1boundary Layer Theory
Transcript of 1boundary Layer Theory
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BOUNDARY LAYER THEORY
(Re>1000)
Unit # 1
Sec 8.6 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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Freestream & Boundary LayerFluid stream over a solid surface may be divided into
two parts:
a) A thin layer adjacent to the surface, where only
viscosity dominates called BOUNDARY LAYER
(It is a viscous flow. It is very thin. The pressure
within the boundary layer may be taken as that at
the wall)
b) An inviscid flow outside this boundary layerthroughout called FREE STREAM
(It is a potential flow)
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Boundary layer begins as a laminar flow with zero thickness atthe leading edge of flat plate or finite thickness on a blunt object.
After some distance downstream the laminar flow undergoes
transition to turbulent flow.
Boundary layer on flat plate
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Laminar & turbulent layer A laminar flow becomes turbulent downstream of
the flow. [watch the smoke from a cigarette and
water from a tap] Similarly the flow inside the boundary layer is
initiallylaminar, goes through a transition region
when large-scale eddies are formed and then
develops into turbulentflow. Transition could
occur at Reynolds number as high as 106.We will
take 0.5x106 as the transition point.
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Laminar to Turbulent BL
Transition from laminar to turbulent when Rex > 500,000
Local Reynolds number, Rex = UxVQ!Ux/K
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Turbulent boundary layer
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DEFINITIONS
BOUNDARY LAYERthickness is the distance
from the wall up to a height where the fluidvelocity is 99% of the free stream velocity
DISPLACEMENT thickness is the distance by
which the boundary layer would have to be
displaced if the entire flow were frictionlessand the same mass flow is maintained
MOMENTUM thickness is the distance from
the surface such that the linear momentum
flow rate for uniform velocity for this height
U is equal to the actual momentum flow rateover the entire boundary layer section using
the actual velocity profile.It is also a
measure of total plate drag
dyU
u
s
g
!
0
* 1H
dyU
u
U
u
ss
!0
1U
)99.0( sUuy !!H
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Figure 8.24 Boundary layerinair withRecrit
= 3 x 105.
Boundary layer
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Shear
stress
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Wind Tunnel
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Home work (Douglas 11.2)
Determine the ratio of momentum and
displacement thickness to the boundary layer
thickness, Hwhen 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
!H
y
U
u