A Time Domain Analysis of Gust-Cascade Interaction Noise

The gust response of a 2–D cascade is studied by solving the full nonlinear Euler equations employing higher order accurate spatial differencing and time stepping techniques. The solutions exhibit the exponential decay of the two circumferential mode orders of the cutoff blade passing frequency (BPF) tone and propagation of one circumferential mode order at 2BPF, as would be expected for the flow configuration considered. Two frequency excitations indicate that the interaction between the frequencies and the self interaction contribute to the amplitude of the propagating mode. 1. INTRODUCTION One of the main contributors to fan tone noise is the so-called rotor-stator interaction noise. It is the result of the interaction of the periodic disturbances of the rotor blade (mean) wakes with the stator vanes. One method of computing rotor-stator interaction was described in detail in [1], in which a two-dimensional strip description of the unsteady aerodynamic interaction between the rotor wakes and the stator vanes is combined with a 3–D acoustic response of an annular cascade to an incident gust. To improve the computation of unsteady aerodynamics, a time-linearized analysis method is used in [2], where a linearized Euler analysis is shown to produce reasonably well the first two harmonics of the blade passing frequency (BPF). On the other hand, nonlinear time-domain analyses would enable understanding of linear-nonlinear regimes, self interactions and interactions of two-frequencies. At NASA Glenn Research Center, an effort is underway to develop a nonlinear time marching algorithm to examine rotor wake - stator interaction noise. In the present paper a non-linear time marching approach is used to compute the gust response of a 2–D cascade. The gust cascade interaction problem can be analyzed employing either a time-linearized approach or a nonlinear time marching approach. A number of time-linearized analyses have been carried out starting with the Sears problem of an airfoil encountering a gust. Some of these studies are summarized in [3]. In a time-linearized analysis, the gust is assumed to be a small harmonic perturbation of the uniform steady mean flow, yielding a system of equations in the frequency domain. However, in the recent linearized Euler analyses (e. g. [2]) fully nonuniform mean flows are considered. In the time-linearized, frequency domain approach,