Publication Date:
2017-06-23
Description:
We investigate the spatial stability of compressible, viscous pipe flows with radius-dependent mean density profiles, subjected to solid body rotations. For a fixed Rossby number (inverse of the rotational speed), as the Reynolds number is increased, the flow transitions from being stable to convectively unstable, usually leading to absolute instability. If flow compressibility is unimportant and is held constant, there appears to be a maximum below which the flow remains stable irrespective of any rotational speed, or a minimum azimuthal Reynolds number is required for any occurrence of absolute instabilities. Once compressible forces are significant, the effect of pressure-density coupling is found to be more severe below a critical , where as rotational speeds are raised, a stable flow almost directly transitions to an absolutely unstable state. This happens at a critical which reduces with increased flow Mach number, pointing to compressibility aiding in the instability at these lower Reynolds numbers. However, at higher , above the critical value, the traditional stabilizing role of compressibility is recovered if mean density stratification exists, where the gradients of density play an equally important role, more so at the higher azimuthal modes. A total disturbance energy-based formulation is used to obtain mechanistic understanding at these stability states, where we find the entropic energy perturbations to dominate as the primary instability mechanism, in sharp contrast to the energy due to axial shear, known to play a leading role in incompressible swirling flows. © 2017 Cambridge University Press.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
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