Turbulent Free Shear Flows Research Articles

Boundary conditions for direct computation of aerodynamic sound generation

A numerical scheme suitable for the computation of both the near field acoustic sources and the far field sound produced by turbulent free shear flows utilizing the Navier-Stokes equations is presented. To produce stable numerical schemes in the presence of shear, damping terms must be added to the boundary conditions. The numerical technique and boundary conditions are found to give stable results for computations of spatially evolving mixing layers.

Turbulent Diffusion of Heavy-Particles in Turbulent Jets

The turbulent dispersion of heavy suspended particles in turbulent shear flows is analyzed when crossing trajectory effects are important. A semiempirical expression for particle diffusion coefficient is developed via a comparison with experimental data of two-phase turbulent jet flows. This expression gives the particle momentum diffusion coefficient in terms of the gas diffusion coefficient, mean relatively velocity, and root mean square of the fluctuating fluid velocity. The proposed expression is used in a two-phase flow mathematical model to predict different particle-laden jet flows. The good agreement between the predictions and data suggests that the developed expression for particle diffusion coefficient is reasonably accurate in predicting particle dispersion in turbulent free shear flows.

Weakly nonlinear models for turbulent mixing in a plane mixing layer

New closure models for turbulent free shear flows are presented in this paper. They are based on a weakly nonlinear theory with a description of the dominant large-scale structures as instability waves. Two models are presented that describe the evolution of the free shear flows in terms of the time-averaged mean flow and the dominant large-scale turbulent structure. The local characteristics of the large-scale motions are described using linear theory. Their amplitude is determined from an energy integral analysis. The models have been applied to the study of an incompressible mixing layer. For both models, predictions of the mean flow development are made. In the second model, predictions of the time-dependent motion of the large-scale structures in the mixing layer are made. The predictions show good agreement with experimental observations.

Anisotropy of Heat Transport and Its Modeling in Homogeneous Turbulent Flow.

With modifications of a two-equation heat-transfer model, a new approach to analysis of heat transport in free turbulent shear flows is proposed. The modified model was tested by application to different homogeneous turbulent flows, namely decaying isotropic turbulence, homogeneous nonisotropic turbulence under a return-to-isotropy process, and homogeneous turbulence with a simple shear. To represent the nonisotropic nature of heat transfer in free turbulence, we have modeled the eddy diffusivity for heat by a second rank tensor on the basis of the generalized gradient diffusion hypothesis. At the same time, when treating the time scale which characterizes the transport process of a passive scalar, we have introduced the scalar-field time scale τθ=((θ2)^^-/2)/eθ. The predictions of turbulent heat flux, temperature variance and its dissipation rate are all in satisfactory agreement with the experimental results.

The effect of Mach number on the stability of a plane supersonic wake

Recent interest in supersonic combustion and problems of transatmospheric flight has prompted renewed research efforts in laminar–turbulent free-shear flow transition. In the present work, the influence of Mach number on the stability of supersonic planar wake flows is investigated to gain insight into the physics of linear, nonlinear, and three-dimensional (3-D) stages of transition. The effect of varying the relative phase difference between a fundamental instability mode and its subharmonic is investigated as a possible means of controlling the evolution of a wake. From a linear stability analysis, it is found that the influence of increasing Mach number is stabilizing, resulting in a growth rate at a Mach number of 3 which is 60% that of an incompressible wake. Direct numerical simulations of the time-dependent compressible Navier–Stokes equations in two and three dimensions are performed for a forced time-developing wake using a spectral collocation method. The results of the two-dimensional (2-D) simulations show the slow rollup of spanwise vortices at high Mach numbers that is attributed to the influence of baroclinic and dilatational effects. Finally, the results of three-dimensional simulations forced with the most unstable Kelvin–Helmholtz wave and a pair of oblique three-dimensional waves show that, depending on the initial phasing between the 2-D and 3-D waves, vortex loops may or may not form as a result of the interaction between the streamwise and spanwise vorticity.

