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TECHNICAT. RffipnflT

Velocity Loss Jfeasuremanfcs •.-«~-«~-,._ „. -.,«*.. — «g«M m a Shock Tube 'by * " "

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VELOCITY EOSS MEASUREMENTS ON SHOCKS IN A SHOCK TUBE

by

~ R-r-<J. jgmrich.

Princeton University and Lehigh University

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. In the shock tube developed at Princeton x~' as an instrument for

• the study of transient fluid dynamics, the determination of incident plane

shock conditions is accomplished through a knowledge of the temperature

and pressure of the undisturbed air and the incident velocity of the shock.

The incident velocity is measured by-timing the transit of the shock be-

tween two stations in the tube preceding the point under study. While a

simple theory öf flow in the tube indicates that the shock proceeds, through

the tube with a constant velocity for a time, it is to be expected that

d-issipative effects operate to cause ä -gradual decrease in the shock

strength and velocity^ ~ The" presently reported: work was undertaken to

measure the amount by which the shock velocity decreases in its travel

through-the tube...

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Ai APPARATUS AND METHOD

1. Shock tube. A shock tube 15 cm in diameter- and 10 meters

long was used in this study' '. The 1Q meter tube, which is sketched in

Fig. 1,. consisted of a 1 meter long compression chamber and a 9 meter

^^pansifln^chamber..—Jjhsse--two-chambers~ware" Jöckea togethei*, by a rembv-

able clamp, with a cellophane diaphragm held between them» Air -was pumped

1. Walker Blcakney, «Shock Waves in a Tube», Phys..Rev, 6?_, 678 (l946)

2. The shock tube, was designed'^, erected by W. T. Read and G. T. Reynolds

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into the compression .chamber at pressures up to several atmospheres,, and

the cellophane diaphragm ruptured with an internal knife. I4 this, as in

other shock tubes, the bursting d5.aphragm releases the high pressure gas-

from the compression chamber into the expansion chamber,, the resulting

flow in the expansion chamber consisting of a shock vhich moves into the

undisturbed gas and a mass motion of the air behind the shock away from

the compression chamber.

The -.expansion chamber of the tube .was constructed of 1/4" wall

brass tubing made in 6 ft. sections bolted, together by flanges -with rub-

ber sealing gaskets. Two of the sections were- fitted with, two pairs of

window ports each, arranged in such a way that a horizontally directed

light beam-passed diametrically through the tube at each of the four- pairs-

of windows. These light beams were used to detect the arrival of the shock

a% the four successive positions as described in. the following section:.

Each window port consisted of a window support :holder soldered

to the cut-away tube wall, a window support .one inch in diameter with a

3fiM X--.3/Ö" ffiiiled slot which fitted into and was fastened to the support

holder,.and a thin circle of plate glass cemented over the slot in the

window suppörti The inside surface of the shock tube was thus distorted

only by a flat 1" diameter recess^ tangent to the tube surface.

The compression chamber was similarly constructed of a shorter

r§ection-öfr brass tubingand pj'ovideA with, .a- valve-to -odrn&fe high; presöüj?"»'

air and d manometer connection-..

Möröury-ih^glass thermometers were affixed to the tube at three

positions? -the thermometer bulbs were immersed in mercury contained In

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steel blocks bolted tq the tube flanges. These inäd'e it possible to check

on the uniformity of temperature of the gas in the tube. The extreme end

of the expansion chamber was open to the atmosphere -whose pressure and

relative humidity wore frequently recorded. After each shot, air was blown

through the tube to remove the fragments of the burst cellophane diaphragmj

this also -assured that the humidity of the air -in. the expansion chamber

was that recorded outside-.

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2. Optical-electronic detection „of. shock. The optical arrange**

merit for detecting, the passage; of the shock at any one of she four positions

in the tube -is shown in Fig. 2, approximately to scale. light from the in- .

candescent filament is prevented from reaching the phototube, when there

is no optical disturbance in. "the shock -tubes, by three parallel knife edges

adjusted to> all meet a single hypothetical plane perpendicular to the tube

axis, i. e., parallel to the shock front.

