Mixing and reaction in curved liquid shear layers

1997 ◽  
Vol 334 ◽  
pp. 381-409 ◽  
Author(s):  
P. S. KARASSO ◽  
M. G. MUNGAL
Keyword(s):  
Growth Rate ◽  
Shear Layers ◽  
Mixing Efficiency ◽  
Concentration Profiles ◽  
Scalar Mixing ◽  
Product Concentration ◽  
Chemical Product ◽  
Unstable Layer ◽  
Mixed Fluid ◽  
Liquid Shear

The concentration field of mixing layers subject to stabilizing and destabilizing streamwise curvature was investigated at post-mixing-transition conditions. A set of operating conditions was implemented, identical to those at which straight layers were previously investigated in the same facility, in order to compare the effects of hydrodynamic instabilities upon scalar mixing. Quantitative imaging of planar laser-induced fluorescence was used for (i) passive scalar measurements, and (ii) chemical product measurements. Similar to the straight mixing layer, the results for the curved layers show that beyond the mixing transition the layer continues to evolve, and undergoes a small change in its scalar structure. At conditions just past the mixing transition both stable and unstable layers have average mixed-fluid compositions which are uniform across the layer, and average chemical product concentration profiles which are symmetric. At more fully developed conditions, the scalar field evolved: the average mixed-fluid concentration developed a small lateral variation, while the chemical product concentration profiles became asymmetric. Similar to the straight layer, the mixture-fraction PDF is believed to be of the tilted type for the most fully developed layer examined, with the marching PDF being a poor representation. Consistent with previous investigations, the growth rate of the unstable layer was found to be higher than that of straight or stable layers. The most important result is that the measured mixing efficiency of all the layers (curved and straight) was found to be the same: both the total mixed-fluid composition, and the volume fraction of mixed fluid were the same for all unstable, stable, and straight layers. The amount of mixed fluid (and of chemical product formed) was larger for the unstable layer, but always in a fixed proportion to the layer's thickness. The lack of increase in the mixing efficiency for the unstable layer is surprising, given that previous hydrodynamic measurements had shown enhanced turbulent transport for the unstable case. Thus, for all liquid shear layers studied, the rate of scalar mixing appears to be directly proportional to the entrainment rate (which essentially determines the layer's growth rate), and not to any hydrodynamic measures.

Scalar mixing and reaction in plane liquid shear layers

1996 ◽  
Vol 323 ◽  
pp. 23-63 ◽  
Author(s):  
P. S. Karasso ◽  
M. G. Mungal
Keyword(s):  
Reynolds Number ◽  
Mixture Fraction ◽  
Initial Boundary ◽  
Passive Scalar ◽  
Asymptotic State ◽  
Concentration Profiles ◽  
Product Concentration ◽  
Chemical Product ◽  
Fluid Concentration ◽  
Mixed Fluid

The scalar (concentration) field of two-dimensional liquid mixing layers was investigated at post-mixing-transition conditions. The planar laser-induced fluorescence technique was used for passive scalar measurements, and for chemical product measurements. Following the approach of Koochesfahani & Dimotakis (1986), the chemical product results were used to make resolution-free estimates of mixed-fluid quantities, thus providing a check on the accuracy of the passive scalar measurements. The operating conditions were systematically varied to study the effect of various parameters (Reynolds number, speed ratio, and initial boundary-layer momentum thickness) on the structure of the layer. At conditions which are just past the mixing transition, the study essentially duplicated the results obtained by Koochesfahani & Dimotakis: the chemical-product concentration profiles at high- and low-stoichio-metric ratios (flip experiments) were symmetric and the average concentration of mixed-fluid was uniform across the layer. However, when the layer was pushed to more fully developed conditions, its scalar field evolved to an asymptotic state: the two flip chemical-product concentration profiles developed modest asymmetries, and the average mixed-fluid concentration developed a small variation across the layer, but the change was less than that observed in gases. Based on the chemical reaction data, we infer that the mixture fraction probability density function (p.d.f.) for the fully-developed liquid layer evolves from a ‘non-marching’ type to a ‘tilted’ type. Despite the observed evolution, the average mixed-fluid concentration remained fixed for all the layers past the mixing transition, while the total mixed-fluid probability (the total amount of mixed fluid normalized by the layer's width) showed only a very slight increasing tendency as the layer reached fully developed conditions. The mixture fraction p.d.f., measured by the passive scalar approach, is shown and discussed for a broad range of cases. While it overpredicts the amount of mixing, it showed a qualitatively-correct ‘non-marching’ character initially, but evolved to a qualitatively-incorrect ‘marching’ character at the asymptotic state. The reasons for the poor estimation of the p.d.f. by the passive scalar approach, at fully developed conditions, are attributed to changes in the flow and lack of resolution and suggests caution when using such measures. Furthermore, the study also showed that the Reynolds number alone is inadequate to characterize the state of the layer. A different parameter (the ‘pairing parameter’), which accounts for the initial boundary layers and scales with the number of vortex mergings, was found to better explain the evolution in the structure of the scalar field.

scholarly journals Incompressible variable-density turbulence in an external acceleration field

2017 ◽  
Vol 827 ◽  
pp. 506-535 ◽  
Author(s):  
Ilana Gat ◽  
Georgios Matheou ◽  
Daniel Chung ◽  
Paul E. Dimotakis
Keyword(s):  
Growth Rate ◽  
Turbulent Flow ◽  
Shear Layers ◽  
Variable Density ◽  
Fluid Composition ◽  
Turbulent Regime ◽  
Low Density ◽  
Acceleration Field ◽  
Density Ratios ◽  
Mixed Fluid

