Browsing by Subject "absolute/convective instability"

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    Linear Stability and Sensitivity of a Low-speed Jet in Cross-flow
    (2018-05) Regan, Marc
    The Jet in Cross-flow (JICF) is characterized by a jet of fluid injected transverse to an incoming cross-flow. Complex vortical structures are generated as the cross-flow boundary layer interacts with the jet. The goal of this dissertation is to increase understanding of the stability and sensitivity of the JICF. Achieving this goal will directly benefit the many engineering applications which use the JICF, including gas turbine combustor dilution jets, film cooling, vertical and/or short take-off and landing (V/STOL) aircraft, and thrust vectoring. The JICF is studied . These equations are key components of this research. The JICF is studied using direct numerical simulation of the Navier-Stokes equations, as well as their adjoint, at a Reynolds number of 2000, and two jet-to-cross-flow velocity ratios: R = 2 with an absolutely unstable upstream shear-layer, and R = 4 with a convectively unstable upstream shear-layer. Linear stability analysis of the JICF reveals that the dominant eigenmodes are shear-layer modes whose frequencies match frequencies of the upstream shear-layer observed in simulation (Iyer & Mahesh, 2016) and experiment (Megerian et al., 2007). Asymmetric modes are shown to be more important to the overall dynamics at higher jet-to-cross-flow ratios. Low-frequency modes persist far downstream, and are connected to wake vortices. For R = 4, downstream shear-layer eigenmodes can be more unstable than the upstream shear-layer modes. Adjoint modes show that the upstream shear-layer is most sensitive to perturbations along the upstream side of the jet nozzle exit. Additionally, the lower frequency downstream modes have sensitive regions that extend upstream into the cross-flow boundary layer. Wavemaker results are shown to be consistent with the transition of the upstream shear-layer from absolute to convective instability. Optimal perturbations reveal that for short-time horizons, perturbations that are asymmetric, and grow along the counter-rotating vortex pair, dominate when R = 2. However, as the time horizon increases, growth is focused along the upstream shear-layer. When R = 4, the optimal perturbations for short-time scales are dominated by growth along the downstream shear-layer. For long-time horizons, the optimal perturbations become hybrid modes that grow along the upstream and downstream shear-layers, simultaneously.