Mixing efficiency in controlled exchange flows

2008 ◽  
Vol 600 ◽  
pp. 235-244 ◽  
Author(s):  
TJIPTO PRASTOWO ◽  
ROSS W. GRIFFITHS ◽  
GRAHAM O. HUGHES ◽  
ANDREW McC. HOGG
Keyword(s):  
Turbulent Mixing ◽  
Reynolds Numbers ◽  
Mixing Efficiency ◽  
Scaling Analysis ◽  
Stratified Turbulence ◽  
Exchange Flows ◽  
Maximum Value ◽  
Direct Measurements ◽  
Overall Efficiency ◽  
Good Agreement

Turbulence and mixing are generated by the shear between two counter-flowing layers in hydraulically controlled buoyancy-driven exchange flows through a constriction. From direct measurements of the density distribution and the amount of turbulent mixing in steady laboratory exchange flows we determine the overall efficiency of the mixing. For sufficiently large Reynolds numbers the mixing efficiency is 0.11(±0.01), independent of the aspect ratio and other details of constriction geometry, in good agreement with a scaling analysis. We conclude that the mixing in shear flows of this type has an overall efficiency significantly less than the maximum value widely proposed for stratified turbulence.

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 Mixing efficiency in stratified turbulence

2016 ◽  
Vol 794 ◽  
Author(s):  
A. Maffioli ◽  
G. Brethouwer ◽  
E. Lindborg
Keyword(s):  
Energy Dissipation ◽  
Froude Number ◽  
Mixing Efficiency ◽  
Scaling Analysis ◽  
Stratified Turbulence ◽  
Atmospheric Measurements ◽  
Order Unity ◽  
Mixing Coefficient ◽  
Simple Scaling ◽  
High Reynolds

We consider mixing of the density field in stratified turbulence and argue that, at sufficiently high Reynolds numbers, stationary turbulence will have a mixing efficiency and closely related mixing coefficient described solely by the turbulent Froude number$Fr={\it\epsilon}_{k}/(Nu^{2})$, where${\it\epsilon}_{k}$is the kinetic energy dissipation,$u$is a turbulent horizontal velocity scale and$N$is the Brunt–Väisälä frequency. For$Fr\gg 1$, in the limit of weakly stratified turbulence, we show through a simple scaling analysis that the mixing coefficient scales as${\it\Gamma}\propto Fr^{-2}$, where${\it\Gamma}={\it\epsilon}_{p}/{\it\epsilon}_{k}$and${\it\epsilon}_{p}$is the potential energy dissipation. In the opposite limit of strongly stratified turbulence with$Fr\ll 1$, we argue that${\it\Gamma}$should reach a constant value of order unity. We carry out direct numerical simulations of forced stratified turbulence across a range of$Fr$and confirm that at high$Fr$,${\it\Gamma}\propto Fr^{-2}$, while at low$Fr$it approaches a constant value close to${\it\Gamma}=0.33$. The parametrization of${\it\Gamma}$based on$Re_{b}$due to Shihet al.(J. Fluid Mech., vol. 525, 2005, pp. 193–214) can be reinterpreted in this light because the observed variation of${\it\Gamma}$in their study as well as in datasets from recent oceanic and atmospheric measurements occurs at a Froude number of order unity, close to the transition value$Fr=0.3$found in our simulations.

scholarly journals Coefficient of heterogeneity in turbulent mixing zone

2000 ◽  
Vol 18 (2) ◽  
pp. 207-212 ◽  
Author(s):  
A.S. KOZLOVSKIH ◽  
D.V. NEUVAZHAYEV
Keyword(s):  
Turbulent Mixing ◽  
Molecular Diffusion ◽  
Reynolds Numbers ◽  
Mixing Zone ◽  
Turbulent Diffusion Coefficient ◽  
Dissipative Term ◽  
Developed Turbulence ◽  
Self Similar Solution ◽  
Self Similar ◽  
Good Agreement