Dynamics and mixing of a variable-density turbulent flow subject to an externally imposed acceleration field in the zero-Mach-number limit are studied in a series of direct numerical simulations. The flow configuration studied consists of alternating slabs of high- and low-density fluid in a triply periodic domain. Density ratios in the range of $1.05\leqslant R\equiv \unicode[STIX]{x1D70C}_{1}/\unicode[STIX]{x1D70C}_{2}\leqslant 10$ are investigated. The flow produces temporally evolving shear layers. A perpendicular density–pressure gradient is maintained in the mean as the flow evolves, with multi-scale baroclinic torques generated in the turbulent flow that ensues. For all density ratios studied, the simulations attain Reynolds numbers at the beginning of the fully developed turbulence regime. An empirical relation for the convection velocity predicts the observed entrainment-ratio and dominant mixed-fluid composition statistics. Two mixing-layer temporal evolution regimes are identified: an initial diffusion-dominated regime with a growth rate ${\sim}t^{1/2}$ followed by a turbulence-dominated regime with a growth rate ${\sim}t^{3}$. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted (‘non-marching’) hump, corresponding to the most probable mole fraction. The shear layers preferentially entrain low-density fluid by volume at all density ratios, which is reflected in the mixed-fluid composition.

Sediment-laden fresh water above salt water: linear stability analysis

2011 ◽  
Vol 691 ◽  
pp. 279-314 ◽  
Author(s):  
P. Burns ◽  
E. Meiburg
Keyword(s):  
Growth Rate ◽  
Linear Stability ◽  
Fresh Water ◽  
Settling Velocity ◽  
Interface Thickness ◽  
Particle Settling ◽  
Salinity Field ◽  
Unstable Layer ◽  
Stability Results ◽  
Double Diffusive

AbstractWhen a layer of particle-laden fresh water is placed above clear, saline water, both Rayleigh–Taylor and double diffusive fingering instabilities may arise. For quasi-steady base profiles, we obtain linear stability results for such situations by means of a rational spectral approximation method with adaptively chosen grid points, which is able to resolve multiple steep gradients in the base state density profile. In the absence of salinity and for a step-like concentration profile, the dominant parameter is the ratio of the particle settling velocity to the viscous velocity scale. As long as this ratio is small, particle settling has a negligible influence on the instability growth. However, when the particles settle more rapidly than the instability grows, the growth rate decreases inversely proportional to the settling velocity. This damping effect is a result of the smearing of the vorticity field, which in turn is caused by the deposition of vorticity onto the fluid elements passing through the interface between clear and particle-laden fluid. In the presence of a stably stratified salinity field, this picture changes dramatically. An important new parameter is the ratio of the particle settling velocity to the diffusive spreading velocity of the salinity, or alternatively the ratio of the unstable layer thickness to the diffusive interface thickness of the salinity profile. As long as this quantity does not exceed unity, the instability of the system and the most amplified wavenumber are primarily determined by double diffusive effects. In contrast to situations without salinity, particle settling can have a destabilizing effect and significantly increase the growth rate. Scaling laws obtained from the linear stability results are seen to be largely consistent with earlier experimental observations and theoretical arguments put forward by other authors. For unstable layer thicknesses much larger than the salinity interface thickness, the particle and salinity interfaces become increasingly decoupled, and the dominant instability mode becomes Rayleigh–Taylor-like, centred at the lower boundary of the particle-laden flow region.

Increasing the Passive Scalar Mixing Quality of Jets in Crossflow With Fluidics Actuators

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Arnaud Lacarelle ◽  
Christian O. Paschereit
Keyword(s):  
High Speed ◽  
Passive Scalar ◽  
Mixing Efficiency ◽  
Scalar Mixing ◽  
Jet In Crossflow ◽  
Mixing Quality ◽  
Single Jet ◽  
Pulsating Jets ◽  
The One

Jets in crossflow are widely used in the industry for homogenization or cooling tasks. Recently, pulsating jets have been investigated as a mean to increase the scalar mixing efficiency of such configurations, whether for a single jet or for an array of jets. To avoid the disadvantages of mechanically actuated flows (costs, maintenance), a new injector based on a fluidics oscillator has been designed. Four injectors have been implemented in a generical jet in crossflow configuration and the mixing efficiency of the setup was compared with the one of the same setup equiped with standard non oscillating jets. With help of high-speed concentration measurement technique, the scalar mixing quality of both setups was measured at three positions downstream of the injection plane. In all the cases tested, the fluidics injectors present a better temporal homogenization, characterized by the Danckwerts unmixedness criterion, than the standard jets. For a defined mixing quality, a decrease of the mixing length by approximately 50% can be achieved with the fluidics injectors. Furthermore, the new injectors exhibit a mixing quality which is less sensitive to variations of the jet to crossflow momentum. The flapping motion of the fluidics injectors induces a wider azimuthal spreading of the fluidics jets immediately downstream of the injection location. This increases the macro- and micro-mixing phenomea which lead then to the high gains in mixing quality. It is thus demonstrated that fluidics oscillators present a strong potential to improve the passive scalar homogenization of jet in crossflow configurations.

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.

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