As indicated in. the diagrammatic- sketch of Figs % which is not

to scale, the -two knife edges nearest the light source limit the light

entering the shock tube to-rays slanting slightly toward the direction of

shock travel. Until the arrival of the shock, these rays strike the third

knife edge and do not reach the phototube- But when the shock enters this

region, the rays are totally refJected by the shock which may be thought

~or äs ä""sürTäöö"äf discontinuity in optical density. The reflected rays

are directed slanting, back from the direction of :shock, travel, and', missing

the third knife edge., fall on the phototube f

It is assumed in the foregoing description, that the light is

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propagated in accordance with geometrical optics, and that the shock repre-

sents a plane surface of optical discontinuity between- two homogeneous

media of constant index of refraction. There is no; doubt that, under the

extremely small angles of deviation which are of interest in the arrange-

ment used; (about l/lO degree), geometrical optics is a poor approximation.

Diffraction effects are of appreciable magnitude as can both be demon-?-

(3) sträted theoretically^' and be observed visually. As to whether the

shock front is a true plane surface of optical discontinuity to the extend-

assumed, there is no evidence, except that we have observed' the increase

of light on the phototube to- be usually in accordance with the predictions.

of this assumption.

The calculation of the rate at which light is reflected to the

phototube" as the' shock moves past the knife eclgee is readily, made when -ray

optics are used. • The result is that, until other eageg. than, the knife

edges limit the rays, the light flux reflected to.the rhötotube-ispröporff

tional to the distance. the, shock travels beyond the knife .edges.. We have

made no attempt to calculate the relationship between reflected light flux

and shock travel by diffraction theory, nor have we calculated the effects

of errors in adjusting the knife edges to strict parallelism.

^

3. With a line source at the first knife edge, diffraction theory shows, that the first maximum__o.f ijrrtensity. .of -the -diffraction pattern Tjf the

" secondläiife edge at the third knife edge is about 0*02 inch from the geometrical shadow,. This corresponds to the distance the shack moves

• -in about oho- microsecond, and the reflection of all rays meeting the shock fro&t. at a grazing angle of less1 than about l/lO degree.

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In these experiments., the phototube used to detect, the changes

in light admitted past the knife edges on passage of the shock was. a type

931Ä. A conventional amplifier using high transconductance tubes with low

load resistances to preserve -6he shape -of the phototube signpl transmitted

the signal by cable to a central station. There the signals from all four

of the detection stations were applied to the deflecting plates of a cath- c

öde-ray oscilloscope -tube by means of a mixing stage.

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3. Distance and time interval.measurements The distances be-

' tween detection stations along the tube (see Fig. l) were determined with

an accuracy,of better than 0*01 percent by cäthetometöirSettings on the

knife edges. The distances remained unchanged during the course of the.se

experiments^ except that half of the measurements were made with the de«?

tection stations in the positions shown, in Fig, 1 and half were made with

both shock tube sections fitted with windows at the extreme end of the tubej

the- distances between knife edges were measured for each of these arrange-.

raents independently.

Time intervals between transits were measured with ä moving film

camera photographing ä cathode-ray osci-llescppe.. -Ä somewhat unusual com-

bination of oscilloscope spot deflection relative to the motion of the

film in the corners, permitted a 20-fold increase in accuracy ^f tine ..intern

val moasurementfor a given film velocity. This is accomplished, at the

"riblT6f~obtaining about 5% of the measurements with, only a lOffold in-

crease- in accuracy, by sweeping the oscilloscope spot back and forth in

a line perpendicular to the direction of film motion and' imposing the

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trar^i-t-^m^Icing pulses to deflect the oscilloscope spot, in thg same direc-

tion as the film, motion.

