Effect of shear on Rayleigh-Taylor mixing at small Atwood number

Akula, Bhanesh; Andrews, Malcolm J.; Ranjan, Desh

doi:10.1103/physreve.87.033013

Cited by 23 publications

(28 citation statements)

References 45 publications

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“…A possible explanation could be that, at low Atwood numbers, the effect of shear velocities and secondary instabilities is more representative and could change the rate of evolution of the Rayleigh-Taylor instability. Actually, this has been experimentally studied only in 2013 by Akula, Andrews and Ranjan [15], who found that shear effects in Rayleigh-Taylor instability increase the evolution rate for low Atwood Numbers, in agreement with Fig. 5.…”

Section: Resultssupporting

confidence: 63%

“…The effect of the Atwood number on the rate of evolution of the instability follows the theoretical expression only for high Atwood numbers; deviations at low numbers have been recently found by experimentalists [15]. One possible explanation is the onset of secondary Kelvin-Helmoltz instabilities, which are more representative at low Atwood numbers and could increase the rate of evolution of the Rayleigh-Taylor instability.…”

Section: Discussionmentioning

confidence: 93%

“…from Eq (15),. is on the order of the Mach number; thus, the calculation errors due to the high gradient at the interface are considerably reduced, since the Mach number is in general very small for both RTI and KHI.…”

mentioning

confidence: 94%

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Study of hydrodynamic instabilities with a multiphase lattice Boltzmann model

Velasco

Muñoz

2015

Comptes Rendus. Mécanique

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Rayleigh-Taylor and Kelvin-Helmholtz hydrodynamic instabilities are frequent in many natural and industrial processes, but their numerical simulation is not an easy challenge. This work simulates both instabilities by using a lattice Boltzmann model on multiphase fluids at a liquid-vapour interface, instead of multicomponent systems like the oil-water one. The model, proposed by He, Chen and Zhang (1999) [1] was modified to increase the precision by computing the pressure gradients with a higher order, as proposed by McCracken and Abraham (2005) [2]. The resulting model correctly simulates both instabilities by using almost the same parameter set. It also reproduces the relation γ ∝ √ A between the growing rate γ of the Rayleigh-Taylor instability and the relative density difference between the fluids (known as the Atwood number A), but including also deviations observed in experiments at low density differences. The results show that the implemented model is a useful tool for the study of hydrodynamic instabilities, drawing a sharp interface and exhibiting numerical stability for moderately high Reynolds numbers.

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Section: Resultssupporting

confidence: 63%

Section: Discussionmentioning

confidence: 93%

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Study of hydrodynamic instabilities with a multiphase lattice Boltzmann model

Velasco

Muñoz

2015

Comptes Rendus. Mécanique

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“…The injected fog is used as a light extinction medium for the light coming from the LED panels. Before the experiment, it is ensured that the absorption due to fog is linearly proportional (thin-medium approximation of the Beer-Lambert law (Akula, Andrews & Ranjan 2013)) to the volume fraction of the fog for the camera settings and the fog flow rate using the wedge calibration technique of Banerjee & Andrews (2006). This calibration is necessary for obtaining the volume fraction contours from the visualization.…”

