Turbulent Mixing Zone Research Articles

The Halo21 absorption modelling challenge: lessons from ‘observing’ synthetic circumgalactic absorption spectra

ABSTRACT In the Halo21 absorption modelling challenge we generated synthetic absorption spectra of the circumgalactic medium (CGM), and attempted to estimate the metallicity, temperature, and density (Z, T, and nH) of the underlying gas using observational methods. We iteratively generated and analysed three increasingly complex data samples: ion column densities of isolated uniform clouds, mock spectra of 1–3 uniform clouds, and mock spectra of high-resolution turbulent mixing zones. We found that the observational estimates were accurate for both uniform cloud samples, with Z, T, and nH retrieved within 0.1 dex of the source value for $\gtrsim 90~{{\ \rm per\ cent}}$ of absorption systems. In the turbulent-mixing scenario, the mass, temperature, and metallicity of the strongest absorption components were also retrieved with high accuracy. However, the underlying properties of the subdominant components were poorly constrained because the corresponding simulated gas contributed only weakly to the H i absorption profiles. On the other hand, including additional components beyond the dominant ones did improve the fit, consistent with the true existence of complex cloud structures in the source data.

The onset and saturation of the Faraday instability in miscible fluids in a rotating environment

We investigate the influence of rotation on the onset and saturation of the Faraday instability in a vertically oscillating two-layer miscible fluid using a theoretical model and direct numerical simulations (DNS). Our analytical approach utilizes Floquet analysis to solve a set of the Mathieu equations obtained from the linear stability analysis. The solution of the Mathieu equations comprises stable and harmonic, and subharmonic unstable regions in a three-dimensional stability diagram. We find that the Coriolis force delays the onset of the subharmonic instability responsible for the growth of the mixing zone size at lower forcing amplitudes. However, at higher forcing amplitudes, the flow is energetic enough to mitigate the instability delaying effect of rotation, and the evolution of the mixing zone size is similar in both rotating and non-rotating environments. These results are corroborated by DNS at different Coriolis frequencies and forcing amplitudes. We also observe that for$(\,f/\omega )^2<0.25$, where$f$is the Coriolis frequency, and$\omega$is the forcing frequency, the instability and the turbulent mixing zone size-$L$saturates. When$(\,f/\omega )^2\geq 0.25$, the turbulent mixing zone size-$L$never saturates and continues to grow.

Ultrafine Particle Flotation in a Concept Flotation Cell Combining Turbulent Mixing Zone and Deep Froth Fractionation with a Special Focus on the Property Vector of Particles

Froth flotation faces increasing challenges in separating particles as those become finer and more complex, thus reducing the efficiency of the separation process. A lab flotation apparatus has been designed combining the advantages of agitator-type froth flotation for high turbulences and column flotation with a deep froth zone for a fractionating effect, also enabling a study on the effect of different particle property vectors. A model system of ultrafine (<10 µm) particles was used for flotation to study how the separation process is influenced by the ultrafine property vectors of shape and wettability. To evaluate the new apparatus, flotation tests were carried out in a benchmark mechanical flotation cell under comparable conditions. Higher wettabilities result in higher recoveries, but the results show that optimum levels of hydrophobicity vary for different particle shapes. Different behaviours are observed for differently shaped particles, depending on their wettability state. The entrainment of unwanted gangue is reduced with increasing froth depth. While higher recoveries are obtained for the benchmark cell, the newly developed apparatus produces concentrates with higher grades. Our findings contribute to ultrafine flotation techniques and especially our understanding of the complex effect of particle shape in combination with the other property vectors.

