6 results
Dynamics of multilayer Rayleigh–Taylor instability at moderately high Atwood numbers
- Prasoon Suchandra, Devesh Ranjan
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- Journal:
- Journal of Fluid Mechanics / Volume 974 / 10 November 2023
- Published online by Cambridge University Press:
- 03 November 2023, A35
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This paper investigates the multilayer Rayleigh–Taylor instability (RTI) using statistically stationary experiments conducted in a gas tunnel. Employing diagnostics such as particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF), we make simultaneous velocity–density measurements to study how dynamics and mixing are linked in this variable density flow. Experiments are conducted in a newly built, blow-down three-layer gas tunnel facility. Mixing between three gas streams is studied, where the top and bottom streams are comprised of air, and the middle stream is an air–helium mixture. Shear is minimized between these streams by matching their inlet velocities. The four experimental conditions investigated here consist of two different density ratios (Atwood numbers 0.3 and 0.6), each investigated at two instability development times (or equivalently, two streamwise locations), and all experiments are with the same middle stream thickness of 3 cm. The growth of the middle layer is measured using laser-based planar Mie scattering visualization. The mixing width is found to grow linearly with time at late times. Various quantitative measures of molecular mixing indicate a very high degree of molecular mixing at late times in the multilayer RTI flow. The vertical turbulent mass flux $a_y$ is calculated. In addition to mostly negative values of $a_y$, typical of buoyancy-dominated flows due to negative correlation between velocity and density fluctuations, positive regions are also observed in profiles of $a_y$ due to entrainment and erosion at the lower edge of the mixing region. Global energy budgets are calculated for the multilayer RTI flow at late times and it is found that the majority of potential energy released has been dissipated due to viscous effects, and a large value of mixing efficiency ($\sim$60 %) is observed.
Turbulent mixing and trajectories of jets in a supersonic cross-flow with different injectants
- Dan Fries, Devesh Ranjan, Suresh Menon
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- Journal:
- Journal of Fluid Mechanics / Volume 911 / 25 March 2021
- Published online by Cambridge University Press:
- 01 February 2021, A45
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We investigate flow fields and trajectories of sonic jets in a supersonic cross-flow with different injectant properties. The cross-flow is held at a fixed condition with Mach number 1.71, static temperature $\sim$375 K and static pressure $\sim$76 kPa. Jet conditions cover momentum flux ratios $J$ from 1 to 6, molecular weights from $\sim$4 to 44 g mol$^{-1}$ and specific heat ratios from $\sim$1.24 to 1.66. Mie-scattering images are used to study turbulent mixing and trajectory development. Qualitative trends suggest that, at $J=4\text {--}6$, the convective Mach number concept applies as discussed in previous literature. At lower $J$, however, trends for changing molecular weights seem to reverse and the boundary layer might influence turbulent mixing. Analytically estimated jet velocities suggest the suppression of hydrodynamic instabilities changes at different rates for different injectants, as $J$ increases. A newly developed, semi-empirical jet trajectory scaling explicitly considers the momentum flux ratio, boundary layer effects and the existence of the jet bow shock. For validation, this scaling is applied to our trajectory data and those of existing literature, extending the covered parameter space. Quantifying the degree of trajectory correlation shows the scaling is specifically relevant at $J \leq 6$ in this study, where the boundary layer and bow shock influence are important. On the other hand, at higher $J$ and for thin boundary layers, the momentum flux ratio plays a more dominant role. The results in this study can guide the design of injection systems for supersonic applications and improve prediction of jet trajectories.
