Linear and nonlinear evolution of a localized disturbance in polymeric channel flow

2014 ◽  
Vol 760 ◽  
pp. 278-303 ◽  
Author(s):  
Akshat Agarwal ◽  
Luca Brandt ◽  
Tamer A. Zaki
Keyword(s):  
Channel Flow ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Polymer Concentration ◽  
Streamwise Velocity ◽  
Transition To Turbulence ◽  
Velocity Perturbation ◽  
Nonlinear Growth ◽  
Energy Growth ◽  
Newtonian Flows

AbstractThe evolution of an initially localized disturbance in polymeric channel flow is investigated, with the FENE-P model used to characterize the viscoelastic behaviour of the flow. In the linear growth regime, the flow response is stabilized by viscoelasticity, and the maximum attainable disturbance-energy amplification is reduced with increasing polymer concentration. The reduction in the energy growth rate is attributed to the polymer work, which plays a dual role. First, a spanwise polymer-work term develops, and is explained by the tilting action of the wall-normal vorticity on the mean streamwise conformation tensor. This resistive term weakens the spanwise velocity perturbation thus reducing the energy of the localized disturbance. The second action of the polymer is analogous, with a wall-normal polymer work term that weakens the vertical velocity perturbation. Its indirect effect on energy growth is substantial since it reduces the production of Reynolds shear stress and in turn of the streamwise velocity perturbation, or streaks. During the early stages of nonlinear growth, the dominant effect of the polymer is to suppress the large-scale streaky structures which are strongly amplified in Newtonian flows. As a result, the process of transition to turbulence is prolonged and, after transition, a drag-reduced turbulent state is attained.

Large-scale structures in a developed flow over a wavy wall

2003 ◽  
Vol 478 ◽  
pp. 257-285 ◽  
Author(s):  
AXEL GÜNTHER ◽  
PHILIPP RUDOLF VON ROHR
Keyword(s):  
Velocity Field ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Water Channel ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Wavy Surface ◽  
Large Scale Structures ◽  
Stress Maximum ◽  
Scale Structures

We address – motivated in part by the findings of Gong et al. (1996) and Miller (1995) – the role of streamwise-oriented large-scale structures in a developed flow between a sinusoidal bottom wall and a flat top wall. Particle image velocimetry (PIV) is used to examine the spatial variation of the velocity in different planes of the flow through a water channel with an aspect ratio of 12:1. The wave amplitude is equal to one tenth of the wall wavelength, Λ, and Reynolds numbers between 500 and 7300, defined with the bulk velocity and the half-height of the channel, are considered. To examine streamwise-oriented structures, the spanwise variation of the velocity field is studied in a plane parallel to the top wall, and in one that intersects the wavy surface at an uphill location. From a proper orthogonal decomposition (POD) of the streamwise velocity fluctuations, we obtain the dominant eigenfunctions with a characteristic spanwise scale of O(1.5Λ), which agrees with the scale of perturbations for the streamwise velocity at laminar conditions. A decomposition of the turbulent velocity field close to the uphill section of the wavy surface reveals smaller structures at a location that coincides with the Reynolds shear stress maximum.

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.

Direct Numerical Simulation of Unstably Stratified Turbulent Channel Flow

1997 ◽  
Vol 119 (1) ◽  
pp. 53-61 ◽  
Author(s):  
O. Iida ◽  
N. Kasagi
Keyword(s):  
Channel Flow ◽  
Transport Mechanism ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Wall Turbulence ◽  
Thermal Plume ◽  
Streamwise Vortices ◽  
Mean Velocity ◽  
Thermal Plumes ◽  
Turbulent Friction

Direct numerical simulations of the fully developed horizontal channel flow under unstable density stratification were carried out to investigate interactive shear and buoyancy effects on the turbulent momentum and heat transport. As the Grashof number is increased, buoyant thermal plumes are generated. The large-scale thermal convection involving the thermal plumes diminishes the quasi-coherent streamwise vortices, which are known to play a major role in the transport mechanism of near-wall turbulence. The destruction of the streamwise vortices result in the increased bulk mean velocity and the decreased turbulent friction coefficient. The vertical fluid motion of thermal plumes drastically changes the transport mechanism of the Reynolds shear stress. The thermal plumes are spatially aligned in the streamwise direction, and the low-speed streaks and vortical structures are concentrated in the region where the thermal plume starts to rise. The Prandtl number effects on the turbulent kinetic energy are also studied when the thermal plumes emerge.

scholarly journals Variational Nonlinear Optimization in Fluid Dynamics: The Case of a Channel Flow with Superhydrophobic Walls

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 53
Author(s):  
Stefania Cherubini ◽  
Francesco Picella ◽  
Jean-Christophe Robinet
Keyword(s):  
Channel Flow ◽  
Degrees Of Freedom ◽  
Slip Length ◽  
Superhydrophobic Surfaces ◽  
Transition To Turbulence ◽  
Growth Mechanisms ◽  
Boundary Slip ◽  
Optimal Perturbation ◽  
Energy Growth ◽  
Optimal Energy