Evolution of turbulent mixing driven by implosion in spherical geometry

The interface instability and turbulent mixing of perturbed multi-modes Air/SF6 interface driven by implosion in spherical geometry are numerically investigated. The results show the complex evolving laws and physical mechanisms of turbulent mixing. After the incident imploding shock, the transmitted shock wave moves towards the centre and bounces off outward to produce the second impact, which is a combination of reshock and Taylor wave rather than a single one like in planar case, and forms the loading/unloading effects. The following rebound impacts repeat this assembled loading/unloading process. In the whole process, the turbulent mixing zone (TMZ) growth is closely related to the multiple loading/unloading features. The Richtmyer-Meshkov instability (RMI), Rayleigh-Taylor instability (RTI), Rayleigh-Taylor stabilization (RTS) and Bell-Plesset (BP) effects coexist, and the competition mechanism results in the TMZ width growing in an oscillatory way. The statistics properties of TMZ are highly related to the multiple shocks process. The fluids mixing across TMZ is asymmetrical but behaves in a self-similar way. The evolution of TMZ has a high degree anisotropy, especially around the two edges of TMZ, the turbulent flow is also highly intermittent. When the turbulent mixing develops fully the energy spectra approach k -1 scaling law at the inertial subrange.

One-dimensional turbulence modeling of compressible flows: II. Full compressible modification and application to shock–turbulence interaction

One-dimensional turbulence (ODT) is a simulation methodology that represents the essential physics of three-dimensional turbulence through stochastic resolution of the full range of length and time scales on a one-dimensional domain. In the present study, full compressible modifications are incorporated into ODT methodology, based on an Eulerian framework and a conservative form of the governing equations. In the deterministic part of this approach, a shock capturing scheme is introduced for the first time. In the stochastic part, one-dimensional eddy events are modeled and sampled according to standard methods for compressible flow simulation. Time advancement adjustments are made to balance comparable time steps between the deterministic and stochastic parts in compressible flows. Canonical shock–turbulence interaction cases involving Richtmyer–Meshkov instability at Mach numbers 1.24, 1.5, and 1.98 are simulated to validate the extended model. The ODT results are compared with available reference data from large eddy simulations and laboratory experiments. The introduction of a shock capturing scheme significantly improves the performance of the ODT method, and the results for turbulent kinetic energy are qualitatively improved compared with those of a previous compressible Lagrangian ODT method [Jozefik et al., “Simulation of shock–turbulence interaction in non-reactive flow and in turbulent deflagration and detonation regimes using one-dimensional turbulence,” Combust. Flame 164, 53 (2016)]. For the time evolution of profiles of the turbulent mixing zone width, ensemble-averaged density, and specific heat ratio, the new model also yields good to reasonable results. Furthermore, it is found that the viscous penalty parameter Z of the ODT model is insensitive to compressibility effects in turbulent flows without wall effects. A small value of Z is appropriate for turbulent flows with weak wall effects, and the parameter Z serves to suppress extremely small eddy events that would be dissipated instantly by viscosity.

Numerical study of Richtmyer–Meshkov instability of a flat interface driven by perturbed and reflected shock waves

In this paper, the Richtmyer–Meshkov instability of a flat gas interface driven by perturbed and reflected shock waves is numerically investigated. The flat gas interface evolves into a “Λ”-shaped structure with a central N2 cavity and steps on both sides, due to the impaction of the perturbed shock wave. After the secondary collision of the reflected shock wave from the high-density region to the low-density region, the gas interface first undergoes phase inversion, and the “Λ” interface then evolves into a bubble and spike structure. Three cases of different Atwood numbers, N2/SF6, N2/Kr, and N2/CO2, are studied. The collision time and position of the reflected shock wave and the interface, the induced spikes, bubbles and gas mixing, are compared in detail. The formation of the spike and bubble is related to the RM instability developed by the collision of the reflected shock wave and the perturbed interface, in which the effect of baroclinic vorticity is highlighted. With the increase in the Atwood number, the density gradient and the baroclinic vorticity become larger, which induces more vortex along the interface. Kelvin Helmholtz unstable vortices are generated on the “legs” of the spikes due to shearing. The main spike structure is stretched and broken with the effect of the vortex, forming a turbulent mixing zone.

