Global linear stability analysis of jets in cross-flow

The stability of low-speed jets in cross-flow (JICF) is studied using tri-global linear stability analysis (GLSA). Simulations are performed at a Reynolds number of 2000, based on the jet exit diameter and the average velocity. A time stepper method is used in conjunction with the implicitly restarted Arnoldi iteration method. GLSA results are shown to capture the complex upstream shear-layer instabilities. The Strouhal numbers from GLSA match upstream shear-layer vertical velocity spectra and dynamic mode decomposition from simulation (Iyer & Mahesh, J. Fluid Mech., vol. 790, 2016, pp. 275–307) and experiment (Megerian et al., J. Fluid Mech., vol. 593, 2007, pp. 93–129). Additionally, the GLSA results are shown to be consistent with the transition from absolute to convective instability that the upstream shear layer of JICFs undergoes between $R=2$ to $R=4$ observed by Megerian et al. (J. Fluid Mech., vol. 593, 2007, pp. 93–129), where $R=\overline{v}_{jet}/u_{\infty }$ is the jet to cross-flow velocity ratio. The upstream shear-layer instability is shown to dominate when $R=2$, whereas downstream shear-layer instabilities are shown to dominate when $R=4$.

Flow Over a Sudden Expansion in an Annular Pipe: Steady Axisymmetric Flow and its Stability

The stability of the axisymmetric incompressible Newtonian flow in an annular pipe suddenly expanding radially inward is investigated. The axisymmetric steady basic flow is discretized using primitive variables and second-order finite volumes on a staggered grid. The resulting algebraic equations are solved by Newton–Raphson iteration. A three-dimensional global linear stability analysis is performed. The solutions to the linear stability problem are represented by normal modes. The generalized eigenvalue problem is solved using an implicitly restarted Arnoldi algorithm which is provided by the ARPACK library and a Cayley transformation. Stability boundaries have been computed for a range of parameters varying the outlet radius ratio. The physical instability mechanisms are studied by a an posteriori analysis of the kinetic energy transferred between the basic state and the critical mode. Neutral curves and critical modes are presented and the instability mechanisms are discussed.