Structure Of Wall Turbulence Research Articles

Large eddy simulation of interacting barchan dunes in a steady, unidirectional flow

We have performed large-eddy simulations of turbulent flow 4 over barchan dunes in a channel with different interdune spacings in the downstream direction at Reynolds number, Re∞ ≃ 26000 (based on the free 6 stream velocity and channel height). Simulations are validated against ex-perimental data (at Re∞ = 55460); the largest interdune spacing (2.38λ, where λ is the length of the barchan model) presents similar characteristics to the isolated dune in the experiment, indicating that at this distance the sheltering effect of the upstream dune is rather weak. We examine 3D realizations of the mean and instantaneous flow to explain features of the flow field relevant to sediment transport. Barchan dunes induce two counter-rotating streamwise vortices, along each of the horns, which direct high-momentum fluid toward the symmetry plane and low-momentum fluid near the bed away from the centerline. The flow near the bed, upstream of the dune, diverges from the centerline plane, decelerates and then rises on the stoss side of the dune while accelerating; the flow close to the centerline plane separates at the crest and reattaches on the bed. Away from the centerline plane and along the horns, flow separation occurs intermittently. The flow in the separation bubble is routed towards the horns and leaves the dune at their tips. The separated flow at the crest reattaches on the bed, except on the centerline symmetry plane of the dune, where a weak saddle point of separation ap- pears at the bed. The distribution of the bed shear-stress, characteristics of the separation and reattachment regions, and instantaneous wall turbulence are discussed. Characteristics of the internal boundary layer developing on the bed after the reattachment region are studied. The interdune spacing isfound to affect significantly the turbulent flow over the stoss side of the downstream dunes; at smaller interdune-spacings, coherent high- and low- speed streaks are shorter but stronger, and the spanwise normal Reynolds stress is larger. The turbulent kinetic energy budgets show the importance of the pressure transport and mean-flow advection in transporting energy from the overlying wake layer to the internal boundary layer over the stoss side of the closely-spaced dunes. The characteristics of the separated-shear layer are altered slightly at smaller interdune spacing; the separation bubble is smaller, the separated-shear layer is stronger, and the bed shear-stress is larger. Away from the dunes, typical wall-turbulence structures are observed, but coher- ent eddies generated in the separated-shear layer due to the Kelvin-Helmholtz instability are dominant near the dune. Coherent structures are generated more frequently at smaller interdune spacing; they move farther away from the bed, towards the free surface, and remain in between the horns. At larger interdune spacings, these coherent structures are advected in the spanwise direction with the mean streamwise vortices and can be observed outside of the dunes.

On coherent structure in wall turbulence

AbstractA new theory of coherent structure in wall turbulence is presented. The theory is the first to predict packets of hairpin vortices and other structure in turbulence, and their dynamics, based on an analysis of the Navier–Stokes equations, under an assumption of a turbulent mean profile. The assumption of the turbulent mean acts as a restriction on the class of possible structures. It is shown that the coherent structure is a manifestation of essentially low-dimensional flow dynamics, arising from a critical-layer mechanism. Using the decomposition presented in McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), complex coherent structure is recreated from minimal superpositions of response modes predicted by the analysis, which take the form of radially varying travelling waves. The leading modes effectively constitute a low-dimensional description of the turbulent flow, which is optimal in the sense of describing the resonant effects around the critical layer and which minimally predicts all types of structure. The approach is general for the full range of scales. By way of example, simple combinations of these modes are offered that predict hairpins and modulated hairpin packets. The example combinations are chosen to represent observed structure, consistent with the nonlinear triadic interaction for wavenumbers that is required for self-interaction of structures. The combination of the three leading response modes at streamwise wavenumbers $6, ~1, ~7$ and spanwise wavenumbers $\pm 6, ~\pm 6, ~\pm 12$, respectively, with phase velocity $2/ 3$, is understood to represent a turbulence ‘kernel’, which, it is proposed, constitutes a self-exciting process analogous to the near-wall cycle. Together, these interactions explain how the mode combinations may self-organize and self-sustain to produce experimentally observed structure. The phase interaction also leads to insight into skewness and correlation results known in the literature. It is also shown that the very large-scale motions act to organize hairpin-like structures such that they co-locate with areas of low streamwise momentum, by a mechanism of locally altering the shear profile. These energetic streamwise structures arise naturally from the resolvent analysis, rather than by a summation of hairpin packets. In addition, these packets are modulated through a ‘beat’ effect. The relationship between Taylor’s hypothesis and coherence is discussed, and both are shown to be the consequence of the localization of the response modes around the critical layer. A pleasing link is made to the classical laminar inviscid theory, whereby the essential mechanism underlying the hairpin vortex is captured by two obliquely interacting Kelvin–Stuart (cat’s eye) vortices. Evidence for the theory is presented based on comparison with observations of structure in turbulent flow reported in the experimental and numerical simulation literature and with exact solutions reported in the transitional literature.

