Zero-pressure Gradient Turbulent Boundary Layer Research Articles

Understanding Low-Speed Streaks and Their Function and Control through Movable Shark Scales Acting as a Passive Separation Control Mechanism

The passive bristling mechanism of the scales on the shortfin mako shark (Isurus oxyrinchus) is hypothesized to play a crucial role in controlling flow separation. In the hypothesized mechanism, the scales are triggered in response to patches of reversed flow at the onset of separation occurring in the low-speed streaks that form in a turbulent boundary layer. The two goals of this investigation were as follows: (1) to measure the reversing flow occurring within the low-speed streaks in a separating turbulent boundary layer; (2) to understand the passive flow control mechanism of movable shark skin scales that inhibit reversing flow within the low-speed streaks. Experiments were conducted using digital particle image velocimetry (DPIV). DPIV was used to analyze the flow in a turbulent boundary layer subjected to an adverse pressure gradient formation over both a smooth flat plate and a flat plate on which shark skin specimens were affixed. The experimental analysis of the flow over the smooth flat plate corroborated the findings of previous direct numerical simulation studies, which indicated that the average spanwise spacing of the low-speed streaks increases in the presence of adverse pressure gradients upstream of the point of separation. However, the characteristics of the flow over the shark skin specimen more closely resemble that of a zero-pressure gradient turbulent boundary layer. A comparative analysis of the width and velocity of the reversed streaks between flat plate and shark skin cases reveals that the mean spanwise spacing decreases, and thus, the number of streaks increases over the shark skin. Additionally, the reversed streaks observed over shark scales are thinner and the highest negative velocity within the streaks falls within the range required to bristle the scales.

Boundary Layer Thickness and Friction Velocity by Symmetry Arguments.

We derive analytically for the first time the downstream evolution of the boundary layer thickness and the friction velocity of the zero-pressure-gradient turbulent boundary layer (ZPGTBL). Lie groups were used to derive the downstream evolution and to obtain the full set of the similarity variables and the leading-order similarity equations. An approximate leading-order solution was obtained using matched asymptotic expansions. The similarities and differences between ZPGTBL and turbulent channel flows in terms of the similarity equations are discussed to support the notion of leading-order universality of the near-wall layer.

Energy transfer in the formation and evolution of energy-containing motions in turbulent boundary layers

This paper examines using direct numerical simulation (DNS) the recovery of the energy-containing scales of motion (energy-containing motions) when these are removed at the inflow boundary condition of a flat plate zero-pressure gradient turbulent boundary layer (ZPG-TBL). The energy-containing motions are identified from the spanwise spectral energy density of the interscale turbulent transport. Analysis of the resulting spanwise spectral energy densitiy of velocity and vorticity suggests that near-wall streaks are the initial energy-containing motions formed with quasi-streamwise vortices only developing further downstream. This result is in agreement with the previous study on turbulent channel flows by Kannadasan et al. [1].

Response of a Turbulent Boundary Layer to an Imposed Synthetic Large-Scale Structure

The dynamic response of a zero-pressure gradient turbulent boundary layer (TBL) to an active flow control actuator was experimentally investigated. The experimental TBL had a sufficiently low momentum thickness Reynolds number, such that there were no energetic organized large-scale structures in the outer region, as evidenced from measurements of the premultiplied wavenumber–frequency spectra. The periodically pulsed plasma actuator, placed inside the outer region of TBL, introduced a synthetic large-scale structure, and the boundary-layer response to this synthetic structure downstream of the actuator at select wall-normal and streamwise locations was investigated. The turbulence amplitude modulating effect of the synthetic large-scale structure, within the inner and log-linear regions of the boundary layer, was isolated and analyzed using a phase-locked analysis. The dynamic interaction of the synthetic large-scale structure and smaller-scale turbulent motions was quantified using a modulation coefficient, and a strong positive correlation within the inner and log regions of the boundary layer was measured. The streamwise development of the synthetic large-scale structure and its modulating effect on the near-wall turbulence across several streamwise locations are described. Profiles of the phase speed at these streamwise locations were extracted and were found to be constant within the log region, further confirming a strong coupling between the near-wall fluctuations in turbulence intensity and the synthetic large-scale motions introduced in the outer region. Overall, the turbulence amplitude modulation effect induced by the synthetic large-scale structure was found to be dynamically similar to the large-scale modulation measured in canonical TBLs at higher Reynolds numbers.