Particle dispersion in a turbulent, plane, free shear layer

The particle dispersion mechanisms in an inhomogeneous, anisotropic, high Reynolds number, turbulent free shear flow are presented. Flow visualization, as well as laser attenuation and diffraction techniques, are used to characterize the evolution of the flow. It is shown that, at each downstream location, the spectral response of the particles to the coherent velocity field that develops in the layer as a result of a Kelvin–Helmholtz type of instability leads to a selective dispersion of the particles across the mixing layer. Furthermore, this particle dispersion layer is shown to be composed of a central core region, characterized by a small mean particle size and two external sublayers with considerably larger mean particle sizes. Finally, the experimental results suggest the dominant role played by the coherent, large scale vortical structure in the dispersion of the particles. Scaling arguments and simplified flow models supporting this hypothesis are also presented.

Finite element simulation of 3D turbulent free shear flows

AbstractThis paper reviews past and current efforts in developing a simple but robust turbulence model for free shear flows. Much of this work has been published previously and this paper is a rearrangement aimed at the conference. The model is presented and is interfaced with FIDAP to solve three‐dimensional flows and a pusher—prop configuration. The eight‐node brick, the penalty formulation and the Broyden method are used to solve the Navier‐Stokes equations. The propeller is modelled as an actuator disc and the direct simulation of a given propeller is considered in detail. Good results are obtained for the square jet. For propeller cases detailed comparison with wind tunnel measurements shows excellent prediction of the velocity and pressure for flows of this complexity.

Monte Carlo solutions of a joint PDF equation for turbulent flows in general orthogonal coordinates

The modeled transport equation for the joint probability density function (pdf) of the velocities and a single scalar composition in a turbulent flow is an integro-differential equation in up to seven independent variables and time. Because of its large dimensionality, this equation may be efficiently solved by a Monte Carlo method. An algorithm is developed that allows the pdf equation to be solved in a general orthogonal coordinate system. The method is based on a Lagrangian approach in which the behavior of fluid particles in a turbulent flow is modeled and particle trajectories are computed in the Monte Carlo solution algorithm. The technique is applied to three self-similar turbulent free shear flows: the plane mixing layer, the plane jet, and the axisymmetric jet. Numerical test results are presented which compare the new algorithm with earlier methods, verify the statistical error estimates, and demonstrate convergence.

A pdf modeling study of self-similar turbulent free shear flows

A modeled transport equation for the joint probability density function (pdf) of the velocities and a scalar has been solved numerically for four self-similar turbulent free shear flows: the plane mixing layer, the plane wake, the plane jet, and the axisymmetric jet. In the pdf equation, convection is treated exactly but the effects of viscosity, molecular diffusion, and the fluctuating pressure gradient have to be modeled. Five different models are evaluated; four of these are based on the Langevin equation for the fluid particle velocities, and the fifth is a particle pair interaction model. In each case, a stochastic mixing model represents the effects of molecular diffusion, and conditional modeling is included to account for intermittency. The resulting modeled pdf equation is solved by a Monte Carlo method. Calculated spreading rates and profiles of the mean velocity and Reynolds stresses show generally good agreement with experimental data for three of the five velocity models. However, discrepancies between the calculated and measured intermittency factor profiles, in particular for the plane mixing layer, reveal weaknesses in the conditional modeling.

Multiple-time-scale modeling of turbulent flows in one-point closures

A particular multiple-scale modeling is developed on the basis of partial integration of spectral evolution equations on wavelength intervals. Several problems of turbulence modeling are considered within this framework such as influence of departure from equilibrium and the return to isotropy process. A simplified version is applied to the prediction of free turbulent shear flows.

