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.

Direct Assessment of the Accuracy of Stereo PIV in Turbulent Channel Flow

Volume 1 ◽  
2004 ◽  
Author(s):  
K. T. Christensen ◽  
Y. Wu
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Single Point ◽  
Outer Region ◽  
Turbulence Models ◽  
Turbulent Channel Flow ◽  
Wall Region ◽  
Mean Velocity ◽  
Velocity Gradients ◽  
The Mean

Stereo particle-image velocimetry (PIV) has become a widely-used method for studying complex flows because it allows one to acquire instantaneous, three-component velocity data on a planar domain with high spatial resolution. However, the accuracy of such measurements must be carefully evaluated before stereo PIV data can be faithfully used in the development of sophisticated turbulence models, assessment of appropriate computational boundary conditions, and in the validation of advanced computations. To this end, the accuracy of stereo PIV is assessed directly in an actual turbulent environment: two-dimensional turbulent channel flow. This flow is a challenging test of stereo PIV because the turbulent velocity fluctuations are quite small compared to the mean (typically less than ten percent of the mean velocity) and strong velocity gradients exist in the near-wall region. Measurements are made in the streamwise–wall-normal plane along the channel’s spanwise centerline using both stereoscopic and conventional 2-D PIV. A large ensemble of statistically independent velocity realizations are acquired with each method at a friction Reynolds number Reτ = u*h/ν = 934. Single-point statistics are computed from the experimental data and compared to statistics determined from a direct numerical simulation (DNS) of turbulent channel flow at a nearly-identical friction Reynolds number of 940 [5]. Excellent agreement is found in the outer region of the flow (y/h > 0.15, where h is the half-height of the channel). For y/h < 0.15, both the conventional and stereo PIV results differ from the DNS data. These differences are most-likely a manifestation of errors associated with strong velocity gradients and intense turbulent events present in this region of the flow.

Direct numerical simulation of turbulent channel flow up to

2015 ◽  
Vol 774 ◽  
pp. 395-415 ◽  
Author(s):  
Myoungkyu Lee ◽  
Robert D. Moser
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Turbulent Flows ◽  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Mean Velocity ◽  
Layer Structures ◽  
High Reynolds

A direct numerical simulation of incompressible channel flow at a friction Reynolds number ($\mathit{Re}_{{\it\tau}}$) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Kármán constant ${\it\kappa}=0.384\pm 0.004$. There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits $k^{-1}$ dependence over a short range in wavenumber $(k)$. Further, consistent with previous experimental observations, when these spectra are multiplied by $k$ (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the $k^{-1}$ range.

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.

scholarly journals Natural logarithms

2013 ◽  
Vol 718 ◽  
pp. 1-4 ◽  
Author(s):  
B. J. McKeon
Keyword(s):  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Wall Turbulence ◽  
Significant Advance ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Logarithmic Scaling ◽  
The Mean ◽  
High Reynolds

AbstractMarusic et al. (J. Fluid Mech., vol. 716, 2013, R3) show the first clear evidence of universal logarithmic scaling emerging naturally (and simultaneously) in the mean velocity and the intensity of the streamwise velocity fluctuations about that mean in canonical turbulent flows near walls. These observations represent a significant advance in understanding of the behaviour of wall turbulence at high Reynolds number, but perhaps the most exciting implication of the experimental results lies in the agreement with the predictions of such scaling from a model introduced by Townsend (J. Fluid Mech., vol. 11, 1961, pp. 97–120), commonly termed the attached eddy hypothesis. The elegantly simple, yet powerful, study by Marusic et al. should spark further investigation of the behaviour of all fluctuating velocity components at high Reynolds numbers and the outstanding predictions of the attached eddy hypothesis.

Relationship between the heat transfer law and the scalar dissipation function in a turbulent channel flow

2017 ◽  
Vol 830 ◽  
pp. 300-325 ◽  
Author(s):  
Hiroyuki Abe ◽  
Robert Anthony Antonia
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Turbulent Channel Flow ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate ◽  
Mean Velocity ◽  
The Mean ◽  
Logarithmic Dependence

