Streamwise Velocity Fluctuations Research Articles

Small-scale Helmholtz resonators with grazing turbulent boundary layer flow

ABSTRACT Helmholtz resonators flush-mounted in a wall beneath turbulent boundary layer flow are studied by focusing on their flow-induced excitation and effect on the grazing turbulent flow. A particular focus lies on single resonators tuned to the most intense spatio-temporal fluctuations in the near-wall vertical velocity and wall-pressure, residing at a spatial scale of λ x + ≈ 250 (or temporal scale of T + ≈ 25 ). Resonators are examined in a boundary layer flow at R e τ ≈ 2280 . Two neck-orifice diameters of d + ≈ 68 and 102 are considered, and for each value of d + three different resonance frequencies are studied (corresponding to a period of T + ≈ 25 , as well as one lower, and one higher, period). The response of the TBL flow is analysed by employing velocity data from hot-wire anemometry and particle image velocimetry measurements. Passive resonance only affects streamwise velocity fluctuations in the region y + ≲ 25 , while vertical velocity fluctuations due to resonance reach up to y + ≈ 100 . A narrow-band increase in streamwise turbulence kinetic energy at the resonance scale co-exists with a more than 20% attenuation of lower-frequency energy. Current findings on single resonator cases will aid in the development of passive surfaces with distributed resonators for boundary-layer flow control.

Evaluation of spatial resolution effects in rough wall-bounded turbulence

This study investigates the impact of insufficient spanwise spatial resolution on the measurement accuracy of streamwise velocity fluctuations over rough walls. We use a direct numerical simulation (DNS) database of turbulent open-channel flow over three-dimensional sinusoidal roughness with varied wavelengths and roughness heights. Employing a triple decomposition, we investigate both the attenuation of the turbulent fluctuations (about the local mean), u′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u^\\prime$$\\end{document} and the dispersive stresses (roughness-induced fluctuations of the time-averaged mean about the global mean), U~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ilde{U}}$$\\end{document}. A boxcar filter on DNS data is applied to investigate the effects of spanwise spatial filtering on these quantities. Our analysis reveals the significance of two key length-scale ratios for velocity measurements over rough walls: the wire length relative to the spatially and temporally plane-averaged Kolmogorov scale at the roughness crest (l/⟨η⟩k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l/\\langle \\eta \\rangle _k$$\\end{document}), and the wire length relative to the roughness spanwise wavelength (l/Λy\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l/\\Lambda _y$$\\end{document}). We observe that maintaining l/⟨η⟩k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l/\\langle \\eta \\rangle _k$$\\end{document} constant while increasing l/Λy\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l/\\Lambda _y$$\\end{document} attenuates the variance of U~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ilde{U}}$$\\end{document} and u′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u^\\prime$$\\end{document} within the roughness sublayer. When fixing l/Λy\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l/\\Lambda _y$$\\end{document}, an increase in l/⟨η⟩k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l/\\langle \\eta \\rangle _k$$\\end{document} influences the turbulent fluctuations across all wall-normal locations. These findings highlight the necessity of considering both length scales when evaluating spanwise spatial resolution in turbulence measurements over rough walls.

Preferential enhancement of convective heat transfer over drag via near-wall turbulence manipulation using spanwise wall oscillations

This study investigates the manipulation of convective heat transfer through spanwise wall oscillations in a turbulent channel flow. Direct numerical simulations are performed at Reτ=180 and Pr=1.The primary focus of this work is to explore the heat transfer response to oscillation parameters that promote drag increase, a regime that has received limited attention. By adopting an extended oscillation period (T+=500) and amplitude (W+=30), which have been reported to enhance drag, a remarkable dissimilarity between momentum and heat transport emerges. Under these conditions, the convective heat transfer undergoes a substantial 15% intensification, while the drag increases by a comparatively moderate 7.7%, effectively breaking the Reynolds analogy. To elucidate the physical mechanisms responsible for this dissimilar behaviour, a comprehensive statistical analysis is conducted. The control effect on the near-wall streaks and the associated mixing of momentum and heat is investigated by examining the energy distribution across scales and wall-normal locations. This analysis provides valuable insights into the control’s impact on the turbulent structures. Furthermore, the correlation between wall-normal velocity fluctuations and both streamwise velocity and temperature fluctuations is scrutinized to understand the modification of sweep and ejection events, which drive the transport of momentum and heat. The Fukagata–Iwamoto–Kasagi (FIK) identity is employed to identify the contributing factors to the changes in drag and heat transfer. The analysis highlights the importance of the pressure term in the streamwise velocity equation and the linearity of the temperature equation. Further investigation is necessary to fully unravel the complex mechanisms governing the decoupling of heat and momentum transport. The results of this study underscore the potential of using unconventional spanwise wall oscillations parameters to preferentially enhance convective heat transfer while minimizing the associated drag penalty.

