hot wire nasa calibration

8/12/2019 Hot Wire Nasa Calibration

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NASA TM 8325419820013686 S Technical Memorandum 83 54

Calibration Technique for aHot Wire Probe Vector nemometer

James Scheiman Charles Marpleand David S Vann

M R H 1982

N \S \


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N S Technical Memorandum 83 54

A Calibration Technique for aHot Wire Probe Vector Anemometer

James Scheiman Charles Marpleand avid VannLangley Research enterHampton Virginia

NJ\S \National Aeronauticsand Space AdministrationScientific and TechnicalInformation Branch98


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SUMM RY

Cal ib ra t ion t e s t s u sin g h ot wires were conducted us ing a newly developed t e s tr ig t h a t grea t ly reduced the da ta -acqu is i t ion t ime. The t e s t s included a t h r ee -wi rerobe and a s ing le -wi re probe opera t ing a t numerous speeds and flow ang les . A com-a r i son of mea su re d and computed ve loc i ty -vec to r magni tu de and di rec t ion ind ica tes

th e necess i ty of c ompl ete p ro be c a lib r at i on t o determine flow i n t e r f e r ence and/oropera t ing l imi ta t ion regions. Cal ib ra t ion r e su l t s ind ica te t h a t flow r a tes with3-percent accuracy and flow angles with 5 accuracy are a t t a inab le .

INTRODUCTIONFlow s i t ua t i ons often a r i s e where the re i s a requ i rement fo r making dynamic

measurements. When the v elo ci ty va r ie s in magnitude and di rec t ion a tf a i r ly r ap id r a t e , only a few types of sensor s can be used to make th e measure-Small sca le models are o ften used which impose s ize l imi ta t ions on the sensor

n order to avoid the problem of flow i n t e r f e r ence by the sensor i t s e l f .Examples of th i s type dynamic environment are flow regions downstream o f a pro

o r a he l i cop t e r r o t o r and within a t i p vor tex . The ve loc i ty vec to r near th eof the blades changes both in magnit ud e and in di rec t ion with each blade pas For some ope ra t in g cond it io n s the ve loc i ty vec to r can completely reverse

Because of the r e l a t i ve ly rapid blade passage, the ve loc i ty sensor shoulda f a i r ly high-f requency response. Also , a l l t h r ee ve loc i ty components a re

In order to gain a be t t e r unders tanding o f the ro ta t ing -b lade dynamic loadsnd to cor r e l a t e with ava i lab le theor ies , blade-generated acous t i c s spe c i f i ca l ly

impu ls iv e b la de noise and measured dynamic ve loc i ty d i s t r i bu t i ons are

A few methods are ava i lab le fo r making dynamic ve loc i ty measurem ents. These arel a se r Doppler ve loc imete r sys tem, a ho t -wi re vec to r system, and a ho t - f i lm sys tem.

he l a s e r Doppler ve loc imete r LDV has the advantage of not in t roducing any flowin to the flow s t r eam. However, t h i s system i s very cos t ly compared with

he hot-wire systems, and an L V system requ i res a r e l a t i ve ly long devel opment t imeo become ope ra t i ona l . For the prope l le r o r he l i cop t e r r o t o r example c i t ed , th e L V

measures pa r t i c le motion through a smal l sens ing volume, and the cor respondingare not continuous as with a h ot-w ire o r ho t - f i lm sensor i . e . , the L V

pa r t i c le motion over a l a rge number o f b lade passages . The ho t -wi re systemas the d is ad va nta ge o f i n t roduc ing a sensor into flow streams t ha t a re being

and thus c rea t ing a flow in te r fe rence which may d is tu rb the flow beingeasured. In add i t ion , flow dis turbances can occur because of th e h ot-w ire prongs

wire suppor t s . The requi red t hr ee v el oc it y components necess i t a t e th ree ho t wires ,nd the cor responding sensor volume i s l a r ge r than the sensor volume fo r an L Vystem. The sensor volume can be impor tan t because the sensor de tec t s the averagee loc i ty within t h a t volume. Thus, i the ve loc i ty g ra d ie n ts w ith in the volume a retoo g re at , e rro rs are in t roduced. Advantages of th e h ot-w ire system are t h a t it i s

r e l a t i ve ly cheap to purchase, r equ i r es very littl development t ime , and has a f a i r lygh -f re quen cy r es pon se . A ho t - f i lm system has advantages and disadvantages s im i l a r

o a hot-wire sys tem, and it i s much l es s vulnerable to damage.


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When us ing a ho t -wi re sys tem, t he q ue st io ns of accuracy and f low-anglel im i t a t i on s immedia te ly come to mind. The user of a t h r ee -ho t -wi re system of tenprov ides very littl ca l i b r a t i on i n fo rma t ion e . g . , r e f s . 1 to 3 ) . There a re severa lreasons fo r t h i s lack of ca l i b r a t i on da t a . A complete-probe ca l i b r a t i on invo lvest e s t i ng a t numerous ve loc i t i e s and d i r e c t i on s ; t hu s , a complete ca l i b r a t i on i s veryd i f f i c u l t to ob ta in . Fur the r , th e p hy sic al endurance of th e t h r ee -ho t -wi re systemcan become a se r i ou s l im i t a t i on i th e ca l i b r a t i on becomes too ex tens ive and r equ i r esa l a rge amount o f opera t ing t e s t t ime . Because of the se problems , th e h ot-w ire probeuse r in many cases cannot o r does not ca l i b r a t e the probe . In ste ad , th e user r e l i e son ana ly t i c a l da ta - r educ t ion equa t ions , and in some cases uses pub l i shed sensor sen s i t i v i t i e s . Such an approach neg lec t s probe o r ho t -wi re suppor t - p rong flow i n t e r f e r ence and any es t imate of accuracy fo r dete rmining ve loc i ty magnitude o r d i r ec t i on .Also , s l i gh t d i f f e r ences between probes because o f fab r ica t ion t o l e r ances areneg l ec t ed . The impor tance o f some of these e f f ec t s can be found, fo r example, inr e f e r ences 4 to When th e flow i s near ly pa r a l l e l to th e lo ng itu din al a xis of oneof th e ho t wi res , o r when ho t -wi re suppor t - p rong in te r fe rence i s encoun te r ed , systemi naccurac ies should be an t i c ip a t ed . Therefo re , t he re a re flow angles where th emeasured r e su l t s should be ques t ioned even though th e measurements may be r epea t ab l e . Some at tempts have been made to es t imate accuracy and probe opera t ingl im i t a t i ons .

The sub j ec t of t h i s paper i s a l imi ted ca l i b r a t i on and a d i scuss ion of someopera t ing problems when using h ot wires to make mean ve loc i ty -vec to r measurements.Recommended procedures were used to reduce th e da ta , and th e r e su l t i ng computedve loc i ty magnitudes and d i rec t ions a re compared with th e cor responding measuredva lues . A spec i a l ca l i b r a t i on r ig was deve loped and used to sh or te n th e da ta a cqu i s i t i on t ime . This r educ t ion was achieved by t ak ing advantage of the r ap idresponse t ime of th e ho t wire and by making use of e l e c t ron i c d ata r ed uc ti ont echn iques . This ca l i b r a t i on r ig i s descr ibed he re in . Two t h r ee -wi re probes andone o ne -w ir e p ro be were t e s t ed . The ho t-w ire o utp ut d ata were reduced a t 5increments in flow angle with r e spec t to the probe ax i s , over a range of 155.These da ta were ob ta ined a t var ious probe r o l l ang les . The flow ve loc i t i e s var iedfrom 8.94 to 40.23 m/s.

SYMBOLS

a

b

c

2

cons t an t determined by ca l i b r a t i on see eq . 1 , vo l t s 2/oC

k2g 1 2ons tan t determined by ca l i b r a t i on s ee eq . 2m

constant determined by ca l ibra t ion see eq. 1 , vol t s 2/ .C m : ~ s ) / 2cons tan t determined by ca l i b r a t i on see eq . 2 2 kg 4 1 2

m - s -vo l t scons tan t determined from the i n t e r cep t o f a l e a s t - s qua r e s - f i t l i ne th roughmeasured and computed mass flow see eq . 4 , ~ 2

m


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cons tan t determined from slope of a l e a s t - squa r e s - f i t l i ne throughmeasured and computed mass flow see eq . 4 , dimens ionless

dc v olt ag e s up pli ed t o wire senso r , vo l t scons t an t in equat ion 3 , dimens ionlesscons t an t ranging from 0.48 to 0 .51 , n 1/2 here int emp er at ure o f envi ronmenta l cool ing f l u id , Ctemperature o f h ot-w ire se nso r, Ct o t a l ve loc i t y -vec to r magnitude, m/sve loc i t y component normal to hot wire , m/sacu te angle between flow d i rec t i on and l ong i t ud ina l ax i s of ho t wi re , degdens i ty of coo l ing f l u id , kg/mprobe r o l l angle measured from ve r t i c a l plane th ro ug h p ro be ax i s to ho t

wire degprobe yaw angle w ith resp ec t to flow d i rec t i on 0 when ve loc i t y i s

al igned with probe ax i s , deg

exper imenta l ca l i b ra t ed angleg eomet ri ca l a ng lei t h hot wire i = 2, 3 fo r th ree -wi re probeminimumdenotes quant i ty a t a pa r t i c u l a r va lue of e

PP R TUS ND TEST PROCEDUREApparatus

Hot-wire sys t em. - Three ho t -w i re p ro be s ystems were t e s t ed in t h i s s tudy . Theof a l l the probes were gold p l a t ed . The wires were p la t inum-p la t ed tungs ten

an ac t ive wire d iameter of and an ac t i ve leng th of 1.25 mm l eng th - t o r a t io of 250 . The t o t a l h ot-w ire le ng th d is ta nc e between prongs was

mm which i s about th ree t imes the ac t ive wire l e ng th . The probes were opera ted i ncons t an t - t empera tu re mode and no l i nea r i ze r was used. The wires were opera ted a t

n overhea t r a t i o of 1 .8 , which i s w ith in th e recommended opera t ing range.Two of the probes were t yp i ca l th ree -wi re probes of i den t i c a l manufacture .probes have th ree wires , each of which i s perpend icu la r to the othe r two.

along the ax i s of the probe, the ho t wires pro j ec t an image onto a normal


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plane of 120 between wires . Figure 1 a i s a photograph of one of these probes .Disregarding flow i nt er fe re n ce s, t hi s probe system could t heo re t i c a l l y measure themagnitude and di rec t ion of the veloc i ty anywhere in a hemisphere.