Coherent structures in wall turbulence and mechanism for drag reduction control

Herein is introduced the mechanism for active control influencing the generation of the near-wall streamwise vortices, which are closely related to the production of high skin friction in wall-bounded turbulent flows. A new opposition control scheme with adjusting control amplitude is proposed and evaluated in turbulent channel flow by direct numerical simulations. The maximum drag reduction rate can be greatly enhanced by the strengthened control. Finally the effectiveness of the control to the coherent structures at high Reynolds numbers is investigated by using a linear transient growth model.

Effect of active control on optimal structures in wall turbulence

The effect of active control imposed at the wall on optimal structures in wall turbulence is studied by using a linear transient growth model. When the detection plane of the control is located in the buffer layer, the influence of the control on the transient growth of large scale motion becomes negligible as Reynolds number increases. However, if the control signal is detected at the plane located in the logarithm region, the transient growth at large scale can be greatly suppressed. New peak values of transient growth resulting from the strong blowing and suction on the wall exist. The study indicates that a proper selection of control imposed on the wall can suppress the large scale motion in the logarithmic region.

J057014 平行平板間流における遷移レイノルズ数(〔J057-01〕乱流における運動量、熱、物質の輸送現象(1))

Recently it is well known that localized turbulent structures in wall turbulence are transient and their survival probabilities decrease exponentially with respect to time. We measure lifetimes of streamweise-localize turbulence in channel flow by using direct numerical simulations. The dependence of a lifetime on span widths is roughly exponential. This indicates that a survival probability may be consider as combination of nearly independent Poisson processes that take place on each lowspeed streak.

Acceleration statistics of solid particles in turbulent channel flow

Direct numerical simulations (DNS) are used here to study inertial particle acceleration statistics in the near-wall region of a turbulent channel flow. The study is motivated by observations in homogeneous isotropic turbulence (HIT) suggesting that when particle inertia increases, particle acceleration variance decreases due to both particle preferential accumulation and the filtering effect of inertia. In accordance with these studies, the present DNS shows that for increasing inertia, solid particle acceleration probability density functions (PDFs), scaled by the acceleration root-mean-square (RMS), depart from that of the fluid. The tails of these PDFs become narrower. However, in turbulent channel flow, as the Stokes number increases up to 5, the streamwise acceleration RMS in the near-wall region increases, while further increase of the Stokes number is characterized by the streamwise acceleration RMS decrease. In parallel, contrary to calculations in homogeneous isotropic turbulence, the conditional acceleration statistics of the fluid seen by the solid particle show that while the vertical and transverse acceleration RMS components remain close to the unconditional fluid acceleration, the longitudinal RMS component is remarkably higher in the near wall region. This feature is more pronounced as the Stokes number is increased. Additionally, the conditional acceleration PDFs overlap almost perfectly with the unconditional fluid PDFs, normalized by the acceleration RMS. The enhanced longitudinal acceleration variance of the fluid seen by the particles may be due to the spanwise alternation of high-and-low speed streaks. Depending on inertia, particles may respond to those fluid solicitations (experiencing an increase of the longitudinal acceleration RMS) or ignore the wall turbulent structures (presenting in that case a more homogeneous concentration).

Comparison of LES of Steady Transitional Flow in an Idealized Stenosed Axisymmetric Artery Model With a RANS Transitional Model

