A CFD-BASED MODEL FOR THE STUDY OF THE STABILITY OF CANTILEVERED COAXIAL CYLINDRICAL-SHELLS CONVEYING VISCOUS-FLUID

A new numerical (CFD-based) model is presented for the study of the effects of unsteady viscous forces on the stability of a cantilevered, flexible cylindrical shell concentrically located inside a rigid cylinder, with incompressible viscous flow in the annulus and with stagnant fluid within the shell. Flugge's modified equations are used to describe shell motions, taking into account the steady viscous forces due to flow pressurization and traction effects on the shell; these equations are subsequently solved by the finite difference method. The unsteady viscous forces exerted on the shell are determined from flow perturbations governed by the linearized, unsteady Navier-Stokes equations, which are solved using a recently developed, finite difference based, time-marching technique with artificial compressibility. It was found that the analytical results obtained for a particular set of system parameters are in excellent quantitative agreement with experiment, although the predicted type of instability is not always the same as that observed; the unsteady viscous effects tend to become reduced with diminishing annular gap width, provided that the gap is moderately small.