The measurement of drag forces in low density flows

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von KARMAN INSTITUTE

FOR FLUID DYNAMICS

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VUEGTUJGBOUW KUNDE

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TECHNICAL NOTE

44

THE MEASUREMENT OF DRAG FORCES IN LOW DENSITY FLOWS

by

J QJ . SMOLDEREN, J.F. WENDT,

J G NAVEAU

von KAR MAN INSTITUTE FOR FLUID DYNAMICS

TECHNICAL NOTE

44

THE MEASUREMENT OF DRAG FORCES IN LOW DENSITY FLOWS

by

J • J. SMOLDEREN, J.F. WENDT,

SUMMARY

A new technique to accurately measure low level forces and its application to the determination of drag coefficients in rarefied hypersonic flow are described. Preliminary results are presented for cylinders and spheres at M

=

8 in the transitional and near-free-molecule flow regimes.

i i

ACKNOWLEDGEMENTS

We gratefully acknow1edge the assistance rendered by two former

VKIFD students : Mr Horst Otto, now at D.F.L. Braunschweig ; and Mr Hubert

Legge, now at A.V.A. G~ttingen.

This research has been sponsored in part by the Air Force Office of Scientific Research through the European Office of Aerospace Research, OAR, United States Air Force under Grant AF EOAR 67-10 and others.

TABLE OF CONTENTS Summary Acknow1edgements Tab1e of content List of symbo1s List of figures Introduction Basic technique Experimenta1 arrangement Flow properties Ca1ibration procedure

Measurement of drag coefficient Ao Cylinder B. Sphere Conc1usions References Page i i i i i i iv v 1 2 3 5 6 7 8 9 10 10 iii

LIST OF SYMBOLS A B CD D F j Kn M n P pCb T V X p cr

,.

st (T) IJ projected area

magnetic field strength drag coefficient

orifice diameter. cylinder or sphere diameter force curren t dens i ty Knudsen number- À

It

Mach number number dens i ty pressure -12 pico-coulomb (10 Coulomb) period or temperature velocity

distance from orifice to point in question maas density

molecular diameter duration of transient

correction factor for molecular diameter

Subscripts

o

stagnation or reservoir condition

~ free stream condition w wall conditions

FoMo free molecule value o

v

LIST OF FIGURES

1 Block diagram of modulated flow system

2 Schematic of force probe

3 Drag coefficient for a cylinder 4 Drag coefficient for a sphere

Introduction

The major difficulty encountered in measuring drag forces under rarefied flow conditions is simply the low level of the forces in-volvedo This fa ct may be illustrated by the following example. The

max-imum useable mean free path in most existing low density wind tunnels is of order 1 cm. Thus, to meaaure drag coefficients well up into the near-free molecule regime (Kn~lO), model dimensions must be of order 1 mmo It can easi1y be shown that under room temperature stagnation conditions, the

3

forces experienced by such mode1s wi11 be of order 1 dyne (10 micrograms -5

force or 10 'Nt •. ) 0 Thus, 1 '7. measurements will require a measuring

sys-tem capable of exhibiting a sensitivity of order 10 micrograms.

The most sensitive balance in use today, to our knowledge, is the null-type beam balance at Berkeley (Refo 1). It has a least count

of 100 micrograms. A1though it is perhaps within the present stateoof-the-art to bui1d a microbalance having a sensitivity of the order desired, it wou1d certain1y be rather bu1ky, expensive, and delicate. Another

tech-nique which has provided considerab1e data on sphere drag up to the transi-tion regime emp10ys the measurement of the trajeetory of a freely falling sphere by means of a chopped photographic system (Ref. 2). It has the obvious advantage of providing a sting-free measurement, but at the expense of cOnsiderable data scatter, and no results, to our knowledge, have been obtained in the near-free molecule regime. In addition, magnetic suspen-sion systems appear to be most promising for fut ure work.

2

-Our approach to this problem has been to use a technique which is standard in high density short duration flaws - the ferroelectric

force transducer - but in such a way as to considerably increase its sen-sitivity. A preliminary discussion of the technique has been previously published. (Ref. 3)

The following sections describe the rationale behind the technique, the experimental arrangement, the calibration procedure, and preliminary results of measurements made to determine the drag coefficients of a cylinder and a sphere in the transitional and near-free molecule

regimes.

