High-speed Streaks Research Articles

Nonlinear evolution of vortical disturbances entrained in the entrance region of a circular pipe

The nonlinear evolution of free-stream vortical disturbances entrained in the entrance region of a circular pipe is investigated using asymptotic and numerical methods. Attention is focused on the low-frequency disturbances that induce streamwise elongated structures. A pair of vortical modes with opposite azimuthal wavenumbers is used to model the free-stream disturbances. Their amplitude is assumed to be intense enough for nonlinear interactions to occur inside the pipe. The formation and evolution of the perturbation flow are described by the nonlinear unsteady boundary-region equations in the cylindrical coordinate system, derived and solved herein for the first time. Matched asymptotic expansions are employed to construct appropriate initial conditions and the initial–boundary value problem is solved numerically by a marching procedure in the streamwise direction. Numerical results show the stabilising effect of nonlinearity on the intense algebraic growth of the disturbances and an increase of the wall-shear stress due to the nonlinear interactions. A parametric study is carried out to evince the effect of the Reynolds number, the streamwise and azimuthal wavelengths, and the radial length scale of the inlet disturbance on the nonlinear flow evolution. Elongated pipe-entrance nonlinear structures (EPENS) occupying the whole pipe cross-section are discovered. EPENS with $h$ -fold rotational symmetry comprise $h$ high-speed streaks positioned near the wall, and $h$ low-speed streaks centred around the pipe core. These distinct structures display a striking resemblance to nonlinear travelling waves found numerically and observed experimentally in fully developed pipe flow. Good agreement of our mean-flow and root mean square data with experimental measurements is obtained.

Nonmodal stability analysis of Poiseuille flow through a porous medium

We unravel the nonmodal stability of a three-dimensional nonstratified Poiseuille flow in a saturated hyperporous medium constrained by impermeable rigid parallel plates. The primary objective is to broaden the scope of previous studies that conducted modal stability analysis for two-dimensional disturbances. Here, we explore both temporal and spatial transient disturbance energy growths for three-dimensional disturbances when the Reynolds number and porosity of the material are high, based on evolution equations with respect to time and space, respectively. Modal stability analysis reveals that the critical Reynolds number for the onset of shear mode instability increases as porosity increases. Moreover, the Darcy viscous drag term stabilizes shear mode instability, resulting in a delay in the transition from laminar flow to turbulence. In addition, it demonstrates the suppression of three-dimensional shear mode instability as the spanwise wavenumber increases, thereby confirming the statement of Squire’s theorem. By contrast, nonmodal stability analysis discloses that both temporal and spatial transient disturbance energy growths curtail as the effect of the Darcy viscous drag force intensifies. But their maximum values behave like O(Re2) for a fixed porous material, where Re is the Reynolds number. However, for different porous materials, the scalings for both temporal and spatial transient disturbance energy growths are different. Furthermore, increasing porosity also suppresses both temporal and spatial disturbance energy growths. Finally, we observe that temporal transient disturbance energy growth becomes larger for a spanwise perturbation, while spatial transient disturbance energy growth becomes larger for a steady perturbation when angular frequency vanishes. The initial disturbance that excites the largest temporal energy amplification generates two sets of alternating high-speed and low-speed elongated streaks in the streamwise direction.

Direct numerical simulation of open-channel flow over a heterogeneous particle bed at low relative submergence

This study investigates turbulent open-channel flows over beds of irregularly arranged particles, using direct numerical simulations at a friction Reynolds number of Reτ=300. Two distinct cases are examined: a polydisperse bed (P800) composed of multiple layers of randomly distributed spheres of varying sizes, and a monodisperse bed (M1015) formed by a random distribution of uniform sized spheres, with a bottommost single layer of varied-sized particles to introduce realistic randomness. Our investigation unveils a rich network of low- and high-speed streaks within the flow field, exhibiting distinctive behaviors in different bed configurations. The P800 case presents a poorly organized flow pattern induced by the varied particle sizes and arrangements, while the M1015 case shows a more regular flow pattern, marked by larger streaks. We also observe that total wall shear stress is substantially influenced by surface roughness-induced drag, extending beyond the effects documented in existing studies of open-channel flows. The present study reveals intricate secondary flow patterns over irregular particle beds. Large-scale circulations are discerned around particle crests in the P800 case and localized circulations with increased turbulence in the M1015 case. Furthermore, analysis of Reynolds stress tensor components indicates that roughness disrupts coherent turbulent eddies, consequently mitigating peak stress. We quantify correlations between drag force and local fluid velocity fluctuations. Notably, a larger deviation in drag is observed in the P800 case compared to M1015, accentuating the influence of particle size and distribution on fluid–particle interactions.

