TY - GEN
T1 - Stability analysis of jets in crossflow
AU - Regan, Marc
AU - Mahesh, Krishnan
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
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M3 - Conference contribution
AN - SCOPUS:85033241472
T3 - 10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017
BT - 10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017
PB - International Symposium on Turbulence and Shear Flow Phenomena, TSFP10
T2 - 10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017
Y2 - 6 July 2017 through 9 July 2017
ER -