Temporal and spatial transients in turbulent boundary layer flow over an oscillating wall

Direct numerical simulations have been performed to study the effect of an oscillating segment of the wall on a turbulent boundary layer flow. Two different oscillation amplitudes with equal oscillation period have been used, which allows a direct comparison between a relatively weak and strong forcing of the flow. The weaker forcing results in 18% drag reduction while the stronger forcing, with twice the amplitude, yields 29% drag reduction. The downstream development of the drag reduction is compared with earlier simulations and experiments. In addition, a simulation with identical oscillation parameters as in previous numerical and experimental investigations allows for an estimation of the effect of the Reynolds number on the drag reduction.Reductions in the Reynolds stresses and the important role that the edge of the Stokes layer has is explained.An estimation of the idealized power consumption shows that a positive energy budget is only possible for the weaker wall velocity case.Spatial and temporal transients are investigated and a transformation between spatial and temporal coordinates via a convection velocity is shown to facilitate a comparison between the two transients in a consistent manner. The streamwise shear exhibits a similar monotonic behavior in the spatial and temporal transients, while the non-monotinic temporal transient of the longitudinal Reynolds stress has no counterpart in the spatial development. Furthermore, the evolution in time of the spanwise Reynolds stress is very similar to previously reported channel flow data.The instantaneous spanwise velocity profile (only averaged in the homogeneous spanwise direction) will for the first time be presented from a boundary layer over an oscillating wall, and comparisons with the analytical solution to the laminar Navier–Stokes equations show very good agreement.     

Numerical and experimental investigation of turbulent characteristics in a drag-reducing flow with surfactant additives

Cetyltrimethyl ammonium chloride (CTAC) surfactant additives, because of their long-life characteristics, can be used as promising drag-reducers in district heating and cooling systems. In the present study we performed both numerical and experimental tests for a 75 ppm CTAC surfactant drag-reducing channel flow. A two-component PIV system was used to measure the instantaneous streamwise and wall-normal velocity components. A Giesekus constitutive equation was adopted to model the extra stress due to the surfactant additives, with the constitutive parameters being determined by well-fitting apparent shear viscosities, as measured by an Advanced Rheometric Expansion System (ARES) rheometer. In the numerical study, we connected the realistic rheological properties with the drag-reduction rate. This is different from previous numerical studies in which the model parameters were set artificially. By performing consistent comparisons between numerical and experimental results, we have obtained an insight into the mechanism of the additive-induced drag-reduction phenomena.

Our simulation showed that the addition of surfactant additives introduces several changes in turbulent flow characteristics: (1) In the viscous sublayer, the mean velocity gradient becomes gentler due to the viscoelastic forces introduced by the additives. The buffer layer becomes expanded and the slope of the velocity profile in the logarithmic layer increases. (2) The locations where the streamwise velocity fluctuation and Reynolds shear stress attain their maximum value shifted from the wall region to the bulk flow region. (3) The root-mean-square velocity fluctuations in the wall-normal direction decrease for the drag-reducing flow. (4) The Reynolds shear stress decreases dramatically and the deficit of the Reynolds shear stress is mainly compensated by the viscoelastic shear stress. (5) The turbulent production becomes much smaller and its peak-value position moves toward the bulk flow region. All of these findings agree qualitatively with experimental measurements.

Regarding flow visualization, the violent streamwise vortices in the near wall region become dramatically suppressed, indicating that the additives weaken the ejection and sweeping motion, and thereby inhibit the generation of turbulence. The reduction in turbulence is accomplished by additive-introduced viscoelastic stress. Surfactant additives have dual effects on frictional drag: (1) introduce viscoelastic shear stress, which increases frictional drag; and (2) dampen the turbulent vortical structures, decrease the turbulent shear stress, and then decrease the frictional drag. Since the second effect is greater than the first one, drag-reduction occurs.     

Skin-friction drag reduction in a high-Reynolds-number turbulent boundary layer via real-time control of large-scale structures

