Numerical simulations of turbulent shear flows

We simulate three-dimensional mixing layers, isotropic turbulence, and rotating turbulence. In the mixing-layer case, we show that high compressibility inhibits helical pairings obtained in the incompressible case, yielding a staggered array of large -shaped vortices. For isotropic turbulence, one shows the existence of large coherent low-pressure vortices, characterized by exponential tails of various p.d.f.'s. We develop also a new subgrid-scale model applied with success to the backward-facing step, and to the compressible boundary layer. Finally, one looks at the influence of solid-body rotation upon free-shear flows or homogeneous turbulence. At moderate Rossby numbers, cyclonic vortices are stabilized, while anticyclonic vortices are disrupted into intense Görtler-type alternate longitudinal vortices.     

Performances of feature tracking in turbulent boundary layer investigation

In this paper, we describe the application of a feature tracking (FT) algorithm for the measurement of velocity statistics in a turbulent boundary layer over a flat plate at Re _θ ≃ 3,700. The feature tracking algorithm is based on an optical flow approach. Displacements are obtained by searching the parameters of the mapping between interrogation windows in the first and second image which minimize a correlation distance between them. The correlation distance is here defined as the minimum of the sum of squared differences of interrogation windows intensities. The linearized equation which governs the minimization problem is solved with an iterative procedure only where the solution is guaranteed to exist, thus maximizing the signal-to-noise ratio. In this process, the interrogation window first undergoes a pure translation, and then a complete affine deformation. Final mapping parameters provide the velocity and velocity gradients values in a lagrangian framework. The interpolation inherent to window-deforming algorithms represents a critical factor for the overall accuracy and particular attention must be devoted to this step. In this paper different schemes are tested, and their effects on algorithm accuracy are first discussed by looking at the distribution of systematic and random errors computed from synthetic images. The same analysis is then performed on the turbulent boundary layer data, where the effects associated with the use of a near-wall logical mask are also investigated. The comparison with single-point data gathered from the literature demonstrate the overall ability of the FT technique to correctly extract all relevant statistical quantities, including the spanwise vorticity distribution. Concerning the mean velocity profile, no evident influence of the interpolation scheme appears, while the near-wall accuracy is improved by the application of the logical mask. On the contrary, for the fluctuating components of the velocity, the interpolation based on B-Spline basis functions is found to perform better compared to the classical Bicubic scheme, particularly in the highly sheared region close to the wall.

---

Influence of large vortices on the structure of turbulent shear flows

Analysis of numerous experimental data reveals an influence of large vortices on the structure and characteristic parameters of flows. An approximate theory is proposed for describing the effect of large vortices on the pressure pulsations, the profiles of the pulsation velocities, the turbulence energy, and the velocity correlations (turbulence friction stresses). Large vortices are shown to have a long-range influence in that they induce pulsations of the pressure and the velocity at large distances, in particular in regions where transverse velocity gradients are absent (jet boundaries, symmetry axis, core of the initial section of a jet, etc.). When the theory is applied to the calculation of the turbulent characteristics of a mixing layer, a planar jet, a combustion jet, and a boundary layer on a flat surface, it is satisfactorily confirmed by the experimental data of a number of authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, p. 10–20, September–October, 1979.I thank A. B. Vatazhin, A. S. Ginevskii, T. A. Girshovich, and A. N. Sekundov for helpful advice.     

Vorticity-based eduction of large-scale structures in turbulent shear flows

This paper is mainly concerned with a vorticity-based conditional sampling technique, which identifies large-scale vorticity-bearing flow events in turbulent shear flows using multiple X-wire probes. Basic ideas and procedures of the technique are described, and several examples of the results are presented. Advantages and limitations of the technique are also discussed from an experimental point of view.     

Prediction of turbulent wall shear flows directly from wall

The fully elliptic Reynolds-averaged Navier–Stokes equations have been used together with Lam and Bremhorst's low-Reynolds-number model, Chen and Patel's two-layer model and a two-point wall function method incorporated into the standard k-? model to predict channel flows and a backward-facig step flow. These flows enable the evaluation of the performance of different near-wall treatments in flows involving streamwise and normal pressure gradients, flows with separation and flows with non-equilibrium turbulence characteristics. Direct numerical simulation (DNS) of a channel flow with Re =3200 further provides the detailed budgets of each modelling term of the k and ?-transport equations. Comparison of model results with DNS data to evaluate the performance of each modelling term is also made in the present study. It is concluded that the low-Reynolds-number model has wider applicability and performs better than the two-layer model and wall function approaches. Comparison with DNS data further shows that large discrepancies exist between the DNS budgets and the modelled production and destruction terms of the ? equation. However, for simple channel flow the discrepancies are similar in magnitude but opposite in sign, so they are cancelled by each other. This may explain why, even when employing such an inaccurately modelled ?-equation, one can still predict satisfactorily some simple turbulent flows.     

