Wall-normal Velocity Research Articles

Velocity spectra and scale decomposition of adverse pressure gradient turbulent boundary layers considering history effects

Experiments at relatively large Reynolds number were conducted to better understand the influence of an adverse pressure gradient on the turbulence in two-dimensional boundary layer flows. One focus is on documenting the scale contributions to the Reynolds normal and shear stress profiles under the influence of a positive streamwise pressure gradient. Toward these aims, velocity spectra at friction Reynolds numbers (7100≤Reτ≤8600) are presented, analyzed, and compared to a zero pressure gradient case from the same facility at nominally matching Reynolds number. Distance-from-the-wall scaling is central to numerous theoretical and modeling considerations of the canonical flat plate flow. Consistently, the present spectral measurements reveal clear evidence for its preservation on the inertial sublayer under modest adverse pressure gradients. Increases are seen in the viscous-scaled premultiplied spectra in the outer region as the pressure gradient increases — commensurate with the increases observed in the outer peaks of the streamwise and wall-normal velocity variances, as well as the Reynolds shear stress. Effects of varying Reτ on the streamwise and wall-normal velocity variances and the Reynolds shear stress are studied by comparing the present data at varying Clauser pressure gradient parameter, β, with previous experiments having similarly varying β at significantly lower Reτ (≈1900). This allows to study the effects of changing Reynolds number at matched β. Cases at similar β and Reynolds number, but with varying flow history are also examined, wherein the same β value is arrived either by starting from a smaller or larger initial β. The effects of β>0 on the large and small scale motions are investigated by segregating the signal contributions according to a cut-off wavelength established in previous zero pressure gradient flows. Under a normalization that uses a hybrid velocity scale this analysis reveals similarity between the outer regions of the spectrally-decomposed variances and Reynolds shear stress. These analyses also reveal a more dramatic reduction in the near-wall large scale contribution to the Reynolds shear stress gradient in the β>0 flow when compared to the β=0 flow.

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.

Attenuation of Tollmien–Schlichting waves using resonating surface-embedded phononic crystals

A novel method for control of convective boundary layer instabilities using metamaterial concepts is investigated. Attenuation of Tollmien–Schlichting (TS) waves with surface-embedded one-dimensional phononic crystals (PCs) is theoretically and numerically modeled, capitalizing on the inherent frequency band stop of PCs. The PC is tuned to the targeted TS wave characteristics through the use of analytical models derived from transfer matrix and interface response theories, verified using a finite elements analysis. The interaction between TS waves and a single PC is investigated using coupled two-dimensional fluid structure interaction simulations in the frequency domain. It is shown that TS waves are either amplified or attenuated depending on whether the PC free-face surface displacement and unsteady perturbation pressure at the wall are in-phase or out-of-phase, respectively. The perturbation pressure acts solely as the driver for the mechanical oscillation of the PC. The emerging hydrodynamic coupling between TS waves and the PC is found to be governed by a combination of the Orr mechanism and wall-normal velocity linear superposition near the wall. Finally, a metasurface comprised of an array of streamwise-distributed PCs is evaluated, resulting in an amplitude growth delay of 11.3% of the TS wavelength along the metasurface extent.

Neutrally- and stably-stratified boundary layers adjustments to a step change in surface roughness

In this work, we study the development of the internal boundary layer (IBL) induced by a surface roughness discontinuity, where the downstream surface has a roughness length greater than that upstream. The work is carried out in the EnFlo meteorological wind tunnel, at the University of Surrey, in both thermally neutral and stable cases with varying degrees of stability. For the neutrally-stratified boundary layer, the IBL development in the log-law region shows good agreement with the diffusion model proposed by Panofsky and Dutton (Atmospheric turbulence, Wiley, New York, 1984) provided that a modified origin condition is introduced and its growth rate is dictated by a constant diffusion term. However, the model over-predicts the growth of the IBL in the outer layer, where the IBL depth grows slowly with fetch following a power function with exponent n being 0.61 (whereas the original model prescribes napprox 0.8). For the stably-stratified boundary layers, n is found to further reduce as the bulk Richardson number, textrm{Ri}_textrm{b}, increases. The analysis of the top region of the IBL shows that the slow growth rate is due to a combination of the decay of the diffusion term and a significantly negative mean wall-normal velocity, which transports fluid elements towards the wall. Considering these two effects, a modified diffusion model is proposed which well captures the growth of the IBL for both neutrally and stably-stratified boundary layers.Graphical abstract

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)].