Basic Technigue

Force measurements with piezoelectric and ferroelectric materials are now standard practice. Their use in rarefied flows would normally not be considered, not only because of charge leakage problems, but also because of the low output level compared to other effects such as drift, pyroelectricity, etc. The best ferroelectric materials (barium titanate; lead zirconate titanate) exhibit a charge sensitivity of the order of 3 x 10-15 coulombs/dyne, while the sensitivity of piezoelectric materia1s,-such. as quartz, is at least an order of magnitude less. Charge amplifiers for such materials are commercially available and typica1ly

-12

yield a 100

mv

output signal per picocoulomb (10 coulomb) on the highest sensitivity range. The voltage sensitivity of a ferroelectri~ transducer plus charge amplifier would then be approximately 0.3 mV/dyne and thus the expected output voltage of such a system, under the rarefied flow conditions described in the above example, could be as small as 100 microvolts. To

perform accurate measurements with such a system, the level of stability required in measuring the voltage output would have to be of order 1 micro-volt.

- 3

-The abave consid~rations clearly indicate that a selective AC amplifier system must be used to reduce drift and background noise. Modulating the low level DC output signal from the transducer, which would normally require a vibrating capacitor-type electrometer because of tha high impedence levels dictated by the transducer, would not eliminate the drift and spurious effects inherent in the transducer itself. We believe that the problem can be solved by mechanically modulating the physical effect itself; namely, the force acting on the transducer; and then processing the resultant AC output with a lock-in amplifier tuned to he frequency of the mechanical modulator. The result of this approach wil1 not only e1im-inate noise in tbe electronic system such as 50 cyc1e pickuPD but a1so noise and drift occuring in the transducer itself. Tbe fina1 read-out provided by tbis metbod wi1l be proportional to tbe force acting on the transducer, and will in fact be the average va1ue of a large number of individua1 events.

Experimental Arrangement

The flow modu1ation technique was tested in the VKIFD low density wind tunnel (Ref. 4). This facility has a pumping speed of 20~000

-3

litres per second in the range of 1 to 5 x 10 Torr. A free jet expansion pravides a hypersonic low density flow. The test gas used in the work reported here was sir and the stagnation temperature was room temperature.

Tbe experimental arrangement is shown in Figure 1. A free jet emanates from a thin plate orifice with a diameter of 0.568 cm. The flow is periodica1ly interrupted by means of a rotating disc fitted with a window which ia p1aced immediately in front of the orifice. Thus, the

forces experieoced by a model placed d~stream have a square wave time dependence. The frequency of rotation was 15 cps. A Brush PZT-5 lead zir-conate· titanate ceramic transforms theAC applied force ioto an AC charge

output which is amplified and converted to an AC output voltage with a Kistler charge amplifier set at 50 mv/pCb. Further amplification with bandpass filtering is provided by a princeton Applied Research (P.A.R.) low noise preamplifier, Model CR-4. The basic structure of the desired signal can generally be distinguished on an 08cil10scope at this point, except under verylow level eonditions. The signal is then fed to a P.A.R. Model JB-6 loek-in amplifier. Aresolver direct1y coupled to the shaft of the rotating disc provides the necessary reference frequency. The 10ck-in

amplifier contains three major components - a tuned amplifier, a demodulator, and a low-pass filter. The input signa1 first enters the tuned amplifier, which uses a narrow band filtering device to reduce the input noise level,

thus preventing saturation or mixing effects. Next, the signal is processed by a phase sensitive demodulator triggered by the reference voltage. The output of the demodulator is proportional to the in-phase component of the signa~ and although this output wi1l be modulated to some extent by fre-quency components near the reference frefre-quency, these may be attenuated to any desired degree by the low-pass filter which effectively sets the over-all bandwidth of the amplifier. Naturover-ally, a narrower bandwidth, which may be obtained by increasing the time constant of the filter, means an increased response time. In our wind tunnel app1ications, time constants of 3 and 10 seconds are used. The voltage divider at the input of the lock-in amplifier is adjusted lock-in such a way as to keep the lock-input signal~ and hen ce the output signal~ constant, thus increasing the reading accuracy of the DC output scale, and, more important, eliminating any non-linearities in the amplifier itselfo