Integration across a fully developed turbulent channel flow of the transport equations for the mean and turbulent parts of the scalar dissipation rate yields relatively simple relations for the bulk mean scalar and wall heat transfer coefficient. These relations are tested using direct numerical simulation datasets obtained with two isothermal boundary conditions (constant heat flux and constant heating source) and a molecular Prandtl number Pr of 0.71. A logarithmic dependence on the Kármán number $h^{+}$ is established for the integrated mean scalar in the range $h^{+}\geqslant 400$ where the mean part of the total scalar dissipation exhibits near constancy, whilst the integral of the turbulent scalar dissipation rate $\overline{\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}}$ increases logarithmically with $h^{+}$. This logarithmic dependence is similar to that established in a previous paper (Abe & Antonia, J. Fluid Mech., vol. 798, 2016, pp. 140–164) for the bulk mean velocity. However, the slope (2.18) for the integrated mean scalar is smaller than that (2.54) for the bulk mean velocity. The ratio of these two slopes is 0.85, which can be identified with the value of the turbulent Prandtl number in the overlap region. It is shown that the logarithmic $h^{+}$ increase of the integrated mean scalar is intrinsically associated with the overlap region of $\overline{\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}}$, established for $h^{+}$ (${\geqslant}400$). The resulting heat transfer law also holds at a smaller $h^{+}$ (${\geqslant}200$) than that derived by assuming a log law for the mean temperature.

Direct Numerical Simulation of Passive Scalar Field in a Turbulent Channel Flow

1992 ◽  
Vol 114 (3) ◽  
pp. 598-606 ◽  
Author(s):  
N. Kasagi ◽  
Y. Tomita ◽  
A. Kuroda
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Streamwise Velocity ◽  
Heat Fluxes ◽  
Wall Region ◽  
Turbulent Heat ◽  
Turbulent Heat Fluxes

A direct numerical simulation (DNS) of the fully developed thermal field in a two-dimensional turbulent channel flow of air was carried out. The isoflux condition was imposed on the two walls so that the local mean temperature increased linearly in the streamwise direction. With any buoyancy effect neglected, temperature was considered as a passive scalar. The computation was executed on 1,589,248 grid points by using a spectral method. The statistics obtained were root-mean-square temperature fluctuations, turbulent heat fluxes, turbulent Prandtl number, and dissipation time scales. They agreed fairly well with existing experimental and numerical simulation data. Each term in the budget equations of temperature variance, its dissipation rate, and turbulent heat fluxes was also calculated. It was found that the temperature fluctuation θ′ was closely correlated with the streamwise velocity fluctuation u′, particularly in the near-wall region. Hence, the distribution of budget terms for the streamwise and wall-normal heat fluxes, u′θ′ and v′θ′, were very similar to those for the two Reynolds stress components, u′u′ and u′v′.

Stokes Mechanism of Drag Reduction

2005 ◽  
Vol 73 (3) ◽  
pp. 483-489 ◽  
Author(s):  
Promode R. Bandyopadhyay
Keyword(s):  
Drag Reduction ◽  
Attenuation Factor ◽  
Viscous Sublayer ◽  
Wall Region ◽  
Mean Velocity ◽  
Turbulence Suppression ◽  
Maximum Drag Reduction ◽  
The Mean ◽  
Stokes Second Problem ◽  
Better Than

The mechanism of drag reduction due to spanwise wall oscillation in a turbulent boundary layer is considered. Published measurements and simulation data are analyzed in light of Stokes’ second problem. A kinematic vorticity reorientation hypothesis of drag reduction is first developed. It is shown that spanwise oscillation seeds the near-wall region with oblique and skewed Stokes vorticity waves. They are attached to the wall and gradually align to the freestream direction away from it. The resulting Stokes layer has an attenuated nature compared to its laminar counterpart. The attenuation factor increases in the buffer and viscous sublayer as the wall is approached. The mean velocity profile at the condition of maximum drag reduction is similar to that due to polymer. The final mean state of maximum drag reduction due to turbulence suppression appears to be universal in nature. Finally, it is shown that the proposed kinematic drag reduction hypothesis describes the measurements significantly better than what current direct numerical simulation does.

Heat Transfer in the Forced Laminar Wall Jet

1997 ◽  
Vol 119 (3) ◽  
pp. 451-459 ◽  
Author(s):  
D. L. Quintana ◽  
M. Amitay ◽  
A. Ortega ◽  
I. J. Wygnanski
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Skin Friction ◽  
Streamwise Velocity ◽  
Wall Heat Flux ◽  
Wall Jet ◽  
Wall Region ◽  
Mean Velocity ◽  
Constant Wall Temperature ◽  
The Mean

The mean and fluctuating characteristics of a plane, unsteady, laminar, wall jet were investigated experimentally for a constant wall-temperature boundary condition. Temperature and streamwise velocity profiles, including the downstream development of the thermal and hydrodynamic boundary layer thicknesses, were obtained through simultaneous hot and cold wire measurements in air. Even at relatively low temperature differences, heating or cooling of a floor surface sufficiently altered the mean velocity profile in the inner, near-wall region to produce significant effects on the jet stability. Selective forcing of the flow at the most amplified frequencies produced profound effects on the temperature and velocity fields and hence the time-averaged heat transfer and shear stress. Large amplitude excitation of the flow (up to 2 percent of the velocity measured at the jet exit plane) at a high frequency resulted in a reduction in the maximum skin friction by as much as 65 percent, with an increase in the maximum wall heat flux as high as 45 percent. The skin friction and wall heat flux were much less susceptible to low-frequency excitation.

