction in the magnitude of the vorticity and pressure gradients around the large-scale vortex centre is observed. In addition to modification of the vortex structures, it is found that the tendency of the accumulation of bubbles becomes weaker in comparison to the one-way coupling case. In seeking quantification of the bubble dispersion, the Eulerian approach based on the bubble number fluxes at different downstream cross-sections of the mixing layer in terms of ensemble trajectory statistics and Lagrangian approach based on the bubble mean square displacement are adopted. It is observed that the ensemble average flux profiles of bubbles for two-way coupling case are farther skewed towards the high-speed stream of the shear layer in contrast to its one-way coupling case.

Simulation and Identification of Organized Structures in Flows. Edited by J. N. SORENSEN, E. J. HOPFINGER & N. AUBRY. Kluwer, 1999. 515 pp. ISBN 0 7923 56039. NLG 395 or US$237 or £104.

This book is the Proceedings of the IUTAM Symposium on ‘‘Simulation and Identification of Organised Structures in Flows,’’ held in Lyngby, Denmark, May 25‐29, 1997. The symposium was one of those specialized symposia in the field of mechanics that the International Union of Theoretical and Applied Mechanics (IUTAM) organizes every year. The IUTAM Symposia are normally reserved to invited participants, and usually provide the state-of-the-art assessment of a particular problem by leading professionals. This book is no exception. It presents a useful overview of organized structures in fluid mechanical applications. It covers a wider range of issues than did a previous Symposium on a similar topic held in October 1992 in Poitiers, France. Selected papers from that Symposium—‘‘Eddy Structure Identification in Free Turbulent Shear Flows’’—were published in a Proceedings edited by J. P. Bonnet and M. N. Glauser (1993). Information on organized structures in flows and their interactions with flow boundaries is of considerable hydraulic engineering importance. For instance, work underway at New Zealand’s National Institute of Water and Atmospheric Research (NIWA) on periphyton (attached aquatic microalgae) interactions with turbulence is revealing significant mechanisms of mass transfer in the near-bed region. Such mechanisms appear to influence periphyton growth and losses. ADV measurements of turbulence in the NIWA outdoor ecohydraulics flume (Fig. 1) show that the appearance of periphyton on a cobble bed does not change appreciably the velocity spectra above the cobble. However, its appearance reduces the total spectral energy and generates a wide spectral peak in the region below cobble tops. Most probably, this peak is formed by penetration of sweep events into that region, ‘‘filtered’’ by the periphyton tufts. Thus, organized structures may be the main mechanism responsible for the delivery of nutrients from the outer region to the biologically active near-bed layer.

Review of Coherent Structures in Turbulent Free Shear Flows and Their Possible Influence on Computational Methods

A review of selected experiments on coherent structures in turbulent shear flows is performed. Different experimental approaches (conditional averages, filtering techniques, wavelets, linear stochastic estimation and proper orthogonal decomposition, etc.) are illustrated and their links with computations (LES, DNS, SDM, etc.) is emphasized. It is particularly shown that some kind of universal behavior of the background turbulence can be retrieved from these various experimental methods.

Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate

This work uses direct numerical simulations of time evolving annular mixing layers, which correspond to the early development of round jets, to study compressibility effects on turbulence in free shear flows. Nine cases were considered with convective Mach numbers ranging from Mc = 0.1 to 1.8 and turbulence Mach numbers reaching as high as Mt = 0.8.Growth rates of the simulated mixing layers are suppressed with increasing Mach number as observed experimentally. Also in accord with experiments, the mean velocity difference across the layer is found to be inadequate for scaling most turbulence statistics. An alternative scaling based on the mean velocity difference across a typical large eddy, whose dimension is determined by two-point spatial correlations, is proposed and validated. Analysis of the budget of the streamwise component of Reynolds stress shows how the new scaling is linked to the observed growth rate suppression. Dilatational contributions to the budget of turbulent kinetic energy are found to increase rapidly with Mach number, but remain small even at Mc = 1.8 despite the fact that shocklets are found at high Mach numbers. Flow visualizations show that at low Mach numbers the mixing region is dominated by large azimuthally correlated rollers whereas at high Mach numbers the flow is dominated by small streamwise oriented structures. An acoustic timescale limitation for supersonically deforming eddies is found to be consistent with the observations and scalings and is offered as a possible explanation for the decrease in transverse lengthscale.