Turbulent pipe flow and heat transfer of a binary mixture at supercritical pressure: Influences of cross-diffusion effects

Cross-diffusion effects, including Soret and Dufour effects, are enhanced around the pseudo-critical temperature (Tpc) of a binary mixture. Their influences on heat transfer at supercritical pressure have been scarcely studied. To bridge this gap, large-eddy simulations (LES) are conducted to investigate forced convective heat transfer of a CO2–ethane mixture at supercritical pressures in a circular pipe subject to a uniform heat flux. Both heating and cooling conditions, along with varying initial concentrations and thermodynamic pressures, are included in the simulations. The LES results reveal that the Soret effect causes concentration separation, resulting in a concentration boundary layer. The magnitudes of the thermodiffusion factor (kT) and the radial temperature gradient control the intensity of separation, which is more pronounced at near-critical pressure and high heat flux. Since kT is significant only around Tpc, downstream decay of the concentration separation is observed as the loci of T=Tpc migrate away from the wall so that the local radial temperature gradient diminishes. The primary factors affecting heat transfer are the variations in thermal conductivity and isobaric specific heat resulting from concentration separation. In contrast, the Dufour effect and the accompanying inter-diffusion play negligible roles. In deterioration scenarios, the bulk Nusselt number (Nub) shows a maximum relative drop of 8%, whereas in enhancement scenarios, Nub shows a maximum relative increase in 10%, with both deterioration and enhancement decaying downstream. Cross-diffusion effects have negligible impacts on density and streamwise velocity, but noticeably alter streamwise velocity fluctuation and turbulent kinetic energy.

Turbulence Modulation By Large Heavy Particles In Wall-Bounded Turbulence

"Most studies on particle laden flows have focused either on small heavy particles or large neutrally buoyant particles. We present, for the first time (to the best of our knowledge), results in the regime of large and heavy particles, investigating the particle-turbulence dynamics over a parameter space covering a wide range of particle-volume fractions, Stokes and Froude numbers. We consider a flow in a pipe aligned with the gravitational vector, thus allowing for the investigation of the two-way coupling between particles and carrier phase turbulence, while excluding the effect of gravity on the wall-normal migration of particles. Time-resolved images of both tracers (10 micrometers particles) and the dispersed particles (700 micrometers in diameter) were taken in the streamwise-wall-normal pipe plane using a planar particle image velocimetry (PIV) system consisting of a high speed camera (Phantom VEO 440), and an Nd:YLF Laser as light source. Using Voronoi tessellations to analyze the inertial particle dynamics, we show a strong deviation from Poisson behaviour for cases with and without turbophoresis. From the time-resolved PIV measurements, we also show that the carrier phase turbulence is modulated even at particle concentrations as low as 0.3% indicating that particle-induced stresses due to distortion of fluid streamlines cannot be neglected. An increase or decrease in the peak streamwise velocity fluctuation in the particle laden flow was observed, depending on the Stokes number, while the radial velocity fluctuation was found either to be the same as in the single phase flow case or higher. Furthermore, pressure drop measurements indicate a linear increase in the skin friction coefficient with volume fraction of particles. This was true for all Stokes and Froude numbers considered. The growth rate (β) of the skin friction coefficient was however observed to be only a function of the Froude number. A power-law fit to the data shows that β scales inversely with the Froude number indicating that for Froude numbers less than 1, the influence of gravity cannot be neglected. "

