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RATIONAL DVISORY OMMITTEE OR ERQNAUTSCS

ACR Note

t 7

**C

TIME HT

ORIGINALLY I S S U ED

March 1946 as Advance Confidential Report 5K27

THEORY AND APPLICATION OF HOT-WIRE NSTRUMENTS IN



N A O A C R No. 5227

N AT I O N A L A D V ISOHY COMMITTEE TO B ERO N A U TICS

A D VA N O B C O N F I D E N T I A L REPpRT

THEORY N D A P P L I C AT I O N O S1 HOT-WIRE INSTRUMENTS IN

THE INVES TIGATION 07 TURBULENT BOUNDARY LAYERS

B y a. B. Schubauer and P. S. Klebanoff

S U M M A R Y

An account l a given of th e recent developments In hot-wire instruments f or use in turbulent boundary layers to determine the magnitude of the several components of the turbulent veloci ty f luctuations together with the correlat ionbetween them and turbulent shearing stress. The instrumentswere developed in order to make possible a study of the



J f f A C A ACE No. 5K27

the fundamental processes in the "boundary layer and containthe explanation of such average characteristics as Telocity_Aiotribu.tion, internal fr ic t ion or shearing stress, and separation in an adverse pressure gradient* I t is therefore not f or l ack of importance that turbulence measurements havbeen negleoted, but rather from a l aok of sui table instruments and techniques f or making the necessary measurements.When the present boundary—layer investigation was undertakenit was deoided to determine as many characteristics of the turbulence as possible, along with the average characteris-tics of the layer, to f i l l in the gap l e f t by former investigators* In order to make the turbulence measurements, it has been necessary f irst to develop some special type of howire anemometer instruments. The present report covers re-search on development of the various hot—wire instruments and their adaptation to the turbulent boundary—layer investigation.

In order to Bee what turbulent characteristics of the layer should be measured to best fur ther an understanding oturbulent boundary layers i t i s wel l to look into the usua



1 J A C A AOH Fo. 6E27

l as f or mean velocity distribution In fair agreement vith experimentj but in cases where a turbulent boundary layer develops under the combined action of friction and large pressure gradients, th e usual assumptions lead to erroneous results and are obviously not valid. This i s particularly true i n large adverse pressure gradients, and it i s here that the greatest need arises for an understanding o f th e

actual nature o f th e turbulent processes* There is need, therefore, for experimental d e J Larmina—

X L i o n s _ o f th e magnitude, o f _ t h e various...jcomponents_of th e fluctuations , . the correlation between components, fkejtur— bulent shearing stresses and mixing"lengths in turbulent boundary layers. These will provide the basic information on which' to base laws governing th e mean motion and th e de-

velopment of the layer. The object in instrument development has been t o obtain th e moans for making measurements that will permit the determination of as many of these quantities as possible.



HACA ACH No. 6K27

R0 a

1

X » IE

temperature ooeff ioient of resistance referredto 0 ° 0

slope of temperature-resistance curve

current through hot wire

mean voltage across hot wire (When two wiresare used, I j denotes mean vol tage aoross wI and Da denotes mean vol tage across wire

Ba" B i B a aum of mean vol tage aoross pair of wires

B ^ j a Bt - B a difference of mean voltage across pair of wi

&BD ohange in 1 -D per radian

e (with various subscripts) vol tage f luctuat ioncompensated f or wire l ag

i



NACA ACH No. 5K27

TQ

hearing tress on he urface or skin friction

of = T/l/2 pUx = 2UT/Ü frlotlon ooeffleient

E UT/U'T1

oorrelatlon coefficient

I

ixing ength

l--

tf --^}

8

boundary—la? er thickness

^

0 - fc - H r

momentum thlcknesn T f c C1 - ¥o * )



KAOA ACH Ho. 5K37

hot—wire anemometers have taken the place of thermal d i ffs i o n apparatus and have found considerable use in the measment of the oroBB—Btroam oomponont of turbulenoe in wind tunnels. Ear ly attempts to use these instrumeuta In turblent boundary layers, whi le not entirely aucoessful , indicated at least that under proper oonditions re l iab le reBultB should be obtainable, Th e principal condition was that the Inst rumen ts be small ooapareat.o ^hjB^^pkneaa the b o J T i l d a r y layerl TETa- s ame ~ c o n d ~ i t £ o n app 11 e B to the measurement of shearing stress.

