Wall-normal Velocity Fluctuations Research Articles

Direct numerical simulation of compressible turbulent channel flows over porous boundaries

The impact of porous boundaries on skin friction and heat transfer in compressible turbulent channel flows is explored through direct numerical simulations. Utilizing the volume-averaged Navier–Stokes equations for the porous media, we examine flows at Mach numbers Mb=0.3 and Mb=1.5, with friction Reynolds numbers ranging from 176 to 220, across three permeability levels: 0 (impermeable), 1.6×10−5, and 1.0×10−4. Our findings reveal a dual impact of porous boundaries on skin friction: a direct reduction due to averaged slip velocity at the interface and an indirect increase from amplified Reynolds shear stress due to enhanced wall-normal permeability. This permeability weakens the wall-blocking effect, leading to intensified wall-normal velocity fluctuations and consequently higher Reynolds stress. Additionally, the Mach number significantly influences flow structures, particularly at higher permeabilities, where it disrupts near-wall streaks at Mb=0.3 but has a diminished effect at Mb=1.5. Thermal analysis confirms the validity of the generalized Reynolds analogy for the mean temperature in these flows, with the turbulent Prandtl number approximating 1, in line with the strong Reynolds analogy. Moreover, a strong spatial correlation between heat flux and wall shear stress fluctuations underscores the intertwined dynamics of momentum and thermal transport at the porous–fluid interface.

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.

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.

Effect of bulk viscosity on the hypersonic compressible turbulent boundary layer

The impact of bulk viscosity is unclear with considering the increased dilatational dissipation and compressibility effects in hypersonic turbulence flows. In this study, we employ direct numerical simulations to conduct comprehensive analysis of the effect of bulk viscosity on hypersonic turbulent boundary layer flow over a flat plate. The results demonstrate that the scaling relations remain valid even when accounting for large bulk viscosity. However, the wall-normal velocity fluctuations $v_{rms}^{\prime \prime }$ decrease significantly in the viscous sublayer due to the enhanced bulk dilatational dissipation. The intensity of travelling-wave-like alternating positive and negative structures of instantaneous pressure fluctuations $p_{rms}^{\prime }$ in the near-wall region decreases distinctly after considering the bulk viscosity, which is attributed mainly to the reduction of compressible pressure fluctuations $p_{c,rms}^{+}$ . Furthermore, the velocity divergence $\partial u_{i} / \partial x_{i}$ undergoes a significant decrease by bulk viscosity. In short, our results indicate that bulk viscosity can weaken the compressibility of the hypersonic turbulent boundary layer and becomes more significant as the Mach number increases and the wall temperature decreases. Notably, when the bulk-to-shear viscosity ratio of the gas reaches a few hundred levels ( $\mu _b/\mu =O(10^2)$ ), and mechanical behaviour of the near-wall region ( $\kern 0.06em y^+\le 30$ ) is of greater interest, the impact of bulk viscosity on the hypersonic cold-wall turbulent boundary layer may not be negligible.

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.

Characteristics of turbulent boundary layers generated by different tripping devices

In this study, we employ a high-fidelity flow visualisation technique to investigate the resemblance between a turbulent boundary layer generated in a lab environment with a limited development length by different tripping devices and a naturally developed canonical turbulent boundary layer. Furthermore, we aim to provide statistics of the wall-normal velocity fluctuation of the tripped boundary layers and analyse them compared with the canonical turbulent boundary layer. This is achieved by conducting two-dimensional particle image velocimetry measurements to acquire the velocity components in the stream-wise wall-normal plane downstream of the tripping location. Different criteria including integral parameters, diagnostic plot, stream-wise and wall-normal turbulence intensities, and mean velocity deficit profiles are employed to compare the boundary layer profiles generated by different trips with well-behaved turbulent boundary layers presented in the literature. The generation of Reynolds shear stress in tripped boundary layers is analysed using quadrant analysis, and suitably sized trips are shown to have contributions of sweeps and ejections in a similar manner to a well-behaved turbulent boundary layer. Furthermore, through the detection of uniform momentum zones, the presence of coherent structures in the logarithmic and outer layers of these well-behaved tripped boundary layers is shown. The findings of this study identify the blockage created by trips as the main factor affecting the turbulence statistics at a certain downstream distance. The results also suggest that the investigation of inner-scaled mean stream-wise velocity is recommended as a simple yet reliable and rapid assessment of the impact of a trip on the turbulent boundary layer development in short test sections.

