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Boundary Layer Fundamentals What is a boundary layer?
stagnation point laminar turbulent transition separation wake velocity deficit
Boundary Layers Lecture 8 ME EN 412 Andrew Ning aning@byu.edu - - PDF document
Boundary Layers Lecture 8 ME EN 412 Andrew Ning aning@byu.edu - - PDF document
Boundary Layers Lecture 8 ME EN 412 Andrew Ning aning@byu.edu Outline Boundary Layer Fundamentals Blasius Solution Boundary Layer Fundamentals What is a boundary layer? transition turbulent laminar separation velocity wake deficit
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laminar turbulent
Boundary Layer Thickness
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Displacement Thickness δ∗ = ∞
- 1 − ρu
ρeVe
- dy
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A practical use of δ∗
actual body effective body
Boundary Layer Momentum Thickness
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θ = ∞ ρu ρeUe
- 1 − u
Ue
- dy
Blasius Solution
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Within a boundary layer, how are these related? ∂ ∂y ? ∂ ∂x and u ? v
∂p ∂y = 0
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∂u ∂x + ∂v ∂y = 0 u∂u ∂x + v∂u ∂y = ν∂2u ∂y2 Analytic solution (flat plate, laminar flow) δ = 5x √Rex δ∗ = 1.72x √Rex θ = 0.664x √Rex
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τw = µ ∂u ∂y
- y=0
cf = τw q∞ cf = 0.664 √Rex cdf = 1.328 √ReL
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empirical relationships for a flat plate
For turbulent flow there is no analytic solution Schlichting: δ = 0.37x Re0.2
x
δ∗ = 0.046x Re0.2
x
θ = 0.036x Re0.2
x
cf = 0.0592 Re0.2
x
cdf = 0.455 (log10ReL)2.58 or cdf = 0.074 Re0.2
L