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Flow Through a Pipe - Fluid/Structure Interaction Problem

Natasha Shekdar

Principal Investigator:
Professor Tayfun E. Tezduyar, T*AFSM

This project involves a fluid-structure interaction problem analysing flow in a pipe using the finite element method. The Deforming-Spatial-Domain/Stabilized-Space-Time (DSD/SST) formulation is being used to simulate the fluid flow inside the deforming pipe. The dynamic motion of the pipe itself is computed using a Semi-Discrete structural code with Newmark time-integration scheme. The software used to simulate this problem was developed by the T*AFSM.In this project, Ms. Shekdar was helped by Mr. Vinay Kalro, at that time a PhD student supervised by Tezduyar.

The solid and fluid codes are weakly modeled in the sense that the exchange of boundary conditions for velocity and stress between them occurs iteratively. The equation used for modeling the solid movement is

where d is the displacement and T is the solid stress tensor for a Hookean material. The fluid motion is modeled using the Navier-Stokes equations

where is the fluid stress tensor, as well as the continuity equation,
Initially the pipe is oriented radially on the z axis, parallel to the ground. An initial tip displacement of (0,0,0.1) facilitates growth of displacement. The initial state of the pipe is shown below.

Initial State of Pipe Showing Magnitude of Pressure
Test run were made on a simulation of a soft rubber like material for the pipe with water flowing through it. The material properties used for the simulation are f, the fluid viscosity, s, the Poisson's ratio for the solid, s, the solid density, f, the fluid density, and E, the solid Young's Modulus. Their nondimensional values are shown in the table below.

The case was run for 3000 timesteps, with data output every 40 timesteps at 0.05 nondimensional time units/40 timesteps for a total of 3.70 nondimensional time units. The cross-section below shows the magnitude of velocity in the fluid, with a distinct boudary layer.

Cross Section of Pipe Showing Magnitude of Velocity
Movement of the pipe was restricted to a single dimension. Preliminary results indicate that the pipe begins to oscillate under the influence of stress exerted by the fluid and the system exhibits time periodic behavior. The graph of the position of a point on the tip of the pipe versus time shows this periodicity. Further testing of effects of different velocities of fluid flow as well as different material for the pipe will be looked into.

To check accuracy of the nonlinear code, a case with very small deflections will be run whose results will be compared with theoretical results.

The three movies below show oscillations of the pipe with respect to time.

Pipe Motion with Magnitude of Surface Pressure
Pipe Motion with Magnitude of Velocity on a Cross Section
Pipe Motion at the Tip of the Pipe, with Velocity Vectors on a Cross Section