Near-field measurements and development of a new boundary layer over a flat plate with localized suction

Suction on a turbulent boundary layer is applied through a narrow strip in order to understand the effects suction can have on the boundary layer development and turbulent structures in the flow. Detailed two-component laser Doppler velocimetry (LDV) and laser-induced fluorescence (LIF) based measurements have been undertaken in regions close to the suction strip and further downstream. The region close to the strip involves a flow reversal accompanied by a change in sign for the Reynolds shear stress and strong gradients in the flow variables. The mean streamwise velocity after suction remains larger than its corresponding no-suction value. Relative to the no-suction case, the velocity fluctuations first decrease with suction followed by a slow recovery which may involve a slight overshoot. LIF visualizations indicate that compared to the no-suction case, the low-speeds streaks stay closer to the wall and exhibit a smaller amount of spanwise and wall-normal oscillations with suction. The visualization results are consistent with two-point velocity correlation measurements. The streamwise and spanwise correlation measurements indicate that the structures are disrupted or removed from the boundary layer due to suction suggesting that the original boundary layer has been strongly influenced by suction. The results are explained by the development of a new inner layer that forms downstream of the suction strip.     

Velocity statistics and flow structures observed in bypass transition using stereo PTV

It is known from smoke visualizations that in a transitional boundary layer subjected to free-stream turbulence, streaks appear and eventually break down to turbulence after wavy motions. In order to observe the streaky structures directly, a stereo particle-tracking velocimetry system using hydrogen bubbles in a water channel has been developed and validated against laser Doppler velocimetry. Mean flow statistics show good agreement with previous results. With the developed measurement system, the instantaneous spanwise distribution of the streamwise and wall-normal velocities can be measured fast enough to resolve the time development of the streaky structures. Measurements of instantaneous spanwise distributions of the streamwise and wall-normal velocity disturbances show strong negative correlation between the wall-normal and streamwise velocities in the streaks. Published online: 19 November 2002     

The effect of streamwise vortices on the turbulence structure of a separating boundary layer

A high Reynolds number flat plate turbulent boundary layer is investigated in a wind-tunnel experiment. The flow is subjected to an adverse pressure gradient which is strong enough to generate a weak separation bubble. This experimental study attempts to shed some new light on separation control by means of streamwise vortices with emphasize on the change in the boundary layer turbulence structure. In the present case, counter-rotating and initially non-equidistant streamwise vortices become and remain equidistant and confined within the boundary layer, contradictory to the prediction by inviscid theory. The viscous diffusion cause the vortices to grow, the swirling velocity component to decrease and the boundary layer to develop towards a two-dimensional state. At the position of the eliminated separation bubble the following changes in the turbulence structure were observed. The anisotropy state in the near-wall region is unchanged, which indicates that it is determined by the presence of the wall rather than the large scale vortices. However, the turbulence in the outer part of the boundary layer becomes overall more isotropic due to an increased wall-normal mixing and a significantly decreased production of streamwise fluctuations. The turbulent kinetic energy is decreased as a consequence of the latter. Despite the complete change in mean flow, the spatial turbulence structure and the anisotropy state, the process of transfer of turbulent kinetic energy to the spanwise fluctuating component seems to be unchanged. Local regions of anisotropy are strongly connected to maxima in the turbulent production. For example, at spanwise positions in between those of symmetry, the spanwise gradient of the streamwise velocity cause significant production of turbulent fluctuations. Transport of turbulence in the spanwise direction occurs in the same direction as the rotation of the vortices.     

Optimal disturbances in suction boundary layers

A well-known optimization procedure is used to find the optimal disturbances in two different suction boundary layers within the spatial framework. The maximum algebraic growth in the asymptotic suction boundary layer is presented and compared to previous temporal results. Furthermore, the spatial approach allows a study of a developing boundary layer in which a region at the leading edge is left free from suction. This new flow, which emulates the base flow of a recent wind-tunnel experiment, is herein denoted a semi-suction boundary layer. It is found that the optimal disturbances for these two suction boundary layers consist of streamwise vortices that develop into streamwise streaks, as previously found for a number of shear flows. It is shown that the maximum energy growth in the semi-suction boundary layer is obtained over the upstream region where no suction is applied. The result indicates that the spanwise scale of the streaks is set in this region, which is in agreement with previous experimental findings.     

