Variational bounds on energy dissipation in incompressible flows. II. Channel flow

1995 ◽  
Vol 51 (4) ◽  
pp. 3192-3198 ◽  
Author(s):  
Peter Constantin ◽  
Charles R. Doering
Keyword(s):  
Energy Dissipation ◽  
Channel Flow ◽  
Incompressible Flows ◽  
Variational Bounds

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

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.

Investigations of the Hydraulic Characteristics of Stilling Basin with Baffle-Blocks Using an Integrated SPH Method

2019 ◽  
Vol 17 (08) ◽  
pp. 1950051
Author(s):  
X. J. Ma ◽  
Y. L. Yan ◽  
G. Y. Li ◽  
M. Geni ◽  
M. Wang
Keyword(s):  
Energy Dissipation ◽  
Incompressible Flows ◽  
Particle Methods ◽  
Solid Boundary ◽  
Discharge Process ◽  
Sph Method ◽  
Stilling Basin ◽  
Dissipation Effect ◽  
Kernel Gradient Correction ◽  
Baffle Block

The stilling basin has been one of the most powerful hydraulic structures for the dissipation of the flow energy. Meshfree and particle methods have special advantages in modeling incompressible flows with free surfaces. In this paper, an integrated smoothed particle hydrodynamics (SPH) method is developed to model energy dissipation process of stilling basins. The integrated SPH includes the kernel gradient correction (KGC) technique, the dynamic solid boundary treatment, [Formula: see text]-SPH model and density reinitialization. We first conducted the simulations of dam-breaking and hydraulic jump to validate the accuracy of the present method. The present simulation results agree well with the experimental observations and numerical results from other sources. Then the discharge process of stilling basin with baffle-blocks is simulated with the integrated SPH. It is demonstrated that the detailed discharge process can be well captured by this method. The energy dissipation effect of stilling basin could be significantly improved by the baffle-blocks. The structure and position of the baffle-block directly affect the energy dissipation effect, while the height of the baffle-block has big influence on the drainage capacity.

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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