Date of Award

Spring 1977

Document Type

Dissertation

Degree Name

Doctor of Engineering Science in Mechanical Engineering

Department

Mechanical Engineering

First Advisor

Amir N. Nahavandi

Second Advisor

Arnold Allentuch

Third Advisor

W. H. Warren Ball

Fourth Advisor

Roman I. Andrushkiw

Fifth Advisor

Benedict C. Sun

Sixth Advisor

Charles E. Wilson

Abstract

Interaction between solid and fluid has been recognized to be an important factor in the areas of aeroelasticity, hydroelasticity, and the study of flow-induced vibration in nuclear reactor components. This study develops a finite element model for interaction between an elastic solid and a fluid medium. Plane triangular finite elements have been used separately for fluid, solid, and solid-fluid continua and the equivalent mass, damping, and stiffness matrices and interaction load arrays for all elements are derived and assembled into global matrices. The global matrix differential equation of motion developed is solved in time to obtain the pressure and velocity distributions in the fluid, as well as the displacements in the solid. Two independent computer programs, each employing different algorithms and numerical solution techniques are used to obtain the dynamic solution. The first program is FLINTS (Fluid Interacting with Solid), a special purpose finite element program developed herein for solid-fluid interaction studies. This program uses the modal superposition technique in which the eigenvalues and eigenvectors for the system are found and used to uncouple the equations. This approach allows an analytic solution in each integration time step. The second program is WECAN (Westinghouse Electric Computer Analysis), a general purpose finite element program in which new element library subroutines for solid-fluid interaction were incorporated. This program can employ a NASTRAN direct integration scheme based on a central difference formula for the acceleration and velocity terms and an implicit representation of the displacement term. This reduces the problem to a matrix equation whose right hand side is updated in every time step and is solved by a variation of the Gaussian elimination method known as the wave front technique. Results have been obtained for the case of water, between two flat elastic parallel plates, initially at rest and accelerated suddenly by applying a step pressure. The results obtained from the above-mentioned two independent finite element programs are in full agreement. This verification provides the confidence needed to initiate parametric studies. Both rigid wall (no solid-fluid interaction) and flexible wall (including solid-fluid interaction) cases were examined. The pressure time histories for the flexible wall configuration show the following features; 1) The observed period of oscillation of the fluid increased with respect to the rigid wall fluid period 2 L/c as expected. This is due to a reduction in the effective speed of sound in the fluid resulting from the solid-fluid interaction: 2) The observed pressure in the fluid is generally lower than the pressure in the rigid wall case except when transversal water hammer occurs. This is also a solid-fluid interaction effect, caused by the motion of the wall as the step pressure wave advances along the channel; 3) Transversal flow due to the motion of the wall is also observed. When the motion of the wall reaches its maximum, the transversal flow is decreased resulting in a water hammer phenomenon. This effect exhibits itself in the form of a pressure surge on the response curve.

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