Hot-wire spatial resolution issues in adverse pressure gradient turbulent boundary layers

The effect of a finite length of hot-wire probe sensor length on the measured streamwise velocity fluctuations is well understood in canonical wall-bounded flow, where the small-scale energy has been found to be universal and invariant with Reynolds number. A straightforward application of that assumption to non-canonical flows such as strong adverse pressure gradient (APG) flows has, however, been hampered since the effect of Re and APG could not conclusively be studied separately due to the lack of data with a clear scale separation. The present experimental investigation at Reτ≈4000 in weak, moderate and strong APGs with different wire length shows that spatial averaging effects are not only limited to the inner layer. A note of caution is hence warranted for measurements that seemingly try to take the bias effect of spatial attenuation into account by performing measurements with albeit long but fixed viscous-scaled wire length.

Fluid Dynamics Effects of a Porous Blockage on Laminar Flow in the Interior Subchannels of a 61-Pin Wire-Wrapped Rod Bundle

Flow blockages in Liquid Metal Fast Reactor (LMFR) fuel assemblies that can cause fuel pin cladding failures require further investigation for the development and optimization of these Generation IV reactor designs. The objective of this study was to experimentally evaluate the effects of a porous blockage accident scenario on laminar flow behavior in the interior subchannels of a prototypical 61-pin wire-wrapped rod bundle. The laminar flow condition is considered because of its importance to natural circulation and loss-of-coolant-accident operating scenarios as well as the limited availability of experimental data. The matched-index-of-refraction method was utilized to obtain two-dimension two-component time-resolved particle image velocimetry (TR-PIV) measurements at three planes centered on blocked and neighboring subchannel regions. Time-averaged first-order and second-order statistics, computed by Reynolds decomposition, were visualized including the mean and fluctuating streamwise and spanwise velocity components. Line profiles described the evolution of flow from upstream regions, to separated flow, and recombination downstream, while a modified Galilean decomposition distinguished differences between flow in the blocked measurement plane and flow in its neighboring counterpart region. Spatial-temporal cross-correlations were performed for the streamwise velocity fluctuations to characterize the convection velocity and decay of traveling vortices in the wake of the porous blockage. The isothermal TR-PIV measurements from this study provide high-fidelity experimental data sets for the validation of computational models and numerical studies to characterize complex fluid phenomena in wire-wrapped rod bundles during the potential accident scenario of a porous, interior flow blockage.

Volumetric visualization of vanishing vortices in wind turbine wakes

Volumetric velocimetry is used to investigate the evolution of tip vortices in the wake of a model wind turbine. The power spectral density of streamwise velocity fluctuations is estimated at several downstream locations, and changes in the magnitude of the frequency peaks corresponding to the blade-pass and turbine rotational frequency are observed. Full volumetric visualization of the coherent structures depicts the vortex merging process responsible for the change in detected frequency peaks, capturing the physical mechanism likely responsible for many similar previous observations. Published by the American Physical Society 2024

Mode transition of a film fluttering in a circular cylinder wake

As a representative model in the investigation into fluid–structure coupling, a flexible film interacting with the wake of a circular cylinder involves intricate patterns of both solid motion and fluid evolution. Recent investigations have found that the interactions could be either periodic or aperiodic in experiments; the latter, however, is often overlooked. In this work, the irregular aperiodic flutter of a flexible film behind a circular cylinder is investigated experimentally. It is determined that the irregular flutter intermittently exhibits transient quasi-periodic mode and aperiodic mode. The former is accompanied by the large-scale vortices alternatively formed against the film surfaces, while the latter is associated with vortices formed downstream of the film's trailing edge, so that the whole film is enveloped by the extended shear layers. In order to separate the data individually pertaining to each of the two modes from the whole dataset, a motion-mode recognition method is proposed, and then conditional statistics of flow fields are achieved. The quasi-periodic mode corresponds to more intense velocity fluctuations in the wake, while in the aperiodic mode, the observed localized instability of shear layers induces an increase in the local streamwise velocity fluctuation.