The th i rd probe had a s ing le wire . Figure 1 b i s a photograph of t h i s probe .This type probe cons t ruc t ion i s designed to min im iz e flow i n t e r fe rence for some t e s tcondi t ions .

Cal ibra t ion r i g . - A complete ca l ib ra t ion of a th ree -hot -wi re probe over a speedrange r equi re s many t e s t condi t ions thousands in th is r epor t ) and can be very t imeconsuming. In order to d e r e s ~ the t ime, a spec i a l ca l i b r a t i on r ig has been cons t ruc t ed . This ca l i b r a t i on r ig makes use of the r ap id response t ime of a hot -wiresystem and grea t ly reduces the t e s t ing t ime . F igure i s a photograph of t h i s r ig .The hot -wire probe shown on the ca l ib ra t ion r ig in f igure can be yawed about apo in t near the center of the ho t w ires . The maximum y aw -ang le r an ge was about 1700data were r ec ord ed o ve r a range of 155 , and the yawing ra te could be var ied fromabout 6 to seconds p er cycle . During the high-speed t e s t s , the aerodynamic dragon the probe suppor t arm was such t h a t the yaw ra te was r e l a t ive ly slow aga ins t thewind and r e l a t ive ly fa s t with the wind. In f ac t , the maximum torque of the yaw motorwas the fac tor t ha t l imi t ed the maximum tunnel t e s t speed. However, even a t the yawra te extremes , the crank-arm t an g e nt ia l v e lo c it y was smal l compared with the flowve loc i t y . The s t ruc tu ra l def l ec t ion of the system was i n s ign i f i c an t .

Figure a l so shows the square -wave yaw-ang le pos i t ion ind ica tor . This i nd i ca tor cons i s ted of a saw tooth and a photoce l l which generated an e l e c t r i c a l squarewave over a range of 155 a t in te rva l s corresponding to every 5 of yaw for theprobe systems. The ca l ib ra t ion of the probe yaw angle and square-wave genera to r i sshown i n tab le 1. The saw-tooth gear was machined very u r t e l y ~ however, theor i en t a t i on of the zero-yaw pos i t ion probe angle with r e spec t to the f ree streamwas not good as seen by the uneven angles in t ab l e 1) . This r es ul te d in f ixedangu la r displacement fo r a l l the yaw angle s . A f l i p - f l op system was incorpora tedin orde r to i nd i ca t e the probe yawing d i rec t i on of ro ta t ion i . e . , clockwise orcounterc lockwise) . The hot-wire p ro be sy stem could he manually or i en ted a t d i f f e r en tr o l l angles about the probe ax i s . op t i ca l system t r an s i t t heodol i t e ) was used toad j us t the r o l l angle of the ho t wires on the ca l ib ra t ion r i g .

Test ProcedureThe t e s t s were conducted in the low-veloc i ty ca l i b r a t i on wind tunnel a t th e

Langl ey Resear ch Center . A photograph of t h i s tunnel i s shown i n f igure 3. Thetunnel t e s t chamber i s 43.2 cm wide, 30.5 cm high , and 76 cm long, and the speedrange i s from 2.2 t o 89.4 m s The tu rbulence leve l in the t e s t chamber i s about0.5 to 0.75 percent , which i s adequate fo r the measurements presented in t h i srepor t . The tunne l veloc i ty can be measured to 0.5-pe rcent accuracy. The f lu idtemperature was the ambient temperature and was cons tan t w ith in the measuringaccuracy .

As the ca l i b r a t i on r ig cycled back and for th through the yawing cyc le s , thee l e c t r i c a l outputs were recorded cont inuous ly and s imultaneous ly on d i f f e r en t channels of an magnet ic- tape recorder . These e l e c t r i c a l outputs cons i s ted of thethree hot -wire vol tages , the square-wave-yaw i d en t i f i c a t ion pulse , and the di rec t ionof-yaw f l ip - f lop i nd i ca t o r . In addi t ion , the probe i d en t i f i c a t ion , probe r o l l or i en t a t ion , probe yawing r a t e , and tunnel speed were manually r ecorded . Two extremeyawing r a t e s , about 6 and seconds per cycle , were used. For Ble cur ren t t e s t s ,4


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he t unne l speed var ied from 8 .9 to 4 s in i n t e rva l s of about 4 .5 s fo r a t o t a lf seven speeds . s viewed along the ax is of the probe, r o l l angles of and0 were chosen fo r the th ree -w ire probes f i r s t with number one hot wire ve r t i c a lnd second with number one ho t wire hor i zon ta l . Looking along the ax is of th e

probe, the projec t ion of the th ree wires in a normal plane are 120 The s ing le -wire probe was also t es ted over the same s peed ra ng e and a t the

r o l l angles of and 90 i . e . , the s ingle wire ve r t i c a l and hor i zon t a l .the previously descr ibed procedures , the t o t a l data-acqui s i t ion t ime was

to a few hours . The hot-wire , yaw-angIe-pulse , and d i r ec t ion -o f - ro t a t ionwere r eco rd ed s imu lt an eou sl y on a magnet ic- tape reco rde r . At l e a s t 40 com

yaw cycles of the probe were recorded fo r each opera t ing t e s t condi t ion . Thedata were reduced as fo l lows. The magnet ic- tape data were d ig i t i zed a t the

r i s e and f a l l pos i t ions ind ica ted by the square-wave yaw-angl e s i gna l .When the probe i s yawing in one d i r ec t i on , the probe yaw angle fo r the r ise on the

wave corresponds to the same probe yaw angle fo r the f a l l o n the square waveyawing in th e o pp os ite d i r ec t ion . In f requen t ly dur ing the record ing of the

quare-wave genera to r s i gna l , a no i se spike or reduced l eve l was recorded . Thisbe detec ted dur ing the d ig i t i z ing process of one complete probe yaw cyc le ,

one square-wave pulse would be added or omit ted . Therefore , before anycomplete cycle of da ta was processed fur ther , the t o t a l number of d ig i t i zed

data po in ts fo r each probe yaw cycle was counted. I f the sum did not add up to 62,l l the data w ith in t ha t cycle were d i sca rded . When the data fo r one yaw cycle werec ep ted , th e h ot-w ire v oltag es corresponding to ea ch p ro be yaw pos i t ion were squared

to ob ta in e l ec t r i c a l power when wire r es i s t ance was assumed cons t an t . These valuesaccumulated fo r a l l the complete cycles and were t he n a ve ra ge d. The data fo r

he d i f f e r en t d i r ec t i ons of yawing ro ta t ion were averaged sepa ra te ly so t h a t thef f e c t s , i f any, of the di rec t ion of yaw could be evaluated . The f i n a l output

vol tage squared values presented here in rep resen t a t l e a s t 40 averaged data po in tsfo r e ac h p ro be yaw pos i t i on . The mean o utp ut v olta ge squared va lues and s tandarddevia t ions were t abula ted and machine p lo t t ed . The s t andard devia t ions were

lc ula te d in order to evaluate the sca t t e r in the da ta .

DISCUSSION O RESULTSThree hot-wire probes were t es ted in the low-veloci ty ca l ib ra t ion wind tunnel a t

he Lang ley Resea rch Center . The probes were t e s t ed a t seven speeds and yaw anglesa range of 155 to determine in te r ference and o th er d ev ia ti on s from t heory .

The r e su l t s a re p resen ted in four sec t ions : 1 probe geometr ic l imi t a t i ons ,2 p ro be r es po ns e with yaw, 3 comparison of two i den t i ca l three-wire probes, and4 veloc i ty magnitude mean flow and d i re c ti o n p r e di ct io n .