Lamb dilatation and its hydrodynamic viscous flux in near-wall incompressible flows

In this paper, we introduce a new physical concept referred to as the wall-normal Lamb dilatation flux (WNLDF), which is defined as the wall-normal derivative of the Lamb dilatation (namely, the divergence of the Lamb vector) multiplied by the dynamic viscosity for incompressible viscous flows. It is proved that the boundary Lamb dilatation flux (BLDF, namely the wall-normal Lamb dilatation flux at the wall) is determined by the boundary enstrophy flux (BEF) and the surface curvature-induced contribution. As the first step to explore this new concept, the present study only considers flow past a stationary no-slip flat wall without curvature-fluid dynamic coupling effects. It is found that the temporal–spatial evolution rate of the WNLDF is contributed by four source terms, which can be explicitly expressed by using the fundamental surface quantities including skin friction (or surface vorticity) and surface pressure. Therefore, the instantaneous near-wall flow structures are directly related to the WNLDF in both laminar and turbulent flows. As an example, for the turbulent channel flow at Reτ=180, the intensification of the temporal–spatial evolution rate of the WNLDF is caused by the strong wall-normal velocity event (SWNVE) associated with quasi-streamwise vortices and high intermittency of the viscous sublayer. In addition, near the SWNVE, this evolution rate is mainly contributed by the dot product of skin friction and surface enstrophy gradient, as well as the coupling between the skin friction divergence and the boundary enstrophy. The exact results presented in this paper could provide new physical insights into complex near-wall flows.

Outer scaling of the mean momentum equation for turbulent boundary layers under adverse pressure gradient

A new scaling of the mean momentum equation is developed for the outer region of turbulent boundary layers (TBLs) under adverse pressure gradient (APG). The maximum Reynolds shear stress location, denoted as $y_{m}$ , is employed to determine the proper scales for the outer region of an APG TBL. An outer length scale is proposed as $\delta _e - y_{m}$ , where $\delta _e$ is the boundary layer thickness. An outer velocity scale for the mean streamwise velocity deficit is proposed as $U_e - U_{m}$ , where $U_e$ and $U_m$ are the mean streamwise velocities at the boundary layer edge and $y_{m}$ , respectively. An outer velocity scale for the mean wall-normal velocity deficit is proposed as $V_e - V_{m}$ , where $V_e$ and $V_{m}$ are the wall-normal velocities at $\delta _e$ and $y_{m}$ , respectively. The maximum Reynolds shear stress is found to scale as $(\delta _e - y_{m}) U_e \,{\rm d}U_e/{{\rm d}x}$ . The new outer scaling collapses well the experimental and numerical data on APG TBLs over a wide range of Reynolds numbers and strengths of pressure gradient. Approximations of the new scaling are developed for TBLs under strong APG and at high Reynolds numbers. The relationships between the new scales and previously proposed scales are discussed.