LES prediction of space-time correlations in turbulent shear flows

We compare the space-time correlations calculated from direct numerical simulation(DNS) and large-eddy simulation(LES) of turbulent channel flows.It is found from the comparisons that the LES with an eddy-viscosity subgrid scale(SGS) model over-predicts the space-time correlations than the DNS.The overpredictions are further quantified by the integral scales of directional correlations and convection velocities.A physical argument for the overprediction is provided that the eddy-viscosity SGS model alone does not includes the backscatter effects although it correctly represents the energy dissipations of SGS motions.This argument is confirmed by the recently developed elliptic model for space-time correlations in turbulent shear flows.It suggests that enstrophy is crucial to the LES prediction of spacetime correlations.The random forcing models and stochastic SGS models are proposed to overcome the overpredictions on space-time correlations.     

Effects of vortex pairing on particle dispersion in turbulent shear flows

Particle dispersion in large-scale dominated turbulent shear flow is investigated numerically with special emphasis on the effects of the vortex-pairing phenomenon. The particle dispersion is visualized numerically by following the particle trajectories in a flow consisting of large vortices which are undergoing pairing interaction. The flow field is generated by a discrete vortex method. Important global and local fiow quantities from the numerical simulation compare reasonably well with experimental measurements.

For both cases of point sources with continuous particle release and an initially distributed line source, the particle dispersion results demonstrate that the extent of particle dispersion depends strongly on the Stokes number, the ratio of the particle aerodynamic response time to the characteristic time of the vortex-pairing flow field. Particles with relatively small Stokes numbers disperse laterally at approximately the saine rate as that of the fluid particles and particles with large Stokes numbers disperse much less than the fluid particles. Particles with intermediate Stokes numbers (0.5-5) may be dispersed laterally farther than the fiuid particles and may actually be flung out of the vortex structures. Due to the strong particie entrainment power, the flow during the vortex-pairing process seems to produce higher particle lateral dispersion than the pre-pairing and post-pairing flows.     

On the motion of particles in turbulent duct flows

Existing knowledge on particle deposition rates on walls from turbulent pipe and channel flows is summarized and it is shown that discrepancies exist between experimental and theoretical findings. To contribute to the existing experimental information, laser Doppler measurements are reported of the flow field of a glass particle-air two-phase flow. The results reveal certain seemingly peculiar behaviors of the particles which obviously defy the predictions of the conventional analyses of turbulent two-phase suspension flows.In an accompanying approximate, yet pragmatic theoretical approach, an attempt is made to find a rational basis for the explanation of these experimentally observed particle behaviors. It is shown for the particles in the present study, there exists a limiting size above which their response to the agitation of the fluctuating motion of the surrounding fluid could be treated as if the flow were laminar. On this rational basis, these experimentally observed particle behaviors can then be qualitatively explained by the existing theory of particle excursion in a laminar shear flow field.Reported also is a suggestion to extend the present analysis to a dispersion of particles of multiple sizes.     

Cycle-to-cycle variation effects on turbulent shear stress measurements in pulsatile flows

Accurate evaluation of turbulent velocity statistics in pulsatile flows is important in estimating potential damage to blood constituents from prosthetic heart valves. Variations in the mean flow from one cycle to the next can result in artificially high estimates. Here we demonstrate a procedure using a digital, low-pass filter to remove the cycle-to-cycle variation from turbulence statistics. The results show that cycle-to-cycle variations can significantly affect estimates of turbulent Reynolds stress and should be either eliminated or demonstrated to be small when reporting pulsatile flow results.List of symbols D inside diameter of aortic valve - R radius of model aorta - t time window - t time - T period of cycle - T duration of outflow pulse from ventricle - U instantaneous axial velocity - U _L low-pass axial velocity - U _p mean periodic axial velocity - U ensemble averaged axial velocity - uv ensemble-average turbulent velocity product - u root-mean-square of turbulent axial velocity - U _max maximum, ensemble-averaged axial velocity - V instantaneous radial velocity - y vertical distance from aorta centerline - z axial distance downstream of prosthetic heart valve This paper was presented at the Tenth Symposium on Turbulence, University of Missouri-Rolla, Sept. 22–24, 1986     

Lagrangian model on the turbulent motion of small solid particle in turbulent boundary layer flows