While large-scale motions are most energetic in the logarithmic region of a high-Reynolds-number turbulent boundary layer, they also have an influence in the inner-region. In this paper we describe an experimental investigation of manipulating the large-scale motions and reveal how this affects the turbulence and skin-friction drag. A boundary layer with a friction Reynolds number of 14 400 is controlled using a spanwise array of nine wall-normal jets operated in an on/off mode and with an exit velocity that causes the jets in cross-flow to penetrate within the log-region. Each jet is triggered in real-time with an active controller, driven by a time-resolved footprint of the large-scale motions acquired upstream. Nominally, the controller injects air into large-scale zones with positive streamwise velocity fluctuations; these zones are associated with positive wall-shear stress fluctuations. This control scheme reduced the streamwise turbulence intensity in the log-region up to a downstream distance of more than five times the boundary layer thickness, δ, from the point of actuation. The highest reduction in spectral energy—more than 30%—was found for wavelengths larger than 5δ in the log-region at 1.7δ downstream of actuation, while scales larger than 2δ still comprised more than 15% energy reduction in the near-wall region. In addition, a 3.2% reduction in mean skin-friction drag was achieved at 1.7δ downstream of actuation. Our reductions of the streamwise turbulence intensity and mean skin-friction drag exceed a base line control-case, for which the jet actuators were operated with the same temporal pattern, but not synchronised with the incoming large-scale zones of positive fluctuating velocity.     

Friction Drag Variation via Spanwise Transversal Surface Waves

The introduction of spanwise velocity is a promising technique to effect the near-wall turbulent flow field to influence friction drag. However, the essential physical mechanism which significantly reduces friction drag has not been understood, yet. It is the objective of this numerical study to improve the fundamental knowledge on the drag reduction mechanism. The investigation is based on spanwise traveling transversal surface waves which are applied to modify the near-wall flow field and to influence friction drag. Two actuation configurations are analyzed in detail. Compared with an unactuated flat plate boundary layer simulation the first wave setup, which represents a low frequency wave at an amplitude larger than the viscous sublayer, leads to a reduced wall-shear stress resulting in friction drag reduction of up to 9%. The second wave setup, which possesses a higher frequency and an amplitude in the range of the viscous sublayer, yields an increase of friction drag of about 8%. Unlike previous investigations which focus on excitation setups to lower friction drag, the comparison of the two wave setups in this study allows to identify the effects which on the one hand, lead to drag reduction and on the other hand, result in drag increase. That is, due to the pronounced differences the major effects determining the friction distribution are more evident. The two key features for drag reduction are the damping of the wall-normal vorticity fluctuations above the entire surface and the decrease of turbulence production. Furthermore, the effect of rearranging streamwise vorticity, which has been stated to be responsible for drag reduction, is found to occur at increasing and decreasing drag, i.e., it is not the effect that lowers the friction drag.     

Transport and deposition of neutral particles in magnetohydrodynamic turbulent channel flows at low magnetic Reynolds numbers

The effect of Lorentz force on particle transport and deposition is studied by using direct numerical simulation of turbulent channel flow of electrically conducting fluids combined with discrete particle simulation of the trajectories of uncharged, spherical particles. The magnetohydrodynamic equations for fluid flows at low magnetic Reynolds numbers are adopted. The particle motion is determined by the drag, added mass, and pressure gradient forces. Results are obtained for flows with particle ensembles of various densities and diameters in the presence of streamwise, wall-normal or spanwise magnetic fields. It is found that the particle dispersion in the wall-normal and spanwise directions is decreased due to the changes of the underlying fluid turbulence by the Lorentz force, while it is increased in the streamwise direction. The particle accumulation in the near-wall region is diminished in the magnetohydrodynamic flows. In addition, the tendency of small inertia particles to concentrate preferentially in the low-speed streaks near the walls is strengthened with increasing Hartmann number. The particle transport by turbophoretic drift and turbulent diffusion is damped by the magnetic field and, consequently, particle deposition is reduced.     

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.     

The Impact of Footprints of Large-Scale Outer Structures on the Near-Wall Layer in the Presence of Drag-Reducing Spanwise Wall Motion

This study is motivated by the observation that the drag-reduction effectiveness achieved by the imposition of oscillatory spanwise wall motion declines with Reynolds number. The question thus posed is whether the decline is linked to the increasingly strong influence of large-scale outer structures in the log layer on the near-wall turbulence, in general, and the streak strength in the viscosity-affected layer, in particular – a process referred to as modulation. This question is addressed via an extensive statistical analysis of DNS data for a channel flow at a friction Reynolds number 1020, subjected to oscillatory spanwise wall motion at a nominal wall-scaled period of 100. The analysis rests on a separation of turbulent scales by means of the Empirical Mode Decomposition. This method is used to derive conditional statistics of small-scale motions and skin friction subject to prescribed intensity of large-scale motions – referred to as footprinting. It is shown that the large-scale fluctuations are responsible, directly on their own, for roughly 30% to the skin friction. Positive large-scale fluctuations are also shown to be the cause of a major amplification of small-scale streaks, relative to weak attenuation by negative fluctuations. This highly asymmetric process is likely to be indirectly influential on the drag-reduction process, although it is not possible to identify this indirect effect in quantitative terms as part of the present analysis.     

