Reynolds number effects on the mixing behavior of axisymmetric turbulent jets

Measurements of time-averaged jet fluid mass fraction and unmixedness are reported along the centerlines of axisymmetric jets having Reynolds numbers (Re) covering a range of 3,950–11,880. Jet gases investigated are propane, carbon tetrafluoride, and sulfur hexafluoride. The slopes for the fall off of inverse centerline mass fraction with distance are found to be independent of Re for moderate downstream distances, but virtual origins for the data are shown to move downstream with increasing Re. Unmixedness measurements show that flows with higher Re require longer flow distances to achieve asymptotic behavior. Results of other investigations reported in the literature are discussed which support the conclusions of this work. The relationship between the centerline mixing and entrainment behaviors of these flows is explored.     

Optimization of turbulent jet mixing

We introduce an approach for controlling jet mixing that combines direct numerical simulation of an incompressible jet flow with stochastic optimization procedures. The jet is excited with helical and combined helical and axial actuations at the orifice. An objective function that measures the spreading of the jet evaluates the performance of the actuation parameters. The optimization procedure searches for the best actuation by automatically varying the parameters and calculating their objective function value. Solutions that lead to a pronounced spreading of the jet are found within reasonable time, although the evaluation of the objective function, the DNS of the jet, is expensive. For a jet flow at low Reynolds number the performance of different search algorithms (simulated annealing and evolution strategies) is evaluated. We compare various objective functions based on radial velocity and the concentration of a passive scalar, including functions that penalize actuation with high amplitudes. We find that a combined axial and helical actuation is much more efficient with respect to jet mixing than a helical actuation alone.     

Spanwise domain effects on the evolution of the plane turbulent mixing layer

Large Eddy Simulation is used to simulate a series of plane mixing layers. The influence of the spanwise domain on the development of the mixing layer, and the evolution of the coherent structures, are considered. The mixing layers originate from laminar conditions, and an idealised inflow condition is found to produce accurate flow predictions when the spanwise computational domain extent is sufficient to avoid confinement effects. Spanwise domain confinement of the flow occurs when the ratio of spanwise domain extent to local momentum thickness reaches a value of ten. Flow confinement results in changes to both the growth mechanism of the turbulent coherent structures, and the nature of the interactions that occur between them. The results demonstrate that simulations of the two-dimensional mixing layer flow requires a three-dimensional computational domain in order that the flow will evolve in a manner that is free from restraints imposed by the spanwise domain.     

Mapping closures for turbulent mixing and reaction

The mapping closure for the one-point pdf of an inert scalar in homogeneous turbulence is explained and developed. It is shown that the pdf's calculated from the closure are in excellent agreement with those obtained from direct numerical simulations. The closure is then extended to many reactive scalars.I believe in the ultimate possibility of developing general computation procedures based on first principles; and under certain circumstances I believe that it is possible to do this rationally.J.L. Lumley (1978) on computational modeling of turbulent flowsDedicated to Professor J.L. Lumley on the occasion of his 60th birthday.This work was supported in part by U.S. Air Force Office of Scientific Research (Grant No. AFOSR-88-0052).     

Mixing and entrainment in the near field of turbulent round jets

In this work, a methodology based on the analysis of single-camera, double-pulse PIV images is described and validated as a tool to characterize fiber-dispersed turbulent flows in large-scale facilities. The methodology consists of image pre-treatment (intensity adjustment, median filtering, threshold binarization and object identification by a recursive connection algorithm) and object-based phase discrimination used to generate two independent snapshots from one single image, one for the dispersed phase and one for the seeding. Snapshots are then processed to calculate the flow field using standard PIV techniques and to calculate fiber concentration and orientation statistics using an object-fitting procedure. The algorithm is tuned and validated by means of artificially generated images and proven to be robust against identified sources of error. The methodology is applied to experimental data collected from a fiber suspension in a turbulent pipe flow. Results show good qualitative agreement with experimental data from the literature and with in-house numerical data.     

