Abstract
The powered resonance tube (PRT) actuator and its variants are new developments in active flow control (AFC) technology. The PRT is attractive because it has no moving parts and can produce acoustic tones that have amplitudes greater than 150 dB over a large frequency bandwidth. The first part of this paper deals with the resonance characteristics of the PRT as a function of the operating parameters such as jet-to-tube spacing (Sp), tube depth (d), and nozzle pressure ratio (NPR). It was found that: (1) at low NPR (3.33), the PRT resonates at discrete combinations of spacing and depth. (2) Using theoretical estimates for predicting shock cell lengths, one could observe a correlation between the theoretical prediction for shock cell length and the spacing at which the PRT resonates. (3) At high NPR (4.29), for a fixed depth, the PRT resonates at virtually all spacings. (4) The frequency at which the PRT resonates remains approximately constant, regardless of spacing. The second part of the study focused on examining the directivity of the acoustic radiation from the PRT—significant for developing orientation strategies of the PRT with respect to the target flow in the end application. The directivity of the fundamental PRT tone and that of its harmonics were studied for a variety of resonance frequencies, both separately as well as cumulatively. It was found that the fundamental part of the actuation signal radiated predominantly in the downstream direction of the jet for low resonance frequencies. As the resonance frequency was increased from 3 to 12 kHz, the directivity changed from downstream of the jet to vertically upward, and finally upstream of the jet at the higher frequencies.
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Notes
It is to be noted that the actual tonal frequency might be off from the quarter wavelength prediction; especially at shallow depths and high NPR, i.e., NPR above 4. At shallow depths, it is the acoustic coupling between the mass of the fluid within the resonance tube and the integration slot (Kerschen 2001); whereas at high NPR, it is the screeching and non-linear effects which are responsible for this deviation (Kerschen et al. 2004).
Abbreviations
- D :
-
Diameter of jet=6.35 mm (0.25 inch)
- d :
-
Resonator tube depth
- f :
-
Fundamental frequency
- λ:
-
Wavelength of the actuator signal
- M :
-
Fully expanded Mach no. based on the plenum pressure
- n :
-
Number of harmonics (e.g., n=2 represents the first harmonic)
- P RMS :
-
RMS value of the pressure
- Sp:
-
Spacing between the PRT nozzle and the resonator tube/integration slot width
- L shock :
-
Shock cell length
- X shock 1 :
-
Shock cell termination distance corresponding to the first shock
- X shock 2 :
-
Shock cell termination distance corresponding to the second shock
- X shock 3 :
-
Shock cell termination distance corresponding to the third shock
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Acknowledgements
This work has been carried out under the support of AFOSR STTR Phase II Contract Number F49620-02-C-0098; Dr. John Schmisseur served as the AFOSR Program Manager.
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Sarpotdar, S., Raman, G. & Cain, A.B. Powered resonance tubes: resonance characteristics and actuation signal directivity. Exp Fluids 39, 1084–1095 (2005). https://doi.org/10.1007/s00348-005-0041-5
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DOI: https://doi.org/10.1007/s00348-005-0041-5