Statistical properties of neutrally and stably stratified boundary layers in response to an abrupt change in surface roughness

We conducted experimental investigations on the effect of stable thermal conditions on rough-wall boundary layers, with a specific focus on their response to abrupt increases in surface roughness. For stably stratified boundary layers, a new analytical relation between the skin-friction coefficient, $C_f$ , and the displacement thickness was proposed. Following the sharp roughness change, the overshoot in $C_f$ is slightly enhanced in stably stratified layers when compared with that of neutral boundary layers. Regarding the velocity defect law, we found that the displacement thickness multiplied by $\sqrt{2/C_f}$ , performs better than the boundary layer thickness alone when describing the similarity within internal boundary layers for both neutral and stable cases. A non-adjusted region located just beneath the upper edge of the internal boundary layer was observed, with large magnitudes of skewness and kurtosis of streamwise and wall-normal velocity fluctuations for both neutral and stable cases. At a fixed wall-normal location, the greater the thermal stratification, the greater the magnitudes of skewness and kurtosis. Quadrant analysis revealed that the non-adjusted region is characterised by an enhancement/reduction of ejection/sweep events, particularly for stably stratified boundary layers. Spatially, these ejections correspond well with peaks of kurtosis, exhibit stronger intensity and occur more frequently following the abrupt change in surface conditions.

Dual-Orthogonal-Plane Particle Image Velocimetry Measurement of the Turbulent Flow in the Channel Head of a Large-Scale Steam Generator Mockup

Abstract In this work, a large-scale mockup of a compact complex system integrating a steam generator (SG) and a reactor coolant pump (RCP) is considered. The three-dimensional turbulent flow in the steam generator channel head (SGCH) is measured in detail. Dual-orthogonal-plane particle image velocimetry (PIV) is employed to extract high-resolution flow information in two orthogonal planes. Two separate measurements are first made to see the three-dimensional time-mean flow dynamics and the statistical quantities in the two planes. These measurements highlight two distinct flow phenomena: jet arrays and massive turbulent separation bubbles (TSBs). These patterns are attributed to mass flow redistribution in the U-shaped tubes. Proper orthogonal decomposition (POD) identifies the first POD mode as corresponding to the TSB breathing-like motion, which significantly intensifies the side view streamwise velocity fluctuations, leading to them reaching 370% of the local mean velocity. To examine the unsteady behavior of massively separated regions, the dual-orthogonal-plane PIV system is then synchronized to simultaneously measure variations in the flow fields, and the missing data due to illumination interference are reconstructed using gappy POD. The synchronized analysis reveals a direct relationship between the low-frequency fluctuations in the side and front views. These fluctuations are in phase across both views, indicating a synchronized behavior that spans the entire field. This large-scale low-frequency breathing motion has critical implications for numerical simulations and sheds light on the unsteady behavior of the RCP system within the SGCH.

Reactive control of velocity fluctuations using an active deformable surface and real-time PIV

This study demonstrates an experimental realization of turbulence control strategies previously explored by Choi et al. (J. Fluid Mech., vol. 262, 1994, pp. 75–110) through numerical simulations. To conduct the experiments, a deformable surface with a streamwise array of 16 independently controlled actuators was developed. A real-time particle image velocimetry (RT-PIV) system was also created for flow measurements. The objective of the control strategy was to target the sweep and ejection motions of the vortex shedding from a spherical cap placed in a laminar boundary layer. Reactive control strategies consisted of wall-normal surface deformations that opposed or complied with the wall-normal (v) or streamwise (u) velocity fluctuations obtained from the RT-PIV. The results showed two primary outcomes of the control approach. Firstly, it effectively hindered the advancement of sweep motions towards the wall. Secondly, it disrupted the periodic shedding of vortices. The v-control with opposing wall motions and u-control with compliant wall motions exhibited strong inhibition of sweep motions, while the v-control with compliant and u-control with opposing wall motions showed weaker inhibition. All reactive control cases resulted in the disruption of vortex shedding. In some instances, this disruption was accompanied by increased turbulent kinetic energy due to the generation of additional flow motions. However, the v-control with opposing wall motions significantly reduced the vortex-shedding energy while maintaining total turbulent kinetic energy close to or below that of the unforced flow. Overall, the experiments show the effectiveness of reactive control strategies in mitigating sweep motions and disrupting vortical structures, offering insights for developing reactive control strategies.

