Characteristics of large-scale and superstructure motions in a turbulent boundary layer overlying complex roughness

The structural attributes of turbulent flow over a complex roughness topography are explored using high-frame-rate stereo particle-image velocimetry measurements in the wall-normal–spanwise plane. The roughness under consideration was replicated from a turbine blade damaged by deposition of foreign materials and contains a broad range of topographical scales arranged in a highly irregular manner. Previous results from Barros and Christensen [Observations of turbulent secondary flows in a rough-wall boundary layer. J Fluid Mech. 2014;748] revealed strong spanwise heterogeneity in the flow attributed to the formation of roughness-induced turbulent secondary flows identified by spanwise-alternating low- and high-momentum flow pathways (HMP & LMP, respectively) in the mean flow marked by enhanced Reynolds stresses and turbulent kinetic energy. Frequency spectra of streamwise velocity at fixed wall-normal location presented herein also display strong dependence on spanwise position. In particular, the roughness promotes enhanced energy content of the large-scale and smaller-scale motions (as opposed to very-large-scale ones). Depending on spanwise position, pre-multiplied spectra highlight significant modification of the energy content of the very large-scale motions (superstructures) due to roughness compared to smooth-wall flow. Of note, a shift in both TKE and RSS content to shorter streamwise scales at an LMP was noted, while less of an impact was found coincident with an HMP.     

Surface roughness effects on the turbulence statistics in a low Reynolds number channel flow

A high-resolution particle image velocimetry was used to characterize a low Reynolds number turbulent flow in a channel. Experiments were conducted over a sand grain-coated surface of large relative roughness, and the results were compared with measurements over a smooth surface. The roughness perturbation significantly modified the outer layer. Even though the streamwise Reynolds stress shows less sensitivity in the outer layer to the boundary condition, significant enhancements were observed in the wall-normal Reynolds stress and the Reynolds shear stress. These modifications were considered as footprints of the larger-scale eddies transporting intense wall-normal motions away from the rough wall. A quadrant decomposition shows that strong and more frequent ejections are responsible for the larger values of the mean Reynolds shear stress over the rough wall. The results also indicate that spanwise vortex cores with mean vorticity of the same sign as the mean shear are the dominant smaller-scale vortical structures over the smooth and rough walls. A linear stochastic estimation-based analysis shows that the average larger-scale structure associated with these vortices is a shear layer that strongly connects the outer layer flow to the near-wall flow. A proper orthogonal decomposition of the flow suggests that the large-scale eddy is more energetic for the rough wall, and contributes more significantly to the resolved turbulent kinetic energy and the Reynolds shear stress than the smooth wall.     

Multi-scale interactions in a compressible boundary layer

The properties of spectral subranges of scales in a boundary layer at Mach=2.3 and friction Reynolds number Reτ = 570 are investigated by analysing DNS data. One major aim is to examine whether footprinting and modulation of small-scale near-wall motions by outer large structures, observed at high Reynolds numbers, also pertain to this low-Reynolds-number case, or whether the logarithmic layer simply contains a continuous hierarchy of motions without specific outer scales playing a distinctive role. To this end, the spectrum of scales is decomposed into modes by application of the “Empirical Mode Decomposition”. The properties of different scales are then investigated by means of spectra, maps of isotropy/anisotropy parameters, the premultiplied derivative of the second-order structure function, correlation coefficients and joint probability density function (PDF), the last constructed from conditionally sampled data for the small-scale motions within the large-scale footprints. A clear commonality is identified between interactions in high-Reynolds-number channel flow and the present low-Reynolds-number boundary layer.     

Transition region where the large-scale and very large scale motions coexist in atmospheric surface layer: wind tunnel investigation

The turbulent structures in atmospheric surface layer (ASL) are investigated in wind tunnel with hot-wire anemometers in present study. The results show that there exist two typical turbulent structures characterised by their streamwise length scales, i.e. large-scale motions (LSMs) and very large scale motions (VLSMs) as reported recently in pipe flow, channel flow, zero-pressure-gradient turbulent boundary layers and near-neutral ASLs. Moreover, a transition region containing both LSMs and VLSMs is first reported in present investigation, and this region depends on the Reynolds numbers. In the transition region, as the wall-normal distance increases, the turbulent energy ratio of LSMs is gradually weakened but VSLMs strengthened.     