Effect of Stokes number and particle-to-fluid density ratio on turbulence modification in channel flows

Two-way momentum-coupled direct numerical simulations of a particle-laden turbulent channel flow are addressed to investigate the effect of the particle Stokes number and of the particle-to-fluid density ratio on the turbulence modification. The exact regularised point-particle method is used to model the interphase momentum exchange in presence of solid boundaries, allowing the exploration of an extensive region of the parameter space. Results show that the particles increase the friction drag in the parameter space region considered, namely the Stokes number $St_+ \in [2,80]$ , and the particle-to-fluid density ratio $\rho _p/\rho _f \in [90,5760]$ at a fixed mass loading $\phi =0.4$ . It is noteworthy that the highest drag occurs for small Stokes number particles. A measurable drag increase occurs for all particle-to-fluid density ratios, the effect being reduced significantly only at the highest value of $\rho _p/\rho _f$ . The modified stress budget and turbulent kinetic energy equation provide the rationale behind the observed behaviour. The particles’ extra stress causes an additional momentum flux towards the wall that modifies the structure of the buffer and of the viscous sublayer where the streamwise and wall-normal velocity fluctuations are increased. Indeed, in the viscous sublayer, additional turbulent kinetic energy is produced by the particles’ back-reaction, resulting in a strong augmentation of the spatial energy flux towards the wall where the energy is ultimately dissipated. This behaviour explains the increase of friction drag in particle-laden wall-bounded flows.

Numerical investigation of the linear evolution of Tollmien–Schlichting waves over longitudinal riblet surface

The effect of longitudinal riblets on the spatially developing Tollmien–Schlichting (T–S) waves within the boundary layer is numerically investigated by direct numerical simulation. The riblets, designed to reduce turbulent drag and featuring a blade-like shape with zero thickness, are the primary focus. Part of the flat plate is replaced by riblet surface, and T–S waves with varying frequencies are introduced prior to the onset of the riblets. Moreover, the influence of riblet size is further discussed, and the underlying mechanism by which riblets affect T–S waves is identified based on the analysis of disturbance energy equation. The results demonstrate that the presence of riblets significantly enhances the growth of T–S waves. The modulation of base flow by riblets results in the emergence of an inflection point in the velocity profile within the boundary layer, thereby enhancing the flow instability. The growth rate of T–S waves and the unstable region on the riblet surface are observed to be considerably amplified, and an increase in riblet's lateral spacing and height to spacing ratio intensifies this amplification. From the perspective of disturbance energy, it is shown that although riblets cause additional energy dissipation in their vicinity, their modification of the mean velocity gradient and the phase difference between streamwise and wall-normal velocity fluctuations contribute to a significant increase in the production term, which consequently accelerates the growth of T–S waves.

Evidence that superstructures comprise self-similar coherent motions in high Reynolds number boundary layers

We present experimental evidence that the superstructures in turbulent boundary layers comprise smaller, geometrically self-similar coherent motions. The evidence comes from identifying and analysing instantaneous superstructures from large-scale particle image velocimetry datasets acquired at high Reynolds numbers, capable of capturing streamwise elongated motions extending up to 12 times the boundary layer thickness. Given the challenge in identifying the constituent motions of the superstructures based on streamwise velocity signatures, a new approach is adopted that analyses the wall-normal velocity fluctuations within these very long motions, which reveals the constituent motions unambiguously. The conditional streamwise energy spectra of the Reynolds shear stress and the wall-normal fluctuations, corresponding exclusively to the superstructure region, are found to exhibit the well-known distance-from-the-wall scaling in the intermediate-scale range. It suggests that geometrically self-similar motions are the constituent motions of these very-large-scale structures. Investigation of the spatial organization of the wall-normal momentum-carrying eddies, within the superstructures, also lends empirical support to the concatenation hypothesis for the formation of these structures. The association between the superstructures and self-similar motions is reaffirmed on comparing the vertical coherence of the Reynolds-shear-stress-carrying motions, by computing conditionally averaged two-point correlations, which are found to match with the mean correlations. The mean vertical coherence of these motions, investigated for the log region across three decades of Reynolds numbers, exhibits a unique distance-from-the-wall scaling invariant with Reynolds number. The findings support modelling of these dynamically significant motions via data-driven coherent structure-based models.

