A spinning hot-wire anemometer for simultaneous measrement of u, v and w

A SPINNING HOT-WIRE ANEMOMETER FOB. SIMULTANEOUS MEASUREMENT CF u, v and w

by M. G. McLeod

A SPINNING Har-WlRE ANEMOMETER FOR SIMULTANEOUS MEASUREMENT OF u, v and w.

by

M. G. McLeod

'

..

Manuscript received December

1967

ACKNOWLEDGEMENTS

~his report was submitted as a thesis for the B.A.Sc. degree to the Department of Engineering Science in January

1967.

Gratitude is expressed to Dr. G. N. Patterson, pirector of the Institute for Aerospace Studies, for providing the opportunityland faciliti.es to do this research.

The author is indebted to Professor BEtkin for his guidance and many helpful suggestions.

Many people co-operated in the experimental work. Special thanks is due Dr.P. C. Hughes, Mr. T. R. Nettleton and especially t~Mr. D. Surry.

This work was made possible through the financial support of the United States Air Force under the research and technology contract

AF33(615)-2305,

of the Control Criteria Branch, Flight Dynamics Laboratory.

SUMMARY

A rotating hot wire anemometer is a device for determining

simul-taneously the velocity components at a poipt in a fluid flow. This is accomplished

by analyzing the output waveform of an inclined hot wire which is rotated on a probe shaft. Two methods have been deve19ped for separating out the velocity

components. The first me~hod employs the first and second harmonies of the signal. The second method uses a calibration curve formed from the signal amplitude and

i t,s De level.

A rotating contact system using mercury was developed for noise-free tapping of the signal from the rot,ating hot wire.

1. 2.

3.

4.

5.

TABLE OF CONTENTS NOTATION INTRODUCTION EXPEI\IMENTAL APPAR.ATUS

2.1 Description of the Probe

SUMMARY OF THE ROTATING HOT WlRE ANEMOMETER THEO~Y

DEVELOPMENT OF PROBE TECHNIQUES

v 1 2

3

4

10

4.1 The Thesis as a Design Problem 10

4.2 Experimen4al Verification of Hot Wire Signal 10

4.3

Two Techniques for t,he Determination of Velocity Components 11

4.4

Experimental Verification of the Techniques

13

4.5

Accuracy of the Techniques

i4

4.6

Usefulness of the Techniques 15

CONCLtJDIING REMARKS REFERENCES APPErqDIX

16

17

18

v

9 cp u v w a

,z

i

i

w

l ... _... ... ... ...

NOTATION

flow velocity vector

component of velocity vector perpendicular to hot wire

,

I

angle between V and the positive prob~ axis

angle made by projecting V into plane perpendicular to probe axis

x component of V

y component of V z component of V

rotational displacement of probe shaft

angle between the hot wire and the plane perpendicular to probe axis

I

I

THE FLOW VELOCITY VECTOR

I 1/ k---~ - - - - --- - - j Jf};;""'"

'I

..., ... I / U. _____

---=-

....

:.=-1/ /

/

/

Ix..

PROBE GEOMETRY

E hot wire signal voltage, volts

De

level or average of hot wire signal, volts

first harmonie of hot wire signal, v0lts seeond harmonie of hot wire signal, volts

(voltage)2 intereept in King's Law equation, volts2

1. INTRODUCTION

There is a definite need for an instrument capable of determining

simultaneo~sly all of the components of the fluid velocity vector at a point.

Such an instrument would h~ve many practical applications, an example of which is the wake survey used in helicopter development.

A stationary hot wire probe is capable of measuring only the com-ponent of the flow velocity which is perpendicular to the wire. Furthermore, it is relatively insensitive to small changes in this velocity component produced by a yawing motion of the probe. By rotating the shaft of the probe it is theoretically possible to evaLuate all components of the flow velocity and at the same time maintain a high sensitivity to changes in the orientation of the velocity vector.

All previous work on this probe was done as a Bachelor's thesis tn

1965

and

1966

by Mr. E. Y. Sarafian at the University of Toronto Institute for Aerospace Stud~es. A complete theoretical analysis of signal waveforms and their harmonies was carried out and a prototype probe was constructed. Be-fore any experimental work could be done with this probe, however, it was necessary to perfect a noise-free electrical contact system to conneet the terminals of the revolving hot wire to the bridge circuit.

The purpose of this thesis was to complete the development of the prototype rotating probe, to compare the signals generated by the probe with theoretical signals, and to devise a technique for determining the com-ponents of the flow velocity from the signals.

2. EXPERIMENTAL APPARATUS

The apparatus used in this experimental analysis, with the exception of the rotating probe itself and the andlog computer consists of the same equipment as that used in normal hot wire anemometry.

(lJ Wind Tunnel

~he test section of the U.T.I.A.S. low-speed wind tunnel is used to create a smooth airflow whose velocity is accurately known. The calibration and testing of the probe is carried out here. Although higher speeds were available, tests were not conducted above 110 feet per second because of vibra-tion of the probe.