Prediction of turbulent free shear flow statistics using a simple stochastic model

One-dimensional turbulence, a stochastic simulation of turbulent flow evolution based on application of a mixing-length-type hypothesis to individual turbulent eddies, is used to predict transverse profiles of single-point statistics up to third order for two time-developing planar free shear flows, a mixing layer and a wake. Comparison of computed results to statistics obtained from direct numerical simulations of these flows indicates that the model, despite its simplicity, captures important features of turbulent free shear flow structure. Implications concerning the possible universality of some aspects of turbulent shear flow are discussed.

Particle dispersion in organized vortex structures within turbulent free shear flows

A discrete vortex model is used to approximate adequately large eddy features in turbulent free shear flows and the effects of such eddy structures on Lagrangian particle trajectories and particle dispersion are investigated. Two independent scaling parameters (i) the ratio of the particle's aerodynamic response time to the characteristic flow time, the Stokes number S t = ρ p d 2 p Δ U(1+ C m / γ)/18 μδ; and (ii) the ratio of inertia to gravitational forces, the Froude number Fr= ΔU/ gδ , together with the mass ratio parameter γ, have been introduced to determine the particle dynamics. The Stokes number has been modified to account for the effect of the density ratio of particles to the carrier fluid on particle dispersion. It is demonstrated that St, Fr and γ, which constitute a dominant single scaling group, can be used to characterise particle transport dynamics in turbulent free shear flows. In seeking quantification of the particle dispersion, the Eulerian approach based on the particle number fluxes at different downstream cross-sections of the mixing layer in terms of ensemble trajectory statistics and Lagrangian approach based on the particle mean square displacement are adopted. The simulations show the existence of different parameter regimes, in which the particle motion is dominated by both the large-scale vortices and gravity. At intermediate Stokes numbers, the particles acquire larger dispersion than the particles do at other ranges of the Stokes number. The particle dispersion patterns obtained are consistent with earlier experimental observations and numerical simulations ( Wen, Kamalu, Chung, Crowe & Troutt, 1992; Crowe, Chung & Troutt, 1993) that heavy particles accumulate at the periphery of the large-scale vortices and particularly near the braid stagnation points between the consecutive vortices.

The noise spectrum of isotropic turbulence

Proudman’s solution for the noise radiated from isotropic turbulence at low Mach numbers and high Reynolds numbers was reviewed by Lilley (1994) following the simulation of Sarkar and Hussaini (1993). It was suggested (Lilley, 1996) that the Lighthill–Proudman theory could be used for the prediction of the radiated acoustic power from turbulent free shear flows in the absence of shock waves. In this approximation the Lighthill ‘‘filter function’’ was used with distributions of the turbulent kinetic energy, the temperature fluctuations, and the turbulent length scale. The results were compared with experimental measurements. But the method (Lilley, 1996) was only concerned with the total acoustic power. Modifications to this theory are required for the estimation of the spectrum and directivity of the radiated sound. The frequency resolution in time-dependent RANS calculation (TRANS) is limited by the grid used. In most, the large scale structure of the turbulence is resolved and consequently the energy containing scales captured. But the high-frequency part of the spectrum is poorly defined. Present work discusses two models for the high-frequency spectral decay and some of the properties of the high-frequency spectrum in turbulent shear layers.