壁面展向周期振动的槽道湍流减阻机理的研究

利用直接数值模拟研究了带有壁面展向周期振动的槽道湍流.壁面在展向的周期运动使湍流受到抑制,并使壁面摩擦阻力减小.通过对雷诺应力输运方程的分析研究了壁面展向周期振动的减阻机理,进一步揭示了压力变形项在湍流抑制中的关键作用.     

Direct simulation of two‐dimensional turbulent flow over a surface‐mounted obstacle

Two‐dimensional turbulent flow over a surface‐mounted obstacle is studied as a numerical experiment that takes place in a wind tunnel. The transient Navier–Stokes equations are solved directly with Galerkin finite elements. The Reynolds number defined with respect to the height of the wind tunnel is 12 518. Instantaneous streamline patterns are shown that give a complete picture of the flow phenomena. Energy and enstrophy spectra yield the dual cascade of two‐dimensional turbulence and the ?1 power law decay of enstrophy. Mean values of velocities and root mean square fluctuations are compared with the available experimental results. Other statistical characteristics of turbulence such as Eulerian autocorrelation coefficients, longitudinal and lateral coefficients are also computed. Finally, oscillation diagrams of computed velocity fluctuations yield the chaotic behaviour of turbulence. Copyright © 2007 John Wiley & Sons, Ltd.     

Imposing virtual origins on the velocity components in direct numerical simulations

The relative wall-normal displacement of the origin perceived by different components of near-wall turbulence is known to produce a change in drag. This effect is produced for instance by drag-reducing surfaces of small texture-size like riblets and superhydrophobic surfaces. To facilitate the research on how these displacements alter near-wall turbulence, this paper studies different strategies to model such displacement effect through manipulated boundary conditions. Previous research has considered the effect of offsetting the virtual origins perceived by the tangential components of the velocity from the reference, boundary plane, where the wall-normal velocity was set to zero. These virtual origins are typically characterised by slip-length coefficients in Robin, slip-like boundary conditions. In this paper, we extend this idea and explore several techniques to define and implement virtual origins for all three velocity components on direct numerical simulations (DNSs) of channel flows, with special emphasis on the wall-normal velocity. The aim of this work is to provide a suitable foundation to extend the existing understanding on how these virtual origins affect the near-wall turbulence, and ultimately aid in the formulation of simplified models that capture the effect of complex surfaces on the overlying flow and on drag, without the need to resolve fully the turbulence and the surface texture. From the techniques tested, Robin boundary conditions for all three velocities are found to be the most satisfactory method to impose virtual origins, relating the velocity components to their respective wall-normal gradients linearly. Our results suggest that the effect of virtual origins on the flow, and hence the change in drag that they produce, can be reduced to an offset between the virtual origin perceived by the mean flow and that perceived by the overlying turbulence, and that turbulence remains otherwise smooth-wall-like, as proposed by Luchini (1996). The origin for turbulence, however, would not be set by the spanwise virtual origin alone, but by a combination of the spanwise and wall-normal origins. These observations suggest the need for an extension of Luchini’s virtual-origin theory to predict the change in drag, accounting for the wall-normal transpiration when its effect is not negligible.     

Predicting Turbulent Spectra in Drag-reduced Flows

In the present work we describe how turbulent skin-friction drag reduction obtained through near-wall turbulence manipulation modifies the spectral content of turbulent fluctuations and Reynolds shear stress with focus on the largest scales. Direct Numerical Simulations (DNS) of turbulent channels up to Re _τ = 1000 are performed in which drag reduction is achieved either via artificially removing wall-normal turbulent fluctuations in the vicinity of the wall or via streamwise-travelling waves of spanwise wall velocity. This near-wall turbulence manipulation is shown to modify turbulent spectra in a broad range of scales throughout the whole channel. Above the buffer layer, the observed changes can be predicted, exploiting the vertical shift of the logarithmic portion of the mean streamwise velocity profile, which is a classic performance measure for wall roughness or drag-reducing riblets. A simple model is developed for predicting the large-scale contribution to turbulent fluctuation and Reynolds shear stress spectra in drag-reduced turbulent channels in which a flow control acts at the wall. Any drag-reducing control that successfully interacts with large scales should deviate from the predictions of the present model, making it a useful benchmark for assessing the capability of a control to affect large scales directly.     

