On the structure of shear stress and turbulent kinetic energy flux across the roughness layer of a gravel-bed channel flow

2009 ◽  
Vol 638 ◽  
pp. 423-452 ◽  
Author(s):  
EMMANUEL MIGNOT ◽  
D. HURTHER ◽  
E. BARTHELEMY
Keyword(s):  
Shear Stress ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Channel Flow ◽  
Mean Flow ◽  
Local Flow ◽  
Gravel Bed ◽  
Wall Flows ◽  
The Mean ◽  
Conditional Statistics

This study examines the structure of shear stress and turbulent kinetic energy (TKE) flux across the roughness layer of a uniform, fully rough gravel-bed channel flow (ks+ ≫ 100, δ/k = 20) using high-resolution acoustic Doppler velocity profiler measurements. The studied gravel-bed roughness layer exhibits a complex random multi-scale roughness structure in strong contrast with conceptualized k- or d-type roughness in standard rough-wall flows. Within the roughness layer, strong spatial variability of all time-averaged flow quantities are observed affecting up to 40% of the boundary layer height. This variability is attributed to the presence of bed zones with emanating bed protuberances (or gravel clusters) acting as local flow obstacles and bed zones of more homogenous roughness of densely packed gravel elements. Considering the strong spatial mean flow variability across the roughness layer, a spatio-temporal averaging procedure, called double averaging (DA), has been applied to the analysed flow quantities. Three aspects have been addressed: (a) the DA shear stress and DA TKE flux in specific bed zones associated with three classes of velocity profiles as previously proposed in Mignot, Barthélemy & Hurther (J. Fluid Mech., vol. 618, 2009, p. 279), (b) the global and per class DA conditional statistics of shear stress and associated TKE flux and (c) the contribution of large-scale coherent shear stress structures (LC3S) to the TKE flux across the roughness layer. The mean Reynolds and dispersive shear structure show good agreement between the protuberance bed zones associated with the S-shape/accelerated classes and recent results obtained in standard k-type rough-wall flows (Djenidi et al., Exp. Fluids, vol. 44, 2008, p. 37; Pokrajac, McEwan & Nikora, Exp. Fluids, vol. 45, 2008, p. 73). These gravel-bed protuberances act as local flow obstacles inducing a strong turbulent activity in their wake regions. The conditional statistics show that the Reynolds stress contribution is fairly well distributed between sweep and ejection events, with threshold values ranging from H = 0 to H = 8. However, the TKE flux across the roughness layer primarily results from the residual shear stress between ejection and sweep of very high magnitude (H = 10–20) and of small turbulent scale. Although LC3S are seen to penetrated the interfacial roughness layer, their TKE flux contribution is found to be negligible compared to the very energetic small-scale sweep events. These sweeps are dominantly produced in the bed zones of local gravel protuberances where the velocity profiles are inflexional of S-shape type and the mean flow properties are of mixing-layer flow type as previously shown in Mignot et al. (2009).

Near-wall measurements in a three-dimensional turbulent boundary layer

1997 ◽  
Vol 350 ◽  
pp. 189-208 ◽  
Author(s):  
DEBORA A. COMPTON ◽  
JOHN K. EATON
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Turbulent Kinetic Energy ◽  
Three Dimensional ◽  
Mean Flow ◽  
The Mean ◽  
Near Wall

An experiment was performed to measure near-wall velocity and Reynolds stress profiles in a pressure-driven three-dimensional turbulent boundary layer. An initially two-dimensional boundary layer (Reθ≈4000) was exposed to a strong spanwise pressure gradient. At the furthest downstream measurement locations there was also a fairly strong favourable streamwise pressure gradient.Measurements were made using a specially designed near-wall laser-Doppler anemometer (LDA), in addition to conventional methods. The LDA used short focal length optics, a mirror probe suspended in the flow, and side-scatter collection to achieve a measuring volume 35 μm in diameter and approximately 65 μm long.The data presented include mean velocity measurements and Reynolds stresses, all extending well below y+=10, at several profile locations. Terms of the turbulent kinetic energy transport equation are presented at two profile locations. The mean flow is nearly collateral (i.e. W is proportional to U) at the wall. Turbulent kinetic energy is mildly suppressed in the near-wall region and the shear stress components are strongly affected by three-dimensionality. As a result, the ratio of shear stress to turbulent kinetic energy is suppressed throughout most of the boundary layer. The angles of stress and strain are misaligned, except very near the wall (around y+=10) where the angles nearly coincide with the mean flow angle. Three-dimensionality appears to mildly reduce the production of turbulent kinetic energy.

