1boundary Layer Theory

8/8/2019 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

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1boundary Layer Theory