Are the dynamics of wall turbulence in minimal channels and larger domain channels equivalent? A graph-theoretic approach

This work proposes two algorithmic approaches to extract critical dynamical mechanisms in wall-bounded turbulence with minimum human bias. In both approaches, multiple types of coherent structures are spatiotemporally tracked, resulting in a complex multilayer network. Network motif analysis, i.e., extracting dominant non-random elemental patterns within these networks, is used to identify the most dominant dynamical mechanisms. Both approaches, combined with network motif analysis, are used to answer whether the main dynamical mechanisms of a minimal flow unit (MFU) and a larger unconstrained channel flow, labeled a full channel (FC), at Reτ ≈ 180, are equivalent. The first approach tracks traditional coherent structures defined as low- and high-speed streaks, ejections, and sweeps. It is found that the roll-streak pairing, consistent with the current understanding of self-sustaining processes, is the most significant and simplest dynamical mechanism in both flows. However, the MFU has a timescale for this mechanism that is approximately 2.83 times slower than that of the FC. In the second approach, we use semi-Lagrangian wavepackets and define coherent structures from their energetic streak, roll, and small-scale phase space. This method also shows similar motifs for both the MFU and FC. It indicates that, on average, the most dominant phase-space motifs are similar between the two flows, with the significant events taking place approximately 2.21 times slower in the MFU than in the FC. This value is more consistent with the implied timescale ratio of only the slow speed streaks taking part in the roll-streak pairing extracted using the first multi-type spatiotemporal approach, which is approximately 2.17 slower in the MFU than the FC.

Preferential accumulation of finite-size particles in near-wall streaks

The preference for particles to accumulate at specific regions in the near-wall part is a widely observed phenomenon in wall-bounded turbulence. Unlike small particles more frequently found in low-speed streaks, finite-size particles can accumulate in either low-speed or high-speed streaks. However, mechanisms and influencing factors leading to the different preferential concentration locations still need to be clarified. The present study conducts particle-resolved direct numerical simulations of particle-laden turbulent channel flows to provide a better understanding of this seemingly puzzling behaviour of preferential accumulation. These simulations cover different particle-to-fluid density ratios, particle volume fractions, particle sizes and degrees of sedimentation intensity. We find that the large particle size is the crucial factor that results in particles accumulating in high-speed streaks. Large particles not only are difficult to be conveyed by the quasi-streamwise vortices to low-speed streaks but also can escape from the near-wall region before moving spanwisely out from high-speed streaks. The sedimentation effect allows particles to gather closer to the channel wall and stay longer in the near-wall regions, reinforcing the sweeping mechanism of quasi-streamwise vortices that transport particles from high- to low-speed streaks. As a result, sedimenting particles tend to accumulate in the low-speed streaks.

Boundary layer transition due to distributed roughness: effect of roughness spacing

The influence of roughness spacing on boundary layer transition over distributed roughness elements is studied using direct numerical simulation and global stability analysis, and compared with isolated roughness elements at the same Reynolds number $Re_h=U_eh/\nu$ ( $U_e$ is the boundary layer edge velocity, h is roughness height and $\nu$ is the kinetic viscosity of the fluid). Small spanwise spacing ( $\lambda _z=2.5h$ ) inhibits the formation of counter-rotating vortex pairs (CVP) and, as a result, hairpin vortices are not generated and the downstream shear layer is steady. For $\lambda _z=5h$ , the CVP and hairpin vortices are induced by the first row of roughness, perturbing the downstream shear layer and causing transition. The temporal periodicity of the primary hairpin vortices appears to be independent of the streamwise spacing. Distributed roughness leads to a lower critical roughness Reynolds number for instability to occur and a more significant breakdown of the boundary layer compared with isolated roughness. When the streamwise spacing is $\lambda _x=5h$ , the high-momentum fluid barely moves downward into the cavities and the wake flow has little impact on the following roughness elements. The leading unstable varicose mode is associated with the central low-speed streaks along the aligned roughness elements, and its frequency is close to the shedding frequency of hairpin vortices in the isolated case. For larger streamwise spacing ( $\lambda _x=10h$ ), two distinct modes are obtained from global stability analysis. The first mode shows varicose symmetry, corresponding to the primary hairpin vortex shedding induced by the first-row roughness. The high-speed streaks formed in the longitudinal grooves are also found to be unstable and interact with the varicose mode. The second mode is a sinuous mode with lower frequency, induced as the wake flow of the first-row roughness runs into the second row. It extracts most energy from the spanwise shear between the high- and low-speed streaks.