New formulations for the mean wall-normal velocity and Reynolds shear stress in a turbulent boundary layer under zero pressure gradient

In this study, a novel analytical solution is derived rigorously for the mean wall-normal velocity in a turbulent boundary layer (TBL) under zero pressure gradient (ZPG), without relying on any a priori assumptions regarding the mean streamwise velocity. By neglecting the higher-order terms in the exact solution, an approximate formulation for the mean wall-normal velocity is obtained. The accuracy of this approximation is then validated through a comparison with data from direct numerical simulations (DNS). Drawing upon the distinct behaviours of force balance in the inner and outer regions of the ZPG TBL, simplified approximate mean momentum equations are derived by decomposing the Reynolds shear stress into inner and outer parts. The inner and outer Reynolds shear stresses are then obtained through integration of the corresponding approximate mean momentum equations. The outer Reynolds shear stress is revealed to exhibit a strong connection to the mean wall-normal velocity. Specifically, it is observed that $R_{uv-{out}}/u^2_\tau \approx 1 - UV/(U_e V_e)$ , where $u_\tau$ represents the friction velocity, and $U_e$ and $V_e$ denote the mean streamwise and wall-normal velocities at the boundary layer edge, respectively. Finally, an approximate formulation for the Reynolds shear stress across the entire TBL is developed by synthesizing the inner and outer parts. Extensive validation against both DNS and experimental data, spanning a wide range of Reynolds numbers, demonstrates the excellent agreement achieved.

Turbulent superstructure statistics in a turbulent boundary layer with pressure gradients

In turbulent boundary layers, streamwise elongated regions of high- and low-momentum in the log-law layer that can extent up to several boundary layer thicknesses are often referred to as turbulent superstructures. These structures contain a relatively large portion of the layer’s turbulent kinetic energy and have been shown to interact with the near-wall flow structures. In the last few decades extensive research on zero-pressure gradient (ZPG) turbulent boundary layers has been done, however by comparison, the structural characteristics for adverse pressure gradient turbulent (APG) boundary layer flows are much less studied despite their strong significance aero-hydrodynamic vehicle design. Therefore, the three-dimensional dynamics of turbulent superstructures in a turbulent boundary layer flow are investigated in the Atmospheric Wind Tunnel Munich (AWM) using a multi-camera 3D time-resolved Lagrangian particle tracking approach. In this study, Lagrangian and Eulerian statistics will be used to characterize the dynamics and interaction of turbulent superstructures within a zero pressure gradient (ZPG) turbulent boundary layer at Reτ = 5000 or Reθ = 14 000 that then flows over a curved plate subjected to a favorable (FPG) and strong adverse (APG) pressure gradient, which eventually separates. An Eulerian analysis, using multi-point correlations of 3D velocity fields, found that the average superstructure topology is modulated by decelerating flow in the APG region when compared to the ZPG region, however the basic shape and spanwise pattern is preserved. Looking into the behavior of individual trajectories, it was found that the dispersion of single particles along trajectories in the log-law layer are capable of moving more than the average Eulerian superstructure spacing in the spanwise direction. Furthermore, the mean square of the single particle dispersion indicates that the maximum dispersion in the spanwise direction comes from particles released at the wall-normal location corresponding to the so-called “second-peak/plateau” region in the streamwise normal Reynolds stress.

