STUDY OF INCOMPRESSIBLE VISCOUS FLOW PAST A SEMISUBMERGED CYLINDER

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STUDY OF INCOMPRESSIBLE VISCOUS FLOW PAST A
SEMI-SUBMERGED CYLINDER

• by Vineet Kumar Birman
• (9829116)
• under the guidance of Prof. L.R Raheja

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TOPICS

• Introduction
• Initial Work
• Submerged Flow
• Semi-submerged Flow
• Conclusion

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INTRODUCTION

• The vortices ahead of ship are bow vortices.
• This bow vortex is simulated in 2-D with
  cylinder.
• Bow vortex are generated in the simulation by
  removing the upperbody of submerged flow at same
  Re and adding gravity effect.
• The initial bow vortex angle and presence of Free
  surface stagnation point is checked. This should
  be in accordance with analytical results.

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INITIAL WORK

• COUETTE FLOW
• This is simple 2-D problem that was solved using
  staggered grid.
• Boundary Conditions were
• u0 and v0 at lower wall
• and
• uUe and v0 at upper wall

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• Result of Couette flow

No. Of Iterations
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• 2. CHANNEL FLOW
• Flow is driven due the pressure difference at
  the ends which determines the reynolds number.
  Flow is solved using SIMPLE method.
• Boundary conditions were
• uv0 at upper wall
• and
• uv0 at bottom wall

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• Results

Profile is at station 10.
Distance (ft)
Velocity (ft/sec)
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Submerged Flow

• The NS equation are transformed using logarithmic
  polar transformation.
• Staggered grid is used
• No Slip condition at wall is used.
• Initially all u, v and p are set to zero.
• Fictitious cells are taken in domain to implement
  boundary conditions.
• SOLA code is used to solve NS equations.

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• Results
• The results are for Re 20,40 and 100 for
  validation purpose and for Re 95083 and 111000
  for solving free surface flow at these Re.
• Cp (p-p8)/(1/2?U82)
• and
• wall vorticity (?w)

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Re 20
Overall View
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Re 20
Aft View
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Re 40
Overall View
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Re 40
Aft View
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Re 100
Overall View
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Re 100
Aft View
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Re 95083
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Re 111000
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SEMI-SUBMERGED FLOW

• Initial condition is taken by removing the
  upperbody flow from the submerged case results.
• At free surface pp(atm) condition is satisfied.
• Same grid and transformation is used as in
  submerged case.
• Cells are flagged as filled, empty, boundary
  (inflow/outflow) and surface cells

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Flagging of cells
? 90
? 270
? 0
? 0
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• SMAC method is used to capture the movement of
  free surface.
• In SMAC marker particles are placed initially in
  region containing fluid.
• These particles follow fluid trajectory and are
  moved with local velocity.
• Velocity of marker particles is found by linear
  interpolation of velocities of nearest nodes
• Cell with no markers, is considered not to
  contain any fluid.
• new marker are initialized at inflow if any
  markers leave outflow boundary.

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FLOWCHART
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• Results
• Case 1
• Re 95083
• Fn 0.6
• u8 0.5943 m/sec
• Case 2
• Re 111000
• Fn 0.7
• u8 0.69375

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• Case 1
• Re 95083

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t 0
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t 8
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t 10
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t 12
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Case 2 Re 111000
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t 0
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t 8
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t 10
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t 12
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FSSP at Re 111000 (with zoomed section showing
zero velocity node)
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CONCLUSION

• The angle of initial bow vortex that was
  generated for both Re 95083 and 111000 matched
  well with analytical results.
• The Free surface stagnation point was also
  observed at distance as predicted analytically.
• The flow pattern around the vortex was not
  satisfactory and needs further work.