Effects of free‐stream turbulence on large‐scale coherent structures of separated boundary layer transition

It has been well established that large‐scale structures, usually called coherent structures, exist in many transitional and turbulent flows. The topology and range of scales of those large‐scale structures vary from flow to flow such as counter‐rotating vortices in wake flows, streaks and hairpin vortices in turbulent boundary layer. There has been relatively little study of large‐scale structures in separated and reattached transitional flows. Large‐eddy simulation (LES) is employed in the current study to investigate a separated boundary layer transition under 2% free‐stream turbulence on a flat plate with a blunt leading edge. The Reynolds number based on the inlet free stream velocity and the plate thickness is 6500. A dynamic subgrid‐scale model is employed to compute the subgrid‐scale stresses more accurately in the current transitional flow case. Flow visualization has shown that the Kelvin–Helmholtz rolls, which have been so clearly visible under no free‐stream turbulence (NFST) are not as apparent in the present study. The Lambda‐shaped vortical structures which can be clearly seen in the NFST case can hardly be identified in the free‐stream turbulence (FST) case. Generally speaking, the effects of free‐stream turbulence have led to an early breakdown of the boundary layer, and hence increased the randomization in the vortical structures, degraded the spanwise coherence of those large‐scale structures. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

Non-Equilibrium Mixing of Turbulence Scales Using a Continuous Hybrid RANS/LES Approach: Application to the Shearless Mixing Layer

A new subgrid-scale (SGS) model based on partially integrated transport method (PITM) is applied to the case of a turbulent spectral non-equilibrium flow created by the mixing of two turbulence fields of differing scales: the shearless mixing layer. The method can be viewed as a continuous hybrid RANS/LES approach. In this model the SGS length scale is no longer given by the size of the discretization step, but is dynamically estimated using an additional transport equation for the dissipation rate. The results are compared to those corresponding to the classical model of Smagorinsky and to the experimental data of Veeravalli and Warhaft. A method for creating an anisotropic analytical pseudo-random field for inflow conditions is also proposed. This approach based on subgrid-scale transport modelling combined with anisotropic inlet conditions gives better results for the prediction of the shearless mixing layer.     

Transport, Mixing and Agglomeration of Particles in Turbulent Flows

This paper describes methods and approaches that have been used to simulate and model the transport, mixing and agglomeration of small particles in a flowing turbulent gas. The transported particles because of their inertia are assumed not to follow the motion of the large scales of the turbulence and or the motion of the small dissipating scales of the turbulence. We show how both these behaviours can be represented by a PDF approach analogous to that used in classical kinetic theory. For large scale dispersion the focus is on transport in simple generic flows like statistically stationary homogeneous and isotropic turbulence and simple shear flows. Special consideration is given to the transport and deposition of particles in turbulent boundary layers. For small scale transport the focus is on how the small scales of turbulence together with the particle inertial response enhance collision processes like particle agglomeration. In this case the importance of segregation and the formation of caustics, singularities and random uncorrelated motion is highlighted and discussed.     

Wave influence on turbulence length scales in free surface channel flows

In order to predict sediment movements in coastal environments, the interaction between these particles and turbulence should be better understood. Although previous studies have particularly shown the importance of the turbulence length scales on sediment transport for current flows, few measurements have been made on wave/current flows. The purpose of our experiments is to get a better knowledge on wave action on these characteristic length scales. For this study, in the context of a grid-generated turbulence, we aimed to describe evolution of turbulence macro and micro scales in two kinds of free surface flow. Indeed, current and wave/current flows are studied. Two data analysis techniques are used to estimate these characteristic length scales depending on flow conditions. Whereas a well-known energetic method is used for current flow, a specific analysis based on correlation measurements is lead to describe temporal evolution of turbulence length scale over the wave period. As a main result, we show that the free surface causes a vortex stretching for current flow and that turbulence length scales follow a periodic evolution with a frequency which is twice as the swell period. The turbulence length scales also depend on wave period and amplitude.     

Local structure of turbulence in free plows with strong intermittency

The results of an experimental verification of the theory of locally homogeneous turbulence in a mixing layer, a boundary layer, two-dimensional and axisymmetric wakes and, moreover, in the three-dimensional wake of a cylinder of finite length are presented. Since the characteristic dimensions of most of the flows investigated were very large (integral scales of turbulence of up to 1 m), at very large Reynolds numbers high resolution was achieved. The measurements showed that the quantities C and characterizing the inertial interval of the turbulence spectrum are not universal constants, as previously assumed, and in the flows in question, irrespective of their type, are uniquely determined by the intermittency factor.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 51–59, November–December, 1988.     

Mixing enhancement behind an oblique shock wave

The possibility of mixing enhancement when a design-condition cocurrent jet passes through a stationary oblique shock is investigated. In [4] the effect of such a shock on the mixing layer of flows with Mach numbers M = 3 and 5 was experimentally investigated and it was shown that behind the shock no turbulence is generated. However, irrespective of its effect on the turbulence characteristics, an oblique shock causes deformation of the jet, modifying its dimensions, and in the three-dimensional case the shape of the cross section. The effect of this deformation on mixing, which is shown to be fairly significant, has been investigated theoretically using a numerical method. An approximate relation describing the variation of the maximum admixture concentration in the jet behind the shock is proposed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 61–68, March–April, 1992.The authors are grateful to V. A. Stepanov for useful discussions.     