(2) The Rotating Probe

A hot wire probe which is fixed measures the component of velocity normal to the wire. By rotating the shaft of the probe a periodic signal is produced, since the normal velocity component varies at the same frequency as the shaft rotation. In order to indicate the rotational position or phase of the shaft at any instant, a second signal - the reference signal is also generated by the probe. This is explained in the detailed description of the probe which will follow.

(3) Disa Constant Temperature Anemometer

This instrument is used to keep the resistance of the hot wire at a constant value and thereby to fix its temperature. A bridge circuit is em-ployed to sense small changes in resistance. The output consists of a signal voltage which is that supplied by the anemometer to the hot wire to keep its temperature constant. Meters on the instrument give' a readout of the D.C. level of this signal voltage and the root-mean-square A.C. level of the signal voltage.

In order to analyze the output signal the following two electronic units are used.

(4)

Pace Analog Computer

By means of a linearizing circuit in the computer (described in the Appendix), the output voltage is linearized and made to be numerically equal to the flow velocity component perpendicular to the hot wire. This is used in a comparison of the theoretical and experimental velocity waveforms.

(5) Bruel and Kjaer Wave Analyzer

Any periodic signal is composed of characteristic harmonics which are easily separated by means of a wave analyzer. Dnly the first two harmonics of the signal are used because the higher harmonics become progressively more difficult to measure with accuracy.

(6) Dual Beam Oscilloscope

For visualization, an oscilloscope with a Polaroid camera was

used to monitor and record all output waveforms. These included the linearized

and non-linearized signals, the first and second harmonies of the non-linearized

signal, and the reference signal. A schematic of the equipment used is given in figure 1.

2.1 Description of the Probe

The rotating probe has four major components: the hot wire,

its contact system, motor and reference signal generator. The hot wire is the

transducer element which is sensitive to the flow velocity. Rotation of the

shaft on which the hot wire is mounted is accomplished by means of a small

6

volt Pitman motor. Electrical contact between the ends of the hot wire on

the rotating shaft and the fixed part of the probe is made by means of a mercury

contact system. This is described in detail in the appendix. In order to

re-late the Disa signal to the rotational position of the probe at any instant, a small reference signal generator was placed on the free end of the motor. It

consists of a cylindrical permanent magnet on the motor shaft, rotating within

a fixed coil. This produces a sinusoid of the same frequency as the hot wire

signal. Ta any point on the Disa signal there corresponds simultaneously a unique voltage on the reference sinusoid. This unique value can be calibrated

against the known angular displacement of the shaft. For example, the minimum

signal voltage occurs when the flow velocity is most nearly parallel to the wire.

Yawing of the probe within the wind tunnel test section was

accomplished by rotating the base of the probe to the required angle. The probe

3 . SUMMARY OF TEE ROTATING HOT WIRE ANEMOMETER THEORY

1. King' s Law

The output of the hot wire anemometer is a voltage

E

which is related to the normal flow velocity Vn by King's Law:

The constants A and B can he determined for any particular wire by a calibration. If

E

2 _{is plotted against ~n then a reasonably straight line} results whose slope is Band whose

E

2 _{intercept is A.}

In order to predict the theoretical rotating hot wire signal it is first Eecessary to derive an expression for Vn as a function of the flow velocity v(v,e,~).

2. _{Determination of the Velocity Waveform Vn}

Any given v(v,e,~) may be resolved into a component parallel to the wire and a component Vn in a plane perpendicular to the wire.

The reference frame is chosen such that the z axis coincides with the probe axis.

Notation:

w

velocity of the airflow inclination of hot wire

rotational displacement of hot wire ...k-_--+ _ _ ---..

v -

-

-

-

-

-

-

J

~

',

/ / /

',I

//

- - -

-

- -- ~/ V

v(v,e,cp)

a

=

angle between hot wire and the plane perpendicular to probe axis

=

~

First, we resolve V into x, y and z components.

u V sin

e

cos

cp

v V sin

e

sin

cp

w V cos

e

/

/

y

/ :t./' _, / IA , / , /

I

·z

I

i

.

1'# \ \ \

,

\ \

,

\ V ~_--L.-.----i_ - - -

y

rn IZ I I n'lp

,-

_,

-

---

-

--- J

\ \ \

,

I'Y'\

Next, w is resolved into compon-ents perpendicular and parallel to the wire.

w cos

ex

=

w sin

ex

Now, u, vare resolved into components perpendicular and parallel to the trace of the wire in the x y plane.

ln u sin ~-v cos ~

m u cos ~+v sin ~

The vector m is resolved further into components perpendicular and parallel to the wire

m m sin

ex

n

~

=

m cos

ex

The only component of velocity which affects the hot wire is the one which is normal to the wire. This component has the following breakdown:

Let the resultant velocity perpendicular to the wire be Vn0

Vn2 (wn - mn)2 + (ln)2

(w cos

a -

m sin

a)2

+ (u sin

~

- v cos

~)2

=

[V cos e cos

a

(u cos ~ + v sin ~) sin aJ2 + [u sin

~

- v cos

~J2

[V cos e cos

a

(V sin e cos ~ cos ~ + V sin e sin ~ sin ~)

sJ..n

.