Sensitivity of TBL Wall-Pressure over the Flat Plate on Numerical Turbulence Model Parameter Variations

A two-fold sensitivity of the zero-pressure gradient (ZPG) turbulent boundary layer (TBL) wall-pressure spectrum to different RANS model parameters is investigated for a flat plate case, which is a close approximation to the aircraft fuselage or wing. The alteration in the mean square pressure fluctuations due choice of semi-empirical pressure model and the choice of computational model parameters like solver, near wall grid clustering, measuring location, and flow velocity are separately studied. The underlying effect of different TBL parameters in the said sensitivity has been studied while numerically replicating wind tunnel experiments and in-flight tests considering different RANS configurations. Initially, the best-predicting pressure spectrum models are selected by comparing them with available in-flight and wind tunnel test data. Subsequently, the accuracy of all the individual model parameters in predicting mean TBL flow quantities like wall shear stress, boundary layer thickness, displacement thickness, momentum thickness, etc., and eventually mean square pressure (MSP) is estimated. The sensitivity of the mean square pressure fluctuations value to the TBL flow quantities and the near-wall grid clustering is observed to be significant. In general, family of models is found to be best in terms of numerical convergence and closeness when compared to the experimental MSP values. family of models is suggested to be avoided while estimating MSP in flat plate TBL case

A Modified Shielding and Rapid Transition DDES Model for Separated Flows

In this paper, the major problems associated with detached eddy simulation (DES) (namely, modeled stress depletion (MSD) and slowing of the RANS to LES transition (RLT)) are discussed and reviewed, and relevant improvements are developed. A modified version for the delayed DES (DDES) method with adaptive modified adequate shielding and rapid transition is proposed; this is called MSRT DDES. The modified shielding strategy can be adjusted adaptively according to the local flow conditions: keeping the RANS behavior in the whole boundary layer when there is no resolved turbulence, and weakening the shielding function when resolved turbulence exists in the mainstream over the boundary layer. This strategy can significantly ameliorate the MSD in the RANS boundary layer, regardless of the mesh refinement, and avoid excessive shielding in the fully developed resolved turbulence that may otherwise delay the development of the separated and reattached flow. Three cases are designed to test the modified DDES, namely, complete shielding in the RANS zone of a boundary layer (the zero-pressure gradient turbulent boundary layer with the refined mesh), modified adaptive improved shielding with a rapid transition (the flow over a hump), and the overall performance in a complex 3D separation (the corner separation in a compressor cascade). The results show that the modified shielding function is more physical than earlier proposals compared to shielding functions, and according to detailed comparisons of the wall skin friction coefficients, velocity profiles, total pressure-loss coefficients, entropy production analyses, and so on, the MSD and RLT problems are moderately alleviated by the MSRT DDES.

Enhancement of PIV measurements via physics-informed neural networks

Physics-informed neural networks (PINN) are machine-learning methods that have been proved to be very successful and effective for solving governing equations of fluid flow. In this work we develop a robust and efficient model within this framework and apply it to a series of two-dimensional three-component stereo particle-image velocimetry (PIV) datasets, to reconstruct the mean velocity field and correct measurements errors in the data. Within this framework, the PINNs-based model solves the Reynolds-averaged-Navier–Stokes equations for zero-pressure-gradient turbulent boundary layer (ZPGTBL) without a prior assumption and only taking the data at the PIV domain boundaries. The turbulent boundary layer (TBL) data has different flow conditions upstream of the measurement location due to the effect of an applied flow control via uniform blowing. The developed PINN model is very robust, adaptable and independent of the upstream flow conditions due to different rates of wall-normal blowing while predicting the mean velocity quantities simultaneously. Hence, this approach enables improving the mean-flow quantities by reducing errors in the PIV data. For comparison, a similar analysis has been applied to numerical data obtained from a spatially-developing ZPGTBL and an adverse-pressure-gradient TBL over a NACA4412 airfoil geometry. The PINNs-predicted results have less than 1% error in the streamwise velocity and are in excellent agreement with the reference data. This shows that PINNs has potential applicability to shear-driven turbulent flows with different flow histories, which includes experiments and numerical simulations for predicting high-fidelity data.

