scholarly journals Vortex-ring-induced stratified mixing: mixing model

2017 ◽  
Vol 837 ◽  
pp. 129-146 ◽  
Author(s):  
Jason Olsthoorn ◽  
Stuart B. Dalziel
Keyword(s):  
Vortex Ring ◽  
Turbulent Mixing ◽  
Quantitative Agreement ◽  
Vortex Rings ◽  
Mixing Efficiency ◽  
Mean Flow ◽  
Density Profiles ◽  
One Dimensional ◽  
Physical Experiments ◽  
Dynamical Features

The study of vortex-ring-induced mixing has been significant for understanding stratified turbulent mixing in the absence of a mean flow. Renewed interest in this topic has prompted the development of a one-dimensional model for the evolution of a stratified system in the context of isolated mixing events. This model is compared to numerical simulations and physical experiments of vortex rings interacting with a stratification. Qualitative agreement between the evolution of the density profiles is observed, along with close quantitative agreement of the mixing efficiency. This model highlights the key dynamical features of such isolated mixing events.

scholarly journals Vortex-ring-induced stratified mixing

2015 ◽  
Vol 781 ◽  
pp. 113-126 ◽  
Author(s):  
Jason Olsthoorn ◽  
Stuart B. Dalziel
Keyword(s):  
Energy Balance ◽  
Vortex Ring ◽  
Turbulent Mixing ◽  
Richardson Number ◽  
Stratified Flows ◽  
Vortex Rings ◽  
Mixing Efficiency ◽  
Responsible Mechanism ◽  
Mixing Regime ◽  
Insight Into

There is tantalizing evidence that some mechanically driven stratified flows tend towards a state of constant mixing efficiency. We provide insight into the energy balance leading to the constant mixing efficiency and isolate the responsible mechanism. The work presented demonstrates an important mixing efficiency regime for periodically forced externally driven stratified flows. Externally forced stratified turbulent mixing is often characterized by the associated eddies within the flow, which are the dominant mixing mechanism (Turner, J. Fluid Mech., vol. 173, 1986, pp. 431–471). Here, we study mixing induced by vortex rings in order to characterize the mixing induced by an individual eddy. By generating a long sequence of independent vortex-ring mixing events in a density-stratified fluid with a sharp interface, we determine the mixing efficiency of each ring. After an initial adjustment phase, we find that the mixing efficiency of each vortex ring is independent of the Richardson number. By studying the mixing mechanism here, we demonstrate consistent features of a volumetrically confined, periodically forced external mixing regime.

Circulation Generation and Vortex Ring Formation by Conic Nozzles

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
Moshe Rosenfeld ◽  
Kakani Katija ◽  
John O. Dabiri
Keyword(s):  
Vortex Ring ◽  
Vortex Generator ◽  
Ring Formation ◽  
Vortex Rings ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Vortex Ring Formation ◽  
Exit Nozzle ◽  
Two Dimensional Flow

Vortex rings are one of the fundamental flow structures in nature. In this paper, the generation of circulation and vortex rings by a vortex generator with a static converging conic nozzle exit is studied numerically. Conic nozzles can manipulate circulation and other flow invariants by accelerating the flow, increasing the Reynolds number, and by establishing a two-dimensional flow at the exit. The increase in the circulation efflux is accompanied by an increase in the vortex circulation. A novel normalization method is suggested to differentiate between two contributions to the circulation generation: a one-dimensional slug-type flow contribution and an inherently two-dimensional flow contribution. The one-dimensional contribution to the circulation increases with the square of the centerline exit velocity, while the two-dimensional contribution increases linearly with the decrease in the exit diameter. The two-dimensional flow contribution to the circulation production is not limited to the impulsive initiation of the flow only (as in straight tube vortex generators), but it persists during the entire ejection. The two-dimensional contribution can reach as much as 44% of the total circulation (in the case of an orifice). The present study offers evidences on the importance of the vortex generator geometry, and in particular, the exit configuration on the emerging flow, circulation generation, and vortex ring formation. It is shown that both total and vortex ring circulations can be controlled to some extent by the shape of the exit nozzle.

scholarly journals Three-dimensional visualization of the interaction of a vortex ring with a stratified interface