On the basis of this experience an investigation of turbulent boundary layer again was undertaken. The requiments of the experimental setup were that the boundary lashould be as thick aa possible in order to avoid the neceof building hot—wire instruments vanishingly small and thathe adverse pressure gradient para l l e l to the surface shobe suff ic ient ly large to produce separation and yet be negligible normal to the surface. This required a long face with small curvature, and accordingly the "wal l " sho

f d h l



H10A. ACE Ho. 5Z27

The simplest kind of hot-wire anemometer, and the kthat ha a been used f or many years, consists simply of a single wire plaoed normal to the wind. This kind of in—s t r u m e n - t , shown in f igure 3a responds only to the magnitof the velocity» Several schemes have been suggested f oproducing hot—wire instruments with directional characteristics. One such scheme is to p lace two wir OB very closetogether and so obtain a differential heat loss that depon the direction of the wind. While some Investigators hareroported success with this scheine, the instrument« appear*to he diff icu l t to construct. She writers' experhas Bhown that it i s much easier f rom the standpoint of technique to take advantage of t f h e directional character-istics of a single wire set at an angle to the wind. Suwires may he used singly as shov-n in f igure 3b or in pairas shown in figures 3c and 3d. When used in pairs th e

wires are close together, but l ie in separate para l le l planes. The oharactor istios of such instruments are treain 'section V I I , and the method of construction i s describin section V. The development and use of hot—wire instruments has been restricted to the types Bhown in f igur



NACA ACH Ho, 5Z37

as close together as practicable 1B mployed in order to place both wires as near ly as possible in a region whore the mean velocity wil l f e e the same f or both.

The turbulent shearing stress T and the correlation coefficient K re obtained f rom

T » - puv"

l )

I «Sf--

2)

So far, no method has been found f or the direct measure-

ment of the mixing length I . However, on the assumption of similarity of f l o w patterns in turbulent exchange, proposed by Ton K a ' r m a ' n (reference l ) , T i s everywhere pro- portional to pi a (dll/dy) s ; and since I is only a r e l - ative measure of the e i s s e of th e f l o w pattern may



JTAOA ACE Ho. 6K37

7. HI V DBS IGHS 0 7 HOT-WIRB ISSTEÜMMTS

AHD MITflOD 0 7 CONSTBUOTION

(a) General TeatureB of tue Hew Design

The instruments ohown In f igure 3 are the types recedeveloped f or boundary—layer investigation. The prongs the vires attached across the tips are shown by a, b, a,and d. f igure 3e shows a oomplete instrument with the sconsisting of a l / 8 — inch brass rod - j j j - Inches long by whithe instrument i s supported on a traversing apparatus, athe f l ex ib le leads a t tached to each prong by which conneion is made to long leads running to the electrical equipment outside of the tunnel.

These instruments employ tungsten wires 0 . 0 0 0 3 1 inchin diameter and about 1/16 inch long. The wires were ma

h t iti it i t ld it ith



JTACA AOH No. 5K27

Breakage rarely ocoure with tungsten wire, but the dirt accumulates Just the sane. However, tungsten wirea are suffic ient ly rugged to permit th e removal of dirt by brush- ing with a small brush.

(b) Method of Attaohing Tungsten Vire

The advantages of the superior strength of tungsten wiref or appl icat ion to hot—wire anemometers has been pointed outby Veske in reference 6, However, there has alwayB been oneserious drawback to the use of tungsten - namely he difficultyof attaohing it to pTongs or holders . Whereas p la t inum wire can be readi ly soldered with ordinary t in—lead solder, no known solders are entirely satisfactory f or tungsten wire.

Welding is a «poss

ibility, but It is

unl ikely that the

aver-age experimenter wil l have the ski l l and equipment required. Weske f i rs t cal led attention to the fact that electroplat ingth e wire with a metal that could be soldered made i t poss ib leto use ordinary soldering methodB. However, Weske1 s scheme



&ACA ACH Ho. 6K27

weeies, and then - f o r no accountable reason a resistance suddenly appeared» After much experimentation a techniquwas found f or making sat isfactory and las t ing connectionswhich, in essence, amounted to plating s l o w l y enough to good adhesion between th e copper and the tungsten, The thickness of the deposit did not appear to matter, a l thouit was suspeoted that the differential expansion "betweencopper and tungsten might have a tendency to "break the

oontaot if the copper deposit was thick. A clean tungstesurface was obviously to he desired, hut no sure method cleaning was found. Fortunately f or the ae-thod, contacttroubles disappeared when a suff ic ient ly s low pla t ing rawas adopted. The e leotrolyte used was the same as that ordinari ly UBed in copper plating: 850 grams of crystal—Used copper sulphate and 75 grams of sulphuric a - o i d perl i ter of eleotrolyte. As a preoaution against corrosion

f rom the soldering f l ux , the wires and prongs were washewith a soda solution.