One criticism of the technique which may be raised is the fact that the force experienced by the model is not truly a square wave, because a finite time is needed for flow establishment. Tests with a hot-wire probe showed that the duration of the transient, which occured when

~ 5

-the flow was being established (while -the window is opening), corresponded almost exactly to the time necessary for the orifice to be completely ex-posed by the rotating disco The ratio of this transient time to the total "open" time, is less than 2 %0 On first consideration, it might be felt that the error caused by sueh transients would therefore be of the order of 2 %. However, the filter amplifier and demodulator system yields'an output very nearly proportional to the Fourier sine coefficient of the sig-nal and hence the influence of a transient of short duration occurring when the sine is vanishing may be shown to be of order

(~/T)2

times the influ-ence of a steady-state signal, ~ being the duration of each of the two transients occurring in each period To Thus the relative error due to the finite time required for flow establishment in our experiments is less than 0.1 1..

Flow Properties

Ashkenas and Sherman (Ref. 5) present the information needed to calculate the flow properties at any point in a free jet expansion on ce the effective nozzle diameter is knowo. The basic assumption in their analysis is that the flow is isentropic.

The effective diameter of the thin plate orifice was deter-mined by the sonie flow method. Stagnation pressures were measur.ed with a Texas Instruments Fused Quartz gauge having an absolute calibration accur-acy of

±

13 x 10.3 Torro Mass flow rates were measured with a set of Rota flowmeterso Within the range of stagnation pressures used in the tests

described below (1 Torr ~ p

!::

35 Torr), the effective orifice diameter

o

was found to be 00550 cm

±

00005. As a point of interest, the throat Reynolds

.., 6

-Tests were conducted to ascertain whether or not the rotating disc produced disturbances in the downstream flow. An internally chamfered 0.6 cm diameter impact pressure probe was used to measure the impact pres-sure distribution up to an X/D of almost 10. Stagnation prespres-sures·.were 10 and 50 Torr. Viscous effects on the probe were unimportant and it was found, af ter applying a small correction for shock displacement effects, that the measured impact pressures agreed with the isentropic values to within 1 - 2 %0 The conclusion is that the flow is not disturbed in the region of the centerline by the presence of the disco

A large settling chamber of 60 litre capacity was constructed to ensure that the fluctuations in s~agnation pressure d~to flow inter-ruptions would be negligibleo Pressure fluctuations are calculated to be less than 1/4 % of the measured stagnation pressure.

In summary, flow properties have been calculated on the bas~

is of Ashkenas and Shermanos method of characteristics solution for the free jet. Freezing effects are neglected although they may be important in the range of the lowest stagnation pressures employed.

Calibration Procedure

An electromagnetic device is used to calibrate the transduc-er. A wire loop is rigidly mounted on the sting of the transducer and a straight well-defined portion of the wire is placed in the airgap of a cal-ibrated permanent magnet. An accurately calculated AC current is passed through the wire loop and thus the resultant j x B force acting on the transducer may be calculated with precision. This technique simulates the actual loading experienced by the transducer in the modulated stream and the output signal is, of course, processed by the same electronic system used in the wind tunnel measurementso When suitable precautions are taken

7

-regarding externa1 vlbrations and power 1ine pickup, readings may be ob-tained wlth a stabllity of

±

1 ~ at force levels down to 50 microgramso Measurements of Dras Coefficients

The modulated force transducer was employed to measure the forces acting on a cylinder and a sphere located at a particu1ar position ln a rarefled hypersonicftee jet. The drag coefficient for each model was then ca1culated as a function of 10ca1 Knudsen number using the definition

= F net

where A is the projected area of the model. Since the mode1s were sting-supported, a tare measurement was performed to account for the sting drag. Thus F 1. the net force acting on the model. It shou1d be noted that

net

with the stagnation temperature fixed, the flow properties at any point in the free jet are a function on1y of the stagnation pressure. Therefore, the experimental procedure was to measure the De output of the loek-in amplifier system as a function of stagnation pressure and then to use the calibration results to convert the DC output readings to an app1ied force.