.

a

]2

+ [V sin e cos ~ sin

~

_ V sin e sin

~

cos

~]2

[V cos e cos

a -

V sine cos

(~-~)

sin

a]2

+

[V sin e sin

(~ _~)]2

For convenience we choose to measure ~ relative to the angular displacement ~ .

V

n V [ (sin

a

cos

~

sin e - cos

a

cos e)2 + (sin

~

This is the fundamental formula of the rotating hot wire probe. There is one other component of velocity perpendicular to the wire. This component, the tangential one, is due to the rotation of the wire itself through the medium.

Y"oto..tiono./

I/elocit)' clish'-\ bu:tlon

Y"oto.t ion

It will be seen later that the contribution to the signal by this component is negligibly small.

Figure

5

shows the non-dimensional normal velocity Vn/V plotted against B, the angular rotation of the probe. As the probe is yawed (e increased) to

45

0 , the amplitude of the waveform increases to a maximum. At

45

0 the wire rotates from a position parallel to the flow to a position perpendicular to the flow.

3.

The Anemometer Signal

The actual output signal voltage is given by King's Law.

(A +

BV~

[(sin

a

cos

~

sin

e -

cos

a

cos B)2 + (sin

~

Thiswaveform, which will be called the unlinearized probe signal, is similar in shape to the linearized probe signalor velocity waveform. At any fixed velocity, the unlinearized signal increases in amplitude when the probe is yawed. This is demonstrated in figure

6.

Also, at any particular yaw angle 9, the amplitude of the signal may be increased by increasing the flow velocity. This can be seen in figure

7.

It should also be pointed out that as the velocity increases the

DÇ

level or average value of the signal also in-creases.

A value of the wire angle

a

must now be chosen.

4.

Optimization of the Wire Angle

a

for Best Sensitivity to 9

v

Consider a standard hot-wire probe mounted with the wire normal to the flow. In this position the instrument is very insensitive to changes in the angle of incidence of the flow velocity. If however, the wire is set with its direct-ion more nearly parallel to the flow, this sensitivity is

immediately improved. Suppose the wire is rotated so that its angle

a

increases from 00 to

90

0 _{• Then the normal velocity} component being measured is

~iven _{by Vn}

=

V cos a and the

::::~t~:it~(:~ :~"1~~~I:

:v

iS

Graphically,

v'"

= V Cos 0( S,: k VsinO(

v

_kV

~---~--~~~

o

~Oo

nor,.,..,a.l c.o".... pO I'"le ",t

It is easily seen that the sensitivity of the probe to

directional changes in the flow velocity is at a maximum when the probe wire is nearly parallel to the flow. For maximum sensitivity to changes in the flow direction then, it is to our advantage to mount the probe wire as nearly

parallel to the probe axis as possible.

There are two practical factors which must be taken into account before the best wire angle can be established. Both concern the probe wire

supports.

(1) As the wire is rotated

(a

is increased) from a position normal to the

probe axis, one probe support must be extended. There is a limit to this

extension - at high speeds the centrifugal force due to the rotation of the

probe causes this support to cantilever outwards. This puts extra: .stresses

on the hot wire itself a nd shortens its life. It can also be seen that in this case a much longer wire filament must be used to span the supports. This may introduce extra problems of vibration.

(2) As the wire angle

a

is

increased, the range of possible incident velocities which the probe can successfully

measure is reduced.· If the flow

is incident upon the probe at an

angle

e

greater than (900 -

a)

it will at some point in the probers rotation pass over the wire itself. This introduces an undesired disturbance into the

only the flows with velocity

vec~or lying inside the cone

generated by the rotating wire

are not disturbed by the probe before measurements.

Therefore, 8max

=

90° -

a

This leads to the question - How large a 8max must the instrument be capable of measuring for it to be useful? Suppose we

con-sider

2

flow with average

vel-ocity ~ and turbulence velocity

of ~ whosetime average is zero.

Then all possible flow

veloeities li~ within a cone

generated by ~ + ~max having

-l/V

max

I

angle 8

=

sin ~

. lVI

If, for example we allowan angle 8

=

450 we are allowing the turbulence

mag-nitude to be 1

lvi

or

70.7%

of the mean velocity. The probe is useful for

measuring

flO~

wIth this amount of turbulence.

The choice of a wire angle is q~i~e arbitrary and a compromise

must be reached between sensitivity to 8 and useful 8-range of operation.

The value of

a

for subsequent experiments was chosen to be 450 .

This allows a high sensitivity in the range 0

<

8

<

450

• As shown before

this choice of

a

allows for a very adequate turbulence level of

70.7%

of the

m.ean velocity.

e

It may be desired to ~ncrease the value of

a

depending upon the

application of the probe. This will increase the sensitivity but reduce the

4.

DEVELOFMENT OF .PROBE TECHNIQUES

4.1

The Thesis as a Design Problem

Fundamentally, this thesis is a problem in instrument design. It is required to find a technique for separating out and determining the flow velocity components from the hot wire signal.

The probe makes available two signals - the linearized signalor velocity waveform, and the unlinearized signal as it comes from the Disa

instru-ment. In order to obtain the linearized signal, additional electronic compon-ents are required {see appendix). Since simplicity is an advàntage for any instrument it was decided to use the unlinearized signal provided it could furnish ~he necessary information about the flow velocity.