Gap ratio effects on the coherent structures surrounding a near-wall square cylinder

Turbulent flow around a square cylinder offset at different heights from an upstream rough wall are investigated using time-resolved particle image velocimetry. The Reynolds number based on the freestream velocity and cylinder height was 12750 and the incoming turbulent boundary layer thickness was 7.2 times the cylinder height. The examined gaps beneath the cylinder were 0.0, 0.3, 0.5, 1.0, 2.0, 4.0, and 8.0 times the cylinder height. The results show that the mean recirculation length remains relatively constant for cases with a gap size greater than or equal to 1.0 times the cylinder height. Flow acceleration through the gap under the cylinder is strongest with a gap size of 2.0 times cylinder height. Downstream of the cylinder, the vertical velocity fluctuations contribute strongly to the production of turbulent kinetic energy by interacting with mean wall-normal velocity gradient in the vertical direction. The dominant frequency embedded in the incoming turbulent boundary layer persists in the wake of the cylinder when the gap size is less than 1.0 cylinder height. Kelvin-Helmholtz vortices originating from the top leading edge of cylinder occur at Strouhal numbers of 2.77-3.11 for the cases with gap ratio ranging from 0.3-8.0 cylinder heights, while spectral migration towards lower frequencies is observed for cases with gap sizes equal to 0.3 and 0.5 cylinder heights. The spatial trajectory of top Kelvin-Helmholtz vortices extends further away from the cylinder as the gap size increases. Spectral proper orthogonal decomposition analysis shows that the von Kármán vortex shedding structures possess the highest spectral energy for all offset cases despite regular vortex shedding being disrupted when the gap size is 0.3 times the cylinder height.

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.

Artificial neural network-based wall-modeled large-eddy simulations of turbulent channel and separated boundary layer flows

Wall-models in a large-eddy simulation (LES) are essential to alleviate the large near-wall resolution requirements for high-Reynolds-number turbulent flow simulations. Among the existing wall-models for a LES, an equilibrium wall-stress model has the highest computational efficiency. Because this model has limitations, such as a lack of non-equilibrium effects and the assumption of a particular law of the wall in the mean velocity, we propose artificial neural network-based wall-stress models (AWMs). The input variables for the AWMs are extracted from the decomposition of the skin-friction coefficient proposed by Fukagata et al. [1], and the AWMs are shown to be able to predict the wall-shear stress in complex flows accurately. The performance of the AWMs is tested for two types of flows, a fully developed turbulent channel flow and a separated turbulent boundary layer flow. A direct comparison of the turbulence statistics with those obtained by previous wall-models (i.e., a log-law-based wall-stress model and a non-equilibrium wall-stress model) shows that better predictions are achieved using the AWMs for both flows, even with untrained Reynolds numbers. When using a coarse grid along the wall-normal direction in wall-modeled LESs (WMLESs) with the AWMs, an upward shift of the mean velocity profile (positive log-layer mismatch, LLM) compared to direct numerical simulation data is found, consistent with previous studies. However, this LLM problem can be overcome by imposing a filtered wall-normal velocity at the wall that is dynamically determined based on the continuity equation and the Taylor series expansion within wall-adjacent cells.

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.

Improved convergence of the spectral proper orthogonal decomposition through time shifting

Spectral proper orthogonal decomposition (SPOD) is an increasingly popular modal analysis method in the field of fluid dynamics due to its specific properties: a linear system forced with white noise should have SPOD modes identical to response modes from resolvent analysis. The SPOD, coupled with the Welch method for spectral estimation, may require long time-resolved datasets. In this work, a linearised Ginzburg–Landau model is considered in order to study the method's convergence. Spectral proper orthogonal decomposition modes of the white-noise forced equation are computed and compared with corresponding response resolvent modes. The quantified error is shown to be related to the time length of Welch blocks (spectral window size) normalised by a convective time. Subsequently, an algorithm based on a temporal data shift is devised to further improve SPOD convergence and is applied to the Ginzburg–Landau system. Next, its efficacy is demonstrated in a numerical database of a boundary layer subject to bypass transition. The proposed approach achieves substantial improvement in mode convergence with smaller spectral window sizes with respect to the standard method. Furthermore, SPOD modes display growing wall-normal and spanwise velocity components along the streamwise direction, a feature which had not yet been observed and is also predicted by a global resolvent calculation. The shifting algorithm for the SPOD opens the possibility for using the method on datasets with time series of moderate duration, often produced by large simulations.

