Numerical Simulation of Multiple Pure Tone Noise Generated by Supersonic Rotor Cascades

The objective of this work is the validation of a moving-body immersed boundary methodology used for the calculation of multiple pure tone noise generated by supersonic rotor cascades. This methodology is based on a discrete-forcing approach for which the boundary conditions are directly imposed on control volumes associated with moving or static surfaces. Four cases are considered: 1) rotor alone in nominal conditions; 2) rotor–stator interaction in nominal conditions; 3) rotor alone with stagger angle variations; and 4) rotor–stator interaction with stagger angle variations. For all cases, the rotor blades are treated by the immersed boundary methodology as moving surfaces with supersonic speed. Cases 1 and 2 are characterized by a regular shock-expansion system, moving along with the supersonic rotor blades, that shows well-defined sawtooth patterns of equal amplitude in the circumferential direction. The decay of the shock intensity of the system along the axial direction show excellent agreement with the theoretical predictions. Case 3 evidences the generation of multiple pure tones, characterized by irregular sawtooth patterns in the circumferential direction that show excellent agreement with the semianalytical method predictions. In case 4, the progressive differences in the upstream direction between the numerical results and the semianalytical method predictions emphasize the influence of the stator vanes in the pressure field that cannot be captured by the latter.