The effect of viscoelasticity on the turbulent kinetic energy cascade

2014 ◽  
Vol 760 ◽  
pp. 39-62 ◽  
Author(s):  
P. C. Valente ◽  
C. B. da Silva ◽  
F. T. Pinho
Keyword(s):  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Relaxation Times ◽  
Turnover Time ◽  
Excess Energy ◽  
Energy Cascade ◽  
Homogeneous Isotropic Turbulence ◽  
Total Energy Flux ◽  
Strong Depletion ◽  
Nonlinear Energy

AbstractDirect numerical simulations of statistically steady homogeneous isotropic turbulence in viscoelastic fluids described by the FENE-P model, such as those laden with polymers, are presented. It is shown that the strong depletion of the turbulence dissipation reported by previous authors does not necessarily imply a depletion of the nonlinear energy cascade. However, for large relaxation times, of the order of the eddy turnover time, the polymers remove more energy from the large scales than they can dissipate and transfer the excess energy back into the turbulent dissipative scales. This is effectively a polymer-induced kinetic energy cascade which competes with the nonlinear energy cascade of the turbulence leading to its depletion. It is also shown that the total energy flux to the small scales from both cascade mechanisms remains approximately the same fraction of the kinetic energy over the turnover time as the nonlinear energy cascade flux in Newtonian turbulence.

Small-scale energy cascade in homogeneous isotropic turbulence

2019 ◽  
Vol 4 (10) ◽  
Author(s):  
Mohamad Ibrahim Cheikh ◽  
James Chen ◽  
Mingjun Wei
Keyword(s):  
Isotropic Turbulence ◽  
Energy Cascade ◽  
Small Scale ◽  
Homogeneous Isotropic Turbulence

Turbulent energy density in scale space for inhomogeneous turbulence

2018 ◽  
Vol 842 ◽  
pp. 532-553 ◽  
Author(s):  
Fujihiro Hamba
Keyword(s):  
Energy Spectrum ◽  
Energy Density ◽  
Isotropic Turbulence ◽  
Scale Space ◽  
Scale Dependence ◽  
Energy Cascade ◽  
Homogeneous Isotropic Turbulence ◽  
Velocity Correlation ◽  
Inhomogeneous Turbulence ◽  
Point Velocity

The energy spectrum is commonly used to describe the scale dependence of the turbulent fluctuations in homogeneous isotropic turbulence. In contrast, one-point statistical quantities, such as the turbulent kinetic energy, are employed for inhomogeneous turbulence modelling. To obtain a better understanding of inhomogeneous turbulence, some attempts have been made to describe its scale dependence by using the second-order structure function and the two-point velocity correlation. However, previous expressions for the energy density in the scale space do not satisfy the requirement that it should be non-negative. In this work, a new expression for the energy density in the scale space is proposed on the basis of the two-point velocity correlation; the integral with a filter function is introduced to satisfy the non-negativity of the energy density. Direct numerical simulation (DNS) data of homogeneous isotropic turbulence were first used to assess the role of the energy density by comparing it with the energy spectrum. DNS data of a turbulent channel flow were then used to investigate the energy density and its transport equation in inhomogeneous turbulence. It was shown that the new energy density is positive in the scale space of the homogeneous direction. The energy transfer was successfully examined in the scale space both in the homogeneous and inhomogeneous directions. The energy cascade from large to small scales was clearly observed. Moreover, the inverse energy cascade from large to very large scales was observed in the scale space of the spanwise direction.

scholarly journals Modulation of fluid temperature fluctuations by particles in turbulence

2021 ◽  
Vol 931 ◽  
Author(s):  
Izumi Saito ◽  
Takeshi Watanabe ◽  
Toshiyuki Gotoh
Keyword(s):  
Isotropic Turbulence ◽  
Thermal Relaxation ◽  
Temperature Fluctuations ◽  
Turnover Time ◽  
Fluid Temperature ◽  
Thermal Coupling ◽  
Homogeneous Isotropic Turbulence ◽  
Large Eddy ◽  
Theoretical Predictions ◽  
Momentum Coupling

Modulation of fluid temperature fluctuations by particles due to thermal interaction in homogeneous isotropic turbulence is studied. For simplicity, only thermal coupling between the fluid and particles is considered, and momentum coupling is neglected. Application of the statistical theory used in cloud turbulence research leads to the prediction that modulation of the intensity of fluid temperature fluctuations by particles is expressed as a function of the Damköhler number, which is defined as the ratio of the turbulence large-eddy turnover time to the fluid thermal relaxation time. Direct numerical simulations are conducted for two-way thermal coupling between the fluid temperature field and point particles in homogeneous isotropic turbulence. The simulation results are shown to agree well with the theoretical predictions.