Regardless of whether th e plating i s thick or thin,plated and unplated portions are wel l defined The copp



SACA ACE No. 5X27

While plat inum wire may be run at much higher tempera-tures, er en to the point of gloving brightly* the wire usua l ly l as ted longer and maintained I ts calibration betterwhen the temperatures were less than 400° 0.

Tl . 1 LI 0 TEI 0 1 L XQTTIFMINB

I h e eleotr loal equipment associated with the hot— wir o Instruments I s fundamen ta l ly th e same as that deser lbed In reference 7« Ch e general scheme always has been to heatthe wire with a known constant current and to measure the mean voltage and the f luc tua t ing vol tage across the wire. Shis Is known as constant—current operation. Since the publ icat ion of reference 7, the hot—wire circuits hare beenmodified by Hr„ Mock to inoludo circuits f or two hot wirse the controls have been modified f or greater convenience of operation, and the equipment genera l ly has been made l ight oand more portable. She assembled equipment is shown in f igure 5 where the three basic units are: the amplif ier A



HACA ACE Ho. 5K27

' or 0 .00031- inch diameter tungsten wire the current i s usual ly no greater than 16 0 mill iamperes. Separate cat-teries are used, f or each vlre. The 12—henry chokes

each "battery circuit provide suffic ient impedance to a ffoconBtant—current operation during Teloci ty variations assciated with turbulence. In more precise terms* the reao—tanoe 2nfL together vith the ohmio resistance in the ccuit is suffic ient to reduce current rariations to negl i -gible proportions f or al l frequencies above the out—off quency of th e amplif ier* ' or different mean velocit ies current must he reset manual ly by means of rheostats, T4—dial decade vol tage divider i s placed in the circuit aspotentiometer or bridge, depending on the position of circuit selector Ho. 2. Circuit selector Ho. 1 permits theoperator to measure the current through either wire, themean voltage across ei ther vire or th e sum o r the differencethe vol tages across the vires, and the resistance of eithvlre at air temperature or the sum of the resistances. other position on selector Ho. 2 impresses the voltages the amplif ier, individual ly or th e sum or the difference

l d b l H Wh i i



ffACA A G I L f f o . 5K27

70 percent of that at frequencies a "bore 10 cycles per secondAs shown b7 Dryden in reference 10 , these frequency characteristics are sat isfactory f or measurements of f luctuat ions ordinarily encountered in Isotropie turbulence. She frequency distribution in turbulent boundary layerB i s not knowand probably varies in different parts of the layer. I t is believed, however, that the ampl i f ie r is Just as satisfactory f or measurements in turbulent boundary layers as in f ie lds of Isotropie turbulence if the proportion of the tur-bulent energy ly ing below 10 cycles per second is the same in the two oases.

Other features of the amplif ier are evident in the cir-cuit diagram. The gain control permits the amplif icat ion tobe varied over wide l imits. A phase inverter and balanced output are used to prevent direct current from f lowing throuthe thermoelements. Thus only th e al ternat ing current pro-duced by th e f luc tua t ing hot—wire vol tage i s read on the ouput meter. The amplif ier i s calibrated by reading the outpumeter with known Input voltages. An unknown mean—square I n



NACA ACE No. 5K27

VII . CHARACTERISTICS OJ HOT VISES AND THEORY

~

F HOT—WISE- MEASUREMENTS

The relation between the air veloci ty normal to a heated wire and th e rate of heat loss as driven by King ( re f -erence 1? ) i s

= Di + Tx fv

4

T - T ,

where the terms Dj and IP j depend on the thermal conduc-ti vity, density, and specific heat of the air and the dimen-sions of the wire as shown in reference 13. Owing to the

methods of using hot wires in "boundary—layer investigations,B x and 'F1 may he regarded f t . a constants.. When the wire iheated by an electric current i, the heat is supplied at

the rate i s R, where R ia the resistance of the wire at

temperature T The temperature head T T in



NACA AOE So. 5137

i n constant. or convenience, the constant terms i n equatio(5) are induded i n the constants on the right, a n d . the eqution i s written

/

c E n 4. •9J ̂

E — a* (6

E Squat ion (6) expresses th e relation between — and

•

a

for a given vire heated with given constant current. Thvoltage B across the wire is simply IE, and is the quan-tity usually observed rather than B, The observations are

•0

usually expressed i n terms of beoause of th e linearE - Ea ^

relation between this quantity and < / T T .

