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 } $.

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

Relationship between the energy dissipation function and the skin friction law in a turbulent channel flow

2016 ◽  
Vol 798 ◽  
pp. 140-164 ◽  
Author(s):  
Hiroyuki Abe ◽  
Robert Anthony Antonia
Keyword(s):  
Energy Dissipation ◽  
Skin Friction ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Turbulent Channel Flow ◽  
Turbulent Energy ◽  
Energy Dissipation Rate ◽  
Turbulent Energy Dissipation Rate ◽  
The Mean ◽  
Overlap Region

Integrals of the mean and turbulent energy dissipation rates are examined using direct numerical simulation (DNS) databases in a turbulent channel flow. Four values of the Kármán number ($h^{+}=180$, 395, 640 and 1020;$h$is the channel half-width) are used. Particular attention is given to the functional$h^{+}$dependence by comparing existing DNS and experimental data up to$h^{+}=10^{4}$. The logarithmic$h^{+}$dependence of the integrated turbulent energy dissipation rate is established for$300\leqslant h^{+}\leqslant 10^{4}$, and is intimately linked to the logarithmic skin friction law,viz.$U_{b}^{+}=2.54\ln (h^{+})+2.41$($U_{b}$ is the bulk mean velocity). This latter relationship is established on the basis of energy balances for both the mean and turbulent kinetic energy. When$h^{+}$is smaller than 300, viscosity affects the integrals of both the mean and turbulent energy dissipation rates significantly due to the lack of distinct separation between inner and outer regions. The logarithmic$h^{+}$dependence of$U_{b}^{+}$is clarified through the scaling behaviour of the turbulent energy dissipation rate$\overline{{\it\varepsilon}}$in different parts of the flow. The overlap between inner and outer regions is readily established in the region$30/h^{+}\leqslant y/h\leqslant 0.2$for$h^{+}\geqslant 300$. At large$h^{+}$(${\geqslant}$5000) when the finite Reynolds number effect disappears, the magnitude of$\overline{{\it\varepsilon}}y/U_{{\it\tau}}^{3}$approaches 2.54 near the lower bound of the overlap region. This value is identical between the channel, pipe and boundary layer as a result of similarity in the constant stress region. As$h^{+}$becomes large, the overlap region tends to contribute exclusively to the$2.54\ln (h^{+})$dependence of the integrated turbulent energy dissipation rate. The present logarithmic$h^{+}$dependence of$U_{b}^{+}$is essentially linked to the overlap region, even at small$h^{+}$.

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.

Micromixing Characteristics in an Aerated Stirred Tank with Half Elliptical Blade Disk Turbine

2014 ◽  
Vol 12 (1) ◽  
pp. 231-243
Author(s):  
Wanbo Li ◽  
Xingye Geng ◽  
Yuyun Bao ◽  
Zhengming Gao
Keyword(s):  
Energy Dissipation ◽  
Specific Energy ◽  
Dissipation Rate ◽  
Gas Flow ◽  
Liquid Surface ◽  
Energy Dissipation Rate ◽  
Reaction Scheme ◽  
Stirred Tank ◽  
Wall Region ◽  
Superficial Gas Velocity

Abstract The parallel-competing iodide-iodate reaction scheme was used to investigate the micromixing efficiency in an aerated stirred tank of 0.30 m diameter agitated by a half elliptical blade disk turbine. The mean specific energy dissipation rate Pm ranged from 0.5 to 2.2 W/kg, while the superficial gas velocity VS ranged from 0.015 to 0.047 m/s. Four sub-surface feed positions were considered. When the tank is fed just under the liquid surface or in the near-wall region, the micromixing efficiency can be enhanced by introducing gases with superficial gas velocities higher than 0.031 m/s. The effects of gas on the micromixing performance become complicated, while the tank is fed in the impeller discharging region. The increase of gas flow rate does not always have good effects on the micromixing performance. Moreover, the way to feed sulfuric acid can strongly affect the efficiency of the reaction scheme. For a single liquid phase, the micromixing time tm according to the incorporation model varies from 5 × 10−3 to 3 × 10−2 s. The dimensionless local specific energy dissipation rate Φ near the liquid surface is almost independent of Pm, while Φ in the impeller discharging area decreases with increasing Pm.

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.