Effects of roughness elements on bypass transition induced by a circular cylinder wake

Abstract  

The bypass transition of flat-plate boundary layer induced by a circular cylinder wake under the influence of roughness elements is experimentally investigated. The hydrogen-bubble visualization results show that the boundary layer separation occurs upstream of the roughness, and the separated shear layer is incised by roughness to different extent, resulting in different kinds of secondary vortices formed immediately downstream of the roughness. During the evolution of the secondary vortex, two types of instabilities are observed, which are denoted as large- and small-scale instabilities, respectively, according to different spatial scale of the hairpin vortices formed afterward. A merging process of hairpin vortices is also observed when the secondary vortices undergo the small-scale instability, and a potential new transition control strategy based on the present observation is proposed.     

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通过使用一排16根冷线探头排在多个空间点同时测量微加热圆柱的尾流温度场, 用小波分析技术对瞬时温度场的时间序列信号进行多尺度分析, 目的是研究不同尺度脉动温度对总体温度场的贡献.直径为d = 12.7 mm 的圆柱产生了被测的尾流, 对应的雷诺数为5500, 测量区域位于下游距离为2d 和 20d 之间. 基于小波多尺度分辨技术, 尾流温度场被分解为不同温度脉动特征尺度的小波分量. 通过分析这些小波分量的瞬时温度等值线图, 能够直接观测到不同特征尺度的涡结构运动特征和湍流间歇过程. 特别地, 我们在近场区从原始信号分解获得的高频区域中发现了K-H涡的存在. 不同尺度的温度方差沿流向的变化表明, 在下游距离为x=3d和 20d之间, 中等尺度的结构比大尺度和小尺度结构对总的温度均方根的贡献更大. 不同尺度的自相关函数表明, 大尺度和中等尺度的结构显示出较大的相关性, 而高频的小波分量则更快地失去了原有的拟序性. 关键词： 湍流尾流 被动标量 小波分析     

Transition from large-scale to small-scale dynamo

The dynamo equations are solved numerically with a helical forcing corresponding to the Roberts flow. In the fully turbulent regime the flow behaves as a Roberts flow on long time scales, plus turbulent fluctuations at short time scales. The dynamo onset is controlled by the long time scales of the flow, in agreement with the former Karlsruhe experimental results. The dynamo mechanism is governed by a generalized α effect, which includes both the usual α effect and turbulent diffusion, plus all higher order effects. Beyond the onset we find that this generalized α effect scales as O(Rm(-1)), suggesting the takeover of small-scale dynamo action. This is confirmed by simulations in which dynamo occurs even if the large-scale field is artificially suppressed.     

Experimental study of noise emitted by circular cylinders with large roughness

The aerodynamic noise generated by high Reynolds number flow around a bluff body with large surface roughness was investigated. This is a relevant problem in many applications, in particular aircraft landing gear noise. A circular cylinder in cross-flow and a zero-pressure-gradient turbulent boundary layer with various types of roughness was tested in a series of wind tunnel experiments. It has been shown that distributed roughness covering a circular cylinder affects the spectra over the entire frequency range. Roughness noise is dominant at high frequencies, and the peak frequency is well described by Howe?s roughness noise model when scaled with the maximum outer velocity. There are differences between hemispherical and cylindrical roughness elements for both the circular cylinder and the zero-pressure-gradient turbulent boundary layer cases, indicating a dependence on roughness shape, not described by the considered roughness noise models. Cylindrical roughness generates higher noise levels at the highest frequencies, especially for the zero-pressure-gradient turbulent boundary layer case. Cable-type roughness aligned with the mean flow does not generate roughness noise, and its spectrum has been found to collapse with the smooth cylinder at medium and high frequencies. At low and medium frequencies the noise spectra have the same features as the smooth cylinder, but with higher shedding peak levels and fall-off levels, despite the decrease in spanwise correlation length. Roughness induces early separation, and thus a shift of the spectra to lower frequencies.     