In this study, two different turbulence methodologies are investigated to predict transitional flow in a 75% stenosed axisymmetric experimental arterial model and in a slightly modified version of the model with an eccentric stenosis. Large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) methods were applied; in the LES simulations eddy viscosity subgrid-scale models were employed (basic and dynamic Smagorinsky) while the RANS method involved the correlation-based transitional version of the hybrid k-ε/k-ω flow model. The RANS simulations used 410,000 and 820,000 element meshes for the axisymmetric and eccentric stenoses, respectively, with y(+) less than 2 viscous wall units for the boundary elements, while the LES used 1,200,000 elements with y(+) less than 1. Implicit filtering was used for LES, giving an overlap between the resolved and modeled eddies, ensuring accurate treatment of near wall turbulence structures. Flow analysis was carried out in terms of vorticity and eddy viscosity magnitudes, velocity, and turbulence intensity profiles and the results were compared both with established experimental data and with available direct numerical simulations (DNSs) from the literature. The simulation results demonstrated that the dynamic Smagorinsky LES and RANS transitional model predicted fairly comparable velocity and turbulence intensity profiles with the experimental data, although the dynamic Smagorinsky model gave the best overall agreement. The present study demonstrated the power of LES methods, although they were computationally more costly, and added further evidence of the promise of the RANS transition model used here, previously tested in pulsatile flow on a similar model. Both dynamic Smagorinsky LES and the RANS model captured the complex transition phenomena under physiological Reynolds numbers in steady flow, including separation and reattachment. In this respect, LES with dynamic Smagorinsky appeared more successful than DNS in replicating the axisymmetric experimental results, although inflow conditions, which are subject to caveats, may have differed. For the eccentric stenosis, LES with Smagorinsky coefficient of 0.13 gave the closest agreement with DNS despite the known shortcomings of fixed coefficients. The relaminarization as the flow escaped the influence of the stenosis was amply demonstrated in the simulations, graphically so in the case of LES.

Turbulence structure and coherent vortices in open-channel flows with wind-induced water waves

When wind-induced water waves appear over the free-surface flows such as natural rivers and artificial channels, large amounts of oxygen gas and heat are transported toward the river bed through the interface between water and wind layers. In contrast, a bed region is a kind of turbulent boundary layer, in which turbulence generation and its transport is promoted by the production of bed shear stress. In particular, coherent hairpin vortices, together with strong ejection events toward the outer part of the layer, promote mass and momentum exchanges between the inner and outer layers. It is inferred that such a near-bed turbulence may be influenced significantly by these air–water interfacial fluctuations accompanied with free-surface velocity shear and wind-induced water waves. However, these wind effects on the wall-turbulence structure are less understood. To address these exciting and challenging topics, we conducted particle imagery velocimetry (PIV) measurements in open-channel flows combined with air flows, and furthermore the present measured data allows us to investigate the effects of air–water interactions on turbulence structure through the whole depth region.

Spatial structure of a turbulent boundary layer with irregular surface roughness

Particle image velocimetry experiments were performed to study the impact of realistic roughness on the spatial structure of wall turbulence at moderate Reynolds number. This roughness was replicated from an actual turbine blade damaged by deposition of foreign materials and its features are quite distinct from most roughness characterizations previously considered as it is highly irregular and embodies a broad range of topographical scales. The spatial structure of flow over this rough surface near the outer edge of the roughness sublayer is contrasted with that of smooth-wall flow to identify any structural modifications due to roughness. Hairpin vortex packets are observed in the outer layer of the rough-wall flow and are found to contribute heavily to the Reynolds shear stress, consistent with smooth-wall flow. While similar qualitative consistency is observed in comparisons of smooth- and rough-wall two-point correlations, some quantitative differences are also apparent. In particular, a reduction in the streamwise extent of two-point correlations of streamwise velocity is noted which could be indicative of a roughness-induced modification of outer-layer vortex organization. Proper orthogonal decomposition analysis reveals the streamwise coherence of the larger scales to be most sensitive to roughness while the spatial characteristics of the smaller scales appear relatively insensitive to such effects.

Wavelet spectrum analysis on energy transfer of multi-scale structures in wall turbulence

The streamwise velocity components at different vertical heights in wall turbulence were measured. Wavelet transform was used to study the turbulent energy spectra, indicating that the global spectrum results from the weighted average of Fourier spectrum based on wavelet scales. Wavelet transform with more vanishing moments can express the declining of turbulent spectrum. The local wavelet spectrum shows that the physical phenomena such as deformation or breakup of eddies are related to the vertical position in the boundary layer, and the energy-containing eddies exist in a multi-scale form. Moreover, the size of these eddies increases with the measured points moving out of the wall. In the buffer region, the small scale energy-containing eddies with higher frequency are excited. In the outer region, the maximal energy is concentrated in the low-frequency large-scale eddies, and the frequency domain of energy-containing eddies becomes narrower.