哈特曼边界层的初级稳定性分析

导电流体在法向外置磁场的作用下,在贴近壁面处会形成哈特曼边界层.哈特曼边界层的稳定性研究对电磁冶金过程和热核聚变反应冷却系统等相关设备的设计和运行都有着十分重要的意义.本文采用非正则模态稳定性分析方法,对两无限大绝缘平行平板内导电流体流动的稳定性进行了研究.通过在时间上迭代求解扰动变量的控制方程组和伴随控制方程组,获得了在磁场作用下初级扰动的增长情况及其空间分布形式,分析了磁场强度对最优扰动增长倍数G_max、最优展向波数β_opt和最优时刻t_opt的影响,并考察了上下两个哈特曼边界层之间的相互作用.结果表明,最优初始扰动的空间分布形式为沿着流场方向的漩涡,关于法向方向对称或者反对称.当哈特曼数Ha较大时(Ha>10),对称漩涡和反对称漩涡形式的初始扰动增长倍数基本相等;上下两个哈特曼边界层可以认为是彼此独立的,不会相互影响,此时最优扰动增长倍数G_max与局部雷诺数R的平方成正比,相应的最优展向波数β_opt和最优时刻t_opt均正比于哈特曼数Ha.当哈特曼数Ha较小时(Ha<10),反对称漩涡形式的初始扰动更为不稳定,其增长倍数大于对称漩涡的增长倍数,且上下两个边界层之间存在着一定的相互作用,并对整个流场的稳定性产生一定的影响.      

Algebraic growth in boundary layers: optimal control by blowing and suction at the wall

The upstream perturbations that maximise the spatial energy growth in a boundary layer are called optimal perturbations. The optimal perturbations correspond to streamwise vortices and the downstream response corresponds to streamwise streaks.The aim of the present paper is to find a control by blowing and suction at the wall that zeros the energy of perturbation, when the initial disturbance is itself optimal. We shall also address the question: which kind of blowing and suction at the wall is most effective in controlling optimal disturbances?The problem is examined by a method of receptivity analysis based on a numerical solution of a system of equations adjoint to the linearised boundary layer equations. We shall investigate both cases of a flat and a concave wall.     

Experiments on localized disturbances in a flat plate boundary layer. Part 1. The receptivity and evolution of a localized free stream disturbance

The receptivity of a laminar boundary layer to free stream disturbances has been experimentally investigated through the introduction of deterministic localized disturbances upstream of a flat plate mounted in a wind tunnel. Hot-wire measurements indicate that the spanwise gradient of the normal velocity component (and hence the streamwise vorticity) plays an essential role in the transfer of disturbance energy into the boundary layer. Inside the laminar boundary layer the disturbances were found to give rise to the formation of longitudinal structures of alternating high and low streamwise velocity. Similar streaky structures exist in laminar boundary layers exposed to free stream turbulence, in which the disturbance amplitude increases in linear proportion to the displacement thickness. In the present study the perturbation amplitude of the streaks was always decaying for the initial amplitudes used, in contrast to the growing fluctuations that are observed in the presence of free stream turbulence. This points out the importance of the continuous influence from the free stream turbulence along the boundary layer edge.     

Periodicity of large-scale coherence in turbulent boundary layers

This study examines the pronounced periodicity of large-scale coherent structures in turbulent boundary layers, which are of the order of the boundary layer thickness (δ) and reside in the logarithmic and wake regions. To this end, a series of multi-camera planar particle image velocimetry (PIV) measurements are conducted in a streamwise/spanwise and streamwise/wall-normal planes at a friction Reynolds number of Re_τ ≈ 2500. The experiments are configured to capture a large field-of-view with velocity fields that cover a streamwise extent in excess of 15δ. The resulting vector fields reveal large-scale streamwise and spanwise organisation instantaneously, which is often lost when only examining mean statistics. By extracting the dominant streamwise and spanwise Fourier modes of the large-scale motions, a clearer picture of these structural organisations and coherence is presented. A targeted inspection of these dominant modes reveal that these features remain coherent over a significant fraction of the boundary layer thickness in the wall-normal direction, but only a fraction of them have coherence that extends to the wall (wall-coherent). Further, the spatial extents and the population density of these wall-coherent and wall-incoherent modes are characterised, with the former conforming to the attached eddy arguments of Townsend (1976) and the subsequent attached eddy models. Collectively, through the evidence gathered here, we provide a conceptual picture of the representative large-scale structures in turbulent boundary layers, which are likely to have implications on the type of representative structures to be used in structure-based models for these flows.     

