A new approach to modelling near-wall turbulence energy and stress dissipation

2002 ◽  
Vol 459 ◽  
pp. 139-166 ◽  
Author(s):  
S. JAKIRLIĆ ◽  
K. HANJALIĆ
Keyword(s):  
Energy Dissipation ◽  
Numerical Simulations ◽  
Transport Equation ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Direct Numerical Simulations ◽  
Turbulence Energy ◽  
Viscous Term ◽  
Dissipation Equation ◽  
Near Wall

A new model for the transport equation for the turbulence energy dissipation rate ε and for the anisotropy of the dissipation rate tensor εij, consistent with the near-wall limits, is derived following the term-by-term approach and using results of direct numerical simulations (DNS) for several generic wall-bounded flows. Based on the two-point velocity covariance analysis of Jovanović, Ye & Durst (1995) and reinterpretation of the viscous term, the transport equation is derived in terms of the ‘homogeneous’ part εh of the energy dissipation rate. The algebraic expression for the components of εij was then reformulated in terms of εh, which makes it possible to satisfy the exact wall limits without using any wall-configuration parameters. Each term in the new equation is modelled separately using DNS information. The rational vorticity transport theory of Bernard (1990) was used to close the mean curvature term appearing in the dissipation equation. A priori evaluation of εij, as well as solving the new dissipation equation as a whole using DNS data for quantities other than εij, for flows in a pipe, plane channel, constant-pressure boundary layer, behind a backward-facing step and in an axially rotating pipe, all show good near-wall behaviour of all terms. Computations of the same flows with the full model in conjunction with the low-Reynolds number transport equation for (uiui) All Overbar, using εh instead of ε, agree well with the direct numerical simulations.

Sensitizing the Dissipation Equation to Irrotational Strains

1980 ◽  
Vol 102 (1) ◽  
pp. 34-40 ◽  
Author(s):  
K. Hanjalic´ ◽  
B. E. Launder
Keyword(s):  
Energy Transfer ◽  
Energy Dissipation ◽  
Boundary Layers ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Turbulent Boundary Layers ◽  
Turbulence Energy ◽  
Turbulence Energy Dissipation ◽  
Dissipation Equation

The paper recommends the addition of an extra term to the conventional approximate transport equation for the turbulence energy dissipation rate. The term may be interpreted as emphasizing the role of irrotational deformations in promoting energy transfer across the spectrum or, equivalently, of augmenting the influence of normal strains. Calculations, including the new term, are reported for the plane and round jet, and for several turbulent boundary layers. In the cases considered the addition of the new term significantly improves agreement with experiment.

Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box

2003 ◽  
Vol 15 (2) ◽  
pp. L21-L24 ◽  
Author(s):  
Yukio Kaneda ◽  
Takashi Ishihara ◽  
Mitsuo Yokokawa ◽  
Ken’ichi Itakura ◽  
Atsuya Uno
Keyword(s):  
Energy Spectrum ◽  
Energy Dissipation ◽  
High Resolution ◽  
Numerical Simulations ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Direct Numerical Simulations

Transport equation for the mean turbulent energy dissipation rate on the centreline of a fully developed channel flow

2015 ◽  
Vol 777 ◽  
pp. 151-177 ◽  
Author(s):  
S. L. Tang ◽  
R. A. Antonia ◽  
L. Djenidi ◽  
H. Abe ◽  
T. Zhou ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Transport Equation ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Turbulent Energy ◽  
Energy Dissipation Rate ◽  
Grid Turbulence ◽  
Normal Velocity ◽  
Turbulent Energy Dissipation Rate ◽  
The Mean

The transport equation for the mean turbulent energy dissipation rate $\overline{{\it\epsilon}}$ along the centreline of a fully developed channel flow is derived by applying the limit at small separations to the two-point budget equation. Since the ratio of the isotropic energy dissipation rate to the mean turbulent energy dissipation rate $\overline{{\it\epsilon}}_{iso}/\overline{{\it\epsilon}}$ is sufficiently close to 1 on the centreline, our main focus is on the isotropic form of the transport equation. It is found that the imbalance between the production of $\overline{{\it\epsilon}}$ due to vortex stretching and the destruction of $\overline{{\it\epsilon}}$ caused by the action of viscosity is governed by the diffusion of $\overline{{\it\epsilon}}$ by the wall-normal velocity fluctuation. This imbalance is intrinsically different from the advection-driven imbalance in decaying-type flows, such as grid turbulence, jets and wakes. In effect, the different types of imbalance represent different constraints on the relation between the skewness of the longitudinal velocity derivative $S_{1,1}$ and the destruction coefficient $G$ of enstrophy in different flows, thus resulting in non-universal approaches of $S_{1,1}$ towards a constant value as the Taylor microscale Reynolds number, $R_{{\it\lambda}}$, increases. For example, the approach is slower for the measured values of $S_{1,1}$ along either the channel or pipe centreline than along the axis in the self-preserving region of a round jet. The data for $S_{1,1}$ collected in different flows strongly suggest that, in each flow, the magnitude of $S_{1,1}$ is bounded, the value being slightly larger than 0.5.

scholarly journals Effect of Wind Transport of Turbulent Inhomogeneities on Estimation of the Turbulence Energy Dissipation Rate from Measurements by a Conically Scanning Coherent Doppler Lidar

2020 ◽  
Vol 12 (17) ◽  
pp. 2802
Author(s):  
Igor N. Smalikho ◽  
Viktor A. Banakh
Keyword(s):  
Energy Dissipation ◽  
Dissipation Rate ◽  
Sonic Anemometer ◽  
Scanning Speed ◽  
Turbulent Energy ◽  
Energy Dissipation Rate ◽  
Stream Line ◽  
Turbulence Energy ◽  
Doppler Lidar ◽  
Coherent Doppler Lidar

A method for estimation of the turbulent energy dissipation rate from measurements by a conically scanning pulsed coherent Doppler lidar (PCDL), with allowance for the wind transport of turbulent velocity fluctuations, has been developed. The method has been tested in comparative atmospheric experiments with a Stream Line PCDL (Halo Photonics, Brockamin, Worcester, United Kingdom) and a sonic anemometer. It has been demonstrated that the method provides unbiased estimates of the dissipation rate at arbitrarily large ratios of the mean wind velocity to the linear scanning speed.

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