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"Leschziner, Michael"
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Near-wall streak modification by spanwise oscillatory wall motion and drag-reduction mechanisms
Direct numerical simulations for fully developed channel flow, subjected to oscillatory spanwise wall motion, have been performed and analysed in an effort to illuminate the fundamental mechanisms responsible for the reduction in turbulent friction drag, observed to result from the spanwise wall motion. A range of statistical data are discussed, including second-moment budgets, joint-probability-density functions, enstrophy and energy-spectra maps. Structural features are also investigated by reference to the response of streak properties to the oscillatory forcing. The unsteady cross-flow straining is shown to cause major spanwise distortions in the streak near-wall structures, leading to a pronounced reduction in the wall-normal momentum exchange in the viscous sublayer, hence disrupting the turbulence contribution to the wall shear stress. The response of the streaks, in terms of their periodic reorientation in wall-parallel planes, the decline and recovery of their intensity during the cyclic actuation, and their wall-normal coherence, is shown to be closely correlated with the temporal variation of the shear-strain vector. Furthermore, a modulating ‘top-to-bottom’ effect, associated with large-scale outer-layer structures, is highlighted and deemed responsible for the observed reduction in the actuation efficiency as the Reynolds number is increased.
Journal Article
Friction-Drag Reduction by Transverse Wall Motion – A Review
The quest for drag reduction is driven by environmental concerns, in general, and the need to reduce fuel consumption in transport applications, in particular. Turbulent friction is especially important in civil aviation, accounting for over 50% of the total drag in cruise. In this context, spatially and/or temporally varying in-plane wall motion, while undoubtedly difficult to implement in practice, has attracted major interest, because of the large drag-reduction margins it yields. It is also a forcing method that is of fundamental interest, as it provokes intriguing interactions between the spanwise Stokes layer induced by the wall motion and the near-wall turbulence-regeneration mechanisms. This article provides a relatively brief, ‘entry-level’, review of research in this area, principally over the past two decades. While far from being exhaustive, the review conveys a reasonably detailed picture of some major physical issues as well as of the outcome of the most important computational and experimental studies. Particular emphasis is placed on the question of how results obtained in idealised laboratory conditions and by simulation at relatively low Reynolds-number values pertain to high values typical of high-speed transport.
Journal Article
Pattern prediction by linear analysis of turbulent flow with drag reduction by wall oscillation
A turbulent flow past a transverse-oscillating wall is considered. The oscillation parameters correspond to the regime where drag reduction is observed. Streak spacing and streak angle obtained from the generalized optimal perturbation approach are compared with results from direct numerical simulations. Other flow features of the generalized optimal perturbation are compared with conditionally-averaged data extracted from numerical simulations. The generalized optimal perturbation at a given instant in time is found to consist of an infinitely long structure at a certain angle to the main flow direction. This angle varies slowly with time for half a period, and then suddenly jumps to a different value, changing both sign and magnitude. The angle variation is shown to be slow, because there is a short time interval in the oscillation period when a small perturbation of a certain angle grows strongly and then remains dominant for almost the entire half-period. The transient growth mechanism of the generalized optimal perturbation is found to be a combination of the Orr mechanism due to the cross-flow shear, acting at the initial stage, followed by the lift-up mechanism of the velocity component directed along the structure by the wall-normal motion also oriented in the same direction.
