scholarly journals On filtering in the viscous-convective subrange for turbulent mixing of high Schmidt number passive scalars

2013 ◽  
Vol 25 (5) ◽  
pp. 055104 ◽  
Author(s):  
Siddhartha Verma ◽  
G. Blanquart
Keyword(s):  
Turbulent Mixing ◽  
Schmidt Number ◽  
Passive Scalars ◽  
High Schmidt Number

Self-similar decay and mixing of a high-Schmidt-number passive scalar in an oscillating boundary layer in the intermittently turbulent regime

2013 ◽  
Vol 726 ◽  
pp. 338-370 ◽  
Author(s):  
Carlo Scalo ◽  
Ugo Piomelli ◽  
Leon Boegman
Keyword(s):  
Boundary Layer ◽  
Scalar Field ◽  
Equilibrium State ◽  
Turbulent Mixing ◽  
Schmidt Number ◽  
Wall Region ◽  
Turbulent Regime ◽  
High Schmidt Number ◽  
Oscillating Boundary ◽  
Non Equilibrium

AbstractWe performed numerical simulations of dissolved oxygen (DO) transfer from a turbulent flow, driven by periodic boundary-layer turbulence in the intermittent regime, to underlying DO-absorbing organic sediment layers. A uniform initial distribution of oxygen is left to decay (with no re-aeration) as the turbulent transport supplies the sediment with oxygen from the outer layers to be absorbed. A very thin diffusive sublayer at the sediment–water interface (SWI), caused by the high Schmidt number of DO in water, limits the overall decay rate. A decomposition of the instantaneous decaying turbulent scalar field is proposed, which results in the development of similarity solutions that collapse the data in time. The decomposition is then tested against the governing equations, leading to a rigorous procedure for the extraction of an ergodic turbulent scalar field. The latter is composed of a statistically periodic and a steady non-decaying field. Temporal averaging is used in lieu of ensemble averaging to evaluate flow statistics, allowing the investigation of turbulent mixing dynamics from a single flow realization. In spite of the highly unsteady state of turbulence, the monotonically decaying component is surprisingly consistent with experimental and numerical correlations valid for steady high-Schmidt-number turbulent mass transfer. Linearly superimposed onto it is the statistically periodic component, which incorporates all the features of the non-equilibrium state of turbulence. It is modulated by the evolution of the turbulent coherent structures driven by the oscillating boundary layer in the intermittent regime, which are responsible for the violent turbulent production mechanisms. These cause, in turn, a rapid increase of the turbulent mass flux at the edge of the diffusive sublayer. This outer-layer forcing mechanism drives a periodic accumulation of high scalar concentration levels in the near-wall region. The resulting modulated scalar flux across the SWI is delayed by a quarter of a cycle with respect to the wall-shear stress, consistently with the non-equilibrium state of the turbulent mixing.

Random-sweeping hypothesis for passive scalars in isotropic turbulence

2002 ◽  
Vol 459 ◽  
pp. 129-138 ◽  
Author(s):  
P. K. YEUNG ◽  
BRIAN L. SAWFORD
Keyword(s):  
Turbulent Mixing ◽  
Large Scale ◽  
Schmidt Number ◽  
Isotropic Turbulence ◽  
Simulation Data ◽  
Passive Scalars ◽  
Direct Numerical Simulation Data ◽  
Rates Of Change ◽  
Small Scales ◽  
Wavenumber Spectrum

The hypothesis of the small scales being passively swept along by the large-scale motions in turbulent flow is extended to passive scalars in isotropic turbulence. A theory based on strong mutual cancellation between local and advective derivatives and other assumptions is shown to capture the Reynolds and Schmidt number dependence of time scales characterizing Eulerian and Lagrangian rates of change. Agreement with direct numerical simulation data improves systematically with increasing Reynolds number. In accordance with the physics of random sweeping, the Eulerian frequency spectrum is very similar in shape to the wavenumber spectrum, but is broadened at higher frequencies compared to its Lagrangian counterpart. Overall the hypothesis appears to be even more valid for transported scalars than for the velocity field, which gives support to the use of Lagrangian approaches in the study of turbulent mixing.

Spectrum of passive scalars of high molecular diffusivity in turbulent mixing

2013 ◽  
Vol 716 ◽  
Author(s):  
P. K. Yeung ◽  
K. R. Sreenivasan
Keyword(s):  
Reynolds Number ◽  
Turbulent Mixing ◽  
Kinematic Viscosity ◽  
Schmidt Number ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Careful Examination ◽  
Passive Scalars ◽  
Molecular Diffusivity ◽  
Schmidt Numbers

