Narrow band sound power spectra: Hanning windowing. 

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... of the segment is multiplied by the geometric periodicity in order to estimate the sound power of the full domain model. For far field analysis, i.e. for the computation of the sound pressure at defined microphone positions in the far field, ACTRAN solves the FW-H equations in the frequency domain by applying the Direct Fourier Transformation (DFT). In general the recorded time samples correspond to a finite or truncated part of a signal provided by CFD simulations. Therefore, the Fourier transformed truncated waveform may result different spectral characteristics compared to a continuous-time signal. To minimize this (leakage) effect, an appropriate window function can be applied. This will enforce a continuity at the end points of the signal and therefore result in a continuous waveform without sharp transitions. Different types of window functions are implemented in ACTRAN; each with their own advantage and preferred application. So for selecting a window function it is advisable to estimate at first the frequency information content of the signal. In principle, the nature of jet mixing creates turbulent eddies which cause a prevalent random sound signal and accordingly a broadband characteristic in the frequency domain. On the other hand, the presence of the mixer adds complexity to the jet flow fields. The nature of the turbulent flow field close to the nozzle exit plane, for example quantified by the turbulent kinetic energy (TKE), shows typically a circumferential periodical pattern, evidently caused by the lobed mixer annulus. This may cause sound modes at frequencies which correlate to the number of lobes. Furthermore, based on practical experience, the forced mixer generates high frequency source noise, commonly labeled “mixer excess noise”. The mixer excess noise is most probably associated with a marked increase in turbulence level in the outer shear layer as penetration increases [Ref. 7]. Following the basic principles of signal analysis, the ‘r ectangular windowing ’ yields the same energy content for the Fourier solution as for the time signal (amplitude accuracy). It is also self-evident to apply rectangular windowing, equivalent to uniform windowing, if the type of signal is random. For comparison, FW-H far-field predictions have also been performed using the Hanning window, which is advised for a better frequency resolution to discover potential tonal spectral characteristics as e.g.’ mixer excess noise ’ . But in contrast to the rectangular window, the Hanning window reduces the energy content of the original signal. As outlined more detailed in chapter III , the prediction results based on both window functions, ‘ r ectangular’ and Hanning, have been compared with benchmark data. Before starting the computations relevant for the benchmark test, Actran results have been successfully cross- checked with the outcome of DLRs FW-H method as described in [Ref. 1]. Within previous full domain simulations i.e. applying the periodic boundary conditions, the sound power spectra (PWL) based on the CFD-data of the given 3 various FW-H surfaces have been predicted by using rectangular windowing (Fig. 5). In view of the benchmark test as described in the next chapter, it is worth noting, that the surfaces (maximum axial extension one nozzle diameter downstream of nozzle exit plane: x*/D= 1) cover not only acoustic sources relevant for forced mixer noise but also sources influenced by the shearing action caused by the relative speed between the exhaust jet and the atmosphere. Regarding Fig. 5, the PWL spectra follow an overall trend as typical for jet noise. Thus, the maximum level occurs in the low frequency range, around the 1/3 octave mid frequency 315 Hz. The total sound power (OAPWL) for the “open” surfaces 05000 and 05100 are almost the same. Deducing from that, both surfaces - even type 05000 radially closer to the unsteady flow field - are suitable to meet the FWH-interface criterion. Compared with the “radia lly closed” surface 04999, the corresponding OAPWL is clearly higher (about 6 dB), because the surface enclose even more acoustic sources. Although the surface topology does not comply with the above mentioned interface criterion, the shape of the spectrum follows the global trend. This study focus on benchmarking the prediction results with obtained mixer noise data, generated by a further developed version of the semi-empirical ISVR/Purdue method [Ref. 7, 8, 9], which is extensively validated with scale model lobed mixer data and full-scale engine noise data, as well. The basis of the semi-empirical method relies on the fact, that the jet plume can be devided axially into regions downstream from the nozzle exit plane. The jet