Direct numerical simulation of turbulent heat transfer over fully resolved anisotropic porous structures

Lattice Boltzmann direct numerical simulations of turbulent heat transfer over and inside anisotropic porous media are performed. This study considers turbulent plane channel flows whose bottom walls are made from the porous media at the bulk Reynolds number of 2900 with isothermal and conjugate heat transfer wall conditions. Four different porous walls are considered. They are walls with only the wall-normal permeability, with the wall-normal and spanwise permeabilities, with the wall-normal and streamwise permeabilities, and with the isotropic wall-normal, spanwise and streamwise permeabilities. The porosity of the porous walls ranges from 0.6 to 0.8. Discussions on the effects of the anisotropic permeability on turbulent thermal fields are carried out by the instantaneous flow visualizations and the statistical quantities. In particular, temperature fluctuations, turbulent and dispersion heat fluxes are examined both inside and outside the porous walls. Finally, the heat transfer performance is discussed considering the effects of the anisotropic permeability.     

Anisotropy measurements in the boundary layer over a flat plate with suction

Laser Doppler velocity measurements are carried out in a turbulent boundary layer subjected to concentrated wall suction (through a porous strip). The measurements are taken over a longitudinal distance of 9× the incoming boundary layer thickness ahead of the suction strip. The mean and rms velocity profiles are affected substantially by suction. Two-point measurements show that the streamwise and wall-normal autocorrelations of the streamwise velocity are reduced by suction. It is found that suction alters the redistribution of the turbulent kinetic energy k between its components. Relative to the no-suction case, the longitudinal Reynolds stress contributes more to k than the other two normal Reynolds stresses; in the outer region, its contribution is reduced which suggests structural changes in the boundary layer. This is observed in the anisotropy of the Reynolds stresses, which depart from the non-disturbed boundary layer. With suction, the anisotropy level in the near-wall region appears to be stronger than that of the undisturbed layer. It is argued that the mean shear induced by suction on the flow is responsible for the alteration of the anisotropy. The variation of the anisotropy of the layer will make the development of a turbulence model quite difficult for the flow behind suction. In that respect, a turbulence model will need to reproduce well the effects of suction on the boundary layer, if the model is to capture the effect of suction on the anisotropy of the Reynolds stresses.     

超临界翼型风洞实验的侧壁干扰研究

本文对模型周围的侧壁附面层抽吸,研究跨音速二元风洞的侧壁干扰。模型的展长大于风洞的宽度,其中央剖面有测压孔,在风洞实验段中可沿展向滑移,使测压剖面相对于风洞的对称平面的展向位置取不同的值。实验表明:在超临界情况,当对模型周围侧壁附面层进行抽吸时,气动力的展向均匀性改善,翼型上的激波向后移。     

Exponential vs Algebraic Growth and Transition Prediction in Boundary Layer Flow

For applications regarding transition prediction, wing design andcontrol of boundary layers, the fundamental understanding of disturbancegrowth in the flat-plate boundary layer is an important issue. In thepresent work we investigate the energy growth of eigenmodes andnon-modal optimal disturbances. We present a set of linear governingequations for the parabolic evolution of wavelike disturbances validboth for the exponential and algebraic growth scenario. The base flow istaken as the Falkner–Skan similarity solution with favorable, adverseand zero pressure gradients. The optimization is carried out over theinitial streamwise position as well as the spanwise wave number andfrequency. The exponential growth is maximized in the sense that theenvelope of the most amplified eigenmode is calculated. In the case ofalgebraic growth, an adjoint-based optimization technique is used. Wefind that the optimal algebraic disturbance introduced at a certaindownstream position gives rise to a larger growth than for the optimaldisturbance introduced at the leading edge. The exponential andalgebraic growth is compared and a unified transition-predictionmethod based on available experimental data is suggested.     