On the interactions between large-scale structure and fine-grained turbulence in a free shear flow I. The development of temporal interactions in the mean

1976 ◽  
Vol 352 (1669) ◽  
pp. 213-247 ◽  
Keyword(s):  
Energy Transfer ◽  
Kinetic Energy ◽  
Shear Layer ◽  
Turbulent Kinetic Energy ◽  
Viscous Dissipation ◽  
Mean Flow ◽  
Fine Grained ◽  
Large Eddy ◽  
The Mean ◽  
Three Components

In this problem a mean turbulent shear layer originally exists, homogeneous in the streamwise direction, formed perhaps by previous instabilities, but in equilibrium with the fine-grained turbulence. At a given time, a large eddy of a fixed horizontal wavenumber is initiated. We study the subsequent time development of the non-equilibrium interactions between the three components of flow as they adjust towards ultimate simultaneous equilibrium, using the integrated energy-balance conservation equations to derive the amplitude equations. This necessarily involves the usual averaging procedure and a conditional or phase-averaging procedure by which the large structure motion is educed from the total fluctuations. In general, the mean flow growth is due to the energy transfer to both fluctuating components, the large eddy gains energy from the mean motion and exchanges energy with the fine-grained turbulence, while the fine-grained turbulence gains energy from the mean flow and exchanges with the large eddy and converts its energy to heat through viscous dissipation of the smallest scales. The closure problem is obtained via the shape assumptions which enter into the interaction integrals. The situation in which the fine-grained turbulent kinetic energy production and viscous dissipation are in local balance is considered, the displacement from equilibrium being due only to the energy transfer from the large eddy. The large eddy shape is taken to be two-dimensional, instability-wavelike, with its vorticity axis perpendicular to the direction of the mean outer stream. Prior to averaging, detailed but approximate calculations of the wave-induced turbulent Reynolds stresses are obtained; the product of these stresses with the appropriate large-eddy rates of strain give the energy transfer mechanism between the two disparate scales of fluctuations. Coupled, nonlinear amplitude or energy density equations for the three components of motion are obtained, the coefficients of which are the interaction integrals guided by the shape assumptions. It is found that for the special case of parallel flow, the energy of the large eddy first undergoes a hydrodynamic-instability type of amplification but eventually decays due to the energy transfer to the fine-grained turbulence, while the turbulent kinetic energy is displaced from an original level of equilibrium to a new one because of the ability of the large eddy to negotiate an indirect energy transfer from the mean flow. For the growing shear layer, approximate considerations show that if the mechanism of energy transfer from the large to the small scale is eventually weakened by the shear layer growth compared to the large-eddy production mechanism so that the amplification and decay process repeats, ‘bursts’ of the remnant of the same large eddy will occur repeatedly until an ultimate equilibrium is reached among the three interacting components of motion. However, for the large eddy whose wavenumber corresponds to that of the initially most amplified case, the ‘bursting’ phenomenon is much less pronounced and equilibrium is very nearly reached at the end of the very first ‘burst’.

scholarly journals The streamwise turbulence intensity in the intermediate layer of turbulent pipe flow

2015 ◽  
Vol 774 ◽  
pp. 324-341 ◽  
Author(s):  
J. C. Vassilicos ◽  
J.-P. Laval ◽  
J.-M. Foucaut ◽  
M. Stanislas
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Intermediate Layer ◽  
High Reynolds Number ◽  
Logarithmic Derivative ◽  
Turbulent Pipe Flow ◽  
Mean Flow ◽  
The Mean ◽  
High Reynolds

The spectral model of Perryet al. (J. Fluid Mech., vol. 165, 1986, pp. 163–199) predicts that the integral length scale varies very slowly with distance to the wall in the intermediate layer. The only way for the integral length scale’s variation to be more realistic while keeping with the Townsend–Perry attached eddy spectrum is to add a new wavenumber range to the model at wavenumbers smaller than that spectrum. This necessary addition can also account for the high-Reynolds-number outer peak of the turbulent kinetic energy in the intermediate layer. An analytic expression is obtained for this outer peak in agreement with extremely high-Reynolds-number data by Hultmarket al. (Phys. Rev. Lett., vol. 108, 2012, 094501;J. Fluid Mech., vol. 728, 2013, pp. 376–395). Townsend’s (The Structure of Turbulent Shear Flows, 1976, Cambridge University Press) production–dissipation balance and the finding of Dallaset al. (Phys. Rev. E, vol. 80, 2009, 046306) that, in the intermediate layer, the eddy turnover time scales with skin friction velocity and distance to the wall implies that the logarithmic derivative of the mean flow has an outer peak at the same location as the turbulent kinetic energy. This is seen in the data of Hultmarket al. (Phys. Rev. Lett., vol. 108, 2012, 094501;J. Fluid Mech., vol. 728, 2013, pp. 376–395). The same approach also predicts that the logarithmic derivative of the mean flow has a logarithmic decay at distances to the wall larger than the position of the outer peak. This qualitative prediction is also supported by the aforementioned data.