Interplay of scales during the spatial evolution of energy-containing motions in wall-bounded turbulent flows

This article extends the previous investigation of the spatial evolution of energy-containing motions in wall-bounded turbulent flows (Kannadasan et al., J. Fluid Mech., vol. 955, 2023, R1) by examining their scale-interactions through spectral analysis based on the spanwise scale decomposition of turbulent kinetic energy and the Reynolds stress transport equation. The energy-containing motions located at the inflow of a turbulent channel flow are artificially removed and the interscale transport mechanisms involved in their spatial evolution are studied. This scale interaction analysis reveals the presence of a significant inverse transfer of streamwise Reynolds stress from the near-wall streaks to larger scales in the spatial evolution of energy-containing motions. This transfer is due to the spanwise variation of streamwise velocity fluctuations, represented by $\partial u'/\partial z$ , which is the primary mechanism of streak instability. The analysis presented in this study also shows that the inverse cascade of spanwise energy may correspond to the regeneration of streamwise vortices in the process of reactivating the self-sustaining mechanism in the spatial evolution of energy-containing motions.

Numerical evaluation of the bubble dynamic influence on the characteristics of multiscale cavitating flow in the bluff body wake

Unsteady cavitating flow around the bluff body widely existed in practical engineering fields. This paper aims to investigate the physics involved in the multi-scale cavitating flow in the wake of a wedge-shaped bluff body, with special emphasis on the bubble effects. Numerical simulation is conducted using the traditional Eulerian-Eulerian (E-E) and newly developed Eulerian-Lagrangian (E-L) methods in OpenFOAM. It is found that, compared with the experimental results, the E-L method can predict more accurate cavitation characteristics than the E-E method due to the contribution of discrete bubbles. Bubbles can significantly influence the behaviors of the multi-scale cavitating flow. Specially, analysis of pressure fluctuations indicates that the bubbles induce a stronger power spectral density in the middle- and high-frequency regions. With the bubble effects considered, the vortex structure is stretched and more extensive in the near wake regions. The strength of time-averaged vorticity distribution decreases in the far wake region. Further analysis of the vortex transport equation shows that bubble dynamics significantly increase the intensity of the stretching term by enhancing the spanwise velocity fluctuations. The intensity of the baroclinic torque term predicted by the E-L method is higher than that by the E-E method near the center line due to the influence of bubbles. On the other hand, the analysis of turbulent kinetic energy distribution indicates that bubbles can induce turbulence by increasing cross-stream velocity fluctuations. The increment of the shear Reynold stress, u′xu′y‾, suggests that the bubbles intensify the coupling between the streamwise and cross-stream velocity fluctuations.

On the streamwise velocity, temperature and passive scalar fields in compressible turbulent channel flows: a viewpoint from multiphysics couplings

It is generally believed that the velocity and passive scalar fields share many similarities and differences in wall-bounded turbulence. In the present study, we conduct a series of direct numerical simulations of compressible channel flows with passive scalars and employ the two-dimensional spectral linear stochastic estimation and the correlation function as diagnostic tools to shed light on these aspects. Particular attention is paid to the relevant multiphysics couplings in the spectral domain, i.e. the velocity–temperature ( $u-T$ ), scalar–temperature ( $g-T$ ) and velocity–scalar ( $u-g$ ) couplings. These couplings are found to be utterly different at a given wall-normal position in the logarithmic and outer regions. Specifically, in the logarithmic region, the $u-T$ and $u-g$ couplings are tight at the scales that correspond to the attached eddies and the very large-scale motions (VLSMs), whereas the $g-T$ coupling is robust in the whole spectral domain. In the outer region, $u-T$ and $u-g$ couplings are only active at the scales corresponding to the VLSMs, whereas the $g-T$ coupling is diminished but still strong at all scales. Further analysis indicates that although the temperature field in the vast majority of zones in a channel can be roughly treated as a passive scalar, its physical properties gradually deviate from those of a pure passive scalar as the wall-normal height increases due to the enhancement of the acoustic mode. Furthermore, the deep involvement of the pressure field in the self-sustaining process of energy-containing motions also drives the streamwise velocity fluctuation away from a passive scalar. The current work is an extension of our previous study (Cheng & Fu, J. Fluid Mech., vol. 964, 2023, A15), and further uncovers the details of the multiphysics couplings in compressible wall turbulence.

