An investigation of the Reynolds-number dependence of the axisymmetric jet mixing layer using a 138 hot-wire probe and the POD

The Proper Orthogonal Decomposition (POD) technique is applied to find the effects of Reynolds number and the characteristics of the organized motions or coherent structures as a function of downstream position in a turbulent axisymmetric shear layer. In this experiment measurements were made at positions of x/D = 2 to 6 spaced 0.5x/D apart along downstream direction for the three different jet Reynolds number of 78 400, 117 600, and 156 800. Data were taken simultaneously at all measuring positions using 138 hot-wire probes. One of the goals of this investigation was to quantify how the energy distribution among the various modes varied as a function of Reynolds number and to determine when or if ever the asymptotic trends become Reynolds number independent. Also, since the earlier experiments were performed at only a single downstream position, another goal was to investigate whether the modal character of the flow changed with downstream position. In brief, the distributions of POD mode energy have strong dependence on x/D. Even more surprising, mode-0 behaves in a manner entirely different than the higher modes. Also, the results are very nearly independent of Reynolds number. The lowest azimuthal mode (mode-0) for all POD Modes, which dominate the dynamics at x/D = 2 dies off rapidly downstream. On the other hand, for the higher azimuthal modes, the peaks shift to lower mode numbers and actually increase with downstream distance. The eigenvalues from the first POD mode vary as a function of mode azimuthal number for (m ≥ 1), downstream distance and Reynolds number. With i ii scaling by x/D, they collapse for all Reynolds numbers onto a single curve. The full-field streamwise instantaneous fluctuating velocity was reconstructed from the POD modes. Modes constructed from these show clearly that the “volcano”like events around x/D = 2 to 3 evolve into a more“propeller”-like pattern where the number of “blades” diminishes downstream. It will be argued that this behavior is similar to that predicted from inviscid instability theory. Acknowledgements I would like to thank, first of all, my mentor Professor William K. George for his unrelenting guidance and support throughout the research and beyond. My stay in TRL (Turbulence Research Laboratory) was a wonderful time to be with him and to discuss turbulence with him. He showed me what the scientist is and how the scientist works as an advisor and a frontier in turbulence. I also want to thank Professor Dale B. Taulbee and Professor Hui Meng for being on my dissertation committee. I would like to thank Professor Lawrence Ukeiley of the University of Mississippi for being the outside reader. I also would like to thank Dr. Mark Glauser (Syracuse University), and Dr. Daniel Ewing (Mcmaster University, Canada) for the constructive comments for my research. I would like to give special thanks to Scott Woodward for his help for my experiments. He was a great helper to finish my research including the operation of the experiment and computer networking as a staff and a good friend with Lu. Also, I would like to appreciate all my colleagues, Dr. Martin Wosnik (CTH, Sweden), Dr. Asad Sadar (Air International), Dr. Honglu Wang, Dr. Luciano Castillo (RPI), PhD. Candidate Stephan Gamard, and PhD candidate Peter Johansson (CTH, Sweden). They are very kind and helped me a lot to settle down this TRL, to enjoy American (Swedish) life, and to improve academic research as well. Also, I could not forger the help from Kenny at machine shop, Daniel Kook at TRL. I would like to thank Heetae, Yoontae, and Hyejung for all their endless love and support in spite of a poor dad and husband. Without their help, I am sure that it iii iv would not have been possible to achieve my research goals. I really appreciate what they have done for me. Also, I would like to thank to my mom and brothers, my parent-in-law and brother-in-law, and sisters-in-law. I would like to express special thanks priest Dominic Jung (St. Andrew Kim at Buffalo) who taught me how to trust God and support me as spiritual guidance. I would like to express my appreciation to the Korea Air Force Head Quarters and Korea Air Force Academy for their financial support and allowing me to have the opportunity for my PhD. program as well. I would like to have a chance to contribute what I learned here to my student as what Bill have done for me.