Robust Volume-Based Approach for the Turbulent Mixing Efficiency

2005 ◽  
Vol 128 (4) ◽  
pp. 864-873 ◽  
Author(s):  
Roberto C. Aguirre ◽  
Haris J. Catrakis ◽  
Jennifer C. Nathman ◽  
Philip J. Garcia
Keyword(s):  
Turbulent Mixing ◽  
Mixture Fraction ◽  
Mixing Efficiency ◽  
Small Scale ◽  
Fluid Interfaces ◽  
Pure Fluid ◽  
Scale Sensitivity ◽  
The Difference ◽  
Mixed Fluid

This paper considers the mixture fraction which is often used to quantify the turbulent mixing efficiency in fluid engineering devices. We contrast a volume-based approach, where the mixture fraction is quantified directly using the volume bounded by the interface between mixed versus pure fluid, to a surface-based approach that requires area integrals of all mixed-fluid interfaces. Experimentally, we investigate the resolution-scale robustness of the volume-based approach compared to the small-scale sensitivity of the surface-based approach. The difference in robustness between these approaches has implications for examining, modeling, and optimizing the turbulent mixing efficiency.

Flow Geometry Effects on the Turbulent Mixing Efficiency

2006 ◽  
Vol 128 (4) ◽  
pp. 874-879 ◽  
Author(s):  
Roberto C. Aguirre ◽  
Jennifer C. Nathman ◽  
Haris C. Catrakis
Keyword(s):  
Shear Layer ◽  
Turbulent Mixing ◽  
Large Scale ◽  
Mixture Fraction ◽  
Mixing Efficiency ◽  
Developed Turbulence ◽  
Planar Shear ◽  
Flow Geometry ◽  
Schmidt Numbers ◽  
Geometry Effects

Flow geometry effects are examined on the turbulent mixing efficiency quantified as the mixture fraction. Two different flow geometries are compared at similar Reynolds numbers, Schmidt numbers, and growth rates, with fully developed turbulence conditions. The two geometries are the round jet and the single-stream planar shear layer. At the flow conditions examined, the jet exhibits an ensemble-averaged mixing efficiency which is approximately double the value for the shear layer. This substantial difference is explained fluid mechanically in terms of the distinct large-scale entrainment and mixing-initiation environments and is therefore directly due to flow geometry effects.

scholarly journals Role of overturns in optimal mixing in stratified mixing layers

2017 ◽  
Vol 826 ◽  
pp. 522-552 ◽  
Author(s):  
A. Mashayek ◽  
C. P. Caulfield ◽  
W. R. Peltier
Keyword(s):  
Numerical Simulations ◽  
Ocean Circulation ◽  
Turbulent Mixing ◽  
Isotropic Turbulence ◽  
Life Cycles ◽  
Shear Instability ◽  
Mixing Efficiency ◽  
Small Scale ◽  
Mean Flow

Turbulent mixing plays a major role in enabling the large-scale ocean circulation. The accuracy of mixing rates estimated from observations depends on our understanding of basic fluid mechanical processes underlying the nature of turbulence in a stratified fluid. Several of the key assumptions made in conventional mixing parameterizations have been increasingly scrutinized in recent years, primarily on the basis of adequately high resolution numerical simulations. We add to this evidence by compiling results from a suite of numerical simulations of the turbulence generated through stratified shear instability processes. We study the inherently intermittent and time-dependent nature of wave-induced turbulent life cycles and more specifically the tight coupling between inherently anisotropic scales upon which small-scale isotropic turbulence grows. The anisotropic scales stir and stretch fluid filaments enhancing irreversible diffusive mixing at smaller scales. We show that the characteristics of turbulent mixing depend on the relative time evolution of the Ozmidov length scale $L_{O}$ compared to the so-called Thorpe overturning scale $L_{T}$ which represents the scale containing available potential energy upon which turbulence feeds and grows. We find that when $L_{T}\sim L_{O}$, the mixing is most active and efficient since stirring by the largest overturns becomes ‘optimal’ in the sense that it is not suppressed by ambient stratification. We argue that the high mixing efficiency associated with this phase, along with observations of $L_{O}/L_{T}\sim 1$ in oceanic turbulent patches, together point to the potential for systematically underestimating mixing in the ocean if the role of overturns is neglected. This neglect, arising through the assumption of a clear separation of scales between the background mean flow and small-scale quasi-isotropic turbulence, leads to the exclusion of an highly efficient mixing phase from conventional parameterizations of the vertical transport of density. Such an exclusion may well be significant if the mechanism of shear-induced turbulence is assumed to be representative of at least some turbulent events in the ocean. While our results are based upon simulations of shear instability, we show that they are potentially more generic by making direct comparisons with $L_{T}-L_{O}$ data from ocean and lake observations which represent a much wider range of turbulence-inducing physical processes.