Instability and Atomization of Liquid Cylinders after Shock Wave’s Impacting

This paper describes an experimental study on the instability and atomization of liquid cylinders after the impact of shock waves. Single row water column, in-line double rows water columns and alongside triple rows water columns were evaluated in a horizontal shock tube. The diameter of water column and the Mach number in the experiments were 2.0–4.14 mm and 1.10–1.25, respectively. The global instability along the axial direction of water cylinders was focused. Using a high-speed camera, the developments of spike height, bubble depth and turbulent mixing zone, width were measured. Some comparison was also made between the present experimental results and the existing theoretical model.

Deep learning technique for examining the mechanism, transport, and behavior of oil-related hazardous material caused by wave breaking and turbulence

A marine oil spill produces oil-related hazardous material (OHM) which can cause damage to the marine ecological environment, and seriously affect coastal economic development such as tourism and aquaculture. The turbulent momentum and energy generated by the wave breaking process have a significant effect on accelerating the mixing of OHM and seawater, which is one of the main factors in oil becoming sunken or submerged. In order to explore the influence of offshore wave breaking on the formation and transportation of OHM, the wave breaking process was simulated in a 2D laboratory flume, and the behavior process of OHM was identified and tracked in this paper. Five groups of breaking waves of different significant wave height (SWH) were set up in the experiment, and then OHM with the same density and mass was added, respectively, in order to observe the sinking process under the action of wave-induced turbulence. The results show that the turbulence intensity is closely related to the phase of the wave, the turbulence activity is violent at the wave crest, and the vertical distribution of the turbulent energy dissipation rate in the turbulent mixing zone remains basically unchanged. Under the actions of wave breaking and turbulence, the OHM’s submergence depth shows a good binomial growth trend. For SWH = 12.45 cm, the OHM stays under the water for nearly 2.32 s, and it reaches the deepest position of 0.165 m. Compared with SWH = 12.45 cm, the submergence depths for waves with SWHs of 20.61 cm, 26.81 cm, 32.32 cm, and 36.54 cm are increased by 8%, 37%, 80%, and 159%, respectively. Then, the submergence depths due to the other four waves are increased progressively, and the growth rates are 8%, 26%, 31%, 44%, respectively (compared with the same period of the previous wave).

Origins of instabilities in turbulent mixing layers behind detonation propagation into reactive–inert gas interfaces

Interactions of mildly irregular detonation waves with sharp interfaces separating combustible mixtures from an inert gas were modeled numerically using the compressible linear eddy model for a large eddy simulation (CLEM-LES) approach. In recent experiments of Lieberman and Shepherd [“Detonation interaction with an interface,” Phys. Fluids 19, 096101 (2007)], such interactions resulted in a transmitted shock-turbulent mixing zone (TMZ) complex as the reactive wave traveled through the interface separating fuel rich ethylene–oxygen mixtures and nitrogen. Kelvin–Helmholtz (K–H) instability was proposed as the main mechanism contributing to the formation of the turbulent mixing zone. This work aims to determine to what extent K–H plays a role and whether or not other sources of instability contribute to the observed evolution of the TMZ. The results show that full-scale simulations using CLEM-LES reproduce well (qualitatively and quantitatively) the experimental flow features. Upon recasting the simulations in the frame of reference of the node (i.e., the location where the detonation wave meets the interface) and by removing the cellular instability from the front, the growth rates of the TMZ only due to K–H instabilities originating from the velocity difference across the mixing layer were found to be insignificant. Conversely, the addition of controlled perturbations to the detonation front pressure resulted in significant growth of the TMZ. This outcome suggests that the TMZ formation and evolution are heavily influenced by instabilities originating at the front. In this regard, transverse waves associated with the detonation front cellular structure are likely to provide the bulk of TMZ growth through additional Richtmyer–Meshkov instabilities.

