C.P. No. 1019

MINISTRY OF TECHNOLOGY

AERONAUTICAL RESEARCH COUNCIL

CURRENT PAPERS

On the Driver-Reservoir Technique

Part 1 Application to Shock and Gun Tunnels

BY

1. Davies and K. Dolman

Part 2 Determination of Optimum Reservoir Size

BY

1. Davies, D. R. Brown and G. Hooper

LONDON: HER MAJESTY’S STATIONERY OFFICE

1968

TEN SHILLINGS NET

C.P. No. 10190

January I%8

On the Driver-Reservoir Technique

Partl- Application to Shock and Gun Tunnels

By L. Davies and K. Dolman

SUMMARY

The driver-reservoir technique, first proposed by Henshdl et al, is of interest to shook tunnel users because of its promise of an increase in running time. The most usual form of termination of running time in the shock tunnel is by the arrival, at. the end plate, of the head of the rarefaction wave which results from the rupture of the main diaphragm. In the driver-reservoir technique, the head of the rarefaction wave interacts with a perforated plate, at the end of the high pressure chamber, which separates this chamber from a larger diameter vessel called the reservoir. Under certain conditions this results in no waves propagating downstream except Mach waves. The head of the expansion wave has therefore been effectively eliminated and this will result in an increasein running time.

In this paper an account of the driver-reservoir technique is given, together with various theoretical analyses. A simple model is proposed which describes the wave processes within the reservoir, and the increase in inning time to be expected from various Sizes of reservoir. Prom this model

r. it is shown that the most important reservoir dimension is the diameter. Experiments from the NPL 2 in. shock tunnel are presented, and the application of the technique to gun tunnels is discussed.

List of Contents

1. Introduction .* . . . . .D 0s . . . . . . . .

2. Theory . . . . .* . . . . -. . . . . .* . . 2.1 Analysis of driver-reservoir technique . . . . . . 2.2 The increase XI running time obtained using the

driver reservoir . . . . .* . . . . . . . . 2.3 Application of the'driver-resemoir technique to

gun-tunnel operation . . DD -. . . . . . .

3. Experxmental Work . . *. sD . . .* . . . . . . 3.1 Shock-tunnel details *. . . . . . . . . . .

c 3.2 Shock-tunnel tests with helium as driver and nitrogen as test gss .e . . . . m. . . .D 0. o.

. .

. .

.s

. .

. .

. .

. .

. . 3.3 Shook-tunnel tests with nitrogen as driver and test gas

4. Conclusions *. . . .* *. 0s *. .* . . . . . .

Acknowledgements 0e 0s 0e 00 .* 0e .* . . . .

References .* 0a sO .* DD oD 00 .* . . . .

w

3

4 4

a

10

11 II

11 12

12

12

13 .

Nomenclature/

l Replaces NFL Aero Reports 1226, 1255 (A.R.C.28 957, 29 857) I

-2-

Nomenclature

A

Ac

An

At

a

*u

a

a*

L

L'

M

JJi

%

53

4

m

P

piJ

P;u/P&

P3s'%

pe

T

Te

cross-sectional area of reservoir

cross-seotional area of channel of shook tunnel

shock-tunnel nozzle throat area

area of hole(s) in perforated plate

diameter of driver and channel of shook tunnel

diameter of gun-tunnel nossle throat

length of driver seotion of shook tunnel

length of driven section of shook tunnel

u/a, &oh number

Maoh number a? flow in reservoir, see Fig. 6

Mach number of primary shock which produces 'crossover' oonditions, see Fig. 4

prin!ary shook Maoh number

primarg shock &oh number for tailored operation

molecular weight

pressure

Pi/Pj

pressure ratio across an unsteady expansim

pressure ratio across a steady expansion

equilibrium pressure in reservoir of gun tunnel

temperature

equilibrium temperature in reservoir af gun tunnel

.

.

.

-3-

time

u /a 3. 3

flow velocity

volume of driver reservoir

(Y + l)/(Y - 1)

0 /o P v' speoifio heat ratio

ratio of A t/O

A

area ratio for 'crossover' conditions shown in Fig. 4

area ratio defined by equation II

area ratio which produces no downstream running waves exoept Mach waves

t

'ij

U

v

a

Y

6

%

6'

%DE.AL

Subscripts

1 ,2,3,4 refer to regions shown in Fig. 1 i 39 aonditions produced *or095 a steady expansion

3u oonditions prcduoed across an unsteady expansion

1. Introduction

The extreme brevity af the available testing time in shook tunnels m&es the task of taking measurements of the flow very difficult. Transducers have to be capable of sub-millisecond response and yet be sensitive enough to make measurements, for example, of pressures in the millimeter Hg range. Any technique which will increase the duration of testing time whilst maintaining the integrib of the working-section flow is therefore of great importanoe.

.F

One such technique has been propceed by Henshell et al'. The basis of this m66hcd is that a vessel of larger diameter than the driver seoti_pnis'o~~~~~~~~~o the end-of the driver and separated fran it interhally b~s3%&5#'~ed pGt6:(see Figs. 1 and 2). The head of the expansion wave;~p&@&dwhen I& main diaphragmbursts, interacts with this perforated plate.---'3%&mpi‘ex QG"situa+n results, leading to no waves propagating downst.tiem, except Msoh waves, when certain conditions are fulfilled. Since' it-is the a~ival of the refleoted head of the expansion wave at the end of the-shock tube whhioh normally terminates the flow in the reflected shook t&&i, ~effective &nination of this wave should result in an increase in running time.

3 Jd

-l&-

In this paper an account is given of the analysis of the driver-reservoir teohnique as proposed by Flagg2, and this is canpared with experiments in the NPL 2 in. shook tunnel, using helium and nitrogen as driver gases and nitrogen as test gas. The driver pressure ranged frcm 1000 to IO 000 psi at roan temperature. An extension of this technique to gun-tunnel use is also discussed.

2. Theory

2.1 Analysis of driver reservoir technique

In simple shock-tunnel flow (shown in Fig. 1 usually terminated by the arrival of the head (or tail

the testing time is of the expansion

wave from the high pressure end of the tube. Teohniques for increasing the mnning time might, as a start, aim at delay3ng the arrival of these waves at the nozzle entrance. One possibility is to lengthen the driver section, thus increasing the time spent by the expansion wave in travelling through this section. For an appreoiable increase in testing time however this becomes impracti0able. Henshall et a$.

An alternative technique has been developed by In this method a reservoir of larger diameter than the

driver is connected to the end of the driver seation and separated frcm it internally by means of a perforated plate. The head of the expansion wave interaots with this plate and fran the ocmplex flow which develops no downstream propagating waves, except %oh waves, will result when certain conditions are fulfilled. These oonditims are derived by Flagg2 in his analysis of the driver-reservoir technique, and a brief description ~8 this analysis will now be given.