Probe Geometric Limi ta t ionsWhen using a th ree -wire probe, t hr ee o pe ra ti ng problem regions a re c on sid er ed :

1 when one ho t wire i s downstream of a no th er w ir e, 2 when the veloc i ty vec to r i sto the axis of a wire , and 3 when the re i s flow in te r ference due to th esuppor ts prongs . The f i r s t two opera t ing regions are discussed in th i s sec

t ion , and these opera t ing l imi t s are ca l l ed p ro be g eomet ri c l imi t s here in . The th i r dregion requ i res a complete ca l ibra t ion and i s discussed here in . r{hen the meanveloc i ty vec to r i s known, the problem of geometr ic l imi t s can be minimized by properr i en t a t ion of the probe with re spec t to the flow d i r ec t i on . However, when the mean

veloc i ty vec to r i s not known, the re i s no way of or ient ing the probe to avoid th epe ra t ing problem regions . Ins tead , i s e ss en tia l to make measurements a t two or

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more probe o r i e n t a t i o n s , reduce t h e d a t a , and compare t h e r e s u l t s f o r s i m i l a r i t y . I fthe r e s u l t s f o r any two probe o r i e n t a t i o n s a r e not s i m i l a r , t h e r e i s no way of know-i n g which measurement, i f e i t h e r , i s c o r r e c t , and a t h i r d o r more measurement i sr e q u i r e d .

The probe geometr ic l i m i t s d i s c u s s e d i n t h i s s e c t i o n a r e a s s o c i a t e d with flow a tsome f i x e d angle t o t h e a x i s of a h o t wire 8. In o r d e r t o ma in ta in a cc u ra cy , t h eprobe o p e r a t i o n should be l i m it e d t o an o p e r a t i n g r e g i o n where t h e flow angle 8 i snot s m all . G en e r a lly , f o r a t h r e e - w i r e probe , t h e i n d i v i d u a l wires a re a li g ne d p e r p e n d i c u l a r t o each o t h e r . This o r i e n t a t i o n s i m p l i f i e s t h e mathematics i n determin-in g the t o t a l flow r a t e from t h e output o f the t h r e e wires e . g . , s e c t i o n 7.3C o fr e f . 12 . From th e wire geometry and t h e known flow angle with r e s p e c t t o theprobe a x i s , th e angle 8 between the v e l o c i t y v e c t o r and any wire a x i s can bedetermined . These comput a ti ona l p r ocedu r es a r e given i n t h e appendix, and t h eg r a p h i c a l r e s u l t s a r e shown i n f i g u r e 4.

The c e n t e r o f th e p o l a r p l o t i n f i g u r e 4 shows t h e o r i e n t a t i o n of the t h r e e hotw ires as seen looking along the a x i s o f t h e probe . The p o l a r angle r o l l angleon t h e f ig ur e r ep re se nt s the d i r e c t i o n o f t h e v e l o c i t y v e c t o r component i n a planenormal t o t h e a x i s o f th e probe . The yaw angle graduated a long a r a d i a l l i n e i nt h e f i g u r e , r e p r e s e n t s th e angle between th e v e l o c i t y v e c t o r and probe a x i s . Thus,any p o i n t on th e p l o t s p e c i f i e s th e a ng ula r p o s i t i o n of th e v e l o c i t y v e c t o r withr e s p ec t t o th e probe c e n t e r of p l o t ) . The a d v e r t i s e d hemispher ica l l i m i t t o probeo p e r a t i o n would be i n d i c a t e d i n the f i g u r e by a c i r c l e with a r a d i u s equal t o

90. The contour l i n e s a r e f o r 8m 20, 30, and 40. This angle em i sd e f i n e d as t h e angle between t h e v e l o c i t y v e c t o r and t h e l o ng it ud in a l ) a xi s of anyh o t wire . The f i g u r e a l s o shows the o r i e n t a t i o n of t h e v e l o c i t y v e c t o r with r e s p e c tt o the f i x e d probe .

The a r e a between t h e c i r c l e f o r = 0 and any 8m curve d e f i n e s the probeo p e r a t i n g region where 8 f o r any of t h e t h r e e h o t wires w i l l always be g r e a t e rthan 8m The p l o t shows t h a t , f o r th e s o l i d l i n e , t h e a n g l e s between th ev e l o c i t y v e c t o r and probe a x i s ) must not be g r e a t e r than about 16. F u r t h e r , f o rt h e 8m = 30 boundary, can be as l a r g e as 23, and f o r t h e 8m 20boundary, can be 36. In o t h e r words, i f th e v e l o c i t y - v e c t o r o r i e n t a t i o n i sunknown, and 8m 20 i s considered a reasonable minimum value r e f s . and 5 ) , then t h e angle between th e h ot - wir e probe a x i s and t h e v e l o c i t y v e c t o r mustbe l e s s than about 36. This r e p r e s e n t s a p h y s i c a l l i m i t f o r probe o p e r a t i o n .

Probe Response With wThe d a t a p r es en te d h e re in a r e well beyond the m a n u f a c t u r e r s recommended yaw

a n g l e s of u s a b i l i t y i . e . , g r e a t e r than hemisphere f o r t h i s s e n s o r . However, s i n c et h i s i s an e x p l o r a t o r y program, the c omplete r an ge o f measured d a t a i s p r e s e n t e d .I n i t i a l l y , t h e probe d a t a recorded when approaching a given yaw angle from upstreamand downs tre am were accumulated and averaged s e p a r a t e l y . This p ro ce du re p rov id ed ane v a l u a t i o n of the e f f e c t o f yawing d i r e c t i o n on t h e r e s u l t s . A comparison betweenaverage probe o u t p u t when approaching a given yaw angle from upstream o r downstreamproved t h e d i f f e r e n c e s were n e g l i g i b l e . T h e r e a f t e r , th e d a t a a t each yaw angle fo rboth d i r e c t i o n s o f yawing were averaged t o g e t h e r . Thus, t h e mean values of t h e o u t p u t v o l t s squared i n f i g u r e s 5 t o 9 a r e averages of a t l e a s t 80 i n d i v i d u a l t e s tp o i n t s f o r each o f t h e 62 probe yaw a n g l e s .

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A s tandard devia t ion was ca lcu la t ed fo r each t e s t condi t ion . The s tandard devi a t ion provides a measure of sca t t e r in the i nd iv idua l data and a l so an e va lu atio n o fthe var ia t ion of the mean value or the number of i nd iv idua l data poin t s required t od ec rea se th e var ia t ion i n the mean value . I t was i n i t i a l l y bel ieved t h a t absolu tes ca t t e r i n the data would be h ighe s t a t probe yaw a ng le s w ith flow i n t e r fe rence onone of the ho t wires i . e . , 8 sma l l . However, t h i s was no t usua l ly the case . Thereason fo r the var ia t ion in the sca t t e r with 8 could n ot be determined .

The one s tandard devia t ion value var i ed from 0.5 percent to 2 percent of th emean value of the o ~ t p u t Let t ing on e s tandard devia t ion equal 2 percen t , two s t an dard devia t ions , which inc lude 95 percent of the da ta , a re with in 4 percent of th emean value . In o the r words, one t e s t poin t would have 4-percent a cc ura cy w ith a95-percent conf idence . Averaged data presented he re i n , which are average values xof about 80 ind iv idua l po in t s , are accu ra te to with in 0.5 percent with a conf idenceof 95 percent ax 0.04/vao .

The bottom p lo t s of f igures 5 a to 5 c are p lo t s of the output aga ins t th eprobe pos i t i on or yaw angle fo r each of the t h ree wires or sensors o f the p robe .Lines are fa i red through the d i sc re t e data po in t s . The sYmbols on the curves areonly used to iden t i fy the var ious mean flow r a t e s each f a i r ed curve inc ludes data a tevery 5 of yaw angle . The top plo t s of f igures 5 a t o 5 c show the ca lcu la t edflow angle 8 with respec t to t h a t wire . When 8 90, the veloc i ty i s pe r pendicu la r to the axis of the wire . The d i f f e r en t curves in the bottom p lo t s off igures Sea to S c are fo r d i f f e r en t mass flow pV F ig ure s S ea , S b , and S care fo r wires 1, 2, ,and 3, r e spec t i ve l y , of the probe. The wires are numbered cons ec uti ve ly i n a c lockwise d i rec t i on when looking from the r ea r of the probe. Inf igure 5, the number one wire was a l igned ve r t i c a l l y . The f igure shows t h a t maximum h ot -w ir e o utp ut cool ing occurs when the f lu id flow i s perpendicu la r to the wire8 = 90 . Discont inu i t i es in the o utp ut c oo lin g ra te or vo l t s suppl ied curves arei nd ica t ions of flow in te r fe rence . For example, fo r wire number one in f igure 5 at he re i s flow i n t e r f e rence for a probe yaw angle of about 75. Figure 5 also showst h a t some of the i n t e r f e rences are veloc i ty dependent r a t he r than geometrydependent. When the i n t e r f e rence occurs a t a l l mass flow ra tes a t the same yawangle ~ t i s pr imar i ly a geometr ic i n t e r f e rence e . g . , f ig . 5 b , ~ 100 .When the i n t e r f e rence occurs a t d i f f e r en t mass flow r a t e s , t i s veloc i ty dependent e . g . , f ig . S b , -24 or 26 . mentioned previous ly , the output datapresented a re a cc ura te to 0.5 percent of mean value w ith a conf idence l im i t of95 percent : t he re fo re , the noted e f f ec t cannot be a t t r ibu ted t o er rors i n dataacquis i t ion .