scholarly journals On Geometrical Aspects of Interior Ocean Mixing

2014 ◽  
Vol 44 (8) ◽  
pp. 2164-2175 ◽  
Author(s):  
Trevor J. McDougall ◽  
Sjoerd Groeskamp ◽  
Stephen M. Griffies
Keyword(s):  
Turbulent Mixing ◽  
Diffusion Tensor ◽  
Three Dimensional ◽  
Small Scale ◽  
Theoretical Studies ◽  
Vertical Diffusion ◽  
Mixing Processes ◽  
Spatial Direction ◽  
Dimensional Diffusion ◽  
The Difference

Abstract The small-slope approximation to the full three-dimensional diffusion tensor of epineutral diffusion gives exactly the same tracer flux as the commonly used projected nonorthogonal diffusive flux of layered ocean models and of theoretical studies. The epineutral diffusion achieved by this small-slope approximation is not exactly in the direction of the correct epineutral tracer gradient. That is, the use of the small-slope approximation leads to a very small flux of tracer in a direction in which there is no epineutral gradient of tracer. For (the tracer) temperature or salinity, the difference between the correct epineutral gradient and the small-slope approximation to it is proportional to neutral helicity. The authors also make the point that small-scale turbulent mixing processes act to diffuse tracers isotropically (i.e., the same in each spatial direction) and hence it is strictly a misnomer to call this process “dianeutral diffusion” or “vertical diffusion.” This realization also has implications for the diffusion tensor.

Rotating Horizontal Convection

2021 ◽  
Vol 54 (1) ◽  
Author(s):  
Bishakdatta Gayen ◽  
Ross W. Griffiths
Keyword(s):  
Turbulent Mixing ◽  
Large Scale ◽  
Mixing Efficiency ◽  
Small Scale ◽  
Annual Review ◽  
Publication Date ◽  
Geostrophic Balance ◽  
Horizontal Convection ◽  
Planetary Rotation ◽  
Circumpolar Current

Global differences of temperature and buoyancy flux at the ocean surface are responsible for small-scale convection at high latitudes, global overturning, and the top-to-bottom density difference in the oceans. With planetary rotation the convection also contributes to the large-scale horizontal, geostrophic circulation, and it crucially involves a 3D linkage between the geostrophic circulation and vertical overturning. The governing dynamics of such a surface-forced convective flow are fundamentally different from Rayleigh–Bénard convection, and the role of buoyancy forcing in the oceans is poorly understood. Geostrophic balance adds to the constraints on transport in horizontal convection, as illustrated by experiments, theoretical scaling, and turbulence-resolving simulations for closed (mid-latitude) basins and an annulus or reentrant zonal (circumpolar) channel. In these geometries, buoyancy drives either horizontal mid-latitude gyre recirculations or a strong Antarctic Circumpolar Current, respectively, in addition to overturning. At large Rayleigh numbers the release of available potential energy by convection leads to turbulent mixing with a mixing efficiency approaching unity. Turbulence-resolving models are also revealing the relative roles of wind stress and buoyancy when there is mixed forcing, and in future work they need to include the effects of turbulent mixing due to energy input from tides. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 54 is January 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

scholarly journals Visual Simulation of Detailed Turbulent Water by Preserving the Thin Sheets of Fluid