noise sources are then characterized by the jet parameters velocity, temperature, diameter and turbulent properties of 4 American Institute of Aeronautics and Astronautics the corresponding regions. For the purpose of comparability, the FW-H solution has been post-processed not only for the whole surface, but also for subareas enclosing the turbulent sources at various relative axial lengths x*/D, ranged from 18% to 100 %. Fig. 6a and 6b show the predicted PWL spectra referring to surface 05000 (reference). The comparison of rectangular versus Hanning windowing results shows spectra of similar trends for x*/D= 18% and 35%, characterized by significant peak levels at frequencies 500 Hz and 6.3 kHz. With increasing axial distance downstream from the nozzle exit, the portion of the low frequency broadband noise rises obviously and overshadows the peak level at 500 Hz. In contrast to the result based on Rectangular windowing, the applied Hanning window resolves the peak level at 6.3 kHz even for the whole available FW-H analysing domain. A more detailed investigation by means of the narrow band spectrum (Fig. 7) and azimuthal directivity at nozzle exit plane of the real parts of the sound pressure p_re (Fig. 8) leads to the following finding: The maximum power level occurs also at the narrow band frequency of 500 Hz and the level decreases clearly at the neighbouring frequencies. The peak levels at 6.15, 6.2, 6.6 and 6.65 kHz contribute significantly to the 1/3 octave level at 6.3 kHz. According to Fig. 8, the real part of the sound pressure of the relevant low frequencies are constant across the whole azimuthal range. In contrast to that, the circumferential p_re patterns referring to peak levels in the 1/3 octave band 6.3 kHz are obviously periodic of mode order 14 equivalent to the mixer’s lobe number. It has been proven, that the directivity curves in the range below the 1/3 octave frequency of 4 kHz show marginal periodical or none periodical patterns of order m=14. The low frequency peak level at 500 Hz appears to correlate with a Strouhal- number St= 2 as given through the relation St= f ∙ D/ v, where v and D are the jet characteristic velocity and diameter, respectively. The value is within the range of experience (St= 1. to 2.5) which have been inferred from noise data of 12-lobed mixer configurations [Ref. 7]. Regarding the interpretation of the characteristic 1/3 octave band level at 6.3 kHz, two points of view are self-evident: On the one hand, the spectral shape deals with high frequency source noise, generated by the forced mixer. On the other hand, the tendency may be probably caused by the periodicity condition from the CFD computation, which distributes the sound energy on sound modes of azimuthal order m= i ∙ 14, with i= 0, 1, 2, etc.. The latter interpretation follows the findings given in [Ref. 6], which compares the results of “classical” full domain with quarter domain simulations by applying periodic boundary condition. These aspects have been taken into consideration by interpreting the prediction results compared with the benchmark data (free-field data i.e. lossless corrected in the sense of atmospheric damping) as shown in Fig. 6b. Thus, the prediction overestimates the mixer noise obviously in the low frequency range around 500 Hz. Regarding the spectral shape around 6.3 kHz, the benchmark curve is typically characterized by broadband noise in contrast to the prediction as mentioned above. For the case of the remaining range within 1 kHz and 4 kHz, the predicted levels are close to the benchmark curve. But even for that range of frequency, we would expect lower levels compared with the benchmark curve, because the benchmark data are deduced from a wider axially extended region of the jet plume, 5-times magnified as for the computational setup. The observed tendency of global overestimation is in line with the conclusion from [Ref. 6]. The comparison with benchmark data have demonstrated, that the prediction by using the FW-H surface integral method applied for DES-data, reproduces the main features of the forced mixer noise spectrum and directivity. Thus, the predicted noise is predominant at low frequencies being verified with Strouhal-numbers of characteristic jet parameters. However, concerns are advisable on the interpretation of the absolute levels and especially spectral characteristics linked to azimuthal directivities, showing mode orders of integer multiples of the lobe numbers of the forced mixer. Thus, the usage of DES data based on segment modeling applying periodic boundary conditions modifies turbulent structures artificially which has a strong influence on the acoustic radiation. Therefore, further studies will focus on the comparison of segment domain with classical full domain simulations to improve the degree of ...