Control effects on coherent structures in a non-uniform adverse-pressure-gradient boundary layer

We examine the effects of three basic but effective control strategies, namely uniform blowing, uniform suction, and body-force damping, on the intense Reynolds-stress events in the turbulent boundary layer (TBL) developing on the suction side of a NACA4412 airfoil. This flow is subjected to a non-uniform adverse pressure gradient (APG), which substantially modifies its turbulence statistics with respect to a zero-pressure-gradient (ZPG) boundary layer, and it also changes how control strategies affect the flow. The strong APG results in intense events that are shorter and more often detached from the wall than in ZPG TBLs. In a quadrant analysis, ejections remain the most relevant structures, but sweeps become more important than in ZPG TBLs, a fact that results in a lower contribution to the wall-normal velocity from intense Reynolds-stress events. Control effects are relatively less important on intense events than on the turbulent statistics. Uniform blowing has an impact similar to that of an even more intense APG, while uniform suction has more complex effects, most likely due to the particular behavior of the wall-normal velocity component near the wall. Body-force damping also reduces the probability of occurrence of very-large attached structures and that of intense events in the proximity of the actuation region. Our results show that intense Reynolds-stress events are robust features of the flow. If control strategies do not target directly these structures, their effects on the strong events is less pronounced than the effects on the mean flow.

Intense large-scale motions in zero and adverse pressure gradient turbulent boundary layers

Proper orthogonal decomposition (POD) is used to study coherent structures in wall-bounded turbulent flows. The present study uses POD in turbulent boundary layers to determine the contributions of the intense large-scale motions (LSMs) to the Reynolds stresses. This study uses the 2C-2D PIV measurements of zero pressure gradient turbulent boundary layers (ZPG-TBL) at Re_{δ2} = 7750, and adverse pressure gradient turbulent boundary layer (APG-TBL) at β = 2.27 and Re_{δ2}= 16240, where Re_{δ2} is the momentum thickness based Reynolds number and β is the Clauser’s pressure gradient parameter. The measurements were obtained in the Laboratoire de Mécanique des Fluides de Lille (LMFL) High-Reynolds-Number (HRN) Boundary Layer Wind Tunnel, Lille, France. The snapshots of the flow field are segregated into those dominated by the intense and mild LSMs based on the intensity of the temporal coefficients of the first POD mode. The intense LSMs are further decomposed into high-momentum (HM) and low-momentum (LM) motions. The relative contributions of the HM motions to the Reynolds stresses are larger near the wall as compared to the LM motions. At the wall-normal distance of the displacement thickness (δ1), HM and LM motions have similar contributions. Beyond δ1, the LM motions have larger contributions with their peaks located closer to the displacement thickness height. This shows that in the presence of an APG, the turbulence activity is shifted closer to the displacement thickness height.

High Spatial Resolution 2C-2D PIV Measurements Using A 47 MPx Sensor Of High Reynolds Number Turbulent Boundary Layer Flow

In the past decade, advances in electronics technology have made larger imaging sensors available to the experimental fluid mechanics community. These advancements have enabled the measurement of 2-component 2-dimensional (2C-2D) velocity fields using particle image velocimetry (PIV) with much higher spatial resolution than previously possible using a single camera. Although previously reported experiments have incorporated multiple-camera arrays to acquire high spatial resolution PIV, using a single large camera can greatly reduce the complexity of the experimental setup as well as the error introduced by the calibration between the cameras. In this paper, the ability of a single large sensor for high spatial resolution PIV is demonstrated by performing the measurement of a zero-pressure-gradient turbulent boundary layer (ZPG-TBL). In post-processing the PIV images, the lens distortion error is of particular importance, as the lens distortion error increases with the size of the imaging sensor. The third-order polynomial functions are used to model the lens distortion in this study, and the correction is performed on the PIV vectors to save computational cost. The first- and second-order statistics are calculated and compared with the profiles captured by small camera arrays, and the result shows that the corrected profiles agree well with the previously acquired data, therefore, the lens distortion error can be corrected.