Numerical simulation of the dynamics of non-zero buoyancy turbulent mixing zone in a linearly stratified medium

Numerical simulation of the dynamics of non-zero buoyancy turbulent mixing zone in a linearly stratified medium

Permanence of large eddies in Richtmyer–Meshkov turbulence for weak shocks and high Atwood numbers

The spectral analysis of the large scales of Richtmyer-Meshkov turbulent mixing zones is extended to the case of high density-contrasts. Large-scale invariants are derived and shown to determine the growth rate of the mixing zone.

Crossover of the relative heat transport contributions of plume ejecting and impacting zones in turbulent Rayleigh-Bénard convection (a) (a)Contribution to the Focus Issue Turbulent Thermal Convection edited by Mahendra Verma and Jörg Schumacher.

Turbulent thermal convection is characterized by the formation of large-scale structures and strong spatial inhomogeneity. This work addresses the relative heat transport contributions of the large-scale plume ejecting vs. plume impacting zones in turbulent Rayleigh-Bénard convection. Based on direct numerical simulations of the two dimensional (2-D) problem, we show the existence of a crossover in the wall heat transport from initially impacting dominated to ultimately ejecting dominated at . This is consistent with the trends observed in 3-D convection at lower Ra, and we therefore expect a similar crossover to also occur there. We identify the development of a turbulent mixing zone, connected to thermal plume emission, as the primary mechanism for the takeover. The mixing zone gradually extends vertically and horizontally, therefore becoming more and more dominant for the overall heat transfer.

Large eddy simulation of the turbulent mixing at an oblique interface induced by non-classical planar shock waves

The interaction between the shock wave and phase interface is one of the classic problems in aerospace and turbulent combustion engineering. In this paper, the instability of the gas–liquid interface driven by non-classical planar shock waves is studied. Based on the volume of fluid model and large eddy simulation method, the deformation process and the turbulent mixing phenomenon of the oblique interface induced by non-classical planar shock waves in a two-dimensional plane are numerically investigated by using a high-performance computer cluster. The effects of incident shock wave intensity, initial amplitude, initial wavelength, and inclined angle of the gas–liquid two-phase oblique interface are analyzed. The results show that the incident shock intensity has the most significant effect on the interface deformation and the development of turbulent mixing, and the initial amplitude and wavelength of the incident shock and the inclined interface angle also play a certain role in the deformation and development process. Overall, the width of the turbulent mixing zone increases with time under a given condition, and the convex structure will fall off and break up at the phase interface in the later stage of turbulent mixing.

Numerical study of turbulent mixed convection in a rotating inter-disk cavity with axial throughflow of cooling air

The paper presents the results of eddy-resolving numerical simulation of mixed convection developing in a rapidly rotating inter-disk cavity with axial throughflow of cooling air. Under conditions of the experiments available in the literature for the case of the cavity heating from the side of the disk surfaces, the computations were performed using two methods: Implicit LES and zonal RANS/ILES, with and without taking into account the gravity effects. In case of the zonal RANS/ILES approach, the axial pipe flow and the zone of turbulent mixing of throughflow with particles of heated gas were simulated on the base of the RANS equations added by a turbulence model, whereas the major part of the buoyancy-controlled cavity flow was computed with the ILES method. The ratio of the cavity width to its outer radius was 0.13. The computations were carried out at the rotational Reynolds number equal to 2·105, if evaluated with the outer radius; the axial flow Reynolds number was 2·104. A moderate size grid used in the computations (of about 5·105 cells) provided a good resolution of quasi-laminar Ekman layers. Data on dynamics of unsteady vortex structures forming in the cavity, on characteristics of local heat transfer, as well as on effects of the gravity force action are reported. The results of computations of the time-averaged local Nusselt number on the disks surfaces are compared with measurement data; an acceptable agreement has been obtained in case of the zonal RANS/ILES approach.

