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BOUNDARY LAYER THEORY
(Re>1000)
Unit # 1
Sec 8.6.1 Potter
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Why study Boundary layer
It would help you understand how aircrafts fly It would help you calculate
drag on surfaces
skin friction on surfaces
boundary layer thickness
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Free-stream vs Boundary LayerA high Reynolds number fluid stream over a solid
surface may be divided into two parts:
a) A thin layer adjacent to the surface, whereonly viscosity dominates calledBOUNDARY LAYER
(It is a viscous flow. It is very thin. Thepressure within the boundary layer may betaken as that at the wall)
b) An inviscid flow outside this boundary layerthroughout calledFREE-STREAM
(It is a potential flow)
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Boundary layer on flat plate
Boundary layer begins as a laminar flow with zero thicknessat the leading edge. After some distance downstream the
laminar flow undergoes transition to turbulent flow.
Pressure in the boundary layer does not vary withy. It issame as that outside of it
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DEFINITIONS
BOUNDARY LAYER () thickness is thedistance from the wall up to a height wherethe fluid velocity is 99% of the free-stream
velocity
DISPLACEMENT () thickness is thedistance by which the boundary layer would
have to be displaced if the entire flow were
frictionless and the same mass flow ismaintained
MOMENTUM thickness ( ) is a measure ofthe deficit of momentum flux in the boundary
layer as compared to potential flow.
It is also a measure of total plate drag
)99.0( == Uuy
dyUu
=
0
* 1
dy
U
u
U
u
=
0
1
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Drag or Shear stress
dy
du
Fluid drag on a bodyis governed by shear
stress on the wall
It is known from thevelocity gradient on
the wall
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Transition of Laminar to Turbulent BL
Boundary layer is initially laminar, goes through a transitionregion when large-scale eddies are formed and then
develops into turbulentflow.
Transition from laminar to turbulent occurs at Rex >500,000. where Rex is local Reynolds number, U x/=U x/
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Turbulentboundary
layer
Turbulent BL has a steeper velocity gradient at the surface
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Problem (Fox-415) A laboratory wind tunnel has a test section, 305 mm
square. Boundary-layer velocity profiles aremeasured at two cross sections and displacementthicknesses are evaluated from the measuredprofiles.
At section(1), where the free-stream speed isU1=26 m/s, the displacement thickness is 1.5 mm.
At section (2), located downstream from section
(1) displacement thickness is 2.1 mm. Calculate the change in static pressure between
sections (1) and (2). Express the result as a fraction
of the free-stream dynamic pressure at section (1).
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Home work (Douglas 11.2)
Determine the ratio of momentum and
displacement thickness to the boundary layer
thickness, when the layer velocity profile is
given by
where u is the velocity at a height y above the
surface and the flow free stream velocity is U.
[ Ans: 0.166 m, 0.33m]
5.0
=
y
U
u
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Summary
Boundary layer applies to the region close to thesurface where viscosity is dominant.
Boundary layer thickness
Displacement thickness
Momentum thickness
)99.0( == Uuy
dyU
u
=
0
* 1
dy
U
u
U
u
=
0
1
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Wind Tunnel
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Boundary layer
Figure 8.24 Boundary layer in air withRecrit
= 3 x 105.