Large-eddy simulation of free-surface turbulent channel flow over square bars

The results of large-eddy simulations of free-surface turbulent channel flow over spanwise-aligned square bars are used to investigate the effects of bed roughness and water surface deformations on the root-mean-squared velocity fluctuations, dispersive shear stress, double-averaged Reynolds shear stress, wake kinetic energy and double-averaged turbulent kinetic energy. Two bar spacings, corresponding to transitional and k-type roughness, at similar Reynolds and Froude numbers are considered. The main peak of all statistical quantities occurs at the bar crest height. The effects of a standing wave at the water surface in flow over k-type roughness is marked by a local peak under the water surface for all statistical quantities considered here except wall-normal and spanwise velocity fluctuations. Quadrant analysis shows that sweeps and ejections are the strongest events contributing to both dispersive and double-averaged Reynolds shear stress but their contributions are different for the two bar spacings. Examining the budgets of dispersive and double-averaged Reynolds shear stress reveals that the dominant terms of these stresses are pressure–strain correlation and pressure transport and the contribution of wake production is similar for both of these stresses but with opposite sign. In addition to the main role of the bars in consuming or producing wake kinetic energy through production and transport and convection, the standing wave at the water surface in flow over k-type roughness induces large convection in the bulk flow too. The dominant terms in the double-averaged turbulent kinetic energy budget are similarly production, transport and convection. Large shear production renders large temporal fluctuations than spatial fluctuations of flow variables. The interaction of bars, bed and water surface is seen in the convection term in flow over k-type roughness.

Turbulence and added drag over acoustic liners

We present pore-resolved compressible direct numerical simulations of turbulent flows grazing over perforated plates, that closely resemble the acoustic liners found on aircraft engines. Our direct numerical simulations explore a large parameter space including the effects of porosity, thickness and viscous-scaled diameter of the perforated plates, at friction Reynolds numbers $\textit {Re}_\tau = 500\unicode{x2013}2000$ , which allows us to develop a robust theory for estimating the added drag induced by acoustic liners. We find that acoustic liners can be regarded as porous surfaces with a wall-normal permeability and that the relevant length scale characterizing their added drag is the inverse of the wall-normal Forchheimer coefficient. Unlike other types of porous surfaces featuring Darcian velocities inside the pores, the flow inside the orifices of acoustic liners is fully turbulent, with a magnitude of the wall-normal velocity fluctuations comparable to the peak in the near-wall cycle. We provide clear evidence of a fully rough regime for acoustic liners, also confirmed by the increasing relevance of pressure drag. Once the fully rough asymptote is reached, canonical acoustic liners provide an added drag comparable to that of sand-grain roughness with viscous-scaled height matching the inverse of the viscous-scaled Forchheimer permeability of the plate.

Impact of flow regime on the performance of anti-biofouling coatings

Biofouling poses significant challenges for marine transportation due to increased skin drag, which results in increased fuel cost and associated text {CO}_2 emissions. Current antifouling methods involving polymer coating, biocides, and self-depleting layers harm marine ecosystems and contribute to marine pollution. Significant advancements have resulted in using bioinspired coatings to address this issue. However, prior investigations have predominantly focused on wettability and adhesion aspects, resulting in a limited understanding of the impact of flow regime on bioinspired structure patterns for antifouling. We conducted comprehensive experiments with two bioinspired coatings1 under laminar and turbulent flow regimes and compared them with a smooth surface. The two coatings are composed of regular arrangements of micropillars measuring 85 μm in height and spaced at 180 μm (pattern A) and 50 μm high micropillars spaced at 220 μm (pattern B). Theoretical arguments indicate that wall-normal velocity fluctuations near the micropillars’ top significantly contribute to reducing the onset of biofouling under turbulence compared to the smooth surface. Pattern A coating can effectively decrease biofouling by 90% for fouling sizes exceeding 80 microns when compared to a smooth surface subjected to a turbulent flow regime. The coatings exhibited comparable anti-biofouling properties under a laminar flow. Also, the smooth surface experienced substantially higher biofouling under laminar flow compared to turbulent conditions. This underscores how the effectiveness of anti-biofouling approaches is critically influenced by the flow regime.