Stability analyses of secondary instability and oblique breakdown in a supersonic boundary layer under the influence of pressure gradients

Studied here is how pressure gradients affect nonlinear transition processes in a supersonic flat-plate boundary layer. Linear stability analysis suggests that a favorable pressure gradient stabilizes the first-mode disturbances significantly, whereas an adverse pressure gradient destabilizes them. Nonlinear stability analysis indicates that the three nonlinear mechanisms of fundamental resonance, subharmonic resonance, and oblique breakdown can induce transition. Oblique breakdown causes the earliest transition, and subharmonic resonance is stronger than fundamental resonance. An adverse pressure gradient significantly destabilizes the primary modes and enhances the nonlinear transition mechanisms. However, a favorable pressure gradient affects the different nonlinear transition processes differently. A weak favorable pressure gradient completely suppresses the transition in fundamental resonance but just delays it slightly in subharmonic resonance. For oblique breakdown, a weak favorable pressure gradient delays the transition significantly, with two high-speed streaks observed clearly. In all cases, a strong favorable pressure gradient leads to a fully laminar flow.

Coherent structures and turbulent model refinement in oblique shock/hypersonic turbulent boundary layer interactions

In the present study, we investigate the evolution of turbulent statistics and coherent structures in hypersonic turbulent boundary layers at the Mach number of 5 impinged by oblique shock waves generated by the wedge with the angles of 14°, 10°, and 6°, inducing strong, mild, and incipient flow separation, by exploiting direct numerical simulation databases, for the purpose of revealing the underlying flow physics that are of significance to turbulent modeling. We found that the large-scale structures are amplified within the interaction zone, manifested in the form of large-scale low- and high-speed streaks with the spanwise length scale of boundary layer thickness, and gradually decay downstream, the process of which is extremely long. The abrupt variation in the characteristic length, time, and velocity scales as well as the incompatible viscous dissipation of the mean and turbulent kinetic energy results in the incorrect predictions by the Reynolds-Averaged Navier–Stokes (RANS) equation simulations, provided the models are established based on solving the transport equations of the turbulent kinetic equation and its viscous dissipation (k−ε or k−ω models, for instance). To amend this issue, we propose to refine the parameters in the model as the functions of wall pressure, the flow quantities related to multiple flow features. The RANS simulations with the k−ω SST model utilizing the proposed refinement improve greatly the accuracy of the skin friction, wall heat flux, and Reynolds shear stress downstream of the interaction zone, and the wall pressure distributions in hypersonic turbulence over compression ramp, suggesting its promising prospect in engineering applications.

Backflow structures in turbulent pipe flows at low to moderate Reynolds numbers

The statistical characteristics and the evolution of the backflow structures are investigated in wall-bounded flows at Reynolds numbers up to $Re_{\tau }=1000$ . The backflow is caused by the joining of large-scale high- and low-speed structures in the vicinity of the wall and is formed at the tail tip of the low-speed structure. The distribution density of the backflow structures and the percentage area of the backflow region on the wall both increase with the Reynolds number. The backflow structures have an average lifespan of 8 wall units which is found to be slightly longer in the pipe than the channel, and they are convected downstream at the average velocities of the buffer region of approximately 10 wall units, similar to Cardesa et al. (J. Fluid Mech., vol. 880, 2019, R3). The backflow structures occasionally split and merge, and can form detached from the wall. Evidence shows that the split, merged and wall-detached backflow structures are caused by the near-wall structures. The split backflow structures are on average, larger and more spanwise-elongated which are split due to the spanwise shearing of the near-wall streaks. A backflow structure is formed detached from the wall when the trailing end of its carrier low-speed structure ‘sits’ on the near-wall high-speed streaks. The wall-detached backflow structures tend to become wall-attached by approaching the wall when undergoing a similar life cycle to the normal backflow of growth and decay with spanwise elongation because the backflow region at the tail of the low-speed structure is continuously pressed down to the wall by the high-speed structure driven by persistent vortical structures in the buffer region.

