ARD-R169 262 CALIBRATION AND USE OF FIVE-HOLE FLOWl DIRECTION PROBES 1/1FOR LOW SPEED MIND.. (U) NATIONAL AERONAUTICALESTABLISHMENT OTTAMA (ONTARIO) R N WICKENS ET AL.

UNCLASSIFIED JUL 85 NRE-RN-29 NRC-24468 F/0 14/2 N

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1.2511.4 i

MIROOP REOUIO3ET8HR

NATIONA 1.1~ O lAWAO 16

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UNLIMITED Cana ( i)UNCLASSIFIED

CALIBRATION AND USE OFFIVE-HOLE FLOW DIRECTIONPROBES FORLOW SPEED WIND TUNNELAPPLICATION

by

R.H. Wickens, C.D. WilliamsNational Aeronautical Establishment

L-LJ

O __j AERONAUTICAL NOTE

- OTTAWA NAE-AN-29

C. JULY 1985 NRC NO. 24468

This document hasbfor publi- rrdcu :e and alo: . t-

distribution is unlimited.

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UNLIMITEDUNCLASSIFIED

CALIBRATION AND USE OF FIVE-HOLE FLOW DIRECTIONS PROBESFOR LOW SPEED WIND TUNNEL APPLICATION

ETALONNAGE ET EMPLOI DE CAPTEURS DE DIRECTION A -

CINQ TROUS EN SOUFFLERIE A BASSE VITESSE

by/par

R.H. Wickens, C.D. Williams

National Aeronautical Establishment

o.

AERONAUTICAL NOTEOTTAWA NAE-AN-29JULY 1985 NRC NO. 24468

" "p

R.J. Templin, Head/Chef

. Low Speed Aerodynamics Laboratory/ G.M. LindbergLaboratoire d'adrodynamique a basse vitesse Director/Directeur ,4

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* .5 .. , , ? , ,: -, : x. , , ' ., , ' ''.. 2,'.2",; b' 2,g'', .. e' o"""-.;," ',', 0" " ,",, ,,

;k

SUMMARY

This note describes a method of calibration and use of five-holeflow direction probes. When used in complex three-dimensional mixed flows,the probe will furnish flow directions, velocity components and total pres-sures. The method described in this note is intended for the use of the windtunnel project engineer in determining flow direction characteristics ofvarious model configurations.

RESUME

La pr6sente note d6crit une mthode d'6talonnage et l'emploi desondes de direction i cinq trous. Utilis6s dans des 6coulements mixtescomplexes & trois dimensions, ces sondes fournissent les directions, leacomposantes vitesses et lea presuions totales des 6coulements. La m6thodedcrite est destin~e & l'ing6nieur de soufflerie, pour lui permettre de d6ter-miner les caract~ristiques des directions des 6coulements de divers profils.

, cCcion For

NTIS CRA&I

C- I" f- IA"'EL 'winnounced Li.4J.i,.fJcjtiofl oric

• ~ ~ i . ....................................... .

*A C! y CO

Dist Seci

" (iii)

.:::. .'.*d* 9 . . v .*.*. 1.,,. ,. . . . '**'f..t* **-.*e-*'': 4-.'- ~.

CONTENTS

pare

SUM M A RY ........................................................... (iii)

APPENDICES ......................................................... (v)

SYMBOLS .... ....................................................... (v)

1.0 INTRODUCTION ...................................................... 1

2.0 METHOD OF PROBE CALIBRATION ...................................... 1

2.1 Angles and Velocity Relative to the Probe ............................... 12.2 Orifice Pressure Coefficients ........................................... 12.3 Probe Calibration Parameters ......................................... . 22.4 Pitch and Yaw Angles of the Flow ..................................... 3

3.0 PROBE CALIBRATION CHARACTERISTICS ............................... 4

3.1 Empirical Representation of the Calibration Data .......................... 5

4.0 USE OF THE PROBE IN AN UNKNOWN FLOW .............................. 6

*5.0 CONCLUSIONS........................................................ 9

6.0 BIBLIOGRAPHY ...................................................... 10

TABLES

Table Page

. I Coefficients for Dynamic Pressure Function PCAL (0, 0) (Eq. (15)) .......... 11

* II Coefficients for Total Pressure Function SCAL (0, 0) (Eq. (16)) ............. 12

ILLUSTRATIONS

" Figure Page

1 General Arrangement and Details of Five-Hole Flow Direction Probe......... 13

2 Angle and Velocity Conventions for a Five-Hole Flow Direction Probe ....... 14

3(a) Probe Roll Angle 0 vs Arctan I Q/R I .................................. 15

3(b) Probe Average Roll Angle 0 vs Arctan I Q/R I ........................ 16

(iv)

. ..

it C,'. , i- . , * l 1 1 )- p- l +')r l- p + i

ILLUSTRATIONS (Cont'd) je.

Figure Page

4(a) Probe Pitch Angle 0 vs + ................................... 17

4(b) Probe Average Pitch Angle 0, Degrees, vs . .Q2_+ P2 ..................... 18

5 Probe Dynamic Pressure Parameter, P = C, - C vs Pitch Angle 0 .......... 19

1- Cp56 Probe Static Pressure Parameter, S - vs Pitch Angle 0 .......... 20

CpS - Cp

APPENDICES

Appendix Page

A Typical Individual Probe Orifice Pressures Coefficients as Functions ofthe Combined Pitch Angle 0, and Roll Angle 0 ........................ 21

B Tabulation of Probe Orifice Pressure Coefficients, Derived fromCalibration Data ............................................... 37

SYMBOLS

Symbol Definition

C Pi probe orifice pressure coefficient (i = 1-5)

C average of four peripheral pressurespCps local static pressure coefficient Cpt - q/qT

pt - PO

Pt local total pressure coefficient1/2 pV-

PO tunnel reference pressure (wall static pressure)

PT tunnel total pressure

P, local static pressure

Pt local total pressure

P dynamic pressure parameter

Q yaw.plane parameter

R pitch-plane parameter

S static pressure parameter(v)

I I Ii%~l I I ll III*~l .. l **I - . . * . . * .. . .. .

SYMBOLS (Cont'd) r.

Symbol Definition

SCA L (0, 0) empirical static pressure parameter

PCAL (0, 0) empirical dynamic pressure parameter

VR resultant flow velocity

VT tunnel velocity

u.vw local flow components

q, qT local and tunnel dynamic pressure

0 inclination of the flow vector in the combined pitch-yaw plane (0 < 0 < +90)

roll angle of the flow vector in the cross flow plane ( 0 < 360') (measuredclockwise from downward vertical axis)

Ci pitch angle of the local flow, in the plane of orifices one and three

* (3 yaw angle of the local flow, in the plane of orifices two and four

(vi)

.,

, *. * * *.o, **, **.' -~** *- - * *

, .* * * * ** '. . * * * . * *.. * * * *

- - - - - - .- ---- - -

CALIBRATION AND USE OF FIVE-HOLE FLOW DIRECTION PROBES FOR

LOW SPEED WIND TUNNEL APPLICATION

1.0 INTRODUCTION

The five-hole flow direction probe is normally used to explore complex three-dimensionalwakes which may be characterized by mixed regions of propulsive flow from jets or propeller slip-streams, and vortex flows, resulting from circulation-induced lift. These wakes are known to have alarge variation of flow direction, flow velocity and total pressure, and it is convenient to be able to usea single probe which will measure alll of these quantities simultaneously, accurately, and without thenecessity of nulling the individual side-hole pressures.

The probe configuration described in this report consists of five pressure orifices, arrangedin the form of a pyramid or cone, facing upwind. The individual pressures reflect the effects of localflow direction and dynamic and total pressure. Figure 1 shows a schematic diagram and photograph ofa typical probe constructed from standard stainless steel tubing. The tube faces have been ground to

,o an included angle of 90 degrees, in the form of a pyramid in which the peripheral orifices are alignedto planes 90 degrees apart. The central orifice, which measures total pressure, is ground normal to theprobe axis.

