Svetlana Marmutova
Laminar flow simulation around circular cylinder
11 of March 2013, Espoo
smarmut@uwasa.fi
Faculty of Technology
Table of content
 Research goals
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Table of content
 Research goals
 Model description
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Table of content
 Research goals
 Model description
 Methods
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Table of content
 Research goals
 Model description
 Methods
 Assumptions
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Table of content
 Research goals
 Model description
 Methods
 Assumptions
 Simulation results
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Table of content
 Research goals
 Model description
 Methods
 Assumptions
 Simulation results
 Conclusions
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Table of content
 Research goals
 Model description
 Methods
 Assumptions
 Simulation results
 Conclusions
 Questions for further studies
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Research goals


Vertical axis wind turbine power coefficient and efficiency calculation
Steps to achieve the final goal:
1. Static
cylinder
Laminar flow
2D;
Turbulent flow
2D,3D


2. Cylinder with static
axis and freely moving
surface
Laminar flow 2D;
Turbulent flow 2D,3D
3. Windside profile
Laminar flow 2D;
Turbulent flow
2D,3D
Listed cases will be studyed with the use of three computational
programs: Comsol, Fluent and Matlab
The first case (static cylinder) is considered in the current presentation.
The goal of the presentation is to show and compare the simulation
results and uncertainties obtained by means of mentioned programs
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2D Laminar flow around static cylinder
R=0,05m
H=2,2m
V=0,4m
Uinlet=1m/s
Figure 1. Model scheme.
Models and simulation programs:
 Comsol, Fluent model: unsteady, laminar, viscous,
incompressible, no-slip boundary conditions;

Matlab model: steady, inviscid, incompressible, laminar flow,
no-slip boundary conditions, initially calculate stream function;
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Methods. Finite difference method
 Ф

 y
Ф i , j 1  Ф i , j  1

 
2y
i, j
Ф i  1 , j  Ф i 1 , j
 Ф 

 
2x
 x i, j
(2)
(3)
Figure 2. Discretization scheme.
Depending on the size of the element (the mesh scale) error
accures. Consider element small enough.
Interpolation (in Matlab)
For smoother plot and better result visualization. It should be
replaced with the finer grid inside the program code.
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Assumptions
Matlab model:
• Steady, inviscid, incompressible, laminar flow, no-slip boundary
conditions;
• Model calculates the stream function;
• Stream function on the boundarie (red line) is equal to zero;
• Stream function on the boundarie (green line) is calculated
through the exact solution.
2

a 
 sin 
0  U  r 
r 


2
r
Figure 3. Matlab model scheme.
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u 
2

y

1 
r r


x
(4)
1 
2

r
2
(6)

2
(5)
0
v

x


y
(7)
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Assumptions (continue)
Figure 4. Matlab model scheme.
Differentials can be replaced by difference between grid points according to
the finite difference method.
Boundary conditions: for angles 0 , π and on the cylinder surface stream
function is equal zero. For R=6 exact solution results are applied.
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 A1;1

 B .; n
 C n ;1

B .;.
A..
D n ;.
C 1; n   1   b1 
    
D .; n    .  b .
   
A n ; n   n   b n 
(8)
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Assumptions
Comsol/Fluent model:
• Unsteady, incompressible (ρ=const), laminar with von Karman vortex street
creation;
• Inlet (velocity is specified), Outlet (gauge pressure is equal to zero), cylinder
and tunnel walls (no-slip conditions);
• Inertia forces are negleged since the laminar flow is considered;
• Incompressibility of the flow is assumed.
R=0,05m
H=2,2m
V=0,4m
Uinlet=1m/s
Figure 1. Model scheme.

d v
dt
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
  p    v   g
2
(9)
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Some Matlab results
Figure 5. Matlab velocity profile (m/s). Linear iterpolation index=3
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Higher interpolation index
Figure 6. Matlab velocity profile (m/s). Linear iterpolation index=5
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Comsol/Fluent Velocity
Figure 7. Comsol velocity profile.
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Figure 8. Fluent velocity profile (m/s).
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Comsol/Fluent Pressure contour
Figure 9. Fluent pressure contour (Pa).
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Figure 10. Comsol pressure contour (Pa).
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Conclusions
• The model output data was calculated by using
Fluent, Matlab and Comsol;
• Slightly different results with the use of different
programs was observed.
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Questions for further studies
Interpolation method, which was used to improve data visualization,
should be replaced with the finer grid implementation inside the Matlab
program code.
Previously studied is flow around static cylinder. No-slip boundary
conditions were applied.
Next case: cylinder under consideration with stationary axis is able to
move with the flow around. The boundary conditions on the cylinder
surface are unknown: particle’s velocity on the cylinder curface is
unknown.
Surface characteristics, mechanic moment, cylinder initial velocity
should be studyed to find out boundary conditions.
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