Theoretical bases for determining the velocity and suspended matter concentration in the swirling zone beyond the transverse dam

Design dependencies to determine the velocity and concentration of suspended matter in the swirling zone beyond the transverse dam in the presence of the initial section of the jet are proposed in the article, using the main provisions of the theory of turbulent jets, the scheme of dividing the flow into hydraulic homogeneous zones: a weakly perturbed core, intense turbulent mixing and reverse currents. The distribution of velocities and concentration of suspended matter (turbidity) in the zone of intense turbulent mixing are affine and obey the theoretical Schlichting-Abramovich relationships; this was substantiated by laboratory and field studies. The equations of continuity and conservation of solid matter along the flow were used to solve the problem. To establish the adequacy of the dependencies obtained, a test problem was implemented in which the velocities in the core and the depth along the flow were assumed constant. The problem was implemented for the following contraction ratios of flow nc 0,1; 0.2; 0.3; 0.4; 0.5. Tabular and graphic dependencies obtained show that with all contraction ratios of flow, the relative backflow velocities first increase, and at the end of the swirling zone, they sharply decrease. The maximum is observed at the intersection of the outer boundary of the zone of intense turbulent mixing with the protected coast and reaches m = 0.317. Comparison of the calculation results with the experimental ones shows their qualitative and quantitative agreement. The relative concentration of suspended matter in reverse currents remains practically constant along the entire length of the swirling zone. It is close to unity for all contraction ratios of flow.

Suspension concentration distribution in a stream constructed by spur No. 19 on the Amu Darya river

The concentration of suspended solids is the main indicator of the flow transporting suspended sediments. Knowing its value, it becomes possible to predict channel processes on rivers, the timing of sedimentation tanks and reservoirs. Establishing patterns of the influence of structures on the redistribution of liquid and solid runoff is also a priority task. The main goal of this work is to establish the regularities of the distribution of the concentration of suspended matter in a stream constrained by a transverse spur. The problem is considered for the second time using materials from field studies conducted on spur No. 19 in 2020 on the left bank of the Amu Darya river. The methodology of field studies remained the same as for the first time on dam No. 30 in 2019. The positions of the sections and verticals during sampling to determine the concentration of suspended matter were assigned based on the hydraulic structure of the constrained flow. Considering the presence of homogeneous zones of a weakly perturbed core, intense turbulent mixing and reverse currents, as is customary in the theory of turbulent jets with an admixture propagating in a confined space. On verticals, samples were taken at two points 0.2H and 0.8H, and at shallow depths at a depth of 0.6H. Field observations established that in the zone of the slightly disturbed core of the distribution of the concentration of suspended matter along the depth, it has the shape of a “boot”; however, the length of the toe is much shorter than that of the dam 30 and is observed only in the sections P-P and O-O, and in the other sections there is a leveling in depth. On other sections, they are close to logarithmic. The maximum concentration of suspended matter was observed in the section of confinement O-O at point 0.8H 7.66 kg / m3, which in the section of confinement under the influence of a new spur occurs deep and lateral erosion of the channel. The distribution in plan in the zone of a weakly disturbed core is close to uniform. Here again, in the zone of intense turbulent mixing, it obeys the theoretical Schlichting-Abramovich dependence for the initial section. With the help of the results obtained, it is possible to predict the siltation of the inter-dam space and the boundaries of the new coastline in the future.

Numerical simulation of a shock–helium bubble interaction

We solve the Euler equations to compute the interaction of a Mach 1.22 shock wave with a helium bubble contaminated by 28% air by mass. A ninth-order upwind scheme is used to calculate the left and the right states of the primitive variables as required by the AUSMD algorithm. The low numerical dissipation of the AUSMD algorithm makes it an ideal choice for computing long-time behavior of the bubble after the shock passes over it. The algorithm combines well with the high spectral accuracy of the ninth-order upwind scheme. The basic trends in the evolving bubble match with earlier experimental and numerical observations. Effect of numerical schemes and grid sizes is also observed for this study. The Euler solver captures a large number of small-scale rolled-up vortices originally generated by the baroclinic torque term in the vorticity transport equation and later enhanced by the Kelvin–Helmholtz instability. Numerical schlieren, mass fraction, and vorticity contour plots are used to visualize the turbulent mixing zone that is a key feature of the translating and deforming bubble.