2.0 METHOD OF PROBE CALIBRATION

2.1 Angles and Velocity Relative to the Probe

Since this probe is to be used in the non-nulling mode, the flow impinging on it will, ingeneral, not be axial. It is therefore necessary to define angular and component velocity conventions

which can be adapted both for calibration and use of the probe. Figure 2 illustrates these angles andvelocities in the vector diagram, as follows:

AO is the resultant flow velocity vector impinging on the probe, whose axis is aligned along OC.The flow direction in the upwash, or a-plane is the angle BOC; flow direction in the sidewash or

- j-plane is the angle DOC. The velocity components associated with the resultant velocity VR are(in aircraft terminology) longitudinal component u (vector CO), upwash w (vector BC) and side-wash v (vector DC).

The angles 0 and 0 are the pitch angle COA of the resultant velocity vector in the a-A planeCOA, and the roll angle BCA in the cross flow plane ABCD respectively.

2.2 Orifice Pressure Coefficients

Before defining orifice pressure coefficients, it is necessary to specify a numbering system,and this is illustrated in the sketch as shown below.

20 0 4"0

3

SKETCH (i) - PROBE ORIFICE ORIENTATION LOOKING DOWNSTREAM

=... ,;- ~** ~ ~ ~ e .- a., *'~ a1 ~ ~ -

-2-

Looking downstream, the peripheral holes are numbered one to four in a counter clockwise direction.Holes one and three are sensitive to flow angularity in the pitch plane while holes two and four aresensitive to flow angularity in the yaw plane. The central or fifth hole measures total pressure, asmodified by the inclination of the resultant flow vector.

Sstatic As in normal wind tunnel procedure, all pressures are measured relative to a referencestatic pressure, p such as the working section static pressure. The pressure coefficients corresponding

: to each of the probe orifices are: ,

pi - POCP" PT - P. (-Cp = (1)

"- PT - PO

i --=Cp2 (2)

i:-~P P PO".

p3 - p0C = (3), PT - P.•p p

:" P4 - Po,:

Cp4 =(4)PT - P

C (5)P5 -TPo:- PT - Po.

1,,

p= - (CpI +Cp 2 +Cp 3 +Cp 4 ) (6)

PT is the tunnel reference total pressure, measured upstream of the probe, (usually in the tunnelsettling chamber) and 15 is the average of all the peripheral pressure coefficients. Thus pT - P is

*- effectively the tunnel (or ambient flow) dynamic pressure, and is not measured by the five-hole probebut from the two auxiliary pressure taps. Listings of the pressure coefficients C to C obtained in

a calibration of a five-hole probe, are presented in Appendix B.

* 2.3 Probe Calibration Parameters

In order to describe the probe calibration procedure, it is necessary to define dimensionlessparameters as follows:

Pitch Plane Parameter R (upwash)

Cp3 - pI

R'= (7)C - -"

* . . • .. . "o-1. .. *. - - %. .~ . -.

%- . -. . . -€ " ." . . '. • o" . " .-

" . . o . , . ' . . . . .° . ' - . ' . " " . " • . " . • . . . • , . ° . ,P

-3-

Yaw Plane Parameter Q (sidewash)

Q Cp2 - Cp4 (8)

p5 - fp

* The sign convention for Q, R, a, and v, w is based on normal wind-tunnel conventions, as indicated, in Figure 2.

Dynamic and static pressure parameters P and S are defined as follows:

-. P=c -C (9)p5 p

I1-s = - (10)

c - cCp5 - p

In a smooth uniform flow directed along the probe axis, C is equivalent to the staticpressure measured at the side holes on a pitot-static Wube, and Cp5 to te total pressure measured atthe probe tip. Thus P is seen to be equivalent to the flow dynamic pressure for smooth uniform flow;in general, however, P is a measure of the local "dynamic" pressure when the real low is both dis-turbed and oblique.

Since CPS is a measure of local total pressure, then 1 - C 5 is a measure of locai staticpressure, and has a value of zero when the probe is fully aligned wiA the flow. The parameter Stherefore, is a measure of local static pressure expressed as a fraction of the local dynamic pressure.

at.the It is important to emphasize that the probe reference pressures po and must be measured

at the same corresponding tunnel wall taps during calibration as in flow measurement; usually po is* the working section sidewall static pressure, and PT the settling chamber total pressure.

*- 2.4 Pitch and Yaw Angles of the Flow

The pitch and yaw angles to which the probe is set during calibration are defined as a, inthe upwash plane, and 1 in the sidewash plane. Other angles, 0 and 0, which are useful in interpretingcalibration data are illustrated in Figure 2, and are defined as follows:

* 0 is the angle between the resultant vector and the probe axis, in the combined a-0 plane COA.

. * is the roll angle BCA of the component resultant velocity vector in a plane normal to the• .probe axis.

A relationship between these angles is as follows:

0"= Arcsin[ Sin 2 p3 + Cos 2 • Sin2a] (11)

. = Arctan Ta J (12)

not

-4-

and the inverse relations are: a = Arctan (Tan 0 • Cos 4), 3 = Arctan (Tan 0 • Sin 4). The angle 0 isalways positive in the range 0 < 0 < 900. The angle 4 is always positive in the range 0 < 4 < 3600. Theangles a and P are in the range - 90 <a c, P < + 900. The five-hole probe cannot normally be used tomeasure flow angles outside of a cone angle 0 of 450 . For larger flow angles, a modified calibrationprocedure can be used, or a seven-hole probe.

3.0 PROBE CALIBRATION CHARACTERISTICS ',

In calibrating the probe, the maximum values to which the pitch and yaw angles c and 3were set were ± 450. The response of each set of side hole pressure differentials was linear up to about30 degrees when pitched in its own plane; they were insensitive to small departures of inclination in

.. the opposite plane. A typical value for the side-hole sensitivity is

APK = = 0.0583 per degree

1/2 p VT 2Aa *T%

Figures (i) -(x) of Appendix A show the response of each individual probe orifice in terms* of either the resultant angle 0 in the combined pitch plane, or the roll angle 4 in the probe crosswind

plane. The central orifice C is seen to be affected mainly by pitch and only very slightly by rollangle 4; its pressure varies from full total pressure in unskewed flow, to about 70% of this when theresultant velocity inclination is 30 degrees. As the inclination of the resultant velocity increases, thepressure sensed by the central hole drops more rapidly.

The pressure in any of the peripheral holes changes significantly with both 0 and 4. When00 or 900 or 1800 or 2700, i.e., the resultant flow in either of the pitch or yaw planes, the pressure

on the windward orifice gradually increases until total pressure is achieved near 0 = 450.

LEEWARDe VR

WWINDWARD

At the same time, the pressure on the leeward orifice decreases rapidly as suction is established on the-- probe head due possibly to a flow detachment on that side.

If the probe is also inclined in the opposite plane, (0 < 4 < 900) the characteristic of the* windward orifice changes considerably, but that of the leeward orifice, not so much.

The calibration-parameters P, Q, R and S have been found to be fairly simple functions ofthe resultant pitch angle 0 and the roll angle 4. Since the parameter Q is sensitive to the yaw compo-nent, and R to the pitch component, then Q/R should be zero for a flow with no yaw component, andlarge for a flow with no pitch component. Hence Arctan (Q/R) is a measure of the roll angle 4 in the

plane normal to the probe axis. Similarly, V Q2 + R 2 is a measure of the magnitude of the velocityvector, and should be approximately independent of roll angle 4), for a resultant flow vector that lieson a cone of constant semi-apex angle 0.

The angle 4 is a scalar quantity, and is determined only in the lower left cross-plane quadrantas shown in Figure 2. The velocity components as determined from 0 and 4 are also scalar and their

Vt~, * *.~.