.Intr0ductionSurfaceerosionofmaterialbysolid-particleimpactisanimportantprobleminmultiphaseflowindustriaIdevicesandthecharacteristicsoftheparticIe'smotioninaturbulentboundarylayerflowisthebaseofthestudyofthematerialsurfaceerosion.Manycalculationmodelshave…     

On the eddy viscosity model of periodic turbulent shear flows

Physical argument shows that eddy viscosity is essentially different from molecular viscosity. By direct numerical simulation, it was shown that for periodic turbulent flows, there is phase difference between Reynolds stress and rate of strain. This finding posed great challenge to turbulence modeling, because most turbulence modeling, which use the idea of eddy viscosity, do not take this effect into account. The project supported by the National Natural Science Foundation of China (19732005) and Liu Hui Center for Applied Mathematics of Nankai & Tianjin University     

A film-based wall shear stress sensor for wall-bounded turbulent flows

In wall-bounded turbulent flows, determination of wall shear stress is an important task. The main objective of the present work is to develop a sensor which is capable of measuring surface shear stress over an extended region applicable to wall-bounded turbulent flows. This sensor, as a direct method for measuring wall shear stress, consists of mounting a thin flexible film on the solid surface. The sensor is made of a homogeneous, isotropic, and incompressible material. The geometry and mechanical properties of the film are measured, and particles with the nominal size of 11 μm in diameter are embedded on the film’s surface to act as markers. An optical technique is used to measure the film deformation caused by the flow. The film has typically deflection of less than 2% of the material thickness under maximum loading. The sensor sensitivity can be adjusted by changing the thickness of the layer or the shear modulus of the film’s material. The paper reports the sensor fabrication, static and dynamic calibration procedure, and its application to a fully developed turbulent channel flow at Reynolds numbers in the range of 90,000–130,000 based on the bulk velocity and channel full height. The results are compared to alternative wall shear stress measurement methods.     

Quantitative visualization of compressible turbulent shear flows using condensate-enhanced Rayleigh scattering

This paper describes several flow visualization experiments carried out in Mach 3 and Mach 8 turbulent shear flows. The experimental technique was based on laser scattering from particles of H₂O or CO₂ condensate that form in the wind tunnel nozzle expansion process. The condensate particles vaporize extremely rapidly on entering the relatively hot fluid within a turbulent structure, so that a sharp vaporization interface marks the outer edge of the rotational shear layer fluid. Calculations indicate that the observed thin interface corresponds to a particle size of 10 nm or less, which is consistent with optical measurements, and that particles of this size track the fluid motions well. Further, calculations and experiments show that the freestream concentration of condensate required for flow visualization has only a small effect on the wind tunnel pressure distribution. Statistics based on the image data were compared to corresponding results from probe measurements and agreement was obtained in statistical measures of speed, scale, and orientation of the large-scale structures in the shear layer turbulence. The condensate-enhanced Rayleigh scattering technique is judged to be a useful tool for quantitative studies of shear layer structure, particularly for identifying the instantaneous boundary layer edge and for extracting comparative information on the large-scale structures represented there.     

Statistical properties of wall shear stress fluctuations in turbulent channel flows

Instantaneous velocity and wall shear stress measurements are conducted in a turbulent channel flow in the Kármán number range of Re_τ = 74–400. A one-dimensional LDA system is used to measure the streamwise velocity fluctuations, and an electrochemical technique is utilized to measure the instantaneous wall shear stress. For the latter, frequency response and nonuniform correction methods are used to provide an accurate, well-resolved wall statistics database. The Reynolds number dependency of the statistical wall quantities is carefully investigated. The corrected relative wall shear stress fluctuations fit well with the best DNS data available and meet the need for clarification of the small discrepancy observed in the literature between the experimental and numerical results of such quantities. Higher-order statistics of the wall shear stress, spectra, and the turbulence kinetic energy budget at the wall are also investigated. The present paper shows that the electrochemical technique is a powerful experimental method for hydrodynamic studies involving highly unsteady flows. The study brings with it important consequences, especially in the context of the current debate regarding the appropriate scaling as well as the validation of new predictive models of near-wall turbulence.     

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. Received: 15 December 1994/Accepted: 18 December 1997     

Modeling of the motion of light-weight particles and bubbles in turbulent flows

The aim of the paper is to present a statistical model of motion and dispersion of light-weight particles and bubbles in turbulent flows. The model is based on a kinetic equation for the probability density function of particle velocities. The results of modeling the parameters of particles and bubbles in a plane-channel flow are compared with known data of direct numerical simulation.     

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.