In his analysis Flagg has ale&ad to use the (p,u) plane method rather than the more laboricus method of characteristics, and explains that this former method will give all the required information about the resulting quasi-steady states. He points out however that for a detailed study of the wave prooesses, which would be desirable in order to establish how the final wave systems are formed, it is of course necessary to use the method of characteristics. Although the (p,u) plane method takes no account of the seoondary interacti~ of oharaoteristios, Flagg notes that the method is valid as long as the strengths 0f the waves involved are not extreme, and mentions that subsequent experimental data gave good agreement with this simple theoretics1 approach.

The driver-reservoir system when set up in the labaratorg Is shown schematically in Fig. 2. When the main diaphragmruptures, the gas initially at rest between the main diaphragm and the perforated plate mdergoes an unsteady expansion to a new state determined by the initial oonaitions. The gas initially at rest in the reservoir un&srgoes a steady expansicn to a condition determined by the area ratio of the perforated plate. Flagg desoribes the pressure ratio aoross an unsteady expansi0n when the gas is initially at rest by the expression:

. ..(I)

4

.

- 5-

and the pressure ratio across a steady expansion when the gas is initially at rest by:

pjs= ,- P4 [

(Y,; I) ( u$,‘4y: ’ . . ..(2)

Fran Fig. 4, which is reprcduced from Flagg's paper, it is shown that the two expansions produce the same end point in the (p,u) plane at only me point other than the initial one, This point is foundby equating (1) sad (2) above, which gives:

[

, (Y,dJN p 1 r: I- v,-1 L” 2a4 2 ( > a4

u% = u 3s

= u,.

. ..(3)

Solving for u where

U J=

4 4

Y, + 1 rM, =

84 3-v; i This analysis, Flagg notes, shows that very rigid restrioticm are set on the

initial conditions if both the tailoring and orossover requirements are to be met. The term "orossover point" is applied to the point shown in Fig. 4 where the steady and unsteady expansions produoe the same end point. F%g only oonsiders the tailored mode of operation.

In order to computa the neoessarg oonditions for eliminating the refleoted head of the expansion wave, FA

it is first required that the ratio be determined, where b$ and MC are the tailored Mach number and

the orossover mndition Mach number respectively (see Fig. 4). The orossover Mach number is that whioh is obtained under the conditions described for the crossover point in Fig. 4.

The oonditim which has to be satisfied for tailored interfaoe operation is:

m (Y, - 1) d

m,(Y,-i) . ..&I

Y+l where a za - and m -1

=, moleculex weight. Y

. . The~sc~oalled orossmer Mach number is given by the expression: .,

. ..(5)

It is then bnly neoessarg, by

54

inspection, to detendne whether the ratio is greater than, equal to or less then unity. For most praotioal

-6-

oases, e.g., lath helium, hydrogen or combustion gases as driver gases and air or nitrogen as driven gas, the ratio is less than unity. Flagg notes

that the oases %!b % = 1 and ->I % %

are not realistic and OnlJ - < %

applies in praotioe. For this case the ratio of the hole area to the cross-sectional area of the driver which is required to eliminate the reflected head of the expansicm wave is given by:

and this is solved by using the relationships:

*v4

!s=,- - (

Y4 -1 Ilk Y4 -1

P4 2 a 4 >

together with equation (2).

. ..(6)

. ..(7)

. ..@I

. ..(v)

. ..(I01

Sane curves of GDm versus driven gas specifio heat ratio, for

given driver gas specific heat ratio, are reproduced frm Flagg’s report and shown in Fig. 5. Fran a oanparison of experiment and theory it is fmnd that Flagg’s analysis provides a useful rule of thumb for estimatixig rmghly the area ratio 6 required. It is then necessary to carry out a series of tests to determine the exact value. In this respeot a semi-empirioal equation obtained by the present authors, us5ng maaentm omservatim prinoiples, wdd appear to provide an equally useful rule of thumb value for determinIng the required area ratio. This fomda isr

be/

.

,

. ..(I11

and is readily use+ in connection with tables of P,,, P,,, u,,, All a8

produced by Bernstein5 for example. A oomparison of the predioted values of 6 obtained from equationrr (6) and (II) and with experiment is given in Table 1.

Table 1

Driver Gas Driven Gas

6'02

(FLAGG) 6 x

0.379

0'333

(FLAW) DAVIES&

%DiuL DOL!dAN

6+

o-382 0.337

o*35l 0.435

EXP $w

o-333 (Ref.11

o-y30 (N.P.L.)

o-39 (N.P.L.)

Taking the values from the above table, the peroentage deviation of the various theoretical prediotions fram the experimental values can be estimated from the ratios presented below.

I “e4 I Nab8

. I

WFLAGG hDEAL)mGG (@~DAVIES

Gi

-LMAN %xP %xP

1'137 I+6

0.876 o-9236

o-97 Not Applioable

l'oll

I++

I.125

For the NPL 2 in. Gun Tunnel with N, as driver and test gas, the predioted value of 6, using equation (11) is 0%.66, whereas the experimental value was found to be 0*4jO6.

7

-a-

2.2 The Increase in runn3.11~ time obtained using the driver reservoir

Although various features of the flaw whzlch result from the interaction of the head of the expansion mve with the perforated plate have been described, no solution to the flow within the reservoir, and henoe a prediction of the expected running time, has been given. A semi-emplrioal approach baa been adopted by Henshall et al, but Flagg has not treated this part of the problem.

In their paper Henshall et al postulate that the ratio af the gain in test time AT, due to the use of the driver reservoir, to the test time in the conventional tunnel (T) is given by the folldng relationship:

AT --nf -,M T (

L' *o v L G-‘- l L'd' ) a

Henshall's experiments showed that the tail of the expansion wave did not affect the runuing time, and the head of the expansion wave had been effeotively eliminate&. Therefore the running time was dependent cmly on the arrival aF the oontaot surface at the working section nozzle throat. Henshall et al suggest tit the effectiveness uf the reserve is terminated by the breakdm of the constant mass flow thrazgh the plate. The simple apprarch adopted In this paper is to assume that the flow in the reservoir is initiated by the passage of the expansian head into the resemoir and that thereafter there are no other external Influenoes. The flow situation is shown in Fig. 6. The first possible interruption to canstant oon&Ltions at the platewill thenbe due to the arrival ofthe expensianhead refleoted fran the end of the reservoir. The time takenforthe e ansimtoarrive back at the plate (t) has been oalculated by Cable and C~C "J , end this is given by the relationship:

t 2

I

Y -1 (Y + l)/I2(Y - 111 -I

' tO

(1 + q) + 2 Mi 3 . ..(I31

where to is the time taken for a disturbenoe travelling at the speed af soundinthe reservoirtotravelthe length of the reservoir assuming the gas to be at rest. M, is given by the equetiau

(Y + 1 M2(Y - 1) I A 1 -=-

At % I

1 +Y+a I

3 . ..(I41

?!$A I

where A is the reservoir cross-sectional area, and At is the erea of the hole in the perforated plate. Aourve of t/to forvari~s Id% end A/A+,,

and fcr y = 1.4, is reproduced fran the paper by Cable and Cax in Pig. 7. Fram this curve it oan be seen that the time the exPandon takes to reaoh the

-9-

plate, after starting the flow is nearly ties the time taken to reaoh the end of the reservoir. In the NPL 2 in. Shook Tumsl when using nitrogen as test gas, this time Is about 5 ms, and in the experiments of Henshall et al is approximately 400 p. Both these times are far shorter than the experimentallg observed increase in rundng time. It is found however that the pressure drop across this first expansion is very small, and would not oause a breakdown in the flow through the nozzle*, although a weak expansion may be propagated downstream.