Effect of channel dimensions and Reynolds numbers on the turbulence modulation for particle-laden turbulent channel flows

The addition of particles to turbulent flows changes the underlying mechanism of turbulence and leads to turbulence modulation. The important parameters are particle Stokes number, mass loading, particle Reynolds number, fluid bulk Reynolds number, etc., that act together and affect the fluid phase turbulence intensities. In the present study, simulations are carried out for different system sizes (2δ/dp=54,81, and 117) and fluid bulk Reynolds numbers (Reb = 5600 and 13 750) to quantify the extent of turbulence attenuation. Here, δ is the half-channel width, dp is the particle diameter, and Reb is the fluid Reynolds number based on the fluid bulk velocity and channel width. Our study shows that system size and fluid bulk Reynolds number are the two crucial parameters that affect the particle feedback force and turbulence modulation more significantly than the other. The extent of turbulence attenuation increases with an increase in system size for the same volume fraction while keeping the Reynolds number fixed. However, for the same volume fraction and fixed channel dimension, the extent of attenuation is low at a higher Reynolds number. The streamwise turbulent structures are observed to become lengthier and fewer with an increase in system size for the same volume fraction and fixed bulk Reynolds number. However, the streamwise high-speed streaks are smaller, thinner, and closely spaced for higher Reynolds numbers than the lower ones for the same volume fraction. Particle phase velocity statistics for different cases have also been reported.

Skin-friction drag reduction by axial oscillations of the inner cylinder in turbulent Taylor–Couette flows

Skin-friction drag reduction by axial oscillations of an inner cylinder is numerically investigated at radius ratio (η = 0.5) using direct numerical simulation. In the present study, at fixed optimal oscillating period, the effect of oscillating amplitude on skin-friction drag reduction is investigated in detail. Furthermore, the effect of Reynolds number (ranging from 1000 to 5000) is also investigated. Our results show that as we keep increasing the oscillating amplitude, the drag reduction first increases and then decreases after a critical threshold dependent on the considered Reynolds number. Crossing the threshold value leads to re-organization of flow into a patchy turbulent state with large presence of small-scale structures. With increasing oscillating amplitude, the near-wall high and low-speed streaks get skewed in the θ–z plane followed by break down of high-speed streaks. Spatial density of the vortical structure decreases till threshold amplitude while the quadrant analysis shows that the movement of high-speed fluid away from walls plays an important role in the attenuation of Reynolds shear stresses.

Wall-attached temperature structures in supersonic turbulent boundary layers

It is well known that low- and high-speed velocity streaks are statistically asymmetric. However, it is unclear how different the low- and high-temperature structures (T-structures) are even though they are strongly coupled with the streamwise velocity. Therefore, this paper identifies three-dimensional wall-attached temperature structures in supersonic turbulent boundary layers over cooled and heated walls (coming from direct numerical simulations) and separates them into positive and negative families. Wall-attached T-structures are self-similar; especially, the length and width of the positive family are linear functions of the height. The superposed temperature variance in both positive and negative families exhibits a logarithmic decay with the wall distance, while the superposed intensity of the wall-normal heat flux in the negative family shows a logarithmic growth. The modified strong Reynolds analogy proposed by Huang, Coleman, and Bradshaw [“Compressible turbulent channel flows: DNS results and modelling,” J. Fluid Mech. 305, 185–218 (1995)] is still valid in the negative family. The relative position between T-structures of opposite signs depends on the wall temperature and that in the cooled-wall case differs significantly from the relative position between low- and high-speed streaks, especially those tall ones. In the cooled-wall case, although positive temperature fluctuations below and above the maximum of the mean temperature can cluster to large-scale wall-attached structures, they are very likely dynamically unrelated.

