scholarly journals Coherent structures in the linearized impulse response of turbulent channel flow

2019 ◽  
Vol 863 ◽  
pp. 1190-1203 ◽  
Author(s):  
Sabarish B. Vadarevu ◽  
Sean Symon ◽  
Simon J. Illingworth ◽  
Ivan Marusic
Keyword(s):  
Channel Flow ◽  
Coherent Structures ◽  
Large Scale ◽  
Body Force ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Kinetic Energy Density ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Velocity Fluctuations

We study the evolution of velocity fluctuations due to an isolated spatio-temporal impulse using the linearized Navier–Stokes equations. The impulse is introduced as an external body force in incompressible channel flow at $Re_{\unicode[STIX]{x1D70F}}=10\,000$. Velocity fluctuations are defined about the turbulent mean velocity profile. A turbulent eddy viscosity is added to the equations to fix the mean velocity as an exact solution, which also serves to model the dissipative effects of the background turbulence on large-scale fluctuations. An impulsive body force produces flow fields that evolve into coherent structures containing long streamwise velocity streaks that are flanked by quasi-streamwise vortices; some of these impulses produce hairpin vortices. As these vortex–streak structures evolve, they grow in size to be nominally self-similar geometrically with an aspect ratio (streamwise to wall-normal) of approximately 10, while their kinetic energy density decays monotonically. The topology of the vortex–streak structures is not sensitive to the location of the impulse, but is dependent on the direction of the impulsive body force. All of these vortex–streak structures are attached to the wall, and their Reynolds stresses collapse when scaled by distance from the wall, consistent with Townsend’s attached-eddy hypothesis.

Spatial organization of large- and very-large-scale motions in a turbulent channel flow

2014 ◽  
Vol 749 ◽  
pp. 818-840 ◽  
Author(s):  
Jin Lee ◽  
Jae Hwa Lee ◽  
Jung-Il Choi ◽  
Hyung Jin Sung
Keyword(s):  
Channel Flow ◽  
Large Scale ◽  
Spatial Organization ◽  
Outer Region ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Velocity Fluctuations ◽  
Spatial Features ◽  
Temporal Features ◽  
Low Speed Streaks

AbstractDirect numerical simulations were carried out to investigate the spatial features of large- and very-large-scale motions (LSMs and VLSMs) in a turbulent channel flow ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}_{\tau }=930$). A streak detection method based on the streamwise velocity fluctuations was used to individually trace the cores of LSMs and VLSMs. We found that both the LSM and VLSM populations were large. Several of the wall-attached LSMs stretched toward the outer regions of the channel. The VLSMs consisted of inclined outer LSMs and near-wall streaks. The number of outer LSMs increased linearly with the streamwise length of the VLSMs. The temporal features of the low-speed streaks in the outer region revealed that growing and merging events dominated the large-scale (1–$3\delta $) structures. The VLSMs $({>}3\delta )$ were primarily created by merging events, and the statistical analysis of these events supported that the merging of large-scale upstream structures contributed to the formation of VLSMs. Because the local convection velocity is proportional to the streamwise velocity fluctuations, the streamwise-aligned structures of the positive- and negative-$u$ patches suggested a primary mechanism underlying the merging events. The alignment of the positive- and negative-$u$ structures may be an essential prerequisite for the formation of VLSMs.

scholarly journals The turbulent/non-turbulent interface bounding a far wake

2002 ◽  
Vol 451 ◽  
pp. 383-410 ◽  
Author(s):  
DAVID K. BISSET ◽  
JULIAN C. R. HUNT ◽  
MICHAEL M. ROGERS
Keyword(s):  
Large Scale ◽  
Turbulence Models ◽  
Passive Scalar ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Eddy Motion ◽  
Order Of Magnitude ◽  
Fixed Reference ◽  
Velocity Variances

