Head

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Heads Method for Modeling Turbulent Boundary
LayersBertin Smith Page 147

• L. Sankar
• November 22, 2004

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Governing EquationsVon Karman Integral Momentum
Equation
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Entrainment Shape Factor, H1
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Solution Procedure

• We have two ODEs, one for q and one for H1.
• These two ODEs may be numerically solved by
  marching from the transition point.
• MATLAB and other languages have libraries for
  integrating system of ODEs.
• See Pablo function called Runge, if you are
  curious about how these two ODEs are integrated.
• You will see some of these libraries in 3515.

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Some code fragments from PABLO

• function yH1ofH(H)
• if H lt1.1
• disp('H lt 1.1 ! -gt H1 16')
• y 16
• else
• if H lt 1.6
• y 3.3 0.8234(H-1.1).(-1.287)
• else
• y 3.3 1.5501(H-0.6778).(-3.064)
• end
• end

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More code Fragments from Pablo

• function HHofH1(H1)
• if H1 lt 3.32
• H 3
• elseif H1 lt 5.3
• H 0.6778 1.1536(H1-3.3).(-0.326)
• else
• H 1.1 0.86(H1-3.3).(-0.777)
• end