Zquation (6) i s found to hold true regardless of th e angle between the axis of the wire and th e wind Th e con



NACA ACH No. 5K27 2

depends on he value of the curve is lin-ear for 'b e noted that, when c p regardless of the value

cp « If c p lies "between 20° and 9all values of U sin p. It Bhouldis constant, the curve is always liof cp» for then quation (7) reduce

to the form of equation

of the constant 1curves are' obtained

(6) with T Vain p taking the placein equation (6). However, separate linefor each value of c p below 20°.

( l ) A



VACA ACB So. 6X27 I

voltages properly compensated f or the l ag of vire: that isthey are determined f rom the output of a properly compensaamplifier. When,proper compensation is used; A and

may he evaluated by the aid of equation (?) . In other worcompensation f or th e l ag of the wire makes it poss ih le to apply equilibrium relat ions even though the equilibrum condition assumed in equations (6) , (6) , and (?) may not actu

a l l y exist. Inasmuch as relat ions (9) are assumed, it is permissib

to regard the f luc tua t ing voltages, angles, and velocities,represented by e , A - t p , u, v, and , respectively, as different ia ls and evaluate A nd y different ia t ingequation (?) . I f « d B is regarded as e, d T T as u, and Udtp s v or w in equations (o) and (9) ,

A a B - *^— dU

d q p



HACA ACE f f o . 5E27

Solving ( lU) f or u» and dividing by I gives

* - 2 ****

u i J J ü T i £ . Ra )

Al l quantities on the right of equation (15), with the ex-ception of T( a ^e determined at each point where u /Uia "being measured, She constant T is determined f or th eparticular wire used by plaoing the instrument in the f r eestream and measuring the mean voltage 3 at several valuesof the velocity t the locat ion of the wire. The quan

tity i s then calculated and plot ted against U to H-E a

obtain a calibration curve as shown in igure is. he slopof this curve is I, since e p °,0°. The current i oustnot only e constant during a run but must be the ame for



FACA ACH Ho. 5K27

I and then rotated 180° a b o u t an axis in l ine with the wind to position I I . f igure 9 shows that the vol tage creases as I T and 9 increase. Therefore in position+ - U . and- +v, as def-ined in f igure 13, "both decrease thvoltage; and the resultant voltage change is the sum oand ea in accordance with equations (9). I n position+ u decreases the vol tage whi le + v increases the voltand the resultant vol tage is the difference "between ee As previously explained, the mean-square of the reant vol tage fluctuation may he determined f rom the outpmeter reading of the compensated amplifier. I f the mesquare resultant f or position I is denoted b y a and mean-square resul tant f or position I I is denoted by b

a = (-ei - e a ) a 0 = (-ei+eaV

Prom equations (9)

a - ( -A x u - Bjv) 3 = AIa u a +2A I BI uv+B I v a



HAC1 ACH No. 6X27

I r e n » equations ( l ) and (19) 1B ound

T, . P (»-*>

2

4 AB

where, according to equations ( l l ) and (12),

i8

Fa

(H-Ha )4

o o s t p AB =

4U Ha

8

Al l the quantities on th e right of equations (20) and (2except- c p and T, are determined at each point where is being determined. According to equation (? ) , is

slope of the straight portion of the ourre in f igure 11,and T is determined f rom calibration curves of this kind

angle c p ay be determined by plot t ing /R—Ea against



I T A C A . ACH So. 5E27 2

(o) Determination of Correlat ion Coefficient

K l a defined by equationand v1 . I ts evaluation

The correlat ion coefficient (2)c Since K involves üv, u' depends on the measurements of these three quantities- There are in fact three ways to evaluate X , . i l l three beiinterrelated b u t involving u' and v' in different ways«Because of experimental errors, the three methods, that



HA C A . ACS No. 5K37 2

Thus Ej may be calcula ted from the data taken in oonnecwith a determination of shearing stress together with an independently measured value of ' .