-5-

signs and the signs of the angles in the a and 1 planes must then be assigned according to the signs ofQ and R as originally determined by Equations 7 and 8. The actual cross-plane resultant vector (AC,Fig. 2) will in general, rotate around the longitudinal axis, as the oncoming flow may take up anyorientation; the actual relationships between the roll angle 4 and the parameters Q and R are listed asfollows:

if Q > 0, R > 0 then 4 is as calculated from Equation (14), i.e. 4 = (14)

if Q>0, R < 0 then ) = 180 -) (14)Zif Q < 0, R < 0 then 4 = 180 + 4) (14)

if Q < 0, R > 0 then 4 = 360 -4 (14)

These functions, i.e. ArctanlQ/RI and 4 Q + R2 are shown in Figures 3(a), 3(b) and 4,. plotted against 4) and 0 respectively. The dynamic and static pressure parameters P CAL and S CAL are

also functions of the two angles 0 and 4) and are illustrated in Figures 5 and 6.

3.1 Empirical Representation of the Calibration Data

Empirical expressions which satisfactorily represent the average of Figure 3 (shown asFig. 3(a) and 4(a)) experimental data, for both 0 and 4) are as follows:

Pitch angle 0

0 = A,4N 7Q2 + R +A 2 (Q2 +R 2 ) +A 3 (Q2 +R2 )3 / 2 + A4 (Q2 +R 2 )2 (13)

whereA, = 8.6603

A2 0.9708

A3 - 0.033444

A4 = 0.019914

These constants are for a typical probe. The resulting angle 0 is in degrees (0 < 0 < 900).

Roll angle 4

B 4=BTan - 1 QI 2 RITan + B Tan- I + B 4 Tan- ' I- (14)

R 3 \a4

-. " Qwhere Tan- I - I is in radians, and

R

B-"= 95.825

B2 = - 75.034

B3 = 33.981

B4 = - 1.2199

- The resulting angle 4 is in degrees (0 < 4 < 900). The signs of Q and R will determine which quadrant4) lies in, as in 3.0 above.

..-

-6-

The dynamic and static pressure parameters PCAL and SCAL can also be represented empir- b

ically as functions of 0 and 0, as follows:

Dynamic pressure parameter PCAL (0, 0) as determined from calibration

PCAL (0,0) = CO + CIO + C2 02 + C3 03 (15)

where: Co = 0.504 for a typical probe

C1 = D1 + D20b +.D302 + D4 3 + D5 04 + D6 5

C2 = El + E20 + E3 02 + .... + E605 ee

C3 = F 1 + F20 + F3 02 + + F6 5

The angles 0 and 0 are in degrees; however the angle 0 is limited to 450 . If > 450 as determined from" Equation (14), then the complement of 0 must be used (i.e. 90- 0), in Equation (15).

The constants Di, Ei and Fi are presented in Table I for a typical probe.

' Static pressure parameter SCA L (0, 0) as determined from calibration

SCAL (0.1) = G,0 2 + G2 04 + G306 + G4 08 + G5 010 (16)

where: G1 = JI + J2 + J + J 3 + J5

G2 = K1 + K 2 + + + K54

G3 = L1 + L2 0 + L3 2 + L4 3 + L5 04

4 = + M120 + M32 + M 3 + MS.

G 5 =N 1 + N 2 + N3 2 + N4 +N

where 0 and 0 are in degrees. If 0 is greater than 450 as determined from Equation (14), then thecomplement of 0 is used (i.e. 90 - 0) in Equation (16).

The constants Ji, Ki, Li, Mi, Ni are presented in Table II for a typical probe.

4.0 USE OF THE PROBE IN AN UNKNOWN FLOW

In normal testing technique, the five orifices of the probe are connected to a differentialtransducer via sequential porting of a Scanivalve system. Tunnel reference pressure p0 is on the backof the transducer, and tunnel total pressure PT is also scanned in sequence. If all five probe orificepressures are required simultaneously, then five transducers and Scanivalve heads can be used, withtunnel p0 and both connected to each separate unit.

0 PT

* 5f ,

-7.

sinle Typical flow measuring techniques use either (a) a single five-hole probe connected to a

single differential pressure transducer mounted in a single Scanivalve, (b) a single probe connecteddirectly to five differential transducers and no Scanivalve is used, or (c) a rake of five-hole probesconnected to five transducers mounted in five Scanivalve units. In all cases it is assumed that all thepressure transducers are referenced to tunnel static pressure po.

For setup (a), the five orifice p, essures are sampled sequentially, so no flow computationscan begin until all seven pressures are sampled. This has the disadvantage that in highly unsteady flows,the flow condition that existed when orifice pressure No. I was sampled may not be the same as whenpressure No. 5 is sampled. The advantage of setup (a) is that only a single transducer, Scanivalve, andADC (analog-to-digital converter) channel are required.

The usual plumbing hookup is with tunnel static pressure p on the first Scanivalve port,TP on the second port and a calibration pressure if required on the third. Probe pressures No. 1 to

No. 5 are on the next five ports, followed by the reference total and static pressures again on the ninthand tenth ports respectively. This type of hookup allows for the transducer tare to be measured (evenwith wind on) as the first and last measurement, so that transducer drift corrections can be applied tothe intermediate measurements, if required.

The advantage of setup (b) is that all seven pressures can be measured simultaneously, ifseven ADC channels are used and the windspeed is measured at the same instant. Whereas in (b) allseven transducers must be calibrated by a separate operation before any measurements can begin,setup (a) provides an "on-line" calibration each time the third Scanivalve port is sampled. In setup (b)tares can be measured only when the wind is off. Calibration of the five transducers in this case can beperformed by sliding a piece of Tygon tubing tightly over the head of the probe thus applying aknown pressure simultaneously to all five channels.

For setup (c) using a rake of N five-hole probes, each of the Scanivalves has tunnel staticpressure po on the first and last ports, tunnel total pressure on the second and next-to-last ports, andthe known calibration pressure on the third port. Scanivalve No. 1 is connected to orifice No. 1 of allN probes. Scanivalves No. 2, 3, 4 and 5 are therefore connected to orifices No. 2, 3, 4 and 5 respec-tively of all N probes. Five ADC channels are used, and a total of (3 + N + 2) Scanivalve ports are re-quired for N probes. This setup has the advantages of (i) on-line wind-on calibration and tares, (ii) theflow computations for a single probe can proceed immediately the Scanivalve has stepped past its port,and (iii) drift corrections can be applied at the end of the stepping sequence. As in setup (a) however,windspeed is measured only at the beginning and end of the sequence. Also, if the five Scanivalvesbecome unsynchronized, the data gathered is meaningless. This latter problem can be eliminated withthe use of ganged, multi-head Scani'alves driven off a single stepper unit, or of the "wafer switch"type of Scanivalve.

A modification of setup (c) using seven transducers and five Scanivalves provides for simul-. taneous measurement of windspeed and the five probe pressures. The po and PT transducers must be

calibrated separately however, and seven ADC channels are required.

With the seven quantities (po, PT' pl, p2, p3, p4 and p5) available from the pressure- I -

measuring system, the probe calibration routines developed in Section 3.0 will furnish the character-

istics of the unknown flow in steps (a) to (g) as follows:

a) Compute probe orifice coefficients CM, CP, Cp 3 Cp4 , Cp, and C from Equations (1) to(6). pp

b) Compute the probe dimensionless parameters P, Q, R from Equations (9), (8) and (7),respectively:

P C -

P C, 5 -

'dV

," .- .'. ' .. ,.. ; . ,. : ." .', .'. .' -. -. .. _. .. ..- -, .. . .. . ., .. .... . .. ... . -, , .- - . .- .- . .- .-.. .- .- . .- .- - .

