Fluid Forces on Rods Vibrating in Finite Length Annular Regions

Abstract

Approximate expressions for the fluid forces acting on a central, rigid rod translating periodically in a finite length annular region of confined fluid are derived from the Navier-Stokes equations for a range of geometric and fluid parameters where viscous damping is significant. Based on the derived forces, lumped added mass, and linear dashpot modeling of an annular gap support typically found in nuclear reactors is employed to predict the fundamental frequency and modal damping of a single beam. Test methods and results for the same beam are presented which indicate the force expressions are applicable for small fluid motions.

One-dimensional leakage-flow vibration instabilities

“…Since circumferential squeeze flow due to center body motion in the annular region is significant only for relatively long annuli [5], the excitation mechanisms for leakage flow between two flat and parallel surfaces can be expected to be similar to those of an annular region for many practical configurations.…”

“…The damping coefficient CD will not decrease to zero as VS + 0 but will attain a finite positive value [5].…”

“…Conservation of mass requires that the net mass flow rate into the control volume, of width H and infinitesimal length in the flow direction, must equal the rate of increase of the mass in the control volume due to the wall motion, or 3U _ dH (5) ax…”

Cross-Flow-Induced-Vibrations in Heat Exchanger Tube Bundles: A Review

“…Support damping has developed a semi-empirical expression to formulate support damping, using Mulcahys' theory (Mulcahy, 1980 (31) where N is the number of spans, b t is the baffle or support plate thickness, and l is the tube unsupported span. A review of two-phase flow damping is presented by (Khushnood et al, 2003).…”

Leakage flow-induced vibration of an eccentric tube-in-tube slip joint

“…The most recent testing [6] concentrated on determining critical flowrates, flow damping, and pressure drops for the slip joint when the telescoping tubes were initially concentric. Here, the same quantities are reported for different degrees of initially eccentric tubes.…”