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Upstream interface 0 shock wave competition, pressure maps for simulations with ~ a ! M ϭ 1.5, ~ b ! M ϭ 2, and ~ c ! M ϭ 3 at the same physical time of t { M ϭ 0.281 ms.
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The passage of a shock wave through a spherical bubble results in the
formation of a vortex ring. In the present study, simple dimensional
analysis is used to show that the circulation is linearly dependent on
the surrounding material speed of sound cs
and the initial bubble radius R. In addition, it is shown that
the velocities characterizing...
Context in source publication
Context 1
... dimensional analysis is performed for an arbitrary velocity, leading to the conclusion that the dependence on the parameters is identical for different velocities. Hence the ratio of two velocities is independent of the parameters and is equal to the ratio of the constant g i . For example, the ratio of the ring velocity and the maximum velocity: V max 0 V ring ϭ g max 0 g ring was computed as a function of the Mach number. The maximum deviation from the average is 4.5%, which is small compared to the variation in the Mach number from 1.22 to 4. In Section 3, it was claimed that the velocity is independent of the initial radius of the bubble. This assertion was investigated by executing simulations with different bubble radii. The radii used are 0.2, 1, and 5 cm, that is, a factor of 5 between each simulation. The simulation results are superimposed on each other in Figure 4. The time and the position axis are normalized by the initial bubble radius: There is a very good agreement in the position and shape of the bubbles. Quantifiably, the normalized ring velocities are 3278, 3297, and 3296, respectively, a deviation of less than 1%. This supports the claim that the velocity is radius independent. In the equation derived for the ring velocity there is an arbitrary dimensionless function of the Mach number, density ratio, and specific heat ratio. Assuming that the variables are separable, the dependence of the velocity on the Mach number can be investigated. The Mach scaling is obtained from the scaling of the circulation derived in the VDM. This value was calculated and compared to the circulation computed for the typical simulation with a deviation of less than 5%. The constant representing the other variables was determined from the ring velocity for the M ϭ 1.22 simulation. The graph of the ring velocity as a function of the Mach number is plotted in Figure 5. There is a comparison of the velocities from the simulations and those calculated using the scaling. There is a good agreement for Mach numbers lower than M ϭ 2, above which a significant difference increases with the Mach number. In addition, there is a change in the shape of the curve. The curve has a linear asymptotic behavior. This can be predicted from the proposed scaling factor. This change is explained by what can be defined as a competition between the incident shock wave and the upstream interface of the bubble. The competition is illus- trated in Figure 6 by the pressure contours of three different simulations at two different times. The three simulations are shown at the same physical time. The time is normalized by the Mach number. In the first time, the transverse shock wave is still located in the bubble, and in the second, the shock wave has already emerged from the ...
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The flow of a vortex advected by a uniform current toward a gap in a straight barrier is studied. This is an idealization of flows observed in the world's oceans, for example, in the Yucatan Channel and in the various passages of the Lesser Antilles. The vortex evolution and the transport properties are studied as a function of three nondimensional...
Citations
... Detailed flow field structures were obtained in their study, and it was found that the generation and distribution of vorticity were the dominant factors for the interface deformation and turbulent mixing. Levy et al. 16 applied an interface-tracking 2D arbitrary Lagrangian-Eulerian (ALE) hydrodynamic code to simulate a SBI, and their numerical model was an extension of Samteney and Zabusky's 14 circulation model to the velocity field scaling, which revealed that the bubble velocity does not rely on the radius of the bubble and that the velocity scaling failed for M > 2. Zhu et al. 17 investigated effects of the Atwood number (At) on the evolution of the shock wave and gas bubble through 2D numerical simulations. Their main conclusion is that the Atwood number has a non-monotonic influence on the evolution of mixedness, average vorticity, and circulation. ...