The fall in pressure In the reservoir due to suooessive refleotians of the expansion wave has also been caloulated by Cable and Cox, and their expression for the pressure after the nth reflsoticm, as a ratio ca? the Mtial pressure in the x-memoir, is given as:

P 2, p4

c

Table 2 shms the results, for the NPL 2 3.n. Shook Tunnel reservoir, af successive refleotions of the expansion wave and the pressures assooiatedwith these reflections. Fran this table it is seen that the pnxmre drop aoross the first few reflebticms is very ma.%

Table 2

.

Reflection p&4

2nd 0*9l4

3fi 0.894.

4th 0.8747

5% 0.79

6th o-73

7th 0*66

8th 0.6

Frm equation (15), it is clear that for decreasing values af M the pressure drop aoross successive refleotions also deoreases. The value 2 M is determined by the area ratio A/A+,. In the experiments oarried ad’by

Iienshall et al,/ ,,,,,-,,,c---;--------i----------------,-,---

‘Flow break&m is defined as teminatlan of oonstant odtims at the perforated plate whsn the pressure in the reservoir fslls below ths oritioal value.

- IO -

Henshall et al, this ratio is vary large, is very small and so M, will be small.

or in terms of Fig. 7 the reciprocal This till result invemweak

expansion waves for theAfirst few reflections and perhaps explains why the pressure reoords obtained by Henshall et al remain so steady over the testing time. Evidence of expansion waves being propagated downstream before the breakdown af' flaw at the perforated plate is mwe evident cm the records obtained in the NPL 2 in. Shook Tunnel where A I! A, and therefore M1, are larger, resulting in larger pressure drops across the expansia waves (see equation (15)).

From this rather simple apprcaoh certain predictions can be made. Extending the length d the reservoir will delay the arrival of the first, refleoticn from the end of the reservoir, but this is a return to the situatia which existed before the use aF the driver reservoir. The best use of the driver reservoir will be made where spaoe is at a premium in the labaratwy, and then when the cross-sectional area of the reservoir is very much greater than the area of the perforation in the tivicUng plate between the reservoir and the driver, in fact the situation ariginally devised by Hen&KU et al. The reservoir in use in the NPL 2 in. Shock Tunnel is not as satisfactory because the ratio A +! A is not small ena.@. Finally, fraa Table 2 it may be inferred that flow breakdown will not occur fcr a time less than faw or five times t/to. Itben the ratio A d A ismuoh smallerthan the NPL 2 in. Shook TunnelvsJ.ue, this ti will be correspondingly lqer.

2.3 Application of the driver-reservoir technique to gun-tunnel operation

In gun-tunnel operation, as in shook-tunnel operation, the head or tail at' the expansion wave is often a deciding factor in determining the running tine. In cader to make full use of the available running time, deterndned by the t&e taken for all the gas between the piston and the end late to flow through the nozzle into the working section, the expansicm head or tail) shcdd not arrive before a time r g given by the fcamula:

L T' = . ..(16)

p41pe4al 1 One means of ensuring this is to use the driver-reservoir technique. Since in simple gun-tunnel flow the- the piston is assumed to accelerate quicldy to the oontact-surface velocity and certain features of the flow are oaloulated using this analogy, the value of 6 required for driver-reservoir operation is computed as far the equivalent shook tunnel, using equation (6) or (II).

This has been done for the NFL 2 in. Gun Tunnel and the results sre described below.

A disturbing feature of the use of gun tunnels at very high pressures is the high peak pre

% sure oexsed by the refleoticm af the shock produced as the

piston slows to rest. As the piston slonrs down a shock wave is prduoed (see Fig. 8) which travels back to the driver sectian, reflects and on reaching

- 11 -

the piston produces a high pressure peak in the gas between the piston and the end face. These pressure peaks can be so high at the highest Operating pressures as to be prohibitive. However when a driver reservoir is being used, this shock, on reaching the end crf the driver section, encounters and interacts with the perforated plate. The result is that the shock is much weakened and reductions in shock strength of up to about 80$have been achieved (see Fig. 9). In these records the top trace is pitot pressure taken in the working seation, and the bottom trace is the reservoti pressure. The shock, produced by piston deceleration, which is reduced occurs near the end of the trace, as indicated (A), and the extent of the reduction is clearly seen In the lower record. It may be concluded that not only does the driver reservoir offer the possibility a? mddng full use of the available nudng time in gun tunnels, especially where there is not enough space fm a long driver section, but may also be said to be an essential feature of high-pressure operation.

3. Experimental Work

3.1 Shock-tunnel details

The NPL 2 in. Shock Tunnel has a 12 ft long law-pressure channel and originally had a 10 ft driver chamber made up of a 7 ft length and a 3 ft length. In crder to examine the driver-reservoir technique the last 3 ft of the ohamber furthest away from the main die hragm were replaced by a 4 in. internal diameter, 3 ft long reservoir (see Fig. 3 P . Inside the tube the original chamber section is divided from the reservoir by means of a O-1 in. thick steel plate with a central hole. The end IX? the reservoir rests against a hydraulic ram which closes the tunnel with a force at' 30 tons. The retrsctcx springs are clearly seen around the tube and. two smaller ones either side of the reservoir. Fuller details of the tunnel may be obtained from &f. 4.

3.2 Shock-tunnel tests with helium as driver and nitrogen 8s test gas

The results of the matching of the open to total area of the perforated plate were judged fran an examination of the reflected shock pressure records, as was done by Henshsll et al'. If the hole is too small, then an expansion wave is propagated down the tube (Fig. IOa). If the hale is too large then the right running wave is a compression wave (Fig. lob). Ideally the correot h$e size should produce no right running wave, except a Mach wave. This was not obtained in practice, hcmever, and the best match was judged to be that shown in Fig. 100, where it can be seen that a small compression wave occurs. In all the records no absolutely level section is obtained after the fFrst disturbace from the perforated plate, even at the 'matched' condition. This tends to suppart the simple analysis proposed in Section 2.2, where it was suggested that even when the correct value of 6 was used, weak expansion waves would. be propagated downstream as a result of reflections of the head of the

. expansion wave within the reservoir. In Fig. 100 there are clear signs of this occurring. In order to minimise this effect, it would be necessary to increase the diameter of the reservoir. This would then reduce the ratio At/", leading to an associated reduction in Mdl, and consequently a reduction in the pressure drops aoross the reflected expansions which occur in the reservoti. When the driver pressure was rsised from ICOO to 10 000 psi, the perforated plate still performed its task of eliminating the reflected head of the expansion, and appeared not to be influence& by bulk compressibility effects (see Fig. IOd). An effective increase a? abolt 2 ms in running time was achieved and a Caaparison of pressure records before and after using the technique is shown in Fig. log.