Analytic investigation of the compatibility condition and the initial evolution of a smooth velocity field for the Navier–Stokes equation in a channel configuration

A partial differential equation has usually a regular solution at the initial time if the initial condition is smooth in space, fulfills the governing equations and is compatible with the boundary condition. In the case of the Navier–Stokes equation, the initial velocity field must also be divergence–free. It is common belief that the initial condition is compatible with the boundary condition if the initial condition fulfills the boundary condition but this is not sufficient. Such a field does not necessarily fulfill the full compatibility condition of the Navier–Stokes equation. If the condition is violated, the solution is not regular at the initial time (). This issue has been known for a while but not in the full breadth of the engineering fluid dynamics community. In this paper, a practical calculation method is presented for checking the compatibility condition. Furthermore, a smooth initial condition is presented in a periodic channel flow that violates the compatibility condition and has therefore no smooth solution at the initial instant. The calculations were performed in an analytical framework. The results for a channel configuration show that in the absence of wall–normal velocity the condition is always fulfilled and the problem has a regular solution. If the wall–normal velocity component is non-zero, the condition is usually not fulfilled but exceptional cases, fulfilling the compatibility condition can be generated with optimization methods. The generation procedure of such a field is useful to provide correct initial conditions for such time-dependent numerical flow simulations, where the very first instances are important from an engineering point of view. The presented methods can provide insight about the applicability of the chosen initial conditions.

Interaction between the turbulent boundary layer flow of superheated vapor and the velocity field induced by liquid vaporization

We consider the heat and mass transfer in the turbulent boundary layer flow over a stationary but evaporating liquid surface via direct numerical simulations. We investigate the influence of the vaporization of a static liquid pool at its saturation temperature on a fully developed turbulent boundary layer of superheated vapor, where the vaporization mass flux is treated as a boundary condition for the wall-normal velocity. It is found that the vaporization enhances the boundary layer growth whilst the friction coefficient and the Stanton number are reduced. Turbulent production is shifted further away from the wall and increased in the logarithmic layer whereas the near-wall dissipation rate is decreased in the viscous sub-layer due to the presence of non-vanishing velocity fluctuations. Spectral analysis showed an associated increase in the cross velocity energy spectrum due to vaporization as well as a shift of the peaks towards smaller wavelengths. A similar behavior is observed for the wall-normal turbulent heat flux spectra. The streamwise velocity energy spectrum decreases in the viscous sub-layer and increases in the logarithmic layer.

Scalings of turbulence dissipation in space and time for turbulent channel flow

We investigate scalings of turbulence dissipation and turbulence length/time scales in the fully developed turbulent channel flow region of wall distances $y$ where the ratio of turbulence production to turbulence dissipation oscillates close to 1. First, we study averages over both time and wall-parallel streamwise ( $x$ ) and spanwise ( $z$ ) planes at $y$ . Turbulent channel flow data with friction velocity $u_{\tau }$ , and global Reynolds number $Re_{\tau }$ ranging from $550$ to $5200$ , suggest that the integral length scales of streamwise fluctuating velocities along the streamwise direction, and of wall-normal fluctuating velocities along the transverse direction, tend towards scaling with $y$ , and that the respective turbulence dissipation coefficients tend towards being constant with increasing $Re_{\tau }$ . However, the data for integral lengths of transverse fluctuating velocities in the transverse direction suggest that these lengths obey an asymptotic scaling $\sqrt {\delta y}$ (where $\delta$ is the channel half-width) with increasing $Re_{\tau }$ . The corresponding turbulence dissipation's scaling seems to tend towards $\sqrt {Re_{\tau }}/Re_{\lambda }$ , which is reminiscent of the non-equilibrium turbulence dissipation scaling found in boundary-free turbulent flows, $Re_{\lambda }$ being a $y$ -local Taylor-length-based Reynolds number. The data do not exclude minor corrections from these asymptotic scalings, and in fact, suggest finite Reynolds number deviations to them. Second, we remove time averaging and study time-fluctuating averages over wall-parallel planes at $y$ . We find that the time fluctuations of the turbulence dissipation coefficients and the Taylor-length-based Reynolds number are very strongly anti-correlated at all wall distances $y$ considered, reflecting a dominance of turbulent kinetic energy fluctuations at the lower frequencies, but a dominance of both turbulent kinetic energy and turbulence dissipation at the higher frequencies. In the case of the turbulence dissipation coefficient corresponding to the integral length of the wall-normal velocity along the transverse direction, it is possible to determine the cross-over frequency $f_c^*$ between these two behaviours, and we find $f_c^{*}\sim u_{\tau }/y$ for $Re_{\tau } = 950$ , but $f_c^* \sim u_{\tau }/\delta$ for $Re_{\tau }=2000$ , where there is evidence of very-large-scale motions.