Numerical analysis of a natural and excited two-dimensional mixing layer

Physical properties of a two-dimensional plane mixing layer are examined by numerical solution of the unsteady Navier-Stokes equations using a pressure velocity formulation. The natural (unforced) mixing layer due to the merging of two streams with a velocity ratio (r = 0.33) is studied at Reynolds numbers /?e = 200, 500, and 1000. Different transition zones are detected: stable, linear, and nonlinear. The roll-up process appears in the nonlinear zone. The main flow features are in agreement with the experimental evidence. The excited mixing layer at the first subharmonic and at the incommensurate frequency are investigated to analyze the coalescence mechanism and the nonlinear interaction. HE merging of two streams initially separated by a thin surface plays an important role in numerous applications such as aerodynamics and combustors. Experiments reported by a number of authors have shown that orderly structures are extant in the turbulent mixing layer. Visualization studies reported by Brown and Roshko1 confirm that large-scale coherent structures are indeed intrinsic features of the turbulent mixing layer at high Reynolds numbers. Furthermore, sequential mergings of the vortices constitute the primary mechanism for the spreading of the mixing layer in the downstream direction, as pointed out by the experiments of Winant and Browand.2 These observations have had a major impact on the understanding of turbulence in free shear flows. The large-scale vortices are observed not only in the early laminar stages of the flow, but also farther downstream in the turbulent region, where they coexist with a fine-scale motion. Hence, two issues need to be examined: the evolution of the large eddies identified in the viscous laminar flow and the link between these eddies and the coherent structures observed in the turbulent flow. The mechanisms of transition and coherent structures play an important role in the correct modeling of turbulent flows. Two main approaches are currently used in the experimental and theoretical analyses used to study these mechanisms: the classical linear hydrodynamic stability theory and the description of vorticity field in the physical space. In the classical hydrodynamic stability theory, the mixing layer is viewed as an overlapping of the instability waves that propagate and amplify in the downstream direction. The flow is naturally described in the Fourier space. Therefore, measured data in the frequency space cannot be easily related to the evolution of the orderly structures.3'4 The second approach, by taking into account the nonlinear character, explains the behavior of coherent structures by studying the evolution of the vorticity field in the physical space. The structures are considered to be vortices of a characteristic size that exhibit different types of interactions.5'6 In this case, the results can be compared with the flow visualization studies.

Coherent motion in excited free shear flows

The application of the inviscid instability approach to externally excited turbulent free shear flows at high Reynolds numbers is explored. Attention is given to the cases of a small-deficit plane turbulent wake, a plane turbulent jet, an axisymmetric jet, the nonlinear evolution of instabilities in free shear flows, the concept of the 'preferred mode', vortex pairing in turbulent mixing layers, and experimental results for the control of free turbulent shear layers. The special features often attributed to pairing or to the preferred mode are found to be difficult to comprehend; the concept of feedback requires further substantiation in the case of incompressible flow.

Flow structures of a basic annular jet

This paper describes the modal expansion and conditional sampling results of static pressure fluctuations in the inner and outer mixing regions of a basic annular jet. An understanding of the mechanism of the wake shed- ding process from the internal recirculating region behind the blunt interface is attempted by conditionally sampled pressure signals. The evolution and characteristics of the shedding wake, wake-induced vortices, and jet vortices in both shear layers are measured and presented. The evolution of the wake-induced vortices in the outer shear layer as a result of excitation by the disturbances associated with the shedding wakes is further supported. In the case of the basic annular jet, another type of coherent structure was found in the outer mixing region, in addition to those associated with the outer jet vortices.5 This additional structure, termed the wake-induced vortex, seemed to be the consequence of the presence of the internal recirculating region and the shedding of the standing vortices or the wake vortices downstream of the blunt interface.5-6 Both the outer jet vortices and wake-induced vortices have, besides the axisymmetrical mode constituents, azimuthal constituents. The constituent of the first mode could be as dominant as that of the axisymmetrical.7 The existence and dominance of the wake-induced vortices depended on the diameter ratio D//Z>0. For large diameter ratios, the wake- induced vortices seemed to be more dominant. The investigation of the influence of the shedding wakes and their associated disturbances on the initial outer shear layers and the subsequent evolution of the induced structures may help to further clarify the phenomena of shear layer ex- citation and large-scale structure dynamics which are fun- damental in the study of turbulent free shear flows. Moreover, the inner region resembles that of a near wake behind an axisymmetric blunt body. Similar studies are rare and the ones reported are limited primarily to the case of a disk in cross flow. The present investigation was an attempt to understand the mechanism of the wake shedding process from the inter- nal recirculating region in the near wake of the blunt inter- face and the mode of evolution of the wake-induced vortices in the outer mixing region. This paper documents the results and interpretations based primarily on a mode expansion technique and a time domain analysis on the static pressure fluctuations. Measurements of the velocity fluctuations are being carried out and will be reported separately.