Section: Visualizationmentioning

confidence: 99%

Dynamics of buoyancy-driven flows at moderately high Atwood numbers

Akula

Ranjan

2016

J. Fluid Mech.

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Simultaneous density and velocity turbulence statistics for Rayleigh-Taylor-driven flows at a moderately high Atwood number (A t ) of 0.73 ± 0.02 are obtained using a new convective type or statistically steady gas tunnel facility. Air and air-helium mixture are used as working fluids to create a density difference in this facility, with a thin splitter plate separating the two streams flowing parallel to each other at the same velocity (U = 3 m s −1 ). At the end of the splitter plate, the two miscible fluids are allowed to mix and the instability develops. Visualization and Mie-scattering techniques are used to obtain structure shape, volume fraction profile and mixing height growth information. Particle image velocimetry (PIV) and hot-wire techniques are used to measure planar and point-wise velocity statistics in the developing mixing layer. Asymmetry is evident in the flow field from the Mie-scattering images, with the spike side showing a more gradual decline in volume fraction than the bubble side. The spike side of the mixing layer grows 50 % faster than the bubble side. PIV is implemented for the first time in these moderately high-Atwood-number experiments (A t > 0.1) to obtain root-mean-square velocities, anisotropy tensor components and Reynolds stresses across the mixing layer. Overall, the turbulence statistics measured have shown different scaling compared to small-Atwood-number experiments. However, the total probability density functions for the velocities and turbulent mass fluxes exhibit behaviour similar to small-Atwood-number experiments. Conditional statistics reveal different values for turbulence statistics for spikes and bubbles, unlike small-Atwood-number experiments.

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“…In particular, they showed that turbulent mixing increases significantly either at large scale, by shear, in case of sheared and neutrally stratified flow or at both large and small scales, by buoyancy, in case of unsheared and unstably stratified flow. Akula et al (2013) reported that the mixing layer is initially dominated by shear associated with roller vortices originating from Kelvin-Helmholtz instability and further downstream the mixing layer is governed by buoyancy with vertical plume structures originating from Rayleigh-Taylor instability. Transition occurs within a wide critical bulk Richardson number range (Ri b from −1.5 to −2.5) for an Atwood number A = 0.035 (A = ρ1−ρ2 ρ1+ρ2 where ρ 1 is the density of the heavier fluid and ρ 2 the density of the lighter fluid).…”

Section: Effects Of Stratificationmentioning

confidence: 99%

Turbulent mixing and entrainment in a stratified horizontal plane shear layer: joint velocity–temperature analysis of experimental data

Carlier¹,

Sodjavi²

2016

J. Fluid Mech.

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Buoyancy effects on the turbulent mixing and entrainment processes were analysed in the case of a stratified plane shear layer between two horizontal air flows in conditions leading to relatively low values of the flux Richardson number ($|Ri_{f}|_{max}\simeq 0.02$). Velocity and temperature measurements were made with a single $\times$-wire probe thermo-anemometry technique, using multi-overheat sequences to deliver simultaneous velocity–temperature data at high frequency. The spatial resolution was found to be fine enough, in relation to the dissipative scale and the thermal diffusive scale, to avoid false mixing enhancement in the analysis of the physical mechanisms through velocity–temperature coupling in statistical turbulence quantities. Probability density functions (PDFs) and joint probability density functions (JPDFs) were used to distinguish between the different mechanisms involved in turbulent mixing, namely entrainment, engulfing, nibbling and mixing, and point to the contribution of entrainment in the mixing process. When comparing an unstably stratified configuration to its stably stratified equivalent, no significant difference could be seen in the PDF and JPDF quantities, but a conditional analysis based on temperature thresholding enabled a separation between mixed fluid and two distinct sets of events associated with unmixed fluid entrained from the hot and cold sides of the mixing layer into the mixing layer. This separation allowed a direct calculation of the entrainment velocities on both sides of the mixing layer. A significant increase of the total entrainment could be seen in the case of unstably stratified configuration. The entrainment ratios were compared to their prediction by the Dimotakis model and both a rather good relevance of the model and some need for improvement were found from the comparison. It was hypothesised that the improvement should come from better taking into account the distinct contributions of nibbling and engulfing inside the process of entrainment and mixing.

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Effect of shear on Rayleigh-Taylor mixing at small Atwood number

Cited by 23 publications

References 45 publications

Study of hydrodynamic instabilities with a multiphase lattice Boltzmann model

Study of hydrodynamic instabilities with a multiphase lattice Boltzmann model

Dynamics of buoyancy-driven flows at moderately high Atwood numbers

Turbulent mixing and entrainment in a stratified horizontal plane shear layer: joint velocity–temperature analysis of experimental data

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