Study of submountain river flow patterns constrained by a combined dam

Great attention around the world is paid to the design and construction of riverbank protection and channel control structures on submountain section of rivers. High slopes (i=0,001÷0,004 and higher), flow kinetics and ability to transport large amount of sediments are the features of submountain section of rivers.Most of the research in this sphere has been conducted on the study of patterns of flow constrained by transverse structures in valley parts of rivers.The main goal of this work is to establish the physical picture of flow around a combined dam in submountian river, the through-flow part of which is made of tetrahedrons, as well as to develop a design method for flow velocity field. Formations of two regimes have been established experimentally, i.e. “calm” at ia<icr and “critical” at ia≥icr. These regimes are mainly affected by flow contraction degree na, and Froude number Fr.The presence of the following zones was established: core, intensive turbulent mixing and backflow zones, as well as the affinity of velocity fields in the zone of mixing by Shlihting-Abramovich. Prandtl has realized the task for “calm” regime with the use of integral relationship expressing law of conservation of momentum in the flow, equation for conservation of discharge and differential equation for nonuniform motion of transit flow with the account of tangential turbulent stresses on lateral surfaces. As opposed to the existing solutions, we accounted for the presence of two regions of spreading with different slopes of water surface, horizontal component of fluid weight, nonuniform distribution of velocities in head section, high roughness and the case when sections of target and vertical contraction do not match. Satisfactory results were obtained by comparing theoretical solution and experimental data.

Early Time Modifications to the Buoyancy-Drag Model for Richtmyer–Meshkov Mixing

Abstract The Buoyancy-Drag model is a simple model, based on ordinary differential equations, for estimating the growth in the width of a turbulent mixing zone at an interface between fluids of different densities due to Richtmyer–Meshkov and Rayleigh–Taylor instabilities. The model is calibrated to give the required self-similar behavior for mixing in simple situations. However, the early stages of the mixing process are very dependent on the initial conditions and modifications to the Buoyancy-Drag model are then needed to obtain correct results. In a recent paper, Thornber et al. (2017, “Late-Time Growth Rate, Mixing, and Anisotropy in the Multimode Narrowband Richtmyer–Meshkov Instability: The θ-Group Collaboration,” Phys. Fluids, 29, p. 105107), a range of three-dimensional simulation techniques was used to calculate the evolution of the mixing zone integral width due to single-shock Richtmyer–Meshkov mixing from narrowband initial random perturbations. Further analysis of the results of these simulations gives greater insight into the transition from the initial linear behavior to late-time self-similar mixing and provides a way of modifying the Buoyancy-Drag model to treat the initial conditions accurately. Higher-resolution simulations are used to calculate the early time behavior more accurately and compare with a multimode model based on the impulsive linear theory. The analysis of the iLES data also gives a new method for estimating the growth exponent, θ (mixing zone width ∼ tθ), which is suitable for simulations which do not fully reach the self-similar state. The estimates of θ are consistent with the theoretical model of Elbaz and Shvarts (2018, “Modal Model Mean Field Self-Similar Solutions to the Asymptotic Evolution of Rayleigh-Taylor and Richtmyer-Meshkov Instabilities and Its Dependence on the Initial Conditions,” Phys. Plasmas, 25, p. 062126).

Numerical Simulation of Dynamics of Weakly Heated Turbulent Mixing Zone in Linearly Stratified Medium

Based on an algebraic model of Reynolds stresses and fluxes, a numerical model of the dynamics of a flat localized region of turbulent perturbations of non-zero buoyancy in a linearly stratified medium was constructed. The evolution of a weakly heated turbulent spot was considered. Presence of non-zero buoyancy leads to increase in the geometrical dimensions of the turbulent spot and generation of internal waves of greater amplitude.