Isotropic Turbulence: Important Differences between True Dissipation Rate and Its One-Dimensional Surrogate

1996 ◽  
Vol 77 (22) ◽  
pp. 4548-4551 ◽  
Author(s):  
Iwao Hosokawa ◽  
Shin-ichi Oide ◽  
Kiyoshi Yamamoto
Keyword(s):  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
One Dimensional

Dissipation rate estimation from PIV in zero-mean isotropic turbulence

2008 ◽  
Vol 46 (3) ◽  
pp. 499-515 ◽  
Author(s):  
J. de Jong ◽  
L. Cao ◽  
S. H. Woodward ◽  
J. P. L. C. Salazar ◽  
L. R. Collins ◽  
...  
Keyword(s):  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Rate Estimation

On the interaction of Taylor length scale size droplets and isotropic turbulence

2016 ◽  
Vol 806 ◽  
pp. 356-412 ◽  
Author(s):  
Michael S. Dodd ◽  
Antonino Ferrante
Keyword(s):  
Surface Tension ◽  
Surface Area ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Droplet Surface ◽  
Rate Of Change ◽  
Length Scale ◽  
Fluid Viscosity ◽  
Carrier Fluid ◽  
Two Fluid

Droplets in turbulent flows behave differently from solid particles, e.g. droplets deform, break up, coalesce and have internal fluid circulation. Our objective is to gain a fundamental understanding of the physical mechanisms of droplet–turbulence interaction. We performed direct numerical simulations (DNS) of 3130 finite-size, non-evaporating droplets of diameter approximately equal to the Taylor length scale and with 5 % droplet volume fraction in decaying isotropic turbulence at initial Taylor-scale Reynolds number $\mathit{Re}_{\unicode[STIX]{x1D706}}=83$. In the droplet-laden cases, we varied one of the following three parameters: the droplet Weber number based on the r.m.s. velocity of turbulence ($0.1\leqslant \mathit{We}_{rms}\leqslant 5$), the droplet- to carrier-fluid density ratio ($1\leqslant \unicode[STIX]{x1D70C}_{d}/\unicode[STIX]{x1D70C}_{c}\leqslant 100$) or the droplet- to carrier-fluid viscosity ratio ($1\leqslant \unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x1D707}_{c}\leqslant 100$). In this work, we derive the turbulence kinetic energy (TKE) equations for the two-fluid, carrier-fluid and droplet-fluid flow. These equations allow us to explain the pathways for TKE exchange between the carrier turbulent flow and the flow inside the droplet. We also explain the role of the interfacial surface energy in the two-fluid TKE equation through the power of the surface tension. Furthermore, we derive the relationship between the power of surface tension and the rate of change of total droplet surface area. This link allows us to explain how droplet deformation, breakup and coalescence play roles in the temporal evolution of TKE. Our DNS results show that increasing $\mathit{We}_{rms}$, $\unicode[STIX]{x1D70C}_{d}/\unicode[STIX]{x1D70C}_{c}$ and $\unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x1D707}_{c}$ increases the decay rate of the two-fluid TKE. The droplets enhance the dissipation rate of TKE by enhancing the local velocity gradients near the droplet interface. The power of the surface tension is a source or sink of the two-fluid TKE depending on the sign of the rate of change of the total droplet surface area. Thus, we show that, through the power of the surface tension, droplet coalescence is a source of TKE and breakup is a sink of TKE. For short times, the power of the surface tension is less than $\pm 5\,\%$ of the dissipation rate. For later times, the power of the surface tension is always a source of TKE, and its magnitude can be up to 50 % of the dissipation rate.

Compressibility effects on the growth and structure of homogeneous turbulent shear flow

1993 ◽  
Vol 256 ◽  
pp. 443-485 ◽  
Author(s):  
G. A. Blaisdell ◽  
N. N. Mansour ◽  
W. C. Reynolds
Keyword(s):  
Growth Rate ◽  
Shear Flow ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Compressible Turbulence ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Homogeneous Shear ◽  
Homogeneous Shear Flow ◽  
Compressibility Effects

Compressibility effects within decaying isotropic turbulence and homogeneous turbulent shear flow have been studied using direct numerical simulation. The objective of this work is to increase our understanding of compressible turbulence and to aid the development of turbulence models for compressible flows. The numerical simulations of compressible isotropic turbulence show that compressibility effects are highly dependent on the initial conditions. The shear flow simulations, on the other hand, show that measures of compressibility evolve to become independent of their initial values and are parameterized by the root mean square Mach number. The growth rate of the turbulence in compressible homogeneous shear flow is reduced compared to that in the incompressible case. The reduced growth rate is the result of an increase in the dissipation rate and energy transfer to internal energy by the pressure–dilatation correlation. Examination of the structure of compressible homogeneous shear flow reveals the presence of eddy shocklets, which are important for the increased dissipation rate of compressible turbulence.

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.

Scalar dissipation rate and dissipative anomaly in isotropic turbulence

2005 ◽  
Vol 532 ◽  
pp. 199-216 ◽  
Author(s):  
D. A. DONZIS ◽  
K. R. SREENIVASAN ◽  
P. K. YEUNG
Keyword(s):  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate
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