3.3/ !A

-'I2 -

3.3 Shock-tunnel tests with nitrogen as driver and test gas

The tests were repeated with nitrogen as both driver and test gas and again the correct value of 6, as judged fran the pressure records (Pig. IOf), did not prcduoe * perfectly level trace. Here again the diameter cf the reservoir should be increased.

In both the helium and nitrogen tests the working-seotion flow was examined, and a flat plate heat transfer traoe is shcwn in Fig. IOe for He : N, cperaticn. From this trace it seems that the running time has been effeotively increased, end with the above suggested mdifioaticm to reservoir geonetxy the flow should be usefil for extended duraticn testing. In fact the flm is perhaps good enough for this purpose already, and should imprcve with inorease in reservoir diameter.

4. Conclusions

(a) The flew which develops as a consequence of the interacticn of the head cf the expansion wave with the perforated plate, Fn drivelrreservcir operation, is sufficiently known to enable a reascaLably close prediction of the size of the hole(s) in the perfcrated plate to be calculated, far speoial predetermined operating conditions.

(b) At the matched ccnditicns no right running waves except Maoh waves result from the interaction of the expansion wave head with the perforated plate. The reflected expansion wave head is therefore effectively eliminated.

(0) The extra nmning time obtained will depend cm the geanetry cf the reservoir. The expansicn wave which passes into the rsservcdz will reflect from the end cf the reservoir and fran the perforated plate, alternately, causing a reducticn in the pressure in the reservoir. Several reflections are required to reduce the reservoir pressure to the oritical pressure at the perforated plate, and so terminate the effectiveness of the reservoir. At each reflectian at the plate, weak expansion waves pass through the plate holes ana propagate downstream. The strength cf these waves depends on the ratio of the area of the hole(s) in the perforated plate to the cross-sectional area of the reservoir. Far most effective operation this ratio should be made as small as possible.

(a) The driver reservoir technique can also be used effectively in gun-tunnel operation. In fact it is suggested that for very high pressure gun-tunnel cperaticn, the driver-reservoir technique, cr a similar arrangement, may be essential Fn order to reduce the strength of the reflection, at the plate, of the shock prduoed e.s the piston slows to rest.

(e) As a result of this investigation it is oonsidered that an experimental investigaticn into the effect of different diameter reservoirs on the flc+v should prove most instructive.

Aclmcwledgements

This project w.ss initially suggested by Dr. L. Pennelegicn. The detailed design cf the driver reservoir was by Mr. J. Godwin in the Design Office, and the oonstructian and assembly in the division workshops was the responsibility of Mr. J. Daroy.

References/ I2

-13 -

Es!& Authodsl

1 B. D. Henshall, R. N. Tew and

A. D. Wood

2 R. F. figg

3 A. J. Cable ana

R. N. Cox

4 L. Daties, L. Pennelagion, P. Gowh

ma K. Dolman

5 L. Bernstein

6 East, B. A. and Perry, J. H.

References

Title. eto,

Development of verg high shook tunnels with extended steady-state test times. AVCO Tech. Rep. RAD-TR-6246. (1962).

A theoretical analysis of the drivexwwervoir method of driving hypersonio shook tunnels. WITAS Tech. Note No.93. April, 1965.

The Ludwieg pressure-tube supersdo windtunnel. Aeronaut. Q., VOLXN, I 963, pp.1431 !57.

The effects of hi&pressure on the flow ia the reflected shock tunnel. A.R.C. C.P. 730, September, 1963.

Tabulated so1utions.d the equilibtium gas properties behind the incident and refleoted normal shock wave in a shock tube. I - Nitrogen. II - Oqgen. A.R.C. C.P. 626, April, 1961.

A study of the characteristics of @n tunnel operation at IO 000 lb/in.2 AASU Report No. 268. April, 1967.

D

FIG.1

Main PO

;

fy$pg m Distance -

High pressure chamber (4) Low pressure channel (I)

I

Simple shock tunnel flow diagram

FIG.2

I_-.--~ _.

L

. -

0 :

5 a

__- -

ir

FIG.4

Velocity “c or Mc

Diagrammatic representation of characteristics of steady and unsteady expansions on the (p, “)-plane.

(After Flagg: see Ref.2 )

17

FIG.5

0.45, y4+4

z

t

M -2-O b, 0.40 T 0

0 5.0 6

o-35 1

6/ X

\ I I I I I I I I-0 I-I l-2 l-3 l-4 l-5 I.6

Y, drivengas specific heat ratio

0.40 - y4

-1.67

i &E 0*35-

MT= 2.0

5-o

I I I I I I I I.0 I.1 I.2 I.3 I.4 1.5 l-6

yl driven gas specific heat ratio

Ideal perforated plate hole area ratlo vs.drlven gas

specific heat ratio.

(After Flagg: Ret 2 )

FIG.6

End of tube

Dividing plate

Flow in reservoir after expansion head has passed through hole in dividinq plate.

NotiCthcit the prQsiUre on! temperature

in re&%i; (A) an&(-$ are assumed to be

equal. This is appco3imtitely true in this case since -M, s O-06.

FIG. 7

I.7 _ I I I I 0 0.2 0.4 0.6 o-0 I

9 0

0 02 0.4 0.6 0.0 0.9 0.95 I-0 Divlding plate hale area

Reservoir cross-sectlonal area

Time of constant flow through dividing plate hole

bafore emergence of reflected expansion head.

(After Cable and Cox, Ref. 33

End wall

Shock produced by piston as it slows down at the end

of the tube

¶J

28 957 FIG. 9

PI tot pressure

t

Stagnatlon pressure -

Pttot pressure

Stagnation ) pressure

4 500 T

psi

+m+ Reflected Shock caused

shock by piston deceleration

La) Straight through driver-no drover reservoir

I I I I I I I I I I 1

I I I I I J / I

I I I I I I (T.

’ I

’ j/jIOpsi

Re’f Iected shock

-+Smsl+ (A) 6 Shock (caused by piston deceleration) is much reduced

(b) T unnel fitted wtth driver - reservotr

Pitot pressure and stagnation pressure traces showing reduction in strenath of shock caused by the deceleration

of the ptston .