Dust entrainment in a shock-induced,turbulent air flow

Dust from a layer on the floor of a shock tube is entrained by the air flow behind the unsteady shock wave. The development of the dust mass concentration profiles is measured by means of an optical extinction method. The concentration profiles which can be described by an exponential law approach a stationary limit consistent with the results of pneumatic transport theory. A theoretical model simulating the dust entrainment by a diffusion process is evaluated numerically and compared with the experimental results.     

Development of turbulent mixing in a fluid

The development of turbulent mixing produced by a linear source in a flat cell is studied with dyes and a laser thermal marker. The velocity field outside the mixing region is determined. The agreement of region size determined by dye diffusion and thermal marker deformation is shown.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 91–95, March–April, 1973.     

An entrainment model for the turbulent jet in a coflow

The entrainment hypothesis was introduced by G.I. Taylor to describe one-dimensionally the development of turbulent jets issuing into a stagnant or coflowing environment. It relates the mass flow rate of surrounding fluid entrained into the jet to the characteristic velocity difference between the jet and the coflow. A model based on this hypothesis along with axial velocity assumed to follow a realistic Gaussian distribution is presented. It possesses an implicit analytical solution, and its results are compared and shown to be fully equivalent to previously published models that are rather based on a spreading hypothesis. All of them are found to be in agreement with experimental results, on a wide range of downstream positions and for various coflow intensities. To cite this article: N. Enjalbert et al., C. R. Mecanique 337 (2009).     

Mean and turbulent velocity measurements of supersonic mixing layers

The behavior of supersonic mixing layers under three conditions has been examined by schlieren photography and laser Doppler velocimetry. In the schlieren photographs, some large-scale, repetitive patterns were observed within the mixing layer; however, these structures do not appear to dominate the mixing layer character under the present flow conditions. It was found that higher levels of secondary freestream turbulence did not increase the peak turbulence intensity observed within the mixing layer, but slightly increased the growth rate. Higher levels of freestream turbulence also reduced the axial distance required for development of the mean velocity. At higher convective Mach numbers, the mixing layer growth rate was found to be smaller than that of an incompressible mixing layer at the same velocity and freestream density ratio. The increase in convective Mach number also caused a decrease in the turbulence intensity ( _u/U).List of symbols a speed of sound - b total mixing layer thickness between U ₁ – 0.1 U and U ₂ + 0.1 U - f normalized third moment of u-velocity, f u³/(U)³ - g normalized triple product of u² , g u²/(U)³ - h normalized triple product of u ², h u ²/(U)³ - l _u axial distance for similarity in the mean velocity - l _u axial distance for similarity in the turbulence intensity - M Mach number - M _c convective Mach number (for ₁ = ₂), M _c (U ₁ – U ₂)/(a ₁ + a ₂) - P static pressure - r freestream velocity ratio, r U ₂/U ₁ - Re unit Reynolds number, Re U/ - s freestream density ratio, s ₂/₁ - T _t total temperature - u instantaneous streamwise velocity - u deviation of u-velocity, uu – U - U local mean streamwise velocity - U ₁ primary freestream velocity - U ₂ secondary freestream velocity - average of freestream velocities, (U ₁ + U ₂)/2 - U freestream velocity difference, U U ₁ – U ₂ - instantaneous transverse velocity - v deviation of -velocity, – V - V local mean transverse velocity - x streamwise coordinate - y transverse coordinate - y ₀ transverse location of the mixing layer centerline - ensemble average - ratio of specific heats - boundary layer thickness (y-location at 99.5% of free-stream velocity) - similarity coordinate, (y – y ₀)/b - compressible boundary layer momentum thickness - viscosity - density - standard deviation - dimensionless velocity, (U – U ₂)/U - 1 primary stream - 2 secondary stream A version of this paper was presented at the 11th Symposium on Turbulence, October 17–19, 1988, University of Missouri-Rolla     

Experimental investigation of turbulent entrainment in an annulus with moving sidewalls

