Zahn, A F

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TECHNICAL NOTES. .
NATIONAL ADVISORY COMMITTEE lKElAE.ROYAUTICS.
.
No. 23.
HORIZONTAL BT.DYMCY IN WIND !T-S .
A. F. Zahn,
Bureau of Constriictiun& Re~ir, U. S. l’?.
.
Nowmber, 1920.
https://ntrs.nasa.gov/search.jsp?R=19930080827 2020-03-17T05:02:08+00:00Z
NATIONAL ADVISORY COMMI!l!TEEFOR AERONAUTICS.
TECHNICAL NOTE N(L 23.
HORIZONTAL BUOYANCY II?WIND TUNNELS.
By
A. F. Zahm
Bureau of Construction& Repair, LLS.N.
The following report on ‘!Horizontal Buoyancy in Wind Tunnelsm was
submitted to the National Advis@ry Comzittee for Aeronautics by Dr, A.
F. Zahm, Member, Ccamittee on Aerodynamics.
Distinction of relative flow.
- F&cm the earnest etudy of hydro-
meohanics it has been assmed that the reaction between a stagn~t
fluid and a body moving through it is the seineas for the fluid pass-
ing the fixed body with the same relative motiom So many experiments
however seemed to disprove the assumption that at one time scme prcmi-
nent investigators questioned its validity. For exanple, Dubuat and
~OhO’min found experimentally mat a ‘platifixed in a str~ of water
has about thirty per cant more resist~ce than when moving through still
water at the sane speed. This Phenomenon was called Wubuatts Paradoxn.
But when dw pr~aution is tw~ to m~e the relative motion the seine
in both cases, as was dons with an apparatus developed by JGUkOVSki
and Kouznetzoff, the assumption is completely vindicated. The reader
may find a description of this apparatus in Jotikovski~sAerodymaique,
Chapter 11.
But suoh equivalence of relative motion can not alwaYs be realized.
When for example,.a body moves through an extended hmogeueous still
fluid the relative velocity of all distant parts of the fluid is uniform,
and the undisturbed horizontal pressure gradient is zero; but when the
fluid moves past the body usually all the distant parts have not the
same velocity, usually ther,eis srxneturbulence, and the pressme grad-
ient is not zero. And if the gradient is not zero there is a horizon-
tal buoyancy to be applied as a correction to make the observed resist-
ance equal that for the still fluid.
Stat%c pressure ~adient. - Inuntagering wind tunnels, for instance,
th8re is amaterial fa31 of static pressure down stream withiu the walled
working portion. If the tunnel is well designed and unobstructed, th=
down-strean pressure gradient is cons-t for any one wind speed, and
varies naarly as the sqyare of thb wind VelocZty. If the tunnel is ~t-
ly obstructed with apparatus, the gradient may, at aq fixed speed, very
in amount from point to point along stream.
on &
face
-2-
Point pressure and rmessure drag. - In general the pressural drag
tind tunnel model, apart from the frictional drag, @qW18 the Sur-
integral of the horizontal ccmponent p= of the point press~e W
Now this latter may be written II= PI + ~-: +13, where PI is the
constant barometric pressure at the reference section A of the ~el,
say where the nose of the model is to “be,and before insertion of the
mCdel; I?2iS the pressure drop down stream frcm A due to the statiC
gradient in the unobstructed tunnel; p3 is the kinetic pressure, or
departure frcm pl, due to the presenoe of tb model ~ the stre~- It
is assumed that the tunnel is”too large for ~terial wall effect.
Obviously the drag due to the constant baraetric pressure p is
zero. The drag due tO p3 would be ZeZO for africtionles8 fluid,%ut
for ZMbtWd fluids is a chief element of re~ist~ce, especially for
bodies of blunt form. Its discussion is irrelevant to the present
treatment. The tiag due to 22 may here be formulated for various con-
ditions.
Camutation of horizontal buoyancy. - The ccmponent of horizontal
buoyanoy at any element of the model’s surface is 1 P2d ~, in ~hi~ 1
is the direction cosine, referred to the tunnel axis, of the normal to
the surface elemeat d S. To find the surfsoe integral of this ccmpc-
nent analytically one must know the equation to S; also to the ~essure
dropp2, in terms of the distance along stre=. Themeth~ of inte-
grating is too familiar to require treatment here.
III wind mel practiioe S.tip ~e US~lly given gra~hioa.lly,ad
may require graphi@ integration tozfind the drag due to pressure drop.
For example, 9 may be a surface of revolution, suoh as a balloon hull;
or a cylinder, such.as a uniform stream-line strut. The static pres-
~e %radient may be given by a curved diagram, i= whichp2 is plotted
against the do~ SWeUI dis~c~ fr~ them~~~s nose; or, aS a p~-
ticularly interesting case, the gradient may be mnstant. These spec-l
i81 e%sm~le$ will be briefly treated in turn.
The pressure-drop dr~ on a s~face of revolution ~th its axis
along stream ia
where P2 is the pressure drop at radius r, and the integral extends
over the whole surface. The integral is found graphically as the area
2, both of which areof the curve obtained by plotting p against r
%assunecito be given for various dis antes along stream. This method
was given in Report No. 107 of the British Advisory Cwamittee for .
AeronautiCS.
The pressure-drop drag on a cylinder held transverse to the stream,
and having a plane of symmetry parallel thereto, is, per unit length,
R=2/p2. d o, --------- ------- (2)
,
-3? .
where r is the smi-th~okness at any point along strea, and the
integral extends fmm front tp rear. The solution is fmxld graphically
as the area of the curve of ~ plotted against r.
If the press=e gradient is a constant, d~dx=a, the pres-
sure-drop drag on a body of whatever shape is
R ba r, -------- ----------- (3)
where v is the voluue of t’hebody. TMs foxmula is the ssme as that
fOr the vertiti buoyenoy of a body imnersed in a Iiqtid, and has
been known from time iumctncmial.
BEethodsof ccmputation in Qraotioal use. - Formula (3) has been
used in the reports frcm the Aero@nsmioal Laboratory., %shington
Navy Yard, sinoe July, 1919, when it was first shown by accurate
measurement that the pressure gradient i6 constant along the working
PO@tion of the 8S x 8~ tunnel freed of obstructions. In scum of the
earlierreports gra~ic~ integration had been employed because rneas-
xmements, too hwried ~ ins-i ~ently &ecked, had indicated a
slightly variable pressure gradient. Thismistake in measuring the
gradient entailed an error of the order of one or two per Oent in
finding the total drag on the models tested.
A detailed aoeount of the calibration of the 81 x 8t tunnel, for
pressure gr~~en~, LS given in tti laboratorys Report No.148.
For streamline bodies of c~siderable b- the pressure-drop eor-
rection is a good percentage of the whole resistance. Xf, therefore,
the tunnel must have a mat~ia press~e ~tii~t, it is fortunate
when this is so nearly constant that formula (3) can be used to can-
pute the pressure-L-op ccrredion. The value of a needbe deter-
mined but once for a given tunnel, and the value of v for a model
of eny shape can easily be found by imnersion in wa~er.
I


Horizontal buoyancy in wind tunnels

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