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 502 ◽  
Author(s):  
Jong-Hyun Kim ◽  
Wook Kim ◽  
Young Kim ◽  
Jung Lee
Keyword(s):  
Turbulent Flows ◽  
Visual Simulation ◽  
Numerical Dissipation ◽  
Small Scale ◽  
Thin Sheets ◽  
Global Flow ◽  
Low Mass ◽  
The Difference ◽  
Water Simulation ◽  
Turbulent Water

When we perform particle-based water simulation, water particles are often increased dramatically because of particle splitting around breaking holes to maintain the thin fluid sheets. Because most of the existing approaches do not consider the volume of the water particles, the water particles must have a very low mass to satisfy the law of the conservation of mass. This phenomenon smears the motion of the water, which would otherwise result in splashing, thereby resulting in artifacts such as numerical dissipation. Thus, we propose a new fluid-implicit, particle-based framework for maintaining and representing the thin sheets and turbulent flows of water. After splitting the water particles, the proposed method uses the ghost density and ghost mass to redistribute the difference in mass based on the volume of the water particles. Next, small-scale turbulent flows are formed in local regions and transferred in a smooth manner to the global flow field. Our results show us the turbulence details as well as the thin sheets of water, thereby obtaining an aesthetically pleasing improvement compared with existing methods.

scholarly journals Analysis of livestock breeders’ perceptions and their adaptation measures to climate change in Morocco‘s arid rangelands

2020 ◽  
Vol 6 (1) ◽  
pp. 1-25
Author(s):  
Wadii Snaibi
Keyword(s):  
Climate Change ◽  
Local Level ◽  
Small Scale ◽  
Climate Data ◽  
Chi Square ◽  
Adaptation Measures ◽  
Significant Difference ◽  
The Difference ◽  
Eastern Morocco ◽  
Climate Analysis

AbstractThe high plateaus of eastern Morocco are already suffering from the adverse impacts of climate change (CC), as the local populations’ livelihoods depend mainly on extensive sheep farming and therefore on natural resources. This research identifies breeders’ perceptions about CC, examines whether they correspond to the recorded climate data and analyses endogenous adaptation practices taking into account the agroecological characteristics of the studied sites and the difference between breeders’ categories based on the size of owned sheep herd. Data on perceptions and adaptation were analyzed using the Chi-square independence and Kruskal-Wallis tests. Climate data were investigated through Mann-Kendall, Pettitt and Buishand tests.Herders’ perceptions are in line with the climate analysis in term of nature and direction of observed climate variations (downward trend in rainfall and upward in temperature). In addition, there is a significant difference in the adoption frequency of adaptive strategies between the studied agroecological sub-zones (χ2 = 14.525, p <.05) due to their contrasting biophysical and socioeconomic conditions, as well as among breeders’ categories (χ2 = 10.568, p < .05) which attributed mainly to the size of sheep flock. Policy options aimed to enhance local-level adaptation should formulate site-specific adaptation programs and prioritise the small-scale herders.

Fluid Flow and Heat Transfer of Liquid Sodium in Small-Scale Heat Sinks With Different Geometries

2021 ◽  
Author(s):  
Mahyar Pourghasemi ◽  
Nima Fathi
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Cross Sections ◽  
Heat Sink ◽  
Volume Ratio ◽  
Heat Sinks ◽  
Liquid Sodium ◽  
Small Scale ◽  
Nusselt Numbers ◽  
The Difference

Abstract 3-D numerical simulations are performed to investigate liquid sodium (Na) flow and the heat transfer within miniature heat sinks with different geometries and hydraulic diameters of less than 5 mm. Two different straight small-scale heat sinks with rectangular and triangular cross-sections are studied in the laminar flow with the Reynolds number up to 1900. The local and average Nusselt numbers are obtained and compared against eachother. At the same surface area to volume ratio, rectangular minichannel heat sink leads to almost 280% higher convective heat transfer rate in comparison with triangular heat sink. It is observed that the difference between thermal efficiencies of rectangular and triangular minichannel heat sinks was independent of flow Reynolds number.

