Frequency-domain computation of inflow broadband noise due to interaction of a rectilinear cascade of flat plates with incident turbulence

Abstract

This paper deals with the broadband noise due to the interaction between convected turbulent gusts and a rectilinear cascade of flat plates bounded by two parallel walls. An analytic formulation for the acoustic power spectrum due to this turbulence-cascade interaction is derived, which can be used to assess the effects of the span-wise wavenumber components of ingesting turbulent gust on the overall acoustic power spectrum. This three-dimensional theory is based on the two-dimensional theory of Cheong et al. (2006Cheong et al. ( , 2009. The threedimensional model is shown to provide a close fit to the measured spectrum of rotor-stator interaction. The predictions using this threedimensional model are also compared with those using the previous two-dimensional model by Cheong et al. (2006;2009). Through this comparison, it is found that the contributions to the acoustic power of the span-wise wavenumber components of incident turbulent gust are increased as the frequency is augmented, which is mainly due to three-dimensional dispersion-relation characteristics of acoustic waves. This implies that the number of incident turbulent gust modes directly involved in generating cut-on acoustic waves increases as the frequency increases. Therefore, in the lower frequency range, three-dimensional acoustic power is less than its corresponding twodimensional one, whereas, as the frequency increases, the three-dimensional acoustic power spectrum closely follows those of twodimension. The formulation is also used to make a parametric study about the effects on the power spectrum of the blade number, stagger angle, gap-chord ratio, and Mach number.

Time- and frequency-domain computations of broadband noise due to interaction between incident turbulence and rectilinear cascade of flat plates

“…This formulation shows that the error is approximately inversely proportional to the sound speed in the spanwise direction of the concerned acoustic modes. This result quantitatively clarifies the limitations of applying the frequency-domain method of Wei & Cheong (2010) to the three-dimensional turbulence-cascade interaction problems. Secondly, the prediction results using the time-domain CAA method are compared with those from the full three-dimensional rectilinear model that is believed (C. Cheong).…”

“…BROLIN3D code [20] and the fully 3D rectilinear cascade model [18,19] are used to predict three-dimensional fan broadband noise in the frequency domain and to compare their results with CAA ones. These frequency-domain methods are summarised briefly in the following subsections.…”

“…The investigation is carried out by comparing the prediction results obtained by employing the time-domain CAA method with those using existing frequency-domain methods. A semi-analytic model (Wei & Cheong, 2010) and a full three-dimensional rectilinear cascade model (Lloyd & Peake, 2008;Lloyd, 2009) are adopted for the frequency-domain computations. By comparing these computation results, the three-dimensional characteristics of inflow turbulence noise are investigated; in particular, the effects of the wavenumber components of ingested turbulence in the spanwise direction are taken into consideration in the investigation.…”

“…After the validation, the two-dimensional CAA code is extended to a three-dimensional one. The predicted broadband noise results from the CAA are firstly compared with those from BROLIN3D code [20] in terms of the modal magnitudes of acoustic pressure in the mode-frequency map and the frequency spectra of the three-dimensional acoustic fields. It is observed that there is a significant difference between the two predicted acoustic pressure modes with higher spanwise mode orders.…”

“…Subsequently, the time-domain CAA results are also compared with those from the full threedimensional rectilinear code [18,19] to validate the three-dimensional CAA code and make clearer the reason of the differences previously observed. In the following section, a brief review of BROLIN3D code [20] and a full three-dimensional rectilinear cascade model [18,19] are presented. In Section 3, the computation of the broadband noise due to the interaction between the incident turbulence and the rectilinear cascade bounded by side walls by using the CAA techniques in the time domain is presented.…”