An example of a record obtained with the apparatus is shown in

Pig. 4-i In this figure, the> horizontal .deflection of the spot is a con-

tinuous motion from left to right for precisely 50 p sec followed by motion

from right to left for 50 \L sebj the vertical deflection of the spot con-

sists p? timing pips 5 .jt sec apart with the trahsi*Tmarking pulses supers

posed. Th© resulting record is spread put vertically due to the film

motion in the. camera. It may be noticed that timing pips occur at the ex-

treme ends of the horizontal sweep. The transit-marking pulses are easily

discerniblej the time Separation between them is measured by counting, the .

number of complete horizontal sweeps between them, corresponding to 100

jx sec each, and measuring the fraction of a swgep at each end of the inter-

val in "terms of the 5 n sec pips. On the original 35 mm f ilia record the

intersection of the linear beginning of the transit^märking pulse, with the

sweep base line can be estimated under a jjjagnlfyahg glass to x/ithin 1 V- sect

and with ä traveling micr^scppe_ cj® bj^ "'When.""""

a transit-marking pulse occurs within a few microseconds of the ends of

the, horizontal sweep, it's measurement is not possible to as high an acr

curacy due to the slightly rounded corners of the horizontal sweep wjavoform..

The time^control of the sweep and the timing pips were obtained

-frojj- a-AOO-KG crystal eohtr-'oliea seJoMary frTaqiuency standards A 10 KG

sinusoidal signal derived from the 100 KC standard .frequency was used to

synchronize- a .10'-KC multivibrator at a slightly variable phase; this raultif

vibrator was also provided with a control to vary sJLightly the relative.

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duration of the two halves of its cycle. Hie resulting wave form, was,

clipped to produce a square, wave- which in turn was introduced to a rela-?

tiyely low time-constant filter to produce the waveform desired for the

horizontal sweep. The two adjustments mentioned above provided the means

to synchronize the sweep with the timing pulses in. such ä way as to bring

timing, pulses at the exact ends of the sweep;

A Dumönt type 5QP .cathode-ray tube with a special low persistence

zinc oxide screen was used with 500Ö volts on the intensivier. This was

photographed with an f/l.9 lens- in ä General Radio moving, film camera modi-

fied by replacing; the film spools with pulleys to permit ä cemented-to-

gether endless belt öf film .87 cm in length to run in the camera* The in-

tensity grid of the cathode ray tube was maintained at a high negative

bias except for a 90 millisecond interval when the bias was reduced nearly

to zero= for a single exposure of the endless strip of film in the camera.

The 90 millisecond rectangular pulse applied to the. cäthode-ray tube in-

tensity grid was initiated by the passage of the shock over a contactor

placed near the diaphragm in the expansion chamber of the shock tube..

B. IffiAvSUREIOTTS. OF DECREASE OF SHOCK WLß'CITS

Various shock strengths are produced in the shock tube by varying

the pressure in the compression chamber before rupturing the diaphragm. In

the present experiments, shock strengths- from as small as could be detected«-

by the optical-electronic pickups to over 10 times the smallest were

studied by adjusting the^ pre-rupture compression chamber pressure to six

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certain values ^and timing the transits of the resulting shocks over the

four stations .arranged as in Fig, I* The velocity of most of the shocks

was found to decrease^ with travel through the tube, but some of the weakest,

shocks were found to be moving faster at the. further end- of the, tube than

at the. end; nearest the diaphragm. This anamolous result was presumed to be

associated with the mode of formation of the shock upon diaphragm rupture-,

and all the velocity measurements were repeated with the four detection

station^ located at the further end of the tube. These measurements showed

that shocks of all strengths studied decreased in velocity with travel.

The distance and time, measurements are~recorded in Table f of the

appendix, along with- temperature and humidity measurements* From' these,

measurements, the fractional loss in velocity per meter of travel was calc

culated and the values are represented graphically for various pre^rupture

(3) compression chamber pressures in Fig. jj* The vertical intervals plotted

about each of the average values include all the measurements made at each

initial pressure.

