Unsteady Annular Viscous Flows Between Oscillating Cylinders. Part I: Computational Solutions Based on a Time-Integration Method

✍ Scribed by D. Mateescu; M.P. Paı̈doussis; F. Belanger

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 581 KB
• Volume: 8
• Category: Article
• ISSN: 0889-9746
• DOI: 10.1006/jfls.1994.1024

✦ Synopsis

The paper presents 2-D and 3-D computational solutions for unsteady annular viscous flows with oscillating boundaries. A time-integration method based on a three-time-level implicit semi-discretization is first formulated in cylindrical coordinates for solving the time-dependent incompressible Navier-Stokes equations. This method uses a pseudo-time integration with artificial compressibility to advance the solution between consecutive real time levels, and a finite-difference spatial discretization based on a stretched staggered grid. A decoupling procedure based on a factored ADI scheme with lagged nonlinearities reduces the problem to the solution of scalar tridiagonal systems. As a result, this method displays very good computing efficency and accuracy in all numerical examples analysed.

The method is first validated for axisymmetric flow over an annular backstep, by comparison with previous results, and is then employed to analyse 2-D unsteady annular flows due to transverse oscillations of the outer boundary. The results obtained with this method are free of spurious, numerically induced, oscillations in the unsteady pressure, which otherwise arise if a Crank-Nicolson scheme is used instead for time-discretization. The 3-D case of oscillating boundaries in annular axial flow is also analysed with this method by considering a fully developed viscous axial flow between two concentric cylinders when the central portion of the outer cylinder executes transverse translational oscillations; the computational solution thus obtained is of interest in the study of flow-induced vibration problems in such configurations.