The seoond expression f or the oorrelation coefficienti s obtained by dividing equation (19) by (18) and solving fuv/u „ I t is found that

K:

Aa '

Ba '

V«

u'

•ft

(3

Here the data taken shearing stress are

of the constants A

nd enter into th e expression

in connection with used in such e way

a determination cfthat only the ratio

B and the ratio of f or the correlation

u1 to ooeff ioient

In this oase both ' and v ' must be determined by independent measurement *



BACA ACE Bo. 5K27

and therefore / B ia less subjeot to error than und B separately. Vhen p ° 46°, the percentage error In t a n c p i s a minimum f or an error in p l"urthermore* aooording to equation (25) no error in 8 esul ts f rom an error in u' / • ' vhen A/ B * v /u 1. Since v l / u ' is not greatly different f rom unity, the optimum conditions appear to be

2

A/ B 9 t a n q p = 1, q p = 45

It is concluded therefore that Ka ia probably the beet value of the correlation coefficient. On the other hand, only 3 wil l be consistent with the measured values of T , u' and 1 . If the d i fference between a and s i s significant, the least certain of the quantities T, u 1 , and ' should be derived f rom equation (27)using Ka . In this way th e best consistent set of resul ts wil l be obtained.

So f ar i t has been assumed that a slant ing wire or an



NAOA ACE Ho. 6X87 2

• and In th e measurement of u' andin a measurement of v1 he effect of

of nd

been.shown that the effeet of and I t has already

v i s negl ig ib le a measurement of 1 She effeot of u nd v In the measurement of 1 wil l be considered presently.

(d) Determination of • ' and w1

As f ar as th e theory i s conoerned, there i s no di ffeence between the measurement of v and She x-wireinstrument is used in both oases — in the xy—plane f or and in the xs—plane f or w1 . Therefore the relat ions f ov1 wil l be derived, and th e same relat ions h o l d true f or

Figure 13 i l lus trates th e position of the wires f ormeasurement of v ' . Whereas f or the measurement of sheastress, the mean—square voltages, denoted by a and ,were determined f or th e wires separately, now the mean—



IA CA A C H H o, 5127 30

, °a1

(-A r - Bjv - Ajju BXI T) a

a„ a J - B_ a a., a a_a i.j + Bj T + AJJ u"+ BJJ v + SAjBjUV SAJAJJU

-SAJBJJUV 2BJAJJUT - BJBJJ-T 8 - ßAjjBjjUT (»2)

a 8 o (-Aju - Bjv Ajju -Bu?)



IACA AOB-Ho. 6X27 i

x—wire instrument nay t oe used to neaeure 1, but due to th e possibi l i ty of obtaining a mixture of components, the single vire normal to the wind i s preferable . In order to-lessen the possibi l i ty of a mixture "of components in the measurement of 1 , B i s made larger than ; that is, the angle 9 1B made less than 45°.

Whi le th e foregoing relations are useful to i l lustra teh ow the characteristics of individual wires can be combineto produce an instrument sensitive to vt these relations,as Buch, are not used to determine v' . In praotice it isunnecessary, as wol l as too laborious to determine the constants B f or the individual wires. Instead, the sum and the difference of the mean vol tage across the pair of wires are determined as a function of velocity and angle, and in this way a calibration ourve is obtained f or deter-mining v ' /U from the root—mean—square voltage f luctuationdirectly. The basis f or this procedure is i l lus trated by the performance character ist ios given in f igures 14 and 15



NACA ACH Ho. 5E37 3

In use, the proper angle f or setting the Instrument is found by making -Q sero regardless of the angle between the stem of the instrument and the wind. If the stem is out of al inement with the wind, f or example, 5° as shown in f igure 14 , the two wires are not set at the same angle with respect to the stem or the wires are imperfect ly matched

The vol tage f luc tuat ion produced by is removed as a

potential souroe of error in the measurement of v* because the subtraction indicated in equation (3 l ) is made before squaring. In other words, if equation (39) were used to f ind < p a positive A q > ould be found f or both wires, and there would be no net effect on the difference voltage.