With each of the six pre.-rupturo compression chamber pressures.*

and with the detection stations in each of the two .arrangements,, five or

more measurements of shock transit times were made. With the same initial

conditions', which resulted in. the sane shock velocity to within one. per ceiit,

the- •decrease in velocity over the interval varies from shot to shot by just

about the same amountas_the: .avenge--decrcass-i^self." While the decrease

in velocity over the interval was quite small - of the order .of one percent

3. Rressuros plotted in Pig. 5 are gauge pressures, ia, -e,, pressure excess' over atmospheric.

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of the velocity - it was, except for the -weakest shocks, more than ten times

the estimated maximüs- error of measurement; it is" believed that there was

possibly a real, variation: in the amount by which a shock of a given strength

decreased in velocity«

C. ©KTEEPRETATION ;ÖF VELOCITY LOSS DATA

m TERMS. OP DECREASE IF SHOCK STRENGTH

A normal shock traveling into undisturbed* gas can be described in

terms of the pressures* and densities on each side of the shock, the gas

velocity behind the .shock, and the propagation velocity of the shock. These

quantities satisfy the Rankine-Hugohiot relations4.-.which, for an ideal gas-,

yield ths relation'

V2

7-^* (1)

*faece-*--fe ^propagation velocity of shock

Y is -ratio of specific heats of gas

a = ^Y pl^i is sound velocity in undisturbed gas

Z =: ^ "Pi

is-shock strength, i» e#, the fractional increase

value in the ^undisturbed gas.

^ Thus, the Jaock strength , is ^louiabl, if ^,. a, and,Y arc to^,

and the measuröments of the decrease in V with travel Mj-aW^.

-y bp represents in terms of .decrease in shock strength with travel.

4. See, e. §-,, Liepnanb and Puckett, "Introduction to Aerodynamics of Compressible. Fluid", page 4.0,. Wiley 1947

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1. Seasurement .of Sound Velocity. While the. velocity of sound

in air has been- measured by many observers using quite different methods,.

(5) the values published differ by more- than the experimental -errors . In

-addition, the corrections to be applied for variations in the composition

of the air are somewhat indefinite. It was relatively simple, with the

apparatus for measuring shock velocities already at :hand-,. to measure sound

velocity in the air in the shock tube directly.. From' this measurement,

small variations in temperature and humidity could be allowed for in cpm-

-put-ing. sound velocity.

The, measurement of sound, velocity was made by placing a steel

plate in pläc'"! of the' cellophane diaphragm at the one end of the expan-

sioS"5hamber to act äs a reflector, and ä microphone composed of a 2 inch

diameter tourmaline crystal at the other end. Inside the tube, about

1,5 meters, from the microphone, a feeble spark generated a sound pulse

which was detected by the microphone first after reaching,it directly and

second after reflection from the closed end of the tube 8.419 meters dis-

tant from the spark. The time interval between the arrival of the direct

and reflected- pulses was determined by applying the microphone signals to

the oscilloscope photographed by the moving film camera.

In-^irrat 25.5°C and ol- 55% relative humidity, the measured

value ^f .sound, velocity was- 347«4 m/secv . -" —~

5. Alexander Wood, "Acoustics'", p. 262, Blackie, 194.0.

6S This measurement when ad'j,usted: for temperature and- humidity by the

Regnault formula quoted by Wood, p., 250, gives 33Q.4 m/seq for sound velocity in dry air at'0°G.

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gy . Decrease,.in shock strength,with travel. Since the measure-

ments showed that shocks of a1 given strength- decreased in velocity by

variable amounts even when the conditions of the tube and gas within the

tube were the same, it- is only feasible to derive the average decrease shock strength with travel. in

shock strength, zs '

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Differentiating, equation (2) withrespect/to> the position coordinate x,

we; have for average conditions pertaining during the measurements.