Two-dimensional and three-dimensional computational fluid dynamics studies of a spherical bubble impacted by a supersonic shock wave (Mach 1.25) have been performed to fully understand the complex process involved in shock–bubble interaction (SBI). The unsteady Reynolds-averaged Navier–Stokes computational approach with a coupled level set and volume of fluid method has been employed in the present study. The predicted velocities of refracted wave, transmitted wave, upstream interface, downstream interface, jet, and vortex ring agree very well with the relevant available experimental data. The predicted non-dimensional bubble and vortex velocities are also in much better agreement with the experiment data than values computed from a simple model of shock-induced Rayleigh–Taylor instability (the Richtmyer–Meshkov instability). Comprehensive flow visualization has been presented and analyzed to elucidate the SBI process from the beginning of bubble compression (continuous reflection and refraction of the acoustic wave fronts as well as the location of the incident, refracted and transmitted waves at the bubble compression stage) up to the formation of vortex rings as well as the production and distribution of vorticity. Furthermore, it is demonstrated that turbulence is generated with some small flow structures formed and more intensive mixing, i.e., turbulent mixing of helium with air starts to develop at the later stage of SBI.
... Later, these cases were numerically modeled highlighting the features of the shock-bubble interactions [39]. Since then, additional cases have been considered, including the bubble composition of SF6 and krypton [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. However, these studies are all conducted at atmospheric pressure and room temperature where the fluids are in a gaseous state. ...
Transcritical shock-droplet interactions (TSDIs) occur in a spectrum of high-speed propulsion systems involving liquid fuel injection. “Transcritical” behavior refers to a condition at which the combustion chamber pressure nears the critical pressure of the fuel-air mixture and, by increasing the temperature, a transition from liquidlike to gaslike state is observed. Our understanding of TSDI is significantly less developed than its gas-phase (ideal-gas or supercritical) or liquid-phase (subcritical) counterparts, which are referred to as shock-bubble interactions (SBIs) and shock-droplet interactions (SDIs), respectively. In this paper, we investigate the interaction of a shockwave with an n-dodecane droplet at supercritical pressures. A fully conservative diffuse-interface framework coupled with the Peng-Robinson equation of state is developed to accurately determine the state of the fluid and the resulting interfacial instabilities as the shock propagates through the droplet. The influence of varying the initial temperature of the fuel, the ambient pressure, and the shockwave strength on the shock structure and the droplet morphological deformation is delineated. The dynamics of the TSDI cases are then compared to the subcritical SDI and supercritical or ideal-gas SBI counterparts. It is shown that, depending on the preshock temperature and pressure, the TSDIs exhibit some common features observed in classical cases of SDIs and SBIs, bridging the gap between the sub- and supercritical problems.
... Table VII shows the well-prediction of Eq. (B2) for the translational speed of the supersonic vortex ring in the shock spherical bubble interaction. Fortunately, Levy et al. 100 conducted a wide range of shock Mach numbers to impact the spherical bubble through numerical simulation. As shown in Fig. 24, the RS model overestimates the vortex ring speed at high shock Mach number, which is also faithfully reported by Ranjan et al. ...
The lift-off flow of the supersonic streamwise vortex in oblique shock-wave/jet interaction (OS/JI), extracted from a wall-mounted ramp injector in the scramjet, is studied through the large-eddy simulation method. The shocked helium jet deforms into a pair of the streamwise vortex with a co-rotating companion vortex. The trajectory of the streamwise vortex center is lifted by the shock interaction. Based on the objective coordinate system in the frame of oblique shock, it is found that the nature of the three-dimensional lift-off structure of the OS/JI is inherently and precisely controlled by the structure kinetics of a corresponding shock bubble interaction (SBI). The striking similarities of both qualitative and quantitative results between the OS/JI and the SBI support the proposition that the lift-off of the streamwise vortex is the result of an underlying two-dimensional vortical motion. By combining the first-stage linear growth mode of Richtmyer-Meshkov instability with the second-stage vortex formation mode, a two-stage vortex propagation model suitable for the SBI is proposed and validated. The lift-off growth of a shocked jet in the OS/JI concerned and in the wall-mounted ramp injector cases from the literature is well explained under the two-stage vortex propagation model of SBI. This model further predicts that increasing ramp compression shows little effect on elevating the streamwise vortex for higher free-stream Mach numbers (Ma > 5). In comparison, evident lift-off may occur for lower Mach numbers (Ma < 3.5), which offers the new way for the preliminary design of a streamwise vortex-based ramp injector in the scramjet. Published under license by AIP Publishing. https://doi.org/10.1063/5.0022449 ., s
... In the following study, the bubble radius (D = 5mm) is 10 times less than the one in the experiment of Haas & Sturtevant (1987) due to the less calculating time. Meanwhile, the influence of bubble diameter has been studied by Levy et al. (2003) whose results show that the vortex dynamics is bubble radius independent, which supports present study as well. Also, the radius is much more larger than the range that viscous effect dominates as studied by Wang et al. (2018). ...