-8,

Qj Cp2 - Cp4

P

R Cp3 - CpI

P

At this point, the signs of the parameters Q and R should be saved in the program forfuture use.

c) Compute the pitch and roll angles, 0 and 0 from the empirical Expressions (13) and (14),as follows:

0 = A1 V 4 +R 2 + A2 (Q2 +R 2 ) + A3 (Q2 +R2) 3/ 2 + A4 (Q2 +R2) 2

- ", 1 a n I I Q Q 2 Q 3 Q 4B B Tan- + B2 (Tan-1 I 2 + B3 (Tan-i ,9 ) + B4 Tan-i I

The signs of Q and R will determine the correct quandrant for 0 as in 3.0 above.

d) Compute the values of the angles a and 3, and assign their signs according to the signs of Qand R, as follows:

ia = Tan 1 [Tan0 • Cos ] (17)

= Tan-l[TanO • Sin ] (18)

all angles are in degrees, -900 < a, 1< +900.

e) Compute flow dynamic pressure and resultant velocity ratios using (Eq. (9) and (15)), asfollows:

Local dynamic pressure

Pq/qT (19)

PCAL (0,0)

where PCAL (0, 0) is given by Equation (15) and P by Equation (9).

Local resultant velocity

VR (20)

VT '

'W,

-C..

q -q*--- ... Y -** .'b*..4**

1',

-9.

SU V Wf) Compute the three velocity components u - - from Equations (20), (13) and

(14) (see Fig. 2), as follows: VT VT'VT

Longitudinal velocity component

u (VRI- ) Cos 0 (21)

Yaw plane velocity component

SSin Sin (22)

VT SineST)

Pitch plane velocity component

V = Sin 0 Cos (23)

The signs of the components V and T are assigned according to the original signs ofVT VT

Q and R respectively, as determined in step (b).

g) Compute local total pressure coefficient in the unknown flow

The flow total pressure is sensed mainly by the central orifice of the probe, however themagnitude of C 5 must be corrected for the effects of flow inclination. The local totalp"

pressure coefficient C is then computed as follows:

Pt-P0

Cpt /2p VT2 p5 SCAL 0) p (24)

where SCAL (0, 0) is given by Equation (16) and P by Equation (9). The local static pressure.*" coefficient Cp, can be computed as follows:

a.? C 5 p = t- q/q,:!N

5.0 CONCLUSIONS

This note has presented a method of calibration and use for five-hole flow direction probes.Since exploration of three-dimensional airflows frequently involves mixed regions of both propulsiveand highly skewed flows, as well as dissipative wakes, this probe technique will furnish flow angles intwo planes, three velocity components, and local total and static pressures.

- r . . .. ..... ...... .. .. .. . .. .. .... .- . ..

-10-

The flow conditions under which this calibration was done corresponded to a low subsonicflow, at a unit Reynolds number of 106. The calibration constants given in Tables I and II, and othersections of this note refer to a specific probe which had been calibrated some time ago, and which is '-

in routine use presently in the Laboratory. In general, all such probes, particularly those which may

have head configurations different than that specified in Figure 1 should be individually calibrated.This note has not presented any details about the calibration installation and fixture but the probeshould be positioned on the centreline of the wind tunnel, with degrees of freedom in upwash (a) andsidewash (f), or in pitch (0) and roll (0). A tunnel test section sidewall static pressure tap and a settlingchamber total pressure probe should be used to obtain the references pressures p. and pT respectively.

6.0 BIBLIOGRAPHY

1. Bryer, D.W. Pressure-Probe Methods for Determining Wind Speed and Flow &'

Pankhurst, R.C. Direction.HMSO, (NPL), 1971.

..-

2. Wickens, R.H. Experimental Developments in VISTOL Wind Tunnel Testing atSouth, P. the National Aeronautical Establishment.Rangi, R.S. Can. Aeronautics and Space Inst., Vol. 19, No. 4, April 1973.Henshaw, D.

'2S

L"

% .-.

.4¢

-11

%

r1

TABLE I

COEFFICIENTS FOR DYNAMIC PRESSURE FUNCTION PCAL (0, €) (Eq. (15))

.'° '

Di Ei Fi in

1 -49.6 654 -352xe- 05 x - 0 7 Xe - 08

2 15.8 -124 20.7xe - 05 xe - 07 xe - 08

3 -0.264 3.54 -0.678x - 05 x -07 xe - 08

4 -7.24 -2.48 -8.4x -08 xe- 10 xe- 11

5 2.16 -7.86 3.71xc - 09 xe- 11 xe - 12

6 -1.33 5.82 -2.45Xe - 11 xe - 13 xe - 14

Note: The values presented in Tables I and II represent those for a typical probe.

,%

',,,,

" p

.p ,-' .,p"

-12-

TABLE H

COEFFICIENTS FOR TOTAL PRESSURE FUNCTION SCAL (0, 0) (Eq. (16))

Ji Ki Li Mi Ni

1 9.288 9.432 -4.320 7.398 2.916xe - 05 xe -07 Xe- 10 xe - 14 xe - 17

2 1.561 -5.927 8.929 -5.663 1.485Xe - 05 xe -08 xe - 11 xe - 14 xe - 17

3 -1.611 5.770 -7.498 4.882 -1.498xe - 06 Xe - 09 xe - 12 Xe - 15 xe - 18

4 7.078 -3.354 5.585 -4.227 1.274| - 0 8 xe - 10 xe - 13 xe - 16 xC- 19

5 -9.873 5.349 -9.743 7.584 -2.228xe - 10 xe - 12 x - 15 xe - 18 xe - 21 .

Note: The values presented in Tables I and II represent those for a typical probe.

% P

P.

" "'i.

-13.

(a)

HOLES SHARP EDGED ANDFREE FROM BURRS

a-0.195044 6.00"

A ~1.5"SOLDER THIS REGION

A 90

2..06 0w K 5 SECTION A(b)

FIG. 1: GENERAL ARRANGEMENT AND DETAILS OF FIVE-HOLEFLOW DIRECTION PROBE

- 14 -

1800

goD C 2700

'IA B0,3600

CROSS FLOW PLANE ABCD

YAW PLANE (DOC)

0=&DO

OA #*:BCA

0 -PTCH PLANE(BOC)

COMBINED PITCHPLANE (COA)B

A ROLL PLANE (ABCD)

FIG. 2: ANGLE AND VELOCITY CONVENTIONS FOR A FIVE-HOLEFLOW DIRECTION PROBE -

-15

a)_ __ _ __ _ _

0 I

* w

z

* 0=00

C)--

8=30* 50

C)-

0 0.2 0.4 06 0.8 1 1.2 1.4 1.6a-ATAN (I Q R1) a..

FIG. 3(a): PROBE ROLL ANGLE 0 vs ARCTAN I Q/R It%

:-.-~*.~.-- .*~ ,~. ~ . 4 /-- A . -ataP,%* ~ a - .' V %a.~a .rV

- 16 -

Lr)

C~%

'tz,

I I -k

*%

0. __

--. w

* .,

.9

FIG..3(b): PROB AVERAGE_ ROL AGL €vARTA IQ/ ______

.° °

-17-

0 .*,0

I I .

-X 40,50,130,140

*'. J: .30,60,120,150

20,70,110,160

CD

CD 10,80,100,170

0,90,180

CY CD 2

* UC)

* 0"

0 5 10 15 20 25 30 35 40 45 a

PITCH ANGLE e, DEG.

FIG. 4(a): PROBE PITCH ANGLE vs +

" A

,1J4

CJ)

CD3

LnI -

CN

AVG( Q2 + R9 R2

FIG. 41b): PROBE AVERAGE PITCH ANGLE 0, DEGRES + R

-19-

o p

Lfl

C)

o IL

00

CD

p'°0 0

10, 80, 100,-170

In

C)

20,70,110,160

cm)

in, 30,60, 120, 150

% 40,50,130,140

0 5 10 15 20 25 30 35 40 45

PITCH ANGLE 6, DEG.

FIG. 5: PROBE DYNAMIC PRESSURE PARAMETER, P =C~ ~v IC NLPIS Z vs PTCH AGLE

-20-

X40,50,130,140

V 30,60,120 ,150

20,70,110,160

* ____) 10,801100,170

10,90,180

0 -

PIS,

FI. :PRBESATCPRSSR PRMEER -nPITCH ANGLE 0,DG

*p 1- .4

FIG.6: ROB STAIC RESURE ARAETE, S - vsPITC ANLE7

-a Ia -. a- - - -~ - -. - - - -

-21- as

I

b

APPENDIX Af

a-

TYPICAL INDIVIDUAL PROBE ORIFICE PRESSURES COEFFICIENTS AS

FUNCTIONS OF THE COMBINED PITCH ANGLE 0, AND ROLL ANGLE ~

tx.