,dz _ 7 V dfr _ 7 V2 . 1 dj __ 7 V2

dx 3 a2 dx 3 a2 V dx " 3 a5"

and the average- fractional decrease in shock strength per meter of travel

z dx 1r— a

k,. the. quantity plotted' in Pig., 5» is the fractional (decrease in velocity V of the shock per meter. -

In 3-able II of the* appendix, the average values of the shock

velocity, sound velocity, arid percent loss: of shock velocity per meter

are tabulated,- the averages computed over the measurements taken with a

j$ven prerEupJ;ur-e„coape^ and arrangement- of detection

stations^ the average sound velocity at each set of conditions has been

obtained by adjusting the measured value at 25.-5-C- and 55% humidity by

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the ftegnault .formulav ,/ for average conditions of temperature and humidity

prevailing; during the measurements1,, From these average values, the aver-

age shock strength- has been computed 'by means of equation (2). and the"

fractional decrease in, shock strength per meter has been computed from

equation (3). In Fig. 6, the latter of these two derived quantities is

presented graphically as a function of the- formerf the. vertical intervals

&\ this graph represent the variation in. the measured decrease in shock velocity*

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From Fig. 6 it is seen that shocks decreased in strength by less

than 2 percent pea?,meter ofjb-ayeit^. and. that, on the average, shocks of

all strengths studied beyond 7 meters fron the diaphragm decreased at the

•rate of around 0,5"percent per ineter of travel.

Comparing tae measurements over the longer distance interval with

those over the shortert it appears that the weakest: shocks increased in

strength at- first and then decreased with travel over the longer interval*

whereas the strongest shocks decreased in strength more rapidly at the be-

ginning than at the end of the longer interval. Shocks of one intermediate

strength (z = 0,/f) seemed to lose strength at ä unj'forarrate, and thpsfj,

furthermore, showed' lesT^är'iatiöhrljrthe measured' velocity loss over both

the 5_.3-J5nd-4-=>0 •aaeter'^intervals l>han"did shocks of either greater or less

strength. An interpretation of these observations may be connected with

7. See footnote 6.

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N- ®3:Äöäe'-gt~formation -of the shock after diaphragm rupture;. A further

ffiilöus.sj in ,of the results follows«.

1. 'Attempts to find source of variations in shock strength.

Since there were, during the time occupied in performing these measurements,

variations in temperature., humidityp .and pressure of the ail* into which the

shock moved, a correlation between the velocity loss and these variables

has been sought. No such correlation lias .been found-, and in fact, several

examples of large differences i'i velocity loss with no variation in the

condition of the undisturbed air may be selected.

An increase in shock1 velocity .over the interval* such as' observed,

with the weakest shocks, can. be' pictured as ä set of one or more shocks,,

less' intense than: the main shock and following behind, eventually coales-

cing with and strengthening the main shock* Such -weak "secondary shocks

might be detects« by the optical-olpetsönic stations.! however, none was

ever recorded* It is not to be expected that secondary shocks would be

recorded in the case of the weakest main shock, because the strength of

these main shocks was at just about the limit of the detectors. In the

case of the stronger main shocks where secondary shocks .would, be capable

of detection* the failure to record any may indicate that any such had ai-

ready coalesced with the main shock' before reaching the first detection.

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8. The strongest shocks appear to have decreased in strength more rapidly near ibhe beginning of the 5.5 meter interval than near the end. This could -be accounted for by rarefaction waves following behind and coalescing with the main shock} rarefaction waves would not be detected by the, optical^electrohie pickups. -- -

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The sources of secondary shoo.1' mentioned' in the preceding parä-

.graph' might be. either of the following:

(X) Reflections from the sides of the shock tube of the initial

curved wave, front -.öf the disturbance'. The cellophane dia-

phragm bulged under the pre-rupture- compression chamber

pressure, so that even if it burst in a negligibly short

time, the escaping gas' had- an initially curved front. The

possibility that the diaphragm when punctured at its center

released' the gas near the center before that near the edges

cannot, be overlooked.

(2) Nrti-simultaneous rupture of multiple layers of cellophane

used as -diaphragm for the higher pressures. For the two

losest pressure's, used, only a single thickness of cellophane

constituted the.diaphragm,-and for the two intermediate pres-

sures, two? thicknesses sufficed, while for the two highest

pressures 4- and 6 thicknesses were needed. It is possible

that the knife merely punctured the first sheet of the multi*

pie layers and the pressure exerted oh the remaining sheets

caused thom; to- rupture in succession, sending a train, of com-

pression or shock waves into the expansion chamber.

