Turbulent kinetic energy estimate in the near wall region of smooth turbulent channel flows

Meccanica ◽  
2021 ◽  
Author(s):  
Kannan Sundaravadivelu ◽  
Rafik Absi
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Energy Estimate ◽  
Channel Flows ◽  
Wall Region ◽  
Turbulent Channel Flows ◽  
Near Wall

A revisit of the equilibrium assumption for predicting near-wall turbulence

2014 ◽  
Vol 760 ◽  
pp. 304-312 ◽  
Author(s):  
Farid Karimpour ◽  
Subhas K. Venayagamoorthy
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Turbulent Viscosity ◽  
Wall Turbulence ◽  
Wall Region ◽  
Turbulence Decay ◽  
Prime 2 ◽  
Near Wall Turbulence ◽  
Near Wall

AbstractIn this study, we revisit the consequence of assuming equilibrium between the rates of production ($P$) and dissipation $({\it\epsilon})$ of the turbulent kinetic energy $(k)$ in the highly anisotropic and inhomogeneous near-wall region. Analytical and dimensional arguments are made to determine the relevant scales inherent in the turbulent viscosity (${\it\nu}_{t}$) formulation of the standard $k{-}{\it\epsilon}$ model, which is one of the most widely used turbulence closure schemes. This turbulent viscosity formulation is developed by assuming equilibrium and use of the turbulent kinetic energy $(k)$ to infer the relevant velocity scale. We show that such turbulent viscosity formulations are not suitable for modelling near-wall turbulence. Furthermore, we use the turbulent viscosity $({\it\nu}_{t})$ formulation suggested by Durbin (Theor. Comput. Fluid Dyn., vol. 3, 1991, pp. 1–13) to highlight the appropriate scales that correctly capture the characteristic scales and behaviour of $P/{\it\epsilon}$ in the near-wall region. We also show that the anisotropic Reynolds stress ($\overline{u^{\prime }v^{\prime }}$) is correlated with the wall-normal, isotropic Reynolds stress ($\overline{v^{\prime 2}}$) as $-\overline{u^{\prime }v^{\prime }}=c_{{\it\mu}}^{\prime }(ST_{L})(\overline{v^{\prime 2}})$, where $S$ is the mean shear rate, $T_{L}=k/{\it\epsilon}$ is the turbulence (decay) time scale and $c_{{\it\mu}}^{\prime }$ is a universal constant. ‘A priori’ tests are performed to assess the validity of the propositions using the direct numerical simulation (DNS) data of unstratified channel flow of Hoyas & Jiménez (Phys. Fluids, vol. 18, 2006, 011702). The comparisons with the data are excellent and confirm our findings.

Reynolds number effects in the near-wall region of turbulent channel flows

2001 ◽  
Vol 13 (6) ◽  
pp. 1755-1767 ◽  
Author(s):  
M. Fischer ◽  
J. Jovanović ◽  
F. Durst
Keyword(s):  
Reynolds Number ◽  
Channel Flows ◽  
Wall Region ◽  
Turbulent Channel Flows ◽  
Reynolds Number Effects ◽  
Near Wall

Turbulent kinetic energy budget in the near-wall region

AIAA Journal ◽  
1988 ◽  
Vol 26 (3) ◽  
pp. 300-302 ◽  
Author(s):  
L. V. Krishnamoorthy ◽  
R. A. Antonia
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Energy Budget ◽  
Wall Region ◽  
Turbulent Kinetic Energy Budget ◽  
Kinetic Energy Budget ◽  
Near Wall

On the near-wall structures and statistics of fluctuating pressure in compressible turbulent channel flows

2020 ◽  
Vol 32 (11) ◽  
pp. 115121 ◽  
Author(s):  
Jiupeng Tang ◽  
Zhiye Zhao ◽  
Zhen-Hua Wan ◽  
Nan-Sheng Liu
Keyword(s):  
Channel Flows ◽  
Fluctuating Pressure ◽  
Turbulent Channel Flows ◽  
Wall Structures ◽  
Near Wall

Turbulent kinetic energy production and flow structures in flows past smooth and rough walls

2019 ◽  
Vol 866 ◽  
pp. 897-928 ◽  
Author(s):  
P. Orlandi
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Energy Production ◽  
Compressive Strain ◽  
Turnover Time ◽  
Flow Structures ◽  
Wall Region ◽  
Rate Of Dissipation