Reinforcement learning of control strategies for reducing skin friction drag in a fully developed turbulent channel flow

Reinforcement learning is applied to the development of control strategies in order to reduce skin friction drag in a fully developed turbulent channel flow at a low Reynolds number. Motivated by the so-called opposition control (Choi et al., J. Fluid Mech., vol. 253, 1993, pp. 509–543), in which a control input is applied so as to cancel the wall-normal velocity fluctuation on a detection plane at a certain distance from the wall, we consider wall blowing and suction as a control input, and its spatial distribution is determined by the instantaneous streamwise and wall-normal velocity fluctuations at distance 15 wall units above the wall. A deep neural network is used to express the nonlinear relationship between the sensing information and the control input, and it is trained so as to maximize the expected long-term reward, i.e. drag reduction. When only the wall-normal velocity fluctuation is measured and a linear network is used, the present framework reproduces successfully the optimal linear weight for the opposition control reported in a previous study (Chung & Talha, Phys. Fluids, vol. 23, 2011, 025102). In contrast, when a nonlinear network is used, more complex control strategies based on the instantaneous streamwise and wall-normal velocity fluctuations are obtained. Specifically, the obtained control strategies switch abruptly between strong wall blowing and suction for downwelling of a high-speed fluid towards the wall and upwelling of a low-speed fluid away from the wall, respectively. Extracting key features from the obtained policies allows us to develop novel control strategies leading to drag reduction rates as high as 37 %, which is higher than the 23 % achieved by the conventional opposition control at the same Reynolds number. Finding such an effective and nonlinear control policy is quite difficult by relying solely on human insights. The present results indicate that reinforcement learning can be a novel framework for the development of effective control strategies through systematic learning based on a large number of trials.

Acoustic receptivity in the airfoil boundary layer: An experimental study in a closed wind tunnel

Airfoil trailing edge noise with a tonal frequency at a medium-Reynolds number (from 2 × 10 5 to 3 × 10 5 in this work) is related to periodic fluctuations in the airfoil boundary layer. Acoustic receptivity plays an important role, in that it constructs a feedback loop to induce ladder-structure phenomena and discrete peak frequencies. The present work is devoted to the experimental study of the acoustic receptivity in the airfoil boundary layer by employing a time-resolved particle image velocimetry method. The symmetric vortex shedding process is noticed, and a hysteresis phenomenon is discovered with the increasing and decreasing wind speed. The author applies the Hilbert transform to show a space-wavenumber spectrum of wall-normal velocity fluctuations to locate resonance points, where acoustic pressure resonates with fluctuations in the boundary layer. The results show that the acoustic reception can affect the local velocity to increase and decrease the wavenumber before and after reach points. The trailing edge noise impacts on the airfoil boundary layer to control the system states and follows the same acoustic feedback loop from Arbey and Bataille [“Noise generated by airfoil profiles placed in a uniform laminar flow,” J. Fluid Mech. 134, 33–47 (1983)].