2017 ◽  
Vol 820 ◽  
pp. 549-579 ◽  
Author(s):  
Jason Olsthoorn ◽  
Stuart B. Dalziel
Keyword(s):  
Vortex Ring ◽  
Time Scale ◽  
Richardson Number ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Vortex Rings ◽  
Mixing Efficiency ◽  
Two Dimensional ◽  
Displacement Mode ◽  
Dimensional Instability

The study of vortex-ring-induced stratified mixing has long played a key role in understanding externally forced stratified turbulent mixing. While several studies have investigated the dynamical evolution of such a system, this study presents an experimental investigation of the mechanical evolution of these vortex rings, including the stratification-modified three-dimensional instability. The aim of this paper is to understand how vortex rings induce mixing of the density field. We begin with a discussion of the Reynolds and Richardson number dependence of the vortex-ring interaction using two-dimensional particle image velocimetry measurements. Then, through the use of modern imaging techniques, we reconstruct from an experiment the full three-dimensional time-resolved velocity field of a vortex ring interacting with a stratified interface. This work agrees with many of the previous two-dimensional experimental studies, while providing insight into the three-dimensional instabilities of the system. Observations indicate that the three-dimensional instability has a similar wavenumber to that found for the unstratified vortex-ring instability at later times. We determine that the time scale associated with this instability growth has an inverse Richardson number dependence. Thus, the time scale associated with the instability is different from the time scale of interface recovery, possibly explaining the significant drop in mixing efficiency at low Richardson numbers. The structure of the underlying instability is a simple displacement mode of the vorticity field.

scholarly journals Efficient mixing in stratified flows: experimental study of a Rayleigh–Taylor unstable interface within an otherwise stable stratification

2014 ◽  
Vol 756 ◽  
pp. 1027-1057 ◽  
Author(s):  
Megan S. Davies Wykes ◽  
Stuart B. Dalziel
Keyword(s):  
Turbulent Mixing ◽  
Laboratory Experiments ◽  
Functional Form ◽  
Salt Water ◽  
Stable Stratification ◽  
Mixing Efficiency ◽  
Final States ◽  
Density Profiles ◽  
Rayleigh Taylor Instability ◽  
Good Agreement

AbstractBoussinesq salt-water laboratory experiments of Rayleigh–Taylor instability (RTI) can achieve mixing efficiencies greater than 0.75 when the unstable interface is confined between two stable stratifications. This is much greater than that found when RTI occurs between two homogeneous layers when the mixing efficiency has been found to approach 0.5. Here, the mixing efficiency is defined as the ratio of energy used in mixing compared with the energy available for mixing. If the initial and final states are quiescent then the mixing efficiency can be calculated from experiments by comparison of the corresponding density profiles. Varying the functional form of the confining stratifications has a strong effect on the mixing efficiency. We derive a buoyancy-diffusion model for the rate of growth of the turbulent mixing region, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\dot{h} = 2 \sqrt{\alpha A g h}$ (where $A = A(h)$ is the Atwood number across the mixing region when it extends a height $h$, $g$ is acceleration due to gravity and $\alpha $ is a constant). This model shows good agreement with experiments when the value of the constant $\alpha $ is set to 0.07, the value found in experiments of RTI between two homogeneous layers (where the height of the turbulent mixing region increases as $h =\alpha A g t^2$, an expression which is equivalent to that derived for $\dot{h}$).

scholarly journals How we compute N matters to estimates of mixing in stratified flows

2017 ◽  
Vol 831 ◽  
Author(s):  
Robert S. Arthur ◽  
Subhas K. Venayagamoorthy ◽  
Jeffrey R. Koseff ◽  
Oliver B. Fringer
Keyword(s):  
Turbulent Mixing ◽  
Numerical Models ◽  
Density Field ◽  
Stratified Flows ◽  
Mixing Efficiency ◽  
Buoyancy Frequency ◽  
Simulation Data ◽  
Density Profiles ◽  
Formula One ◽  
Vertical Density