Variational optimization has been recently applied to nonlinear systems with many degrees of freedom such as shear flows undergoing transition to turbulence. This technique has unveiled powerful energy growth mechanisms able to produce typical coherent structures currently observed in transition and turbulence. However, it is still not clear the extent to which these nonlinear optimal energy growth mechanisms are robust with respect to external disturbances or wall imperfections. Within this framework, this work aims at investigating how nano-roughnesses such as those of superhydrophobic surfaces affect optimal energy growth mechanisms relying on nonlinearity. Nonlinear optimizations have been carried out in a channel flow with no-slip and slippery boundaries, mimicking the presence of superhydrophobic surfaces. For increasing slip length, the energy threshold for obtaining hairpin-like nonlinear optimal perturbations slightly rises, scaling approximately with Re−2.36 no matter the slip length. The corresponding energy gain increases with Re with a slope that reduces with the slip length, being almost halved for the largest slip and Reynolds number considered. This suggests a strong effect of boundary slip on the energy growth of these perturbations. While energy is considerably decreased, the shape of the optimal perturbation barely changes, indicating the robustness of optimal perturbations with respect to wall slip.

On the wall structure of the turbulent boundary layer

1976 ◽  
Vol 76 (1) ◽  
pp. 89-112 ◽  
Author(s):  
R. F. Blackwelder ◽  
R. E. Kaplan
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Streamwise Velocity ◽  
Mean Value ◽  
Wall Structure ◽  
Spanwise Direction ◽  
Normal Velocity ◽  
Conditional Sampling

The wall structure of the turbulent boundary layer was examined using hot-wire rakes and conditional sampling techniques. Instantaneous velocity measurements indicate a high degree of coherence over a considerable area in the direction normal to the wall. Aty+= 15, there is some evidence of large-scale correlation in the spanwise direction, but almost no indication of the streamwise streaks that exist in the lower regions of the boundary layer. Conditional sampling showed that the normal velocity is directed outwards in regions of strong stream-wise-momentum deficit, and inwards when the streamwise velocity exceeds its mean value. The conditionally averaged Reynolds shear stress was approximately an order of magnitude greater than its conventionally averaged value and decayed slowly downstream.

scholarly journals Local transport of passive scalar released from a point source in a turbulent boundary layer

2018 ◽  
Vol 846 ◽  
pp. 292-317 ◽  
Author(s):  
K. M. Talluru ◽  
J. Philip ◽  
K. A. Chauhan
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Phase Relationship ◽  
Passive Scalar ◽  
Streamwise Velocity ◽  
Concentration Fluctuations ◽  
Normal Velocity ◽  
Velocity Fluctuations

Simultaneous measurements of streamwise velocity ($\tilde{U}$) and concentration ($\tilde{C}$) for a horizontal plume released at eight different vertical locations within a turbulent boundary layer are discussed in this paper. These are supplemented by limited simultaneous three-component velocity and concentration measurements. Results of the integral time scale ($\unicode[STIX]{x1D70F}_{c}$) of concentration fluctuations across the width of the plume are presented here for the first time. It is found that$\unicode[STIX]{x1D70F}_{c}$has two distinct peaks: one closer to the plume centreline and the other at a vertical distance of plume half-width above the centreline. The time-averaged streamwise concentration flux is found to be positive and negative, respectively, below and above the plume centreline. This behaviour is a resultant of wall-normal velocity fluctuations ($w$) and Reynolds shear stress ($\overline{uw}$). Confirmation of these observations is found in the results of joint probability density functions of$u$(streamwise velocity fluctuations) and$\tilde{C}$as well as that of$w$and$\tilde{C}$. Results of cross-correlation coefficient show that high- and low-momentum regions have a distinctive role in the transport of passive scalar. Above the plume centreline, low-speed structures have a lead over the meandering plume, while high-momentum regions are seen to lag behind the plume below its centreline. Further examination of the phase relationship between time-varying$u$and$c$(concentration fluctuations) via cross-spectrum analysis is consistent with this observation. Based on these observations, a phenomenological model is presented for the relative arrangement of a passive scalar plume with respect to large-scale velocity structures in the flow.

Two mechanisms of modulation of very-large-scale motions by inertial particles in open channel flow

2019 ◽  
Vol 868 ◽  
pp. 538-559 ◽  
Author(s):  
G. Wang ◽  
D. H. Richter
Keyword(s):  
Channel Flow ◽  
Large Scale ◽  
Open Channel ◽  
Reynolds Shear Stress ◽  
Outer Region ◽  
Open Channel Flow ◽  
Inertial Particles ◽  
Turbulent Structures ◽  
Outer Flow ◽  
Particle Distributions

Very-large-scale motions (VLSMs) and large-scale motions (LSMs) coexist at moderate Reynolds numbers in a very long open channel flow. Direct numerical simulations two-way coupled with inertial particles are analysed using spectral information to investigate the modulation of VLSMs. In the wall-normal direction, particle distributions (mean/preferential concentration) exhibit two distinct behaviours in the inner flow and outer flow, corresponding to two highly anisotropic turbulent structures, LSMs and VLSMs. This results in particle inertia’s non-monotonic effects on the VLSMs: low inertia (based on the inner scale) and high inertia (based on the outer scale) both strengthen the VLSMs, whereas moderate and very high inertia have little influence. Through conditional tests, low- and high-inertia particles enhance VLSMs following two distinct routes. Low-inertia particles promote VLSMs indirectly through the enhancement of the regeneration cycle (the self-sustaining mechanism of LSMs) in the inner region, whereas high-inertia particles enhance the VLSM directly through contribution to the Reynolds shear stress at similar temporal scales in the outer region. This understanding also provides more general insight into inner–outer interaction in high-Reynolds-number, wall-bounded flows.

