On the Taylor hypothesis in forced unsteady wall flows

Experiments on the modulation characteristics of the wall shear stress τ′-longitudinal velocity u′ and u′−u′ space–time correlations are reported in a forced turbulent channel flow in a wide range of imposed frequencies. The resulting integral and Taylor scale properties are discussed in detail in the low buffer layer under steady and unsteady flow conditions. It is shown that the small-scale turbulence is sensitive to the imposed unsteadiness since the amplitude and phase of the Taylor length scale vary considerably in the imposed frequency range investigated here. The Taylor hypothesis is acceptably valid in steady and unsteady wall layers just above the low buffer layer. Production and instantaneous pressure gradients are mostly responsible for the deviation of the frozen turbulence-state in the viscous and low buffer sublayers.     

Communication between the buffer layer and the wall in a turbulent channel flow

Direct numerical simulations obtained in large computational domains of a fully developed turbulent channel flow up to the Karman number 1100 are analyzed to determine the scaling of the spanwise correlation coefficients and the effect of the outer eddies. The local fluctuating velocity field is narrow-band-pass and low-pass filtered along the streamwise wavenumber. The spanwise correlations of the narrow-band passed signals in the low buffer layer adequately provide length scales and signatures of the active structures. The low-pass filtering is used to investigate the relative role of the outer eddies. The impact of the active and passive eddies on the wall is analyzed separately through the cross-correlations of the filtered velocity field with the wall shear stress fluctuations. Characteristic length-scales resulting from the analysis of the velocity field differ depending on the quantity and some are related to the conventional streak spacing but not all. The quasi-streamwise vortex paradigm, for the most part, allows the interpretation of these characteristics, but fails in some cases.     

An experimental study into the effects of streamwise and spanwise acceleration in a turbulent boundary layer

We compare two turbulent boundary layers produced in a low-speed water channel experiment. Both are subjected to an identical streamwise pressure gradient generated via a lateral contraction of the channel, and an additional spanwise pressure gradient is imposed on one of the layers by curving the contraction walls. Despite a relatively high streamwise acceleration, hot-film probe measurements of the mean-velocity distributions show that the Reynolds number increases whilst the coefficient of friction decreases downstream. Visualization of the viscous layers using hydrogen bubbles reveal an increase in the non-dimensional streak spacing in response to the acceleration. Changes in statistical moments of the streamwise velocity near the wall suggest an increased dominance of high-velocity fluctuations. The near-wall streaks and velocity statistics have little sensitivity to the boundary layer three-dimensionality induced by the spanwise pressure gradient, with the boundary-layer crossflow velocity reaching 11 % that of the local freestream velocity.     

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.     

Unsteady compressible boundary layer flow over a circular cone near a plane of symmetry

An analysis has been performed to study the unsteady laminar compressible boundary layer governing the hypersonic flow over a circular cone at an angle of attack near a plane of symmetry with either inflow or outflow in the presence of suction. The flow is assumed to be steady at time t=0 and at t>0 it becomes unsteady due to the time-dependent free stream velocity which varies arbitrarily with time. The nonlinear coupled parabolic partial differential equations under boundary layer approximations have been solved by using an implicit finite-difference method. It is found that suction plays an important role in stabilising the fluid motion and in obtaining unique solution of the problem. The effect of the cross flow parameter is found to be more pronounced on the cross flow surface shear stress than on the streamwise surface shear stress and surface heat transfer. Beyond a certain value of the cross flow parameter overshoot in the cross flow velocity occurs and the magnitude of this overshoot increases with the cross flow parameter. The time variation of the streamwise surface shear stress is more significant than that of the cross flow surface shear stress and surface heat transfer. The suction and the total enthalpy at the wall exert strong influence on the streamwise and cross flow surface shear stresses and the surface heat transfer except that the effect of suction on the cross flow surface shear stress is small.     

