Abstract
A mathematical model is developed to analyze the suppression of rotating stall in a low speed centrifugal compressor, thereby addressing the important need for centrifugal compressor rotating stall and surge control. In this model, the precursor to instability is a weak rotating potential velocity perturbation that eventually develops into a (mite disturbance. To suppress the growth of this potential disturbance, a rotating control vortical velocity disturbance is introduced into the impeller inlet flow. The effectiveness of this control is analyzed by matching the perturbation pressure in the compressor inlet and exit flow fields with a model for the unsteady behavior of the compressor. The model predicts that favorable extensions of the compressor operating range are possible with such a control system.
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Abbreviations
- i:
-
unit vector, rotor-relative
- j:
-
unit vector, fixed reference
- n :
-
wave number
- p t :
-
total pressure
- p :
-
static pressure
- r :
-
radial coordinate
- s :
-
distance along mean flow path
- V :
-
absolute flow velocity
- W :
-
relative flow velocity
- z :
-
axial coordinate
- β:
-
control phase
- γ:
-
mean path direction cosine
- \({{\bar{\eta }}_{c}}\) :
-
isentropic efficiency
- қ:
-
specific heat ratio
- \(\Delta \bar{\phi }\%\) :
-
change in \(\bar{\phi }{{|}_{{stall}}}\) due to control
- \(\bar{\psi }\) :
-
\(\frac{{{{{\bar{p}}}_{5}} - {{{\bar{p}}}_{{{{t}_{3}}}}}}}{{\rho {{U}^{2}}}}\)
- ω:
-
disturbance frequency
- ωI :
-
impeller angular velocity
- ξ:
-
\(\phi _{v}^{\prime }\rho {{U}^{2}}/p\prime {{|}_{3}}\)
- ζ:
-
\(\phi _{v}^{\prime }/\phi _{p}^{\prime }\)
- *:
-
rotor-relative coordinate
- ’:
-
perturbation value
- -:
-
mean, axisymmetric
- asy:
-
asymmetric
- D:
-
diffuser
- I:
-
impeller
- m :
-
mean flow direction
- p :
-
potential
- r :
-
radial direction
- u :
-
unsteady
- v :
-
vortical
References
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© 1993 Springer-Verlag New York, Inc.
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Lawless, P.B., Fleeter, S. (1993). Active Control of Centrifugal Compressor Rotating Stall. In: Atassi, H.M. (eds) Unsteady Aerodynamics, Aeroacoustics, and Aeroelasticity of Turbomachines and Propellers. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9341-2_20
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DOI: https://doi.org/10.1007/978-1-4613-9341-2_20
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Print ISBN: 978-1-4613-9343-6
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