Compressible Turbulence and Energetic Scales: What Is Known from Experiments in Supersonic Flows?

Some properties of large-scale structures in supersonic turbulent flows are examined through experiments. The large eddies considered here include energetic scales, which contribute predominantly to, say, turbulent energy and coherent structures. Different features are presented, such as the level of energy in supersonic free shear flows, the average size of energetic structures, and their characteristic timescales. It is shown that compressibility affects the level of velocity and the size of the energetic eddies, but in many common supersonic situations, the estimation of the timescales can be made from rules valid for solenoidal turbulence. Some implications for compressible turbulence modeling are suggested. Finally, the properties of coherent structures are considered in the case of mixing layers and in a separated shock/boundary layer interaction. Some features relative to the organization of the large eddies are given and the importance of the shock motion is discussed in relation to the shock/layer interaction. This revised version was published online in August 2006 with corrections to the Cover Date.     

Compressibility and structure of turbulence in supersonic shear flows

In this paper, different aspects of supersonic turbulent flows are discussed, in connection with some properties of compressible turbulence. The discussion is based on experiments, in which particular features have been found. The first point is the influence of density gradients. It is shown that changing the density gradient in a boundary layer does not change the particularly small size of the energetic scales. This effect is attributed to compressibility and not to density stratification, probably by modifying the `inactive motions'. The second point is about the importance of acoustics in a mixing layer. The results show that turbulent transport of momentum and heat follows the same analogy as in boundary layers, and that the energy losses by acoustic radiation are too weak to explain the reduction of the spreading rate, which is the major global effect of compressibility.     

The structure and dynamics of reacting plane mixing layers

The reacting two-dimensional plane mixing layer has been studied in two configurations: a rearward facing step and a two-stream mixing layer. Observations have been made of the steady state behavior, and the unsteady behavior when the flow was forced by a specific acoustic frequency. The steady behavior of the mean properties of the reacting flows is similar to that of non-reacting free shear flows except for the global effects of thermodynamic property changes. The structure of these flows is qualitatively similar to that of non-reacting flows. Vortices form by the two-dimensional Kelvin-Helmholtz instability and grow by subharmonic combination until the mixing layer interacts with the walls. Entrainment is dominated by the two-dimensional vortex motion. Three-dimensional instabilities give rise to secondary vortices which are coherent over several Kelvin-Helmholtz structures and dominate the fine scale mixing process. The mixing transition corresponds to a loss of coherence in the layer. Unsteady behavior occurs when there are resonant interactions with the Kelvin-Helmholtz instability or the instability associated with the recirculation vortex in the rearward facing step flow. Modeling efforts are reported which show promise of simulating the essential features of plane mixing layers.A version of this paper was presented at the ASME Winter Annual Meeting of 1984 and printed in AMD-Vol. 66     

A method to estimate turbulence intensity and transverse Taylor microscale in turbulent flows from spatially averaged hot-wire data

A new approach to evaluate turbulence intensity and transverse Taylor microscale in turbulent flows is presented. The method is based on a correction scheme that compensates for probe resolution effects and is applied by combining the response of two single hot-wire sensors with different wire lengths. Even though the technique, when compared to other correction schemes, requires two independent measurements, it provides, for the same data, an estimate of the spanwise Taylor microscale. The method is here applied to streamwise turbulence intensity distributions of turbulent boundary layer flows but it is applicable generally in any turbulent flow. The technique has been firstly validated against spatially averaged DNS data of a zero pressure-gradient turbulent boundary layer showing a good capacity to reconstruct the actual profiles and to predict a qualitatively correct and quantitatively agreeing transverse Taylor microscale over the entire height of the boundary layer. Finally, the proposed method has been applied to available higher Reynolds number data from recent boundary layer experiments where an estimation of the turbulence intensity and of the Taylor microscale has been performed.     

The possibility of measuring turbulence by a correlation method

In [1] a correlation method for measuring the velocity pulsations in stationary plasma flows was described. The magnitude of the pulsations was determined from the value of the frequency deviation in the spectrum of the cross-correlation functions of optical fluctuations at two closely arranged points along the flow.In the present work, an attempt is made to justify such a method for measuring the characteristics of turbulence both in plasma and in any low-temperature gas flows.     