Journal Article
Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions
High-resolution large-eddy simulation is used to investigate the mean and turbulence properties of a separated flow in a channel constricted by periodically distributed hill-shaped protrusions on one wall that obstruct the channel by 33% of its height and are arranged 9 hill heights apart. The geometry is a modification of an experimental configuration, the adaptation providing an extended region of post-reattachment recovery and allowing high-quality simulations to be performed at acceptable computing costs. The Reynolds number, based on the hill height and the bulk velocity above the crest is 10595. The simulated domain is streamwise as well as spanwise periodic, extending from one hill crest to the next in the streamwise direction and over 4.5 hill heights in the spanwise direction. This arrangement minimizes uncertainties associated with boundary conditions and makes the flow an especially attractive generic test case for validating turbulence closures for statistically two-dimensional separation. The emphasis of the study is on elucidating the turbulence mechanisms associated with separation, recirculation reattachment, acceleration and wall proximity. Hence, careful attention has been paid to resolution, and a body-fitted, low-aspect-ratio, nearly orthogonal numerical grid of close to 5 million nodes has been used. Unusually, the results of two entirely independent simulations with different codes for identical flow and numerical conditions are compared and shown to agree closely. Results are included for mean velocity, Reynolds stresses, anisotropy measures, spectra and budgets for the Reynolds stresses. Moreover, an analysis of structural characteristics is undertaken on the basis of instantaneous realizations, and links to features observed in the statistical results are identified and interpreted. Among a number of interesting features, a distinct ‘splatting’ of eddies on the windward hill side following reattachment is observed, which generates strong spanwise fluctuations that are reflected, statistically, by the spanwise normal stress near the wall exceeding that of the streamwise stress by a substantial margin, despite the absence of spanwise strain.
Journal Article
Simulation of slot and round synthetic jets in the context of boundary-layer separation control
Synthetic jets-also referred to as mass-less jets-offer the potential of effective, on-demand, fluid-based control of separating boundary layers on highly loaded aerodynamic surfaces, without the need for a mass source. However, the control authority that may optimally be derived from such jets, and any generality of the underlying flow physics are obscured by the wide range of geometric and flow parameters that contribute to their performance characteristics. The present article reviews the state-of-the art in the area of computational modelling and simulation of synthetic jets, with emphasis placed on key fluid-mechanics phenomena. The review is divided into two principal parts, one focusing on slot jets and the other on round jets. Within the latter part, ongoing research by the authors on the simulation of synthetic jets discharged into a separated boundary layer is highlighted as an example of the current status in this area.
Journal Article
Statistical analysis of outer large-scale/inner-layer interactions in channel flow subjected to oscillatory drag-reducing wall motion using a multiple-variable joint-probability-density function methodology
Full flow-field data derived from a direct numerical simulation for channel flow subjected to drag-reducing oscillatory spanwise motion are analysed by means of a recently developed methodology, which consolidates the entire simulation data set within multiple-variable joint-probability-density functions (PDFs). A wide variety of statistical data of interest are then extracted from the joint PDF without recourse to any of the original simulation data. The nominal friction Reynolds number of the baseline (unactuated) flow is 1025, and the actuation is effected at a wall-scaled period of 100, at which value the drag-reduction level is approximately 30 %, while any actuation-induced phase fluctuations in the streamwise direction are minimal. Interest focuses on the elucidation of the mechanisms by which the near-wall turbulence is modified by the action of footprints of large-scale structures in the outer parts of the log-law region, which tend to intensify as the Reynolds number rises. To elucidate these mechanisms, the Reynolds stresses and their production rates, conditional on the intensity of large-scale skin-friction fluctuations, are examined. The investigation includes a separation of the Reynolds stresses into large-scale and small-scale components by means the empirical mode decomposition, allowing the intensity of footprinting and of small-scale modulation of the near-wall turbulence to be quantified separately. The conditional statistical properties are presented in the form of maps in planes having the wall-normal distance and large-scale skin friction as coordinates, supplemented by wall-normal property profiles and an examination of large-scale and small-scale contributions to the skin friction. The analysis highlights the strongly asymmetric response of the production rate and the turbulence level in the buffer layer to positive vs. negative footprints, the former strongly enhancing small-scale turbulence. This is proposed to be at least a partial explanation of the decline in the drag-reduction effectiveness of oscillatory spanwise wall motion with increasing Reynolds number.
