Wavelet transform as a tool to identify turbulent spots within a transitional boundary layerSatyajit De*, Aditya Anand*, Sourabh S. Diwan**Gas turbine blades are subjected to high freestream turbulence and hence the boundary layers formed over them undergo “bypass transition”. Moreover, rust on the blades and accumulated roughness in the form of soot, aerosols etc. also contribute to making the flow transitional. This type of transition takes place through generation, propagation and merging of “turbulent spots”. The spots are small bursts of turbulent patches embedded in a quasi-laminar flow. The spots grow in size and merge together to give rise to a fully turbulent boundary layer. Identifying spots in the entire transition region in an experiment is a difficult task as the disturbance field in a transitional boundary layer is broadband. Moreover, noise in the signal further corrupts the data. In this work we present a method based on wavelet transform (Torrence &amp; Compo, 1998) to identify the spotty regions within a transitional zone. Identifying spots is important as it reveals the location of spot generation and how they propagate; this in turn helps to predict the macroscopic properties of the flow, such as skin-friction coefficient. Towards this purpose, experiments were carried out on a flat plate kept in a low-speed open circuit wind tunnel (Anand &amp; Diwan, 2020). A roughness strip was pasted near the leading edge to trip the boundary layer to make it transitional; this mimics the roughness present near the leading edge on a gas turbine blade. Single axis hotwire measurements were made at different downstream locations spanning the entire transition zone and the velocity signals are subjected to wavelet analysis. The major benefit of the wavelet transform over the traditional Fourier transform is that it is also able to preserve timewise information along with the frequency; for example, see Zhang et. al. (2018). Broadband energy peaks are clearly visible in the wavelet transform contours wherever the turbulent spots appear in the velocity signals and contour regions for laminar zones remain inactive. We exploit this feature to distinguish between the laminar and turbulent patches within a signal. The existing methods for detecting turbulent spots largely rely on the first or second derivative of velocity fluctuations (Jahanmiri 2011), but the resulting “detector” function does not always lead to a good ‘discriminator”, especially towards the beginning and the end of the transition zone. Also, manual intervention is typically needed to remove false detections. On the other hand, our wavelet transform method provides a good discriminator over the entire transition zone and can be used as an effective tool for identifying turbulent spots in a transitional boundary layer. &nbsp;In particular we identify five regions within the transition zone, namely, laminar, onset of transition, transitional, nearly turbulent and fully turbulent, and present our results using the wavelet analysis. The method can be applied to any velocity signal, including that obtained for the boundary-layer transition over gas turbine blades.* Doctoral student, IISc Bangalore, India** Assistant Professor, IISc Bangalore, IndiaReferencesTorrence, C. and Compo, G. P. (1998). “A practical guide to wavelet analysis". Bull. Amer. Met. Soc. 79.1, 61-78.&nbsp;Anand, Aditya &amp; Diwan, Sourabh. (2020). “Time-frequency analysis for two cases of boundary-layer transition induced by random distributed roughness”. Exp. Fluids. 61. Issue 2.Mohsen Jahanmiri, (2011) “Turbulent-Nonturbulent Interface Detection methods in Transitional flows”, Division of Fluid Dynamics Department of Applied Mechanics Chalmers University of Technology, Research report:11Wen Zhang, Peiqing Liu, and Hao Guo, (June 2018) “Conditional Sampling and Wavelet Analysis in Early Stage of Step-Generated Transition” AIAA J. Vol. 56, No. 6&nbsp;

Wavelet Transform as a Tool to Identify Turbulent Spots Within a Transitional Boundary Layer

Paper Proceedings: https://asmedigitalcollection.asme.org/GTINDIA/GTINDIA2021/volume/85536

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