For the lowest mass flow pV = 10.89 , t here are two curves . These two curveswere obta ined by cycl ing the ca l ib ra t ion r ig a t yaw ra tes of 6 and 2 seconds percyc le . I t was expected t h a t the l a rge s t di f fe rence induced by the cycl ing r a t e wouldoccur a t the lowest flow r a t e . seen in the f i gu re , the curves fo r the two cyc l ingr a t e s a re near ly i d en t i c a l . Therefore , t i s concluded t h a t for the lowes t mass flowt e s t ed , the cycl ing ra te or yawing veloc i ty had very l ttl e f fec t on wire output .

Figure 5 a l so shows two curves fo r a mass flow r a t e pV of 21.81. These twocurves were obta ined from data taken on d i f f e r en t days . Differences i n these curvesprov ide an i nd ica t ion of c a li b ra ti o n r e p e at a b il it y and wire de te r io ra t ion with usage.Figure 5 b fo r wire 2 i nd i ca t e s some unexpla inable s h i f t in the mean value . Theother two sensors on th e probe do i nd i ca t e some d i f f e rences , bu t they are r e l a t ive lysmall ~ 0 5 percen t .

7


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For anyone curve in f igure 5, the mass flow ra te i s cons tan t ; t he re fo re , theoutput wire cool ing or power suppl ied i s d i re c tl y r el at ed to flow ang le 8 withr e spec t to each wire . When 8 i s h ig he st , the cool ing i s highes t ; when 8 i slow est, the cool ing i s lowest . The l a rge r the v ar ia tio n in 8 w ith probe yaw, thel a rger the v ar i a tio n in ou tpu t vo l t s squared . The var ia t ion i n 8 was ca lcu la tedfrom the known geometry of each sensor on the probe and the measured probe yawpos i t i on .

The data presented in f igure 6 fol low the same format as thef igure 5. The f igure 6 data a re fo r the same probe; however wirelooking from the r ea r , wire i s to the l e f t . In f igure 5 wireF igure 6 a shows t h a t t here i s a l inear r e l a t i onsh i p between 8expected. A ls o, b ec au se of probe symmetry, wires 2 and 3 shouldca l geometr ical cha rac t e r i s t i c s with v ar i a tio n in yaw angle .

d ata p re se nt ed in i s hor i zonta l was ve r t i c a l .and ~ a s would be

and do have i d en t i -

Figure 6 shows many of the same cha rac t e r i s t i c s al ready seen in f igure 5.For example, some of the cool ing i n t e r fe rences are s l igh t ly veloc i ty dependent f ig . 6 a , ~ = 75 and some i n t e r fe rences a re geometr ic f i g . 6 b , = -133 , orf ig . 6 c , ~ = -123 . The outpu t vo l t s squared curves show t h a t the geometr ici n t e r f e rences fo r wires 2 and 3 around ~ = -123 a re not the same. This may bebecause the wires are symmetr ical and the s en so r s up po rt prongs a re no t .

The var ia t ion i n output i s a funct ion of the var ia t ion in the flow angle 8with r e spec t to each wire . In genera l , f igure 6 shows t ha t the same w ire w ith equalva lues of 8 bu t with d i f f e r en t values of can have d i f f e r en t cool ing r a t e s .This i s i nd ica t ive of the di f fe rences in flow i n t e r fe rence over the extreme yaw-anglerange. For example, i n f igure 6 a fo r p = 15.13, the maximum output values fo r8 = 90 a t ~ = -143 and 35 a re not equa l . Likewise , fo r the same wire and thesame p the minimum output values are unequal fo r 8 0 a t -54 and 120.Fur the r i nd ica t ions of flow i n t e r fe rence are shown by comparing the ca lcu la t ed yawang les fo r minimum cool ing 8 = 0 with the measured va lues . For example, in f ig ure 6 a the ca lcu la t ed yaw angles fo r minimum co olin g are -52 .7 and 127.7 , whereasthe measured minimum cool ing i s a t about = -48 and 130. This same e f f ec t can beseen in o the r data e . g . , f i g . 7 c . This implies t h a t the probe yaw angles ~should be r e s t r i c t ed to perhaps 500 t o 700. Also, the angular flow l im i t a t i onsdescr ibed in f igu re 4, which a re based on p ro be g eome tr y, may be too r e s t r i c t i ve .

Figure 7 presen t s the response cha rac t e r i s t i c s of a second th ree -wi re probei den t i c a l to the probe used to obta in the data presented i n f igures 5 and 6. Thisprobe had wire a l igned ve r t i c a l ly ; t herefore the data can be compared d i r ec t l y withthe data in f igure 5. The r e su l t s a re s im i l a r fo r the two probes .

In addi t ion t o the three-wire probes , the s ing le -wi re probe shown in f igure 1 bwas t e s ted on the ca l i b r a t i on r i g . Figure 8 a shows the response fo r t h i s probewith the wire a l igned ve r t i c a l ly , and f igure 8 b shows the response with the wireal igned hor izon ta l ly . In f igure 8 a , the mass flow d i rec t i on i s always a t 90 tothe wire the sensor i s yawed about i t s axis as the ca l ib ra t ion r ig cycles in yaw .Figure 8 a shows t h a t the o utp ut c oo lin g r a t e i s near ly cons tan t wi th in pe r cent as the yaw var ies . There i s severe i n t e r fe rence by th e w ire -p ro ng su pp orts a ton e of the extreme yaw pos i t i ons ~ = 111 and not a t the o the r . This would beexpected from th e p hy sic al c on str uc ti on of t h i s type probe.

In f igure 8 b , where the s ing le wire i s o r ie n te d ho r iz o n ta l ly , the massang le 8 va r i e s l inear ly with the probe yaw angle . Note the symmetry in thecool ing r a t e , even fo r the poin t s of minimum cool ing a t ~ 85 and 900.8

flowoutpu tThe


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data in f igu re 8 fo r th e s ingle-wire probe ind ica te a lack of in te r ferences asexpec ted . This f ac t i s i l l u s t r a t ed by the smoothness of the cu rv es w ith var i a t i onsin e i the r mass flow ra te or yaw angle .

Comparison of Two Similar T hr ee -W i re P ro be sA comparison of the re sp on se o f the two three-wire probes which are of i d en t i c a l

model and manufacture i s presented in f igure 9. The d ata p re se nt ed in f igure 9 wereobta ined by of f se t t i ng the mean vol tage l eve ls by th e same amount fo r a l l th ree wireson one probe. This was done to obta in a r e l a t i ve comparison fo r the two probes . Thes lopes of these curves ind ica te the capab i l i t y of determining flow di rec t ion from theth ree curves fo r anyone sensor . Since the slopes fo r each wire on the two probesare about the same, the re i s a s t rong s imi l a r i t y in the ind iv idua l w ires of e le twoprobes .

The m ajor flow in te r ferences seem to occur a t the same probe yaw ang les . Mostnot iceable i s the l a r ge r number of in te r ferences fo r probe 1 as compared withprobe 2. These d i f fe rences are most probably due to the hot -wire- -prong j o in tconnect ion d i f fe rences on a very sm all sca l e . This seems apparent fo r a l l th reewires on probe 1, especia l ly fo r w i r ~ Although these d i f fe rences are on the orderof only a few percen t , t he y u nd er sc or e th e need fo r ca l ib ra t ing each ind iv idua l probethrough a range of ve loc i t i e s and yaw and r o l l angles i f accuracy i s to bea t t a ined . This ca l ib ra t ion should be extensive enough to obta in da ta - reduc t ioncons tan ts and an a sse ss me nt o f the in te r ference fo r each probe. Unfor tunate ly , anys ingle probe may not l a s t long enough to perform the ca l i b r a t i on as i s the casehere in with probe 1, which fa i led during ca l i b r a ti on .

Veloci ty Magnitude and Direc t ion Pred ic t ionThroughout th i s repor t th e d is cu ss io n has been assoc ia ted with mass flow r a tepV r a t he r than ve loc i t y . There are a number of equ iva len t ways to d es crib e th es e

t e rms. F or e xa mp le , when th e d en si ty i s known, the mass flow can be conver tedd i r ec t ly to ve loc i t y . Another common procedure i s to conver t the ac tua l mass flowr a te to tha t of s tandard-densi ty mass flow r a t e . With th i s unders tanding the massflow ra te and veloc i ty terms are used in terchangeably here in .