Experimental investigation on evolution characteristics of high- and low-speed streaks in supersonic turbulent boundary layer

High-speed and low-speed streak structures in the near wall region of a turbulent boundary layer with a Mach number of 3 are experimentally examined by employing the spatiotemporally resolved nanoparticle plane laser scattering technique. The time evolution characteristics of the high-speed and low-speed streaks in the supersonic turbulent boundary layer are systematically investigated through the speed field sequence results at various time intervals. The obtained results reveal that the dynamic behavior of the bands is chiefly represented by the translation along the flow direction. The process of dissipation of the existing streaks and the formation of a new streak is also observed and analyzed. The duration values of the high-speed and low-speed streak structures are assessed by utilizing the time-resolved characteristics of the speed field, and the predicted duration of the streak structure and the maximum flow length exceed 306 µs and 23.6 times the thickness of the boundary layers, respectively. Finally, the merging phenomenon of medium and low-speed streaks in the turbulent boundary layer is carefully scrutinized. The merging of low-speed streaks observed under supersonic conditions is consistent with the vortex packet merging model proposed by Tomkins and Adrian.

PIV Analysis Of Skin Friction And Coherent Structures In Turbulent Drag Reduction Regimes

In the present work, planar and tomographic PIV are used to investigate how the organisation of wall turbulence is altered when actuators are operated with the objective of reducing the skin friction drag. When the wall is mechanically oscillated in the spanwise direction, high-resolution planar PIV enable the direct measurement of wall shear and a 15% reduction of skin friction is observed. The use of tomographic PIV enables access to the threedimensional organisation of low- and high-speed streaks, along with ejection events and associated hairpin vortices. These observations help forming a conceptual model of the salient drag reduction mechanism, whereby hairpin autogeneration is inhibited through a tilting action at the tail of low-speed streaks. The second part of the study documents an effort to surrogate the mechanical oscillation by means of a densely distributed array of AC-DBD plasma actuators. The latter are first characterised in quiescent flow, where the induced velocity distribution is obtained and compared to the solution of the classical second Stokes problem that models the mechanical oscillation. The induced peak of spanwise velocity is found to surpass the velocity of the oscillating wall. However, the wall jet height develops further away from the wall. More importantly, the spatially inhomogeneous distribution of the unsteady body force produces an unwanted lattice of starting streamwise vortices. The latter are deemed to be detrimental for the purpose of drag reduction, compared to the orderly and homogeneous sideways motion induced by mechanical wall motion. The application of the AC-DBD actuator currently leads to a pronounced momentum deficit in the logarithmic region and increases skin friction. Finally, further research directions are anticipated, that potentially circumvent the formation of streamwise vortices by means of AC-DBD actuators operating in steady regime.

Experimental study on drag reduction of the turbulent boundary layer via porous media under nonzero pressure gradient

The complex surface of an aircraft generates a nonzero pressure gradient flow. In this study, the boundary conditions of favorable and adverse pressure gradients are constructed in a small low-turbulence wind tunnel test section. Hot-wire anemometers and time-resolved image velocimetry are used to analyze the flow structure in a fully developed turbulent boundary layer with porous media. The effects of the porous surface on the statistical characteristics of the turbulent flow field and turbulent flow structure are analyzed and discussed. The results show that porous media reduce the velocity gradient in the linear layer, and the friction drag reduction effect is higher downstream of the porous wall. The drag reduction effect decreases along the flow direction. A wall with a 10 pores per inch produces a slightly better drag reduction effect than smooth wall. The maximum local drag reduction effect of a 10-pores-per-inch porous wall is 43.7% under a favorable pressure gradient and 42.3% under an adverse pressure gradient. The velocity streaks in the inner layer show that the porous wall widens the low-velocity streaks, making them more stable, while the high-speed streaks decrease in size under the pressure gradient. In the case of the adverse pressure gradient, the structure of the streaks becomes blurred, and their strength weakens. Under both favorable and adverse pressure gradients, the porous media lift up the coherent structures near the wall, thus weakening the large-scale coherent wall structures.