Considering variable density effect on mixing enhancement is inherently existed in application of scramjet, the intrinsic coupling mechanism between variable density characteristic and mixing is still unknown. In this paper, a canonical variable density (VD) mixing protocol that is shock bubble interaction (SBI) abstracted from supersonic streamwise vortex, is studied by comparing with a counterpart of passive scalar (PS) mixing. A concrete vortex is formed for both VD and PS case expect that mixing of maximum concentration from vortical stretching decays much faster in VD than in PS case regardless of the shock Mach number concerned. By investigating the azimuthal velocity that stretches the bubble, besides the quasi-Lamb-Oseen type velocity distribution in PS case, a local accelerated stretching relating to secondary barcolinic vorticity in VD SBI explains the faster mixing enhancement and the increase of local mixing rate. Based on secondary baroclinic vorticity production, the fundamental mechanism of the additional accelerated stretching is modelled by inertial velocity difference between shocked light gas bubble and shocked heavy ambient air.Through combining the baroclinic accelerated stretching model and initial compression from shock, a new defined mixing time of VD SBI, , is theoretically proposed based on solving advection-diffusion equation under the local accelerated azimuthal velocity. The proposed mixing time further shows well prediction of mixing enhancement behavior in the range of and . A density stratification distribution is raised accordingly from density inertial effect to control the mixing time behavior which implies the novel method for mixing enhancement of supersonic streamwise vortex.
... In the experiments ( [1,3,6,19]), the pressure ratio P r used to generate the shock wave is not specified. For this reason, we initially run several simulations with the goal to determine which P r brings to a shock wave with Ma = 1.22, as in Haas [1] and Quirk [6]. ...
... In fact, the identification of the different shapes is usually performed visually and, therefore, a certain inaccuracy is expected. The data presented in Figure 7 are from Haas & Sturtevant [1], Levy [19] and Layes [7,25] and refer to conditions analogous to our SPH model. Results are only presented for the air-helium system. ...
In this study, we propose a smoothed particle hydrodynamics model for simulating a shock wave interacting with cylindrical gas inhomogeneities inside a shock tube. When the gas inhomogeneity interacts with the shock wave, it assumes different shapes depending on the difference in densities between the gas inhomogeneity and the external gas. The model uses a piecewise smoothing length approach and is validated by comparing the results obtained with experimental and CFD data available in the literature. In all the cases considered, the evolution of the inhomogeneity is similar to the experimental shadowgraphs and is at least as accurate as the CFD results in terms of timescale and shape of the gas inhomogeneity.
... In the aspect of the scaling and similarity of the Richtmyer-Meshkov instability, circulation deposition was modeled and scaling laws was given in [6]. Furthermore, the scaling relations in the Richtmyer-Meshkov instability and shock-bubble interaction (also a kind of Richtmyer-Meshkov instability) has been illustrated in [7,8]. Satisfying agreements had been obtained between the scaling theory, numerical simulations and the experiments. ...
... It has been claimed that for the cases in macroscale, the flow configurations will be of similarity between different cases with only the variation in scale [7]. In order to investigate the similarity in flow configurations in microscale Richtmyer-Meshkov instability, Fig. 4 was demonstrated. ...
The direct simulation Monte Carlo method was employed in the numerically investigation of the Richtmyer-Meshkov instability in five different scales. The characteristic length varies from 1µm to 5µm. The larger scale cases show high similarity in flow configuration and vorticity distribution. While the reduction in the scale of case leads to the breakdown of that similarity, and the larger scale cases have more concentrated vorticity distribution. In consideration of the circulation and area-weighted enstrophy evolution, the results reveal some principles about the magnitude of dissipation and diffusion for cases in different scales. The change in scale will not change the magnitude of dissipation significantly, but will affect the magnitude of diffusion remarkably. Cases with smaller scale has higher magnitude of diffusion, explaining the less concentrated vorticity and lower area-weighted enstrophy.