The velocity fields of a turbulent wake behind a flat plate obtained from the direct numerical simulations of Moser et al. (1998) are used to study the structure of the flow in the intermittent zone where there are, alternately, regions of fully turbulent flow and non-turbulent velocity fluctuations on either side of a thin randomly moving interface. Comparisons are made with a wake that is ‘forced’ by amplifying initial velocity fluctuations. A temperature field T, with constant values of 1.0 and 0 above and below the wake, is transported across the wake as a passive scalar. The value of the Reynolds number based on the centreplane mean velocity defect and half-width b of the wake is Re ≈ 2000.The thickness of the continuous interface is about 0.07b, whereas the amplitude of fluctuations of the instantaneous interface displacement yI(t) is an order of magnitude larger, being about 0.5b. This explains why the mean statistics of vorticity in the intermittent zone can be calculated in terms of the probability distribution of yI and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of y−yI the conditional mean velocity 〈U〉 and temperature 〈T〉 profiles show sharp jumps at the interface adjacent to a thick zone where 〈U〉 and 〈T〉 vary much more slowly.Statistics for the conditional vorticity and velocity variances, available in such detail only from DNS data, show how streamwise and spanwise components of vorticity are generated by vortex stretching in the bulges of the interface. While mean Reynolds stresses (in the fixed reference frame) decrease gradually in the intermittent zone, conditional stresses are roughly constant and then decrease sharply towards zero at the interface. Flow fields around the interface, analysed in terms of the local streamline pattern, confirm and explain previous results that the advancement of the vortical interface into the irrotational flow is driven by large-scale eddy motion.Terms used in one-point turbulence models are evaluated both conventionally and conditionally in the interface region, and the current practice in statistical models of approximating entrainment by a diffusion process is assessed.

Modeling the Transport of Fuel Mixture Perturbations and Entropy Waves in the Linearized Framework

2020 ◽  
Author(s):  
Thomas Ludwig Kaiser ◽  
Kilian Oberleithner
Keyword(s):  
Turbulent Flows ◽  
Channel Flow ◽  
Turbulent Mixing ◽  
Equivalence Ratio ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Computational Domain ◽  
Reynolds Stresses ◽  
Mean Flow

Abstract In this paper a new method is introduced to model the transport of entropy waves and equivalence ratio fluctuations in turbulent flows. The model is based on the Navier-Stokes equations and includes a transport equation for a passive scalar, which may stand for entropy or equivalence ratio fluctuations. The equations are linearized around the mean turbulent fields, which serve as the input to the model in addition to a turbulent eddy viscosity, which accounts for turbulent diffusion of the perturbations. Based on these inputs, the framework is able to predict the linear response of the flow velocity and passive scalar to harmonic perturbations that are imposed at the boundaries of the computational domain. These in this study are fluctuations in the passive scalar and/or velocities at the inlet of a channel flow. The code is first validated against analytic results, showing very good agreement. Then the method is applied to predict the convection, mean flow dispersion and turbulent mixing of passive scalar fluctuations in a turbulent channel flow, which has been studied in previous work with Direct Numerical Simulations (DNS). Results show that our code reproduces the dynamics of coherent passive scalar transport in the DNS with very high accuracy and low numerical costs, when the DNS mean flow and Reynolds stresses are provided. Furthermore, we demonstrate that turbulent mixing has a significant effect on the transport of the passive scalar fluctuations. Finally, we apply the method to explain experimental observations of transport of equivalence ratio fluctuations in the mixing duct of a model burner.

scholarly journals Simultaneous Stereo PIV and MPS3 Wall-Shear Stress Measurements in Turbulent Channel Flow

Optics ◽  
2020 ◽  
Vol 1 (1) ◽  
pp. 40-51
Author(s):  
Esther Mäteling ◽  
Michael Klaas ◽  
Wolfgang Schröder
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Channel Flow ◽  
Inclination Angle ◽  
Large Scale ◽  
Turbulent Channel Flow ◽  
Two Dimensional ◽  
Velocity Fluctuations ◽  
Wall Shear ◽  
Near Wall