A physical mechanism of the energy cascade in homogeneous isotropic turbulence

2008 ◽  
Vol 605 ◽  
pp. 355-366 ◽  
Author(s):  
SUSUMU GOTO
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Transfer Rate ◽  
Physical Mechanism ◽  
Isotropic Turbulence ◽  
Scale Space ◽  
Energy Cascade ◽  
Homogeneous Isotropic Turbulence ◽  
Moderate Reynolds Number

In order to investigate the physical mechanism of the energy cascade in homogeneous isotropic turbulence, the internal energy and its transfer rate are defined as a function of scale, space and time. Direct numerical simulation of turbulence at a moderate Reynolds number verifies that the energy cascade can be caused by the successive creation of smaller-scale tubular vortices in the larger-scale straining regions existing between pairs of larger-scale tubular vortices. Movies are available with the online version of the paper.

DNS study of decaying homogeneous isotropic turbulence with polymer additives

2010 ◽  
Vol 665 ◽  
pp. 334-356 ◽  
Author(s):  
W.-H. CAI ◽  
F.-C. LI ◽  
H.-N. ZHANG
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Newtonian Fluid ◽  
Isotropic Turbulence ◽  
Transport Equations ◽  
Vortex Structures ◽  
Small Scale ◽  
Polymer Additives ◽  
Homogeneous Isotropic Turbulence ◽  
Turbulent Drag

In order to investigate the turbulent drag reduction phenomenon and understand its mechanism, direct numerical simulation (DNS) was carried out on decaying homogeneous isotropic turbulence (DHIT) with and without polymer additives. We explored the polymer effect on DHIT from the energetic viewpoint, i.e. the decay of the total turbulent kinetic energy and energy distribution at each scale in Fourier space and from the phenomenological viewpoint, i.e. the alterations of vortex structures, the enstrophy and the strain. It was obtained that in DHIT with polymer additives the decay of the turbulent kinetic energy is faster than that in the Newtonian fluid case and a modification of the turbulent kinetic energy transfer process for the Newtonian fluid flow is observed due to the release of the polymer elastic energy into flow structures at certain small scales. Besides, we deduced the transport equations of the enstrophy and the strain, respectively, for DHIT with polymer additives. Based on the analyses of these transport equations, it was found that polymer additives depress both the enstrophy and the strain in DHIT as compared to the Newtonian fluid case, indicating the inhibition effect on small-scale vortex structures and turbulence intensity by polymers.

Direct numerical simulation of turbulence modulation by particles in isotropic turbulence

1998 ◽  
Vol 375 ◽  
pp. 235-263 ◽  
Author(s):  
MARC BOIVIN ◽  
OLIVIER SIMONIN ◽  
KYLE D. SQUIRES
Keyword(s):  
Numerical Simulation ◽  
Kinetic Energy ◽  
Direct Numerical Simulation ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Relaxation Times ◽  
Relative Increase ◽  
Fluid Particle ◽  
Small Scale ◽  
Small Particles

The modulation of isotropic turbulence by particles has been investigated using direct numerical simulation (DNS). The particular focus of the present work is on the class of dilute flows in which particle volume fractions and inter-particle collisions are negligible. Gravitational settling is also neglected and particle motion is assumed to be governed by drag with particle relaxation times ranging from the Kolmogorov scale to the Eulerian time scale of the turbulence and particle mass loadings up to 1. The velocity field was made statistically stationary by forcing the low wavenumbers of the flow. The calculations were performed using 963 collocation points and the Taylor-scale Reynolds number for the stationary flow was 62. The effect of particles on the turbulence was included in the Navier–Stokes equations using the point-force approximation in which 963 particles were used in the calculations. DNS results show that particles increasingly dissipate fluid kinetic energy with increased loading, with the reduction in kinetic energy being relatively independent of the particle relaxation time. Viscous dissipation in the fluid decreases with increased loading and is larger for particles with smaller relaxation times. Fluid energy spectra show that there is a non-uniform distortion of the turbulence with a relative increase in small-scale energy. The non-uniform distortion significantly affects the transport of the dissipation rate, with the production and destruction of dissipation exhibiting completely different behaviours. The spectrum of the fluid–particle energy exchange rate shows that the fluid drags particles at low wavenumbers while the converse is true at high wavenumbers for small particles. A spectral analysis shows that the increase of the high-wavenumber portion of the fluid energy spectrum can be attributed to transfer of the fluid–particle covariance by the fluid turbulence. This in turn explains the relative increase of small-scale energy caused by small particles observed in the present simulations as well as those of Squires & Eaton (1990) and Elghobashi & Truesdell (1993).

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