Reply to the note on the flow behaviour of combustion gas in the boundary layer of an MHD generator

The temperature profile in Fig. 3 of Ref. 1 is better approximated by a relation for a turbulent boundary layer than a laminar boundary layer. The critical Reynolds number is expected to be lowered in the flow train of MHD combustion gas because of large turbulence in the combustor and by roughness along the duct.     

Steady large-scale modulation of a moderately turbulent co-flow jet

The effects of a spatial modulation acting at the inflow of a moderately turbulent planar jet surrounded by a faster co-flow are investigated using direct numerical simulation of the Navier–Stokes equations. We adopt a superposition of spatially filtered small-scale random perturbations and a structured large-scale flow modulation. The large-scale modulation is characterised in terms of a Beltrami flow, specified by a wavenumber K. These large-scale modulations are steady and spatially periodic, while the random small-scale perturbations fluctuate in time and in space. The flow configuration studied in this paper is agitated by this combined large- and small-scale agitation at the inflow plane of a rectangular domain of size L × L × 2L in the x-, y- and streamwise z-directions. The inflow perturbation is focused on a strip of size L × D in the x- and y-directions. A parametric variation is carried out considering different choices for the wavenumber of the large-scale modulation. We focus on effects that the inflow modulation has on global characteristics of the flow, e.g. the width of the mixing region formed between the two streams and the dissipation rate, ?. Results show that the width of the mixing region increases faster compared to the case without the large-scale perturbation, when the flow is agitated by structures of size comparable to the integral scales of the flow. For the dissipation rate, results show the presence of a maximum response at a certain wavenumber K in case we apply a large-scale modulation. This maximum is attained at modulation scales that vary locally with respect to the distance from the inflow plane. Close to the inflow, the maximum response occurs at small modulation scales, while further into the domain a maximum response is present at comparably large modulation scales.     

Recycling inflow method for simulations of spatially evolving turbulent boundary layers over rough surfaces

The technique by Lund et al. to generate turbulent inflow for simulations of developing boundary layers over smooth flat plates is extended to the case of surfaces with roughness elements. In the Lund et al. method, turbulent velocities on a sampling plane are rescaled and recycled back to the inlet as inflow boundary condition. To rescale mean and fluctuating velocities, appropriate length scales need be identified and for smooth surfaces, the viscous scale l_ν = ν/u_τ (where ν is the kinematic viscosity and u_τ is the friction velocity) is employed for the inner layer. Different from smooth surfaces, in rough wall boundary layers the length scale of the inner layer, i.e. the roughness sub-layer scale l_d, must be determined by the geometric details of the surface roughness elements and the flow around them. In the proposed approach, it is determined by diagnosing dispersive stresses that quantify the spatial inhomogeneity caused by the roughness elements in the flow. The scale l_d is used for rescaling in the inner layer, and the boundary layer thickness δ is used in the outer region. Both parts are then combined for recycling using a blending function. Unlike the blending function proposed by Lund et al. which transitions from the inner layer to the outer layer at approximately 0.2δ, here the location of blending is shifted upwards to enable simulations of very rough surfaces in which the roughness length may exceed the height of 0.2δ assumed in the traditional method. The extended rescaling–recycling method is tested in large eddy simulation of flow over surfaces with various types of roughness element shapes.     