The Knudsen number used as a corre1ation parameter in this work is ,based on the following deflnition of the loca1 mean free path :

where

W~2

is the hard sphere cross section and12J" (T) is a correct ion fac-tor accounting for deviations from hard sphere behavior. Va1ues for the correction factor. which is based on the,Lennard-Jones (6-12) potential,

- 8 ~

are tabulated as a function of temperature (Ref. 6).

A. Cylinder

The drag coefficient of a cylinder was determined using the modulated force technique and a knowledge of the expected local density and stream velocity. The location of the cylinder was at an X/D of 10.4 and thus the corresponding local Mach number was 8.8. Cylinder length was 1.02 cm and diameter was 0.10 cm. Stagnation pressures varied from 0.85 Torr to 35 Torr . Forces on the model af ter correction for the sting support ranged from 30 milligrams down to 1.2 milligrams. The sting cor-rection varied from 8 to 15

1.

of the total force (model plus sting). The results are plotted in Figure 3 in the form of CD versus Kn.

Two main points may be noted from the results. The most im-portant, from our point of view, is the relatively.small amount of scatter exhibited by the data. This appears to substantiate our hopes regarding the sensitivity of the modulation technique. The second point is that the data appears to approach the free molecule value for diffuse reflection, but then abruptly veers upward. It appears likely that this effect is

cau.ed by the large thickness of the terminal shock wave which could there-fore be felt far upstreamo This has been substantiated by recent electron beam measurements (Ref. 7). The characteristics of our pumping system are such that the terminal shock will move forward as the stagnation pressure is decreased (and hence as the Knudsen number is increased). At aoy rate, the data to the right of the cross-hatched line cannot be considered sig

-nificant. It is shown here for the sake of completeness and also as a warning to other experimenters who might use the free jet for similar aero~ dynamic testing purposes.

9

-The data of Tang (Ref. 8) is also shown in Figure 3. That the agreement is rather poor should not be taken as a criticism of either work, but is due to the fact that TangOs Knudsen number is formulated in a different manner than ours and we have not been able to obtain the data to which he refers.

B. Sphere

The drag coefficient of a sphere was determined using the modulated flow technique, together with calculated values for the free stream propertieso The sphere was located at an X/D = 9.1 and the corres-ponding Mach number was 8.3. Stagnation pressures varied from 26 Torr to 1.1 Torr. The forces acting on the model, af ter correcting for the sting effect, ranged from 5.9 milligrams to 0.35 milligrams. The sting correc-tion varied from 13 to 20 % of the total force. Results are shown in Figure 4 in the form of CD versus Kn.

Again, as in the case of the cylinder measurements, the scatter is seen to be reasonably sma1l. The inf1uence of the downstream shock is also again clearly seen, and the data to the right of the cross-hatched line should not be considered significant.

Our sphere data is compared with that of Kinslow and Potter (Ref. 2) in Figure 5. Note that the abscissa is now taken as the free stream Knudsen number based on a hard sphere model in order to use their results direetly. Only our data to the left of the cross-hatched 11ne is shown here. It wi11 be noted that the two sets of data show reasonable agreement. The reduced seatter in our data eompared to that of Kinslow and Potter, appears to speak well for the modulation teehnique.

~ 10

-Conclusions

It has been shown that by modulating a physical effect of interest, in this case the force applied to a model in a rarefied flow~

and by treating the output signal with a tuned amplifier plus a phase-sensitive demodulator system, the signal of interest can be recovered cleanly as a result of the strong rejection of the spurious signals in

the source itself. In fact, each data point recorded is essentially a long-time average of thousands of individual experiments •

The fact that the scatter in the final data is small suggests that the basic concept is sound o It remains ncw to optimize the flow

conditions, if possible, to allow measurements to be made throughout the

near-free molecule regime without suffering from the influence of the

downstream shock. Future research wil1 concentrate on higher stagnation temperatures in order to obtain data of more practical interest; namely, in the hypersonic cold wall regime.