An extended experimental method is presented in which the micro-pillar shear-stress sensor (MPS 3 ) and high-speed stereo particle-image velocimetry measurements are simultaneously performed in turbulent channel flow to conduct concurrent time-resolved measurements of the two-dimensional wall-shear stress (WSS) distribution and the velocity field in the outer flow. The extended experimental setup, which involves a modified MPS 3 measurement setup and data evaluation compared to the standard method, is presented and used to investigate the footprint of the outer, large-scale motions (LSM) onto the near-wall small-scale motions. The measurements were performed in a fully developed, turbulent channel flow at a friction Reynolds number R e τ = 969 . A separation between large and small scales of the velocity fluctuations and the WSS fluctuations was performed by two-dimensional empirical mode decomposition. A subsequent cross-correlation analysis between the large-scale velocity fluctuations and the large-scale WSS fluctuations shows that the streamwise inclination angle between the LSM in the outer layer and the large-scale footprint imposed onto the near-wall dynamics has a mean value of Θ ¯ x = 16.53 ∘ , which is consistent with the literature relying on direct numerical simulations and hot-wire anemometry data. When also considering the spatial shift in the spanwise direction, the mean inclination angle reduces to Θ ¯ x z = 13.92 ∘ .

scholarly journals Statistics and structure of spanwise rotating turbulent channel flow at moderate Reynolds numbers

2017 ◽  
Vol 828 ◽  
pp. 424-458 ◽  
Author(s):  
Geert Brethouwer
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Large Scale ◽  
Linear Part ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Reynolds Stresses ◽  
System Rotation ◽  
The Mean ◽  
Spanwise Rotation

A study of fully developed plane turbulent channel flow subject to spanwise system rotation through direct numerical simulations is presented. In order to study both the influence of the Reynolds number and spanwise rotation on channel flow, the Reynolds number $Re=U_{b}h/\unicode[STIX]{x1D708}$ is varied from a low 3000 to a moderate 31 600 and the rotation number $Ro=2\unicode[STIX]{x1D6FA}h/U_{b}$ is varied from 0 to 2.7, where $U_{b}$ is the mean bulk velocity, $h$ the channel half-gap, $\unicode[STIX]{x1D708}$ the viscosity and $\unicode[STIX]{x1D6FA}$ the system rotation rate. The mean streamwise velocity profile displays also at higher $Re$ a characteristic linear part with a slope near to $2\unicode[STIX]{x1D6FA}$, and a corresponding linear part in the profiles of the production and dissipation rate of turbulent kinetic energy appears. With increasing $Ro$, a distinct unstable side with large spanwise and wall-normal Reynolds stresses and a stable side with much weaker turbulence develops in the channel. The flow starts to relaminarize on the stable side of the channel and persisting turbulent–laminar patterns appear at higher $Re$. If $Ro$ is further increased, the flow on the stable side becomes laminar-like while at yet higher $Ro$ the whole flow relaminarizes, although the calm periods might be disrupted by repeating bursts of turbulence, as explained by Brethouwer (Phys. Rev. Fluids, vol. 1, 2016, 054404). The influence of the Reynolds number is considerable, in particular on the stable side of the channel where velocity fluctuations are stronger and the flow relaminarizes less quickly at higher $Re$. Visualizations and statistics show that, at $Ro=0.15$ and 0.45, large-scale structures and large counter-rotating streamwise roll cells develop on the unstable side. These become less noticeable and eventually vanish when $Ro$ rises, especially at higher $Re$. At high $Ro$, the largest energetic structures are larger at lower $Re$.

Coherent structures near the wall in a turbulent channel flow

1997 ◽  
Vol 332 ◽  
pp. 185-214 ◽  
Author(s):  
J. Jeong ◽  
F. Hussain ◽  
W. Schoppa ◽  
J. Kim
Keyword(s):  
Channel Flow ◽  
Coherent Structures ◽  
Turbulent Channel Flow ◽  
Normal Velocity ◽  
Reynolds Stresses ◽  
Hairpin Vortices ◽  
Vortical Structures ◽  
Instantaneous Flow Field ◽  
Strong Shear ◽  
Low Speed Streaks