Skin-friction drag reduction in turbulent channel flow based on streamwise shear control

It is known that stretching and intensification of a hairpin vortex by mean shear play an important role to create a hairpin vortex packet, which generates the large Reynolds shear stress associated with skin-friction drag in wall-bounded turbulent flows. In order to suppress the mean shear at the wall for high efficient drag reduction (DR), in the present study, we explore an active flow control concept using streamwise shear control (SSC) at the wall. The longitudinal control surface is periodically spanwise-arranged with no-control surface while varying the structural spacing, and an amplitude parameter for imposing the strength of the actuating streamwise velocity at the wall is introduced to further enhance the skin-friction DR. Significant DR is observed with an increase in the two parameters with an accompanying reduction of the Reynolds stresses and vorticity fluctuations, although a further increase in the parameters amplifies the turbulence activity in the near-wall region. In order to study the direct relationship between turbulent vortical structures and DR under the SSC, temporal evolution with initial eddies extracted by conditional averages for Reynolds-stress-maximizing Q2 events are examined. It is shown that the generation of new vortices is dramatically inhibited with an increase in the parameters throughout the flow, causing fewer vortices to be generated under the control. However, when the structural spacing is sufficiently large, the generation of new vortex is not suppressed over the no-control surface in the near-wall region, resulting in an increase of the second- and fourth-quadrant Reynolds shear stresses. Although strong actuating velocity intensifies the near-wall turbulence, the increase in the turbulence activity is attributed to the generation of counter-clockwise near-wall vortices by the increased vortex transport.     

Turbulent transport dissimilarity with modulated turbulence structure in channel flow of viscoelastic fluid

This experimental study investigated the turbulent transport dissimilarity with a modulated turbulence structure in a channel flow of a viscoelastic fluid using simultaneous particle image velocimetry and planar laser-induced fluorescence measurements. An instantaneous dye concentration field with fluctuating velocity vectors showed that mass was transferred by hierarchically large-scale wavy motions with inclination. A co-spectral analysis showed that the spatial phase modulation of the streamwise velocity and dye concentration fluctuations for the wall-normal velocity fluctuation corresponded to the relaxation time. The occurrence of intense dye concentration fluctuation and small streamwise velocity fluctuation in a thin boundary layer caused dissimilar turbulent transport because of the non-zero negative correlation of the streamwise velocity and dye concentration fluctuations for the wall-normal velocity fluctuation only on large scales. This explains the turbulent transport dissimilarity which leads to the zero averaged Reynolds shear stress and non-zero wall-normal turbulent mass flux.     

Pulsating turbulent pipe flow in the current dominated regime at high and very-high frequencies

The paper presents Direct Numerical Simulations of sinusoidal pulsating turbulent flow, at low bulk Reynolds numbers, with high frequency, in a straight pipe. Our objective is to study pulsating flow considering it as the superposition of a temporal unsteadiness on a mean current, and from this viewpoint, to decompose the flow in a mean and an oscillating part. Firstly, we examine the time-averaged statistics, which show that the parent flow retains its properties. Then, we analyze the oscillating part of the flow, and confirm the notion that for rapidly pulsating flow, the amplitude of the streamwise velocity and the phase lag at different radial locations follow the solution of the laminar Stokes problem. In addition, we find that the modulation of the turbulent fluctuations follows approximately the sinusoidal form of the imposed pulsation, and that the ratio of the frequency parameter to the amplitude of the streamwise velocity can be used as a scaling factor. We investigate the effects of the amplitude and the frequency of the imposed unsteadiness on the modulation of the time-averaged properties and the turbulence statistics, through a systematic analysis. Finally, we examine the time evolution of the mean velocity and the turbulent fluctuations. These results indicate that a lower limit for the high frequency regime can be identified, based on the level of conformity of the phase-averaged profiles on their steady-state counterparts. For very high frequencies, we find that that the flow behavior does not change, indicating the absence of an upper limit for the high frequency regime.     

