Evaluation of a Cascade-Based Acoustic Model for Fan Tonal Noise Prediction

Abstract

This study aims at evaluating an analytical model for the prediction of tonal fan noise created by the rotor-stator interaction. The methodology consists of comparing unsteady flow simulations with the cascade-based acoustic model to quantify the influence of some technological effects not included in the model. The simulations are performed with a dedicated turbomachinery flow solver Turb'Flow on a simplified stator vane cascade. They allow discussing the effects of both model assumptions of no vane thickness and inviscid flow on the predictions of the acoustic sources as well as on the modal acoustic powers radiated within the duct. The Kutta condition is found to be efficient to locally represent the viscosity effects, and the vane thickness tends to moderately modify the distributions of the sources and the amplitudes of the duct modes. Moreover, a three-dimensional decomposition of the aerodynamic excitation is proposed and coupled with the three-dimensional analytical cascade response. This fully three-dimensional acoustic model is evaluated by comparisons with an unsteady simulation of a realistic axial compressor stage. An improvement in the prediction of the acoustic sources and powers is clearly shown with respect to the previously used twodimensional version of the model. Nomenclature a = index of intervane channel acoustic mode B = number of rotor blades C = chord, m c 0 = speed of sound, m · s −1 d = nonoverlapping distance of the cascade, m E m;μ = duct radial function of the mode m; μ e = thickness, m f = force per surface unity, N · m −2 G = Green's function h = normal intervane distance, m j = index of the harmonic of the blade-passing frequency k = index of rectilinear cascade acoustic mode k r = spanwise aerodynamic wave number, m −1 M = Mach number m = order of azimuthal duct mode p = acoustic pressure, Pa p = order of the spanwise aerodynamic wave number S = surface, m 2 s= intervane distance, m T r = duct span, m t = time, s U xc = axial velocity in the rectilinear cascade reference frame, m · s −1 U xd = axial velocity in the duct reference frame, m · s −1 V = number of stator vaneŝ W j = azimuthal Fourier coefficient of w, m · s −1 W j;p = azimuthal and radial Fourier coefficient of w, m · s −1 w = upwash velocity (aerodynamic excitation), m · s −1 x, r, θ = cylindrical coordinates y = dimensionless wall distance ΔP = pressure jump across a flat plate (vane response), Pa μ = order of radial duct mode Π j = tonal acoustic power, W σ = intervane phase angle, rad χ m;μ = duct eigenvalue of the duct mode m; μ, m −1 χ s = vane stagger angle, rad Ω = rotational velocity, rad · s −1 Subscripts c = relative to the cascade reference frame d = relative to the duct reference frame H = relative to hub T = relative to tip

Turbomachinery Noise Predictions: Present and Future

“…A comparison between the above analytical model and the u-RANS results is shown in Figure 4 for both the blade response (the noise source) and the sound power level radiated upstream at the first blade passing frequency (BPF). Comparable results have also been found at the first two harmonics of the BPF with the correct modal decomposition [34]. Similar results were found for differents flow regimes and stator configurations for the NASA-ANCF rotor-stator configuration at all BPF with a maximum discrepancy of 5-10 dB on higher-order modes [17].…”

“…Such a flow interaction is for instance shown in Figure 3a in the simulation of the actual CME2 research low-pressure compressor (three rotor blades and four stator vanes) [33]. With a simpler configuration involving the stator only in Figure 3b, de Laborderie could also study several technological effects on tonal noise, such as viscosity, thickness and camber [34]. The first two were found to be negligible whereas the third needed to be accounted for and a modification of the analytical model based on flat plates was then proposed [18].…”

Effect of Distortion on Turbofan Tonal Noise at Cutback with Hybrid Methods

“…The modes caused by the WSI mechanism are all linked to the fluctuations on the OGVs at 2BPF as shown by Equation (9). No particular evolution of these mode amplitudes can be drawn, and the effect of the air-inlet distortion on the WSI mechanism is spread over all modes.…”

“…Hybrid methods stem from the acoustic analogy introduced by Lighthill [1] where source generation and noise propagation are separated steps. Acoustic sources can be extracted from a computational fluid dynamics (CFD) simulation or can be evaluated with analytical models, initially developed for isolated airfoils [2,3] and now extended to account for geometrical and cascade effects [4][5][6][7][8][9][10][11]. These sources can then be propagated either numerically by a computational aeroacoustics (CAA) simulation or analytically by an acoustic analogy.…”