... µ * has minimal significance in this flow regime, and circulation is an effective parameter for describing the strength of the well-formed countering-rotating vortex pair. To authors' best knowledge, the current SBI investigations 11,18,20,27,34,45,46 are mainly conducted in this regime as well as the studies concerning reactive cylindrical bubbles. 47,48 Numerous circulation models have been extensively established, allowing for the theoretical prediction of the circulation deposition in the equilibrium state regardless of µ * . ...
In shock accelerated flows such as supersonic injection, it is normally recognised that flow structures are well scaled by the characteristic length under the continuity hypothesis. By investigating the interaction between the incident shock and cylindrical bubbles ranging from dozens of millimetres to dozens of micrometres, a breakdown of the vortex formation is observed within the Navier-Stokes-suitable scale. The vortex breakdown phenomenon characterised by the specific stretching factor is directly reflected by the decline in normalised circulation. Further insight into the physical mechanism of decreased circulation reveals that the effect of viscous dissipation against baroclinic production is intensified in microscale interactions. In order to measure the extent of vortex breakdown, a dimensionless scaling vortex breakdown number μ*, which reflects the competing contribution from dissipation and baroclinicity, is proposed through order-of-magnitude analysis. According to the viscous effect on the vortex formation, μ* is classified under three flow regimes exhibiting different vorticity dynamics (μ* < 10⁻³, 10⁻³ < μ* < 10⁻¹, and μ* > 10⁻¹, which indicates inviscid, transient, and viscous regimes, respectively). In nature, the introduction of the nonlinear factor such as viscous dissipation in flow development causes the scaling breakdown, where the accurate modeling and simulation of the nonlinear factor are the core challenges in understanding the microscale dynamics.
... In simulations of large-scale structures, filaments are also common features. For instance, in galactic winds and fountains (e.g., Strickland & Stevens 2000;Melioli et al. 2008Melioli et al. , 2009Fujita et al. 2009;Cooper et al. 2008Cooper et al. , 2009Melioli, de Gouveia Dal Pino & Geraissate 2013), galaxy clusters (e.g., Marcolini, Brighenti & D'Ercole 2003;Recchi & Hensler 2007;Kronberger et al. 2008;Dursi & Pfrommer 2008;Pfrommer & Dursi 2010;Vijayaraghavan & Ricker 2015), and more specialised numerical studies of wind/shock-cloud systems (e.g., Klein, McKee & Colella 1994, Mac Low et al. 1994Xu & Stone 1995;Jones, Ryu & Tregillis 1996;Gregori et al. 1999Gregori et al. , 2000Fragile et al. 2005;Nakamura et al. 2006;Shin et al. 2008;Pittard et al. 2009;Yirak, Frank & Cunningham 2010;Pittard, Hartquist & Falle 2010;Pittard et al. 2011;Pittard 2011;Li et al. 2013b;McCourt et al. 2015) and shock-bubble systems (e.g., Cowperthwaite 1989;Quirk & Karni 1996;Bagabir & Drikakis 2001;Levy et al. 2003;Niederhaus 2007;Niederhaus et al. 2008;Ranjan et al. 2008a,b;Ranjan, Oakley & Bonazza 2011). ...
Filaments are ubiquitous in the interstellar medium, yet their formation, internal structure, magnetic properties, and longevity have not been analysed in detail. In this thesis I report the results from a comprehensive numerical study that investigates the characteristics, formation, dynamics, and global evolution of filamentary structures arising from (magneto)hydrodynamic interactions between supersonic winds and interstellar clouds. Here I improve on previous wind-cloud simulations by utilising higher numerical resolutions, sharper density contrasts, more complex magnetic field configurations, and more realistic systems with turbulent clouds.
I use gas multi-tracking algorithms and state-of-the-art visualisation techniques to study the physical mechanisms acting upon wind-swept clouds. I find that material originally in the envelopes of the clouds is removed and transported downstream to form filamentary tails, while the cores of the clouds serve as footpoints and late-stage outer layers of these low-density tails. The evolution of filaments comprises four phases: 1) tail formation, 2) tail erosion, 3) footpoint dispersion, and 4) filament free floating. Overall, wind-cloud interactions produce filaments with aspect ratios >10, lateral expansions 1-3 of the core radius, mixing fractions 10-30%, velocity dispersions 0.02-0.05 of the wind speed, and magnetic field amplifications by factors of 10-100.