One-information suboptimal control repercussion on the fine structure of wall turbulence

The suboptimal control with the cost function directly connected to the wall shear and introduced for a while has been revisited through direct numerical simulations of high temporal and spatial resolution. Its effect on the fine structure of the wall turbulence has been analyzed in details, essentially through the spanwise vorticity transport mechanism. It is shown that only half of the viscous sublayer is mainly affected by the control. The actuation efficiency is limited in terms of the wall shear stress reduction, but is high as long as the turbulent wall activity is concerned. The wall shear stress is reduced due both to the reduction of the shear production in the viscous sublayer and to the contribution of the turbulent body force. The dissipation involving in the streamwise vorticity fluctuations transport equation increases significantly and overcomes the production in a thin layer near the wall leading to a drastic diminution of the turbulent wall shear stress fluctuations.

Turbulent flow through a rectangular duct with a partially blocked exit

This paper contains data on and insights into the origins of turbulence associated with a partial blockage at the exit of a two-dimensional, laminar, horizontal duct flow. In essence, this is the upstream approach region of the forward-facing step problem. This work was motivated by the need to identify and control unsteady streamwise vortices generated in the headbox (i.e. contraction section) of an industrial paper machine. The duct was 57.2 cm wide × 10.16 cm high, with up to a 50 % blockage. Experiments were scaled to match Reynolds numbers found in paper machines; exit velocities were as large as 200 cm s−1. The goal of the research was to map the flow at the exit and to examine the response of the flat-plate turbulent boundary layer on the opposing wall under the partial blockage. Laser-induced fluorescence (LIF) and digital particle image velocimetry (DPIV) were used to examine flow in three orthogonal planes at various stations upstream of the duct exit. Mean and instantaneous DPIV vector fields clearly show that an unsteady spanwise vortex forms in the corner formed by the top nozzle wall and partial blockage which, in turn, gives rise to turbulent streamwise vortices.A turbulent boundary layer was initiated on the duct wall opposite the blockage, upstream of a two-dimensional contraction. Results show that even though the acceleration parameter, K, exceeded the nominal critical level of 3.0 × 10−6 for relaminarization beneath the blockage, the flow did not reach a quasi-laminar state. In addition, there did not appear to be direct interaction between unsteady vortex formation at the partial blockage on the upper wall and bottom-wall turbulent boundary layer structures.

Organised structures in wall turbulence as deduced from stability theory-based methods

In earlier work, we have explored the relevance of hydrodynamic stability theory to fully developed turbulent wall flows. Using an extended Orr-Sommerfeld Equation, based on an anisotropic eddy-viscosity model, it was shown that there exists a wide range of unstable wave numbers (wall modes), which mimic some of the key features of turbulent wall flows. Here we present experimental confirmation for the same. There is good qualitative and quantitative agreement between theory and experiment. Once the dominant coherent structure is obtained from stability theory, control of turbulence would be the next logical step. As shown, the use of a compliant wall shows considerable promise.

Conditional analysis in a turbulent boundary layer with strong density differences

A study of the fine structure of wall turbulence in the presence of strong density variations through a conditional analysis of experimental data obtained in a wind tunnel is presented in this paper. Density variations within the boundary layer are produced by injection of air or helium into a mixture of these two components. The conditional analysis carried out in this study shows that the injection of helium into the boundary layer generates more violent ejections than in the case of an injection of air. This result is confirmed by the significant contribution of the ejections to the turbulent mass flux. The results obtained show that in the fully turbulent zone the ejections are associated with strong velocity fluctuations for the two injected gases. This is even more so for the fluctuations of density when an injection of helium is considered. At two locations of the flow (x/e = 8.3 and x/e = 33.3, where e = 3 mm is the slot width) we show that the contributions of a large excursion in the two quadrants of the u' – ρ' plane, corresponding to the two events of the fluid movement, the ejection and sweeping, are very intermittent owing to the fact that they are associated only to a very low number of measurement points. The ejections at y+ > 50 are more significant and much more energetic in the case of helium.

Multi-scale coherent structures in turbulent boundary layer detected by locally averaged velocity structure functions

The time sequence of longitudinal velocity component at different vertical locations in turbulent boundary layer was finely measured in a wind tunnel. The concept of coarse-grained velocity structure functions, which describes the relative motions of straining and compressing for multi-scale eddy structures in turbulent flows, was put forward based on the theory of locally multi-scale average. Based on the consistency between coarse-grained velocity structure function and Harr wavelet transformation, detecting method was presented, by which the coherent structures and their intermittency was identified by multi-scale flatness factor calculated by locally average structure function. Phase-averaged evolution course for multi-scale coherent eddy structures in wall turbulence were extracted by this conditional sampling to educe scheme. The dynamics course of multi-scale coherent eddy structures and their effects on statistics of turbulent flows were studied.