Coherent structures (CS) near the wall (i.e.y+ ≤ 60) in a numerically simulated turbulent channel flow are educed using a conditional sampling scheme which extracts the entire extent of dominant vortical structures. Such structures are detected from the instantaneous flow field using our newly developed vortex definition (Jeong & Hussain 1995) - a region of negativeλ2, the second largest eigenvalue of the tensorSikSkj+ ΩikΩkj- which accurately captures the structure details (unlike velocity-, vorticity- or pressure-based eduction). Extensive testing has shown thatλ2correctly captures vortical structures, even in the presence of the strong shear occurring near the wall of a boundary layer. We have shown that the dominant near-wall educed (i.e. ensemble averaged after proper alignment) CS are highly elongated quasi-streamwise vortices; the CS are inclined 9° in the vertical (x, y)-plane and tilted ±4° in the horizontal (x, z)-plane. The vortices of alternating sign overlap inxas a staggered array; there is no indication near the wall of hairpin vortices, not only in the educed data but also in instantaneous fields. Our model of the CS array reproduces nearly all experimentally observed events reported in the literature, such as VITA, Reynolds stress distribution, wall pressure variation, elongated low-speed streaks, spanwise shear, etc. In particular, a phase difference (in space) between streamwise and normal velocity fluctuations created by CS advection causes Q4 ('sweep’) events to dominate Q2 ('ejection’) and also creates counter-gradient Reynolds stresses (such as Ql and Q3 events) above and below the CS. We also show that these effects are adequately modelled by half of a Batchelor's dipole embedded in (and decoupled from) a background shearU(y). The CS tilting (in the (x, z)-plane) is found to be responsible for sustaining CS through redistribution of streamwise turbulent kinetic energy to normal and spanwise components via coherent pressure-strain effects.

The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow

1974 ◽  
Vol 65 (3) ◽  
pp. 439-459 ◽  
Author(s):  
Helmut Eckelmann
Keyword(s):  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Viscous Sublayer ◽  
Wall Region ◽  
Normal Velocity ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Mean Values ◽  
The Mean

Hot-film anemometer measurements have been carried out in a fully developed turbulent channel flow. An oil channel with a thick viscous sublayer was used, which permitted measurements very close to the wall. In the viscous sublayer between y+ ≃ 0·1 and y+ = 5, the streamwise velocity fluctuations decreased at a higher rate than the mean velocity; in the region y+ [lsim ] 0·1, these fluctuations vanished at the same rate as the mean velocity.The streamwise velocity fluctuations u observed in the viscous sublayer and the fluctuations (∂u/∂y)0 of the gradient at the wall were almost identical in form, but the fluctuations of the gradient at the wall were found to lag behind the velocity fluctuations with a lag time proportional to the distance from the wall. Probability density distributions of the streamwise velocity fluctuations were measured. Furthermore, measurements of the skewness and flatness factors made by Kreplin (1973) in the same flow channel are discussed. Measurements of the normal velocity fluctuations v at the wall and of the instantaneous Reynolds stress −ρuv were also made. Periods of quiescence in the − ρuv signal were observed in the viscous sublayer as well as very active periods where ratios of peak to mean values as high as 30:1 occurred.

scholarly journals Direct numerical simulation of the scouring of a brittle streambed in a turbulent channel flow

2021 ◽  
Author(s):  
Federico Dalla Barba ◽  
Francesco Picano
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Channel Flow ◽  
Large Scale ◽  
Stokes Equations ◽  
Wall Stress ◽  
Turbulent Channel Flow ◽  
Numerical Approach ◽  
Immersed Boundary ◽  
Turbulent Structures