Receptivity of the Blunt-Leading-Edge Plate Boundary Layer to Unsteady Vortex Perturbations

The response of the boundary layer on a plate with a blunt leading edge to frozen-in vortex perturbations whose vorticity is normal to the plate surface is found. It is shown that these vortices generate an inhomogeneity of the streamwise velocity component in the boundary layer. This inhomogeneity is analogous to the streaky structure developing as the degree of free-stream turbulence increases. The dependence of the amplitude and shape of the boundary layer inhomogeneity on the distance from the leading edge, the streamwise and spanwise scales, and other parameters is found for periodic and local initial perturbations. It is shown that the receptivity of the boundary layer decreases with increase in the frequency and with decrease in the streamwise perturbation scale.     

Observations of meandering superstructures in the roughness sublayer of a turbulent boundary layer

The existence of meandering superstructures in a turbulent boundary layer overlying irregular roughness is explored with high-frame-rate particle-image velocimetry measurements within the roughness sublayer at moderate Reynolds number. Elongated streamwise fields of view reconstructed from this data using a Taylor’s hypothesis approach revealed spanwise-meandering regions of low-streamwise-momentum fluid that extended several boundary-layer thicknesses in the streamwise direction. Such signatures are consistent with previous observations of superstructures in smooth-wall turbulence. Counter-rotating wall-normal vortex cores were found to reside along the spanwise boundaries of these superstructure patterns, consistent with the spatial characteristics of hairpin vortex packets.     

Transient growth in the asymptotic suction boundary layer

In the present experimental setup, the transient disturbance growth in a spatially invariant boundary layer flow, i.e., the asymptotic suction boundary layer (ASBL), has been investigated. The choice of the ASBL brings along several advantages compared with an ordinary spatially growing boundary layer. A unique feature of the ASBL is that the Reynolds number (Re) can be varied without changing the boundary layer thickness, which in turn allows for parameter variations not possible to carry out in traditional boundary layer flows. A spanwise array of discrete surface roughness elements was mounted on the surface to trigger modes with different spanwise wavenumbers (β). It is concluded that for each mode there exists a threshold roughness Reynolds number (Re _k ), below which no significant transient growth is present. The experimental data suggests that this threshold Re _k is both a function of β and Re. An interesting result is that the energy growth curves respond differently to a change in Re _k when caused by a change in roughness height k, implying that Re remains constant, compared with a change in the free-stream velocity U_￥U_\infty, which also affects the Re. The scaling of the energy growth curves both in level and the downstream direction is treated and appropriate scalings are found. The result shows a complex non-linear receptivity mechanism. Optimal perturbation theory, which has failed to predict the energy evolution in growing boundary layers, is tested for the ASBL and shows that it may satisfactorily predict the evolution of all transiently growing modes that are triggered by the roughness elements.     

Turbulence structure in non-equilibrium boundary layers with favorable and adverse pressure gradients

An experimental study was conducted to document the turbulence in boundary layers on smooth walls subject to a favorable pressure gradient followed by a zero pressure gradient recovery and an adverse pressure gradient. Two component velocity profiles were acquired along the spanwise centerline of the test section, and velocity fields were obtained at the same locations in streamwise wall-normal and streamwise–spanwise planes using PIV. The FPG was shown to reduce the turbulence in the outer part of the boundary layer, reducing the transport of this turbulence and the effect of sweeps toward the wall. This reduced the inclination angle of the large structures and increased their length scale, particularly in the streamwise and spanwise directions. Recovery from the FPG to a ZPG was rapid. The APG reduced the near wall shear, resulting in a reduced effect of ejections relative to sweeps. The APG had an opposite but smaller effect on the shape and size of structures compared to the FPG.     