IIV

S.

.J.

5'

.5,

* 5,

* 5'

'5

I.,

.:.. -, '%~ >'% %s'% .5'%% ~V%%'~'%%%%%% *~%~*q *5,*:%~'~~'**~%' *.% 9.*5,~% ~%

-23-

*0

_____ _____ _____170,180.190

J 160,200c___ 0______ _ _ _ ___ ___ 150,210

0 ---19140,220C)

C) V 130,230

120, 240 h

CDJ

\ r110,250 a

o) 100,260

0 90,270

70,29060,300

c 50,310

4032

CD 30,330

30 2034

M

- 10,350* 0,360

a'0 5 10 15 20 25 30 35 40 45

a' PITCH ANGLE 8, DEG.

FIG. Al: PROBE SIDE ORIFICE PRESSURE COEFFICIENT, Cp1

LA

-24-

9 so__ ___ __ __ __ 90,100* 70:110

c* 60 1

o 50,130

0

30,150

k 20.160

*c U

CD 10,170

o 0,180,360

ot 190, 350

200,3 40210,330

C) 1220,320

0 I 240,3100

4 0, 300

0 0 -250,290

c) 31260, 280270

0 5 10 15 20 25 30 35 40 45

PITCH ANGLE 9, DEG.

FIG. A2: PROBE SIDE ORIFICE PRESSURE COEFFICIENT, C 2

p2,

-25- .

0,10,350,36020, 340

_____ _____ _____ _____30,330

40,320

>50,310 a~

60,300

70,290

CD 80, 280

C)90,270

100,260

c; - 110,250120,240130,230

140,220

0 0 150,210

CD )160, 200

170,190180

0 5 10 15 20 25 30 35 40 45PITCH ANGLE eDEG.

FIG. Al: PROBE SIDE ORIFICE PRESSURE COEFFICIENT, C 3

.* U' *t ' *. . . . . ~ a, * .* . .

- 26 -

____ __ __ ____ ___ _ _ ___260,270,280

250,290

____ ___ _ _____ ____240,300

230,310

220,320

0t

210,330

3200,340

04

C) 190,350

0,180,360

)10, 170

20,16030,15040, 140

50,130

c 1 0. 60, 120

3 0 70,110

0 5 10 15 20 25 30 35 40 45

PITCH ANGLE 6, DE G.

FIG. A4: PROBE SIDE ORIFICE PRESSURE COEFFICIENT, Cp4

-27-

9 0) 5

ar)

in N

o'o

00

PITC ANLE8'DG

IPIS

, n .._.

,.

Cv_ _ _ _ _ _ _40,50

I ° ,30,6o ,9°0I 10,,,,80o-

--""2 z fr 4 0

0 5 10 15 20 25 30 35 40 45'-" PITCH ANGLE e, DEG. t

~~~FIG. A5: PROBE CENTRAL ORIFICE PRESSURE COEFFICIENT, Cp5 .',

4. -28-

, 0 0A 0 in 0 on

C)

0

co-

0

zo

.1U

Coj

C) U.

--- 10 ..

- 29-

C3'

0 O

CD6w

-- J

La 0

0m

CLL

NLU

w

o!

z

.9L

'90

-300

C3

(0

(N

co

t a-

- 0a.

(.0.

00

III6R LOOOO7qtOtOOObO 09 C-4 05 -j8I

(D . '

-31-

C

C

C)-onC)

0D

-FCDw

z:

0

--C:3cn u..

w3 LJ L

wi

LO' i

* ~ ~~~~~~~~~ Et- 6 o o O Oo O P O U O oO - O O O I0 Cc

* t0

C) cb.

1 0 * ~ * * * % .' 9 ' - - , ' *

p. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ : % LU * ** 9 y - r*' ~ r *r 9 - . - . 1 9 9

- 32 -

0 A 010Il)re) 6.:

-(N

C3.

mN U

a.LO

U-uJ

0_ 0

w ~ a

C) w

-- o J

-

(r)

0

CD

V,I

00

- %-Q

0 01

o C3

~~~~ 00-s>12 ~

- 33.

#0

oD 0, 360c* 10,350

20,340

- 430,320

-1 0

c ~>50,310

60,300* CD

70,290

________S180,280

C)0 90,270CL

I; 100,260

I 110,250

CD

o6 120,240

* I130,230

____ _ _ ____ ___ __ _ ___ ___ __ ____ __ ___ 140,220

*0 5 10 15 20 25 30 35 40 4 180PITCH ANGLE e, DEG.

FIG. All: PROBE ORIFICE PRESSURE DIFFERENTIAL (Cp3 -p Ir) - UPWASH

L -34.

C)) 0

-w

CD'

00)

CD)

C.)

LA

Id RI3-3 o

-35-

CD M 1

('13

-

c;-'

* 0

0 19,5

CD

C)

240,300

0 5 1 0 1 5 2 0 2 5 3 0 35 40 -127PITCH ANGLE 9, DEG.

FIG. A13: PROBE ORIFICE PRESSURE DIFFERENTIAL (Cr- Cr4 DOWNWASH

**-'~~~~~~~.I~~~~~~p p4)~~~F4

* **- ****~ ----.

-36-

0

C,vi x

Lo ~~ --4 ~ N I 8 A

o

CD

- 04

-(-

LU0 u

UI-

CDD u

~' ~*. -. *., .. * . * ~p****~..**.,*-' .. *3

- 37 -

APPENDIX B

":TABULATION OF PROBE ORIFICE PRESSURE COEFFICIENTS, -

i DERIVED FROM CALIBRATION DATA

.

.''I

,p',

.39-

PITCHANGLE ROLL ANGLE. PHITHETA 0. Id* 20. 30. 40. SO* 609 70. SOO 90.0. 0.496 0.496 0.496 0.496 0.496 0.496 0.496 0.496 0.496 0.496 a

S. 0.354 0.355 09361 0.375 0.394 0.415 0.437 0.460 0.461 0.50110. 0.146 0.151 0.169 0.207 0.259 0.316 0.375 0.428 0.470 0.50815. -0.021 -0.017 0e012 09065 0.152 0.245 0.326 0.390 0.455 0.50820. -0*201 -0.195 -0.153 -0.074 0*047 0.169 0.262 0.333 0.414 0.47325. -0.390 -0.376 -0.32? -0o212 -0.067 0.068 0.171 0.260 0.340 0o41130. -0.571 -0.554 -0.503 -0.359 -0.186 -0.058 0.049 0.156 0.247 0e31735. -0.746 -0.728 -0*663 -0.490 -0*309 -0.168 -0.085 0.010 0*122 0.205

*40. -0.919 -0.696 -0.615 -0.611 -0*437 -0.332 -0.268 -0.196 -0.064 0.04545o -1.041 -1.014 -0.922 -0.734 -0.589 -0.506 -0.450 -0.397 -0.326 -00209PITCHANGLE ROLL ANGLE* PHITHETA 100. 110. 120. 130. 140. 1500 160. 170. 160. 190.0o 0*496 0.496 0.496 0.496 0*496 0.496 0.496 0.496 0.496 0.4965. 0.519 0.540 09560 0.578 0.594 0.607 0.618 0.623 0.625 0.623

10. 0.545 0.586 0.624 0.659 0.687 0.710 0.729 0.738 0.741 0.73815o 0.550 0.602 0.657 0.712 0.756 0.791 0.813 0.824 0.626 0.62420. 0.522 0.593 0.670 0.742 0.009 0.853 06894 0.699 0.902 0.899

*25o 0.467 0.553 09656 0.753 0.838 0.903 0.938 0.954 0.956 0.95430o 0.380 0.485 0.617 0.746 0.852 0.927 0.972 0.986 0.988 0.96635. 0.269 0.393 0.550 0.707 0.845 0.939 0982 0.996 0.998 0.99640. 0.129 0.271 0.456 0.656 0.623 0.935 0.987 0.998 19000 0.99845o -0.106 0.108 0.360 0.592 0.776 0.913 0.978 1.000 1.001 1.000PITCH

*ANGLE ROLL ANGLE. PHITHETA 200o 210a 220. 230. 240o 250. 260. 270. 280. 290.