Analysis of the Contribution of Large Scale Motions to the Skin Friction of a Zero-Pressure-Gradient Turbulent Boundary Layer Using the Renard-Deck Decomposition

Coherent flow structures in turbulent boundary layers have been an active field of research for many decades, as they might be the key to reveal the mechanics of turbulence production and transport in turbulent shear flows. Renard and Deck (2016) proposed a theoretical decomposition for the mean skin-friction coefficient based on the mean kinetic energy budget in the streamwise direction. This decomposition, referred to as the Renard-Deck (RD) decomposition, decomposes the mean skin friction generation into three physical mechanisms in an absolute reference frame, namely, direct viscous dissipation, turbulent kinetic energy production, and spatial growth. In this study, the large scale motions (LSMs) are extracted using a proper orthogonal decomposition (POD) of the velocity field based on high-spatial-resolution two-dimensional – two-component particle image velocimetry (HSR 2C-2D PIV) of a zero-pressure-gradient turbulent boundary layer (ZPG-TBL), and their effect on the skin friction via RD decomposition.

STREAmS: A high-fidelity accelerated solver for direct numerical simulation of compressible turbulent flows

We present STREAmS, an in-house high-fidelity solver for direct numerical simulations (DNS) of canonical compressible wall-bounded flows, namely turbulent plane channel, zero-pressure gradient turbulent boundary layer and supersonic oblique shock-wave/boundary layer interaction. The solver incorporates state-of-the-art numerical algorithms, specifically designed to cope with the challenging problems associated with the solution of high-speed turbulent flows and can be used across a wide range of Mach numbers, extending from the low subsonic up to the hypersonic regime. From the computational viewpoint, STREAmS is oriented to modern HPC platforms thanks to MPI parallelization and the ability to run on multi-GPU architectures. This paper discusses the main implementation strategies, with particular reference to the CUDA paradigm, the management of a single code for traditional and multi-GPU architectures, and the optimization process to take advantage of the latest generation of NVIDIA GPUs. Performance measurements show that single-GPU optimization more than halves the computing time as compared to the baseline version. At the same time, the asynchronous patterns implemented in STREAmS for MPI communications guarantee very good parallel performance especially in the weak scaling spirit, with efficiency exceeding 97% on 1024 GPUs. For overall evaluation of STREAmS with respect to other compressible solvers, comparison with a recent GPU-enabled community solver is presented. It turns out that, although STREAmS is much more limited in terms of flow configurations that can be addressed, the advantage in terms of accuracy, computing time and memory occupation is substantial, which makes it an ideal candidate for large-scale simulations of high-Reynolds number, compressible wall-bounded turbulent flows. The solver is released open source under GPLv3 license. Program summaryProgram Title: STREAmSCPC Library link to program files:https://doi.org/10.17632/hdcgjpzr3y.1Developer’s repository link:https://github.com/matteobernardini/STREAmSCode Ocean capsule:https://codeocean.com/capsule/8931507/tree/v2Licensing provisions: GPLv3Programming language: Fortran 90, CUDA Fortran, MPINature of problem: Solving the three-dimensional compressible Navier–Stokes equations for low and high Mach regimes in a Cartesian domain configured for channel, boundary layer or shock-boundary layer interaction flows.Solution method: The convective terms are discretized using a hybrid energy-conservative shock-capturing scheme in locally conservative form. Shock-capturing capabilities rely on the use of Lax–Friedrichs flux vector splitting and weighted essentially non-oscillatory (WENO) reconstruction. The system is advanced in time using a three-stage, third-order RK scheme. Two-dimensional pencil distributed MPI parallelization is implemented alongside different patterns of GPU (CUDA Fortran) accelerated routines.