Robust relation of streamwise velocity autocorrelation in atmospheric surface layers based on an autoregressive moving average model

We construct an autoregressive moving average (ARMA) model consisting of the history and random effects for the streamwise velocity fluctuation in boundary-layer turbulence. The distance to the wall and the boundary-layer thickness determine the time step and the order of the ARMA model, respectively. Based on the autocorrelation's analytical expression of the ARMA model, we obtain a global analytical expression for the second-order structure function, which asymptotically captures the inertial, dynamic and large-scale ranges. Specifically, the exponential autocorrelation of the ARMA model arises from the autoregressive coefficients and is modified to logarithmic behaviour by the moving-average coefficients. The asymptotic expressions enable us to determine model coefficients by existing parameters, such as the Kolmogorov and the Townsend–Perry constants. A consequent double-log expression for the characteristic length scale is derived and is justified by direct numerical simulation data with $Re_\tau \approx 5200$ and field-measured neutral atmospheric surface layer data with $Re_\tau \sim O(10^6)$ from the Qingtu Lake Observation Array site. This relation is robust because it applies to $Re_\tau$ from $O(10^4)$ to $O(10^6)$ , and even when the statistics of natural ASL deviate from those of canonical boundary-layer turbulence, e.g. in the case of imbalance in energy production and dissipation, and when the Townsend–Perry constant deviates from traditional values.

Reynolds-number scaling of wall-pressure–velocity correlations in wall-bounded turbulence

Wall-pressure fluctuations are a practically robust input for real-time control systems aimed at modifying wall-bounded turbulence. The scaling behaviour of the wall-pressure–velocity coupling requires investigation to properly design a controller with such input data so that it can actuate upon the desired turbulent structures. A comprehensive database from direct numerical simulations (DNS) of turbulent channel flow is used for this purpose, spanning a Reynolds-number range $Re_\tau \approx 550\unicode{x2013}5200$ . Spectral analysis reveals that the streamwise velocity is most strongly coupled to the linear term of the wall pressure, at a Reynolds-number invariant distance-from-the-wall scaling of $\lambda _x/y \approx 14$ (and $\lambda _x/y \approx 8$ for the wall-normal velocity). When extending the analysis to both homogeneous directions in $x$ and $y$ , the peak coherence is centred at $\lambda _x/\lambda _z \approx 2$ and $\lambda _x/\lambda _z \approx 1$ for $p_w$ and $u$ , and $p_w$ and $v$ , respectively. A stronger coherence is retrieved when the quadratic term of the wall pressure is concerned, but there is only little evidence for a wall-attached-eddy type of scaling. An experimental dataset comprising simultaneous measurements of wall pressure and velocity complements the DNS-based findings at one value of $Re_\tau \approx 2$ k, with ample evidence that the DNS-inferred correlations can be replicated with experimental pressure data subject to significant levels of (acoustic) facility noise. It is furthermore shown that velocity-state estimations can be achieved with good accuracy by including both the linear and quadratic terms of the wall pressure. An accuracy of up to 72 % in the binary state of the streamwise velocity fluctuations in the logarithmic region is achieved; this corresponds to a correlation coefficient of $\approx$ 0.6. This thus demonstrates that wall-pressure sensing for velocity-state estimation – e.g. for use in real-time control of wall-bounded turbulence – has merit in terms of its realization at a range of Reynolds numbers.