Effect of Impeller Speed Perturbation in a Rushton Impeller Stirred Tank

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Somnath Roy ◽  
Sumanta Acharya
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Rotational Speed ◽  
Stirred Tank ◽  
Azimuthal Direction ◽  
Mean Flow ◽  
Eddy Simulation ◽  
Large Eddy ◽  
The Mean ◽  
Rushton Impeller

Flow inside an unbaffled Rushton-impeller stirred tank reactor (STR) is perturbed using a time dependent impeller rotational speed. Large eddy simulation (LES) revealed that the perturbation increased the width of impeller jet compared to the constant rotational speed cases. The turbulent fluctuations were also observed to be enhanced in the perturbed flow and showed higher values of production and convection of turbulent kinetic energy. Changes in the mean flow-field during the perturbation cycle are investigated. The trailing edge vortices were observed to propagate farther both in the radial and azimuthal direction in the perturbed case. Production of turbulent kinetic energy is observed to be related to the breakup of the impeller jet in the perturbed case. Dissipation of turbulent kinetic energy is augmented due to the perturbation ensuring a better mixing at the molecular scale.

Turbulent boundary layers absent mean shear

2017 ◽  
Vol 835 ◽  
pp. 217-251 ◽  
Author(s):  
Blair A. Johnson ◽  
Edwin A. Cowen
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Turbulent Kinetic Energy ◽  
Temporal Frequency ◽  
Synthetic Jet ◽  
Mean Flow ◽  
Frequency Spectra ◽  
Empirical Constant ◽  
The Mean

We perform an experimental study to investigate the turbulent boundary layer above a stationary solid glass bed in the absence of mean shear. High Reynolds number $(Re_{\unicode[STIX]{x1D706}}\sim 300)$ horizontally homogeneous isotropic turbulence is generated via randomly actuated synthetic jet arrays (RASJA – Variano & Cowen J. Fluid Mech. vol. 604, 2008, pp. 1–32). Each of the arrays is controlled by a spatio-temporally varying algorithm, which in turn minimizes the formation of secondary mean flows. One array consists of an $8\times 8$ grid of jets, while the other is a $16\times 16$ array. Particle image velocimetry measurements are used to study the isotropic turbulent region and the boundary layer formed beneath as the turbulence encounters a stationary wall. The flow is characterized with statistical metrics including the mean flow and turbulent velocities, turbulent kinetic energy, integral scales and the turbulent kinetic energy transport equation, which includes the energy dissipation rate, production and turbulent transport. The empirical constant in the Tennekes (J. Fluid Mech. vol. 67, 1975, pp. 561–567) model of Eulerian frequency spectra is calculated based on the dissipation results and temporal frequency spectra from acoustic Doppler velocimetry measurements. We compare our results to prior literature that addresses mean shear free turbulent boundary layer characterizations via grid-stirred tank experiments, moving-bed experiments, rapid-distortion theory and direct numerical simulations in a forced turbulent box. By varying the operational parameters of the randomly actuated synthetic jet array, we also find that we are able to control the turbulence levels, including integral length scales and dissipation rates, by changing the mean on-times in the jet algorithm.

Turbulent kinetic energy budget in a gravel-bed channel flow

2008 ◽  
Vol 56 (3) ◽  
pp. 601-613 ◽  
Author(s):  
Emmanuel Mignot ◽  
Eric Barthélemy ◽  
David Hurther
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Channel Flow ◽  
Energy Budget ◽  
Turbulent Kinetic Energy Budget ◽  
Gravel Bed ◽  
Kinetic Energy Budget

scholarly journals Numerical Study of Heat Transfer Mechanism in Turbulent Supercritical CO2 Channel Flow

2007 ◽  
Author(s):  
Xinliang Li ◽  
Katsumi Hashimoto ◽  
Mamoru Tanahashi ◽  
Toshio Miyauchi
Keyword(s):  
Heat Transfer ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Channel Flow ◽  
Supercritical Co2 ◽  
Fine Scale ◽  
Heat Transfer Mechanism ◽  
Low Speed ◽  
The Mean ◽  
Low Speed Streaks

Direct numerical simulation (DNS) of supercritical CO2 turbulent channel flow is performed to investigate the heat transfer mechanism of supercritical fluid. In the present DNS, full compressible Navier-Stokes equations and Peng-Robison state equation are solved. Due to effects of the mean density variation in the wall normal direction, mean velocity in the cooling region becomes high compared with that in the heating region. The mean width between high- and low-speed streaks near the wall decreases in the cooling region, which means that turbulence in the cooling region is enhanced and lots of fine scale eddies are created due to the local high Reynolds number effects. From the turbulent kinetic energy budget, it is found that compressibility effects related with pressure fluctuation and dilatation of velocity fluctuation can be ignored even for supercritical condition. However, the effect of density fluctuation on turbulent kinetic energy cannot be ignored. In the cooling region, low kinematic viscosity and high thermal conductivity in the low speed streaks modify fine scale structure and turbulent transport of temperature, which results in high Nusselt number in the cooling condition of the supercritical CO2.