Influence of short roughness strip on the turbulent boundary layer structure

Hot-wire measurements have been undertaken in a turbulent boundary layer which is subjected to an impulse in form of a short roughness strip with the aim of examining its influence on the structure of the turbulent boundary layer. The results indicate that, while the energy containing motion is shifted from low wave number to high wave number near the wall due to the interfering of the roughness strip with the near-wall structure, the reverse is the case in the outer region. While the anisotropy at small scale changes appreciably, there is no discernable change at the large scale when distance from the wall is increased as reflected in the collapses of spectra shear correlation coefficient at the low wave number. It further shows that the roughness strip alters the flow dynamics of the boundary layer as shown in the changes in the mixing length distribution.     

On the use of spires for generating inflow conditions with energetic coherent structures in large eddy simulation

While it has long been a practice to place spires near the inlet of a wind tunnel to quickly develop a turbulent boundary layer with similarities to an atmospheric boundary layer, this has not been the case for creating turbulent boundary layer inflow in large eddy simulations (LESs) of turbulent flows. We carry out LES with the curvilinear immersed boundary method to simulate the flow in a wind tunnel with a series of spires in order to investigate the feasibility of numerically developing inflow conditions from a precursory spire LES and assessing the similarities of the turbulence statistics to those of an atmospheric boundary layer. The simulated mean velocity field demonstrates that a turbulent boundary layer with height equal to the spire height develops very quickly, within five spire heights downstream. The major attribute of using spires for precursory simulations is the spatially evolving coherent structures that form downstream of the spires offering a range of length scales at both the vertical and streamwise directions allowing multiple turbulent inflow conditions to be extracted from a single simulation. While the distribution of length scales far from the spires resembles an atmospheric boundary layer, some turbulence statistics have some significant differences.     

Three-dimensional turbulent flow over cube-obstacles

In order to investigate the influence of surface roughness on turbulent flow and examine the wall-similarity hypothesis of Townsend, three-dimensional numerical study of turbulent channel flow over smooth and cube-rough walls with different roughness height has been carried out by using large eddy simulation(LES) coupled with immersed boundary method(IBM). The effects of surface roughness array on mean and fluctuating velocity profiles, Reynolds shear stress, and typical coherent structures such as quasi-streamwise vortices(QSV) in turbulent channel flow are obtained. The significant influences on turbulent fluctuations and structures are observed in roughness sub-layer(five times of roughness height).However, no dramatic modification of the log-law of the mean flow velocity and turbulence fluctuations can be found by surface cube roughness in the outer layer. Therefore, the results support the wall-similarity hypothesis. Moreover, the von Karman constant decreases with the increase of roughness height in the present simulation results. Besides, the larger size of QSV and more intense ejections are induced by the roughness elements, which is crucial for heat and mass transfer enhancement.     

Revisiting the boundary layer structure used in Craig and Gordon's model of isotope fractionation in evaporation

Craig and Gordon's (CG) model of isotope fractionation in evaporation was derived more than 40 years ago and was based on the turbulent boundary layer structure model acceptable at that time. That view suggested that turbulent flows consist of eddies with a wide range of length scales moving randomly in the flow domain. There is evidence that some parameters in CG model do not fully correspond to data in the literature. Owing to advances in fluid dynamics research techniques, it has been shown in recent decades that the apparent chaotic flow in turbulent boundary layers is in fact governed by few well-organised structures. This article reviews the major characteristics of these coherent structures based on available results from experimental, numerical and theoretical studies of turbulent and laminar boundary layers. The review points on some differences between past and present views of the boundary layer structure and on their relation and possible influence on power laws in CG model.     

Kolmogorov scaling of turbulent flow in the vicinity of the wall

How to scale even the simplest of turbulent flows continues to be a cause for considerable controversy. In the present research, a data base compiling results from channel flow direct numerical simulations and turbulent boundary layer experiments is employed to investigate the properties of shear and normal Reynolds stresses very close to the wall. Two types of scaling based on Kolmogorov length and velocity scales are analyzed. It is shown that it is highly likely that large length scales of the order of the channel half-width or the boundary layer thickness play an important role even in the innermost regions of wall-bounded turbulent flows, which hints at the persistence of Reynolds number effects in even high Reynolds number flows.     