AbstractThe natural processes involved in the scouring of submerged sediments are crucially relevant in geomorphology along with environmental, fluvial, and oceanographic engineering. Despite their relevance, the phenomena involved are far from being completely understood, in particular for what concerns cohesive or stony substrates with brittle bulk mechanical properties. In this frame, we address the investigation of the mechanisms that govern the scouring and pattern formation on an initially flattened bed of homogenous and brittle material in a turbulent channel flow, employing direct numerical simulation. The problem is numerically tackled in the frame of peridynamic theory, which has intrinsic capabilities of reliably reproducing crack formation, coupled with the Navier–Stokes equations by the immersed boundary method. The numerical approach is reported in detail here and in the references, where extensive and fully coupled benchmarks are provided. The present paper focuses on the role of turbulence in promoting the brittle fragmentation of a solid, brittle streambed. A detailed characterization of the bedforms that originate on the brittle substrate is provided, alongside an analysis of the correlation between bed shape and the turbulent structures of the flow. We find that turbulent fluctuations locally increase the intensity of the wall-stresses producing localized damages. The accumulation of damage drives the scouring of the solid bed via a turbulence-driven fatigue mechanism. The formation, propagation, and coalescence of scouring structures are observed. In turn, these affect both the small- and large-scale structures of the turbulent flow, producing an enhancement of turbulence intensity and wall-stresses. At the small length scales, this phenomenology is put in relation to the formation of vortical cells that persist over the peaks of the channel bed. Similarly, large-scale irregularities are found to promote the formation of stationary turbulent stripes and large-scale vortices that enhance the widening and deepening of scour holes. As a result, we observe a quadratic increment of the volumetric erosion rate of the streambed, as well as a widening of the probability density of high-intensity wall stress on the channel bed.

Inner–outer interactions of large-scale structures in turbulent channel flow

2016 ◽  
Vol 790 ◽  
pp. 128-157 ◽  
Author(s):  
Jinyul Hwang ◽  
Jin Lee ◽  
Hyung Jin Sung ◽  
Tamer A. Zaki
Keyword(s):  
Channel Flow ◽  
High Speed ◽  
Large Scale ◽  
Spatial Coherence ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Velocity Fluctuations ◽  
Merging Process ◽  
Convection Speed ◽  
Near Wall

Direct numerical simulation data of turbulent channel flow ($Re_{{\it\tau}}=930$) are used to investigate the statistics of long motions of streamwise velocity fluctuations ($u$), and the interaction of these structures with the near-wall disturbances, which is facilitated by their associated large-scale circulations. In the log layer, the negative-$u$ structures are organized into longer streamwise extent (${>}3{\it\delta}$) in comparison to the positive-$u$ counterparts. Near the wall, the footprint of negative-$u$ structures is relatively narrow in comparison to the footprint of positive-$u$ structures. This difference is due to the opposite spanwise motions in the vicinity of the footprints, which are either congregative or dispersive depending on the circulation of the outer roll cells. Conditional sampling of the footprints shows that the spanwise velocity fluctuations ($w$) are significantly enhanced by the dispersive motions of high-speed structures. On the other hand, the near-wall congregative motions of negative-$u$ structures generate relatively weak $w$ but intense negative-$u$ regions due, in part, to the spanwise collective migration of near-wall streaks. The concentrated near-wall regions of negative-$u$ upwell during the merging of the outer long scales – an effect that is demonstrated using statistical analysis of the merging process. This leads to a reduction of the convection speed of downstream negative-$u$ structures and thus promotes the merging with upstream ones. These top-down and bottom-up interactions enhance the spatial coherence of long negative-$u$ structures in the log region.

Burgers turbulence model for a channel flow

1971 ◽  
Vol 47 (2) ◽  
pp. 321-335 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Channel Flow ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Amplitude Equations ◽  
Fourier Amplitude ◽  
Navier Stokes Equations ◽  
Burgers Model ◽  
Model Dynamics

The truncated Burgers models have a unique equilibrium state which is defined continuously for all the Reynolds numbers and attainable from a realizable class of initial disturbances. Hence, they represent a sequence of convergent approximations to the original (untruncated) Burgers problem. We have pointed out that consideration of certain degenerate equilibrium states can lead to the successive turbulence-turbulence transitions and finite-jump transitions that were suggested by Case & Chiu. As a prototype of the Navier–Stokes equations, Burgers model can simulate the initial-value type of numerical integration of the Fourier amplitude equations for a turbulent channel flow. Thus, the Burgers model dynamics display certain idiosyncrasies of the actual channel flow problem described by a truncated set of Fourier amplitude equations, which includes only a modest number of modes due to the limited capability of the computer at hand.

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