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 $Re$.

High-fidelity measurements in channel flow with polymer wall injection

2018 ◽  
Vol 859 ◽  
pp. 851-886 ◽  
Author(s):  
John R. Elsnab ◽  
Jason P. Monty ◽  
Christopher M. White ◽  
Manoochehr M. Koochesfahani ◽  
Joseph C. Klewicki
Keyword(s):  
Shear Stress ◽  
Drag Reduction ◽  
Channel Flow ◽  
Polymer Concentration ◽  
Streamwise Velocity ◽  
Velocity Profiles ◽  
Order Structure ◽  
Dynamical Structure ◽  
Molecular Tagging Velocimetry ◽  
The Mean

Streamwise velocity profiles and their wall-normal derivatives were used to investigate the properties of turbulent channel flow in the low polymer drag reduction$(DR)$regime ($DR=6.5\,\%$to$26\,\%$), as realized via polymer injection at the channel surface. Streamwise velocity data were obtained over a friction Reynolds number ranging from$650$to$1800$using the single-velocity-component version of molecular tagging velocimetry (1c-MTV). This adaptation of the MTV technique has the ability to accurately capture instantaneous profiles at very high spatial resolution (${\gtrsim}850$data points per wall-normal profile), and thus generate well-resolved derivative information as well. Owing to this ability, the present study is able to build upon and extend the recent numerical simulation analysis of Whiteet al. (J. Fluid Mech., vol. 834, 2018, pp. 409–433) that examined the mean dynamical structure of polymer drag-reduced channel flow at friction Reynolds numbers up to$1000$. Consistently, the present mean velocity profiles indicate that the extent of the logarithmic region diminishes with increasing polymer concentration, while statistically significant increases in the logarithmic profile slope begin to occur for drag reductions less than$15\,\%$. Profiles of the r.m.s. streamwise velocity indicate that the maximum moves farther from the wall and increases in magnitude with reductions in drag. Similarly, with increasing drag reduction, the profile of the combined Reynolds and polymer shear stress exhibits a decrease in its maximum value that also moves farther from the wall. Correlations are presented that estimate the location and value of the maximum r.m.s. streamwise velocity and combined Reynolds and polymer shear stress. Over the range of$DR$investigated, these effects consistently exhibit approximately linear trends as a function of$DR$. The present measurements allow reconstruction of the mean momentum balance (MMB) for channel flow, which provides further insights regarding the physics described in the study by Whiteet al. In particular, the present findings support a physical scenario in which the self-similar properties on the inertial domain identified from the leading-order structure of the MMB begin to detectably and continuously vary for drag reductions less than$10\,\%$.

Radiofrequency plasma stabilization of a low-Reynolds-number channel flow

2014 ◽  
Vol 748 ◽  
pp. 663-691 ◽  
Author(s):  
Timothy J. Fuller ◽  
Andrea G. Hsu ◽  
Rodrigo Sanchez-Gonzalez ◽  
Jacob C. Dean ◽  
Simon W. North ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Low Reynolds Number ◽  
Plasma Heating ◽  
Shear Stresses ◽  
Exponential Factor ◽  
Turbulence Decay ◽  
Low Reynolds

AbstractThe effects of plasma heating and thermal non-equilibrium on the statistical properties of a low-Reynolds-number ($Re_{\tau } = 49$) turbulent channel flow were experimentally quantified using particle image velocimetry, two-line planar laser-induced fluorescence, coherent anti-Stokes Raman spectroscopy and emission spectroscopy. Tests were conducted at two radiofrequency plasma settings. The nitrogen, in air, was vibrationally excited to $T_{vib} \sim 1240\ \mathrm{K}$ and 1550 K for 150 W and 300 W plasma settings, respectively, while the vibrational temperature of the oxygen and the rotational/translational temperatures of all species remained near room temperature. The peak axial turbulence intensities in the shear layers were reduced by 15 and 30 % in moving across the plasma for the 150 and 300 W cases, respectively. The plasma did not alter the transverse intensities. The Reynolds shear stresses were reduced by 30 and 50 % for the 150 and 300 W cases. The corresponding Reynolds shear stress correlation coefficient was also reduced, which indicates that the large-scale structures were diminished. Finally, the plasma enhanced the turbulence decay in the zero-shear regions, where the power law decay $t^{-1/n}$ exponential factor $n$ decreased from 1.0 to 0.8.

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