The paper considers the equation for heterogeneity coefficient within the turbulent mixing area in the approximation of big Reynolds numbers and small Mach numbers. A mechanism is studied of the heterogeneity coefficient dissipation due to molecular diffusion. The Kolmogorov's hypothesis on developed turbulence is used to calculate a dissipative term. The model presented allows us to take into account the heterogeneity degree in LV- and KE-models of turbulent mixing. A system of equations allowing us to calculate directly the heterogeneity degree is derived for the case of the LV-model with the turbulent diffusion coefficient which is constant over the turbulent mixing area. A self-similar solution is derived for the heterogeneity coefficient which is in good agreement with the results of experiments and direct numerical simulations. The heterogeneity coefficient averaged over the mixing area is shown to depend weakly on the density drop between the mixing materials. Thus, it is kH = 0.25 at the drop n = 1–3, and at the drop n = 20 − kH = 0.23.

Axisymmetric turbulent mass transfer in a circular tube

1969 ◽  
Vol 38 (3) ◽  
pp. 433-455 ◽  
Author(s):  
Alan Quarmby ◽  
R. K. Anand
Keyword(s):  
Mass Transfer ◽  
Velocity Profile ◽  
Circular Tube ◽  
Eddy Diffusivity ◽  
Reynolds Numbers ◽  
Eddy Diffusivities ◽  
Direct Measurements ◽  
Fluid Properties ◽  
Fully Developed Turbulent Flow ◽  
Good Agreement

Solutions of the diffusion equation are obtained for mass transfer in a fully developed turbulent flow in a plain circular tube in two axisymmetric situations. The cases studied are a point source positioned at the centre of the tube and a ring source in the tube wall in which there is a uniform mass flux along a short length of the tube. The purpose of the work is to establish the correctness of the descriptions of the velocity profile and radial eddy diffusivities of mass and momentum in order to provide a firm base from which consideration of the non-axisymmetric situation could proceed.The turbulent velocity profile is deduced from a two-part model based on a sublayer profile and the Von Kármán similarity hypothesis. The radial eddy diffusivity of momentum is described by an expression due to Reichardt and Van Driest and from this the radial eddy diffusivity of mass as a function of radius is obtained by use of a ratio which takes account of fluid properties and the value of the radial eddy diffusivity.The analysis is substantiated by experiments carried out with nitrous oxide, Schmidt number = 0·77, for Reynolds numbers from 20,000 to 130,000. The concentration profiles measured at several axial positions downstream from the source are in good agreement with the analytical solutions in both cases. Direct measurements of the eddy diffusivity of mass and momentum were obtained as added confirmation and also gave good agreement with the theory.

scholarly journals Mixing efficiency in run-down gravity currents

2016 ◽  
Vol 809 ◽  
pp. 691-704 ◽  
Author(s):  
G. O. Hughes ◽  
P. F. Linden
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Gravity Currents ◽  
Mixing Efficiency ◽  
The Novel ◽  
High Reynolds Numbers ◽  
High Reynolds ◽  
Good Agreement

This paper presents measurements of mixing efficiency of the two counter-flowing gravity currents created by symmetric lock exchange in a channel. The novel feature of this work is that the buoyancy Reynolds number of the currents is higher than in previous experiments, so that the mixing is not significantly affected by viscosity. We find that the mixing efficiency asymptotes to 0.08 at high Reynolds numbers. We present a model of the mixing based on the evolution of idealized mean profiles of velocity and density at the interface between the two currents, the results of which are in good agreement with the measurements of mixing efficiency.

scholarly journals Parametric instability and wave turbulence driven by tidal excitation of internal waves

2018 ◽  
Vol 840 ◽  
pp. 498-529 ◽  
Author(s):  
Thomas Le Reun ◽  
Benjamin Favier ◽  
Michael Le Bars
Keyword(s):  
Internal Waves ◽  
Parametric Instability ◽  
Reynolds Numbers ◽  
Temporal Analysis ◽  
Base Flow ◽  
Wave Turbulence ◽  
Mixing Efficiency ◽  
Stratified Turbulence ◽  
Frequency Branch ◽  
Spatio Temporal

