Chp9_331

# Chp9_331 - 86 9 Boundary Layers The concept of a boundary...

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Unformatted text preview: 86 9. Boundary Layers The concept of a boundary layer is due to Prandtl. Many viscous flows can be analyzed by dividing the flow into two regions, one close to the solid boundaries, the other covering the rest of the flow. Only in the thin region adjacent to a solid boundary (the boundary layer) is the effect of viscosity important. Inside the thin layer the velocity of the fluid increases from zero at the wall (no slip) to its full value which corresponds to the external flow. In the region outside of the boundary layer, the effect of viscosity is negligible and the fluid may be treated as inviscid. The flow in the boundary layer may be either laminar or turbulent. Among the factors that affect boundary-layer transition are pressure gradient, surface roughness, heat transfer, body forces, and free stream disturbances. transition turbulent laminar U U U 87 Under typical flow conditions, transition is usually considered to occur at a Reynolds number of 5 ⋅ 10 5 . However, it can be delayed to Re in a range of 3-5 ⋅ 10 6 if external disturbances are minimized. 9.1. Estimation of boundary layer thickness The boundary layer thickness, δ , is defined as the distance from the surface to the point where the velocity is within 1% of its free stream value. Since the velocity profile merges smoothly and asymptotically into the free stream, it is difficult to measure the boundary layer thickness, δ . Alternative definitions include the displacement, δ * , and the momentum thickness, θ , defines as: dy U u dy U u ∫ ∫ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ≈ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ≡ ∞ δ δ * 1 1 dy U u U u dy U u U u ∫ ∫ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ≈ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ≡ ∞ δ θ 1 1 88 The laminar boundary layer thickness can be estimated following the assumption that friction forces and inertia forces are of comparable order of magnitude inside the boundary layer....
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Chp9_331 - 86 9 Boundary Layers The concept of a boundary...

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