Fluid Structure Interaction Applications

Computational Study of Forces Past Three Cylinder
Arranged in Right Faced Vertical Equilatral Triangle
By
Sobia Siraj
MS Thesis
Session 2021 – 2023
Supervised By:
Dr. Ghazala Nazeer
Department of Mathematics
The Government Sadiq College Women University
Bahawalpur

CONTENTS
 Fluid Structure Interaction (FSI)
 Fluid Structure Interaction Application
 Computational Fluid Dynamics (CFD)
 Lattice Boltzmann Method
 Advantages of Lattice Boltzmann Method
 Governing Equation
 Physical Parameters
 Geometry
 Different Flow Past
 References

Fluid-Structure Interaction
FSI is the interaction of a fluid flow with a solid structure of any shape and design. The
problem of FSI becomes more complex when single bluff body is replaced with multiple
bluff bodies having different shapes, sizes and alignments due to presence of drag force
which effects the wake formation and shear layer separation. For example engines, bridges,
automobiles, airplanes and rockets etc.

Computational Fluid Dynamics
 Computational Fluid Dynamics use numerical analysis and data structure to analyze
and solve problems that involving fluid flows.
 It convert partial differential equation into algebraic equation.
 CFD are used to analyze the problems that involving the
 Fluid-fluid interaction
 Fluid solid interaction

Lattice Boltzmann Method
Lattice Boltzmann Method originated from the lattice gas automata method, is
a class of computational fluid dynamics method for fluid simulation. Lattice
Boltzmann Method is used to simulate the flow of a fluid viscosity. Using
streaming and collision (relaxation) processes, a fluid density on a lattice is
simulated as opposed to say directly solving the Navier Stockes Equations.

Advantages of Lattice Boltzmann Method
• It is easy to process and complete the parallel tasks based LBM.
• It is easy to program, and the processing before and after is also
very simple.

Governing Equation
• The governing equations for two-dimensional flow problem for three
staggered square cylinders are given as follow.
 Equation of Continuity:
𝜕u
𝜕x
+
𝜕v
𝜕y
= 0…………………………………………………………..…..(a)
 Two-dimensional Navier stokes Equation:
u
𝜕u
𝜕x
+ v
𝜕u
𝜕y
+
𝜕u
𝜕t
= −
𝜕P
𝜕x
+
1
Re
𝜕2u
𝜕x2 +
𝜕2u
𝜕y2 . . ……………..(b)
u
𝜕v
𝜕x
+ v
𝜕v
𝜕y
+
𝜕v
𝜕t
= −
𝜕P
𝜕y
+
1
Re
𝜕2v
𝜕x2 +
𝜕2v
𝜕y2 … … …………..(c)

Streamline Body
A streamline body is an object, where a significant portion of the
surface area is not separated flow.
Bluff Body
A bluff body is an object, where a significant portion of the surface
area is separated flow.

Physical Parameters
 Reynolds Number (Re):
Reynolds number (Re) is a dimensionless number given by
Re = U∞L
ν
 Gap Spacing(g):
The Gap spacing(g) is a dimensionless quantity which indicates the
distance between two objects.

 Equal Gap Spacing:
 Un-Equal Gap Spacing:
Physical Parameters

1. Solo Bluff Body Vertically Expanded Flow Pattern
(a) Vorticity Snapshot (b - c) Drag and Lift Graph
(d - f) Power spectrum Analysis

2. Wavy Flow Pattern
(a) Vorticity Snapshot
(b - c) Drag and Lift Graph
(d - f) Power Spectrum Analysis

3. Distorted Bluff Body Flow Pattern

4. Two Rows Vertex Street along Centrically Segregated Negative Vortex Line

5. Wavy Jumbled Flow

6. Jumbled Flow

7. Wavy Flow Pattern

8. Steady Jumbled Flow Pattern

9. Initially Anti-Phase and Later Chaotic Flow Pattern

10. In-Phase Jumbled Flow Pattern

11. In-Phase and Anti-Phase Jumbled Flow Pattern

References
 Canpolat, C. (2015). Characteristics of flow past a circular cylinder with a
rectangular groove. Flow Measurement and Instrumentation, 45, 233-246.
 Grucelski, A., & Pozorski, J. (2015). Lattice Boltzmann simulations of heat
transfer in flow past a cylinder and in simple porous media. International
Journal of Heat and Mass Transfer, 86, 139-148.
 Tang, G. Q., Chen, C. Q., Zhao, M., & Lu, L. (2015). Numerical simulation of
flow past twin near-wall circular cylinders in tandem arrangement at low
Reynolds number. Water Science and Engineering, 8(4), 315-325.

 Al-Mdallal, Q. M. (2015). Numerical simulation of viscous flow past a circular
cylinder subject to a circular motion. European Journal of Mechanics-
B/Fluids, 49, 121-136.
 Kumar, A., & Ray, R. K. (2015). Numerical study of shear flow past a square
cylinder at Reynolds numbers 100, 200. Procedia Engineering, 127, 102-109.
 Zhang, K., Katsuchi, H., Zhou, D., Yamada, H., & Han, Z. (2016). Numerical
study on the effect of shape modification to the flow around circular
cylinders. Journal of Wind Engineering and Industrial Aerodynamics, 152, 23-
40.

Fluid Structure Interaction Applications

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