MHD Turbulence at the Laboratory Scale: Established Ideas and New Challenges

The properties of MHD turbulence in the electrically conducting fluids available in the laboratory (where the magnetic Reynolds number is significantly smaller than unity) may be summarised as follows:(1) The Alfven waves, even under their degenerated form at this scale, are responsible for a tendency to two-dimensionality. Eddies tend to become aligned with the applied magnetic field and inertia tends to restore isotropy. The competition between these mechanisms results in a spectral law t^-2k^-3.(2) When insulating walls, perpendicular to the magnetic field, are present and close enough to each other, two-dimensionality can be established with a good approximation within the large scales, and the predominant mechanism is the inverse energy cascade.(3) These columnar eddies are nevertheless submitted to a dissipation within the Hartmann boundary layers present at their ends, whose time scale is independent of the wave number. When this damping effect is negligible, ordinary 2D turbulence is observed with k^-5/3 spectra. On the contrary when this (ohmic and viscous) damping is significant this 2D turbulence exhibits k^-3 spectra.Besides these homogeneous (except within the Hartmann layers) conditions, for instance in shear flows such as mixing layers, almost nothing is known except that two-dimensionality may be well established. The first results of a recent experimental investigation (still in development) are presented. Some challenging questions are raised, such as the interpretation of a surprising difference between the transport of momentum and the transport of a scalar quantity (heat) across that layer. A video was shown during the oral presentation of this paper, illustrating the energy transfer toward the large scales and the weakness of the dissipation suffered by this 2D velocity field.     

稳定分层流动中湍流特性的研究综述

本文总结了近60 年来分层流动中湍流特性研究的成果. 主要从两个方面进行了综述:(1) 分层流动中湍流场的演变和混合. 在这方面主要分析稳定分层对湍流混合和湍流结构的影响, 以及混合层内湍流结构的特性和混合层的演化规律. (2) 分层流动中湍流的扩散和输运. 动量和标量的逆梯度输运特性是分层湍流研究的一个重要方向;分析分层对湍流扩散的影响. 并指出了一些值得今后进一步研究的方向.     

Estimate of the correlation between pressure pulsations and the divergence of the velocity in subsonic flows of variable density

In flows with variable density, the turbulence energy equation contains a large number of correlations, about which little is at present known [1]. One of the least studied is the correlation between the pressure and the divergence of the velocity. Usually, this correlation is ignored [2, 3]. The aim of the present paper is to estimate the pulsations of the divergence of the velocity and the correlation with the pressure pulsations in a subsonic turbulent flow with variable density. Three cases are considered: 1) mixing of gases having different densities, 2) diffusion combustion, 3) combustion of a homogeneous mixture. It is assumed that the Mach number is small, the Reynolds number large, and the coefficients of molecular diffusion and thermal diffusivity equal; external forces are absent.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 4–11, May–June, 1979.     

Two-scale semiempirical theory of turbulent boundary layers and jets

To characterize the turbulence of boundary layers in the energy-bearing interval of wave numbers several turbulence scales are sometimes used (for example, [1, 2]). In particular, the universality of the semiempirical model of turbulence [2] can be extended in this way. A turbulence model with one equation (energy balance of the turbulence) has been constructed and used [3–6] and it has been established that the number of problems that can be solved for a universal choice of the values of the empirical coefficients increases appreciably if not one but two turbulent scales are used. In the present paper, it is shown that the introduction of a second scale makes it possible to take into account the interaction of shear layers in flows with two shear layers (for example, a channel or jet), and also to take into account the influence of turbulence of an external flow on a boundary layer. The interaction of shear layers is taken into account in theories containing a transport equation for the turbulent frictional stress _t (for example, [7]), in which the essence of the interaction reduces to diffusion of _t from layer to layer. In the present paper, a predominant volume interaction effect is assumed. It takes the form of a difference between the interaction of large-scale vortices with a shear deformation motion in flows with one and two shear layers, and also in the presence of turbulence in an external flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 8, pp. 17–25, November–December, 1982.     

Heat transfer in laminar pulsating flows of fluids with temperature dependent viscosities

The effect of time-dependent pressure pulsations on heat transfer in a pipe flow with constant temperature boundaries is analysed numerically when the viscosity of the pulsating fluid is an inverse linear function of the temperature. The coupled differential equations are solved using Crank-Nicholson semi-implicit finite difference formulation with some modifications.The results indicate local variations in heat transfer due to pulsations. They are useful in the design of heat exchangers working under pulsating flow conditions. The analytical results are presented for both heating and cooling. The conditions under which pulsating flows can augment the heat transfer are discussed. The results are applicable for heat exchangers with fluids of high Prandtl number.     

Effects of free stream turbulence on the distribution of heat transfer around turbine blade sections

Local convective heat transfer coefficients to a number of modern gas turbine blade sections have been measured under a wide range of mainstream conditions, from notionally steady flows to highly perturbed turbulent flows. The paper discusses the results and, through a detailed analysis of the pertinent boundary layer flow parameters and their relation to the observed experimental results, tests criteria for the occurrence of transition from laminar to turbulent boundary layers, a factor which all the data from this work confirm as critical in predicting the quantitative effects of mainstream turbulence on heat transfer rates. Artificially induced mainstream turbulence, which is endemic in the flows in a real turbine, enhances significantly the heat transfer rates, especially to the leading edge regions and on the pressure surface, particularly when the acceleration is tending to suppress transition. The results presented here confirm existing criteria for laminarisation and the applicability of some of those available for predicting laminar-turbulent transition. The observations also demonstrate how surface geometry can influence the stability of the flows, and the uncertainties which remain in assessing the effect of Goertler vortices and their role in the convective heat transfer process.