11

FIG. 10 (a & b)

Expansion m 2mS P---i

Rhflected shock

Ill I I I bul-l I -

(a)

p4 = 1000 lb/In.2

He : N2 M, = 3.6

6 = 0.316

J 2mS . l-1 ‘Reflected shock

(b)

p4 = 1000 lb/in.2

He : N2 M = 3.6

6 = 0.562

Reflected-shock oressure records

FIG. lO(csd)

ImS i---l

(cl

P4 = 1000prl

He:N2 bvfl = 3.6

6 = 0.300

(d)

P4 = l0000pri

He N2 M = 3.73

6 = 0.380

Reflected-shock pressure records

FIG. IO (e&f)

(Q)

ps = 1000 psi

HeIN M= 3-6

u = 0.38

Working section flat plate heat transfer record (Ho : N2)

5mS

(f ) Pq = 2000 lb/ in?

N2:N2 MI =2

u = 039

FIG.10 g

Using driver reservoir

I

-A Before using

I

driver reservoir

Reflected shock

Comparison of pressure traces obtained before and

after usina the driver reservoir techniaue.

Helium as driver and nitrogen as driven gas.

1.

2.

3.

4.

5.

1.

Part 2 - Determination of Optimum Reservoir Size

By L. Davies,+ D. B. Brown*

and

C. Hccpe;

List of Contents

Introauction . . . . . . . . . . . . . . . . . . . .

Determination of Hole Siee in Orifice Plate . . . . . . . .

Determination of Optimum Reservoir Sise . . . . . . . .

Experimental Investigation . . . . . . . . . . . . . .

Conclusions . . . . . . . . . . . . . . . . . . . .

Introduction

*

. . 1

. . 2

. . 3

. . 5

. . 7

The driver-reservoir technique is employed in a shock tube, shock tunnel or gun-tunnel, when it is necessary to prevent the head of the expansion wave (see Fig. 1) reaching the end of the low pressure channel during the testing time. This is achieved by ellowing the head of the expansion wave to interact with a perforated plate situated at the end of the high pressure chamber. This perforated plate separates the driver from a large volume vessel known as the reservoir (see Fig. 2). By adjusting the sixe of the holes, or hole, in the perforated plate, a matching condition can be found such that only a Mach wave is propagated downstream. By this means an increase in running time of three or four times was demonstrated by Henshall et alI, who devised the technique.

The purpose of the reservoir is to ensure that the flow through the perforated plate (referred to throughout the paper 88 the orifice plate) after passage of the expansion wave, is not interrupted durFng the running time. In this respect the dimensions of the reservoir are most important.

i National Physical Laboratory. * University College of Whales, Aberystwyth. 21

-2-

In this paper the factors which determine the choxe of reservoir dimensions are ducussed, and the method of finding the optimum reservoir size for a particular facility is given. The experiments which formed part of this lnvestlgation are described, and include a study of the flow within the reservoir.

2. Determination of the Hole Size in the Orifice Plate

Unless otherwise stated it will be assumed throughout this paper that there is only one hole central in the orifice plate. A detailed experimental study of the determination of the hole size necessary to eliminate the reflected head of the expansion wave has been described by Henshsll et all, and Davies and Dolman2 . A theoretical study has been carried out by Flagg3 , who only considers the interaction of the expansion wave with the perforated plate. From this work the ratio of hole area to driver cross-section area which is required to eliminate the reflected head of the expansion wave is found to be given by the equation3.

(Y)+ + 1)

6 = (Y4yT-J F [1-y”;’ (~)~,* ... (1)

where 6 = A d Ad .

6 is obtained from equation 1 using the following relationshzps:

where MST is the Tailored primary shock Mach number.

f2 = ( ,- (vp) . 5 AL

Y4 - 1 2

‘4 “4

)

yy;, = [ y4(y;m,)]” pLp3s . [I +(;I; yyJ

3 = ,- “4

[I “42m” (:)a]”

The vCiues cslculatdfor 6 are intended to serve as a guide, and the practical value must be determined experimentally. In the present study a shock tube 14 ft long (4*27m), made of wave guide 2 in. x 1 in. (908 cm x 2* 54 cm), was used. The test section was 10 ft (jm) long and the drover section

4 ft/ 28

-3-

4 ft (I.22 m) long. In this tube when air was used as both.driver and test gas at a primary shock Mach number of 2, the expermental value of 6 was found to be D383 as compared wkth @379 predicted by equation (I). When hellurn was used as tilver gas and air as test gas, then the experimental value of 6 was found to be 0.32.

The evaluation of 6 when Mach numbers other than the tailoring value Bpe used, 1s discussed XII Refs. I and 2.

3. Determination of the Optimum Reservoir Szse

Henshall et al have shown that the reservoir volume must be large enough to ensure that the pressure within the reservoir does not fall significantly durjng the runrung tune. An analysis of the flow within the reservoir has been suggested in Ref. 2 following an argument outlined in Ref. 4.

The essential points are as follows:

Just after the main diaphragm bursts, (see Fig. 1) interacts with the orifice plate.

the head of the expansion wave Part of the expansion wave passes

through the hole in the plate and into the reservoir. mitted wave is a function of (At/~r).

The strength of this trans- This wave reflects from the end of the

reservoir and on reach- the orifzce plate, it will reflect as from a closed end if the ratio A d A, is very small. A weak transmitted wave propagates downstream through the orifice plate. The relationship between the strength of this trans- matted wave and the ratio A t/r A is to be determined so that the conditions at the end of the low pressure sectIon will not be significantly sf'fected during the running time.

A simple theoretical approach to this problem 1s to assume that the expansion wave which passes into the reservoir at the start of the in is a single concentrated wave. This follows the Ludwelg tube analyst of Cable and Co& . These authors suggest that if the rat.10 'dAr is very small, then the flow Mach number betid. the expansion fan is small, and thus the wzdth of the fan is small compared to the length of the reservoir. The assumption of a single concentrated wave is then a goad approximation for the frost few reflections. It is thus possible to think in terns of reflections of this single wave at the ends of the reservou.

In the present ease this is not a particularly realistic description of the flow within the reservoir, but the agreement with experiment warrants Its use as a first approximation. It is found, 111 fact, that pressure within the reservoir falls initially in a series of dlsorete steps (see Fig. 2b), which is in accord with the simple theory. The time between these steps also agrees closely with the theoretical tmes.

In terms of this model, *he length of the reservoir will then determine the number of refleotlons of the expansion wzthrn the reservoir during the running time. This u turn decdes the rate of fall in pressure. The task is to deter-e the optimum reservoir cross section, which controls the strength of the wave, and then to determine the optimum reservoir length.