Data available in the literature from direct numerical simulations of two-dimensional turbulent channels by Lee & Moser (J. Fluid Mech., vol. 774, 2015, pp. 395–415), Bernardini et al. (J. Fluid Mech., 742, 2014, pp. 171–191), Yamamoto & Tsuji (Phys. Rev. Fluids, vol. 3, 2018, 012062) and Orlandi et al. (J. Fluid Mech., 770, 2015, pp. 424–441) in a large range of Reynolds number have been used to find that $S^{\ast }$ the ratio between the eddy turnover time ($q^{2}/\unicode[STIX]{x1D716}$, with $q^{2}$ being twice the turbulent kinetic energy and $\unicode[STIX]{x1D716}$ the isotropic rate of dissipation) and the time scale of the mean deformation ($1/S$), scales very well with the Reynolds number in the wall region. The good scaling is due to the eddy turnover time, although the turbulent kinetic energy and the rate of isotropic dissipation show a Reynolds dependence near the wall; $S^{\ast }$, as well as $-\langle Q\rangle =\langle s_{ij}s_{ji}\rangle -\langle \unicode[STIX]{x1D714}_{i}\unicode[STIX]{x1D714}_{i}/2\rangle$ are linked to the flow structures, and also the latter quantity presents a good scaling near the wall. It has been found that the maximum of turbulent kinetic energy production $P_{k}$ occurs in the layer with $-\langle Q\rangle \approx 0$, that is, where the unstable sheet-like structures roll-up to become rods. The decomposition of $P_{k}$ in the contribution of elongational and compressive strain demonstrates that the two contributions present a good scaling. However, the good scaling holds when the wall and the outer structures are separated. The same statistics have been evaluated by direct simulations of turbulent flows in the presence of different types of corrugations on both walls. The flow physics in the layer near the plane of the crests is strongly linked to the shape of the surface and it has been demonstrated that the $u_{2}$ (normal to the wall) fluctuations are responsible for the modification of the flow structures, for the increase of the resistance and of the turbulent kinetic energy production.

Interactions of Flow Structure With Nano- and Micro-Particles in Turbulent Channel Flows

2018 ◽  
Author(s):  
Amir A. Mofakham ◽  
Goodarz Ahmadi ◽  
John McLaughlin
Keyword(s):  
Relaxation Time ◽  
Coherent Structures ◽  
Concentration Distribution ◽  
Channel Flows ◽  
Small Scale ◽  
Turbulence Structure ◽  
Micro Particles ◽  
Turbulent Channel Flows ◽  
Wide Range ◽  
Near Wall

This study is concerned with the effects of the flow structures including the near-wall coherent eddies in turbulent channel flows on the dispersion and deposition of nano- and micro-particles. A pseudo-spectral computational code was used for direct numerical simulations (DNS) of the Navier-Stokes equations and the corresponding time histories of the instantaneous fluid velocities were evaluated. Under the oneway coupling assumption, the trajectories of a wide range of particle sizes from 10 nm to 80 μm with dimensionless relaxation time of 2.2e−6 to 142 were obtained by solving the particle equation of motion including Stokes drag and Brownian excitations. Dispersion and deposition of particles in the turbulent flow were evaluated and the effects of turbulence structure on different size particles were studied. The simulation results showed that the concentration distribution of small particles that behave like fluid tracer particles were quite random. However, the preferential concentrations appeared as the dimensionless relaxation time increased to 2–20. In particular, the influence of coherent structures in the near-wall regions was clearly detectable on the concentration distribution of particles, as well as, in their deposition pattern. For τ+ = 20 particles due to the increase of relaxation time and inertia of particles, the small-scale turbulent features were filtered out and only the effect of large-scale turbulent eddies could be identified. For τ+ = 2–20 particles, the ensemble/time average of the position of the deposited particles showed specific spacing which was comparable to the size of the near-wall coherent structures.

The structure of the near-wall region of two-dimensional turbulent separated flow

1991 ◽  
Vol 336 (1640) ◽  
pp. 5-17 ◽  
Keyword(s):  
Kinetic Energy ◽  
Shear Layer ◽  
Large Scale ◽  
Outer Region ◽  
Turbulence Kinetic Energy ◽  
Shear Stresses ◽  
Wall Region ◽  
Freestream Velocity ◽  
Outer Flow ◽  
Near Wall

The time-dependent structure of the wall region of separating, separated, and reattaching flows is considerably different than that of attached turbulent boundary layers. Large-scale structures, whose frequency of passage scales on the freestream velocity and shear layer thickness, produce large Reynolds shearing stresses and most of the turbulence kinetic energy in the outer region of the shear layer and transport it into the low velocity reversed flow next to the wall. This outer flow impresses a near wall streamwise streaky structure of spanwise spacing λ z simultaneously across the wall over a distance of the order of several λ z . The near wall structures produce negligible Reynolds shear stresses and turbulence kinetic energy.

An improved near-wall treatment for turbulent channel flows

2011 ◽  
Vol 25 (1) ◽  
pp. 41-46 ◽  
Author(s):  
Najla El Gharbi ◽  
Rafik Absi ◽  
Ahmed Benzaoui ◽  
Rachid Bennacer
Keyword(s):  
Channel Flows ◽  
Turbulent Channel Flows ◽  
Near Wall
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