S.S. Chen

Flow-Induced Vibration of Circular Cylindrical Structures

This report summarizes the flow-induced vibration of circular cylinders in quiescent fluid, axial flow, and crossflow, and applications of the analytical methods and experimental data in design evaluation of various system components consisting of circular cylinders.

Vibration of nuclear fuel bundles

Abstract Several mathematical models have been proposed for calculating fuel rod responses in axial flows based on a single rod consideration. The spacing between fuel rods in liquid metal fast breeder reactors (LMFBRs) is small; hence fuel rods will interact with one another due to fluid coupling. The objective of this paper is to study the coupled vibration of fuel bundles. To account for the fluid coupling, a computer code (AMASS) is developed to calculate added mass coefficients for a group of circular cylinders based on the potential flow theory. The equations of motion for rod bundles are then derived including hydrodynamic forces, drag forces, fluid pressure, gravity effect, axial tension and damping. Based on the equations, a method of analysis is presented to study the free and forced vibrations of rod bundles. Finally, the method is applied to a typical LMFBR fuel bundle consisting of seven rods.

Parallel-flow-induced vibration of fuel rods

A mathematical model is proposed to describe the phenomena of parallel-flow-induced vibrations of a flexible rod, and a solution is obtained for a rod with arbitrary end conditions; the solution can be used for fixed, hinged, cantilevered, and other elastically supported end conditions. Comparisons between model predictions and flow-test data for rods with fixed and cantilevered end conditions show that the model successfully predicts the essential features of the system behavior: (1) the adjacent rods and duct wall may considerably increase the added mass; (2) the fundamental frequency may increase or decrease with flow velocity, depending on the end conditions; (3) the system damping increases with increasing flow velocity, and is attributed to the normal drag force and the Coriolis acceleration; (4) the rms rod response increases with flow velocity and follows an approximate power function relationship; and (5) the increase in rigidity at the ends tends to reduce the rms response.

GUIDELINES FOR THE INSTABILITY FLOW VELOCITY OF TUBE ARRAYS IN CROSSFLOW

Abstract Fluid flowing across a tube array can cause dynamic instability. Once large-amplitude oscillations occur, severe damage may result in a short time. Such instability must be avoided in design. This paper presents a brief review of different instability models and stability maps developed based on a semi-analytical model and published experimental data.

A general theory for dynamic instability of tube arrays in crossflow

A general theory of fluidelastic instability for a tube array in crossflow is presented. Various techniques to obtain the motion-dependent fluid-force coefficients are discussed and the general instability characteristics are summarized. The theory is also used to evaluate the results of other mathematical models for crossflow-induced instability.

Experiments on fluid elastic instability in tube banks subjected to liquid cross flow

An extensive test program was carried out to study fluid elastic instability of tube arrays subjected to cross flow. Critical flow velocities for 12 tube arrays with different spacing, mass ratio, damping, and detuning are established. From the experimental data, a stability map has been prepared; this is useful in design to avoid detrimental fluid elastic instability.

Dynamics of a coupled shell-fluid system

Abstract This paper presents a study of two concentrically located circular cylindrical shells containing and separated by fluids. An exact frequency equation is derived for the general case and an approximate closed-form solution is obtained for the shell system with an incompressible fluid. It is found that the lowest frequency of the coupled system is associated with one of the out-of-phase modes, and is lower than the frequencies of the individual shells.

Crossflow-induced vibrations of heat exchanger tube banks

Abstract This paper presents a mathematical model for crossflow-induced vibration of tube banks. Motion-dependent fluid forces and various types of flow noises are incorporated in the model. An analytical solution for the fluid inertia force, hydrodynamic damping force, and fluid elastic force is given for tube banks arranged in an arbitrary pattern. Based on the model, a better understanding of the vibrations of heat exchanger tube banks subjected to various flow excitations can be developed.

Flow-induced in-plane instabilities of curved pipes

Abstract The equation of motion of curved pipes conveying fluid is derived from Hamiltons principle. Depending on the end conditions, the system may be conservative or nonconservative. It is shown that when the flow velocity exceeds a certain value, the conservative system becomes subject to buckling-type instability and the nonconservative system becomes subject to fluttering-type and buckling-type instabilities. The critical flow velocity at which the pipe loses stability has been computed for four end conditions.

The effect of fluid viscosity on coupled tube/fluid vibrations

This paper presents an analytical study of coupled vibration of two coaxial tubes separated by an imcompressible viscous fluid. Tube vibrations are in beam modes and fluid motion is assumed to take place in a plane perpendicular to the axis of the tubes. First, the fluid forces acting on the tubes associated with small tube displacements are obtained in closed form based on the linearized two-dimensional Navier-Stokes equation. Then free and forced vibrations of the coupled tube/fluid system are analyzed. Finally, numerical results for free vibrations of simply supported tubes are presented for several cases to illustrate the effect of various sytem parameters.