The pressure (pn) at the orifice plate end of the reservoir after the

n th. reflection of the expansion wave at that end is given by the equation:

*n -= *4 I l-

(Y& - 1)

2 * 5

(y4 - 1) I+

2 %

-4-

2y4b - 1)

Yq- 1 1

c I+

(y4 - 1)

Ml 3

5J(Y4- 1)

2

. . . (2)

when? p 4 is the initial reservc~ pressure and M, is the flow Mach number

behind the expansion wave, following its first entry into the reservoir via the crifxe plate. b$ 1s obtained from the equation

(Y)+ + M2(Y4 - I)'1

A 1

, + (Y& - 1)

-f 2 "1' =-

At %

r I

Yq + 1

2

Curves of pn/p4 versus n for various AdA+, are shown in Fxg. Ja for air and Fig. jb for helium. The maximum allowable fall in pressure 1s to 85$ of the initial pressure. Thu value was examined emplrxa~~y, and the 85% line 1s therefore used to assess the effect of A If At ratlcs. Above a particular value of A A l-4 the gain is small. For au‘ th.zz value is about 100, and from the engineering aspect, this is the optimum cross section since the strength of the expansion wave is not significantly reduced for larger values. (See Fig. 4a). In Fig. 4a the pressure after an arbitrarily chosen 12 reflectzons of the wave is plotted as a function of A 4 At . The time taken for the wave to travel from the orifice plate to the end of the reservoir and back is given by equation (3).

t 2 -= to (1 + M,) c

, + (vq-')

2 5

3

(Y)+ + M2(Y4 - 111 . . . (3)

where t, 1s the time taken for a disturbance travelling at the lnitlal speed of sound to travel the length of the reservoir assuming the gas to be at rest.

The time taken for the n+l reflection 1s

Y. + 1

t n+l 2 =

to 1 + Id, c ,+(Yp) 2&) M

2 1

3

If the pressure fall in the reservoir, after a gwen time, is examined as a function of reservoir length, it is clear from Fig. 4b that after 12 in. (30 Cm) there 1s no significant gain from incresslng the length. 12 in. 1s

therefore/

-5-

therefore about the optimum value in the time it takes for the reflected shock to absence of the expsnslon wave head, this

present case. The wglven tlmew 1s the travel up the tube and back. In the process mll limit the runnmg time at the

end plate. Clearly, the time involved will depend on the length of the driver and test sections and as a rough guide may be consIdered to vary linearly with these lengths. The optimum reservoir length will therefore vary 111 a similar manner.

The length of the reservoir and its cross-sectional area are determined separately, for phys.~oslly realzstio conditions. Clearly, any AdAt will do if the length 1s mfmite, end conversely length will not matter if' AdAt is infirute. The reason for using the driver-reservoir technique, however, is to obtm B large increase m running time mthout having to resort to using very long driver sections. This -edlately limits the length of the driver-reservoir, i.e. It must not be much longer than the original driver sectIon. Secondly, from the constructional aspect there IS no reason for going to .s larger reservoir than neoesssry especLll.y If high pressure operation is anticipated. This sets an upper limit to the area.

The area of the ho+ in the orifice plate is determined independently of the reservoir dimensions, since the elimination of the reflected expansion head is effected solely by the interaction of the expansion wave head with the orifice plate.

4. Experimental Investigatzon

For the experiments where air was used as driver gas, the primary shock Mach number was arbitrarily chosen as 2, whereas for helium as driver gas the tailoring Mach number, 3.4, was used. The principles involved will however apply at other Mach numbers than these. In all oases air was used as test gas.

Determination of correct orifice plate hole size

The determination of the correct orifice plate hole sloe was carried out as outlined in Itefs. 1 and 2. The results for both driver gases are shown in Figs. 5a, b, c and d. In Fxg. .5a the sketch of the reflected shock pressure-time profile indicates the important features. The pressure at the' end of the shock tube first ryes to a value which, in the air case, is the equiilbrium interface v*lm (P,) 3 and in the helium drover case will be the reflected shock pressure p5. With the end of the driver section blocked (or nearly so), a strong expansion wave reaches the end plate and terminates the running tzme. This is labelled in the sketch s,s "hole too small", and the lower bound is where 6 = 0 . For increasing values of 6 the strength of the expansion wave decreases. The "hole too large" 1-e refers to the condition when the orifice plate hole is larger than ideal and.a oompresslon wave results.

hl is shown on the sketch as referring to values

greater than p, (or p,) and it is also used to inhcate the deviation for smaller pressures. Therefore, if an expansion wave occurs (h,/h2) 1s plotted as a

negative value, and if a oompresslon wave occurs (h,/h2) is plotted as a positive value. In this ws.y it is possible, by drawing a line through the series of points produced, to obtain the ideal (At/Ad) as an intercept on the 6 axis. For this value of 6 only a Mach wave is produced when the expansion head interacts with the orifice plate.

The pressure traces for sir are shown in Fig. 5c. The two extreme 6 oases, ia. Gnlty and 0 , and the ideal case are demonstrated. SimilUlY, the pressure records for helium are shown in Fig. 5d.

Determination/

-6-

Determination of optimum reservoir cross-sectional area

It has been shown in Section 3 that the theoretical optimum length for air .ss driver gas is about 12 in. This length was therefore used for most of the reservoirs since, as discussed in the cross section, the optimum AdAt is obtained independent of the length. The various reservoir dimensions, together with their identifying numbers, are given in Table I.

Beservou‘ number

0

i

2

3

3a

Jb

4

5

6

TABLE1

area (i2) "JAt length

1.627 2.164 12 in.

6.56 10-541 12 in.

29.6 47.56 12 in.

66-6 107.2 12 in.

66-6 107.2 6 in.

66.6 707.2 24 in.

t23'2 197-Y 12 in.

139.2 223.68 12 in.

353'9 247'3 12 in.

An indication that the area ratio of a particular reservoir is below the minimum allowable value is that the pressure pe starts to fall away significantly before the end of the running time. This is demonstrated in Fig. 6. In the sketch at the top of the page the essential features are indicated. pef is the final value of p, before the arrival of the shock wave which terminates the running time.

As regards the pressure traces, that for reservoir I shows that even though the correct orifice plate is used, there is still an expansion wave travel- ling down the tube. Clearly, this is due to the fact that expansion waves from within the reservoir which are transmitted downstream through the hole in the orifice plate are too strong, as predicted by the theory. For reservoir 2 the expansion wave is not 8s strong, and from reservoir 3 on (i.e. increasing area ratio), there is no significant fall in pressure and no significant improvement. Reservoir 3 is therefore the one with the optimum area ratio (i.e.-- 100).

The helium driver case is also demonstrated in FQ.6. Here the optimum area ratio is not reached until reservoir 6 is used. (Area ratio -, 250).

Determination of optimum reservoir length

Some tests on the effect of reservosr length were carried out with sir as driver gas and using the optimum area ratio. Three reservoirs were used, numbers 3, 3a and Jb. From Table 1 it can be seen that their lengths bear a simple relation to one another.

In/

-?-

in Fig. 7 the top trace is for reservoir 3a (L = 6 in., 15 cm) and here there 1s a significant fall away in pressure before the end of the Nllning tune. In the bottom trace, for reservoir 31 (L = 24 in., 61 on) there is no significant improvement over the trace obtained for reservoir 3 (L = 12 in., 30 cn) and which is shown in Fig. 6. This indxates that for these conditions 12 in. (30 cm) is about the optimum length and bears out the theoretical prediction.