Statistical properties of wall shear stress fluctuations in turbulent channel flows

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

Turbulence modulation in a particle-laden flow over a hemisphere-roughened wall

Turbulence modulation by the inertia particles in a spatially developing turbulent boundary layer flow over a hemisphere-roughened wall was investigated using the direct numerical simulation method. The Eulerian and Lagrangian approaches were used for the gas- and particle-phases, respectively. An immersed boundary method was employed to resolve the hemispherical roughness element. The hemispheres were staggered in the downstream direction and arranged periodically in the streamwise and spanwise directions with spacing of p_x/d= 4 and p_z/d= 2 (where p_x and p_z are the streamwise and spanwise spacing of the hemispheres, and d is the diameter). The effects of particles on the turbulent coherent structures, turbulent statistics and quadrant events were analyzed. The results show that the addition of particles significantly damps the vortices structures and increases the length scales of streak structures. Compared with the particle-laden flow over the smooth wall, the existence of the wall roughness decreases the mean streamwise velocity in the near wall region, and makes the peaks of Reynolds stresses profiles shift up. In addition, the existence of particles also increases the percentage contributions to Reynolds shear stress from the Q4 events, however, decreases the percentage contributions from other quadrant events.     

The artificial buffer layer and the effects of forcing in hybrid LES/RANS

The present study is focused on large eddy simulations (LES) that use a statistical (RANS) turbulence model near solid walls, and on the artificial buffer layer that is formed at the interface between these two modeling regions. Additional forcing is used to trigger resolved motions in the LES region more quickly, and leads to improved results in several ways. The study investigates the artificial buffer layer and how it changes with the use of forcing in an in-depth manner, with the purpose of increased understanding of the increasingly popular hybrid LES/RANS group of methods.

The artificial buffer layer is shown to extend from below the modeling interface to well above it, in fact up to 20% of the boundary layer thickness for the cases studied here. The artificial buffer layer is found to be similar to the true buffer layer in many aspects, including a high correlation between the streamwise and wall normal velocity components in the ‘superstreaks’. This indicates that while the superstreaks are highly anisotropic and have unphysical length scales, they still contribute to the resolved shear stress. The forcing does not remove the artificial buffer layer, but it does reduce its extent and increases the resolved shear stress. This increase is mainly associated with increased fluctuations of the wall normal velocity.

A simple, low-dimensional forcing model is proposed and tested, with favorable results. The model is simple to implement and easily generalized to more complex geometries.     

Turbulence production in flow over a wavy wall

Measurements of the spatial and time variation of two components of the velocity have been made over a sinusoidal solid wavy boundary with a height to length ratio of 2a/λ = 0.10 and with a dimensionless wave number of α⁺ = (2π/λ)(v/u ^?) = 0.02. For these conditions, both intermittent and time-mean flow reversals are observed near the troughs of the waves. Statistical quantities that are determined are the mean streamwise and normal velocities, the root-meansquare of the fluctuations of the streamwise and normal velocities, and the Reynolds shear stresses. Turbulence production is calculated from these measurements. The flow is characterized by an outer flow and by an inner flow extending to a distance of about α^?1 from the mean level of the surface. Turbulence production in the inner region is fundamentally different from flow over a flat surface in that it is mainly associated with a shear layer that separates from the back of the wave. Flow close to the surface is best described by an interaction between the shear layer and the wall, which produces a retarded zone and a boundary-layer with large wall shear stresses. Measurements of the outer flow compare favorably with measurements over a flat wall if velocities are made dimensionless by a friction velocity defined with a shear stress obtained by extrapolating measurements of the Reynolds stress to the mean levels of the surface (rather than from the drag on the wall).     

减阻工况下壁面周期扰动对湍流边界层多尺度的影响

通过在平板壁面施加不同频率振幅的压电陶瓷振子周期性扰动,进行了湍流边界层主动控制减阻的实验研究.在压电陶瓷振子最大减阻工况下(80 V和160Hz),使用单丝边界层探针对压电振子自由端下游2mm处进行测量,得到不同法向位置流向速度信号的时间序列.通过对比施加控制前后的多尺度分析,发现压电振子产生的扰动只对近壁区产生影响,使得近壁区大尺度脉动降低,小尺度脉动强度增大,而对边界层的外区则基本没有影响.进一步对大尺度和小尺度的脉动信号进行条件平均,发现压电振子产生的扰动对小尺度脉动的影响在时间相位上并不均匀,小尺度脉动强度在大尺度脉动为正时比在大尺度脉动为负时具有更明显的增加.这表明壁面周期扰动主要通过使大尺度高速扫掠流体破碎为小尺度结构,来影响相应的高壁面摩擦事件,从而达到减阻效果.      