She effeot of found quite simply v/ U hen ac tua l ly

being measured or

u in a measurement of ' by considering that p is it is v Then ac tua l ly

T T + S tu approximately

may be assumed

v/U±uto is

be



NACA ACS No. 5K27 3

In reference 10 an express I on f or

is derived f or the more general oaee In which the heating current varies vith the resistance of the wire. However, only oonBtant—current operation "and" therefore equation- (-41)--will he considered here

As a matter of convenience, the terms on the right of equation (4 l ) are separated into those that depend on the wire and those that depend on the operating conditions. Equa-

tion (4 l ) then "becomes

(42)

where Mc depends on the wire and - .. a

depends on perat—

ing conditions. According to equation (4l) M i B given by



N A C A C E No. 53C27

Wire length Mc (mm)

1. 1 50 4 X10~ 7

2.5 389

3 36 6

The alue of M0 calculated by equation (43) Is

263x 0-».

It will be observed that the experimentally determine

M0 increaaeB with decreasing wire length; whereas, according to equation 43), Hc should e independent of wire

length. This effect is due to the conduction of heat fromthe ends of the wire to the prongs, which is not taken in

h i i f ( l) f



HAOA AC2 Ho, 6K27

in the resul ts of other Investigator« ( reference 13). Fothis reason it is planned to redetermine some of the velocdistributions at the same time * measurements are madesince the same hot—wire" instrument serves both-purposes. The velooity distributions determined BO f ar by the hot ware shown in f igure 17. She veloci ty distributions are aimportant adjunct to turbulence data f or a number of pur-poses, one being to calcula te mixing length by equation (

The results that demonstrate th e applicat ion of hot-wire instruments are given in figures 19, SO, SI , and SS. She mean veloci ty contours and the boundary—layer thicknesshown in f igure 18, are Inc luded here a long with figures and 17 to show the kind of boundary layer in which the turlence measurements were made. The measurements were madeEN = 15.3 mil l ion . Al l these curves were obtained by taki

observations at various distances f rom th e surface with thtraversing device shown in figure 1. A description of t hdevice wil l be omitted hore, part ly because the wanner oftraversing is incidental to the Investigation and part ly

th t t l f t f th d i h t



KA3A ACH Ho. K27

friction at this point. Theoretically, the turbulent shearing stress should decrease in the laminar sublayer and actu- ally fall to zero at the surface. Beyond the laminar sub— layer 4wt till close to the-surface the turbulent shearing stress may be expected to agree with o ThiB appears to be the case, ince the points nearest the surface are well outside of the laminar sublayer. She correlation coefficientscalculated by the three different methods (equations ( 3 4 ) . , ( 3 5) ,

and (27)) are giTen in figure 21. Coefficients Kx and a

agree, but K3 B bout 17 percent above the other two. Thisdifference, hioh indioates experimental error, has not yet been accounted for. More observations are necessary before it s possible to decide which of the quantities uv, u', rv' is least ertain and thereby make use of the procedure suggested in section Til for obtaining the best consistent set f results.

figure 2 , 2 shows the distribution of u'/U at several stations n the region of adverse pressure gradient. I t willbe noted that the ordinates here are the ratio of u' to



UACA A CE ffo. 6K27 9

easily obtained. When the fluctuations are o longer small,errors arise from the interaction of components, improper compensation or lag, and the nonlinearity of the oltage—relooity- urve nd he voltage-angle our re or a hot wire operated with constant heating current. T he latter concernsthe errors in A and D resulting rom the ssumption thatu, v, and w are infinitesimals. When the several kinds of errors are considered, it is found that errors in A an

B are robably the largest and therefore eserve first cosideration.

Since the wave form of turbulent fluctuations is ir-regular and Jagged, and qualitatively has the appearance ocomplete andomness, an accurate estimate of the errors inA and B seems to be impossible. A crude method is to assume sinusoidal fluctuations and to find A from experi-

mental voltage—velocity curves and B from experimental

voltage—angle curves vith bhe relations for A and B given by



HACA AGE Ho. 6K27

i a in such a direction as to make the measured shearing sttoo high.