Low-Reynolds-number effects in a fully developed turbulent channel flow

1992 ◽  
Vol 236 ◽  
pp. 579-605 ◽  
Author(s):  
R. A. Antonia ◽  
M. Teitel ◽  
J. Kim ◽  
L. W. B. Browne
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Low Reynolds Number ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Wall Region ◽  
Low Reynolds Numbers ◽  
Reynolds Number Effects ◽  
Low Reynolds ◽  
Inner Region

Low-Reynolds-number effects are observed in the inner region of a fully developed turbulent channel flow, using data obtained either from experiments or by direct numerical simulations. The Reynolds-number influence is observed on the turbulence intensities and to a lesser degree on the average production and dissipation of the turbulent energy. In the near-wall region, the data confirm Wei & Willmarth's (1989) conclusion that the Reynolds stresses do not scale on wall variables. One of the reasons proposed by these authors to account for this behaviour, namely the ‘geometry’ effect or direct interaction between inner regions on opposite walls, was investigated in some detail by introducing temperature at one of the walls, both in experiment and simulation. Although the extent of penetration of thermal excursions into the opposite side of the channel can be significant at low Reynolds numbers, the contribution these excursions make to the Reynolds shear stress and the spanwise vorticity in the opposite wall region is negligible. In the inner region, spectra and co-spectra of the velocity fluctuations u and v change rapidly with the Reynolds number, the variations being mainly confined to low wavenumbers in the u spectrum. These spectra, and the corresponding variances, are discussed in the context of the active/inactive motion concept and the possibility of increased vortex stretching at the wall. A comparison is made between the channel and the boundary layer at low Reynolds numbers.

On the universality of local dissipation scales in turbulent channel flow

2015 ◽  
Vol 786 ◽  
pp. 234-252 ◽  
Author(s):  
S. C. C. Bailey ◽  
B. M. Witte
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Small Scale ◽  
Length Scale ◽  
Scaling Behaviour ◽  
Sixth Moment

Well-resolved measurements of the small-scale dissipation statistics within turbulent channel flow are reported for a range of Reynolds numbers from $Re_{{\it\tau}}\approx 500$ to 4000. In this flow, the local large-scale Reynolds number based on the longitudinal integral length scale is found to poorly describe the Reynolds number dependence of the small-scale statistics. When a length scale based on Townsend’s attached-eddy hypothesis is used to define the local large-scale Reynolds number, the Reynolds number scaling behaviour was found to be more consistent with that observed in homogeneous, isotropic turbulence. The Reynolds number scaling of the dissipation moments up to the sixth moment was examined and the results were found to be in good agreement with predicted scaling behaviour (Schumacher et al., Proc. Natl Acad. Sci. USA, vol. 111, 2014, pp. 10961–10965). The probability density functions of the local dissipation scales (Yakhot, Physica D, vol. 215 (2), 2006, pp. 166–174) were also determined and, when the revised local large-scale Reynolds number is used for normalization, provide support for the existence of a universal distribution which scales differently for inner and outer regions.

Evolution of the scalar dissipation rate downstream of a concentrated line source in turbulent channel flow

2014 ◽  
Vol 749 ◽  
pp. 227-274 ◽  
Author(s):  
E. Germaine ◽  
L. Mydlarski ◽  
L. Cortelezzi
Keyword(s):  
Scalar Field ◽  
Channel Flow ◽  
Line Source ◽  
Dissipation Rate ◽  
Turbulent Channel Flow ◽  
Scalar Fields ◽  
Small Scale ◽  
Wall Region ◽  
Small Scales ◽  
Near Wall

AbstractThe dissipation rate,$\varepsilon _{\theta }$, of a passive scalar (temperature in air) emitted from a concentrated source into a fully developed high-aspect-ratio turbulent channel flow is studied. The goal of the present work is to investigate the return to isotropy of the scalar field when the scalar is injected in a highly anisotropic manner into an inhomogeneous turbulent flow at small scales. Both experiments and direct numerical simulations (DNS) were used to study the downstream evolution of$\varepsilon _{\theta }$for scalar fields generated by line sources located at the channel centreline$(y_s/h = 1.0)$and near the wall$(y_s/h = 0.17)$. The temperature fluctuations and temperature derivatives were measured by means of a pair of parallel cold-wire thermometers in a flow at$Re_{\tau } = 520$. The DNS were performed at$Re_{\tau } = 190$using a spectral method to solve the continuity and Navier–Stokes equations, and a flux integral method (Germaine, Mydlarski & Cortelezzi,J. Comput. Phys., vol. 174, 2001, pp. 614–648) for the advection–diffusion equation. The statistics of the scalar field computed from both experimental and numerical data were found to be in good agreement, with certain discrepancies that were attributable to the difference in the Reynolds numbers of the two flows. A return to isotropy of the small scales was never perfectly observed in any region of the channel for the downstream distances studied herein. However, a continuous decay of the small-scale anisotropy was observed for the scalar field generated by the centreline line source in both the experiments and DNS. The scalar mixing was found to be more rapid in the near-wall region, where the experimental results exhibited low levels of small-scale anisotropy. However, the DNS, which were performed at lower$Re_{\tau }$, showed that persistent anisotropy can also exist near the wall, independently of the downstream location. The role of the mean velocity gradient in the production of$\varepsilon _{\theta }$(and therefore anisotropy) in the near-wall region was highlighted.

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