The establishment of a turbulent mixed layer in a two-layer stratified shear flow, and the rate of entrainment into that layer were studied experimentally in a modified annulus. The modification of the conventional annulus was made by replacing the upper rotating screen with inner rotating sidewalls, extending over the upper half of the channel, so that the flow in the upper layer was nearly uniform and almost laminar, while the bottom layer was quiescent. Vertical density profile measurements were conducted using single electrode conductivity probes. The flow was visualized during the various stages of the experiment using the hydrogen bubble technique.After the start of the sidewalls rotation, the upper layer accelerates from rest, and consequently a transition process is taking place during which the initial density interface between the two layers is developed into a turbulent mixed layer. This turbulent layer is bounded by two sharp interfaces, each separating it from an outer non-turbulent zone. The generation of this five-layer structure seemed to be dominated by instabilities activated by the velocity difference between the upper and lower layer.Once a turbulent mixed layer is formed, entrainment of nonturbulent fluid into that layer is taking place causing its thickness to increase continuously. Depending on the overall Richardson number, based on the channel width, the slope of the entrainment law curve was found to have two different values, each indicating the dominance of a different source of turbulent energy production. For relatively low Richardson numbers, the slope is close to -1.8, implying that the velocity shear across each interface contributes significantly to the entrainment. On the other hand, for larger Richardson numbers the slope is about -1.25, in agreement with previous results of shear-free entrainment experiments.The measured velocity profiles indicate that as long as the mixed layer is not too thick, the radial inhomogeneities are small and the flow may be considered as nearly one-dimensional. It seems, therefore, that for the understanding of entrainment processes occurring in realistic stratified flows, the modified annulus is a more reliable tool than the conventional one.     

Momentum transport in a turbulent mixing layer

The turbulent momentum transport phenomena in a two-dimensional mixing layer are investigated numerically by a discrete vortex method. The numerical model and calculations are verified through a comparison with existing numerical simulations and experimental measurements. The main emphasis is placed on the exploration of the detailed time-dependent instantaneous local momentum fluctuations and on the comparison of numerical results with available experimental measurements. The current simulations confirm qualitatively the various trends in the turbulent momentum flux and fluctuating components of the velocity in the mixing layer found with several experimental results. The study shows that similarity exists in turbulent momentum quantities along the axial direction of the mixing layer. The calculations also show a definite correlation between the passage of a large-scale structure and a burst in the turbulent momentum flux. The probability density functions of the fluctuating quantities are shown to be mostly Gaussian-like, with only a few exceptions.     

Compressible closure models for turbulent multifluid mixing

This paper studies governing equations describing the turbulent fluid mixing behavior effectively. The goal is to propose a closure for compressible multiphase flow models with transport and surface tension, which satisfy the boundary conditions at the mixing zone edges, the conservation requirements, and an entropy inequality constraint. Implicitness of positivity for the entropy of averaging requires entropy inequality as opposed to conservation of entropy for microphysically adiabatic processes.     

Isoenstrophy points and surfaces in turbulent flow and mixing

Vorticity ω magnitude is measured by the enstrophy field ω². Equations describing the motion of surfaces of constant enstrophy, and lines and points of extreme enstrophy, are derived. The purpose is to develop better tools for studies of small scale processes of turbulence and turbulent mixing.     

Instantaneous velocity and pressure measurements in turbulent mixing layers

This paper presents a comprehensive comparison of the mean velocity and turbulence measurements from a four-hole pressure probe, also known as the Cobra probe, and an X-probe in plane mixing layers. The objective is to validate the measurement accuracy of the Cobra probe in a flow where the turbulence reaches high levels, but whose properties are well known. The comparison is made for the mean velocities, Reynolds stresses, triple products, and spectra, and demonstrates that the Cobra probe has reasonable accuracy for some of these quantities, such as the mean streamwise velocity and primary shear stress, but not for others, such as the mean normal velocity. The correlation of the pressure and the streamwise velocity, measured by the Cobra probe, behaves correctly in the potential flow. However, the correlation of the pressure and the cross-stream velocity, which appears in the transport equation for the turbulent kinetic energy, and the pressure redistribution term in the corresponding equation for the streamwise normal stress, are poorly measured.     

