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Shock-bubble interactions: Features of divergent shock-refraction geometry observed in experiments and simulations
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10.1063/1.2840198
/content/aip/journal/pof2/20/3/10.1063/1.2840198
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/3/10.1063/1.2840198

Figures

Image of FIG. 1.
FIG. 1.

Schematic view of a shock-bubble interaction in divergent refraction geometry : (a) compression phase, just before shock passage; (b) formation of primary vortex ring; (c) seeding of secondary vortex ring; (d) late-time separation of primary and secondary vortex rings.

Image of FIG. 2.
FIG. 2.

Schematic view of experimental setup (not drawn to scale), showing the configuration (1) before and (2) after retraction of the bubble injector.

Image of FIG. 3.
FIG. 3.

Sauter mean diameter of spherical droplets produced in shock-wave atomization of a spherical drop having the same mass as the experimental film layer, plotted against the Mach number of the incident shock wave.

Image of FIG. 4.
FIG. 4.

Schematic view of three-dimensional Cartesian mesh used for the present simulations (not drawn to scale). “S” indicates symmetry boundary conditions; “O” indicates outflow boundary conditions.

Image of FIG. 5.
FIG. 5.

Flowfield evolution for . Numerical images show (on the left) the total density with the isosurface of plotted in red, and (on the right) vorticity magnitude. Dimensionless times are (a) 2.4, (b) 2.5, (c) 11.5, (d) 2.4, (e) 4.8, (f) 7.7, (g) 21.6, (h) 38.7, (i) 57.9, (j) 21.8, (k) 38.9, and (l) 57.9. The width of the field of view in each image is .

Image of FIG. 6.
FIG. 6.

Flowfield evolution for . Numerical images show (on the left) the total density with the isosurface of plotted in red, and (on the right) vorticity magnitude. Dimensionless times are (a) 2.0, (b) 6.6, (c) 41.7, (d) 2.2, (e) 5.8, and (f) 37.9. The width of the field of view in each image is .

Image of FIG. 7.
FIG. 7.

Flowfield evolution for . Numerical images show (on the left) the total density with the isosurface of plotted in red, and (on the right) vorticity magnitude. Dimensionless times are (a) 1.3, (b) 4.0, (c) 7.7, (d) 1.3, (e) 4.1, (f) 7.7, (g) 11.4, (h) 11.6, (i) 23.8, (j) 11.5, (k) 11.8, and (l) 23.6. The width of the field of view in each image is .

Image of FIG. 8.
FIG. 8.

Late-time flowfield visualizations. Numerical images show (on the left) the helium volume fraction on a logarithmic gray scale peaked at , and (on the right) vorticity magnitude . The left column [(a), (d)] is , the center column [(b), (e)] is , and the right column [(c), (f)] is . Dimensionless times are (a) 105.8, (b) 63.4, (c) 69.5, (d) 105.8, (e) 63.5, and (f) 63.5. The width of the field of view in each image is . White dashed lines denote cropping locations for experimental images.

Image of FIG. 9.
FIG. 9.

Normalized translation speed of primary vortex ring in simulations, plotted on a dimensionless time scale based on the ambient shocked flow speed . Horizontal lines on the right margin indicate normalized translation speeds predicted by the Picone–Boris model.

Image of FIG. 10.
FIG. 10.

Streamwise dimension of the shocked bubble, plotted on a dimensionless time scale based on (a) the incident shocked ambient flow speed , (b) the incident shock wave speed , and (c) the transmitted shock wave speed . Symbols represent experimental data; lines represent simulation results.

Image of FIG. 11.
FIG. 11.

Lateral dimension of the shocked bubble, plotted on a dimensionless time scale based on (a) the incident shocked ambient flow speed , (b) the incident shock wave speed , and (c) the transmitted shock wave speed . Symbols represent experimental data; lines represent simulation results.

Image of FIG. 12.
FIG. 12.

Schematic diagram of shock-bubble interaction at the instant of shock passage, showing integration path and flow variables used in the one-dimensional-gasdynamics reconstruction model for circulation, given in Eqs. (24) and (25).

Image of FIG. 13.
FIG. 13.

Decomposed circulation for the scenario, plotted on a dimensionless time scale based on . (Dark lines) Numerical results obtained using Eq. (19). (Open symbols) Numerical results obtained using Eq. (21) (Kelvin’s model). (Closed symbols) Experimental results obtained using Eq. (21). (Light lines) Analytical models.

Image of FIG. 14.
FIG. 14.

Decomposed circulation for the scenario, plotted on a dimensionless time scale based on . (Dark lines) Numerical results obtained using Eq. (19). (Open symbols) Numerical results obtained using Eq. (21) (Kelvin’s model). (Closed symbols) Experimental results obtained using Eq. (21). (Light lines) Analytical models.

Image of FIG. 15.
FIG. 15.

Decomposed circulation for the scenario, plotted on a dimensionless time scale based on . (Dark lines) Numerical results obtained using Eq. (19). (Open symbols) Numerical results obtained using Eq. (21) (Kelvin’s model). (Closed symbols) Experimental results obtained using Eq. (21). (Light lines) Analytical models.

Image of FIG. 16.
FIG. 16.

Normalized circulation: ratio of the positive component of circulation obtained from simulations to the circulation predicted by the one-dimensional gasdynamics reconstruction (R) model.

Tables

Generic image for table
Table I.

Initial properties of gases present in the calculations. The initial pressure and temperature in the system are and , respectively.

Generic image for table
Table II.

Overview of flow parameters for three simulations, including the incident shock Mach number , the Atwood number at the unshocked interface, and lab-frame speeds , , and of the incident shock wave, shocked ambient gas, and transmitted shock wave, respectively.

Generic image for table
Table III.

Normalized primary vortex ring translation speed, computed from simulations, measured in experiments, and predicted by the Picone–Boris (PB) and Rudinger–Somers (RS) models. In experiments and simulations, the value is computed as a mean of velocities measured for .

Generic image for table
Table IV.

Mean circulation extracted from simulations and experiments for , and predicted by analytical models. Circulation values are given in units of .

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/content/aip/journal/pof2/20/3/10.1063/1.2840198
2008-03-14
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Shock-bubble interactions: Features of divergent shock-refraction geometry observed in experiments and simulations
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/3/10.1063/1.2840198
10.1063/1.2840198
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