The transition to turbulence in shock-driven mixing: effects of Mach number and initial conditions
- Mohammad Mohaghar, John Carter, Gokul Pathikonda, Devesh Ranjan
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- Journal:
- Journal of Fluid Mechanics / Volume 871 / 25 July 2019
- Published online by Cambridge University Press:
- 24 May 2019, pp. 595-635
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The effects of incident shock strength on the mixing transition in the Richtmyer–Meshkov instability (RMI) are experimentally investigated using simultaneous density–velocity measurements. This effort uses a shock with an incident Mach number of 1.9, in concert with previous work at Mach 1.55 (Mohaghar et al., J. Fluid Mech., vol. 831, 2017 pp. 779–825) where each case is followed by a reshock wave. Single- and multi-mode interfaces are used to quantify the effect of initial conditions on the evolution of the RMI. The interface between light and heavy gases ($\text{N}_{2}/\text{CO}_{2}$, Atwood number, $A\approx 0.22$; amplitude to wavelength ratio of 0.088) is created in an inclined shock tube at $80^{\circ }$ relative to the horizontal, resulting in a predominantly single-mode perturbation. To investigate the effects of initial perturbations on the mixing transition, a multi-mode inclined interface is also created via shear and buoyancy superposed on the dominant inclined perturbation. The evolution of mixing is investigated via the density fields by computing mixed mass and mixed-mass thickness, along with mixing width, mixedness and the density self-correlation (DSC). It is shown that the amount of mixing is dependent on both initial conditions and incident shock Mach number. Evolution of the density self-correlation is discussed and the relative importance of different DSC terms is shown through fields and spanwise-averaged profiles. The localized distribution of vorticity and the development of roll-up features in the flow are studied through the evolution of interface wrinkling and length of the interface edge, which indicate that the vorticity concentration shows a strong dependence on the Mach number. The contribution of different terms in the Favre-averaged Reynolds stress is shown, and while the mean density-velocity fluctuation correlation term, $\langle \unicode[STIX]{x1D70C}\rangle \langle u_{i}^{\prime }u_{j}^{\prime }\rangle$, is dominant, a high dependency on the initial condition and reshock is observed for the turbulent mass-flux term. Mixing transition is analysed through two criteria: the Reynolds number (Dimotakis, J. Fluid Mech., vol. 409, 2000, pp. 69–98) for mixing transition and Zhou (Phys. Plasmas, vol. 14 (8), 2007, 082701 for minimum state) and the time-dependent length scales (Robey et al., Phys. Plasmas, vol. 10 (3), 2003, 614622; Zhou et al., Phys. Rev. E, vol. 67 (5), 2003, 056305). The Reynolds number threshold is surpassed in all cases after reshock. In addition, the Reynolds number is around the threshold range for the multi-mode, high Mach number case ($M\sim 1.9$) before reshock. However, the time-dependent length-scale threshold is surpassed by all cases only at the latest time after reshock, while all cases at early times after reshock and the high Mach number case at the latest time before reshock fall around the threshold. The scaling analysis of the turbulent kinetic energy spectra after reshock at the latest time, at which mixing transition analysis suggests that an inertial range has formed, indicates power scaling of $-1.8\pm 0.05$ for the low Mach number case and $-2.1\pm 0.1$ for the higher Mach number case. This could possibly be related to the high anisotropy observed in this flow resulting from strong, large-scale streamwise fluctuations produced by large-scale shear.
Evaluation of turbulent mixing transition in a shock-driven variable-density flow
- Mohammad Mohaghar, John Carter, Benjamin Musci, David Reilly, Jacob McFarland, Devesh Ranjan
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- Journal:
- Journal of Fluid Mechanics / Volume 831 / 25 November 2017
- Published online by Cambridge University Press:
- 20 October 2017, pp. 779-825
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The effect of initial conditions on transition to turbulence is studied in a variable-density shock-driven flow. Richtmyer–Meshkov instability (RMI) evolution of fluid interfaces with two different imposed initial perturbations is observed before and after interaction with a second shock reflected from the end wall of a shock tube (reshock). The first perturbation is a predominantly single-mode long-wavelength interface which is formed by inclining the entire tube to 80$^{\circ }$ relative to the horizontal, yielding an amplitude-to-wavelength ratio, $\unicode[STIX]{x1D702}/\unicode[STIX]{x1D706}=0.088$, and thus can be considered as half the wavelength of a triangular wave. The second interface is multi-mode, and contains additional shorter-wavelength perturbations due to the imposition of shear and buoyancy on the inclined perturbation