For more information:
tezduyar@gmail.com
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Flow Through a Pipe - Fluid/Structure Interaction Problem
Natasha Shekdar
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
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