*0. 0.496 0.496 0.496 0.496 0.496 09496 0.496 0.496 0.496 0.4965o 0.618 0.607 0.594 0.578 0.560 0.540 0.519 0.501 0.481 0*460

10. 0.729 0.710 0.687 0.659 0.624 0.586 0.545 0.506 0.470 0.42815o 0.813 0.791 0.756 0.712 0.657 0.602 0.550 0.508 0.455 0.390

*20. 0.884 0.853 0.809 0.742 0.670 0.593 0*522 0.473 0.414 0933325. 0.938 0.903 0o838 0.753 0.656 0.553 0.467 0.411 0.340 0.260

*30. 0.972 0.927 0.652 0.746 0.617 0.485 0.380 0.317 0.247 0.15635e 0.982 0.939 0.645 0.707 0.550 0.393 0.269 0.205 0.122 0901040. 0.987 0.935 0.823 0.656 0.458 0.271 0.129 0.045 -0.064 -0*196

*45. 0.978 0.913 0.776 0.592 0.360 0.108 -0.106 -0.209 -0.326 -09397* PITCH*ANGLE ROLL ANGLE. PHI

THETA 300. 310o 320. 3230. 340. 350. 360.0. 0.496 0.496 0.496 0.496 0.496 0.496 0.496I5. 0.437 0.415 0.394 0.375 0.361 0.355 0.354

*10s 0.375 0.316 0.259 0.207 0.169 0.151 0.14815. 0.326 0.245 0*152 0.065 0.012 -0.017 -0.021 0 Q

*20o 0.262 0.169 0.047 -0.074 -0.153 -0.195 -0.20125. 0.171 0.068 -0.067 -0.212 -0.327 -0.376 -0.390030. 0.049 -0.058 -0.186 -0.359 -0.503 -0.554 -0e571 3 a

35o -0o085 -0.188 -0.309 -0.490 -0.663 -0.728 -0.748 cpl*40o -09268 -0.332 -0.437 -0.611 -0.815 -0.896 -0e919 p

45. -0.450 -0.!C0t -0.589 -0.734 -0.922 -1.014 -1.041

-40-

PITCH

ANGL" POLL ANGLE. P H.!THFTA C. 10. 200 30. 40. 50. bO. 700 80. 90.

0o. C0496 0*496 u*496 G.496 0.49b 0.496 0.496 0.496 0.496 0.496

S 0.501 0.519 0.540 0.560 0.578 0*594 0.607 0.618 0.623 0.625

10. 0.508 0.545 0@586 0*624 0.659 0*687 0.710 0.729 0.738 0.741

15. 0.508 0.550 C*602 G.657 0.712 0.756 0.791 0.813 0.824 0.828

20. 0.473 0.522 0.593 0.670 0.742 0.809 0.853 0.884 0.899 0.90225o 0.411 0.467 0.553 0.656 0.753 0.838 09903 0*938 0.954 0095b

30o 0.317 0.380 0.485 0.617 0.746 0.852 0.927 0.972 0.986 0.988

35o 0.205 0.269 0.393 0.550 0.70? 0.845 0.939 0.982 0.996 0.998

40. 0.045 0.129 0.271 Co458 0,656 0.823 0.935 0.987 0.998 1.000

45o -0.209 -0.106 09108 0.360 0.592 0.776 0.913 0.978 1.000 1.001

PITCH I

ANGLE POLL ANGLE. PHITHETA 100a 110. 120. 130. 140a 1500 160. 170. 1800 190.

0. 0.496 0.496 0.496 0.496 0.496 0.496 0.496 0,496 0.496 0.496

5. C.b23 0.618 06C7 0.594 0.578 0.560 0.540 0*519 0.501 0.481

10a 0*738 0*729 0.710 0.687 0.659 0.624 0.586 0.545 0,508 0.470

15o 0.824 09813 0.791 09756 0.712 0.657 0.602 0.550 0.508 0.455

20. 0.899 0.884 0.853 0.809 0.742 0.670 0.593 0.522 0.473 0.41425. 0.954 0.938 0.903 0*838 0.753 0.656 0.553 0.467 0.411 0.340

30. 0.986 0.972 0.927 0,852 0.746 0.617 0.485 0m3&C 0,317 0.24735. 0.99C 0,982 0.939 0.845 0.707 0.550 0.393 0.269 09205 0.122

4C. 0.998 0.987 0.935 0.823 0.656 0.458 0.271 0.129 0.045 -0.064

45. 1.000 0.978 0.913 0.776 0.592 0.360 0.108 -0e106 -0.209 -0.326PITCH

ANGLE ROLL ANGLE. PHITHETA 2CG 210o 220o 230* 240s 250o 260o 270. 280. 290.

0. 0.496 0*496 0.496 0.496 0.496 0.496 0.496 0*496 0.496 0.4965. 0.460 0.437 0.415 C394 0.375 0*361 0.355 0.354 0.355 0.361

10. 0.428 0&375 0.316 0,259 0.207 0,169 0.151 09148 0.151 0.16915. 0.390 0.326 0.245 0.152 0.065 0.012 -0.017 -0.021 -0o017 0.012

20o 0.333 0,262 0.169 0o047 -0o074 -0.153 -0.195 -09201 -0.195 -0.153

25o 0.260 0.171 0o008 -0.067 -0,212 -0,327 -0.376 -0.390 -0.376 -0.327

30. 0.156 0.049 -0.058 -0.186 -0.359 -0*503 -0.554 -0.571 -0.554 -0.503

35. o0O0 -0.085 -0.188 -0.309 -0.490 -0663 -0.728 -0.748 -0.728 -0.66340. -0,196 -0o2f8 -0.332 -0.437 -0.611 -0.815 -0e896 -0o919 -0.896 -0.815

45o -0.397 -0*450 -0.506 -0.589 -0*734 -0.922 -1.014 -1.041 -1.014 -0.922

PITCH

ANGLE ROLL ANGLE. PHITHFITA 300o 310. 320. 330. 340o 350. 360. 50. 0.496 0.496 0.496 0,496 09496 0.496 0.496 15. 0.375 0.394 0.415 0.437 0.460 0.481 0.501 010. 0,207 0.259 0.316 0.375 09428 0.470 0.50815. 0065 0152 0.245 0.326 0.390 0.455 0.508 20

20. -0.074 0.047 0,169 0.262 0.333 0.414 0.473?b -0.212 -0.067 C.068 0.171 0.260 0.340 04110

30. -0o359 -0.186 -0.058 0.049 0.156 0.247 0.317 335. -0.490 -0.309 -0.188 -0.085 0.010 0.122 0.205 Cp240. -0.611 -0.437 -0.332 -0.2t,8 -0.196 -0.064 0.045

45a -0.734 -0.589 -0.506 -0@450 -0s397 -0.326 -0e209

.9 **~* ~\' *'** *~ .~ ~ : v -. ' 9 ** ~9 ' 9,**..-~.

