Energy dissipation rate surrogates in incompressible Navier–Stokes turbulence

2012 ◽  
Vol 697 ◽  
pp. 204-236 ◽  
Author(s):  
Saba Almalkie ◽  
Stephen M. de Bruyn Kops
Keyword(s):  
Energy Dissipation ◽  
Strain Rate ◽  
Dissipation Rate ◽  
Reynolds Numbers ◽  
Energy Dissipation Rate ◽  
Navier Stokes ◽  
Strain Rate Tensor ◽  
One Dimensional ◽  
Probability Densities ◽  
The One

AbstractHigh-resolution direct numerical simulations of isotropic homogeneous turbulence are used to understand the differences between the effects of spatial intermittency on the energy dissipation rate and on surrogates for the dissipation rate that are based on measurements of a subset of the strain rate tensor. In particular, the one-dimensional longitudinal and transverse surrogates, as well as a surrogate based on the asymmetric part of the strain rate tensor, are considered. The instantaneous surrogates are studied locally, locally averaged in space and conditionally averaged to see what statistics of the dissipation rate might accurately be inferred given measurements of the surrogates. The simulations with the Reynolds numbers based on the Taylor microscale of 102–235 are highly resolved for accurate evaluation of higher-order statistics. The probability densities of the local and locally averaged surrogates are significantly different from the corresponding statistics for the dissipation rate itself. All of the surrogates are more intermittent than the dissipation rate, the transverse surrogate is more intermittent than the longitudinal and these trends are still prominent even when the fields are spatially averaged at length scales close to the integral length scale. As a consequence, the intermittency exponent computed from the moments of the locally averaged longitudinal and transverse surrogates is approximately 1.5 and 2.2 times higher, respectively, than that computed by the same method from the dissipation rate field. In addition, while different methods of computing intermittency exponent from the dissipation rate field yield the same result, different methods applied to a surrogate are inconsistent.

scholarly journals Local Turbulent Energy Dissipation Rate in a Vessel Agitated by a Rushton Turbine

2015 ◽  
Vol 36 (2) ◽  
pp. 135-149 ◽  
Author(s):  
Radek Šulc ◽  
Vít Pešava ◽  
Pavel Ditl
Keyword(s):  
Energy Dissipation ◽  
Dissipation Rate ◽  
Reynolds Numbers ◽  
Turbulent Energy ◽  
Energy Dissipation Rate ◽  
Turbulent Fluctuation ◽  
Rushton Turbine ◽  
Turbulent Energy Dissipation Rate ◽  
High Reynolds ◽  
The One

Abstract The scaling of turbulence characteristics such as turbulent fluctuation velocity, turbulent kinetic energy and turbulent energy dissipation rate was investigated in a mechanically agitated vessel 300 mm in inner diameter stirred by a Rushton turbine at high Reynolds numbers in the range 50 000 < Re < 100 000. The hydrodynamics and flow field was measured using 2-D TR PIV. The convective velocity formulas proposed by Antonia et al. (1980) and Van Doorn (1981) were tested. The turbulent energy dissipation rate estimated independently in both radial and axial directions using the one-dimensional approach was not found to be the same in each direction. Using the proposed correction, the values in both directions were found to be close to each other. The relation ε/(N3·D2) ∞ const. was not conclusively confirmed.

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 } $.

On the applicability of Taylor's hypothesis, including small sampling velocities

2021 ◽  
Vol 932 ◽  
Author(s):  
Hans L. Pécseli ◽  
Jan K. Trulsen
Keyword(s):  
Energy Dissipation ◽  
Structure Function ◽  
Specific Energy ◽  
Numerical Solutions ◽  
Energy Dissipation Rate ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Size Dependent ◽  
Taylor’S Hypothesis ◽  
The One

Taylor's hypothesis, or the frozen turbulence approximation, can be used to estimate also the specific energy dissipation rate $\epsilon$ by comparing experimental results with the Kolmogorov–Obukhov expression. The hypothesis assumes that a frequency detected by an instrument moving with a constant large velocity $V$ can be related to a wavenumber by $\omega = k V$ . It is, however, not obvious how large the translational velocity has to be in order to make the hypothesis valid, or at least applicable with some acceptable uncertainty. Using the space–time-varying structure function for homogeneous and isotropic conditions, this question is addressed in the present study with emphasis on small velocities $V$ . The structure function is obtained using results from numerical solutions of the Navier–Stokes equation. Particular attention is given to the $V$ variation of the estimated specific energy dissipation, $\epsilon _{est}$ , compared with the actual value, $\epsilon$ , used in the numerical calculations. In contrast to previous studies, the results emphasize velocities $V$ less than or comparable to the one-component root-mean-square velocity, $u_{rms}$ . We find that $\epsilon$ can be determined to an acceptable accuracy for $V \geq 0.3\,u_{rms}$ . A simple analytical model is suggested to explain the main features of the observations, both Eulerian and Lagrangian. The model assumes that the observed time variations are solely due to eddies moving past the observer, thus ignoring eddy deformation and intermittency effects. In spite of these simplifications, the analysis accounts for most of the numerical results when also eddy-size-dependent velocities are accounted for.

scholarly journals A Comparative Study of Fatigue Energy Dissipation of Additive Manufactured and Cast AlSi10Mg Alloy

Metals ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1274
Author(s):  
Chunxia Yang ◽  
Ke Zhu ◽  
Yayan Liu ◽  
Yusheng Cai ◽  
Wencheng Liu ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Fatigue Damage ◽  
Energy Dissipation Rate ◽  
Diffusion Problem ◽  
Gravity Casting ◽  
Powder Bed ◽  
One Dimensional ◽  
Function Fitting ◽  
The One ◽  
Good Agreement

In this paper, the fatigue energy dissipation of Gravity Casting (GC) and Laser-based Powder Bed Fusion (LPBF) AlSi10Mg alloys under cyclic loading are investigated. The increase in surface temperature related to the energy dissipation effect is decoupled and used to predict the fatigue limits of GC and LPBF AlSi10Mg alloys as being 55.8% UTS and 33.9% UTS, respectively. The energy dissipation rate is obtained by solving the one-dimensional thermal diffusion problem. This energy dissipation is separated into related and unrelated fatigue damage using polynomial function fitting. The energy dissipation related to fatigue damage for LPBF specimens is observed to be higher than that of GC specimens, which indicates worse fatigue performance. The fatigue damage entropy is employed to predict the fatigue life of both GC and LPBF AlSi10Mg alloys, which has a good agreement with the results of a traditional fatigue experiment.

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