There are three units of information which must be o~tained from the signal, namely, the three flow components. This requires at least three measurements. The signal variables most readily available are DC level, first harmonic, second harmonic, phase dllgle, RMS value of the signal, and peak to peak signal voltage.

Each of the above can be determined fr om the theoretical wave-form. This has the advantage that a complete analysis of the probe can be carried out theoretically rather than empirically. The analysis, however, is useful only if the actual probe signal coincides closely with its theoretical coUnterpart.

The first requirements, then, is to examine the output voltage of the rotating hot wire and to compare it with the calculated theoretical signal.

4.2

Experimental Verification of Hot Wire Signal

The first step as in standard hot wire anemometry was to calibrate the probe to find the King's Law constants A and B. This was carried out in the wind tunnel test section with the wire normal to the flow and the probe shaft stationary.

The probe Shaft was then rotated at a speed of about

40

cycles per seconde (Speeds of

60

cycles per second and its associated harmonics should be avoided for the noise level to be minimized.) Oscilloscope photographs of the probe signal were then taken for yaw angles of

0,

10,

20, 30,

40 and

45

degrees, and at each yaw angle flow speeds of

0,

40

and

80

feet per second were used. Since the wire angle

a

was

45

degrees, the yaw angle was limited to

45

degrees in either direction.

Figure

8

shows the photograph of a typical signal for values of 8 =

40

degrees and V =

81.1

feet per seconde In figure

9

this waveform is com-pared with the theoretical waveform as calculated from King's Law using the calibration curve wire constants.

Several observations are immediate. The DC level of the two curves is not the same. The cusp of the probe signal is not as pointed as it is theoretically predicted to be. THis can be attributed in part to the lack

of high frequency response of the electronics which is used to produce the signal. (The cusp caq be considered as made up of high frequency Fourier components

which are attenuated.) Another factor which may be involved here is an effect

observed in ordinary hot wire anemometry. If a hot wire which is normal to the

flow is yawed in the flow, the normal component is given by _Vn ~ V cos 9. But

the response of the anemometer does not obey this law as the wire becomes more

parallel to the flow. At 9

=

90 degrees the calculated normal velocity component

is not zero but a small positive value.

~he dip in the signal at ~

=

180 degrees is also observed at yaw

angles down to 30 degrees. This dip is a characteristic 0f signals whose yaw

angle exceeds the hot wire _ '. angle

ex

and should only be present in signals

where 9 is greater than 45 degrees. It cannot be attributed to errors in

ex

and

6, for

ex

was determined to

± 1 degree and

6 to ± ~ degree. Self-induced

distur-bances are not the cause. These would be created when the wire is parallel to

the flow and would affect the wire when it had rotated to a position perpendicular

to the flow. The probe shaft rotates once every 1/40th of a seconde In this

time a flow of 100 feet per second has moved 2.5 feet which is some three orders

of magnitude greater than the hot wire length. Therefore, all flow disturbances

created by the wire in the parallel position are downstream long before they can

be detected by the wire in a position normal to the flow where the irregularity

occurs. It is felt that the dip in the signal was actually caused by a flow

deflection, produced by the shroud over the probe. The effect of this deflection

is that the angle 6 relative to the hot wire is actually greater than the true

angle 9 relative to the probe.

Photographs for one hot wire were taken with the probe shaft

ro-tating first in one direction and then in the other. (Figure 11.) The second

photograph indicates that this wire was not mounted symmetrically with respect

to the mounting needles. This demonstrates the importance of precision in

fix-ing the hot wire to the probe.

Another observation made in the first experiment was that the

nor-mal component of velocity produced by the rotation of the wire itself is negligible.

The DC level with the probe stat~onary was 3.87 volts, while with the probe

rotat-ing, it was 3.92 volts. On the calibration cruve this corresponded.to a velocity of 0.3 feet per seconde

Although the theory and experiment do not agree closely, it was

decided to carry on with the analysis. The criterion for the usefulness of the

probe is not whether individual waveforms agree with theory, but whether the

changes which are produced in the waveform as V and 6 are varied can be used profi tably.

4.3 ~wo Techniques for the petermination of Velocity Components

JWo approaches were finally adopted for the separation of the V

and 6 components:

(1) analysis employing the signal harmonics El and E2

(2) construction of a set of calibration curves

and twice the fundamental frequency respectively. Since the fundamental fre-quency is equal to the rotational speed of the probe, the filters must be matched to this rotational speed.

The second approach offers simplicity. No special electronics is required over and above that used in normal hot wire anemometry. If the probe is accurately calibrated in a wind tunnel and is consistent, it will have corresponding accuracy when put into use. The problèm remaining is to find the best variables in terms of which the calibration is to be made.

No mention has been made to this point of the velocity co-ordinate

~. This is because ~ can always be determined quite easily and independently of V and 8 • A phase meter is employed to give the phase difference between the reference signal and the hot wire signal. These signals may requirefiltering at the fundamental frequency before their phase dif~erence can be measured. The reading of the phase mèter will always differ fr om ~ by a constant.