High-performance simulations of turbulent boundary layer flow using Intel Xeon Phi many-core processors

Direct numerical simulations (DNS) of turbulent flows have increasing importance because they not only provide fundamental understanding of turbulent flows but also complement and extend experimental results. DNS of high Reynolds numbers, however, require huge computing cost so high-performance computing has been strongly pursued. In this study, we examine the feasibility of cost-efficient DNS on Intel Xeon Phi many-core processors that are currently adopted by 10% of the 100 largest supercomputers in the world as listed in the Top500 site. For this purpose, we port and optimize our in-house turbulent flow solver named as DNS-TBL (direct numerical simulation-turbulent boundary layer) on Xeon Phi Knights Landing (KNL) many-core processors and conduct benchmark tests on KNL and conventional multicore processors. The key architectural features of KNL processors and strategies to exploit them for performance enhancement are discussed. The optimized code is validated by conducting numerical simulations of zero-pressure gradient turbulent boundary layers at high Reynolds numbers and by comparing simulated turbulent statistics to those reported in previous studies. With the details of optimization strategies and validation processes, this work can serve as a practical guideline for acceleration of large-scale and precise DNS with many-core computing.

The turbulent/non-turbulent interface in an adverse pressure gradient turbulent boundary layer

The turbulent/non-turbulent interface (TNTI) in an adverse pressure gradient (APG, β = 1.45) turbulent boundary layer (TBL) is explored here by using direct numerical simulation (DNS) data; β is the Clauser pressure gradient parameter. For comparison, the DNS data for a zero pressure gradient (ZPG) TBL is included. The interface is extracted with an approach based on enstrophy criteria. Depending on the enstrophy, the outer boundary layer flow can be classified into the free stream, boundary layer wake, and intermittent flow regimes. The fractal dimension of the interface is obtained by using the box-counting algorithm, and was found to be constant over a long range of box sizes. The TNTI shows a monofractal behavior. The geometric complexity of a TNTI can be determined in terms of the genus, which is defined as the number of handles in a geometric object. We examine the volume and projection area of the genus of the TNTI to analyze the entrainment process. The geometric complexity of the APG TBL interface and the local entrainment are greater than those of the ZPG TBL, as is evident in the increases in the genus near the interface. The local entrainment velocity is dominantly affected by the viscous diffusion at the interface.

Boundary layer turbulence statistics over transitionally rough marine fouling control coatings

The results of a dedicated boundary layer measurement campaign, which was conducted by using a 2D LDV system over transitionally rough and irregular marine surfaces in a large flow-channel, are presented and discussed in this study. The experimental campaign aimed to investigate the turbulence statistics for zero-pressure gradient turbulent boundary layers developed over marine fouling control coatings, which represent transitionally rough and irregular surfaces, along with hydraulically smooth and fully-rough reference surfaces. A particular emphasis was placed on the wall outer layer similarity. At the same time, the main characteristics of the boundary layer flow such as the velocity defect profiles, Reynolds stresses, triple correlations of turbulence velocities, skewness distributions and flatness factors were comparatively discussed for six different surfaces. The surface roughness properties, boundary layer characteristic parameters, wake parameters and frictional drag properties were also presented for the tested surfaces along with their roughness functions. The outer layer similarity was observed for the surfaces coated with the fouling control coatings in general. The current study presented, perhaps for the first time in such details, the higher-order statistics of turbulence for the turbulent boundary layer flow developed over the state-of-the-art marine fouling control coatings.

Analysis of the spanwise extent and time persistence of uniform momentum zones in zero pressure gradient and adverse pressure gradient turbulent boundary layers

