Hohenemser, K. H. and Yin, Shen-Kuang, "Some Applications of the Method of Multi-blade Coordinates," Journals of the American Helicopter Society, Vol. 17, No. 3, July 1972, pp. 3-12. Coleman, R. P., "Theory of Self-Excited Mechanical Oscillations of Hinged Rotor Blades," NACA Advanced Restricted Rept. 3G29, Republished as Rept. 1351,1943, NACA. Miller, R. H., "Helicopter Control and Stability in Hovering Flight," Journal of the Aeronautical Sciences, Vol. 15, No. 8, Aug. 1948, pp. 453-472. Azuma, A., "Dynamic Analysis of the Rigid Rotor System," Journal of Aircraft, Vol. 4, No. 3, May-June 1967, pp. 203-209. Curtiss, H. C., Jr. and Shupe, N. K., "A Stability and Control Theory for Hingeless Rotors," American Helicopter 27th Annual National V/STOL Forum, Washington, D. C., May 1971. Ward, J. F., "Exploratory Flight Investigation and Analysis of Structural Loads Encountered By A Helicopter Hingeless Rotor System," D-3676, Nov. 1966, NASA. Harris, F. D., "Articulated Rotor Blade Flapping Motion at Low Advance Ration," Journal of the American Helicopter Society, Vol. 17, No. 1, Jan. 1972, pp. 41-48. Ormiston, R. A. and Peters, D. A., "Hingeless Helicopter Rotor Response with Nonuniform Inflow and Elastic Blade Bending," Journal of Aircraft, Vol. 9, No. 10, Oct. 1972, pp. 730736.

Vortex Noise of Isolated Airfoils

This paper presents the first numerical investigation via direct numerical simulation of the tone noise phenomenon occurring in the flow past laminar airfoils. This phenomenon corresponds to the radiation of discrete acoustic tones in some specific flow conditions, and has received much attention since the 1970s, and several experimental studies have been carried out to identify and understand the underlying physical mechanisms. However, several points remain to be clarified in order to provide a complete explanation of its origin. The flow around a two-dimensional NACA0012 airfoil is considered in order to have a deeper understanding of the tone noise phenomenon. Consistently with previous experimental studies, it is shown that depending on the Reynolds number and angle of attack, two different types of acoustic spectrum are observed: one which exhibits a broadband contribution with a dominant frequency together with a sequence of regularly spaced discrete frequencies, while the other one is only characterized by a simple broadband contribution. The first configuration is typical of the tone noise phenomenon. The present work shows that in this case, the mean flow on the pressure side of the airfoil exhibits a separation bubble near the trailing edge and the main tone frequency is close to the most amplified frequency of the boundary layer. The mechanism proposed in previous works for the main tone generation – which implies the existence of a separation bubble at the pressure side – is therefore validated by numerical simulation. On the other hand, the analysis of the suction side boundary layer reveals that there is no separation and that the most amplified frequency is different from the main tonal one. However, the suction side boundary layer is highly receptive to the tone frequency. Finally, an original explanation for the existence of the secondary discrete frequencies observed in the radiated pressure spectrum is given. They are associated to a bifurcation of the airfoil wake from a symmetric to a non-symmetric vortex pattern. A possible explanation for the existence of this bifurcation is the interaction between the disturbances which are the most amplified by the suction side boundary layer and those originating in the forcing of the suction side flow by the main tone noise mechanism.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112007007896

Numerical investigation of the tone noise mechanism over laminar airfoils

The acoustic spectrum of axial flow machines

techniques QN x 10~ -9.3, 10.5, 20.9, for CSORb, GSb, and Jb, respectively and QNA0 >9.3 for SO/?/, due to computational times incurred in determining the optimum value of a( = 1.1 in this case). Testing of the four techniques for other configurations and Mach numbers, subsonic and supersonic, have been performed within the methods of Ref. 1 with essentially equivalent results. Thus, it has been demonstrated that the use of CSOR b results in material savings in computational times over the use of Jh, GSh, andSORh.

Prediction of Airfoil Tone Frequencies

Direct numerical simulations are carried out to investigate the flow features responsible for secondary tones arising in trailing-edge noise at moderate Reynolds numbers. Simulations are performed for a NACA 0012 airfoil at freestream Mach numbers 0.1, 0.2 and 0.3 for angle of incidence 0 deg. and for Mach number 0.3 at 3 deg. angle of incidence. The Reynolds number based on the airfoil chord is fixed at R e c = 1 0 5 . Flow configurations are investigated where noise generation arises from the scattering of boundary layer instabilities at the trailing edge. Results show that noise emission has a main tone with equidistant secondary tones, as discussed in literature. An interesting feature of the present flows at zero incidence is shown; despite the geometric symmetry, the flows become non-symmetric with a separation bubble only on one side of the airfoil. A separation bubble is also observed for the non-zero incidence flow. For both angles of incidence analyzed, it is shown that low-frequency motion of the separation bubbles induce a frequency modulation of the flow instabilities developed along the airfoil boundary layer. When the airfoil is at 0 deg. angle of attack an intense amplitude modulation is also observed in the flow quantities, resulting in a complex vortex interaction mechanism at the trailing edge. Both amplitude and frequency modulations directly affect the velocity and pressure fluctuations that are scattered at the trailing edge, what leads to secondary tones in the acoustic radiation.

On secondary tones arising in trailing-edge noise at moderate Reynolds numbers

: The noise associated with a flight vehicle is generated by two distinct type sources: (1) the propulsion system and (2) the aerodynamic noise associated with movement of the vehicle through the atmosphere. The minimum noise will be radiated when the propulsion noise is eliminated. Measurements were taken of the noise radiated from three sailplanes in order to define the aerodynamic noise and to determine its relation to aircraft size and velocity. The report presents the results obtained from one microphone and relates the overall sound pressure level (SPL) to aircraft parameters.

R. P. Paxson

Papers

Measurements of the radiated noise from sailplanes