Linear stability analysis of turbulent mixing layers and jets in shallow water layers

Free turbulent shear flows, such as mixing layers or jets, can exist in a shallow fluid layer. Flows of these types have many hydraulic, environmental or geophysical applications. The instability characteristics of these laterally sheared flow types have been studied by means of a modified depth-averaged Orr-Sommerfeld equation that describes spatial and temporal growth of disturbances in the nominally parallel flow. Two major parameters, a bed-friction parameter and a Reynolds number control the flow behavior. In addition, the width of the flow domain relative to the sheared zone width can have secondary influences. Results are presented as stability diagrams for the separate and joint effects of viscosity and bed-friction, respectively. Comparisons with available experimental evidence are given.

Interaction of a two-phase turbulent/bubbly submerged water jet with a single-phase jet: Measurements of the enhanced hydrodynamic near-field spectrum, part II

The interaction of mutually perpendicular submerged turbulent water jets is studied from measurements of the hydrodynamic near-field pressure spectrum. One jet is a conventional single-phase, free turbulent shear flow circular jet, while the other jet is a two-phase bubbly jet of similar construction. The overlap region is located at four nozzle diameters (4D) away from each orifice. A small hydrophone located outside the overlap region on the symmetry line 45° from each jet axis (and in the far quadrant from each nozzle exit) measures the near-field pressure signature. Spectra are measured at different radial positions from the overlap region (typically 4D–10D). Very small gas bubbles are generated in the two−phase turbulent jet by pressurized N2 gas passing through a fritted disk housed in a Buchner funnel located near the nozzle entrance. Spectra are compared for different void fractions and different Reynolds numbers (based on jet diameter). Typically, volume void fractions ∼0.001 significantly amplify the flow noise coming from jet nozzles (D=0.635 cm) with nozzle exit velocities of 10 m/s. [See earlier work, J. Acoust. Soc. Am. 102, 3184(A) (1997).] [Work supported by the Naval Acad. Res. Council.]

Collaborative testing of eddy structure identification methods in free turbulent shear flows

The thrust of this paper is to validate, test and compare several Coherent Structure eduction methods utilizing the same data base. The flow chosen was that of an experimental study of a plane, incompressible, fully developed turbulent two-stream mixing layer. The mixing layer was chosen as the data base because it has been studied extensively from a coherent structures point of view. In addition, its characteristics (similarity, convection velocities, etc.) are well documented. There are also no wall effects so that comparisons between techniques are simplified. The data was collected from hot wire rakes with good spatial resolution thus allowing the contributors to apply and test different structure eduction techniques. The techniques chosen for discussion and used here have found wide utilization over the past decade, and all hold forth the promise of extensive application in the future. These include: Conditional Sampling (Vorticity-based and other methods); Wavelets; Pattern Recognition Analysis; Proper Orthogonal Decomposition; Stochastic Estimation; Topological Concept-based methods; Full Field Methods (e.g., pseudo flow visualization). All are illustrated by application to the mixing layer data base, and comparisons made between the results. This common study has shown that direct comparisons between results of several methods are now possible. Good quantitive and qualitative agreement between the different methods have been observed as well as some differences noted. As an example, the size of the averaged structures computed from the various methods compare to within 6 percent.

Mutual interaction of a two-phase turbulent/bubbly submerged water jet with a single-phase jet for the measurement of the enhanced hydrodynamic near-field pressure spectrum

The interaction of mutually perpendicular submerged turbulent water jets is studied from the measurement of the enhanced hydrodynamic near-field pressure spectrum. One jet is a conventional single-phase, free turbulent shear flow circular jet, while the other jet is a two-phase bubbly jet of similar construction. The overlap region is located at four-nozzle diameters (4D) away from each orifice. A small hydrophone located outside the overlap region (4D away from the interaction region and 45 deg from the jet axis) measures the near-field pressure spectrum. Very small gas bubbles are required for this two-phase turbulent jet. They are generated by pressurized carbonated water flowing through a thin circular nozzle plate having an array of small holes. These CO2 gas bubbles are mixed within the entrance to the tapered jet nozzle. Alternatively, bubbles are generated by pressurized N2 gas passing through a fritted disk housed in a Buchner funnel located near the nozzle entrance. Spectra are measured and compared for different void fractions and different Reynolds numbers that are based on the jet diameter.

