Similarity between turbulent kinetic energy and temperature spectra in the near‐wall region

1991 ◽  
Vol 3 (5) ◽  
pp. 989-991 ◽  
Author(s):  
R. A. Antonia ◽  
J. Kim
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Wall Region ◽  
Temperature Spectra ◽  
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.

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.

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.

scholarly journals Secondary Flow in Smooth and Rough Turbulent Circular Pipes: Turbulence Kinetic Energy Budgets

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 448
Author(s):  
Paolo Orlandi ◽  
Sergio Pirozzoli
Keyword(s):  
Kinetic Energy ◽  
Flow Direction ◽  
Turbulence Kinetic Energy ◽  
Energy Budgets ◽  
Immersed Boundary ◽  
Wall Region ◽  
Turbulent Structures ◽  
Circular Pipes ◽  
Turbulence Kinetic Energy Budget ◽  
Near Wall

Direct Numerical Simulations have been performed for turbulent flow in circular pipes with smooth and corrugated walls. The numerical method, based on second-order finite discretization together with the immersed boundary technique, was validated and applied to various types of flows. The analysis is focused on the turbulence kinetic energy and its budget. Large differences have been found in the near-wall region at low Reynolds number. The change in the near-wall turbulent structures is responsible for increase of drag and turbulence kinetic energy. To investigatselinae the effects of wall corrugations, the velocity fields have been decomposed so as to isolate coherent and incoherent motions. For corrugated walls, we find that coherent motions are strongest for walls covered with square bars aligned with the flow direction. In particular, the coherent contribution is substantial when the bars are spaced apart by a distance larger than their height. Detailed analysis of the turbulence kinetic energy budget shows for this set-up a very different behavior than for the other types of corrugations.

A Near-Wall Eddy Conductivity Model for Fluids With Different Prandtl Numbers

1994 ◽  
Vol 116 (4) ◽  
pp. 844-854 ◽  
Author(s):  
R. M. C. So ◽  
T. P. Sommer
Keyword(s):  
Kinetic Energy ◽  
Prandtl Number ◽  
Turbulent Kinetic Energy ◽  
Dissipation Rate ◽  
Reynolds Numbers ◽  
Turbulence Statistics ◽  
Temperature Variance ◽  
Prandtl Numbers ◽  
Good Agreement ◽  
Near Wall

Near-wall turbulence models for the velocity and temperature fields based on the transport equations for the Reynolds stresses, the dissipation rate of turbulent kinetic energy, and the temperature variance and its dissipation rate are formulated for flows with widely different Prandtl numbers. Conventional high-Reynolds-number models are used to close these equations and modifications are proposed to render them asymptotically correct near a wall compared to the behavior of the corresponding exact equations. Thus formulated, two additional constants are introduced into the definition of the eddy conductivity. These constants are found to be parametric in the Prandtl number. The near-wall models are used to calculate flows with different wall thermal boundary conditions covering a wide range of Reynolds numbers and Prandtl numbers. The calculated Nusselt number variations with Prandtl number are in good agreement with established formulae at two different Reynolds numbers. Furthermore, the mean profiles, turbulence statistics, heat flux, temperature variance, and the dissipation rates of turbulent kinetic energy and temperature variance are compared with measurements and direct numerical simulation data. These comparisons show that correct near-wall asymptotic behavior is recovered for the calculated turbulence statistics and the calculations are in good agreement with measurements over the range of Prandtl numbers investigated.

Flow patterns and dissipation of turbulent kinetic energy in near-wall turbulence

1998 ◽  
Vol 43 (2) ◽  
pp. 117-120 ◽  
Author(s):  
Zhaoshun Zhang ◽  
Bing Ma ◽  
Guixiang Cui ◽  
Chunxiao Xu
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Flow Patterns ◽  
Wall Turbulence ◽  
Near Wall Turbulence ◽  
Near Wall

Prediction of Turbulent Source Flow Between Corotating Disks With an Anisotropic Two-Equation Turbulence Model

1988 ◽  
Vol 110 (2) ◽  
pp. 187-194 ◽  
Author(s):  
S. A. Shirazi ◽  
C. R. Truman
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulence Model ◽  
Ad Hoc ◽  
Low Reynolds Number ◽  
Wall Region ◽  
Mixing Length ◽  
Mean Flow ◽  
Low Reynolds

An anisotropic form of a low-Reynolds-number two-equation turbulence model has been implemented in a numerical solution for incompressible turbulent flow between corotating parallel disks. Transport equations for turbulent kinetic energy and dissipation rate were solved simultaneously with the governing equations for the mean-flow variables. Comparisons with earlier mixing-length predictions and with measurements are presented. Good agreement between the present predictions and the measurements of velocity components and turbulent kinetic energy was obtained. The low-Reynolds-number two-equation model was found to model adequately the near-wall region as well as the effects of rotation and streamline divergence, which required ad hoc assumptions in the mixing-length model.

Direct numerical simulation of inertio-elastic turbulent Taylor–Couette flow

2021 ◽  
Vol 926 ◽  
Author(s):  
Jiaxing Song ◽  
Fenghui Lin ◽  
Nansheng Liu ◽  
Xi-Yun Lu ◽  
Bamin Khomami
Keyword(s):  
Numerical Simulation ◽  
Kinetic Energy ◽  
Direct Numerical Simulation ◽  
Couette Flow ◽  
Flow Structures ◽  
Small Scale ◽  
Wall Region ◽  
Flow Physics ◽  
Taylor Couette ◽  
Near Wall

The flow physics of inertio-elastic turbulent Taylor–Couette flow for a radius ratio of $0.5$ in the Reynolds number ( $Re$ ) range of $500$ to $8000$ is investigated via direct numerical simulation. It is shown that as $Re$ is increased the turbulence dynamics can be subdivided into two distinct regimes: (i) a low $Re \leqslant 1000$ regime where the flow physics is essentially dominated by nonlinear elastic forces and the main contribution to transport and mixing of momentum, stress and energy comes from large-scale flow structures in the bulk region and (ii) a high $Re \geqslant 5000$ regime where inertial forces govern the flow physics and the flow dynamics is mainly governed by small-scale flow structures in the near-wall region. Flow–microstructure coupling analysis reveals that the elastic Görtler instability in the near-wall region is triggered via significant polymer extension and commensurately high hoop stresses. This instability gives rise to small-scale elastic vortical structures identified as elastic Görtler vortices which are present at all $Re$ considered. In fact, these vortices develop herringbone streaks near the inner wall that have a longer average life span than their Newtonian counterparts due to their elastic origin. Examination of the budgets of mean streamwise enstrophy, mean kinetic energy, turbulent kinetic energy and Reynolds shear stress demonstrates that increasing fluid inertia hinders the generation of elastic stresses, leading to a monotonic reduction of the elastic-related effects on the flow physics.

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