scholarly journals Inhomogeneous Mixing in Lagrangian Cloud Models: Effects on the Production of Precipitation Embryos

2018 ◽  
Vol 76 (1) ◽  
pp. 113-133 ◽  
Author(s):  
Fabian Hoffmann ◽  
Takanobu Yamaguchi ◽  
Graham Feingold
Keyword(s):  
Turbulent Mixing ◽  
Cloud Model ◽  
Small Scale ◽  
New Approach ◽  
Air Masses ◽  
Lagrangian Particles ◽  
Cloud Models ◽  
Large Eddy ◽  
Salutary Effect ◽  
Linear Eddy Model

Abstract Although small-scale turbulent mixing at cloud edge has substantial effects on the microphysics of clouds, most models do not represent these processes explicitly, or parameterize them rather crudely. This study presents a first use of the linear eddy model (LEM) to represent unresolved turbulent mixing at the subgrid scale (SGS) of large-eddy simulations (LESs) with a coupled Lagrangian cloud model (LCM). The method utilizes Lagrangian particles to provide the trajectory of air masses within LES grid boxes, while the LEM is used to redistribute these air masses among the Lagrangian particles based on the local features of turbulence, allowing for the appropriate representation of inhomogeneous to homogeneous SGS mixing. The new approach has the salutary effect of mitigating spurious supersaturations. At low turbulence intensities, as found in the early stages of an idealized bubble cloud simulation, cloud-edge SGS mixing tends to be inhomogeneous and the new approach is shown to be essential for the production of raindrop embryos. At higher turbulence intensities, as found in a field of shallow cumulus, SGS mixing tends to be more homogeneous and the new approach does not significantly alter the results, indicating that a grid spacing of 20 m may be sufficient to resolve all relevant scales of inhomogeneous mixing. In both cases, droplet in-cloud residence times are important for the production of precipitation embryos in the absence of small-scale inhomogeneous mixing, either naturally due to strong turbulence or artificially as a result of coarse resolution or by not using the LEM as an SGS model.

scholarly journals Mixing and chemical reactions in a turbulent liquid mixing layer

1986 ◽  
Vol 170 ◽  
pp. 83-112 ◽  
Author(s):  
M. M. Koochesfahani ◽  
P. E. Dimotakis
Keyword(s):  
Reynolds Number ◽  
Gas Phase ◽  
Turbulent Mixing ◽  
High Speed ◽  
High Reynolds Number ◽  
Schmidt Number ◽  
Mixing Layer ◽  
Entrainment Ratio ◽  
High Reynolds ◽  
Mixed Fluid

An experimental investigation of entrainment and mixing in reacting and non-reacting turbulent mixing layers at large Schmidt number is presented. In non-reacting cases, a passive scalar is used to measure the probability density function (p.d.f.) of the composition field. Chemically reacting experiments employ a diffusion-limited acid–base reaction to directly measure the extent of molecular mixing. The measurements make use of laser-induced fluorescence diagnostics and high-speed, real-time digital image-acquisition techniques.Our results show that the vortical structures in the mixing layer initially roll-up with a large excess of fluid from the high-speed stream entrapped in the cores. During the mixing transition, not only does the amount of mixed fluid increase, but its composition also changes. It is found that the range of compositions of the mixed fluid, above the mixing transition and also throughout the transition region, is essentially uniform across the entire transverse extent of the layer. Our measurements indicate that the probability of finding unmixed fluid in the centre of the layer, above the mixing transition, can be as high as 0.45. In addition, the mean concentration of mixed fluid across the layer is found to be approximately constant at a value corresponding to the entrainment ratio. Comparisons with gas-phase data show that the normalized amount of chemical product formed in the liquid layer, at high Reynolds number, is 50% less than the corresponding quantity measured in the gas-phase case. We therefore conclude that Schmidt number plays a role in turbulent mixing of high-Reynolds-number flows.

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