Laminar and turbulent flow development study in a rectangular duct with 180° sharp bend by using stereo particle image velocimetry and liquid crystal thermography measurements

This work presents a detailed insight into the flow progression and surface heat transfer distribution across the sharp 180° bend of a two-pass rectangular duct for laminar (Re = 800) and turbulent (Re = 6500) in-flow conditions. Stereoscopic particle image velocimetry (stereo PIV) as well as two-dimensional and two-component PIV measurements and liquid crystal thermography techniques are appropriately used for flow and heat transfer characterization across the complete sharp 180° bend. The centrifugal instabilities arise due to the sharp bend, which induces the secondary flows in the form of counter-rotating vortex pairs commonly known as Dean vortices. These secondary vortices play a significant role in the localized laminar–turbulent transition and turbulence augmentations for laminar and turbulent inflow conditions. Subsequently, quantitative analysis shows that complete 180° turning of flow resulted in intense augmentation of spatially averaged turbulence quantities. Root mean square (RMS) fluctuations in the transverse direction V¯T|rms increase by 298% and 186% for respective flow conditions. Augmentation of ∼ 287% (laminar) and 260% (turbulent) in the wall-normal RMS fluctuations (V¯N|rms) are observed. These augments in transverse and wall-normal velocity fluctuations result in a very sharp amplification of spatially averaged turbulent kinetic energy (k¯), that is, 1825% for inlet laminar and 928% for inlet turbulent flow regimes.

Drag reduction of blowing-based active control in a turbulent boundary layer

Direct numerical simulations are conducted to gain insight into the blowing-based active control in a spatially developing turbulent boundary layer at a low Reynolds number. The drag reduction properties and mechanisms of different blowing velocity distribution forms under constant wall-normal mass flux are comparatively studied, including uniform blowing and blowing-only opposition control (BOOC). After the application of blowing control, the self-similarity of the Reynolds shear stress is influenced. The property of drag reduction and control gain of the blowing-based active control schemes in the turbulent boundary layer is similar to that in turbulent channel flow, i.e., the BOOC scheme can achieve higher drag reduction than uniform blowing, but the control gain reduces. Due to the coexistence of the opposition effect and the induction effect, the negative wall-normal velocity fluctuations accompanied by the sweep motion are induced to form small-scale flow structures in the near-wall region. The decomposition of the skin-friction drag coefficient shows that the changes of each contribution term are basically the same for different blowing schemes, except that the BOOC scheme has a more substantial influence on mean convection and spatial development. According to the property that the drag reduction of the BOOC scheme with additional threshold limitation is equivalent to that without the restriction, it can be determined that the effect of blowing-based active control is mainly based on the temporal and spatial averaging effects of blowing, including the opposition effect and the induction effect.

Interaction between thermal stratification and turbulence in channel flow

Transport phenomena in high Reynolds number wall-bounded stratified flows are dominated by the interplay between the turbulence structures generated at the wall and the buoyancy-induced large-scale waves populating the channel core. In this study, we want to investigate the flow physics of wall-bounded stratified turbulence at relatively high shear Reynolds number $Re_\tau$ and for mild to moderate stratification level – quantified here by the shear Richardson number varying in the range $0\leqslant Ri_{\tau } \leqslant 300$ . By increasing stratification, active turbulence is sustained only in the near-wall region, whereas intermittent turbulence, modulated by the presence of non-turbulent wavy structures (internal gravity waves), is observed at the channel core. In such conditions, the wall-normal transport of momentum and heat is considerably reduced compared with the case of non-stratified turbulence. A careful characterization of the flow-field statistics shows that, despite temperature and wall-normal velocity fluctuations being very large at the channel centre, the mean value of their product – the buoyancy flux – vanishes for $Ri_{\tau } \geqslant 200$ . We show that this behaviour is due to the presence of a $\sim {\rm \pi}/2$ phase delay between the temperature and the wall-normal velocity signals: when wall-normal velocity fluctuations are large (in magnitude), temperature fluctuations are almost zero, and vice versa. This constitutes a blockage effect to the wall-normal exchange of energy. In addition, we show that the friction factor scales as $C_f \sim Ri_{\tau }^{-1/3}$ , and we propose a new scaling for the Nusselt number, $Nu \cdot Re_{\tau }^{-2/3} \sim Ri_{\tau }^{-1/3}$ . These scaling laws, which seem to be robust over the explored range of parameters, complement and extend previous experimental and numerical data, and are expected to help the development of improved models and parametrizations of stratified flows at large $Re_{\tau }$ .