Since ~ is a relative angle, suppose it is chosen that ~

=

0 when the flow is incident upon the probe in the plane which is vertically below the shaft (the plane wtiich includes the probe support). Suppose, moreover, that the phase meter reads ~o for this orientation of the f.low. If the flow angle ~is changed to " then the phase meter will read ~o + , or ~o - , depending upon the direction of rotation of the probe shaft.

(1) Analysis by Means of Signal Harmonics

It can be seen that when El is plotted against 8, a family of curves is generated, each curve being for a particular velocity. The curves are nearly linear and pass through the origine A similar set of curves is given ~y plotting E2 against 82 • The unique aspect of the two curve sets is that they appear to depend upon the flow velocity in the same fashion. This suggests a division of E2 by El to lose the functional dependence upon V and the result is a fUnction of 8 alone.

Supponse _El = f(V) E2 = g(V) then E2

$t

El = f V 8 82

8 k8 where k is a constant by the hypothesis that g(V) - k f(V) This result is further supported by dimensional analysis. Since E2/El and 8 are dimensionless then k must also be dimensionless.

The theoretical values of the first and second harmonics were evaluated by computer from the defining formulae.

1 El (v,8)

=

7T

rE

cos t) dt) 0 27T E2(V, ) 1

I

E cos 2t) dt3 7T 0

Not only is the theoretical E2/El independent of velocity, but

its variation with ~ is linear. (See figure 13).

Once 8 is kno~, the flow velocity magnitude can be obtained

from the graph of (DC level) against V. This is a family of curves with a

curve for each 8 . (See fig~e 12)

(2) rConstruction of Calibration Curves

Suppose that for a given flow velocity, the probe is yawed so

that the angle 8 is varied. As 8 increases from 0 to 450_{, the peak to peak}

amplitude of the signal increases (See figure 6). This peak to peak amplitude will be increased still further at any 8 if the flow speed is increased. (See figure 7.)

Af ter a careful analysis it was decided to plot the peak to peak

amplitude against the square of the DC level. Va~es of 8 ranged from 0 to 45

degrees and velocities from 0 to 100 feet per seconde Calculations using King's

Law were done again by computer.

2 The results are shown in figure 14. As velocity increased the

(DC level) increases ac c or di ngly . Lines of constant velocityare almost

ver-tical. By inereasing

e

at any velocity the peak to peak voltage is increased.

Lines of constant 8 are almost linear and have an (E₀

7

2 intercept of A.

The significanee of this figure is that by obtaining simultaneously the peak to peak signal amplitude and the DC level, it is possible to determine

both V and 8 in one operation from the calibration eh art,.

4.4 Experimental Verifieation of the Techniques

(1) Harmonie Analysis

The probe was eali"Qrated a:s··hefore and the ea.libration c.urve

drawn. T~en with the probe in rotation, readings of DC level, first harmonie

and seeond harmonic were recorded. (The same values of 8 were used but this

time the intervals of the velocity span were shortened - 0, 8, 13, 35, 56, 72,

86, 95, 99 and 108 fee.:t per --s-eeond·. ) !.Phe-fr€-s·peeds w€rre· used beeause the wind tunnel motor speed was not continuously varia.ble, but opera.ted in steps. The

wind tunnel had to be stopped whenever it was necessary to change 8. As a

re-sult the same velocity was never aehieved twiee.

The curves of the. harmonies ~l and E2 were not plotted up

di-reetly. Instea.d, by plotting the harmonies agaihst V, their values were

inter-polated at velocities of 100, 81, 36 and 16 feet per seeond. These are shown

in figure 13.

The fundamental discrepaney between theory and exper"iment lies

in the slope of the curve. The eXperimental harmonie ratio is 1.4 times larger

than its theoretieal v&lue. Linea.rity was approaehed at high veloeities. The

non-linearity at low flow veloeities is probably due to fluetuations in the

(2) Calibration Curves )

J

Af ter calibration, oscilloscope ... ,15trot·ographs were taken of the

waveform for values of

e

and V as in

par~t

,

F -"Tne DC level was recorded

simultaneously with the photograph. Fig -_ '5-shows the amplitude plot and

should be compared wi th figure 14. FOT . ')si..ven V and

e,

the experimental

signal amplitude is

a~oJJt b'tW.t

_:

:

~±~~l:

"

value. Th~s

amplitude reduction

is sufferrd most by slgnals. f

e

-Lt q0+~:~.~e~s. ThlS effect has ~lready

been accounted for by the dlp at the top

-or

t'~al and the attenuatlon of

the cusp. -,

It was not possible uo set up grid lirtes of constant velocity

since as explained previously, the wind tunnel could not reproduce any

particu-lar flow condition.

4.5 Accuracy of the Techniques

A precise analysis of sensi tivities of "the probe to V,

e

and cp

using the two techniques is beyond the scope of this thesis. However, a good

indication of sensitivity can be gained from an error analysis. The .accuracy of measurement of V,

e

and cp increases as V is increased. The amount of error in cp depends upon the ability of the phase meter to give the phase .angle between the reference signal and the first harmonie of the wire signal. Maximal

errors in

V

and

e

are estimated using a combination of scatter of the

experi-mental points and the amount of separation this represents in the variable

be-ing determined from the graph. (1) Harmonie Method

(i)

e

is determined from the plot of E2/El against

e.