To eva lua te th e capabi l i ty of determining the magnitude of the veloc i ty from thethree-wire probe , th e fol lowing procedure i s normally used. From equat ion 1 o freference where the mass flow i s perpend icu la r to the wire sensor , i ee = 90 ,

By solv ing equat ion 1 fo r th e mass flow r a t e pv and r eca l l i ngtempera ture opera t ion Ts i s cons tan t fo r the cur ren t t e s t Teconstant t h a t Ts - Te can be considered cons t an t , equat ion 1

pV 1/2 = bE 2 a

1

tha t fo r cons tan t i s su f f i c ien t lycan be rewr i t t en as

9


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where th e c o n s t a n t s a and b a r e de te rmined from t h e d a t a t a b u l a t e d f o r t h e t e s t sh e r e i n . Since one probe was t e s t e d with w i r e 1 i n two p o s i t i o n s f i g s . 5 and 6 ) ,t h e a and b c o n s t a n t s were de te rmined s e p a r a t e l y f o r both s e r i e s o f t e s t s . Asrecommended by t h e m a n u f a c t u r e r , each wire on t h e probe should be c a l i b r a t e d with t h emass flow a t 9 t o t h e wire 8 = 90 Data a t some probe yaw p o s i t i o n s were d i s carded because flow i n t e r f e r e n c e was p r e s e n t . See f i g s . 5 and 6 . ) A f t e r s p e c i f y i n ga p a r t i c u l a r probe yaw p o s i t i o n n e a r 8 = 90 f o r each w i r e , a l l t h e pv d a t a andt h e c o r r e s p o n d i n g E2 e xp e ri m en ta l d a ta were accumulated and a l e a s t - s q u a r e s - f i ts t r a i g h t l i n e through t h e d a t a was determined . The c o n s t a n t s a and b c o r r e s p o n dt o t h e i n t e r c e p t and s l o p e o f t h e l e a s t - s q u a r e s - f i t l i n e . Table 2 summarizes t h er e s u l t s . In t a b l e 2 t h e r e a r e f o u r v a l u e s o f t h e a and b c o n s t a n t s f o r each wireon t h e p ro b e. Normal ly , t h e c a l i b r a t i o n p r o c e d u r e i s t o de te rmine only one v a l u e f o reach w i r e . For any o f t h e t h r e e w ir e s , t h e d i f f e r e n c e s between t h e c o n s t a n t s a r esmal l f o r t h e same probe r o l l p o s i t i o n as i n d i c a t e d by h o r i z o n t a l o r v e r t i c a l p o s i t i o n o f w ire 1 . There i s a r e l a t i v e l y l a r g e d i f f e r e n c e between t h e c o ns t a n t s f o rt h e same wire when t h e probe r o l l p o s i t i o n s a r e d i f f e r e n t . T h i s v a r i a t i o n f o r t h ea and b c o n s t a n t s , e s p e c i a l l y f o r w i r e s 2 and 3, c o u l d be a t t r i b u t e d t od e t e r i o r a t i o n o f t h e i n d i v i d u a l w i r e s with u s a g e . The f i r s t s e r i e s o f t e s t s werec ondu ct ed w it h t h e probe r o l l a n g l e such t h a t wire 1 was v e r t i c a l f i g . 5 . Thiss e r i e s o f t e s t s r e q u i r e d about 3 hours o f w i n d - t u n n e l a i r blowing a c ro ss t h e p r o b e .While c o n d u c t i n g t h e second s e r i e s o f t e s t s wi th t h e probe r o l l a n g l e such t h a tw i r e 1 was h o r i z o n t a l ) , w i r e s 2 and 3 f a i l e d . The i m p l i c a t i o n i s t h a t t h e w i r eendurance i s n o t s u f f i c i e n t t o l a s t through a complete c a l i b r a t i o n . The w i r e s wereo p e r a t i n g a t a c c e p t a b l e t e m p e r a t u r e l i m i t s ; however , smal l p a r t i c l e s may have s t r u c kt h e s e two w i r e s on t h e p r o b e .

V e l o c i t y magnitude c a l i b r a t i o n . - To c o n t i n u e t h e e va lu at io n o f t h e mass flowp r e d i c t i o n a c c u r a c y , t h e tw o v a l u e s f o r th e c o n s t a n t s a and b de te rmined w i t hw i r e 1 v e r t i c a l , which were almos t t h e same, were averaged t o g e t h e r . The mass flowr a t e s de te rmined from each o f t h e t h r e e w i r e s can be combined i n t o a t o t a l mass flowby u s i n g t h e f o l l o w i n g e q u a t i o n from s e c t i o n 7.3C o f r e f e r e n c e 12:

2pV + 2pV2 22 + K 3

During th e d e r i v a t i o n o f t h i s e q u a t i o n , i s assumed t h a t th e v alu es o f K f o r eachwire a r e a l l e q u a l and t h a t t h e i n d i v i d u a l w i r e s a re p er p e nd ic u la r t o each o t h e r .

For one probe yaw angle f i g . 5 and t h e a and b c o n s t a n t s f o r each wireand t h e o u tp u t v o l t s squared f o r each w i r e , pVi 2 c o u l d be de te rmined by u s i n ge q u a t i o n 2 ) . The numera tor o f t h e r ig h t- ha n d s i d e o f e q ua t i o n 3 c o u l d t h e n bec a l c u l a t e d . c a l c u l a t e d v a l u e c o u l d t h e n be compared w i t h t h e a c t u a l measuredmass flow r a t e l e f t - h a n d s i d e o f eq. 3 . These r e s u l t s a r e shown i n f i g u r e 1 f o rv a r i o u s probe yaw a n g l e s . Also shown i n f i g u r e 1 a r e l e a s t - s q u a r e s - f i t s t r a i g h tl i n e s through th e d a t a which a re r ep re se nt e d by

10

pu 2 2pv. + C1 4


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c and d a re cons t an t s . The c and d c on sta nts a re t abu la ted in t ab le 3,shows t h a t the cons tan t c the i n t e r c ep t fo r th e s t r a i gh t l i nes in f i g . 10

s sm all as would be expected . This shows e l a t th e computed mass flow from the i nd i wire ou tpu t i s near ly zero when th e ac tu a l flow i s zero . The c or re la tio n in10 n eg le cte d th e denominator on th e r ig ht-h an d s id e o f equat ion 3 , 2 + K2 .

va lue cor responds to the value of d determined from the l e a s t - s qua r e s - f i tl i n e . Solv ing fo r K2 from d = 1 / 2 K2 r e su l t s in n eg at iv e v al ue s

o r K2 , which i s con t r a ry to recommended va lues e .g ., r e f. 13 . Using th e recomvalue of K2 as 0.02 r e su l t s in d = 1 / 2 K2 = 0.495 . Comparing t h i s

with the d value in t a b l e 3, it can be seen t h a t th e capab i l i t y of us ing th efo r p red i c t i ng th e mass flow r a t e good if th e pred ic t ed hot-wire values

re with in 3 percen t of the measured va lues . The same a and b cons tan t s used inhe above cor r e l a t i on , which i s based on da ta from f igu re 5, were used to pr ed i c t the

r a t e s fo r th e probe t e s t s w ith w ire 1 hor izon ta l as fo r f i g . 6 . As might befrom th e p re vio us d isc uss io n of probe de t e r i o r a t i on , th e co r r e l a t i on o f theand ac tu a l flow r a t e s was poor . When a and b cons tan t s determined from

w ith w ire 1 ho r i zon t a l were used see t ab le 2 , th e co r r e l a t i on d id no t improve

Veloci ty d i r e c t i on ca l i b r a t i on . - For an eva lua t ion of th e use of the t h r ee -wi reto pr ed i c t th e flow d i r ec t i on , th e fo llowin g procedure was used. The f low

de te rmina t ion with r e spec t to the probe i s dependent upon th e capab i l i t y o ft ermi nin g t he flow ang le 8 with r espec t to th e i nd iv id u a l w i re s. From th e s i n e

aw r e l a t i onsh ip in r e f e r ence 12, it can be determined t h a t

2pV 8 2 2 2 = s in 8 K cos 82 pv 8=90 0 r u s in g e qu at io n 2 , equat ion 5 can be rewr i t t en as

6

func t ion r ep resen t s the r e l a t i on sh ip between the maximum mass flow coo l ing r a t ePV8=90 0 and th e mass flow coo l ing r a t e when the f l u i d i s moving a t some ang le 8r e spec t t o th e i nd i v i dua l wire . Equat ion 6 can be used to solve fo r th e flow

8 with r e spec t to one o f the wires fo r any measured ou tpu t vo l t s squared ,e le cons tan t K and the maximum coo l ing r a t e PV8=90 0 have been determined .e cons tan t K i s a func t ion of flow r a t e pV o r and was determined here in as

funct ion of flow r a t e . Cons tan t s a and b fo r each wire have a l ready beenand a re known to prov ide good r e su l t s fo r p re di ct i ng th e mass flow r a t e

o r th e probe descr ibed in f igu re 5 and t a b l e 2. From f igu re 5, tw o probe yaw angleschosen t h a t were known to be f ree of i n t e r f e r ence ; one yaw ang le cor responds to

he maximum coo l ing 8 = 90 0 and the o the r yaw a ng le c or re sp on ds to near-minimumFrom the measured ou tpu t a t t hese two probe yaw angles and with th e known

and b cons tan ts , pV 2 and PV8=90 0 2 were determined . These quan t i t i e sin t u rn used with th e known wire flow ang le 8 and equa t ion 6 to determinehe cons tan t K. The cons tan t K was determined fo r both the maximum and minimum

flow r a t e s fo r each wire , and th e squares of t hese values are t abu la ted in


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t ab le 4. As s t a t ed previous ly , with K known, equat ion 6 was used to compute theflow angle e with r e spec t to each wire from the measured wire output vo l t ssquared a t numerous probe yaw angles f i g . 5 . From the top por t ion of f igures 5 ato 5 c , the geometr ic flow angle e was a lso determined fo r the same probe yawang le . The r e su l t i ng comparison of the computed geometr ic angles and the flow anglesfrom appl i ca t ion of the ca l ib ra t ion data and ca lcu la t ed from equat ion 6 a re shownin f igure 11.