Examination of the pressure-time variation in the reservoir

The variation of the pressure in the reservoir was examined using the pressure gauge station shown in Fig. 2. In Figs 8a, b, c, d the experimental and thegreticsl pressure-time variations sre compared for different reservoirs and for helium and air as driver gases. In Fig. 8a the variation in reservoirs 3, 3a and jb (increasing length) for air are shown. In Fig. 8b the pressure-time variations in reservoirs I, 2 and 5 (increasing area) are shown, also for air. It is seen that the theoretical curves indicate the actual trends reascnably well considering the simplifying assumptions used in the theoretxal model (see Ref. 4). In the helium Cases shown in Figs 8c and 8d the agreement between experiment and theory is not good. It is scne consolation, however, that the theory is tOa pessimistic in predxting the fall in reservoir pressure with time, and this suggests that the actual optimum area ratio will be less than the theoretical. This will be of use when constructing a driver-reservoir system.

The increase in running time obtained usinn the driver-reservoir techniaue

By eliminating the reflected head of the expansion wave an increase of four times the original testing time was obtained by Henshall et ali , using hy&O- gen as driver gas and sir as test gas. In the present investigation the increase for air as driver and test gas was three times the original, and using helium the increase was four times,in accordance with the results i,n Ref.1.

5. Conclusions

The following conclusions an? drawn from this investigation:

1. For most efficient use of the driver-reservoir technique there is an optimum reservoir size which depends on the shock-tube dimensions and the initial conditions.

2. The optimum cross-sectional area is determined by the strength of the expansion wave which is transmitted through the orifice plate into the reservoir. The strength of this wave in the reserrroir is a function of the ratio of the orifice plate hole to the reservoir area. The madnum allowable strength thus determines the optimum area.

3. The optimum length of the reservoir is obtained by ensuring that the fall in reservoir pressure will not cause a significant drop in pressure at the end of the low pressure channel during the testing time.

4. The f& 111 pressure in the reservoir and tie strength cf expansion waves transmitted through the orifice plate into the shock tube will then have no significant effect on the flow 111 the tu e during the testing time.

5. The method cf determining the correct orifice plate hole siee 1,2,3 , and optimum res6rrrok dimensions are described in this paper, and it is shown that the optimum driver cross-sectional area is independent of the length.

6./

-a-

6. Using the drver-reservoir technique an increase in testing time of three to four times may be obtained in a simple shook tube.

Nomenclature

A

Aa

At

A r a

% Id

%

%

Pi

P U

t

b

%

%s U iU

yi

6

Subscripts

1,2,3...

Cross-sectxxd area

Draver cross-sectional area

Driver cross-sectional, .area of orifice plate hole

Reservoir cross-sectional area

Sound speed

Sound speed in region i

Mach number

Mach number of primary shock

Mach number in region i

Pressure in region i

Pi/Pj

Time

Time taken for a disturbance travelling at speed of sound to travel the length of the reservoti assuming the gas to be at rest

Velocity in region i

Velocity in region i due to steady gas expansion

Velocity in region i due to unsteady gas expansion

Ratm of specific heats in region v

At/Ad

Refer to regionsshown in Fig. 1 unless otherwise stated.

References/

-Y-

5. Author(sl

I B. D. Henshall, R. N. Teng ana A. D. Wood

2 L. Davies ma K. Doliwm

3 R. F. Flagg

4 A. J. Cable aa R. N. cox

Title, etc.

Development of very high enthalpy shock tunnels with extended steady state test times. AK0 Tech .Rep .RAD-m-62-l , 6. 1962.

On the driver-reservoir technique in shock aa gun tunnels. NPL Aero Report 1226. A.R.C.28 757. <967.

A theoretical. analysis of the driver-reservoir method of driving hypersonic shock tunnels. UTIAS Tech.Note No. 93. 176.5.

The Ludwieg pressure-tube supersonu wind tunnel. Aeron.Quart., vol.XIV. 1963

\ ‘\

l .

‘\

(4)

/- , / (2) \

/ I] / , / 1’ !zbmpkry (I) b Reservoir +k Driver -’

t

section 0 x-

Main Distance along tube

Perforated diaphragm

plate

Flow in shock-tube using driver-reservoir technique

t

Time

FIG 2 a

Reservoir rif ic e plate

Main diaphragm

Test set tion

- 3*0m -p End plate

cm

Experimental layout

pressure gauge position

FIG. 2 b

Pressure time variation within reservoir 2

Ar/At=47-56 showing the

pressure falling in discrete steps. Test gas Air

140-

130-

IZO-

FIG 5a

x

I IO-

IOO-

90-

80-

70-

60-

50-

40-

30-

20-

IO- Clored

end

0 I I I 0.1 0 2 0.3 &4 o-5 0.6 0.7 0.8 09 I-O

/ 6-

-lO- X

-2o- / -3o- 1”

X - ExperImental value5

Values of hl/h2 ~5. 6

hole

I hole

2 2

6 * area of plate hole area of rhock tube

where hl and h2 are deftned

in the sketch . Negative va lue5 refer to pres5ure tall and poslti\ie value5 to pre55ure Increo5e5

Air a5 driver go5

FIG. 3b

I.00

O-98

0.96

o-94

0.92

o-90

0.80

O-86

O-84

O-82

O-80

0.78

0.76

o-74

O-72

o-70.

Equation (2) -

0 2 4 6 8 lo I2 14 16 18 20 22 24 26 28 30 Reflection number (n)

Pressure in reservoir after n reflections, normalised with

rerpect to pqr versus reflection number

FIG. 4(a)r(b) FIG 414

90

80

70

60

50

40

30

20

IO

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

Pressure ratio after 12th reflection versus area mtlo

FIG.4(b) FIG.4(b)

Length (in)

Pressure after qive time versus reservoir length, where

&,/At E 107 initial pressure, p4

140-

130-

IZO-

FIG 5a

x

I IO-

IOO-

90-

80-

70-

60-

50-

40-

30-

20-

IO- Clored

end

0 I I I 0.1 0 2 0.3 &4 o-5 0.6 0.7 0.8 09 I-O

/ 6-

-lO- X

-2o- / -3o- 1”

X - ExperImental value5

Values of hl/h2 ~5. 6

hole

I hole

2 2

6 * area of plate hole area of rhock tube

where hl and h2 are deftned

in the sketch . Negative va lue5 refer to pres5ure tall and poslti\ie value5 to pre55ure Increo5e5

Air a5 driver go5

FIG 5 b

I 50 r

140

130

I20

I IO

100 i

:ose

00

70

60

50

40

Closed 6 Open end \

OJI I I/K I I I I I "(, @I 0.2 #3 0.4 0.5 0.6 0.7 04 0.9 I 0 ~

-10

11

0

- 20 *

- 30 $

-60

o-

o- Experimental values

Negative values refer to pressure tall, and posit 8 ve values to pressure rise

Valuer of h,/h2 VI 6 (Helium)

