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Rayleigh and parametric thermo-vibrational instabilities in supercritical fluids under weightlessness
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10.1063/1.4811400
/content/aip/journal/pof2/25/6/10.1063/1.4811400
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/6/10.1063/1.4811400

Figures

Image of FIG. 1.
FIG. 1.

Three different computational configurations: (a) isothermal conditions on all 4 walls, (b) isothermal conditions on vertical walls and adiabatic conditions on horizontal walls, and (c) isothermal conditions on horizontal walls and adiabatic conditions on vertical walls.

Image of FIG. 2.
FIG. 2.

Evolution of the thermal field for the configuration of Fig. 1(a) (4 isothermal walls) with  ′ = 5.56 Hz, ′ = 20 mm, Δ ′ = 1 K, and δ ′ = 100 mK. Different types of instabilities are evidenced: (1) corner instability; (2)–(6) parametric instability on the vertical walls; and (4)–(6) Rayleigh vibrational instability on the horizontal walls.

Image of FIG. 3.
FIG. 3.

Evolution of the corner instability at each period of vibration. Configuration of Fig. 1(c) (adiabatic vertical walls, isothermal horizontal walls):  ′ = 2.78 Hz (period 0.36 s), a′ = 20 mm, Δ ′ = 1 K with a temperature quench of 100 mK. (a) and (f) 1.44 s, (b) and (g) 1.8 s, (c) and (h) 2.16 s, (d) and (i) 2.52 s, and (e) and (j) 2.88 s, respectively. Top row: temperature fields; bottom row: corresponding stream lines. PV: primary vortex and SV: secondary vortex.

Image of FIG. 4.
FIG. 4.

Stability curves for the corner instability for Δ ′ = 10 mK with a quench of 1 mK and for Δ ′ = 100 mK with a quench of 10 mK. The fluid is unstable above the curve and stable below it.

Image of FIG. 5.
FIG. 5.

Parametric instability in Fig. 1(b) configuration (adiabatic horizontal walls, isothermal vertical walls) for the case  ′ = 2.78 Hz (period 0.36 s), ′ = 20 mm, Δ ′ = 100 mK, and δ ′ = 10 mK in 6 consecutive half periods of vibration. (a) and (g) 14.58 s, (b) and (h) 14.76 s, (c) and (i) 14.94 s, (d) and (j) 15.12 s, (e) and (k) 15.3 s, and (f) and (l) 15.48 s Upper row: temperature fields; lower row: corresponding streamlines.

Image of FIG. 6.
FIG. 6.

(a)–(d) Temperature field of the parametric instability in Fig. 1(b) configuration (adiabatic horizontal walls, isothermal vertical walls) for the case  ′ = 2.78 Hz (period 0.36 s), ′ = 20 mm, Δ ′ = 100 mK, and δ ′ = 10 mK in 4 consecutive time periods at (a) 14.4 s, (b) 14.76 s, (c) 15.12 s, and (d) 15.48 s, respectively, plotted for the same vibration phase. (e)–(h) Temperature field of the parametric instability for ′ = 20 mm, Δ ′ = 100 mK, δ ′ = 10 mK for frequencies: (e) 2.78 Hz, (f) 5.56 Hz, (g) 8.33 Hz, and (h) 16.66 Hz.

Image of FIG. 7.
FIG. 7.

(a) Reduced wavelength () of the parametric instability versus reduced acceleration () for the cases Δ ′ = 10 mK, 100 mK, and 1000 mK with corresponding quenches of δ ′ = 1 mK, 10 mK, and 100 mK, respectively (log-log plot). Line: best fit (see text). (b) Reduced wavelength () of the parametric instability versus critical point proximity (Δ ′) for  ′ = 2.78 Hz, 5.56 Hz, and 8.33 Hz and ′ = 15 mm (log-log plot).

Image of FIG. 8.
FIG. 8.

ω′(ρ′ + ρ′) vs plot for Δ ′ = 10 mK, 100 mK, and 1000 mK.

Image of FIG. 9.
FIG. 9.

Stability curves for the parametric instability showing the critical amplitude () vs frequency ( ′) for (a) Δ ′ = 100 mK and 10 mK with quenches of δ ′ = 10 mK and 1 mK, respectively, and (b) Δ ′ = 100 mK with quenches of δ ′ = 10 mK and 5 mK,

Image of FIG. 10.
FIG. 10.

Critical vibrational acceleration vs frequency ( ′) of vibration for the parametric instability for (a) Δ ′ = 100 mK and 10 mK with quenches of δ ′ = 10 mK and 1 mK, respectively, and (b) Δ ′ = 100 mK with quenches of δ ′ = 10 mK and 5 mK.

Image of FIG. 11.
FIG. 11.

Critical Rayleigh vibrational number Rav for two proximities to the critical point: (a) vs frequency and (b) vs amplitude.

Image of FIG. 12.
FIG. 12.

Critical Rayleigh vibrational number vs critical point proximity Δ ′ for  ′ = 2.78 Hz, 5.56 Hz, and 8.33 Hz and ′ = 10 mm. The solid lines are the corresponding variations in CO from Ref. with slopes −0.83 for Δ ′ < 0.1 K and −0.31 for Δ ′ > 0.1 K.

Image of FIG. 13.
FIG. 13.

(a) Stability curve (amplitude vs frequency  ′) for the Rayleigh vibrational instability for Δ ′ = 10 mK and 100 mK with quenches δ ′ = 1 mK and 10 mK, respectively. (b) Critical velocity ( ′) vs frequency plot for Δ ′ = 10 mK and 100 mK with quenches δ ′ = 1 mK and 10 mK, respectively.

Image of FIG. 14.
FIG. 14.

Stability domain for the three types of instabilities: corner (solid line with dots), parametric instability (solid line with boxes), and Rayleigh vibrational instability (solid line with circles) for (a) Δ ′ = 0.1 K and (b) Δ ′ = 0.01 K.

Tables

Generic image for table
Table I.

Thermo-physical data for n-H with .

Generic image for table
Table II.

Orders of magnitude of various time scales involved in the problem for two typical critical point proximities.

Generic image for table
Table III.

Comparison of the size of the cavity with the length ′β′δ ′ for ′ = 30 mm.

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/content/aip/journal/pof2/25/6/10.1063/1.4811400
2013-06-21
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Rayleigh and parametric thermo-vibrational instabilities in supercritical fluids under weightlessness
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/6/10.1063/1.4811400
10.1063/1.4811400
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