Numerical investigation of distributed roughness effects on separated flow transition over a highly loaded compressor blade

Large eddy simulations were conducted to investigate the effects of distributed roughness on separated flow transitions over a highly loaded compressor blade at a Reynolds number (Re) of 1.5 × 105. The distributed roughness elements were located downstream of the velocity peak on the suction surface, and four numerical cases with increasing peak amplitude of the roughness elements (k+ = 0, 23, 50, and 112) were considered. The results showed that low- and high-speed streamwise streaks appeared alternately along the spanwise direction over the distributed roughness elements. The streaks remained steady earlier; however, as the streamwise counter-rotating vortices were induced by a significant spanwise velocity component, the low-momentum fluid in the near-wall region was transported away from the blade surface and interacted with the outer separated shear layers, which caused unsteady merging of streaks and promoted the destabilization of separated shear layers. Compared with the baseline case (k+ = 0), the strong shear effect between the low- and high-speed streamwise streaks near the roughened blade surface accelerated the distortion of spanwise vortices, and three-dimensional hairpin vortex structures broke down into small-scale turbulent eddies at a shorter streamwise distance. With increase in the roughness magnitude, the level of the production term of turbulent kinetic energy was reduced due to weakened vortex dynamics, and the viscous dissipation in turbulent boundary layers also became weaker. Therefore, the profile losses of the three roughness cases, k+ = 23, 50, and 112, were decreased by 7.2%, 10.1%, and 15.5%, respectively.

Effect of finite Weissenberg number on turbulent channel flows of an elastoviscoplastic fluid

Direct numerical simulations are carried out to study the effect of finite Weissenberg number up to $Wi=16$ on laminar and turbulent channel flows of an elastoviscoplastic (EVP) fluid, at a fixed bulk Reynolds number of $2800$ . The incompressible flow equations are coupled with the evolution equation for the EVP stress tensor by a modified Saramito model that extends both the Bingham viscoplastic and the finite extensible nonlinear elastic-Peterlin (FENE-P) viscoelastic models. In turbulent flow, we find that drag decreases with both the Bingham and Weissenberg numbers, until the flow laminarises at high enough elastic and yield stresses. Hence, a higher drag reduction is achieved than in the viscoelastic flow at the same Weissenberg number. The drag reduction persists at Bingham numbers up to 20, in contrast to viscoplastic flow, where the drag increases in the laminar regime compared with a Newtonian flow. Moreover, elasticity affects the laminarisation of an EVP flow in a non-monotonic fashion, delaying it at lower and promoting it at higher Weissenberg numbers. A hibernation phenomenon is observed in the EVP flow, leading to large changes in the unyielded regions. Finally, plasticity is observed to affect both low- and high-speed streaks equally, attenuating the turbulent dissipation and the fragmentation of turbulent structures.

Evaluation of tilt control for wind-turbine arrays in the atmospheric boundary layer

Abstract. Wake redirection is a promising approach designed to mitigate turbine–wake interactions which have a negative impact on the performance and lifetime of wind farms. It has recently been found that substantial power gains can be obtained by tilting the rotors of spanwise-periodic wind-turbine arrays. Rotor tilt is associated with the generation of coherent streamwise vortices which deflect wakes towards the ground and, by exploiting the vertical wind shear, replace them with higher-momentum fluid (high-speed streaks). The objective of this work is to evaluate power gains that can be obtained by tilting rotors in spanwise-periodic wind-turbine arrays immersed in the atmospheric boundary layer and, in particular, to analyze the influence of the rotor size on power gains in the case where the turbines emerge from the atmospheric surface layer. We show that, for the case of wind-aligned arrays, large power gains can be obtained for positive tilt angles of the order of 30∘. Power gains are substantially enhanced by operating tilted-rotor turbines at thrust coefficients higher than in the reference configuration. These power gains initially increase with the rotor size reaching a maximum for rotor diameters of the order of 3.6 boundary layer momentum thicknesses (for the considered cases) and decrease for larger sizes. Maximum power gains are obtained for wind-turbine spanwise spacings which are very similar to those of large-scale and very-large-scale streaky motions which are naturally amplified in turbulent boundary layers. These results are all congruent with the findings of previous investigations of passive control of canonical boundary layers for drag-reduction applications where high-speed streaks replaced wakes of spanwise-periodic rows of wall-mounted roughness elements.

Early evolution of optimal perturbations in a viscosity-stratified channel

Abstract

Minimal multi-scale dynamics of near-wall turbulence

Abstract