FIG 5.c

t!iiiiiiiiiJ I I I

I I

(‘)

( 11)

pi)

b=O

Hole rize too small (Blocked end)rerul ting in expansion wave

/

Ideal hole size 6 = 0.30

6s I.0

Hole SIZU too large

(Open end) resulting in

retlected compression wave \

Air as driver gas. M,=2, p4 I atm.pressUre . Sn sets per

division time base

FIG. 5 d

I I I I I I I I

- I I I I I I I I

I I I I

--I I- Ims

(4

(ii)

(iii)

6=0

Hole rize too small (Blocked end) resulting in expansion wave rc Ideal hole sire

6=0-32

Hole size too large

(Open end) resulting compression wave

in

Determination of 6 for Helium driver gas

w

FIG. 6

‘*..flOrlglnal expansion wave profile

Ttme -

(i) Identification of pressure levels

In all cases Ms = 2, p4 = atm pressure Time base !i m sea/air

Air as driver gas

Reservoir No. I

h = IO*541 At

Reservoir No. 2

Ar - = 47.56 At

Determination of optimum reservoir cross-sectional area

FIG. 6 (cont.)

Ii I I i i i I I I ii i I I I i I iJ I 1

Reservoir No. 2

Ar - = 50 At

Reservoir No. 3

Ar = 107 At

Reservoir No.6

Ar

sit = 250 (About the ideal value)

Minimum area ratio I I

‘2 mk

Determination of optimum Ar/At for helium driver gas

FIG 6 (cent)

Reservoir No.3

Ar - = 107.02 (‘.e about the At ideal volue)

Minimum area ratio for

Pe * pef

Reservoir No. 6 Ar - = 247.3 At

No significant improvement over rerervoir No. 3

Infinite case

Ar -== At

No significant improvement over reservoir No.3

Air as driver gas

FIG. 7

I I I I I I I I I I I

Length = 6 in., Reservoir No 3 (a) shows fall in pressure po-ppp1 due to drop in reservoir pressure

Length =24 in., Reservoir No. 3 (b) no signltlcant improvement over reservoir No. 3 (see Fig. 6) where length = 12 in .

Ar Effects of reservoir length. Ms-Z*0 p4= atm pressore.(Air) z = 107

,

FIG. 8 (a,

shock tube

reservoir 6 in. --

0 2 4 6 0 IO 12 14 16 10 20 22 24 26 20 30 Time in m set -

Comparison between experimental and theoretical values of pn/p4 vs time for

reservoirs 3, 3a and 3b Ar/At = 107.2 , y = I.4 (Air)

FIG.a(b)

\ Ar

I I G = 10~541

Ar _ - =47*56

I \ At

I 0 2 4 6 8 to 12 14 16 I6 20 22 24 26 20 30

Time in m set -

Comparison between experimental and theoretical values of p4/p, vs time

y = I.4 (Air)

FIG. 8 (c)

t

--0-- Exp. NPL(2xl in.

0 2 4 6 8 10 12 14 I6 18 20 22 24 26 28 30 Time In m, set -

ComParison between experimental and theoretical values of pn/p4 vs time for

reservoirs 3, 3a and 3b. &/At=lOO, y= 1.66, He

FIG. 8 (d)

0.95 -

t 0*90- pn

p4 O-85 -

0.80 -

o-75 -

0.70 -

I I I I L. ’ rticbl &es n.1

I I \I I\ I I I I

Comparison between experimental and theoretical values of pn /p,, VI time for

reservoirs 2,3 and 6 Y 1.667 (He)

I I I I I I I I I I

0123456 7 8 9 IO II I2 Time in m sac -

D 1ce840/1/135a45 K.3 o/m P

A.R.C. C.P. No.1019

JammY 1968

Da~les~ L.. Brwm. D. R. end HoePer. 0.

ON THE DRI”ER-RESER”OIR TECKNI‘YE PART 1. APPLICATICN TO SHOCK AND CLIN lWNNFU PART 2. DETERnINATIOW OF OPTIPUH RUER”OIR SIZE

The dr*v.?PreSersD*r cechn1que 1s used when M 1ncreaee I” NM1n.s time is required in shock or 6~” tunnels. The increase 1s echlned by effectlosly ellmlnat.lnS the reflected head of the exppnsion weve prcduced

when the meln dlepbram buzats. A theoretical end experimental Pppreleel is S,ven of the appllcatlon of the teohnlque In sltuetlohs ef practice1 Interest, wd P method 1s described for the detenelnetlon of optlmm

reaerrolr ~1x0 to ensure ef!lclent use of the technique.

A.RC. C.P. No.1019 Jnmrery 1968

Devles, L., B-r D.R. end HOOpOr. 0.

ON THE DRIVER-PESERWIR TECSNIQJB PART 1. APPLICATION M SHOCK AND GUN lUhNEM PA!a 2. DETERnINATION OF OPTRUM RESERVOIR SIZE

The drlvex-reser~olr Cechnlque 18 Used when en IncrePBe In N”r,l”S time Is required in shock or KU” tunnels. The Increase Is eehleved by etrectloely ellmlnatlng the reflected head of the exPanslon rave pmduced flhen the msln dle.Pbragm bwxts. A theoretical end experimental aprrelsal 1s Slven of the eppllcetlon of the technique in 8ltUPtlollS Of preCtlcP1 Merest, end e methcd la described for the detennlnatlon of OFtlmun reselsolr slae to ensure elilclent “se of the technique.

A.RC. C.P. No.lOl9 Jenuaw l%S

Davies, L., Bram, D. R. end Ilooper. 0.

ON THE DRIVER-PUERVOIR TCCHNIWE PAra 1. APPLICATION TO SHOCK AND LTIN ‘IUNEIE PART 2. DETEPHINATION W OPTIMM RESERVOIR SIZE

The drlver-reseroolr technique 1s wed when M IncI‘BeSe In Rmning time Is x-equlred In shock or gun tunnels. The IncreaSe IS ach1ered by elfeothely elimlnetlng the reflected head of the expansion we- produced when the mln dlaahragm bmts. A theoretical am, experfmental appPlSp1 Is Slven ol the eppllcatlon of the technique In 8ltu~flons of pl~ctical Interest, am, P method Is described for the detemlnation of OptI-

reservofr she to enwu-e efflclent use o? the teohnlque.

. c l , .

0 Crown copyright 1968

Pnnted and pubhshed by HER MAJESTY’S STATIONERY OFFICE

To be purchased from 49 Hgh Holborn, London w c 1

13~ Castle Street. Edmburgh 2 109 St Mary Street, Cardiff CFI 11~

Brazennose Street, Manchester 2 50 Faxfax Street, Bristol BSI 3DE

258 Broad Street, Blrmmgham 1 7 Lmenhall Street, Belfast BT2 8AY

or through any bookseller

Prrnted m England

C.P. No. 1019

C.P. No. 1019 so cede NO 23-9018-19