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.     

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.     

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.     

The effect of boundary layer fluctuations on the streamwise vortex structure in simulated plane turbulent mixing layers

This paper details the influence of the magnitude of imposed inflow fluctuations on Large Eddy Simulations of a spatially developing turbulent mixing layer originating from laminar boundary layers. The fluctuations are physically-correlated, and produced by an inflow generation technique. The imposed high-speed side boundary layer fluctuation magnitude is varied from a low-level, up to a magnitude sufficiently high that the boundary layer can be considered, in a mean sense, as nominally laminar. Cross-plane flow visualisation shows that each simulation contains streamwise vortices in the laminar and turbulent regions of the mixing layer. Statistical analysis of the secondary shear stress reveals that mixing layers originating from boundary layers with low-level fluctuations contain a spatially stationary streamwise structure. Increasing the high-speed side boundary layer fluctuation magnitude leads to a weakening of this stationary streamwise structure, or its removal from the flow entirely. The mixing layer growth rate reduces with increasing initial fluctuation level. These findings are discussed in terms of the available experimental data on mixing layers, and recommendations for both future experimental and numerical research into the mixing layer are made.     

An experimental study of the dynamic characteristics in boundary layer in the flow past a two-dimensional circular cylinder at subcritical reynolds numbers

An experimental study of the dynamic characteristics of flow past a two-dimensional circular cylinder is described. The fluctuationsoof wall shear stress, surface-pressure and velocity of the flow are measured with hot-film, hot-wire and pressure transducer. The frequency feature of fluctuations of wall shear stress is given. The cross-correlation functions of these fluctuations at any two points are calculated. The experimental results reveal that there is an overall syncronous fluctuation, at the shedding frequency, in boundary layer in the flow past a two-dimensional circular cylinder at subcritical Reynolds number.     

Measurements in the vicinity of a stagnation point

This paper presents measurements of a plane jet impinging onto a normal flat plate placed up to five jet widths from the jet outlet. The small spacing ensured that the stagnation streamline remained in the potential core of the jet. The plate shear stress distribution compared well to that from an analytical solution for the laminar development of the plate boundary layer whose external velocity was determined from the measured pressure. By comparing the shear stress measured under the present low level of free stream turbulence (0.35%) at the jet exit with that of Tu and Wood [Exp. Thermal Fluid Sci. 13 (1996) 364–373] made at about 4%, it is concluded that the turbulence level at the nozzle exit has only a second-order influence on the surface shear stress around the stagnation point. Some spanwise non-uniformity was observed in the plate shear stress, but this was confined largely to the transition region. The mean velocity, Reynolds stresses, and fluctuating pressure were measured along the stagnation streamline using a fast-response pressure probe. A significant increase in the streamwise normal stress and the mean square of the pressure fluctuations occurred before they were eventually attenuated by the plate. This increase occurred in the region where the streamwise velocity was decreasing close to the plate causing extra energy production through the normal stresses. Spectra of the velocity and pressure fluctuations showed that the increase in level was mainly due to the low frequency motion, whereas the subsequent decrease occurred at higher frequencies.     

On streamwise vortices in Large Eddy Simulations of initially laminar plane mixing layers

This paper details the influence of the nature of imposed inflow fluctuations on Large Eddy Simulations of a spatially developing turbulent mixing layer originating from laminar boundary layers. A simulation with imposed white-noise random fluctuations, commonly used in numerical simulations, produces mean-flow statistics that agree well with reference experimental data. Whilst flow visualisation images show evidence for streamwise vorticity in this simulation, quantitative statistics do not reveal the presence of statistically stationary streamwise vortices. A further simulation that uses physically-correlated inflow fluctuations also produces good mean-flow statistical agreement with reference data. From secondary shear stress contours it can be inferred that this simulation does, however, predict the presence of statistically stationary streamwise vortices. The properties of the streamwise vortices are in good agreement with experimental data. The data presented here indicate that, even for initially laminar conditions, plane mixing layer simulations require accurate physically correlated inflow conditions in order to reproduce the flow features found experimentally.