Idealized motor chamber and its coordinate system.
Variation of (a) the Strouhal number and (b) over a range of motor aspect ratios and the first three acoustic oscillation modes.
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.
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.
Stability behavior for a range of and shown at (a) , (b) 10, and (c) 100 and .
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 .
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 .
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 .
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 .
Linear growth rate corrections and the critical parameters delineating stability boundaries.
Physical parameters for representative motors.
Numerical integrals of irrotational, rotational, and individual growth rates .
Analytical estimates of irrotational, rotational, and individual growth rates .
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