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Acoustically generated unsteady vorticity field in a long narrow cylinder with sidewall injection. (English) Zbl 1012.76086

Authors’ summary: Asymptotic and computational analyses of a well-posed initial-boundary value problem are used to describe the time history of co-existing acoustic and rotational velocity disturbances in a long narrow cylinder with uniform steady sidewall mass injection. Transient planar pressure disturbances prescribed on the open exit plane of the cylinder are the source of acoustic disturbances in the axisymmetric flow. Both asymptotic and numerical solutions describe the nonlinear aspects of flow interactions. The full computational results are compared favorably with those of the asymptotic study to show that: (1) transient vorticity is generated near the injection surface and is transported into the cylinder by the radial velocity component of flow field, (2) at any sufficiently small value of time, a well-defined front separates the fluid containing transient vorticity from a flow field in the interior of the cylinder containing a much smaller amplitude vorticity and, (3) at sufficiently large values of time, vorticity is present throughout the cylinder. In addition, an analytically derived acoustic solution obtained from the asymptotic analysis is used to show that the present numerical solution and all earlier studies of similar problems are missing travelling waves (eigenfunctions) which should be present in a complete mathematical solution of the above initial-boundary value problem.

MSC:

76Q05 Hydro- and aero-acoustics
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
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