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.
- Fluids Engineering Division
Flow Over a Sudden Expansion in an Annular Pipe: Steady Axisymmetric Flow and its Stability
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Beladi, B, & Kuhlmann, HC. "Flow Over a Sudden Expansion in an Annular Pipe: Steady Axisymmetric Flow and its Stability." Proceedings of the ASME 2016 Fluids Engineering Division Summer Meeting collocated with the ASME 2016 Heat Transfer Summer Conference and the ASME 2016 14th International Conference on Nanochannels, Microchannels, and Minichannels. Volume 1B, Symposia: Fluid Mechanics (Fundamental Issues and Perspectives; Industrial and Environmental Applications); Multiphase Flow and Systems (Multiscale Methods; Noninvasive Measurements; Numerical Methods; Heat Transfer; Performance); Transport Phenomena (Clean Energy; Mixing; Manufacturing and Materials Processing); Turbulent Flows — Issues and Perspectives; Algorithms and Applications for High Performance CFD Computation; Fluid Power; Fluid Dynamics of Wind Energy; Marine Hydrodynamics. Washington, DC, USA. July 10–14, 2016. V01BT14A014. ASME. https://doi.org/10.1115/FEDSM2016-7896
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