Feed-forward Control of Vortices Using Real-Time Particle Image Velocimetry

Active flow control (AFC) is a topic with enormous potential for improving a wide array of technologies. This work presents the use and evaluation of a novel AFC system to apply feed-forward control to vortices formed in the wake of a wall-mounted spherical cap. A real-time particle image velocimetry (RT-PIV) system served as the sensor for the AFC system. The RT-PIV system produced 7.35 vector fields per second, each consisting of a two-dimensional grid of 5 × 37 velocity vectors. The actuator system consisted of a rubber surface that could deform using 16 independently controlled linear actuators. The actuators were controlled to apply wall-normal surface deformation at velocities proportional to wall-normal velocities measured by the RT-PIV system upstream of each of the 16 actuators. Analysis of the RT-PIV measurements in comparison to those from an offline PIV system run in parallel indicated that the RT-PIV system produced accurate flow measurements. As well, it was found that the RT-PIV system had a delay of approximately 0.09 seconds. The evaluation of the actuator system indicated that the actuator displacements were consistently damped by 20-25% and lagged the control signal by approximately 0.1 seconds relative to the input signal to the actuators. Therefore, the AFC system had a total delay of approximately 0.2 seconds and applied slightly weaker than specified actuations. These results were within anticipated values and, overall, the AFC system functioned adequately. The impacts of the flow control included disruption of the coherent ejection and sweep structures formed in the wake of the spherical cap and the formation of numerous smaller turbulent structures. As well, several of the control cases showed altered wall-normal velocity fluctuation variance fields in comparison to that of the unforced wake. This is a promising result for AFC using deformable surface actuators as it shows that the active control had a significant effect on an average quantity of the flow.

A driving mechanism of near-wall turbulence subject to adverse pressure gradient in a plane Couette flow

The effect of adverse pressure gradient (APG) on near-wall turbulence is studied, with a particular attention to the turbulence production mechanism. A plane turbulent Couette flow is considered for several values of constant APG in the lower wall region. A direct numerical simulation (DNS) in a large computational domain shows that turbulence near the lower wall continues to exist even at sufficiently large APGs. On increasing the APG, the cross-streamwise turbulence intensities increase, and the near-wall streaks gradually disappear. A linear analysis using the optimal transient growth indicates that the APG inhibits the generation of near-wall streaks due to the significant reduction of the mean shear in the region near the lower wall. The turbulent fluctuation dynamics beyond the linear regime is studied with a DNS in a minimal flow unit. The near-wall self-sustaining process involving streaks is significantly weakened or destroyed as APG increases, while the turbulent fluctuations become more isotropic and localised. Using a conditional averaging analysis, a new mechanism of near-wall turbulence production under strong APG is uncovered. This mechanism is initiated by the wall-normal nonlinear transport of an outer wall-normal velocity fluctuation to the near-wall region. The transported wall-normal velocity fluctuation is subsequently amplified via the Orr mechanism, resulting in the non-zero turbulence production involving spatially localised vortical structures. This mechanism is also confirmed by DNS of the flow in a large computational domain, where strong correlation between the wall-normal nonlinear transport and turbulence production is observed.

波状壁の上を通過する粘弾性流体のせん断流れの数値解析

A two-dimensional shear flow of a viscoelastic fluid over a wavy wall was numerically analyzed by the finite difference method. The upper convected Maxwell (UCM) model was used as the constitutive equation, and the unsteady flow problem was solved numerically using the stream function-vorticity method. Variables are discretized using a staggered grid with uniform mesh width. The volume penalization method was used to represent the moving upper wall and the fixed lower wavy wall that induces a vorticity perturbation. The flow in an infinitely long channel is computed using periodic boundary conditions in the flow direction. The results show that the vorticity intensifies over the wavy surface with positive and negative vorticity stripes, at which extreme wall-normal velocity fluctuations are also observed. At relatively high Deborah numbers, the lower ends of these extreme fluctuation regions are close to the critical line associated with a change of type of the governing partial differential equations in a Couette flow. In contrast, the upper ends of the extreme fluctuation region are close to the critical layer of the shear flow, where the flow velocity coincides with the viscoelastic Alfvén wave speed.