Unsteady Annular Viscous Flows Between Oscillating Cylinders. Part II: A Hybrid Time-Integration Solution Based on Azimuthal Fourier Expansions for Configurations with Annular Backsteps

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

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 568 KB
• Volume: 8
• Category: Article
• ISSN: 0889-9746
• DOI: 10.1006/jfls.1994.1025

✦ Synopsis

A hybrid time-integration method based on azimuthal Fourier expansions for solving the time-dependent incompressible Navier-Stokes equations has been developed in order to obtain superior computational efficiency; this will permit the simultaneous time-integration of the coupled systems of equations of fluid and structural unsteady motions. The hybrid method uses highly convergent Fourier expansions in the azimuthal angular coordinate for the unsteady pressure and velocity components while maintaining the same efficient finite-difference formulation for time and the axial and radial spatial coordinates as in the basic time-integration method previously developed (in Part I). This method has been first applied for validation to several 2-D and 3-D unsteady flows in annular passages with oscillating boundaries, leading to solutions which were found to be in very good agreement with the results obtained with the basic method. A rigorous Navier-Stokes solution has been obtained for the first time with this method for 3-D unsteady flow in nonuniform annular passages with an annular backstep, and with oscillating boundaries. The hybrid method displays excellent computational efficiency, at least one order of magnitude better than the basic time-integration method (itself very efficient) in all cases tested; hence, this method is well suited for eventual use in the simultaneous time-integration of the coupled systems of equations in fluid-structure interaction problems.