An Adaptive Finite Element Scheme for Turbulent Free Shear Flows

This paper presents an adaptive finite element method for solving incompressible turbulent flows using the k-e model of turbulence. Solutions are obtained in primitive variables using a highly accurate quadratic finite element on unstructured grids. Turbulence is modeled using the k-e model. A projection error estimator is presented that takes into account the relative importance of the errors in velocity, pressure, turbulence variables and eddy viscosity. The methodology is verified by solving problems with known analytical solutions. The method is then applied to turbulent free shear flows and predictions are compared to experiment.

Compressibility effects and mixing enhancement in turbulent free shear flows

Computational simulations have been performed to study compressible, spatially developing turbulent free shear layers with various velocity regimes—subsonic/subsonic, supersonic/subsonic, and supersonic/supersonic— for convective Mach numbers in the range of 0.14-1.28. The numerical code used the finite volume technique and a modified Godunov's scheme. The computed results for the supersonic/subsonic case are first compared with experimental axial mean-velocity profiles, vorticity thickness, and turbulence parameters. Mixing layers with various velocity regimes are then calculated to investigate compressibility effects on the evolution of large-scale structures through the flow visualization of the vorticity field, growth rate of the vorticity thickness, and vorticity dynamics analysis. Various forcing frequencies are applied at the inflow boundary to examine mixing enhancement for free shear layers with higher convective Mach numbers. It is found for the first time that the growth rate of supersonic/supersonic free shear layers increases markedly when the forced layers move up and down with time instead of forming vortex roll-up and pairing.

Roles of pressure transport and intermittency for computation of turbulent free shear flows

A Reynolds stress model that includes the recent models of the pressure transport term and the intermittency interaction term is applied to compute various free shear flows. The test computations reveal favorable improvements by the pressure transport model near the free-stream edges of the free shear flows. Inclusion of an intermittency interaction term in the dissipation rate equation also significantly enhances the prediction capability of the Reynolds stress model. In particular, predictions of the Reynolds stresses in the high-velocity side of a plane mixing layer and in the outer layer of a plane wake are remarkably improved.

Adaptive finite element method for turbulent flow near a propeller

We present an adaptive finite element method based on remeshing to solve incompressible turbulent free shear flow near a propeller. Solutions are obtained in primitive variables using a highly accurate finite element approximation on unstructured grids. Turbulence is modeled by a mixing length formulation. Two general purpose error estimators, which take into account swirl and the variation or the eddy viscosity, are presented and applied to the turbulent wake or a propeller. The proposed adaptive scheme is robust, reliable and cost effective

DEVELOPMENT OF A REYNOLDS STRESS MODEL WITH A CROSS DIFFUSION OFκIN THEϵEQUATION

SUMMARY This study intends to improve the predictability of the existing second-order closure turbulence models without tuning the model constants. For this purpose, a Reynolds stress model with a cross diffusion of κ in the ϵ equation is derived based on the physically more realistic assumption that small turbulent eddies can be anisotropic. The proposed Reynolds stress model differs from the existing Reynolds stress model in two aspects; an anisotropic dissipation model, , is adopted, and an additional cross diffusion term, Cϵ 3 ϵ/ κ ∂(κ 2/ ϵ ∂κ/∂ Xt)/∂ Xt is included in the ϵ equation. The proposed Reynolds stress turbulence model (RSMX), the existing Reynolds stress model (RSM) and a two-equation eddy viscosity model, the κ - ϵ model, are then tested in three turbulent free shear flows, namely plane jet, round jet, and plane mixing layer flows. It is shown that the proposed RSMX of turbulence model performs better than the existing turbulence models in all the three free shear flows concerned.