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Lecture 3:
Wind Tunnel Corrections
G. Dimitriadis
Experimental AerodynamicsExperimental Aerodynamics
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Wind tunnel corrections
! Wind tunnels cannot recreate flowfieldsidentical to the original.
! Wind tunnel flows are different to theoriginal due to several factors.
! These differences necessitate correctionsto be applied to measurements obtained inwind tunnels.
! The type and number of correctionsdepends on whether the simulated flow is2D or 3D.
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2D Wind tunnel corrections! In 2D experiments, the model is
constrained between flat plates or walls toforce the flowfield to be nearly 2D.
! There are several sources of inaccuracyfor 2D experiments in wind tunnels.
! The most important are:! Buoyancy! Solid blockage
!Wake blockage! Streamline curvature
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Buoyancy
! Wind tunnel buoyancy is caused by the factthat the boundary layer grows on the walls ofthe working section.
!Boundary layer growth is equivalent to acontraction of the working section area.
! The flow is accelerated, causing a drop in staticpressure.
! Therefore, models with a big frontal area arepushed backwards.
! Buoyancy artificially increases the drag
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Longitudinal pressure gradient! The longitudinal pressure drop is nearly
linear.
! The longitudinal pressure gradient is givenby:! Where k=0.016-0.040 is a factor that must
be measured for a given wind tunnel.! h is the height of the working section.
dp
dl= !k
"V2
2h
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Buoyancy correction
! The buoyancy correction depends on thelongitudinal pressure gradient and the volumeof the body, i.e.
! Where !DB
is the correction to be applied to themeasured drag force and V
Bthe body volume.
! More accurate corrections have been estimatedfor airfoils, Rankine ovals, ellipses and othersimple shapes.
!DB = dpdl
VB
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Solid blockage
! The presence of a model in the workingsection reduces the area through which
the air can flow.
! The air velocity is increased over themodel.
! This effect is called solid blockage.! The effect can be corrected by increasing
the effective wind tunnel airspeed.
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Solid blockage correction! The correction to the airspeed for a circular
cylinder is given by:
! Where Vu
is the uncorrected airspeed and !sb
is
given by:
! For a more general shape,
! WhereK1=0.74 for a horizontal model and 0.52 fora vertical model. Sis the working section area.
!V = "sbV
u
!sb
="
2
3
R
2
h2
!sb
=
K1VB
S3 / 2
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Wake blockage
Velocity < V
Velocity < V
Velocity > V
hV
The airspeed in the wake must be lower than V. In a
closed duct this means that the airspeed outside the
wake must be larger than Vfor a constant mass flowrate.
The wake blockage effect can also be corrected using
an increment in the effective airspeed.
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Wake blockage correction
! The airspeed correction is given by!
Where!
wb is given by:
! Where c is the models length (or wingchord) and
cdu is the uncorrected 2D dragcoefficient.
!V = "wbV
u
!wb
=
c
2hcdu
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Streamline curvature
! The wind tunnel ceiling and floor artificiallystraighten the curvature of the flow
streamlines around the model.
! The model appears to have more camberthan it really has, i.e. it has too much lift.
! This effect requires corrections to angle ofattack, lift coefficient and momentcoefficient
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Streamline curvature
corrections! The angle of attack becomes:! The lift coefficient becomes:! The moment coefficient around the half
chord becomes:
! Where !=!sb+!wband
! =!u+57.3"
2#clu+ 4c
m1/ 2u( )
cl= c
lu1!"! 2#( )
cm1/ 2
= cm1/ 2u
1! 2"( ) +#c
l
4
! ="
2
48
c
h
#$%
&'(2
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Total corrections
! The total corrected airspeed is:!
The total corrected dynamic pressure:
! The total corrected Reynolds number:! The total corrected drag (zero-lift):
V =Vu1+ !( )
q = qu1+ 2!( )
Re = Reu1+ !( )
cd0
= cd0u
1! 3"sb! 2"
wb( )