ANALYSIS OF 2-D AND 3-D UNSTEADY ANNULAR FLOWS WITH OSCILLATING BOUNDARIES, BASED ON A TIME-DEPENDENT COORDINATE TRANSFORMATION

The paper presents 2-D and 3-D solutions for unsteady annular, viscous laminar hows between oscillating cylinders, which are accurate for bo th large and small amplitude oscillations. These solutions are obtaine d with a newly developed method based on a time-dependent coordinate t ransformation, which permits a rigorous implementation of the boundary conditions on the moving boundaries, without resorting to any restric tive assumptions. The present solutions are compared with previous res ults obtained for the 2-D case with methods based on the small amplitu de assumption. It was found that the two sets of results are increasin gly different for larger amplitudes of oscillations, especially as reg ards the imaginary components of the unsteady pressure, which determin e its phase lag with respect to the solid wall oscillations (of intere st in how-induced vibration analysis). Furthermore, 3-D solutions are obtained for both uniform annular passages and configurations with an annular backstep, subjected or not to axial flow. The present solution s are also compared with unsteady pressure measurements made by the au thors. Very good agreement was found between the present solutions and experimental results. (C) 1996 Academic Press Limited