An Experimental Study of the Rotational Effects on Separated Turbulent Flow During Stall Delay

Three-dimensional velocity fields were measured using tomographic particle image velocimetry (Tomo-PIV) on a model of the blade of a small-scale horizontal axis wind turbine (HAWT) to study the effects of rotation on separated turbulent flows during stall delay at a global tip speed ratio (TSR) of 3 and a Reynolds number of 4800. The flow fields on a static airfoil were also measured at a similar angle-of-attack (AOA) and Reynolds number for comparison. It was observed that the blade’s rotation in the streamwise direction significantly affected both the mean flow and the turbulence statistics over the suction surface. The mean velocity fields revealed that, different from the airfoil flow at large AOA, the recirculation region with reversed flow did not exist on the suction surface of the blade and the flow was rather attached. Mean spanwise flow from blade’s root to its tip was also generated by the rotation. The mean vorticity vector of the blade flow was found to be tilted in the rotational direction of the blade, as well as in the wall-normal direction. Of particular effects of the rotation on Reynolds stresses were the enhancement of 〈w ²〉 and the creation of strong 〈v w〉. The production of Reynolds stresses was also affected by blade’s rotation directly through the rotational production terms and indirectly by dramatically changing the fluctuating velocity fields. The distribution of enstrophy was observed to be modified by rotation, too.     

3-D measurements of separated flow over rigid plates with spanwise periodic cambering at low Reynolds number

Measurements of the flow field around a flat plate and rigid plates with spanwise periodic cambering were performed using volumetric three-component velocimetry (V3V) at a Reynolds numbers of 28,000 at α=12° where the flow is fully separated. The Reynolds normal and shear stresses, and the streamwise, spanwise and normal components of the vorticity vector are investigated for three-dimensionality. Flow features are discussed in context of the periodic cambering and corresponding aerodynamic force measurements. The periodic cambering results in spanwise variation in the reversed-flow region, Reynolds stresses and spanwise vorticity. These spanwise variations are induced by streamwise and normal vortices of opposite directions of rotation. Moreover, measurements were carried out for the cambered plates at α=8°, where a long separation bubble exists, to further understand the behavior of the streamwise and normal vortices. These vortices become more organized and increase in strength and size at the lower angle of attack. It is also speculated that these vortices contribute to the increase in lift at and beyond the onset of stall angle of attack.     

Velocity measurements of streamwise roll cells in rotating plane Couette flow

For the first time, quantitative velocity measurements in rotating plane Couette flow are demonstrated. Particle image velocimetry is used at a low Reynolds number with anti-cyclonic, i.e. destabilising rotation, where the instability is expected to give rise to steady streamwise-oriented roll cells. The streamwise and spanwise velocities of the roll cells were measured on the centreplane of the flow and at two planes on either side. The streamwise velocity is spanwise periodic with an amplitude variation approximately ±42 % of half the velocity difference between the moving walls. The wall-normal velocity was estimated by assuming steady, laminar and streamwise-independent flow. Despite the large amplitude of the disturbance, both the spanwise wave length and amplitude ratio between the streamwise and wall-normal components were close to what is obtained from linear theory. A splitting event of a roll cell was also captured by the velocity measurements and its development followed in time.     

Modeling of drag reduction in turbulent channel flow with hydrophobic walls by FVM method and weakly-compressible flow equations

In this paper the effects of hydrophobic wall on skin-friction drag in the channel flow are investigated through large eddy simulation on the basis of weaklycompressible flow equations with the MacCormack's scheme on collocated mesh in the FVM framework. The slip length model is adopted to describe the behavior of the slip velocities in the streamwise and spanwise directions at the interface between the hydrophobic wall and turbulent channel flow. Simulation results are presented by analyzing flow behaviors over hydrophobic wall with the Smagorinky subgrid-scale model and a dynamic model on computational meshes of different resolutions. Comparison and analysis are made on the distributions of timeaveraged velocity, velocity fluctuations, Reynolds stress as well as the skin-friction drag. Excellent agreement between the present study and previous results demonstrates the accuracy of the simple classical second-order scheme in representing turbulent vertox near hydrophobic wall. In addition, the relation of drag reduction efficiency versus time-averaged slip velocity is established. It is also foundthat the decrease of velocity gradient in the close wall region is responsible for the drag reduction. Considering its advantages of high calculation precision and efficiency, the present method has good prospect in its application to practical projects.     