Most commonly used models for turbulent mixing in the ocean rely on a background stratification against which turbulence must work to stir the fluid. While this background stratification is typically well defined in idealized numerical models, it is more difficult to capture in observations. Here, a potential discrepancy in ocean mixing estimates due to the chosen calculation of the background stratification is explored using direct numerical simulation data of breaking internal waves on slopes. Two different methods for computing the buoyancy frequency $N$, one based on a three-dimensionally sorted density field (often used in numerical models) and the other based on locally sorted vertical density profiles (often used in the field), are used to quantify the effect of $N$ on turbulence quantities. It is shown that how $N$ is calculated changes not only the flux Richardson number $R_{f}$, which is often used to parameterize turbulent mixing, but also the turbulence activity number or the Gibson number $Gi$, leading to potential errors in estimates of the mixing efficiency using $Gi$-based parameterizations.

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.

Simple explicit model of liquid mean flow in region above axial impeller

1985 ◽  
Vol 50 (11) ◽  
pp. 2396-2410
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Vortex Flow ◽  
Flow Model ◽  
Quantitative Agreement ◽  
Mean Flow ◽  
Flat Bottom ◽  
Proposed Model ◽  
Minimum Number ◽  
The Mean ◽  
Model Equations ◽  
Radial Circulation

The study describes a method of modelling axial-radial circulation in a tank with an axial impeller and radial baffles. The proposed model is based on the analytical solution of the equation for vortex transport in the mean flow of turbulent liquid. The obtained vortex flow model is tested by the results of experiments carried out in a tank of diameter 1 m and with the bottom in the shape of truncated cone as well as by the data published for the vessel of diameter 0.29 m with flat bottom. Though the model equations are expressed in a simple form, good qualitative and even quantitative agreement of the model with reality is stated. Apart from its simplicity, the model has other advantages: minimum number of experimental data necessary for the completion of boundary conditions and integral nature of these data.

Model of vortex flow of charge in a vessel with turbine impeller

1987 ◽  
Vol 52 (8) ◽  
pp. 1888-1904
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Theoretical Data ◽  
Eddy Diffusion ◽  
Quantitative Agreement ◽  
Creeping Flow ◽  
Model Parameters ◽  
Mean Flow ◽  
Two Dimensional Flow ◽  
Vorticity Transport

A theoretical model is described of the mean two-dimensional flow of homogeneous charge in a flat-bottomed cylindrical tank with radial baffles and six-blade turbine disc impeller. The model starts from the concept of vorticity transport in the bulk of vortex liquid flow through the mechanism of eddy diffusion characterized by a constant value of turbulent (eddy) viscosity. The result of solution of the equation which is analogous to the Stokes simplification of equations of motion for creeping flow is the description of field of the stream function and of the axial and radial velocity components of mean flow in the whole charge. The results of modelling are compared with the experimental and theoretical data published by different authors, a good qualitative and quantitative agreement being stated. Advantage of the model proposed is a very simple schematization of the system volume necessary to introduce the boundary conditions (only the parts above the impeller plane of symmetry and below it are distinguished), the explicit character of the model with respect to the model parameters (model lucidity, low demands on the capacity of computer), and, in the end, the possibility to modify the given model by changing boundary conditions even for another agitating set-up with radially-axial character of flow.

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.

Transport processes between fluids and clouds of suspended particles: some exact solutions

1957 ◽  
Vol 242 (1231) ◽  
pp. 430-443 ◽  
Keyword(s):  
Exact Solutions ◽  
Turbulent Mixing ◽  
Liquid Fuel ◽  
Transport Processes ◽  
Dimensional System ◽  
Unsteady Heat Transfer ◽  
One Dimensional ◽  
Homogeneous Reactor ◽  
Fourier Equation ◽  
Gas Component

The paper relates to processes such as the burning of pulverized solid fuel and of liquid fuel sprays, absorption of a gas component by a solvent spray, etc., and takes account of convection and turbulent mixing of the cloud. The Eulerian equation of conservation for the steady process is shown to be transformable into the Fourier equation for unsteady heat transfer in a flowing medium. Exact solutions are given for a one-dimensional system, an axially symmetrical system, and the steady-flow homogeneous reactor. Numerical methods are indicated for more complex systems, and the possibility of solution by means of an analogue is pointed out.

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