# Orifice versus Converging-Nozzle Grid Turbulence: A Wavelet Perspective
## 5 Conclusions  
Velocity signals across the cross-section were measured at X/D = 10 downstream of a turbulence generator using a 3-D hotwire inside a wind tunnel. Two types of perforated plates, an OPP and CNPP, were utilised as the turbulence generator. The perforated plate was mounted at the entrance to the test section, and experiments were carried out at \(\mathrm{Re_{D}}\) of 18,700 and 28,400. The measured turbulent flow was scrutinised using statistical methods and spectral and wavelet analyses to perform a comparative study of the homogeneity level, energy cascade, and nature of coherent structures for both plates. The conclusions drawn from the analysis are presented below. The normalised streamwise time-averaged velocity profiles suggest that both the OPP and CNPP can produce homogeneous turbulence flow at the lower studied \(\mathrm{Re_{D}}\). The relatively thick converging holes of the CNPP become more noticeable at the higher \(\mathrm{Re_{D}}\), resulting in 10% from \(U_{mean}\). Spatial- and temporal-averaged turbulence intensity (\(Tu_{mean}\)) reveals that the OPP can produce more intense and homogeneous turbulence compared to the CNPP. The power spectrum from Fourier analysis confirms that a dominant share of the kinetic energy is associated with the large eddies for both plates. For low frequencies (large eddies), the spectrum for the CNPP lies below the OPP values, bespeaking relatively more energetic large vortical structures are present in OPP-induced turbulence. At the higher studied \(\mathrm{Re_{D}}\) of 28,400, the kinetic energy associated with the moderate frequencies, \(f\approx 140\)-800 Hz, produced by the CNPP somewhat exceeds that of the OPP counterpart. Wavelet analysis decomposes a time series over a time-frequency space, allowing for a more thorough and comprehensive examination of signal information than Fourier analysis. Discrete wavelet transform is used on the fluctuating velocity signal to evaluate the corresponding energy contribution of frequency components. At very high frequencies,i.e., \(f_{\rm a}\gtrsim 6923\) Hz, the detail coefficients clearly show some significant fluctuations in the CNPP with \(\rm Re_{D}=28,400\) case, whereas the fluctuations for the OPP are hardly observed. The higher percentage energy contribution for the detailed component for the CNPP over a wide range of frequencies confirms that small-scale eddies have not yet fully decayed at 10D downstream, and energy is distributed from small-scale to large-scale eddies in the case of the CNPP. Continuous wavelet spectrum provides a clear picture of energy distribution between multi-scale localised structures in the time-frequency space. At lower \(\rm Re_{D}\), the most turbulent bursts lie in the low-frequency range for both plates, with some prominent localised intense-energy regions observed for the OPP at \(f_{\rm a}\lesssim 28.9\). These turbulent bursts are regularly distributed in the time domain, which means that the coherent structures are quasi-static and mostly non-intermittent in nature. However, at higher \(\rm Re_{D}\), turbulence is more intense and non-intermittent for the OPP owing to higher energy magnitudes and a more regular distribution of coherent structures in comparison to the CNPP, where multi-scale coherent structures are sporadically present in the flow. Wavelet analyses revealed sporadic bursts of intense energy over the intermediate range of the turbulence energy cascade produced by the CNPP. This appears to contribute to notable intermittencies and hence inhomogeneity, especially at the higher wind speed. The origin of these intermittent fluctuations is speculated to be associated with the converging channels (nozzles) of the CNPP. Note that the \"zero-thickness\" orificed perforated plate furnishes no such venue for the spawning of these sporadic flow events. Conceptualization, D.S.-K.T. ; methodology, A.R. and Y.Y. ; software, A.R. ; validation, A.R., Y.Y. and D.S.-K.T. ; formal analysis, A.R. ; investigation, A.R. and D.S.-K.T. ; resources, D.S.-K.T. ; data curation, Y.Y.