ANITCE POLL ANGLE. PHI

*TH2ETA 0. 10. 20. 30. 40. =106 60. 700 80. 90.0'

'). 0 ).41F-b .4' - 0. 496 0.496& 0.496 0#446 O.496 0.496 0.496 0.496

5. 0.625 0*623 0#61a C*607 0.594 0.578 0.560 0.540 0.519 005C1

10. 09741 O.738 0.729 0.710 0.687 0*659 0.624 0.586 0.545 0.508

15. 0.828 0.824 0.813 0.7'91 0.756 0.712 0.65? 0.602 0.550 0.508

20. C.902 0.899 C.884 C.853 0.809 0.742 0.670 0.593 0.522 00473

25. 09956 0.954 0.935 0.903 0.838 0.753 n.656 0.553 0.467 0.411

30. 0.988 0.986 0.972 0.927 0.852 0.746 0.617 0.485 0.380 0.317

35e 0*99b ' .996 0.982 0.939 0.845 0.707 0.550 0.393 0.269 0.205

40o 1.000 0.998 0.987 0.935 0.823 O.656 0.458 0*271 0*129 0.045

45. 1.001 1.000 0.978 0.913 0.776 0.592 0.360 0.108 -0.106 -0*209

PITCH*ANGLE' RCLL ANGLE. PHI

*THETA 100. 11G. 120. 13Co 1409 1500 160o 1700 1a0. 190.

*0. 0.496 0.(' 0496 0 .496 0 .49DA6 0.496 0.496 0.496 0*496 0.496

5o n.481 0.460 0.437 0.415 09394 0.375 0.361 0.355 0.354 0.355

10o C.470 0.428 0.375 0.316 0.259 0.207 0.169 0.151 0.148 0.91S

15o 0.455 0.390 0.326 0.245 0.152 0.065 0.012 -0.017 -0*021 -0.017

*20. 0.414 0.333 0.262 0.160 0.047 -0&074 -0.153 -0.195 -0.201 -0.195

25. 0*340 0.260 0.171 0.068 -0.067 -0.212 -0.327 -0*376 -0.390 -0@376

30e 0.24' 0.156 0.049 -0.058 -0.186 -0.359 -0.503 -0.554 -0.571 -0.554

2 5o 0.122 09010 -0.085 -0.188 -0*309 -0.490 -0.663 -0.728 -0.748 -0.728

40. -0.064 -0919f -0.268 -0.332 -0@437 -0.611 -0.815 -0.896 -0.919 -0*896

459 -0.326 -0*397 -0&450 -0*506 -0.589 -0.734 -0.922 -1.014 -1.041 -1*014

* PITCHANGLE POLL ANGLE. PHI

*THETA 200. 21C. 220. 230a 240o 250. 260. 2700 280. 290.

*0. 0.496 C#496 0.496 0.496 09496 0.496 0.496 0.496 0.496 0.4'J6

5e 0.361 0.375 0.394 Oo41!: 0,437 0.460 0.481 0.501 09519 0.540

10. 0.169i 0*207 0.259 0.316 0*375 0.428 0.470 0.508 0.545 0.596

*15. 0.012 C*069 0.152 0.245 0.326 0.390 0.455 0.508 0.550 0.602

*20o -0.153 -0.074 0 a04 7 0 o16f9 0.262 0.333 O.414 O.473 09522 0.5Q3

*25. -0.32? -0*212. -CQ07 0.069 0.171 0.260 09340 0.411 0.467 0.553

*30. -0.503 -0.359 -0.186l -0*058 0.049 0.156 0.247 0.317 0.380 0.485

*35. -00663 -0.490 -0.309 -00188 -0.085 0.010 0@122 0.205 0.269 0.393

40o -0.825 -C.611 -0.437 -C*332 -0.268 -0.196 -0.064 0.045 0.12Q 0.271

45. -0.922 -0.734 -0.589 -0.50f -0.450 -09397 -0.326 -0.209 -0.106 0.109

* PITCH*AN(iLF ROLL ANGLE. PHI .

*THCTA 300o 310s 320. 330. 340. 350. 360. 50. 0.496 0.496 0.496 0.49f' 0.496 0.496 0.496 1

So 0.560 0.578 0.594 0.607 0.618 0.623 0.625 010. 09624 0.659 0.687 0.710 0.729 0.738 0.741ZIS*5 0.657 0.712 0.756 0.791 0.813 0.824 C.828 2Q 0420. 0.6?0 0.742 0.809 0.853 0.884 00899 00902

25. 0.656 0.753 0.838 09903 0.9?8 0.954 0.9560

30. 0.617 0.746 C9852 0.927 0.972 0.986 0.988 335o 0.550 0.707 0.845 0*939 0.982 e.996 O.998

40. 0.458 0.656 0.e23 0.935 0.987 0.998 1.000 P45. 0.360 0.5Q2 0.776 C9913 0.978 1.000 1.001

V' ~ '. ~ '. ;~' ~ ~ ~ , ~,~.* -* * *f,.**...**~*~i. * * ~ ~ *:e:

- 42.

P ITCHANGLE RCLL ANGLE. PHITHETA 0. 10. 20o 300 40. 50. 60. 70a B0. 90. fC. 0.496 C.496 Co496 0.496 0.496 0.496 0.496 0.496 0.496 0.4965. 0.501 0.481 0.460 0.437 0.415 0.394 09375 O.361 0.355 0a,354

10. 0.508 0.47C 0.428 0.375 0.316 0.259 0.207 0*161 0.151 0.14815. 0.50b 0.455 0.390 0.326 0.245 0.152 0.065 0.012 -0o017 -0.02120. 0.473 0.414 0.333 0.262 O.169 0.047 -0.074 -0.153 -0.195 -0.201

*25. 0.411 0.340 0.260 C. 171 0.068 -0.067 -0.212 -0.327 -0.376 -0.390*30. 09317 0.247 0.156 0.049 -0.058 -0.186 -0.359 -0.503 -0.554 -0.571

3 5o 0.205 0.122 0.010 -0.085 -0.188 -0.309 -0.490 -0.663 -0.728 -0.748*4C. CoC45 -0.C64 -C.196 -0.268 -0.332 -0.437 -0e611 -0.815 -0.896 -0*919

459 -09209 -0.326 -0.397 -0.450 -0.506 0.o589 -0.734 -0.922 -1.014 -1o041P1ITCHANGLE ROLL ANGLE. PHITHETA 130o 110. 120. 1 JG 140. 150. 160. 170o 180. 190.0. 3.496 094c-t 3.496 0.496 0.496 0.496 0.496 0.496 0.496 0.496c- C. 0355 0.361 O.375 0*394 0.415 0.437 0.460 0.481 0.501 0.519

*1). 0.*151 0.169 lo207 0.259 09316 0.375 0.428 0.470 0.508 0.54515o -0.017 0.012- 0.065 0.152 0.245 0.326 0.390 0.455 0.508 0.550

*?0. -09195 -0o153 -0o.)74 0.047 0.169 0.262 0.333 0*414 0.473 0.5221*25o -0.o376 -0*327 -3.e212 -0.067 0#0C8 0.171 0.260 0.340 0.A11 0.467

3 0. -0.b54 -0.50' -C*359 -C.186 -0*058 0s049 C.156 0.247 0.317 0.38035o -O.728 -0.667 -0.490 -Oo30c. -0.188 -0o085 0.010 0.122 09205 0.o269

*40a -0*8?6 -0.b15 -0.611 -C.4.37 -0.232 -0.268 -0.196 -0o064 0.045 0.12945o -1oG14 -0.922 -C.734 -Co5Aq -09506~ -0.450 -0.397 -0.326 -0.209 -0.106PITCHANGLE F-CLL ANGLE. PHI

*TH:-TA 2%;04 210o 220. 230. 240. 250a 260. 2 70. 280. 290e!)o 0.49L- 0.496 0 .496 0 .O496 0.496 0.496 0.406 0.496 0.496So 5. .4C C*56C 0.578 Co594 Co6C7 0.618 0.623 0.625 0*623 0.618

*10o 095d6 O.624 0.659 0.687 0.710 0.729 0.738 0.741 0*738 0.72915. 0.502 0o657 C.712 0.75f 0.791 0.813 0.824 0.828 0.824 0.8132C. 0.593 0967C 0.*742 0.809 C*853 0.884 0.899 0.902 0.899 0.88425. 0.553 0.656 0.753 0.838 0.903 0.938 0.954 0.956 0.954 0.93830o 0.485 0.617 0.746 0.852 0.9Z7 0.972 09986 0.988 0.986 0.972