Direct numerical simulation of a particle-laden flow in a flat plate boundary layer

In this paper, a direct numerical simulation of particle-laden flow in a flat plate boundary layer is performed, using the Eulerian–Lagrangian point-particle approach. This is, as far as we know, the first simulation of a particle-laden spatially-developing turbulent boundary layer with two-way coupling. A local minimum of the particle number density is observed in the close vicinity of the wall. The present simulation results indicate that the inertial particles displace the quasi-streamwise vortices towards the wall, which, in turn, enhance the mean streamwise fluid velocity. As a result, the skin-friction coefficient is increased whereas the boundary layer integral thicknesses are reduced. The presence of particles augments the streamwise fluctuating velocity in the near-wall region but attenuates it in the outer layer. Nevertheless, the wall-normal and spanwise velocity fluctuations are significantly damped, and so is the Reynolds stress. In addition, the combined effect of a reduced energy production and an increased viscous dissipation leads to the attenuation of the turbulent kinetic energy.     

Large-scale spanwise periodicity in a turbulent boundary layer induced by highly ordered and directional surface roughness

The effect of converging–diverging riblet-type surface roughness (riblets arranged in a ‘herringbone’ pattern) are investigated experimentally in a zero pressure gradient turbulent boundary layer. For this initial parametric investigation three different parameters of the surface roughness are analysed in detail; the converging–diverging riblet yaw angle α, the streamwise fetch or development length over the rough surface F_x and the viscous-scaled riblet height h⁺. It is observed that this highly directional surface roughness pattern induces a large-scale spanwise periodicity onto the boundary layer, resulting in a pronounced spanwise modification of the boundary layer thickness. Hot-wire measurements reveal that above the diverging region, the local mean velocity increases while the turbulent intensity decreases, resulting in a thinner overall boundary layer thickness in these locations. The opposite situation occurs over the converging region, where the local mean velocity is decreased and the turbulent intensity increases, producing a locally thicker boundary layer. Increasing the converging–diverging angle or the viscous-scaled riblet height results in stronger spanwise perturbations. For the strongest convergent–divergent angle, the spanwise variation of the boundary layer thickness between the diverging and converging region is almost a factor of two. Such a large variation is remarkable considering that the riblet height is only 1% of the unperturbed boundary layer thickness. Increasing the fetch seems to cause the perturbations to grow further from the surface, while the overall strength of the induced high and low speed regions remain relatively unaltered. Further analysis of the pre-multiplied energy spectra suggests that the surface roughness has modified or redistributed the largest scale energetic structures.     

On Tollmien–Schlichting-like waves in streaky boundary layers

The linear stability of the boundary layer developing on a flat plate in the presence of finite-amplitude, steady and spanwise periodic streamwise streaks is investigated. The streak amplitudes considered here are below the threshold for onset of the inviscid inflectional instability of sinuous perturbations. It is found that, as the amplitude of the streaks is increased, the most unstable viscous waves evolve from two-dimensional Tollmien–Schlichting waves into three-dimensional varicose fundamental modes which compare well with early experimental findings. The analysis of the growth rates of these modes confirms the stabilising effect of the streaks on the viscous instability and that this stabilising effect increases with the streak amplitude. Varicose subharmonic modes are also found to be unstable but they have growth rates which typically are an order of magnitude lower than those of fundamental modes. The perturbation kinetic energy production associated with the spanwise shear of the streaky flow is found to play an essential role in the observed stabilisation. The possible relevance of the streak stabilising role for applications in boundary layer transition delay is discussed.     

Receptivity of the Swept Wing Boundary Layer to a Steady Flow Inhomogeneity

The boundary layer on a plate with an inclined blunt leading edge is investigated for a free-stream flow with a small span-periodic velocity inhomogeneity. This flow simulates the penetration of the outer turbulence into the swept wing boundary layer. It is shown that the boundary layer perturbations generated by the inhomogeneity generally have a streamwise velocity component significantly greater than the initial inhomogeneity amplitude. The dependence of the perturbations on the distance from the leading edge and the spanwise inhomogeneity period is found. It is shown that the swept wing boundary layer is less sensitive to the perturbation type in question than the straight wing boundary layer.