We investigate the stability of stratified fluid layers undergoing homogeneous and periodic tidal deformation. We first introduce a local model which allows us to study velocity and buoyancy fluctuations in a Lagrangian domain periodically stretched and sheared by the tidal base flow. While keeping the key physical ingredients only, such a model is efficient in simulating planetary regimes where tidal amplitudes and dissipation are small. With this model, we prove that tidal flows are able to drive parametric subharmonic resonances of internal waves, in a way reminiscent of the elliptical instability in rotating fluids. The growth rates computed via direct numerical simulations (DNSs) are in very good agreement with Wentzel–Kramers–Brillouin analysis and Floquet theory. We also investigate the turbulence driven by this instability mechanism. With spatio-temporal analysis, we show that it is weak internal wave turbulence occurring at small Froude and buoyancy Reynolds numbers. When the gap between the excitation and the Brunt–Väisälä frequencies is increased, the frequency spectrum of this wave turbulence displays a $-2$ power law reminiscent of the high-frequency branch of the Garett and Munk spectrum (Geophys. Fluid Dyn., vol. 3 (1), 1972, pp. 225–264) which has been measured in the oceans. In addition, we find that the mixing efficiency is altered compared to what is computed in the context of DNS of stratified turbulence excited at small Froude and large buoyancy Reynolds numbers and is consistent with a superposition of waves.

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

Heat Transfer in a Surfactant Drag-Reducing Solution—A Comparison With Predictions for Laminar Flow

2005 ◽  
Vol 128 (6) ◽  
pp. 557-563 ◽  
Author(s):  
Paul L. Sears ◽  
Libing Yang
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Reynolds Numbers ◽  
High Heat ◽  
High Heat Flux ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Nusselt Numbers ◽  
Drag Reducing Additive ◽  
Good Agreement

Heat transfer coefficients were measured for a solution of surfactant drag-reducing additive in the entrance region of a uniformly heated horizontal cylindrical pipe with Reynolds numbers from 25,000 to 140,000 and temperatures from 30to70°C. In the absence of circumferential buoyancy effects, the measured Nusselt numbers were found to be in good agreement with theoretical results for laminar flow. Buoyancy effects, manifested as substantially higher Nusselt numbers, were seen in experiments carried out at high heat flux.

Predictions of the Effect of Roughness on Heat Transfer From Turbine Airfoils

1998 ◽  
Author(s):  
Anil K. Tolpadi ◽  
Michael E. Crawford
Keyword(s):  
Heat Transfer ◽  
Side Surface ◽  
Suction Side ◽  
Reynolds Numbers ◽  
Surface Finishing ◽  
Transfer Coefficients ◽  
Average Roughness ◽  
Wide Range ◽  
Turbine Airfoils ◽  
Good Agreement

The heat transfer and aerodynamic performance of turbine airfoils are greatly influenced by the gas side surface finish. In order to operate at higher efficiencies and to have reduced cooling requirements, airfoil designs require better surface finishing processes to create smoother surfaces. In this paper, three different cast airfoils were analyzed: the first airfoil was grit blasted and codep coated, the second airfoil was tumbled and aluminide coated, and the third airfoil was polished further. Each of these airfoils had different levels of roughness. The TEXSTAN boundary layer code was used to make predictions of the heat transfer along both the pressure and suction sides of all three airfoils. These predictions have been compared to corresponding heat transfer data reported earlier by Abuaf et al. (1997). The data were obtained over a wide range of Reynolds numbers simulating typical aircraft engine conditions. A three-parameter full-cone based roughness model was implemented in TEXSTAN and used for the predictions. The three parameters were the centerline average roughness, the cone height and the cone-to-cone pitch. The heat transfer coefficient predictions indicated good agreement with the data over most Reynolds numbers and for all airfoils-both pressure and suction sides. The transition location on the pressure side was well predicted for all airfoils; on the suction side, transition was well predicted at the higher Reynolds numbers but was computed to be somewhat early at the lower Reynolds numbers. Also, at lower Reynolds numbers, the heat transfer coefficients were not in very good agreement with the data on the suction side.

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.

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