Validation of a Moving-Body High-Order Immersed Boundary Method for the Multiple Pure Tone Noise Generated by Supersonic Rotor Cascades

Abstract

The objective of this work is the validation of an immersed boundary methodology used for the calculation of the multiple pure tone noise generated by supersonic rotor cascades. This methodology is based on a discrete forcing approach where the boundary conditions are directly imposed on the control volumes that contain the immersed body boundary points, resulting in a sharp representation of the static and moving boundaries. The time-dependent and compressible Euler equations are numerically solved using a finite volume discretization with fourth-order spatial precision, while the time marching process is achieved using a third order Runge-Kutta scheme. The geometry used in the numerical simulations correspond to the tip of the rotor blades and stator vanes of the Advanced Noise Control Fan (ANCF) and the rotor velocity corresponds to an off-design Mach number of 1.1. Four cases are considered: (i) rotor alone in nominal conditions; (ii) rotor-stator interaction in nominal conditions; (iii) rotor alone with stagger angle variations and (iv) rotor-stator interaction with stagger angle variations. These variations are imposed to generate multiple pure tone (MPT) noise in the last two cases and are characterized by a variation of ±0.75 degrees in the stagger angle, randomly distributed along the rotor blades. The first two cases show similar results, where regular rotor shock-waves systems result in spectra dominated by the blade-passing frequency and its harmonics. For those cases, well defined sawtooth patterns of equal amplitude in circumferential stations distributed along the axis direction were observed, which are associated with a shock amplitude decay in the upstream direction that shows excellent agreement with the levels predicted theoretically. In the third case, as a result of the stagger angle variation introduced at each rotor blade, the multiple pure tone generation is clearly observed, characterized by an irregular rotor shock-waves system associated with a spectra clearly dominated by the shaft order and its harmonics. In the fourth case, the influence of the stator vanes is clearly seen by the strong differences of the last two circumferential pressure results, showing the stator vanes effect on the expansion waves between the shocks. In all cases the numerical results are in excellent concordance with the theoretical ones, validating the high-order and moving-body immersed boundary methodology for multiple pure tone generation in two-dimensional rotor and stator cascades.