Figures 11 a , 11 b , and 11 c present the co r re l a t i on for each of the th reewires on the probe . These data correspond to the p ro be r es po ns e data shown in f ig ure 5, where wire was al igned ve r t i c a l ly . The co r re l a t i on for the maximum andminimum flow ra tes a re both shown in f igu re 11. The data presented inc lude probeyawing i n both d i r ec t i ons . Also, data a re included fo r probe opera t ion well beyondi t s opera t ing l im i t s , namely with yaw angles grea te r than 90 f lagged symbols orflow from the r ea r of the probe. The so l i d symbols are data poin t s from f igure 5t ha t a re suspected o f in vo lv in g probe flow in te r fe rence . Figure a l so shows thei d ea l c o rr e la ti on l i n e . While equat ion 6 i s simple to use and i s recommended bythe manufacturers , to obta in more accura te r e su l t s a complete ca l i b r a t i on with avary ing K value or more complex equat ion should be used e .g . , see r e f s . 7, 8 , 9,10, and 14 .

Figure 11 a , which i s fo r wire 1, inc ludes flow angles e from 55 to 90,which correspond to the e values in f igu re 5 a . The data in f igure 11 a showgood co r r e l a t i on , w ith only a few data poin t s showing an er ror grea t e r than 5. Thetwo data po in ts in f igu re 11 a where flow i n t e r f e rence i s suspec ted so l id symbolsshow r e l a t i ve ly poor cor re la t ion . Without some knowledge of flow i n t e r fe rence orprobe l im i t a t i ons , probe o pe ra tio n i n th i s region would r e su l t i n poor accuracy .Note the la r3e negat ive values of K fo r wire in tab le 4. Of c ou rse , thesevalues of K do not appreciab ly a f f ec t the co r r e l a t i on . This i s because of ther e l a t ive ly l a rge va lues of e F or ex ample, from equat ion 6 , with e 55 asin f igure 11 a , the s in e term i s dominant compared with the cos e term.

Figure 11 b i s fo r wire and corresponds to the data in f igu re 5 b . F ig ure 11 b shows f a i r co r re l a t i on a t r e l a t ive ly low flow angle s , 25 < e < 35, andpoor co r re l a t i on a t l a rge flow ang les , 60 < e < 80. The poor co r re l a t i on thev ic in i ty of e = 90 i s not unde rs tood becau se the same values of a and b weresuccessfu l ly p red ic ted in the mass flow in f igure 10. The co r re l a t i on in f ig -ure 11 b shows f low-angle e r ro r s up to 20.

Figure 11 c present s the co r re l a t i on for wire 3 on the probe and cor responds tothe response data in f igure 5 c . The data for probe opera t ion with suspec ted flowi n t e r f e rence and fo r extreme probe yaw angles do not seem to a f fec t the cor re la t ion .In gene ra l , the cor re la t ion i nd ica tes t h a t the flow angles fo r t h i s sensor can bepred ic t ed with in 5 , which i s cons idered good.

I t i s concluded t h a t for the th ree -wi re probe t e s t ed he re in , fo r prob e flowangles l e s s than 30 , and with a de qu at e p ro be ca l i b r a t i on , the mass flow ra te canbe predic ted with in a few percent f i g . 10 . However, with inadequate probe ca l ib ra t i on , the flow angles may have er rors as la rge as 20. Furthermore, withou t a comp le t e probe ca l i b r a t i on , e r ro r s of a t le a s t t h i s magnitude should be expec ted . withthe flow angle d et ermi ne d w it h r e spec t t o each w ire , the t o t a l veloc i ty vector i scompletely def ined in space, and t h i s vector can be reso lved i n to any des i redcoordina te system.

12


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To complete the f low-angle ca l ib ra t ion s tudy , the s ing le -wi re probe w ith theire i n the ho ri zo n ta l p o s it io n was eva lua ted . The cor re la t ion i s shown in f igure 12hich was determined from the sensor response data shown i n f igure 8 b . With the

s ing le wire hor i zon t a l , the probe yaw angle i s equal to the mass flow angle withr e spec t to the wire . C orre la tio n fo r the maximum and minimum flow r a t e s are shown.The data p r es en t ed i nc lude probe yaw angles i n both d i r ec t i ons . The data i n f i g -ure 2 show t h a t the f low-angle va lues predic ted from the sensor response are a lmosta l l lower than the i dea l va lues . An e r ro r i n t he d et erm in a ti on of K2 would have amore pronounced e f fec t on the c o rr el at io n e rr o rs fo r the smalle r values of e andwould have l ttl e f f e c t a t the l a rge r va lues o f e From equat ion 5 fo r eapproaching 90, the s in 2 e approaches and the K 2 . cos2 e approaches 0,whereas fo r e approaching 0, the s in 2 e approaches and the K2 cos 2 eapproaches K2 Therefore , the r e su l ti n g c o rr el at io n er rors shown i n f igu re 2 mustbe a t t r ibu ted to the determinat ion of pV/PVe=90 2 in equat ion 5 . I f a minimumof cor re la t ion data had been recorded to determine t he a p pr op ri at e da ta - reduc t ioncons tan t s , the flow angle determined with a s ing le -wi re probe would be approximately5 i n e r ro r .

CONCLUDING REM RKS

Hot-wire ca l i b r a t i on t e s t s were conducted with a newly developed t e s t r i g . Thisprocedure cons i s t s of the record ing of th e analog hot-wire output alo ng w ith asquare-wave-generator s i gna l as the probe cycles cont inuously through a range of flowangle s . The data are then e l ec t ro n i ca l ly d i gi ti ze d and analyzed a t i n t e rva l sd ic ta ted by the square-wave gene ra tor . The t e s t r ig u ti l iz ed was e ffe ct iv e inacqui r ing and process ing a l a rge amount of data i n a r e l a t ive ly sho r t per iod of t ime.

A comparison of two probes of i den t i c a l model and manufacture i nd ica ted somed if fe re nc es in response and flow i n t e r f e rence . A s t a t i s t i c a l ana lys i s of the sca t t e rin the ind iv idua l da ta poin t s vo l t s i nd i ca t e s a s ca t t e r of about 4 percen t . Asshown by i ncreas ing the number of poin t s averaged, the sca t t e r of the mean values canbe reduced to approximately percent with a 95-percent -confidence l im i t .

Flow i n t e r f e rence i s one major cont r ibu tor of e r ro r in using a th ree -wi re probewithou t an extens ive ca l i b r a t i on or withou t severe ly l imi t ing the opera t ion of theprobe. Because of the l imi t ed endurance of the probe, t i s s t rongly recommendedt h a t preca l ib ra t ions and pos tca l ib ra t ions be performed even when the ca l i b r a t i on i scu r ta i l ed . When a comparison of the two ca l i b r a t i ons do not ag ree , the data shouldnot be used. With pre ca l ib ra t ions and pos tca l ib ra t ions and opera t ion f low-anglel im i t s with re sp ec t to the ax is of the probe of 30, 3-percent accuracy indetermining mass flow r a t e s was a t t a ined . F urth erm ore , w ith on ly l imi t ed probeca l ib ra t ion , f low-angle er rors of 20 were observed. However, with extens iveca l ib ra t ions , these f low-angle e r ro r s can be decreased to 5.

Langley Research CenterAeronaut ics and Space Adminis t ra t ion

Hampton, V 23665January 28, 1982

3


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APPENDIX.An unknown veloc l ty vec to r V can be resolved in to components with re spec t to

th e probe coord ina te system by determining the r o l l angle and yaw angle shownin th e sketch which fo l lows:

//- I / ~

< iVc

A

Since only the angle between a ho t wire and th e veloc i ty vec to r i s des i red th emagnitude of the ve loc i ty vector i s s e t equal to one IVI = 1 . The t angen t o f ei s equal to the component of the ve loc i ty perpend icu la r to the wire divided by thecomponent pa r a l l e l to the w ire . The vector dot produc t of V and HW r e su l t s in th eve loc i t y component pa r a l l e l to the wire and th e corresponding vector cross produc tr e su l t s in th e veloc i ty perpendicular to the w ire . The magnitude of the c rossproduct i s the square roo t of the sum of th e square o f each component. Thereforefo r HW

i 2 2 < i 2 2 _ 2 f2 r 2 3 c s 3 c 3 < ista n eHW V x HW A2V HW

15


20/52

APPENDIXand for HW2 an d HW3

2c6

1 2- c ~ O}s.c]

A3

~ 1 2 2 2 ~ r a Os s c]s ~ < I 2 ~ < I 2 c2 {3 s 3 c

t n eHW3 A 4 e Os


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REFERENCES1. Rorke, James B.; and Moffi t t , Robert C.: Wind Tunnel Simulation of Ful l ScaleVortices. NASA CR-2180, 1973.2 . Jacobsen , Robert A.: Hot-Wire Anemometry for In-Fl ight Measurement of Aircraf t

Wake Vortices. Advancements in Fl ight Tes t Engineer ing, Fif th Annual SymposiumProceedings, Soc. Flight Test Eng., c.1974, pp. 4-13 - 4-24.3. Corsigl ia , Victor R .; Ja cobse n, Robert A.; and Chigier, Norman: An ExperimentalInvest igat ion of Trai l ing Vortices Behind a Wing With a Vortex Dissipator .