Influence of drag-reducing polymers on turbulence: effects of Reynolds number, concentration and mixing

 Measurements of turbulence properties of solutions of polymers have been made over a large range of drag-reduction, in a fully-developed channel flow. At flows close to maximum drag-reduction the Reynolds stresses were approximately zero over the whole cross section of the channel. Added mean polymer stresses were observed in the viscous wall region for small drag-reduction and over the whole cross-section for large drag-reduction. Even though the Reynolds stresses are zero, the velocity profile is not parabolic because of the presence of these mean stresses. We interpret the results by arguing that the interaction of turbulence with the polymers introduces mean and fluctuating polymer stresses which can create turbulence. The observation that the turbulence modification depends on the manner by which the polymers are introduced into the flow supports the notion that the polymers need to form aggregates in order to be effective. Received: 29 September 1998 / Accepted: 10 February 1999     

TRPIV MEASUREMENT OF DRAG-REDUCTION IN THE TURBULENT BOUNDARY LAYER OVER RIBLETS PLATE

采用高时间分辨率粒子图像测速技术对沟槽壁面平板湍流边界层速度矢量场的时间序列及其统计量进行了实验测量,讨论了在同一来流速度下沟槽壁面对平均速度剖面﹑雷诺切应力及湍流强度的影响. 用流向速度分量的多尺度空间局部平均结构函数辨识壁湍流多尺度相干结构,用条件采样和相位平均技术提取壁湍流多尺度相干结构喷射和扫掠事件的脉动速度、展向涡量的二维空间拓扑形态. 结果表明,与同材料光滑壁面对比,沟槽壁面实现了10.73%的摩阻减小量;沟槽壁面湍流边界层湍流强度及雷诺切应力皆比光滑平板湍流边界层对应统计量小,说明沟槽壁面有效降低了湍流边界层内流体的脉动. 通过比较壁湍流相干结构猝发事件各脉动速度分量与展向涡量的空间分布特征,肯定了沟槽壁面的减阻效果,发现沟槽壁面通过抑制相干结构猝发事件实现减阻.     

Using digital holographic microscopy for simultaneous measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer

A digital holographic microscope is used to simultaneously measure the instantaneous 3D flow structure in the inner part of a turbulent boundary layer over a smooth wall, and the spatial distribution of wall shear stresses. The measurements are performed in a fully developed turbulent channel flow within square duct, at a moderately high Reynolds number. The sample volume size is 90 × 145 × 90 wall units, and the spatial resolution of the measurements is 3–8 wall units in streamwise and spanwise directions and one wall unit in the wall-normal direction. The paper describes the data acquisition and analysis procedures, including the particle tracking method and associated method for matching of particle pairs. The uncertainty in velocity is estimated to be better than 1 mm/s, less than 0.05% of the free stream velocity, by comparing the statistics of the normalized velocity divergence to divergence obtained by randomly adding an error of 1 mm/s to the data. Spatial distributions of wall shear stresses are approximated with the least square fit of velocity measurements in the viscous sublayer. Mean flow profiles and statistics of velocity fluctuations agree very well with expectations. Joint probability density distributions of instantaneous spanwise and streamwise wall shear stresses demonstrate the significance of near-wall coherent structures. The near wall 3D flow structures are classified into three groups, the first containing a pair of counter-rotating, quasi streamwise vortices and high streak-like shear stresses; the second group is characterized by multiple streamwise vortices and little variations in wall stress; and the third group has no buffer layer structures.     

Evaluation of a Modified Reynolds Stress Model for Turbulent Dispersed Two-Phase Flows Including Two-Way Coupling

A modified Reynolds stress turbulence model for the pressure rate of strain can be derived for dispersed two-phase flows taking into account gas-particle interaction. The transport equations for the Reynolds stresses as well as the equation for the fluctuating pressure can be derived starting from the multiphase Navier–Stokes equations. The unknown pressure rate of strain correlation in the Reynolds stress equations is then modelled by considering the multiphase equation for the fluctuating pressure. This leads to a multiphase pressure rate of strain model. The extra particle interaction source terms occurring in the model for the pressure rate of strain can be constructed easily, with no noticeable extra computational cost. Eulerian–Lagrangian simulation results of a turbulent dispersed two-phase jet are presented to show the differences in results with and without the new two-way coupling terms.     

Higher-order moments and spectra of velocity fluctuations in adverse-pressure-gradient turbulent boundary layer

The characteristics of turbulent boundary layer flows with adverse pressure gradients (APGs) differ significantly from those of canonical boundary layers. We have investigated the effects of an APG on the higher-order moments and spectra of velocity fluctuations. The local wavelet spectra reveal a large difference in energy-containing frequencies of streamwise and wall-normal components of turbulent velocities, which results in smaller Reynolds shear stress production. Moreover, an analysis of bispectra in the Fourier space has revealed that non-local interactions, consisting of streamwise fluctuating velocity with low frequency and wall-normal velocity with high frequency, occur in the APG flow. However, the small-scale motions are not affected by imposing an APG.