Stability analysis of jets in crossflow

Marc Regan, Krishnan Mahesh

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Jets in crossflow (JICFs), or transverse jets, are a canonical flow where a jet of fluid is injected normal to a crossflow. The interaction between the incoming flat-plate boundary layer and the jet is dependent on the Reynolds number (Re = vjD/v), based on the average velocity (vjet) at the jet exit and the diameter (D), as well as the jet-to-crossflow ratio (R = vjet/u). Megerian et al. (2007) performed experiments at Re = 2000 and collected vertical velocity spectra along the upstream shear-layer. They observed that the upstream shear-layer transitions from absolutely to convectively unstable between R = 2 and R = 4. Using an unstructured, incompressible, direct numerical simulation (DNS) solver, Iyer & Mahesh (2016) performed simulations matching the experimental setup of Megerian et al. (2007). Vertical velocity spectra taken along the upstream shear-layer from simulation show good agreement with experiment, marking the first high-fidelity simulation able to fully capture the complex shear-layer instabilities in low speed jets in crossflow. Iyer & Mahesh (2016) proposed an analogy to counter-current mixing along the leading edge shear-layer to explain the transition from an absolute to convective instability. In addition, Iyer & Mahesh (2016) performed dynamic mode decomposition (DMD) of the velocity field, which reproduced the dominant frequencies obtained from the upstream shear-layer spectra. In the present work, the stability of JICFs is studied when R = 2 and R = 4 using global linear stability analysis (GLSA) (i.e Tri-Global linear stability analysis), where the baseflow is fully three-dimensional. A variant of the implicitly restarted Arnoldi method (IRAM) in conjunction with a time-stepper approach is implemented to efficiently calculate the leading eigenvalues and their associated eigenmodes. The Strouhal frequencies (St = fD/vjet), based on the peak velocity (vjet) at the jet exit and the diameter (D), from linear stability analysis are compared with experiments (Megerian et al., 2007) and simulations (Iyer & Mahesh, 2016). The eigenmodes are analyzed and show evidence that supports the transition from an absolutely to convectively unstable flow. Additionally, the adjoint sensitivity of the upstream shear-layer is studied for the case when R = 2. The location of the most sensitive areas is shown to be localized to the upstream side of the jet nozzle near the jet exit. The wavemaker for the upstream shear-layer is then calculated using the direct and adjoint eigenmodes for case R = 2. The results further justify the absolutely unstable nature of the region near the upstream side of the jet nozzle exit.

Original languageEnglish (US)
Title of host publication10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017
PublisherInternational Symposium on Turbulence and Shear Flow Phenomena, TSFP10
Volume3
ISBN (Electronic)9780000000002
StatePublished - Jan 1 2017
Event10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017 - Chicago, United States
Duration: Jul 6 2017Jul 9 2017

Other

Other10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017
CountryUnited States
CityChicago
Period7/6/177/9/17

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