The second'of these possible- sources of secondary disturbance 'has,

it is feltfcjbeon .eliminated- ä-s a -major-source of' variability by a set of

subsidiary measurements with diaphragm materials other than the usual cello-

phane,, and with multiple shoots of cellophane us,ed when one. would- withstand

the pressure,* No effect of the multiplicity of the diaph>agin on. the shock

.velocity or the, amount of decrease was noted within thcr variations which

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occurred faith a single diaphragm, as indeed, is evidenced further by the

nain set cjf measurements whore singl§ sheets- of cellophane at the lower1'

pressures, were not associated with variations less than were multiple lay-

er's at the higher pressures.

The iapst probable source of variation in shock strength and

amount of decrease in shock strength is thus believed to be associated with

tho pro-rupture shape of the diaphragn and the Banner- in which the. gas is

permitted to escape fron the compression phsaber,

2. Persistent decrease- ill shock strength. Aside from the in-

creases ,and decreases in shock strength as secondary disturbances associated

.with- diaphragn rupture coalesce with the nain shock, there appears to be a

decrease in shock strength öf about 0^5 percent per neter which persists

with continued travel through the tube* The sources of this dissipation are.

possibly shall disturbances continuously produced at the wall of the tube

where the gas moving through the tube behind the shock meets irregularities.

These disturbances would consist of small rarefactions which would be con-,

tinually traveling in the air behind the nain shock toward tho main shock

and decreasing its strength as: they -coalesce with it. Further experiments

with :shock tubes, of different size, and with varying roughness of the walls

are needed to. support this explanation.

The measurements described herein wore performed at Princeton

ohi.vor.sity in the summer of 194-7';by F.- J3. Harrison and. the. author* She-

stlmulation andr support of the work by W» Bleakney, G. T* Reynolds, asd

.A,- Taub' is appreciated. .

IX*

c APPENDS

C

Distance and time measurements for -shocks of various strengths

appear in Table I. The four detection stations are numbered 1, 2, 3> and

4, in the order öf increasing distance from the shook tube diaphragm, The

symbols used in the table have the .following meanings:

P - compression chamber gauge pressure before diaphragm rupture

Sg'-S^, etc. r distances between detection stations

t2-tvjf,. etö. - time intervals between teansit3

At = (t,-t„)t - (tp-t^) - difference in time of travel over nearly - - equal distances, at two places in shock

tube

H - relative "Humidity

f *• temperature of shock tube near first detection~station

AT ^ temperature hear first detection station minus temperature1

near third detection station

At* r> adjusted average value of At to, represent difference in. time, of travel over equal distances of 0,-761& m a* the two places in shock tube and to take into account tem- perature variation along tube as follows:

For a normal shock ^ , IP = a 11 + ^— zj, where V is

shock velocity, ä is. sound velocity, Y is> ratio of heat

capacities, z = (p^-pO/p., is shock strength, ,i». §•>.

fractional increase in pressure behind shock over that, inv

front of shock. Using y - 1.4- for air, W ^ a 11 + 7} •?').»

z, in these experiments ranges from 0^05 to ^.7.». asd. It

thus ranges between 1*00 a arid 1.27 a. Variations in

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1

c Appendix Page 2

temperature .of the; air in the tube lead to VITHP+W 4 ^^ ^ x.aa TO variations- in accordance with.

ä = ^, where R is the gas constant and T Kelvin temperature, Thus,

ä*A = AT/2T -which is at the mpst 0.05- percent. a* **<* on # of '

the small average measured differences in temperature at the two posi-

tions is, subtracted frpm the average pf the „r^ values of At for ä

given. Pc and arrangement of detection stations. • i

k = At* fs'i-S^Ui "i»t'? : " fractional loss in velocity _pf

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