Variational bounds on energy dissipation in an incompressible channel flow with uniform injection and suction

2002 ◽  
Vol 159 (1-4) ◽  
pp. 1-9 ◽  
Author(s):  
Q. Wei
Keyword(s):  
Energy Dissipation ◽  
Channel Flow ◽  
Variational Bounds ◽  
Uniform Injection

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.

Variational bounds on energy dissipation in incompressible flows: Shear flow

1994 ◽  
Vol 49 (5) ◽  
pp. 4087-4099 ◽  
Author(s):  
Charles R. Doering ◽  
Peter Constantin
Keyword(s):  
Energy Dissipation ◽  
Shear Flow ◽  
Incompressible Flows ◽  
Variational Bounds

Variational bounds on energy dissipation in incompressible flows. III. Convection

1996 ◽  
Vol 53 (6) ◽  
pp. 5957-5981 ◽  
Author(s):  
Charles R. Doering ◽  
Peter Constantin
Keyword(s):  
Energy Dissipation ◽  
Incompressible Flows ◽  
Variational Bounds

scholarly journals Statistics of the energy dissipation rate and local enstrophy in turbulent channel flow

2012 ◽  
Vol 241 (3) ◽  
pp. 169-177 ◽  
Author(s):  
Peter E. Hamlington ◽  
Dmitry Krasnov ◽  
Thomas Boeck ◽  
Jörg Schumacher
Keyword(s):  
Energy Dissipation ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Turbulent Channel Flow ◽  
Energy Dissipation Rate

scholarly journals Local dissipation scales and energy dissipation-rate moments in channel flow

2012 ◽  
Vol 701 ◽  
pp. 419-429 ◽  
Author(s):  
P. E. Hamlington ◽  
D. Krasnov ◽  
T. Boeck ◽  
J. Schumacher
Keyword(s):  
Energy Dissipation ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Energy Dissipation Rate ◽  
Wall Region ◽  
Dissipation Scale ◽  
High Order Statistics

AbstractLocal dissipation-scale distributions and high-order statistics of the energy dissipation rate are examined in turbulent channel flow using very high-resolution direct numerical simulations at Reynolds numbers ${\mathit{Re}}_{\tau } = 180$, $381$ and $590$. For sufficiently large ${\mathit{Re}}_{\tau } $, the dissipation-scale distributions and energy dissipation moments in the channel bulk flow agree with those in homogeneous isotropic turbulence, including only a weak Reynolds-number dependence of both the finest and largest scales. Systematic, but ${\mathit{Re}}_{\tau } $-independent, variations in the distributions and moments arise as the wall is approached for ${y}^{+ } \lesssim 100$. In the range $100\lt {y}^{+ } \lt 200$, there are substantial differences in the moments between the lowest and the two larger values of ${\mathit{Re}}_{\tau } $. This is most likely caused by coherent vortices from the near-wall region, which fill the whole channel for low ${\mathit{Re}}_{\tau } $.

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