Shear-Improved Smagorinsky Modeling of Turbulent Channel Flow Using Generalized Lattice Boltzmann Equation

2010 ◽  
Author(s):  
Saeed Jafari ◽  
Mohammad Rahnama
Keyword(s):  
Boltzmann Equation ◽  
Channel Flow ◽  
Lattice Boltzmann ◽  
Computational Cost ◽  
Turbulent Channel Flow ◽  
Lattice Boltzmann Equation ◽  
Wall Region ◽  
Smagorinsky Model ◽  
Mean Velocity ◽  
Turbulent Statistics

Generalized Lattice Boltzmann Equation (GLBE) was used for computation of turbulent channel flow for which Large Eddy Simulation (LES) was employed as a turbulence model. The subgrid-Scale turbulence effects were simulated through a Shear-Improved Smagorinsky Model (SISM) which is capable of predicting turbulent near wall region accurately without any wall function. Computations were done for a relatively coarse grid with shear Reynolds number of 180 in a parallelized code. Good numerical stability was observed for this computational framework. Results of mean velocity distribution across the channel showed good correspondence with Direct Numerical Simulation (DNS) data. Negligible discrepancies were observed for computed turbulent statistics between present computations and those reported from DNS. Three-dimensional instantaneous vorticity contours showed complex vortical structures appeared in such flow geometries. It is concluded that such framework is capable of predicting accurate results for turbulent channel flow without adding significant complication and computational cost to the standard Smagorinsky model.

scholarly journals Acceleration in turbulent channel flow: universalities in statistics, subgrid stochastic models and an application

2013 ◽  
Vol 721 ◽  
pp. 627-668 ◽  
Author(s):  
Rémi Zamansky ◽  
Ivana Vinkovic ◽  
Mikhael Gorokhovski
Keyword(s):  
Stochastic Model ◽  
Channel Flow ◽  
Scaling Law ◽  
Stochastic Modelling ◽  
Turbulent Channel Flow ◽  
Mean Value ◽  
Mean Velocity ◽  
Wall Distance ◽  
Eddy Simulation ◽  
The Mean

AbstractThis paper focuses on the characterization and the stochastic modelling of the fluid acceleration in turbulent channel flow. In the first part, the acceleration is studied by direct numerical simulation (DNS) at three Reynolds numbers (${\mathit{Re}}_{\ast } = {u}_{\ast } h/ \nu = 180$, 590 and 1000). It is observed that whatever the wall distance is, the norm of acceleration is log-normally distributed and that the variance of the norm is very close to its mean value. It is also observed that from the wall to the centreline of the channel, the orientation of acceleration relaxes statistically towards isotropy. On the basis of dimensional analysis, a universal scaling law for the acceleration norm is proposed. In the second part, in the framework of the norm/orientation decomposition, a stochastic model of the acceleration is introduced. The stochastic model for the norm is based on fragmentation process which evolves across the channel with the wall distance. Simultaneously the orientation is simulated by a random walk on the surface of a unit sphere. The process is generated in such a way that the mean components of the orientation vector are equal to zero, whereas with increasing wall distance, all directions become equally probable. In the third part, the models are assessed in the framework of large-eddy simulation with stochastic subgrid acceleration model (LES–SSAM), introduced recently by Sabel’nikov, Chtab-Desportes & Gorokhovski (Euro. Phys. J. B, vol. 80, 2011, p. 177–187), and designed to account for the intermittency at subgrid scales. Computations by LES–SSAM and its assessment using DNS data show that the prediction of important statistics to characterize the flow, such as the mean velocity, the energy spectra at small scales, the viscous and turbulent stresses, the distribution of the acceleration can be considerably improved in comparison with standard LES. In the last part of this paper, the advantage of LES–SSAM in accounting for the subgrid flow structure is demonstrated in simulation of particle-laden turbulent channel flows. Compared to standard LES, it is shown that for different Stokes numbers, the particle dynamics and the turbophoresis effect can be predicted significantly better when LES–SSAM is applied.

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