(ii) !I'or this value of

e,

V is therr determined from the family of curves of (DC level)2 versus V.

(iii) cp is determined by the phase angle between El and the reference signal. Maximum Error In

Velocity

e

V cp

100 fps + -20 + - 2 fps + 10 60 fps + 2.50 +

_-

2.5 fps + 1.50 30 fps + 3.50 + 1.5 fps +

-

20 (2) Peak to Peak Signal Me'bhod

{i)

e

is determined from the plot of peak to peak voltage arld (DC level)2 (ii) For this value of

e,

V is determined from the DC level curves.

(iii) cp is determined by the phase angle between El and the reference signal.

Velocity 100 fps

60 fps 30 fps

4.6

Usef~lness of the Techniques ( Maximum Error 9 V ~

3

0 +

3

fps

-+

₃

0 +

₃

_fps ~

3

0 +

_-

_{1 fps} In cp +

_-

₁0 +

_1.5

0

-+

_-

₂0

All experiments in this thesis were conducted under steady con-ditions. The effectiveness of these methods in unsteady conditions can only be postulated. High amounts of turbulence will cause the harmonics and the DC level to fluctuate. Since the filters and measuring devices have transients in their dynamic response it is not known whether the averaging processes involved would yield the true averages of the velocity components. This is one course for future investigation.

The photographic method when combined wi th a sensi tive averaging device for the DC level would give instantaneous velocity component values. For obtainirig mean values, statistical methods could be applied to a series of measurements.

For measurements in unsteady conditions, the probe shaft velocity

would have to be increased. If this is not done, the waveform will appear to distort before its cycle has bee~ completely traced out. Higher rotational

5 . CONCLUDING REMARKS

Spherical velocity components can be obtained simultaneously us-ing a rotatus-ing hot wire probe. A linearizus-ing network is not required for this determination.

A good set of mercury contacts is essential to the operation of the probe.

Although the voltage waveform of the probe has several anomalous characteristics, the variation of the signal with components V and 8 can be used profitably to identify these components.

TWo methods have been found for use and they appear almost equal in sensitivity to the velocity components.

One refinement required is the method of fixing the wire filament to the supports. If the filament was welded electronically on to the supports

it could be positioned with much greater prec.1.s1.on. When the wire is attached

by soldering, on the other hand, it must be placed to one side of the supports. Future probe designs could be reduced irl size if the motor was in an external unit and attached to the probe by means of a flexible cable. A small flywheel on the shaft could be used for reducing speed variations. By reducing the shaft size the mercury contacts could be miniaturized.

It is felt ~hat the rotating hot wire anemometer has great potential

1. Sarafiap., E. Y • 2. Kidron,. I.

3

.

Hinze, J.O.

4

.

Schlichting , H.

5.

Clauss, F.J. Kingery, M.K. REFERENCES

Rotating Hot Wire Velocity Probe, UTIAS Bach.

Thesis,

1966.

On the Measurement of Dynamic Flow Phenomena with the Cogstant Temperature Anemometer.

Disa Eiektronik

AlS,

Har lev , Denmark.

Turbulence. McGraw Hill

1959.

Boundary Layer Theory.

New York, McGraw Hill

1965.

Sliding Electrical Contact Materials for Use in Ultrahigh Vacuum.

APPENDIX

The Rotatipg Contact Problem

The largest single technical problem encountered in the develop-ment of the probe was th at of devising a technique for establishing

noise-free electrical contact with the two hot-wire terminals on the rot,ating shaft.

It was imperative that a solution to this problem be found before experimental work could be resumed.

Many configurations and types of metal to metal contacts were

tried, but without success. Only during this experimentation was the importance

of clean electrical contacts realized. Firstly, the signal from the hot wire

had to be intelligible. With a varying resistance of contact this was impossible.

The second, and most important reason concerned the electronics of hot wire

anemometry. The bridge circuit of the Disa instrument responds to changes in

probe resistance. If the resistance sudden~y i~creases then the electronics

interprets this as an increase in temperature. In order to bring ~he

tempera-ture back to its normal value, the bridge circui~ reduces the probe current.

If contact is momentarily broken with the hot wire the current flow will stop.

Once contact is re-established, the low resistance of the cold w.ire is

respond-ed to with a large current surge. But the minute tungsten filament will with-stand only a limited number of these surges before it breaks. This explains the short wire life when poor metal contacts were used.

For test purposes it was essential that a single wire be used

under many conditions of incident air velocity. ~very wire has different

characteristics - a change of the probe wire in the middle of a test makes a comparison of the nonlinearized signal very difficult.