Interfaces of high- and low-speed large-scale structures in compressible turbulent mixing layers: compressibility effects and structures

Direct numerical simulations of temporally developing mixing layers have been performed to investigate the effects of compressibility on statistics and structures near the interfaces of high- and low-speed large-scale structures (LSSs), covering a range of convective Mach numbers from $M_c=0.2$ to $1.8$ and Taylor Reynolds numbers up to 290. The interfaces of LSSs are directly defined by the isosurface of zero fluctuating streamwise velocity. The characteristic velocity jump at the interfaces grows rapidly in the transition stage and then decreases until reaching a gradual self-similar stage. The evolution of velocity jump is evidently delayed as the convective Mach number increases. The interface layer is formed by the shearing motion of neighbouring LSSs. A small vortical motion characterized by the Kolmogorov scale is induced in the interface layer by shear-dominated outer regions. The strengths of outer shearing motion and central vortical motion are greater at the leading edge, but smaller at the trailing edge, which is also reflected in a larger velocity jump at the leading edge. As the convective Mach number increases, the small-scale vortical structure is obviously suppressed by compressibility. At high convective Mach number $M_c=1.8$ , the compressive shear-dominated outer regions are linked with a sheet-like structure passing through the centre of the expansion region corresponding to a small-scale vortical structure. The compressibility and shearing strength near the interface are highly dependent on the interface orientation.

Reynolds number dependence of turbulent flows over a highly permeable wall

Direct numerical simulations of turbulent flows over highly permeable porous walls were performed at various Reynolds numbers to examine the effects of the Reynolds number on permeable wall turbulence. The porous medium consisted of Kelvin cell arrays with porosity $0.95$ , and the permeability Reynolds number $Re_K$ ranged from approximately 7 to 50. Simulations with thin and thick porous walls were performed to investigate the effects of spanwise roller vortices associated with the Kelvin–Helmholtz instability. The results show that the effect of the Kelvin–Helmholtz instability becomes more significant with increasing the permeability Reynolds number, and spanwise rollers, for which length scale is an order of channel height, dominate turbulence when $Re_K \gtrsim 30$ . Spanwise rollers reinforce the negative correlation between the wall-normal and streamwise velocity fluctuations close to the porous/fluid interface, and intensify the turbulent velocity fluctuations away from the porous walls, leading to increased frictional resistance. An investigation of the Reynolds number dependence of the modified logarithmic law indicates that the zero-plane displacement and equivalent roughness height are proportional to the square root of permeability, whereas the von Kármán constant increases with the permeability Reynolds number because of the increased mixing length resulting from the relatively large-scale velocity fluctuations induced by spanwise rollers. We developed a model for the modified log law for permeable wall turbulence based on permeability, and confirmed that the skin friction coefficient obtained from the model reasonably predicts the skin friction coefficient for several types of high-porosity porous media. Hence, permeability is a key parameter that characterizes the logarithmic mean velocity profiles over a variety of porous media with high porosity.

Effects of inflow Mach numbers on shock train dynamics and turbulence features in a backpressured supersonic channel flow

Investigations on shock train dynamics and relevant turbulence features in a backpressured supersonic channel flow are carried out using direct numerical simulation for three inflow Mach numbers of Ma0= 1.61, 2.0, and 2.45. As Ma0 increases, the shock train undergoes a structural change characterized by the leading shock which changes from the symmetric “λ” (Ma0=1.61) to the symmetric “X” (Ma0=2.00) and then to the asymmetric “X” pattern (Ma0=2.45). The symmetry breaking of shock structures induces asymmetric separation, which significantly alters the distribution characteristics of wall variables such as wall pressure and friction. To examine the unsteady behaviors of the shock train, a mode decomposition technique, namely, reduced-order variational mode decomposition [Liao et al., J. Fluid Mech. 966, A7 (2023)], is adopted taking its merit of adaptively extracting time-frequency features of dynamic systems. The modal analysis reveals that the shock train system exhibits significant centralization of low-frequency energy. Specifically, two basic types of low-frequency oscillation modes dominate the unsteady motion of the shock train: one depicts overall translating oscillation while another represents accordion-like oscillation. The analysis of turbulent kinetic energy shows that turbulence amplification is mainly dominated by the interaction of the decelerating mean flow with streamwise velocity fluctuations in the vicinity of the leading shock for all three cases, which is unaffected by the symmetry breaking of shock structures.