NASA paper presented a t the Symposium on Aircraf t Wake Turbulence Seat t le ,Wash. , Sept. 1970.4. Zalay, Andrew D.; White, Richard P.; and Balcerak, John C.: Invest igat ion of

Viscous L ine Vortices With and Without the Inject ion of Core Turbulence.Rep. 74-01 Contract No. N00014-71-C-0226 , Rochester Appl. Sci. Assoc. , Inc . ,Feb. 1974. Available from DTIC as 785 256.

5. Yavuzkurt , Savas ; Crawford, Michael E.; and Moffat, Robert J . : Real-Time HotWire Measurements in Three-Dimensional Flows. Symposium on Turbulence, G K.Patterson and J . L. Zakin, eds . , Science Press, c.1979, pp. 265-279.6. Larsen, Soren E.; Mathiassen, Olaf; and Busch, Niels E.: Analysis of Data From3-Dimensional Hot-Wire Probes Using Comparison With Profi le Instrumentat ion forCalibrat ion. Proceedings of the Dynamic Flow Conference 1978 on Dynamic

Measurements in Unsteady Flows, c.1978, pp. 591-597.7. Champagne F. H.; Sleicher , C. A.; and Wehrmann o. H.: Turbulence Measurements

with Inclined Hot-Wires. Pt. 1. Heat Transfer Experiments with Inclined HotWire. J . Fluid Mech., vol . 28 , p t. 1, Apr. 12, 1967, pp. 153-175.

8. Gilmore, D C.: The Probe I nt er fe rence Ef fe c t of Hot Wire Anemomete rs. TN. 67-3D. R. B. Grant No. 9551-12 , McGill Univ. Montreal , July 1967.9. Friehe, C. A.; and Schwarz, W H.:Cylindrical Anemometer Sensors.

no. 4, Dec. 1968, pp. 655-662.Deviations From the Cosine Law for YawedTrans. ASME Sere E: J . Appl. Mech., vol . 35,

10. Kjellstrom, Bjorn; andHot-wire Anemometer.1968.

Hedberg, Stel lan: Calibrat ion Experiments With a DISAAE-338, Aktiebolaget Atomenergi Stockholm, Sweden , Nov.

11. Coll is , D C.; and Williams, M J . : Two-Dimensional Convection From HeatedWires a t Low Reynolds Numbers. J . Fluid Mech., vol . 6, p t . 3, Oct. 1959,pp. 357-384.

12. Hot Film and Hot Wire Anemometry - Theory and Applicat ion. Bull . TB5 ThermoSystems, Inc.

13. Webster, C. A. G.: A Note on the Sensi t ivi ty to Yaw of a Hot-Wire Anemometer.J . Fluid Mech., vol . 13, p t . 2, June 1962, pp. 307-312.

14. Delleur, Jacques W.: Flow Direction Measurement by Hot-wire Anemometry. J . Eng.Mech. Div., American Soc. Civil Eng., vol . 92, no. EM4 Aug. 1966, pp. 45-70.17


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18

TABLE 1 PROBE YAW POSITION CALIBRATION

Probe posi t ion number 1 Probe yaw angle2

148405 12340984015 73402 484025 23403 12035 26204 512045 762050 1012055 126206 1512061 15620

1Each probe posi t ion number represents a 5 yawang le inc remen t.2posi t ive yaw angles represent flow from l t ofprobe axis when looking upstream.


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TABLE 2 . ONST NTS FOR USE WITH EQU TION 2

Probe r o l l Probe yawpos i t i on angle deg a b S deg

Wire 1Wire 1 98 .7 -0 .2738 0.7216 85.0

ve r t i c a l 88 .7 .2575 .7044 90.7Wire 1 26.3 -0 .2470 0.7384 81.1

hor i zonta l 41.3 .2464 .7275 83.9Wire 2

Wire 1 43 .7 -0 .1611 0.4608 81.4ve r t i c a l 38 .7 - .1707 .4601 89.5

Wire 1 58 .7 -0 .2448 0.6892 87.2hor i zon t a l 121.3 - .2581 .6878 87.2

Wire 3Wire 1 31.3 -0 .2206 0.6678 82.8

ve r t i c a l 41.3 .2235 .6675 88Wire 1 63 .7 -0 .3081 0.8092 83.7

hor i zon t a l 53 .7 .3029 .8031 89.2

19


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20

TABLE 3 CONST NTS FOR USE WITH EQU TION 4

V g c 0.4993 0.001581 .5173 .00121

-10 .5022 .0014920 .5164 .00134

-20 .5040 .00090430 .4980 .00129

-30 .4752 .00133

T LE 4 CONST NTS FOR USE WITH EQU TION 6

Probe/sensor pV kg/m 2 s K2Three-wire probe , wire 1 43.82 -0 .4034

v e r t i c l ~ wire 1 10.89 - .7244Three-wire p r o e ~ wire 1 43.82 0.1471

v e r t i c l ~ wire 2 10.89 .1536Three-wire p r o e ~ wire 1 43.82 -0 .02485

v e r t i c l ~ ~ r i r 3 10.89 - .04879Sing le wi re sensor 43.30 0.00330Single wire sensor 10.82 .00499


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a Thr ee -w ir e p ro b e.F igure 1 w types of hot wi re probes t e s t ed

L-77-1073

21


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22

b ingle wire probe.Figure 1 Concluded.

L 77 1 7


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Wind tunnel o o r ~

ot wireprobe

Yaw angle position ndicatorsqua re w ve photo ell systemYaw angle drive motor

L 77 1069 1Figure 2 Hot wire c a lib ra tio n r ig

L 76 1321 1 igure 3 Low v e loc i ty ca l i b r a t i on wind tunne l a t the Langley Research Center

23


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p

4

Figure 4 inimum angle e with re spec t to and Probe or i en t t i on m S so w n n cen te r of p l o t


29/52

90 80 \Q0

q60

40

2

10.89 6 sec/cyclee \0.89 20 sec/cycle B 16.40

21 81 day A 27.35

33.18 38.44 e 43.82

21 81 day 215 20000050100150200

.6

O - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ~ - - - - - -1.2

1.0 ~0ZN 8w

deg

a) Wire Figure 5 Response of a three-wire hot-wire probe for various mass flow ra tesand probe yaw angles. Wire i s aligned ver t ica l ly . Upper figure displaystheoret ica l angle between mass flow and hot wire.

25


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9080

g 60C

40

20

Ol L l . . L I ---l.. l l

1.6

1.4 ;::

0 1.2N

1.0

.8

6

10.89 6 sec/cycle

e 10.89 20 sec/cycleB 16.40

21 8 day I27.35

h 33.18--- - 8 448 43. 82

21 81 day 24

I-200 -150 -100 \-50 o 50 ,deg

b) Wire 2.

100 150 200

26

Figure 5 Cont inued.


31/52


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9080

CZ 60

4200 150 100 50 0 50 100 150 200

t ga Wire 1.

~ i g u r 6. Response of a t h r ~ e w i r e ho t i r e probe fo r v ario us mass flow ra tes andprobe ya a n g l ~ s Wire 1 i s al igned hor i zon t a l l y Upper f igure d isp lays

~ h c o r e ~ i c a l angle between mass flow and ho t w ire .


33/52

9080

60t Tl 0CZ 40

pV20 O 76

e 690 -e-- 2 961 2 4 66

6 71f r1 0 9 18

:: ::::0 - - 11 97:

.8LLJ 8 15 13

.6

.4200 150 100 50 o

deg

50 100 150 200

b Wire 2.Figure 6 .- Continued.


34/52

90

\80 1 600

CZ

40p

20 O 76 e 69

2.96B1.2 4.66---b- 6.71 1.0V>

h 9.18N tT 11.97Ll .8 e 15.13

.6

.4I I I I I I I I I200 150 100 50 50 1 15 200

lJ degc Wire 3.

Figure 6 . Concluded.

3


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90

80

C lQC 60

40

20

10 82

-e - 16 32B 21 62 26 94 32 78h 37 82 tr 43 03 8 48 30

OL __ - - - J L - - I ---J1 2

1 0N

8NUJ

6

4I I I I I I I I I

200 150 100 50 50 5 200 g

a Wire 1 Figure 7 Response of a second t hr ee wir e ho t w ir e probe for various mass flowra tes and probe yaw angles Wire 1 is aligned ver t ica l ly . Upper figuredisplays theoret ical angle between mass flow and hot w ire

31


36/52

9080

60

40

20

10 82

16 32B 21 62

26 94 32 78

37 82 43 03 48 30

5O0501001502004

I

1 0

O ~ . . . . . L1 2

8

NI.LJ

.6

degb Wire 2.

Figure 7 Continued.

32


37/52

9080

60 0

40

20

pV10.82

--e- 16.32B 21 62

26.94 32 78 h 37.82 r 43. 03--e- 48 306

1.2

0. J - - I L I - - .....1.4

1.00Z

N .UJ 8

4200 150 100 50 o 50

g100 150 200

c Wire 3.Figure 7 . Concluded.

33


38/52


39/52


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pV10 89

Probe I ----0 27 35 38 44

10 82Probe 2


41/52

NLLI

N:::::oZ

T

Probe

Probe 2

-/

pV10 89 27 35

38 44

10 82 26 94

37 82

200 50 g

b Wire 2.Figure 9 Continued.

37


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43/52

C\Jl ilIC\JE .:s:.C\J

:::>Q..

C\JInIC\JE .:s:.