Mercury Contact System

The major obJect ion to the use of mercury in a contact system

lies in the nature of mercury itself. If it escapes from its container i~ will

corrode most metal surfaces - bearings and especial~y solder joints. For this

reason, tight mylar seals were used. The advantage of mercury is that as a

liquid it can be employed in such a manner as to give large surface contact area. Also, mercury readily forms an amalgam with silver and this results in excelleny conduction properties for the mercury-silver interface. For this

reason, silver discs were used for the rotating part of the contact. The

mercyry was placed in each of two cylindrical compartments enclosing the silver discs. Viscostty acting along with the whirling of the silver discs provided the centrifugal force necessary to hold the mercury to the cylindrical

retain-ing walls. In this position the chance of mercury escaping was considerably

lessened.

One slight disadvantage of this system is that as the speed of probe rotation changes, the contact surface area also changes resulting in a change of probe resistance. However, if the contact area is initially very large, the change of contact resistance will be very slight in comparison with the signal-producing resistance changes of the hot wire.

Linearization of the Hot Wire Signal

The hot wire signal can be made proportional to t~e normal

com-ponents of the velocity of flow by following the linearization technique

suggested by King's Law.

King's Law

s~ates tha~

B

In order to linearize the signal we must square it, subtract the E2 intercepB (A) and then square the result. This will be proportional to the component of flow velocity perpendicular to the hot wire.

The following program was used on a Pace Analog Computer:

-/OK,e ~/oo KIr: A

I----~/O TL 00 -/00 /(,I0E 2 _ /00 /(,~ A FSOOL - - - . FsooA

•

_F500R

E is the hot wire signal plot of 100 K12E2 with V the value of circuit by means of poteRtiometer POl. porportional to Vn0 By adjusting Tl on

AOI SM\ -A I="SOOL.

AO"

from the Disa instrument. By making a 100 K12A2 was determined and set in the

The output of amplifier A1H was then P02 a direct readout of Vn was obtained. A complete calibration was run with the probe in the wind tunnel. Errors in Vn were less than 2% in ~he range 10 fps

<

_Vn

<

100 fps, but as high as

40%

for the range 0

<

_Vn

<

10 fps.

ROTATING PROBE ~

11

Referenee Signa I

IYYY

Wave

/\/V\-Analyzer

_V\/V\/\.fV\

I

I

D

_{LJ--iLi nearizer}

_Hl

_rvv-\

DC

D

AC RMS Level Bridge Voltage DISA CONSTANT TEMPERATURE ANEMOMETER OSCfLLOSCOPE Unlinearized Signal I st Harmonie 2nd Harmonie

11

Linearlzed Signal

bercury motor slonol __ Shroud Not Icontoefs _g~nJlUJlo..r - _ _ ,..r ---~ ~, Shown

'"

/ I / ... / Reference Signal Varioble 6V Supply Disa Circuit Base Rotates

Cylindrical Plastic Shell

Mercury -

held to outside bythe

centrifugal force

supplied by

viscous acti on

I

1

_

.

. .

j~

-

-

e;j \

r

Ir

p;ij:t.:::::

Mylar Seals -

~etain

mercury

te

Disa

Circuit

Silver Discs -

silver forms

amalgam

MERCURY

CONTACT

Magnification;

1 1/2

times

V

_n

V

1-0

08

y~...-= =:...,,~ "~

9=0

0

,7

V ,

0·6

9=10°

0(

=

45°

0·4

9=20°

9=30°

0·2

0-0

K

9=

40"

E

[VOlts]

7'(}1 LLL:/' ~ __

---

~"

""

e=o

0 0

e

=

10

,"-...

C(

=45

0 0

A =17'1

\,

" e =

20

B

=

3,68

\

"-.... e

=30

0 6'~

I

V

=

100 fps

e

=

40

0 o

e

=45

0

0 1800

.1.3

o

360

E

[VOlts]

7-0

6-0

50

0{ =45 o

A= 17-1

B =3-68

o

6=45

V=IOO fps V=80 V= 60 V=

40

V= 20

v=o

De

level

=

6.93

volt s

vertical: 0.5 volts/cm

horizontal: 5 msec/cm

FIGURE

8

PHOTOGRAPH OF UNLINEARIZED SIGNAL

0(,

=

45

o

e

=40

0

v=

81.1 rps

A=17.1

E

[VOlts]

7

6

5

I

,

I

,

I I I I I I I I I

,

I I I I I I

,

,

I I I ""

...

, , . , ,

---

--, ,

"

De

Level ;' ;' ;' ;'

"

"

"

"

"

0(=45 o V = 81·12 fps o 9=40 A = 17·1 B =3·92 \ \ \ \ \

Theory---\

\ \ \ \ \ \ \ \ \ \ \

Linearized Signal

DG

level =65.5 volts

vertical: 20 volts/cm

1 volt =1 fps

Unlinearized Signal

DG

level

=6.61

volts

vertical: 0.5 volts/cm

horizontal: 5 msec/cm

0(.=43

0

e

=25

0 V

=99.4

fps

A -15.0

B

=).58

_.,' - =:;;;;;;- , ' 1 ' " ' - 1 ._""".

!

I ~ II!:;~ _11'

lI!iIi

~

I

I ~ ~ I

I

I

I

I I /

I

_IIII!II !

~

.

n' _I,!l!!!

