LINEAR STABILITY NORMAL MODE ANALYSIS OF VISCOELASTIC FLUID FLOWS

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LINEAR STABILITY (NORMAL MODE) ANALYSIS OF
VISCOELASTIC FLUID FLOWS

• Mehmet SAHIN Helen J. WILSON
• Department of Mathematics, UCL
• Gower Street, London, WC1E 6BT, UK
• 21-22 September 2006

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Computed Base Flow for Periodic Array of Half
Cylinders Placed on Channel Walls at We2.8.
H4R and L2.5R
Principle stress difference
u-velocity
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Linear Stability (Normal Mode) Analysis
Base Flow Leading Eigenfunction
Three-dimensional streamtraces
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Computed Leading Eigenfunction
Txx (Anti-symmetric)
w-velocity (Anti-symmetric)
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Computational Unstructured Mesh for Experimental
818 Contraction-Expansion Case
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Computed Base Flow for Rolie-Poly Fluid with
?0.1, We55 and We_R1.1.
u-velocity
Principle stress difference
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Linear Stability (Normal Mode) Analysis
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Conclusions

• A parallel adaptive unstructured normal mode
  analysis code has been developed to investigate
  flow instabilities for both Oldroyd-B and
  Rolie-Poly fluids.
• The accuracy of the code is verified for the
  Oldroyd-B fluid past periodic array of
  cylinders.
• The code may need to be modified for the
  multi-mode version of Rolie-Poly equations.
• More accurate experimental values are recently
  become available for the Rolie-Ploy fluid in the
  818 experimental contraction expansion case.
• More work is needed for the efficient solution of
  Stokes problem in 3D in order to simulate 3D flow
  instabilities.