C\J:::>Q..

m i l l ~ r l ~ ~ l , , ~ ~ i [ : 'I:; ~ ~ ~ : ~ g :,g :iii ~ ~ ; ~ ~ ~ ~ , iiii ~ ~ ~ , , ~ : : : : ; ~ , ~ r i ~ , ~ , [:[:iii iiii j ~ i [ : l'P I : ~ i [:t: \jJ deg iii: iii ::i: if.'; it : iii: , , ~ : i[:i : ; ~ i iii: i'ii : i ~ : ; i ~ 'ii: iii' i, i [ : ~ : ; 'i:;2000 m m :m ; ~ : ~ ~ _:g IMeasured ~ :m ~ l l i m: ml :m :m ;;;: ;;;-*H ~ 0 : ~ ;i [ : ~ i f ~ ~ l:i liii iii iiB [ : i ~ , : , ~ '2 ~ i i i iff: :ig iii ii: ,,,: ?: -i : [: lil' I iiiill :iF. irE f..f ::1i iii: B' == ILeast-squares-fit sii iii: :;;; [ ; i ~ :iii r..j: I ~ : I :::i i i ~ ~ il :l ? 8 :i ~ i i ~ i :if if : ~ ~ : 'Iit : ilii lif. iiii ~ i i i ~ i i i i ~ H ~ U ~ ~ i l il j : iiii iii i i ~ ~ i i ~ ~ i i :FF ie , ~ ~ ~ i ~ : I:'i I ~ ~ : ~ ', : i ~ ~ ~ ~ i i ~ ~ ~ ~iiE lU 'lil gii iif. Ui L I [:} f: :r , : : ~ :iii iii I*; Y ::i i i i ~ iiI ~ ~ i : ~ ~ i ~ [ : , , ~ ~ i i l ~ i I

F:ii i : : ~ ~ j j iiii iTt : : ~ i i ~ iii: ;ii :3 ii :;:: iW ;5 ji :i, iii: if ~ ;.;ii : i.j: i' : iiii i : i ~ ii :ii :iii ~ ~ ~ iif, ill ii: Ii' iii m: iii: 'i i 'ii 'iii :Ig ; ~ ~ 2 :tii :Fe: :::; :: i ::l: ; f u : ~ ii iF liil ~ i : ~ : i iii :;: :;:: it : i i::im: ~ ~ j ~ ~ ~ ; ; : r ~ ~ t : ~ ~ ~ ~ ~ ~ P ? : ~ ~ ~ ~ (b) Yaw angle \jJ = + m m;;m ;'li1000 I:ii ::ii i i ~ ~ ' lill : I:: :Fii ~ i i l iiE lit Ji ~ : : : : f::ig;r:i?:2 tt:: .j l;i ,,_: '*. 'i i 'ii, i iii :::':i ~ i : F :ii I:F ~ ~ ~ : i il Ii,

i i l ~ i ~ iff Iii liri iii i [ : ~ m: fUa 112 [: lEi :tt: - I ip Iill;:: ilii i ;: , ~ i i I iiii : ; ~ : iiii i i i ~ i i ~ i il:: > :iii i ii ::i:~ ~ ~ ~ ~ i l i ; ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ = ; ~ s ; ~ ~ ; f i l i ~ ~ ~ i mi m; lli iW:m:m;m m

::E iili tE fil':-2 : , , ~ ill- _ : ~ . , . .::. 11 - . : ; t ; : : ~ I::: ,i::i, ;; ii' : ~ : F l::i ~ , , ~ :i:i i ~ : I i I : ~ i i ~ : ~ : ~iIl::if': :'i; :::: IiiI liii ;;:: : q ~ : _ ~ : _ :::,:iE ill #'i ::-. ::;: Hi: :;; .::: i : : ~ ::'jci ii: liIi :Ii iIIi :II: iili :ii' :i': : I ~ : eli: : ~ ~U Ii. if i ifJ m II ~ , 1 i :::: - -::; ~ . : : ~ ; ~ ; p .. : ., ;:, :,:i:tt:::: if: lsi fii: I'ii ii:: IIlI Ii:: iiii 'Iii ~ i i ~ ~ ~ j if : i:; i: i~ iii ~ r ~ j [:it ~ , . ~ ::;; ::i f:1 f8 fililiE tE. ~ - ' : ; : : iii 'ili I : ; ; ; ~ : g ii S :iii fig : : j ~ I ~ f i ',:: f:1 'iti iii' ~ : i i :rol ifi iii I: i ~ I :~ g ; H W EEHJD gg illi mf gg ~ i i i ::: I;: : 5 : : n : ~ :i l ip ;nl .. ; : : ~ :q; ; ~ i ~ : f: ~ ~ ~ ~ ~ ~ g ~ ~ u ~ U ; ~ l g U ~ l ~ ~ g ~ ; in: ~ i ~ :U++ ::;i fin ffii tiP FP fin mi nn in; :tn tiP fm ml Hr ii mf ,:71 i i ~ ~ fii: mi im m: ; f ~ l ;;i ~ i i i ~ i i i f ~ i i i ; ~ iii; iii

00 1000 2000 3000 4000 pV 2, (kg m -s)2

Figure 10 Comparison of ac tua l mass flow ra te (pU) with flow r a te determined fromho t wi re probe for d i f f e r en t probe flow ang les

39


44/52

4

enl- l

Figure 10 Concluded


45/52

90

8

70

6

50

8 deg9 30

20

EJ El J pV kgfm 2so 43 8o 10 9Ideal correlationSolid symbols are for flow

interference

a Three-wire probe w it h w ir e 1 ver t ic l data for wire 1.Figure 11.- Comparison of geomet ri cal angle between mass flow and hot wire and computed flow angle for eachof th e individual wires of a three-wire probe.


46/52

90

80 EJ

EJ q

Q 070

50

409 deg

30

20

o

J

2V kg m -s )o 43 8o 10 9---Ideal correlationFlagged symbols for probe yawangles greater than 900Solid symbols are for flowinte rfe rence

20 3 40 50 60 709e deg80 90

b) Three-wire probe with wire 1 aligned ver t ic l data for wire 2.Figure 11.- Continued.


47/52

9

8

7

6

50g deg

pV kg m 2So 43 8o 10.9

Ideal correlationFlagged symbols for probe yaw anglesgreater than 9 0Solid symbols are for flow interference

5 6dege7 8 9

W

c Three-wire p ro be w ith w ire 1 a l igned ve r t i c a l da ta fo r wire 3 .Figure 11 . Concluded.


48/52

p V kg m so 43 3 1 8 Ideal correlation

8

7

2 3 4 5 6e deg 7 89

F ig ure 1 2 Comparison of geometrical angle between mass flow and hot wire and computed flow anglefo r a single wire p ~ o e Wire horizontal


49/52


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r 1 Report No.NASA TM-83254

2. Government Accession No. 3. R ec ip ie nt s Ca ta log No.4. Ti tle and SubtitleA CALIBRATION TECHNIQUE FOR A HOT-WIRE-PROBE

VECTOR ANEMOMETER5. Report Date

March 19826. P er fo rm in g O rg an iz at io n C od e

505-31-33-097 Author s)

James Scheiman, Charles Marple, and David S. Vann8 . P erfo rm ing O rgan izatio n Report No.

L-1444510. Work Unit No.

9. P erform in g O rgan izatio n N am e andNASA Lang ley Resear ch CenterHampton, VA 23665

11. Contract or Grant No.

12. S po ns or in g A ge nc y N am e and AddressNationa l Aeronaut ics and Space Adminis t ra t ionWashington, DC 20546

13. Type o f Repo rt and P eriod C ov eredTechnica l Memorandum

. 14. Spons or ing Age nc y Code

15. Supplementary Notes

Abstract

Cal ib r a t ion t e s t s using hot wires were conducted using a newly developed t e s t r igth at g re at ly reduced the da ta acqu is i t ion t ime . A comparison of mea su re d andcomputed ve loc i ty vec to r magnitude and d i rec t ion i nd ica t e s the necess i ty of comp l e t e probe ca l ib ra t ion to determine flow in te r fe rence and/or opera t ing l imi t a t ionregions Cal ibra t ion r esu l t s ind ica te tha t flow r a tes with 3 percen t accuracy andflow angles with 5 accuracy are a t t a inab le

18. Distribution StatementUnclass i f ied - Unlimited

17. Key Words S u g g ~ t e d by Author s))Hot-wire ca l ib ra t ionThree -w i re p ro beVeloc i ty vec tor pred ic t ionAnemometer

Subjec t Category 35f . : : : = : : ~ _ : _ ~ _ _ : _ : _ . . . . L . . . - - - - - - _ _ _ - - - - - - - - - - - - ~I Security Classif. of this reporti 20. Security C1assif. of this page) 21. No. of Pages 22. Price

Unclass i f ied Unclass i f ied 45 A03 L L I or sale by the National Technical Information Service Srringfleld Virginia 6 NASA Langl ey , 1982


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National Aeronautics andSpace AdministrationWashington, D.C.20546Official BusinessPenalty for Private Use, 3

THIRD-CLASS BULK RATE Postage and Fees Paid Iational Aeronautics and pace AdministrationNASA-451U S M IL

NI\SI\ POSTMASTER: Undeliverable Section 158Postal Manual Do Not Return

hot wire nasa calibration

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