Statistical analysis of high-order moments in a turbulent boundary layer with large density gradients

An experimental study of the effects of large density variations on the turbulent transfers in a boundary layer is carried out in this paper. Density differences were generated by tangential injection of air or helium in a mixture of these two components. In order to study the fine structure of wall turbulence in the presence of significant density variations, a statistical analysis of the experimental data, obtained in a wind tunnel, is carried out. The results show that the relaxation of the skewness factor of u′(Su′) is carried out more quickly in the external layer than close to the wall, for the air injection as well as for the helium injection. Su′ grows close to the injection slot in an appreciable way, and this increase definitely is stronger for the air injection than for the helium injection. This growth of the skewness factor close to the injection slot can be explained by the increase in the longitudinal convective flux of turbulent energy in this zone. For the distributions of the flatness factor Fu′ the results show that there is no significant effect of the density gradient on the intermittent structure of the instantaneous longitudinal velocity in the developed zone, x/δ≥5, where δ is the boundary-layer thickness. Differences remain, of course, between the profiles of Fu′ for density gradients Open image in new window in the relaxation zone, where the longitudinal gradients are significant. It should, however, be noted that Open image in new window has a smaller effect on the flatness factor compared to the skewness factor. The statistical analysis carried out in this study shows that the helium injection in the boundary layer generates more violent ejections than the air injection. This result is confirmed by the significant contribution of the ejections to turbulent mass flux.

Near-wall Coherent Structure and Large-scale Structure in Wall Turbulence

Near-wall Coherent Structure and Large-scale Structure in Wall Turbulence

Direct Numerical Simulation of Wind-Driven Turbulent Flow (Investigation of the Computational Accuracy)

In this study, investigation of the effects of grid resolution and computational domain dependency on the DNS results of the wind-driven turbulent flow by means of direct numerical solution procedure for a coupled gas-liquid flow, i. e., MARS (Multi-Interfaces Advection and Reconstruction Solver) method, was conducted. Growing wind-driven surfaces, large computational domain size for the streamwise direction was demanded. On the other hand, the requirement computational domain size for the spanwise direction was closely linked with the typical wall turbulent structures consisted of the high and low speed streaks on the gas layer. The spectra of grown wind-driven surfaces follow the-4 power law. And the validities of the present DNS results, CASE 1 and 2 as the fully-developed wind-driven turbulent flows are revealed.

Spanwise growth of vortex structure in wall turbulence

Recent studies of the structure of wall turbulence have lead to the development of a conceptual model that validates and integrates many elements of previous models into a relatively simple picture based on self-assembling packets of hairpin vortex eddies. By continually spawning new hairpins the packets grow longer in the streamwise direction, and by mutual induction between adjacent hairpins the hairpins are strained so that they grow taller and wider as they age. The result is a characteristic growth angle in the streamwise-wall normal plane. The spanwise growth of individual packets implies that packets must either merge or pass through each other when they come into contact. Direct numerical simulations of the growth and interaction of spanwise adjacent hairpins shows that they merge by the vortex connection mechanism originally proposed by Wark and Nagib (1990). In this mechanism the quasi-streamwise legs of two hairpins annihilate each other, by virtue of having opposite vorticity, leaving a new hairpin of approximately double the width of the individuals. P1V measurements in planes parallel to the wall support this picture. DNS of multiple hairpins shows how the spanwise scale doubles when the hairpins form an array.

On the role of large-scale structures in wall turbulence

Recent experimental and computational studies by Adrian and co-workers, such as Adrian et al. [J. Fluid Mech. 422, 1 (2000)] and Zhou et al. [J. Fluid Mech. 387, 353 (1999)], have proposed that a dominant structure in wall turbulence is the organization of hairpin vortices in spatially correlated packets or trains of vortices. In this study this scenario is investigated using the attached eddy model of Perry and Marusic [J. Fluid Mech. 298, 361 (1995)] by calculating structure angles, two-point velocity correlations and autocorrelations and comparing them to experimental measurements across a zero-pressure-gradient turbulent boundary layer. The results support the conclusion that spatially coherent packets are a statistically significant structure for Reynolds stresses and transport processes in the logarithmic region of the flow.