Journal Article
On the departure of near-wall turbulence from the quasi-steady state
An examination is undertaken of the validity and limitations of the quasi-steady hypothesis of near-wall turbulence. This hypothesis is based on the supposition that the statistics of the turbulent fluctuations are universal if scaled by the local, instantaneous, wall shear when its variations are determined from footprints of large-scale, energetic, structures that reside in the outer part of the logarithmic layer. The examination is performed with the aid of direct numerical simulation data for a single Reynolds number, which are processed in a manner that brings out the variability of locally scaled statistics when conditioned on the local value of the wall friction. The key question is to what extent this variability is insignificant, thus reflecting universality. It is shown that the validity of the quasi-steady hypothesis is confined, at best, to a thin layer above the viscous sublayer. Beyond this layer, substantial variations in the conditioned shear-induced production rate of large-scale turbulence cause substantial departures from the hypothesis. Even within the wall-proximate layer, moderate departures are provoked by large-scale distortions in the conditioned strain rate that result in variations in small-scale production of turbulence down to the viscous sublayer.
Journal Article
The connection between the spectrum of turbulent scales and the skin-friction statistics in channel flow at
Data from a direct numerical simulation for channel flow at a friction Reynolds number of 1000 are analysed to derive statistical properties that offer insight into the mechanisms by which large-scale structures in the log-law region affect the small-scale turbulence field close to the wall and the statistical skin-friction properties. The data comprise full-volume velocity fields at 150 time levels separated by 50 wall-scaled viscous time units. The scales are separated into wavelength bands by means of the ‘empirical mode decomposition’, of which the two lowest modes are considered to represent the small scales and three upper modes to represent the large scales. Joint and conditional probability density functions are then derived for various scale-specific statistics, with particular emphasis placed on the streamwise and shear stresses conditional on the large-scale fluctuations of the skin friction, generally referred to as ‘footprinting’. Statistics for the small-scale stresses, conditional on the footprints, allow the amplification and attenuation of the small-scale skin friction, generally referred to as ‘modulation’, to be quantified in dependence on the footprints. The analysis leads to the conclusion that modulation does not reflect a direct interaction between small scales and large scales, but arises from variations in shear-induced production that arise from corresponding changes in the conditional velocity profile. This causal relationship also explains the wall-normal change in sign in the correlation between large scales and small scales at a wall-scaled wall distance of approximately 100. The effects of different scales on the skin friction are investigated by means of two identities that describe the relationship between the shear-stress components and the skin friction, one identity based on integral momentum and the other on energy production/dissipation. The two identities yield significant differences in the balance of scale-specific contributions, and the origins of these differences are discussed.
Journal Article
The connection between the spectrum of turbulent scales and the skin-friction statistics in channel flow at $Re_{\\unicodeSTIX{x1D70F}}\\approx 1000
Data from a direct numerical simulation for channel flow at a friction Reynolds number of 1000 are analysed to derive statistical properties that offer insight into the mechanisms by which large-scale structures in the log-law region affect the small-scale turbulence field close to the wall and the statistical skin-friction properties. The data comprise full-volume velocity fields at 150 time levels separated by 50 wall-scaled viscous time units. The scales are separated into wavelength bands by means of the ‘empirical mode decomposition’, of which the two lowest modes are considered to represent the small scales and three upper modes to represent the large scales. Joint and conditional probability density functions are then derived for various scale-specific statistics, with particular emphasis placed on the streamwise and shear stresses conditional on the large-scale fluctuations of the skin friction, generally referred to as ‘footprinting’. Statistics for the small-scale stresses, conditional on the footprints, allow the amplification and attenuation of the small-scale skin friction, generally referred to as ‘modulation’, to be quantified in dependence on the footprints. The analysis leads to the conclusion that modulation does not reflect a direct interaction between small scales and large scales, but arises from variations in shear-induced production that arise from corresponding changes in the conditional velocity profile. This causal relationship also explains the wall-normal change in sign in the correlation between large scales and small scales at a wall-scaled wall distance of approximately 100. The effects of different scales on the skin friction are investigated by means of two identities that describe the relationship between the shear-stress components and the skin friction, one identity based on integral momentum and the other on energy production/dissipation. The two identities yield significant differences in the balance of scale-specific contributions, and the origins of these differences are discussed.
Journal Article