AbstractWe consider the mixing of passive scalars transported in turbulent flow, with a molecular diffusivity that is large compared to the kinematic viscosity of the fluid. This particular case of mixing has not received much attention in experiment or simulation even though the first putative theory, due to Batchelor, Howells & Townsend (J. Fluid Mech., vol. 5, 1959, pp. 134–139), is now more than 50 years old. We study the problem using direct numerical simulation of decaying scalar fields in steadily sustained homogeneous turbulence as the Schmidt number (the ratio of the kinematic viscosity of the fluid to the molecular diffusivity of the scalar) is allowed to vary from $1/ 8$ to $1/ 2048$ for two values of the microscale Reynolds number, ${R}_{\lambda } \approx 140$ and $\approx $240. The simulations show that the passive scalar spectrum assumes a slope of $- 17/ 3$ in a range of scales, as predicted by the theory, when the Schmidt number is small and the Reynolds number is simultaneously large. The observed agreement between theory and simulation in the prefactor in the spectrum is not perfect. We assess the reasons for this discrepancy by a careful examination of the scalar evolution equation in the light of the assumptions of the theory, and conclude that the finite range of scales resolved in simulations is the main reason. Numerical issues specific to the regime of very low Schmidt numbers are also addressed briefly.

An Experimental Study on Turbulent Mixing of High-Schmidt-Number Scalar in Grid Turbulence by Means of PIV and PLIF

2011 ◽  
Author(s):  
Hiroki Suzuki ◽  
Kouji Nagata ◽  
Yasuhiko Sakai ◽  
Ryota Ukai
Keyword(s):  
Turbulent Mixing ◽  
Schmidt Number ◽  
Water Channel ◽  
Concentration Field ◽  
Outer Region ◽  
Passive Scalar ◽  
Spatiotemporal Variation ◽  
Grid Turbulence ◽  
High Schmidt Number ◽  
Scalar Variance

Turbulent mixing of high-Schmidt-number passive scalar in shear-free grid turbulence is experimentally investigated using a water channel. The Reynolds number based on the mesh size of the grid and cross-sectionally averaged mean velocity is 2,500. Rhodamine B (fluorescent dye) was used as a high-Schmidt-number passive scalar. The Schmidt number is about 2,100. The time-resolved particle image velocimetry (PIV) and the planar laser induced fluorescence (PLIF) technique were used to measure instantaneous two-component velocities and nondimensional concentration. Our PLIF algorithm corrects the following errors: spatiotemporal variation of local excitation intensity due to an inhomogeneous concentration field along the light path, time variation of fluorescence quantum yield, and spatiotemporal variation of incident laser intensity. The results show that the vertical profile of mean scalar can be well approximated by the error function. In contrast, the profile of scalar variance in outer region of the mixing layer cannot be approximated by the Gaussian profile. In addition, the half width of mean scalar is larger than that of the scalar variance profile.

scholarly journals Differential diffusion of high-Schmidt-number passive scalars in a turbulent jet

2008 ◽  
Vol 612 ◽  
pp. 439-475 ◽  
Author(s):  
T. M. LAVERTU ◽  
L. MYDLARSKI ◽  
S. J. GASKIN
Keyword(s):  
Reynolds Number ◽  
Schmidt Number ◽  
Reynolds Numbers ◽  
Turbulent Jet ◽  
Passive Scalars ◽  
Concentration Difference ◽  
Differential Diffusion ◽  
High Schmidt Number ◽  
Diffusion Effects ◽  
High Reynolds

The separate evolution, or differential diffusion, of high-Schmidt-number passive scalars in a turbulent jet is studied experimentally. The two scalars under consideration are disodium fluorescein (Sc≡ ν/D= 2000) and sulforhodamine 101 (Sc= 5000). The objectives of the research are twofold: to determine (i) the Reynolds-number-dependence, and (ii) the radial distribution of differential diffusion effects in the self-similar region of the jet. Punctual laser-induced fluorescence (LIF) measurements were obtained 50 jet diameters downstream of the nozzle exit for five Reynolds numbers (Re≡uod/ν = 900, 2100, 4300, 6700 and 10600, whereu0is the jet exit velocity,dis the jet diameter, and ν is the kinematic viscosity) and for radial positions extending from the centreline to the edges of the jet cross-section (0 ≤r/d≤ 7.5). Statistics of the normalized concentration difference,Z, were used to quantify the differential diffusion. The latter were found to decay slowly with increasing Reynolds number, with the root mean square ofZscaling asZrms≡ 〈Z2〉1/2∝Re−0.1, (or alternatively 〈Z2〉 ∝Re−0.2). Regardless of Reynolds number, differential diffusion effects were found to increase away from the centreline. The increase in differential diffusion effects with radial position, along with their increase with decreasing Reynolds number, support the hypothesis of increased differential diffusion at interfaces between the jet and ambient fluids. Power spectral densities ofZwere also studied. These spectra decreased with increasing wavenumber – an observation attributed to the decay of the scalar fluctuations in a turbulent jet. Furthermore, these spectra showed that significant differential diffusion effects persist at scales larger than the Kolmogorov scale, even for moderately high Reynolds numbers.

Sign in / Sign up

Export Citation Format

Share Document