References

1. Goj. MASLACH and RoN. LATZ Force Measurements in Lew Density

Hyper-sonic Air Flowso Advances in Vacuum Science and Technology

Pergamon Press, New York, 1960, Volo 11, pp 809-8120 2. Mo KINSLOW and JoLo POTTER The drag of Spheres in Rarefied

Hyper-velocity Flowo AEDC-TDR-62-20S, December 1962.

30 JoJ. SMOLDEREN Modulation Techniques for Measurements in Low Density

Hypersonic Wind Tunnels. Presented at 22nd Semi-annual SoToA. Meeting, VKIFD, Rhode-Saint-Genèse, Belgium, Septem~

ber 24-25, 1964.

4. J.J. SMOLDEREN and J. NAVEAU The VKIFD Low Density Wind Tunnel. The Fluid Dynamic Aspects of Space Flight, AGARDograph 87, Gordon and Breach, New York, 1966, Vol. I, pp 127-137.

- 11

-5. Ho ASHKENAS and FoS. SHERMAN The Structure and Utilization of Super-sonic Free Jets in Low Density Wind Tunnels. Rarefied Gas Dynamics - Supplement 3, Ed o JoHo de LEEUW, Academie Prees, New York, 1966, Vol. 11 pp 84-105.

6. J.O. HIRSCHFELDER, C.F. CURTlSS, and R.B. BlRD Mo1ecu1ar Theory of Gases and Liquids. John Wiley and Sons, Inc., New York, 1954. 7. P.V. MARRONE Rotational Temperature and Density Measurements in

Underexpanded Jets and Shock Waves Using an Electron Beam Probe. U .T.I.A.S. Re,port N° 113, April 1966.

8. S.S. TANG Cylinder Drag in the Hypersonic Free Jets of a Rarefied Air Stream. Univo of California Report AS-64-3, January

THIN PLATE ORIF/CE

(

fREE JET CHARGE LOW NOISE

[

MODEL AMPLIFIER AMPLIFIER

~TRATDUCER_r

.--_1

___

_

~SOLVER

~TA TlNG OISC

Figure

1 BLOCK DIAGRAM

VOLTAGE DIVIDER

T

LoeK-IN AMPLIFIER

I

BNC CONNECTOR PLEXIGLASS _{,..-_._}

-\ BRASS LoeK NUT

-"\ -

-\ \, FERR_o7t~CTRIC TRANSDUCER PLEXIGLASS 50 OlMENSIONS IN mm 5 TING SHIELD 9° 37 . ---_.

__

._-_._---_.

__

. ~

Figure 2

SCHEMATIC OF FORCE PROBE

j1 0.41 SPHERE; 1.60

-r-

\

Co

3.2

3.1

M = 8.8

3.0

T

_o

=

301

oK

2.9

2.8

2.1

2.6

2.5

2.4

2.3

_r

-0.5

0.6

0.8

1.0

Figure

3

El [!] 1.5 2.0

3.0

Kn

REG/ON OF SHOCK /NTERACT/ON El EI FREE MOLECULE VALUE ~=~ El 8 El I!l m DATA OF TANG (964) M = 9.85

4.0

6.0 ·8,0 10

3.1 3.0

~

M = 8.3 T

_o

=

298

oK

2.9

L

\

_,

REG/ON ( OF SHOCK 2.8

t

.( INTER~CTlON

Co

2.7

)

~

FREE MOLECULE

---VALUE T

_w

=T

_o

~ /

2.6

2.5

2.4

2.3

2.2

0.3

0.4

0.6

0.8

1.0

1.5

2.0

3.0

4.0

6.0

8.0

Kn

.

Figure 4

1.0 1 0 10

t-

e

e 0.9

_l-

_x l!l 0 x G x x

Co

t

Xx _~ G x (!J x

Co

(!) _x F.M. 0.8 Xx MaJ Tw/Ta, I- Ij x _x Xx ₀ PRESENT WORK 8.3 15 x

I-

(!) (!) x x KINSLOW- POTTER 70.7 2.3 0.7

!!Ix xx x !!I KINSLOW- POTTER 10.7 4-.0

x x l- _{x x x} 0.6 ) x 0.1 0.15 0.2 0.3 0.4- 0.6 0.8 1.0 1.5 2.0 3.0 4.0 5.0

Kn

(BASED ON HA RD SPHERE)