Physics and modelling of turbulent particle deposition and entrainment: Review of a systematic study

Deposition and entrainment of particles in turbulent flows are crucial in a number of technological applications and environmental processes. We present a review of recent results from our previous works, which led to physical insights on these phenomena. These results were obtained from a systematic numerical study based on the accurate resolution – Direct Numerical Simulation via a pseudo-spectral approach – of the turbulent flow field, and on Lagrangian tracking of particles under different modelling assumptions. We underline the multiscale aspect of wall turbulence, which has challenged scientists to devise simple theoretical models adequate to fit experimental data, and we show that a sound rendering of wall turbulence mechanisms is required to produce a physical understanding of particle deposition and re-entrainment. This physical understanding can be implemented in more applied simulation techniques, such as Large-Eddy Simulation. Our arguments are based also on the phenomenology of coherent structures and on the examination of flow topology in connection with particle preferential distribution. Starting from these concepts, reasons why theoretical predictions may fail are examined together with the requirements which must be fulfilled by suitable predictive models.     

On harmonic perturbations in a turbulent mixing layer

A theoretical model of harmonic perturbations in a turbulent mixing layer is proposed. The model is based on the triple decomposition method. It is assumed that the instantaneous velocities and pressure consist of three distinctive components: the mean (time average), the coherent (phase average), and the random (turbulent) motion. The interaction between incoherent turbulent fluctuations and large-scale coherent disturbances is incorporated by the Newtonian eddy viscosity model. A slight divergence of the flow is also taken into account, and the results are compared with experimental data. For a high amplitude of the perturbations, the nonlinear feedback to the mean flow is taken into account by means of the coherent Reynolds stresses. The results reveal the possibility of a negative spreading rate of the mixing layer. A simultaneous consideration of the mean flow divergence and nonlinear self-interaction results in Landau-like amplitude equations. It is observed that the nonlinear term in the amplitude equation is not significant at the levels of amplitude considered. The velocity disturbance profiles of the second harmonic are also presented and, at low-level amplitude, they are in good agreement with experiments.     

Heat release effects on mixing scales of non-premixed turbulent wall-jets: A direct numerical simulation study

The present study concerns the role of heat release effects on characteristics mixing scales of turbulence in reacting wall-jet flows. Direct numerical simulations of exothermic reacting turbulent wall-jets are performed and compared to the isothermal reacting case. An evaluation of the heat-release effects on the structure of turbulence is given by examining the mixture fraction surface characteristics, diagnosing vortices and exploring the dissipation rate of the fuel and passive scalar concentrations, and moreover by illustration of probability density functions of reacting species and scatter plots of the local temperature against the mixture fraction. Primarily, heat release effects delay the transition, enlarge the fluctuation intensities of density and pressure and also enhance the fluctuation level of the species concentrations. However, it has a damping effect on all velocity fluctuation intensities and the Reynolds shear stress. A key result is that the fine-scale structures of turbulence are damped, the surface wrinkling is diminished and the vortices become larger due to heat-release effects. Taking into account the varying density by using semi-local scaling improves the collapse of the turbulence statistics in the inner region, but does not eliminate heat release induced differences in the outer region. Examining the two-dimensional premultiplied spanwise spectra of the streamwise velocity fluctuations indicates a shifting in the positions of the outer peaks, associated with large energetic structures, toward the inner region.     

Measurement of spectral characteristics of the turbulent mixing zone

Experiments with two pairs of gases with different densities with the initial values of the Atwood number A = 0.21 and 0.83 are performed in a multifunctional shock tube. Statistical and spectral characteristics of the mixing zone formed owing to the Richtmyer-Meshkov and Rayleigh-Taylor instability are obtained by the laser sheet technique, and the range of lengths of the main waves in the structure of this zone is determined.     

Air entrainment in two-dimensional turbulent shear flows with partially developed inflow conditions

In plunging jet flows and at hydraulic jumps, large quantities of air are entrained at the intersection of the impinging flow and the receiving body of water. The air bubbles are entrained into a turbulent shear layer and strong interactions take place between the air bubble advection/diffusion process and the momentum shear region. New air-water flow experiments were conducted with two free shear layer flows: a vertical supported jet and a horizontal hydraulic jump. The inflows were partially developed boundary layers, characterized by the presence of a velocity potential core next to the entrapment point. In both cases, the distributions of air concentration exhibit a Gaussian distribution profile with an exponential longitudinal decay of the maximum air content. Interestingly, the location of the maximum air content and the half-value band width are identical for both flow situations, i.e. independent of buoyancy effects.