Master Thesis Nr' 285

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Master Thesis Nr. 285
IMPLEMENTATION OF A CONSERVATIVE LOAD PROJECTION
METHOD FOR FLUID-STRUCTURE INTERACTION PROBLEMS
IMPLEMENTATION OF A CONSERVATIVE LOAD PROJECTION
METHOD FOR FLUID-STRUCTURE INTERACTION PROBLEMS
By Noman Kabir (matr. no. 2644479)
Institute for Aircraft Design and Lightweight
Structures Technical University of
Braunschweig April, 2003
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Introduction

• The numerical simulation of fluid-structure
  interaction is a challenge concerning
• the algorithmic complexity
• the computational costs
• since fluid and structure have different
  properties and must be coupled at at their
  interface.
• In the loose coupling some problems arise, namely
  data transfer from fluid to structure,
• due to possible different discretizations for
  the fluid and structure domains.
• Normal interpolation technique may lose some data
  under certain conditions. Therefore, the
• data transfer between the two grids needs a
  different technique known as Conservative
• Load Projection Method based on Gauss
  integration.
• The main criterion of the scheme is
• Total loads on the fluid and on the structure are
  the same
• Which insures no information is lost

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Application areas

• Interaction of fluid-structure in the design of
• Aircraft, wind turbine, gas turbine
• Automobile and high speed train
• High speed marine vehicles
• Atmospheric re-entry of the space vehicle
• Bridges, high-rise structures (Interaction
  with wind). Also important for fabric tensile
• structures of light and flexible
  materials often used for large roof systems,
  capacious
• umbrellas, tents, canopies or
  pavilions.

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Description of the work

• The current work includes
• detail algorithms for conservative load
  projection method.
• the programming of conservative load projection
  method in C, using a powerful library,
  Visualisation Toolkit (VTK)
• test programs in Python language.

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Coupling techniques

• Basically two types of coupling strong and weak
• Strong coupling
• Fluid and structure are discretized, and
  solved as a single problem. No communication
• between regimes is required.
• system matrix is ill-conditioned due to
  differences of stiffness and the discretizations
• of the two domains
• Requires high memory as the single coupled
  system of equations are solved
• simultaneously.
• Loose coupling
• Discretizations are different in two
  different geometries and they are solved
  separately.
• Additional cost of communicating interface
  data.
• Existing developed fluid and structure codes
  and analysis tools can be used. This is

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Conservation load projection method
When the grid sizes of the two domains are
comparable, then normal interpolation works
fine. Unfortunately this approach fails under
certain cases.
Figure 1 Case where the pressure is not fully
transmitted from fluid to structure because of
non-conservative properties of the interpolation.
If Pf , Ps are the total pressures of the
fluid and structure at their interface
respectively then according to the load
conservation property
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Conservation load projection method
Conservation load projection method
Using Galerkin method the equation can be written
in discretized form with shape functions and
nodal loads.
We can find out the structure load from this
equation. Mass and R matrices are in terms of
shape functions and jacobian matrix.


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Loop over structure elements
One dimensional case
Two dimensional case Figure 2 Introducing Gauss
points on CSD faces is not conservative
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Loop over fluid elements
One dimensional case
Two dimensional
case Figure 3 Introducing Gauss points on CFD
faces is conservative, but some CSD points may
receive no pressure
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Loop over fluid elements
Figure 4 Introducing Gauss points on CFD faces
that are recursively refined is conservative and
every CSD point receives some pressure.
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Making a Third Mesh

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Making a Third Mesh

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ALGORITHMS
ALGORITHMS

• Construction of a third mesh with fluid and
  structure mesh. If fluid element (FE)
• overlaps structure element (SE), cut the FE
  along with the intersecting edges of the
• SE. Then the FE part inside the SE is a
  cell in the third mesh
• Formulation of mass matrix
• Finally we construct R matrix and solve the
  equation system to get
• the load on solid

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GENERATING A THIRD MESH
GENERATING A THIRD MESH

• We make the following strategy to get an easy
  solution
• First convert all edges in the mesh (fluid /
  structure) into a set of lines.
• Find out the intersection points between the
  fluid line and structure line.
• Take into account all points including
  intersected points avoiding all duplication.
• Arrange the points in order and create lines
• The lines are converted into polygons. Finally
  the polygons are converted into triangles.

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Test Result
10 0
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10 0
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Structure Mesh
Fluid mesh
Total load on the fluid surface
30866.6660156 Total load on the structure surface
(Conservative load projection)
30867.0507813 Total load on the structure surface
(Traditional interpolation) 50400.0
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