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Some rotational corrections to the acoustic energy equation in injection-driven enclosures
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10.1063/1.1920647
/content/aip/journal/pof2/17/7/10.1063/1.1920647
http://aip.metastore.ingenta.com/content/aip/journal/pof2/17/7/10.1063/1.1920647

Figures

Image of FIG. 1.
FIG. 1.

Idealized motor chamber and its coordinate system.

Image of FIG. 2.
FIG. 2.

Variation of (a) the Strouhal number and (b) over a range of motor aspect ratios and the first three acoustic oscillation modes.

Image of FIG. 3.
FIG. 3.

Comparison of exact representations and polynomial approximations for (a) and (b) . In both cases, the leading-order linear approximation outperforms the higher-order polynomials in the domain above the wall where most meaningful interactions take place.

Image of FIG. 4.
FIG. 4.

Numerically integrated stability growth rate shown over a range of and , 2. Results are for two values of corresponding to (a) 0.001 and (b) 0.01. In both cases, increasing or increases system stability. Conversely, increasing the aspect ratio at fixed , and moves the system in the direction of acoustic instability.

Image of FIG. 5.
FIG. 5.

Stability behavior for a range of and shown at (a) , (b) 10, and (c) 100 and .

Image of FIG. 6.
FIG. 6.

Numerical stability curves at constant shown over a useful range of and select values of . The system is more sensitive to the stabilizing role of at the highest . Here , and .

Image of FIG. 7.
FIG. 7.

Numerical stability curves at constant shown over a useful range of and select values of . The rotational formulation predicts a less stable system when is lowered or when or are increased. This explains, in part, the additional instabilities observed in elongated motors. The irrotational formulation predicts the opposite trends. Here and .

Image of FIG. 8.
FIG. 8.

Numerical stability curves shown at constant over a useful range of and select values of and . Both rotational and irrotational formulations predict less stable systems with successive increases in . However, they differ in their dependence on other parameters. Here and .

Image of FIG. 9.
FIG. 9.

Numerical stability curves shown at constant over a useful range of and select values of and . The rotational formulation associates acoustic instability with increasing or with reducing . Opposite trends are projected by the irrotational formulation. Here and .

Tables

Generic image for table
Table I.

Linear growth rate corrections and the critical parameters delineating stability boundaries.

Generic image for table
Table II.

Physical parameters for representative motors.

Generic image for table
Table III.

Numerical integrals of irrotational, rotational, and individual growth rates .

Generic image for table
Table IV.

Analytical estimates of irrotational, rotational, and individual growth rates .

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/content/aip/journal/pof2/17/7/10.1063/1.1920647
2005-06-27
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Some rotational corrections to the acoustic energy equation in injection-driven enclosures
http://aip.metastore.ingenta.com/content/aip/journal/pof2/17/7/10.1063/1.1920647
10.1063/1.1920647
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