of the first case. In both cases, the interface consists of a nitrogen-acetone mixture as the light gas over carbon dioxide as the heavy gas (Atwood number, $A\sim 0.22$) and the shock Mach number is $M\approx 1.55$. The initial condition was characterized through Proper Orthogonal Decomposition and density energy spectra from a large set of initial condition images. The evolving density and velocity fields are measured simultaneously using planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) techniques. Density, velocity, and density–velocity cross-statistics are calculated using ensemble averaging to investigate the effects of additional modes on the mixing and turbulence quantities. The density and velocity data show that a distinct memory of the initial conditions is maintained in the flow before interaction with reshock. After reshock, the influence of the long-wavelength inclined perturbation present in both initial conditions is still apparent, but the distinction between the two cases becomes less evident as smaller scales are present even in the single-mode case. Several methods are used to calculate the Reynolds number and turbulence length scales, which indicate a transition to a more turbulent state after reshock. Further evidence of transition to turbulence after reshock is observed in the velocity and density fluctuation spectra, where a scaling close to $k^{-5/3}$ is observed for almost one decade, and in the enstrophy fluctuation spectra, where a scaling close to $k^{1/3}$ is observed for a similar range. Also, based on normalized cross correlation spectra, local isotropy is reached at lower wave numbers in the multi-mode case compared with the single-mode case before reshock. By breakdown of large scales to small scales after reshock, rapid decay can be observed in cross-correlation spectra in both cases.
Dynamics of unstably stratified free shear flows: an experimental investigation of coupled Kelvin–Helmholtz and Rayleigh–Taylor instability
- Bhanesh Akula, Prasoon Suchandra, Mark Mikhaeil, Devesh Ranjan
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- Journal:
- Journal of Fluid Mechanics / Volume 816 / 10 April 2017
- Published online by Cambridge University Press:
- 08 March 2017, pp. 619-660
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The dynamics of the coupled Kelvin–Helmholtz (KH) and Rayleigh–Taylor (RT) instability (referred to as KHRT instability or KHRTI) is studied using statistically steady experiments performed in a multi-layer gas tunnel. Experiments are performed at four density ratios ranging in Atwood number $A_{t}$ from 0.035 to 0.159, with varying amounts of shear and $\unicode[STIX]{x0394}U/U$ ranging from 0 to 0.48, where $\unicode[STIX]{x0394}U$ is the speed difference between the two flow streams being investigated and $U$ is the mean velocity of these two streams. Three types of diagnostics – back-lit visualization, hot-wire anemometry and particle image velocimetry (PIV) – are employed to obtain the mixing widths, velocity field and density field. The flow is found to be governed by KH dynamics at early times and RT dynamics at late times. This transition from KH-instability-like to RT-instability-like behaviour is quantified using the Richardson number. Transitional Richardson number magnitudes obtained for the present KHRT flows are found to be in the range 0.17–0.56 similar to the critical Richardson numbers for stably stratified free shear flows. Comparing the evolution of density and velocity mixing widths, the density mixing layer is found to be approximately two times as thick as the velocity mixing layer. Scaling of velocity fluctuations is attempted using combinations of KH and RT scales. It is found that the proposed KHRT velocity scale, obtained using the combined mixing-layer growth equation, is appropriate for intermediate stages of the flow when both KH and RT dynamics are comparable. Probability density functions (p.d.f.s) for different fluctuating quantities are presented. Multiple peaks in p.d.f.s are qualitatively explained from the development of coherent KH roll-ups and their subsequent transition into turbulent pockets. The evolution of energy spectra indicates that density fluctuations start to show an inertial subrange from earlier times compared to velocity fluctuations. The spectra exhibit a slightly steeper slope than the Kolmogorov–Obukhov five-thirds law.
Dynamics of buoyancy-driven flows at moderately high Atwood numbers
- Bhanesh Akula, Devesh Ranjan
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- Journal:
- Journal of Fluid Mechanics / Volume 795 / 25 May 2016
- Published online by Cambridge University Press:
- 14 April 2016, pp. 313-355
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Simultaneous density and velocity turbulence statistics for Rayleigh–Taylor-driven flows at a moderately high Atwood number ($A_{t}$) of $0.73\pm 0.02$ 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 ($U=3~\text{m}~\text{s}^{-1}$). 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.