'.~,

II

,

-,-

~",-

UI 0(.

=45

o

e

=45

0

Probe shaft rotated in one direct ion and then the other

40

Callbratlon Curve 0 A=\7-\ B= 3-68

30

DC Leve I Curves e.4~·

•

e-30·

•

e.

O· •

20

A-o

2

4

₈

₁₀

§.

EI

I-O·

0-0'4

0'2

o 0(.

=

45 A :r 17-1 B =

3'68

o

IOOfps 6 81 fps • 36fps 16fps

E

_peok

ta

peok

3·0

[ VOlts]

2.0

I-0(= 45 o A= 17·1

B= 3-92

2-0 2e

,

_,

120fps I I

,

I I

,

130 fps I 1

,

_,

I I ,50fps I

,

_,

I

,

170fps I I

,

I I I

e

=

45

,

_,

I I I 'IOOfps 1 o

9=40

o o

9= 30

o

9

=

20

o I I , ....

9

=

10

I I • ' • I , I . , I I

+

T

I I I

,

o

9=0

30 3e

40

45

(oe

LEVEL)2

Epeak

ta

peak

2·

rVO

lts]

1'6

1·2

0'8

0·4

o ()(= 45 As _l7'1 8=3'92

e=45°

o

e-40

1-e_30

0

e_20

0

•

e_lo

O

•

_•

o.oJ

~o

0 • 0 0 0 0 0 0

.eco·

E

_peak to peak 3·0 [ vOlts]

2·0

1·0 O{= 45 0 A= 17·1 B

=

3·92 THEORY EXPERIMENT -/ / /

'"

'"

/ / / /

"

"

/ / / /

"

,,"

/ . , / ' / / ' / / ....

"

/ '" / ... /

"

"

'"

"

"

/

,,"

/

"

/

.,,"

/

'"

/ , , / / ." /

"

I /'" / ~ ~ 20 25 30 /

.,

/ / .... '" /

"

/

.,

/ / /

"

.,

-

-=----35 /

"

"

"

/ /

"

"

/

"

....-

"....-40

'"

/ ...

....-/ / / / ... .... ... /

"

"

/

"....-... " 45

"

/

9=45°

,," 9=40°

9=20°

"

9=45

°

9=40°

9= 20°

.>(". 50 2 (De LEVEL)

VrL'\.S TECHNICAL N(Y]$ NO. 12)

Institute for Aerospace Studies, University of Toronto

~

A Spinniug Hot-Wire Anemometer for Simultaneous Measurement of u, v and w.

~1. G. McLeod 19 pages

1. Anemometers

3. Velocity Measurement

1. McLeod, M.G.

16 figures 2. Hot-wire Anemometer 4. Turbulence

11. UTIAS Technical Note No. 125'

A rotating hot wire anemometer is a device for determining simultaneously the velocity

components· at a point in a fluid flow. T.his is accomplished by analyzing the output waveform of an inclined hot wire which is rotated on a probe shaft. Two methods have

been developed for separating out the velocity components. The first method employs

the first and second harmonies of the signal. The second method uses a calibration

curve formed from the signal amplitude and its DC level. A rotating contact system us

-ing mercury was developed for noise-free tapping of the signal from the rotating hot wire.

Avoilable eopies of this report are limited. Rehwn thls eard to UTIAS, if you require a eopy.

UTL'\.S TECHNICAL NOTE NO. 125

Institute for Aerospace Studies, University of Toronto

~

A Spinning Hot-Wire Anemometer for Simultaneous Measurement of u, v and w.

M. G. McLeod 19 pages 1. Anemometers

3. Velocity Measurement I. McLeod, M.G.

16 figures 2. Hot-wire Anemometer 4. Turbulence

11. UTIAS Technical Note No. 125'

A rotating hot wire anemometer is a device for determining simultaneously the velocity

components at a point in a fluid flow. This is accomplished by analyzing the output

·w3.veform of an inclined hot \lire which is rotated on a probe shaft. Two methods have been developed for separating out the velocity components. The first method employs the first and second harmonies of the signal. The second method uses a calibration

CUl've formed from the signal amplitude and its DC level. A rotating contact system us

-ing mercury was developed for noise-free tapping of the signal from the rotating hot

wire.

,ll'lAS TEC1U'lJICI\.L NarE NO. 12)

Institute for Aerospace Studies, University of Toronto

A Spinnillg Hot-Wire Anemometer for Simultaneous Measurement of u, v and >T.

~I. G. McLeod 19 pages 1. Anemometers

16 figures

2. Hot-wire Anemometer

4. Turbulence

~

3. Velocity Measurement

1. McLeod, M.G. 11. UTIAS Technical Note No. 125'

A rotating hot wire anemometer is a device for determining simultaneous1y the velocity components at a point in a fluid flow. This is accomplished by analyzing the output waveform of an inclined hot wire which is rotated on a probe shaft. Two methods have been developed for separating out the velocity components. The first method employs the first and second harmonies of the signal. The second method uses a calibration

curve formed from the signal amplitude and its DC level. A rotating contact system us

-ing mercury was developed for noise-free tapping of the signal from the rotating hot wire.