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.

A Conservation-Based Transitional Boundary Layer Model

Abstract A simple, flow-physics-based model of flat-plate, transitional boundary layer skin friction and heat transfer is presented. The model is based on the assumption of negligible time-, spanwise-, and streamwise-average wall-normal velocity at the top of the boundary layer. This results in a threefold increase in boundary layer thickness over the transition region. This simple velocity assumption and its boundary-layer growth implications seem to be reasonably consistent with more sophisticated (direct numerical simulation (DNS)) modeling simulations. Only two modeling parameters need to be assumed, the Reynolds numbers at the onset and at the completion of transition, for which there is guidance based on freestream turbulence intensity for smooth plates. Several experimental datasets for air are modeled. New criteria are proposed to help define the onset and completion of transition: zero net vertical (wall-normal) velocity or mass flux (integrated in time and space, spanwise and streamwise) at the top of the boundary layer, and tripling of boundary layer thickness. Also presented is a minor improvement to a previously published unheated starting length factor for flat-plate laminar boundary layers with uniform wall heat flux.

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.

Prediction of polymer extension, drag reduction, and vortex interaction in direct numerical simulation of turbulent channel flows

Hydrodynamic and viscoelastic interactions between the turbulent fluid within a channel at Reτ=180 and a polymeric phase are investigated numerically using a multiscale hybrid approach. Direct numerical simulations are performed to predict the continuous phase and Brownian dynamics simulations using the finitely extensible nonlinear elastic dumbbell approach are carried out to model the trajectories of polymer extension vectors within the flow, using parallel computations to achieve reasonable computation timeframes on large-scale flows. Upon validating the polymeric configuration solver against theoretical predictions in equilibrium conditions, with excellent agreement observed, the distributions of velocity gradient tensor components are analyzed throughout the channel flow wall-normal regions. Impact on polymer stretching is discussed, with streamwise extension dominant close to the wall, and wall-normal extension driven by high streamwise gradients of wall-normal velocity. In this case, it is shown that chains already possessing high wall-normal extensions may attempt to orientate more in the streamwise direction, causing a curling effect. These effects are observed in instantaneous snapshots of polymer extension, and the effects of the bulk Weissenberg number show that increased WeB leads to more stretched configurations and more streamwise orientated conformities close to the wall, whereas, in the bulk flow and log-law regions, the polymers tend to trace fluid turbulence structures. Chain orientation angles are also considered, with WeB demonstrating little influence on the isotropic distributions in the log-law and bulk flow regions. Polymer–fluid coupling is implemented through a polymer contribution to the viscoelastic stress tensor. The effect of the polymer relaxation time on the turbulent drag reduction is discussed, with greater Weissenberg numbers leading to more impactful reduction. Finally, the velocity gradient tensor invariants are calculated for the drag-reduced flows, with polymers having a significant impact on the Q–R phase diagrams, with the presence of polymers narrowing the range of R values in the wall regions and causing flow structures to become more two-dimensional.