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Numerical investigation of feedback control of thermocapillary instability
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10.1063/1.1896370
/content/aip/journal/pof2/17/5/10.1063/1.1896370
http://aip.metastore.ingenta.com/content/aip/journal/pof2/17/5/10.1063/1.1896370

Figures

Image of FIG. 1.
FIG. 1.

The geometry of the simulated annular configuration.

Image of FIG. 2.
FIG. 2.

The radial temperature distribution for a steady subcritical case, with and . Diamonds are results from the present code, stars are from Lavalley et al. (Ref. 14).

Image of FIG. 3.
FIG. 3.

Full spectral decomposition of the surface temperature at for . A denotes the amplitude of the waves.

Image of FIG. 4.
FIG. 4.

Amplitudes of the critical azimuthal wavenumber (squares) and the first and second harmonic modes, (circles) and 9 (stars) over a range of . The lines denote .

Image of FIG. 5.
FIG. 5.

A time sequence of surface isotherms from 0 to 1 of the oscillation with single actuator control. The inset on the upper left shows the positions of the sensor and the heater . Parameter values are .

Image of FIG. 6.
FIG. 6.

Temporal signals at the sensor positions . . The inset to the left shows the positions of the sensors and the heaters . Parameter values are .

Image of FIG. 7.
FIG. 7.

Temporal signals at . . Sensor and heater positions are the same as indicated in Fig. 6.

Image of FIG. 8.
FIG. 8.

Spectral decomposition at for the saturated oscillation in Fig. 7.

Image of FIG. 9.
FIG. 9.

A time sequence of surface isotherms from 0 to 1 of the saturated oscillation in Fig. 7. The inset to the left shows the positions of the sensors and the heaters .

Image of FIG. 10.
FIG. 10.

Spectral decomposition at for the saturated oscillation with control with high gain and short heater.

Image of FIG. 11.
FIG. 11.

Spectral decomposition at for the saturated oscillation with control, using a heater three times as long as in Fig. 10. .

Image of FIG. 12.
FIG. 12.

Temperature signals at the two sensor positions for the sensor positioning with positive gain. The two sensors are placed at an angle of , as indicated in the inset. . .

Image of FIG. 13.
FIG. 13.

Spectral decomposition of the temperature signals at the sensors for the case in Fig. 12. .

Image of FIG. 14.
FIG. 14.

Comparison between temperature signals at the sensor positions for the case of ideal heating and cooling, and the case of heat flux restricted to the heating phase, as in Eq. (19). (—): Alternate heating and cooling with . (——): Heating only with . . .

Tables

Generic image for table
Table I.

Result on computation of two-dimensional base flow for different grids. and are radial velocities for and 39 200.

Generic image for table
Table II.

Magnitudes of the outstanding Fourier modes of the temperature, at the midgap on the surface, , for various number of Fourier modes, . . . denotes the azimuthal wavenumber. The critical wavenumber is .

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/content/aip/journal/pof2/17/5/10.1063/1.1896370
2005-04-29
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Numerical investigation of feedback control of thermocapillary instability
http://aip.metastore.ingenta.com/content/aip/journal/pof2/17/5/10.1063/1.1896370
10.1063/1.1896370
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