Hydrodynamics of wave-current interaction at a right angle over rough beds

2021 ◽  
Author(s):  
Massimiliano Marino ◽  
Carla Faraci ◽  
Rosaria Ester Musumeci
Keyword(s):  
Shear Stress ◽  
Oscillatory Flow ◽  
Flow Analysis ◽  
Mean Flow ◽  
Gravel Bed ◽  
Combined Flow ◽  
Waves And Currents ◽  
The Mean ◽  
Rough Beds ◽  
The Waves

<p>In the present work, an investigation on the hydrodynamics of waves and currents interacting at right angle over rough beds has been carried out. The work focuses on the effects of wave motion superposed on the current steady boundary layer, and on how the oscillatory flow affects the current velocity distribution, in the presence of gravel and sand beds.</p><p>A laboratory experimental campaign on wave-current orthogonal interaction has been carried out in a shallow water basin at DHI Water and Environment (Hørsholm, Denmark).</p><p>Mean flow has been investigated by computing time- and space-averaged velocity profiles. Friction velocity and equivalent roughness have been inferred from the velocity profiles by best fit technique, in order to measure the shear stress experienced by the current mean flow.</p><p>Tests in the presence of only current, only waves and combined flow have been performed.</p><p>Instantaneous velocities have been Reynolds-averaged to obtain turbulent fluctuations time series and compute turbulence related quantities, such as turbulence intensities and Reynolds stresses.</p><p>The analysis of the mean flow revealed a complex interaction of the waves and currents combined flow. Depending on the relative strength of the current with respect to the waves, the superposition of the oscillatory flow may determine an increase or a decrease of the bottom friction experienced by the current.</p><p>The superposition of waves always induces an increase of turbulence intensity, except over gravel bed in which a decrease is observed in the very proximity of the bottom. Over gravel bed, the presence of the oscillatory flow determines a decrease of the turbulent intensity gradient, which may be related to the decrease of bottom friction observed in the mean flow analysis.</p><p>A turbulence quadrant analysis has been performed and showed that, in the presence of a lone current over a flat gravel bed, the turbulent ejection-sweep mechanism reaches parts of the water column closer to the water surface, similar to what has been observed in the turbulence intensity profiles.</p><p>The superposition of the oscillatory flow appears to induce an increment of ejections and sweeps intensity, which is associated with the shear stress increase at the bottom observed in the mean flow analysis. Moreover, a decrease of the number of ejection and sweep events has been recorded, which suggests a suppression of the ejection-sweep events alongside an enhancement of their intensity.</p>

Interactions Between the Shear Layer Emanating From Rectangular Cylinders and the Near Wake Region

2021 ◽  
Author(s):  
Sedem Kumahor ◽  
Samuel Addai ◽  
Mark F. Tachie
Keyword(s):  
Kinetic Energy ◽  
Shear Layer ◽  
Turbulent Kinetic Energy ◽  
Leading Edge ◽  
Wake Region ◽  
Mean Flow ◽  
Near Wake ◽  
Aspect Ratios ◽  
The Mean ◽  
Rectangular Cylinders

Abstract The interactions between the separated shear layer and the near wake region of rectangular cylinders of varying streamwise extents in a uniform flow are investigated using time resolved particle image velocimetry. The streamwise aspect ratios (AR) tested were 1 and 5, and the Reynolds number based on the oncoming flow velocity and cylinder height is 16200. The effects of varying AR on the mean flow, turbulent kinetic energy and Reynolds shear stresses are studied. Furthermore, the unsteady characteristics of the separation bubbles are examined in terms of frequency spectra analysis. The mean flow topology shows flow separation at the leading edge is not affected by the streamwise aspect ratios. However, the primary, secondary and wake vortexes show significant differences. Mean flow reattaches over the cylinder at 4.30 cylinder heights in the AR5 case while there is no mean reattachment in the AR1 case. The magnitudes of turbulent kinetic energy and Reynolds shear stress in the wake region are an order of magnitude higher in AR1 compared to AR5. Depending on the streamwise location, the vortex shedding motions in the near wake region reflect the dominant and second harmonic of the shear layer shedding frequency measured near the leading edge.

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