Time-resolved velocity fields from direct numerical simulations (DNS) are used to investigate the spanwise extent and the time persistence of uniform momentum zones (UMZs) in a zero pressure gradient turbulent boundary layer (ZPG-TBL) and a self-similar adverse pressure gradient turbulent boundary layer (APG-TBL) at the verge of separation. The instantaneous detection methodology introduced by Adrian et al. [1] is used to detect the UMZs and is extended to take into account the spanwise domain length and the temporal evolution of the UMZs. The Reynolds number based on friction velocity (Reτ) ranges from 1176 to 1277 for the ZPG-TBL and from 1652 to 1745 for the self-similar APG-TBL within the domain of interest. For both the TBL cases, probability density functions (PDFs) of the number of UMZs are computed as a function of the streamwise extent, spanwise extent and time extent. For the ZPG-TBL, when the streamwise length of the domain is greater than or equal to 3 boundary layer thickness, the probability of finding 4 UMZs becomes almost negligible. For the APG-TBL, even when the streamwise domain length is taken as large as 1.3 boundary layer thickness, the probability of finding 4 UMZs is still significant. The spanwise extent of the UMZs is found to be shorter than their streamwise extent regardless of the pressure gradient in the flow. In the ZPG-TBL flow, the majority of the UMZs have a spanwise extent of the order of one-tenth of a boundary layer thickness while for the APG-TBL, it is found to be on the order of one-hundredth of a boundary layer thickness. In the ZPG-TBL, the probability of finding 2 UMZs that persist over a time period of 2 integral time scale is around 50%. Similarly, for the APG-TBL, the probability of finding 2 UMZs with a time persistence of 0.4 integral time scale is over 50%. In the case of the ZPG-TBL, it is observed that some of the UMZs with higher persistence in time have higher streamwise momentum and are found to be closer to the free-stream in general. This result is consistent with the previous observations by Laskari et al. [2]. In contrast, for the APG-TBL, UMZs with longer time persistence are found closer to the wall with lower streamwise momentum.

Drag Reduction and Energy Saving by Spanwise Traveling Transversal Surface Waves for Flat Plate Flow

Wall-resolved large-eddy simulations are performed to study the impact of spanwise traveling transversal surface waves in zero-pressure gradient turbulent boundary layer flow.Eighty variations of wavelength, period, and amplitude of the space- and time-dependent sinusoidal wall motion are considered for a boundary layer at a momentum thickness based Reynolds number of {rm Re}_theta = 1000. The results show a strong decrease of friction drag of up to 26% and considerable net power saving of up to 10%. However, the highest net power saving does not occur at the maximum drag reduction. The drag reduction is modeled as a function of the actuation parameters by support vector regression using the LES data.A dependence of the spanwise pressure drag on the wavelength is found. A substantial attenuation of the near-wall turbulence intensity and especially a weakening of the near-wall velocity streaks are observed. Similarities between the current actuation technique and the method of a spanwise oscillating wall without any normal surface deflection are reported. In particular, the generation of a directional spanwise oscillating Stokes layer is found to be related to skin-friction reduction.

Effect of adverse pressure gradients on turbulent wing boundary layers

The characteristics of turbulent boundary layers (TBLs) subjected to adverse pressure gradients are analysed through well-resolved large-eddy simulations. The geometries under study are the NACA0012 and NACA4412 wing sections, at and angle of attack, respectively, both of them at a Reynolds number based on inflow velocity and chord length of . The turbulence statistics show that adverse pressure gradients (APGs) have a significant effect on the mean velocity, velocity fluctuations and turbulent kinetic energy budget, and this effect is more prominent on the outer region of the boundary layer. Furthermore, the effect of flow history is assessed by means of an integrated Clauser pressure-gradient parameter (Vinuesa et al., Flow Turbul. Combust., vol. 99, 2017, pp. 565–587), through the study of cases with matching local values of and the friction Reynolds number to isolate this effect. Our results show a noticeable effect of the flow history on the outer region, however the differences in the near-wall peak of the tangential velocity fluctuations appear to be mostly produced by the local APG magnitude. The one-dimensional power-spectral density shows energetic small scales in the outer region of APG TBLs, whereas these energetic scales do not appear in zero-pressure-gradient (ZPG) TBLs, suggesting that small scales near the wall are advected towards the outer layer by the APG. Moreover, the linear coherence spectra show that the spectral outer peak of high-Reynolds-number ZPG TBLs is highly correlated with the near-wall region (Baars et al., J. Fluid Mech., vol. 823, 2017, R2), unlike APG TBLs which do not show such a correlation. This result, together with the different two-dimensional spectra of APG and high-Reynolds-number ZPG TBLs, suggests different energisation mechanisms due to APG and increase in Reynolds number. To the authors’ knowledge, this is the first in-depth analysis of the TBL characteristics over wings, including detailed single-point statistics, spectra and coherence.