Effect of tensor representations for high-order turbulence correlations in complex axi-symmetric flow fields

Afsar, M. Z. and Gryazev, V. and Markesteijn, A. and Karabasov, S.; (2021) Effect of tensor representations for high-order turbulence correlations in complex axi-symmetric flow fields. In: AIAA Aviation 2021 Forum. AIAA, USA. ISBN 9781624106101 (https://doi.org/10.2514/6.2021-2280)

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Dual-stream flows are common feature of turbofan engines in civil aviation. For jet flows with a significant (i.e. proportional of total mass flow) bypass stream, transport of momentum through mixing between streams may cause an apparent departure of axi-symmetric turbu- lence conditions. One of the pertinent features of such departure is the difference in amplitude of transverse diagonal components of velocity and Reynolds stress based correlation function– that is correlation tensors of rank 2 and 4 respectively. Since these functions play a direct role in, among other things, the sound generation process, their accurate representation into an irreducible tensor form is vital in Engineering analysis. This paper builds on our previ- ous work (AIAA 2020-2573, [1]) in which we assessed the kinematic structure of generalized auto-covariance tensor using turbulence data obtained by highly resolved Large-Eddy Simu- lations of complex dual stream jets. Now, however, we extend this work further by showing how a generalized form of the axisymmetric representation theory of the appropriate tensor correlation functions can be determined by exploiting the experimental observation that such correlation metrics are localized in small azimuthal separations for axisymmetric jets. The paper summarizes the new theory and shows initial comparisons of an appropriate tensor form using LES data reported in our previous work.