Before" investigating the error in correlation coefficiit is noted that errors in ' / U and ' /U are not thosedicated in column 4 of tab le I . Th e contro l l ing factor h1B he shape of the broken curve in f igure 14. I f the amptude of the f luctuat ion does not go beyond the l iner porti

of this curve, the only error in v ' /U and 1

/U associawith size arises f rom the assumption that v/U and /U given by , 9 when ac tua l ly they are given by tanAep Terror wil l genera l ly be neglibiblo f or amplitudes that l iewithin the l inear portion of the curve. According to f igu14, the ampli tude of a sinusoidal f luctuat ion will go beyothe l inear portion when ^ /U or w' /U exceeds 0.19. Itwil l be assumed that th e error arising from ' /U may be

corrected by means of equation (3?) , and v ' /U and w ' / Uwil l be regarded as being f ree f rom error due to eise f or values up to 0.19. I t wil l be necessary to pass over the question of errors f or values greater than 0.19.



NACA ACH Ho, 5E27

the e lse of a tern

Snfä'K-

where is th e ampli tude of the resistance ohanges divided by -Ha . I t 1B shown that the error is leas than 2 percent when nf a M is no greater than 0.14. Since the diatribu—

tion of ampli tude with frequency in a turbulent boundary layeris not known, no estimate of the actual error oan be made. The faot that an error in compensation i s l ike ly to enter to a greater and greater degree as the f luctuations increase -in else is fur ther argument f or using wires of th e smallest possible diameter.

X, CONCLUSIONS

An aooount has been given of th e recent developments



NACA ACR No. 5K27

fur ther development of other methods of operation that a"better adapted to th e measurement of large f luctuations ,s u . c h as the constant-temperature method with l inearizingcircuits proposed by Weske in'reference- 11.

National Bureau of Standards Washington, D, C, June 29 , 19^5»

REFERENCES

1. von Karman, Th.: Turbulence and Skin Friction. Jour.Aero. Sei., vol 1 , no. 1, Jan, 193^, pp. 1-20.

2 . Sfc&U&auer, G. B , : A Turbulence Indicator Uti l iz ing the Diffus ion of Reat. NACA Eep. No. 52k , 1935.

3 . Taylor, G . I .: Diffus ion b y Continuous Movements.



NACA ACE No. 5K37

10 . Dryden, Hugh L.i Isotropio Turbulence In Theory and Experiment. Appl . Mechanics, Theodore Ton Karman

. nniversary Vol . , May 11, 1941, pp. 85-102.

11. Weske, John H,: A Hot-Wire Circuit with Very Small TimeLag. NAOA TV Ho. 881,1943,

12. King, L. V.: On the Convection of Heat f rom Small Cylin-ders in a Stream of Fluid: Determination of the Con— v-eotion Constants of Small Platinum Wires with Appli-cations to Hat—Wire Anemomotry. Phi l . Trans. Hoy. Soc. London, ser. A, vol. 214, 1914, pp. 373—432.

13 . Ton Doenhoff , Albert X., and Tetervin, Heal : Determinatioof General Eolations f or the Behavior of Turbulent Boundary Layers. ffACA ACE Ho. 3013, 19 43.



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TITLE: Theory and Application oi Hot-Wire Instruments in the Investigation of Turbulent Boundary Layers

A U T H O R ( S ) : Schubauer, G. B.: Hebanoff, P. S. O R I G I N AT I N GGENCY i lAd i C i i A i W hi D C

ÄYD- 79(N

O3I0. CD y

CR 5K



O R I G I N AT I N G GENCY: ational Advisory Committee ior Aeronautics, Washington, D. C . P U B L I S H E D Y: (Same)

. .CR-5KPU3WMN0 O

MIS

March '4 6 D O C OAB.

Unciass. c o m m r

2L&.

Eng, ILUmsAtlOM

photos, tables, diagrs, graphs ABSTRACT:

Investigation involves th e measurement oi pressure distribution, distribution oi mean velocity across the layer, boundary layer thickness, nd shape parameter as well as measurements oi the turbulent characteristics oi the ayer. It was found that the m-portant characteristics oi the turbulence needed to further an understanding of tur-

bulent layers may be measured. Average characteristics of the layer are shown by thpressure distribution, mean velocity distribution, thickness, and separation point

D I S T R I B U T I O N : equest copies of this report only from Originating Agency

DIVISION: SECTION:

Aerodynamics 2) Boundary Layer (5)

ATI HEET O.: R-2-5-10

S U B J E C T E A D I N G S : Boundary layer, Turbulent - T(18470); Boundary layer, urbulent Measureme

Ai r ocvmontt iviiron, ntatlrOMC» tpor tmenl Ai r otariol emmond

AID ECHNICAL NDEX Wrigtrt-

RICTED

hot wire instrument

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