Vorticity,backscatter and counter-gradient transport predictions using two-level simulation of turbulent flows

The two-level simulation (TLS) method evolves both the large-and the small-scale fields in a two-scale approach and has shown good predictive capabilities in both isotropic and wall-bounded high Reynolds number (Re) turbulent flows in the past. Sensitivity and ability of this modelling approach to predict fundamental features (such as backscatter, counter-gradient turbulent transport, small-scale vorticity, etc.) seen in high Re turbulent flows is assessed here by using two direct numerical simulation (DNS) datasets corresponding to a forced isotropic turbulence at Taylor’s microscale-based Reynolds number Re_λ ≈ 433 and a fully developed turbulent flow in a periodic channel at friction Reynolds number Re_τ ≈ 1000. It is shown that TLS captures the dynamics of local co-/counter-gradient transport and backscatter at the requisite scales of interest. These observations are further confirmed through a posteriori investigation of the flow in a periodic channel at Re_τ = 2000. The results reveal that the TLS method can capture both the large- and the small-scale flow physics in a consistent manner, and at a reduced overall cost when compared to the estimated DNS or wall-resolved LES cost.     

合成冷/热射流控制超声速边界层流动稳定性

为了探究超声速边界层流动稳定性及其转捩控制机理,提出基于合成冷/热射流的边界层速度-温度耦合控制方法,并通过数值模拟研究了Ma=4.5超声速平板边界层不稳定波的传播,采用线性稳定性理论中的时间模式分析了壁面吹吸、射流温度、扰动频率、扰动振幅等对不稳定波控制效果的影响.结果表明:无射流控制时,边界层内同时存在不稳定的第一模态扰动波和第二模态扰动波,且二维波形式的第二模态占主导地位;壁面吹吸作用下,仅出现更加不稳定的第二模态,第一模态被抑制;速度-温度耦合控制下,射流温度对扰动模态的不稳定区域大小及扰动增长率影响显著,射流温度与来流温度不同时,温度的脉动使得流动转捩为湍流的速度加快,边界层速度型更加饱满,抗干扰能力增强,流动稳定性提高;高频的吹吸扰动对流场的控制效果优于低频扰动,扰动频率超过400 Hz时,第二模态扰动波时间增长率降低,扰动分量对边界层速度剖面和温度剖面的修正加快,第二模态更加稳定;扰动振幅减小为主流速度的1%时,仅出现时间增长率较小的第二模态,控制效果较好,进一步减小时,第一模态重新出现,并且波数范围与第二模态先重合后分离,对应的时间增长率先增加后减小.研究结果为边界层转捩控制技术提供了新的思路.     

Effects of forcing in three-dimensional turbulent flows

We present the results of a numerical investigation of three-dimensional homogeneous and isotropic turbulence, stirred by a random forcing with a power-law spectrum, E(f)(k) approximately k(3-y). Numerical simulations are performed at different resolutions up to 512(3). We show that at varying the spectrum slope y, small-scale turbulent fluctuations change from a forcing independent to a forcing dominated statistics. We argue that the critical value separating the two behaviors, in three dimensions, is y(c)=4. When the statistics is forcing dominated, for yy(c), we find the same anomalous scaling measured in flows forced only at large scales. We connect these results with the issue of universality in turbulent flows.     

Random roughness enhances lift in supersonic flow

We study the scattering of shock waves by a rough wedge using second-order perturbation analysis and stochastic simulations employed synergistically to cover a large range in correlation length A and amplitude epsilon of the profile roughness (with length d). For small epsilon and A/d<1, the mean of the perturbed pressure scales alpha epsilon2 and alpha (A/d)(-2), while the corresponding variance scales alpha epsilon and alpha (A/d)(-1). However, for large epsilon, the mean pressure scales approximately alpha epsilon, while for A/d>1 it is independent of A. Our results are useful in evaluating the effects of roughness in high-speed flight but also in designing novel enhanced-lift aerodynamic surfaces using rough skin concepts.