I find that the strength of magnetic fields regulates vorticity production: sinuous filamentary towers arise in non-magnetic environments, while strong magnetic fields inhibit small-scale Kelvin-Helmholtz perturbations at boundary layers making tails less turbulent. The orientation of magnetic fields also influences the morphology of filaments: magnetic field components aligned with the direction of the wind favour the formation of pressure-confined flux ropes inside the tails, whilst transverse components tend to form current sheets and favour the growth of Rayleigh-Taylor perturbations at the leading edge of the clouds.
I also investigate how turbulence influences the formation of filaments by sequentially adding log-normal density profiles, Gaussian velocity fields, and turbulent magnetic fields into the initial clouds. The porosity of turbulent density profiles aids the propagation of internal shocks through filament material, accelerating mixing and increasing the internal velocity dispersion. The inclusion of subsonically-turbulent velocity fields has little effect on the evolution, while supersonically-turbulent velocity fields accelerate the cloud expansion and subsequent break-up. Line stretching and compression amplify the magnetic energy of turbulent filaments creating highly-magnetised knots and sub-filaments along their tails. In all models the magnetic energy enhancement saturates when the ratio of turbulent kinetic to turbulent magnetic energy densities is 5-10.
At the end of this thesis I discuss the relevance of this work for the study of clouds and filaments in the Galactic centre and provide my perspectives on potential future research in this field. Using ray-tracing techniques I create synthetic emission maps of wind-swept clouds and compare them with radio observations of high-latitude H I clouds and non-thermal filaments in this region of the Galaxy. I interpret these structures as remains of the interplay between outflows driven by localised star formation and dense clouds in the surrounding medium. The simulated morphology, lifespan, magnetic properties, and kinematics are consistent with those inferred from observations of these clouds and non-thermal filaments.
... Finally, results are presented for the well-known shock-bubble interaction problem [50,51]. Numerical settings for this problem are described in detail in [49]. ...
... Once the shock wave impacts the helium bubble, two vortices are formed which begin to split the bubble into two pieces connected by a thin filament. This behavior is observed in the experimental data, see, for example, [50,51]. The numerical results are in good qualitative agreement with the experimental data - Fig. 76. ...
... −6 ; helium bubble shown in blue, air shown in red. Right -experimental results,[50,51]. ...
Disclaimer: Los Alamos National Laboratory, an affirmative action/equal opportunity employer,is operated by the Los Alamos National Security, LLC for the National NuclearSecurity Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396. By approving this article, the publisher recognizes that the U.S. Government retains nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes. Los Alamos National Laboratory requests that the publisher identify this article as work performed under the auspices of the U.S. Departmentof Energy. Los Alamos National Laboratory strongly supports academic freedom and a researcher's right to publish; as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness. Abstract
... Bagabir and Drikakis [86] perform calculations for a helium bubble based on the geometry of Hass and Sturtevant [91] experiments for a range of incident Mach numbers from 1 to 6 using Euler equations and a Godunov-type scheme. Giordano and Burtschell [92] simulate experiments of Levy et al. [93] for krypton and helium bubbles with a viscous model using a monotone scheme for the convective terms. Shankar et al. [94] solve a viscous model with an artificial viscosity method. ...
The Wavelet Adaptive Multiresolution Representation (WAMR) method
provides a robust method for controlling spatial grid adaption --- fine
grid spacing in regions of a solution requiring high resolution (i.e.
near steep gradients, singularities, or near- singularities) and using
much coarser grid spacing where the solution is slowly varying. The
sparse grids produced using the WAMR method exhibit very high
compression ratios compared to uniform grids of equivalent resolution.
Subsequently, a wide range of spatial scales often occurring in
continuum physics models can be captured efficiently. Furthermore, the
wavelet transform provides a direct measure of local error at each grid
point, effectively producing automatically verified solutions. The
algorithm is parallelized using an MPI-based domain decomposition
approach suitable for a wide range of distributed-memory parallel
architectures. The method is applied to the solution of the
compressible, reactive Navier-Stokes equations and includes
multi-component diffusive transport and chemical kinetics models.
Results for the method's parallel performance are reported, and its
effectiveness on several challenging compressible reacting flow problems
is highlighted.