Turbulence suppression in free turbulent shear flows under controlled excitation. Part 2. Jet-noise reduction

It is shown that reduction of broadband (even total) far-field jet noise can be achieved via controlled excitation of a jet at a frequency in the range 0.01 < Stθ < 0.02, where Stθ is the Strouhal number based on the exit momentum thickness of the shear layer. Hot-wire measurements in the noise-producing region of the jet reveal that the noise suppression is a direct consequence of turbulence suppression, produced by early saturation and breakdown of maximally growing instability modes.

Free shear turbulence intensity anisotropies and the energy cascade

An extended energy cascade theory is presented, which correctly predicts the Reynolds number dependence of centerline turbulence intensities in the self-preserving region of fully turbulent free shear flows, shown clearly by the experimental measurements. The model indicates that below Re = 10 6 too few stages exist to completely erase the cascade's “memory” of initial conditions.

Pressure spectra in turbulent free shear flows

Spectral models for turbulent pressure fluctuations are developed by directly Fourier transforming the integral solution to the Poisson equation for a homogeneous constantmean-shear flow. The turbulence-turbulence interaction is seen to possess the well-knownk−7/3inertial subrange and to dominate the high-wavenumber region. The turbulence–mean-shear contribution is seen to be dominant in the energy-containing range and falls off as$k^{-\frac{11}{3}}$in the inertial subrange. The subrange constants and the mean-square pressure fluctuation are evaluated using a spectral model for the velocity. A spectral analysis of the velocity contamination of a pressure probe is also presented. Results are compared with spectral measurements with a static-pressure probe in the mixing layer of an axisymmetric jet.

Points of symmetry in turbulent shear flows

Both turbulent wall shear flows and free shear flows exhibit at least one location where the probability density function of temperature is symmetrical but non-Gaussian. The available experimental evidence indicates that this location corresponds approximately to a local maximum in the temperature variance and reflects the presence of the organised motion.

Entrainment interface in free turbulent shear flows

Entrainment interface in free turbulent shear flows

Role of coherent structures in turbulent shear flows

A definition for the large-scale coherent structure is presented, and the nature and role of coherent structures in turbulent shear flows are examined. The equations governing the coherent motions and the experimental considerations as well as constraints in the investigations of coherent structures in wall-bounded and free turbulent shear flows are discussed. Results from a few of our recent and ongoing studies of coherent structures in excited and unexcited free turbulent shear flows are reviewed. These results show that coherent structures are dominant in transport in the early stages of their formation, but not in the self-preserving regions of turbulent shear flows.

Kolmogorov constants for structure functions in turbulent shear flows

AbstractKolmogorov constants in the inertial sub‐range expressions for the second‐order velocity structure function and the one‐dimensional spectrum of the streamwise velocity fluctuation have been estimated for both laboratory turbulent free shear flows and the atmospheric surface layer. A unique relation between the spectral constant α1, and the structure function constant is expected when the Reynolds number is infinitely large. the relation is found to be inadequate in both the laboratory and the atmosphere where values of α1, obtained via the structure function are, on average, smaller by about 15% than spectral estimates of α1. For the present atmospheric data the average estimate, from the second‐order structure function data, of α1 is about 0.54 in reasonable agreement with an estimate from the skewness of the structure function. the additive constant in the r3 law is approximately zero for the laboratory data.