*35o 0.393 C*55C 0.707 0.845 0.939 0.982 0.996 0.998 0.996 0.9824 AC. 0*271 0.456 C*656 0.823 0.935 0.987 0.998 1.000 00998 3.98745o 0.108 0.360 0.592 0.776 0.913 C*978 1.000 1.001 1.000 0.978

P ITCH-ANGLF kCLL ANGLE. PHI-TH-=TA 300. 310. 320. 330. 340. 350o 360e*3o 0.4qt 0*496 0.49C 0.496 0.496 0.496 0.4460*5o 0.607 0*594 0.578 0.560 0.540 0.519 0.501

10o 0.710 C.687 0.659 C.624 0.586 0.545 0*508 20413. 0.791 0*7* 6 0.712 0.657 0.602 0.55n 0.508210 006t>3 0oa0'r 0.742 0.67C 0.593 0.522 0.473 0

S5. 0 .9C3 a 32! C*753 0.656. 0.553 0.467 1.41130 20. .927 (1 ..3 12 *).746 0.617 0.0485 C * 80 0.317

*5. 0.')39 0.' 0707 0.550 03Q3 C 0269 C 3 5 Cp4U. *-;o5 0. o 0. 72O65E 0.458 0.271 0.12q 0.045

450 00413 3.77' 0.597? 0.360 oolC ' -0010f. -)0 ?:)9

-43-

PITCH

* ANGLE ROLL ANGLSe PHI

- THETA 0. 10. 20. 30. 40. 50. 60. 70. 80. 90.

0. 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1000

5. 0.999 0.999 0.999 0.999 0*999 0.999 0.999 00999 009Q9 0.999

10. 0.991 0.991 0.993 0.994 0.996 0.996 0.994 0,993 0,991 0.991

15. 0.967 0.966 0.970 0.971 0.974 0*974 0.971 0.970 0.966 0.967

20. 0.917 0.913 0.916 0.922 0.927 0.927 0.922 0.916 0.913 09917

25. 0.838 0.833 0.834 C.843 09850 0.850 0.843 0.834 0.833 0.838

30. 0.722 0.716 0.714 0.722 0.739 0.739 0.722 0.714 0.716 0.723

Z5. 0*587 0.573 0.570 0.588 0.607 0*607 0.588 0.570 0.573 0o587

40. C.413 0.398 0.396 0.415 0*436 00436 0.415 0*3if, 0.398 0*413

45. 0.187 0.166 0.168 0.180 0.206 0*206 )o180 0lV..9 09166 0*117

P ITCHA N.GLE POLL ANGLrE PHI

TH TA 100. 110. 120. 130. 140. 150. 160. 170. 180. 190.

0. 1.000 lCoo lco.0 1.00C 1,C0o 1o000 10000 1.000 1.000 1.000

5. 0.999 0.999 0*999 0*999 0.999 0099Q 0.999 0.999 0.999 0A99

10. 0.991 0.993 0.994 0099C 0.996 0.994 0.993 0.991 0,991 0.991

15. 0.9b6 0.970 0.971 0.974 0.974 0.971 0.970 0.966 0.967 0.966

20. 0.913 0.91f 0.922 0.9Z7 0.927 0.922 0.916 0.913 00917 0.91i

* 25. :). 3Z3 0.834 0.43 0*850 0*850 0*2 0.334 0*833 0.838 0o33-.

30. G.716 0.714 0.722 0.739 0.739 0.722 0.714 0.716 0.723 0.716.

S250. C.573 0.570 0.588 0.607 0.607 0.588 &1.570 0.573 0.587 0.573

. 40, 0.398 0.396 0.415 0.436 0*436 0.415 0.396 0.398 0.413 0.398

" 45. 0.166 0.168 0.180 0.206 0.206 0.180 J.168 09166 0.187 0.Zet

PITCHA, NGL FCLL ANGL., 0141

TH-CTA 200. 210. 220. 270. 240a 250. 25)3 27). 283. iy0.

0. 1.000 1.000 1.000 1.0C 1.000 1000 1.000 1,000 1.000 1.000

5. 0.999 G.999 0.999 0.999 09999 C*99q Z.999 O.999 0.999 0.999

10. 0.vi43 0.994 0.996 Ge996 0.994 0.993 ).991 0.991 0.991 0,993

15. 0.970 0.971 0.974 0.974 0.971 0907C 2.966 0.967 0.966 0.070

20. 0.916 0.922 0.927 0.927 0.922 0.916 0.913 0.q17 0.913 0.916

25. 0.834 0*84. 0.850 09850 0.843 0.834 0*833 0.838 0.O33 0.834 S.

30. 0.714 0.722 0.739 0.739 0.722 0.714 0&716 0.723 0.716 0.714

" 35. 0.570 0.588 0.607 09607 0.58 0.570 0.573 0.587 0.573 0.570

40. 0.396 0.415 4.436 0@436 0.415 09396 0.398 0.413 0.398 0.396

45. 0.168 0-18C 0.206 0.206 0.18C 0,168 0.166 0.187 0.166 0.168

PITCH

ANGt.r ROLL ANGLEv PHI

- THETA 3C0 310. 320. 33C. 340. 350. 360o 5

O 1.000 1.000 1.000 1.000 1.000 1.000 1.000 __

5. 0.999 0.999 0.999 0.999 0.999 0.999 0.999

,10 0.994 0.99e 0.996 0.904 0.993 0.991 0.991 20 ao15. 0971 0974 0974 0.971 0970 0966 (.967

20. 0.922 0.927 0.927 0.922 0.916 0.913 C.917 025e 0:943 0:850 0:850 0.843 0.834 0.833 0.838 0

30o 0*722 0*729 0739 0722 0.714 0971f 0.723

35. 0.56 C.6C7 .607 c.sep 0.570 0.*53 7 Cp 5

40. 0.415 0.436 0.436 0.4!5 0.396 0a6')3 '.413

45. 010 0.20(- C.236 0180 01b5 0.e16 1 137

,.

,47 Jl4'I

REPORT DOCUMENTATION PAGE / PAGE DE DOCUMENTATION DE RAPPORT

____ ____ ____ ___/9i b

REPORTIRAPPORT REPORTIRAPPORT 6.

NAE-AN-29 NRC No. 24468

18 lb

REPORT SECURITY CLASSI FICATION DISTRIBUTION (LIMITATIONS)CLASSIFICATION DE SECURITE DE RAPPORT

2 Unclassified 3 Unlimited

TITLE/SUBTITLEITITRE/SOUS-TITRE

Calibration and Use of Five-Hole Flow Direction Probes for Low Speed Wind Tunnel Application4

AUTHOR(S) IAUTEUR(S)

R.H. Wickens, C.D. Williams5

SERIES/SERIE

Aeronautical Note6

CORPORATE AUTHOR/PERFORMING AGENCY/AUTEUR D'ENTREPRISE/AGENCE D'EXgCUTION

National Research Council CanadaNational Aeronautical Establishment Low Speed Aerodynamics Laboratory

7

* SPONSORING AGENCY/AGENCE DE SUBVENTION

8

. DATE FILEIDOSSIER LAB. ORDER PAGES FIGS/DIAGRAMMESCOMMANDE DU LAB.

85-07 49 69 10 11 12a 12b

NOTES

13

*" DESCRIPTORS (KEY WOROS)/MOTS-CLES

1. Wind tunnels - instrumentation

14

SUMMARY/SOMMAIRE

A ~This note describes a method of calibration and use of five-hole

". flow direction probes. When used in complex three-dimensional mixed flows,,* the probe will furnish flow directions, velocity components and total pres-

sures. The method described in this note is intended for the use of the windtunnel project engineer in determining flow direction characteristics ofvariousmodelconfigurations. r ,, -"

e er I

*1

'4

NNN

N

FILMEDI

* 11-85

.4

DTIC. . .

* . . . - * . .

................................................

.4 -................-.- *