Some Notes on the Performance of Small High Speed Wind Tunnels

VLIEG iliiGBOUWKüNDE

' .jct195ö'

REPORT No. 23 December» 1948 > ' T H-E G O L L E & E O F A E R O M A U T I C S G R A N F I E L D » '

Some Notes on the Performance of Small High Speed Yfind Txinnels

-by-G.M. Lilley, D.I.C., M.Sc., of the Department of Aerodynamics

~ o O o ~

SUJ/aiARY f

There is a need for high speed wind tunnels of modest dimensions and costs in establishments teaching the fundamentals of compressible flow. This paper discusses briefly the layouts and performances of various tjrpes of tunnel which might be sioitable for colleges and universities. The subject is still in its infancy and this report should not be regarded as more than an attempt at reviev/ing the present position.

21 Octl950

2

-velocity of sound

specific heat of dry air at constant pressure

specific heat of dry air at constant

volume

mechanical eqi^ivaloüt of heat.

Mach n^mber

mass flow ratio

r.p.m. of vacuum pump

pressvire

gas constant in equation of state

working section area

number of stages in air compressor

time

absolute temperature

•

velocity

volume of storage tank

svrept volume per stroke i n vacuum p\mp

diffuser efficiency

efficiency of pump

density

mass flow' in unit time

ratio of specific heats Suffices

refers to atmospheric conditions

refers to stagnation conditions in the settling chamber of a straight-through tunnel

refers to stagnation conditions upstream of working-section

refers to stagnation conditions in reservoir

2, Introduction

The various types of high speed wind tunnel can be classified as

follows.-(a) Continuous flow ,

(i) Direct drive return flow

(ii) Direct flow ' straight-through' tunnel

(iii) Induction tunnel return flow

(iv) Induction • straight-through' tunnel

(b) Intermittent flow

(i) ' Straight-through' v/ith high pressure reservoir at entry

(ii) ' Straight-through' with vacu-um tank at exit

(iii) Induction ' straight-through' tijnnel

(c) As (a) and (b) but using gases other than air (e.g., superheated steam).

Since we are consideriiiqg tunnels likely to be within the resources of colleges and universities the schemes considered will be limited to those using less than 100 b.h.p. The calculations have

been confined to tunnels having working sections of dimensions 2in. x 2ino J the value of smaller tunnels for research and demonstration purposes is likely to be severely limited. The calculations can, however, be readily generalised to tiinnels of other sizes.

In estimating the performance of the different designs it will be ass\ffiied that

(i) the shape of the nozzle (effuser) has been correctly designed, due allowance having been made for boundary layer thicknossj

(ii) the subsonic diffuser has an efficiency above 75 per cent.

(iii) the kinetic energy at the diffuser exit is small enough to be neglected when compared with that at the working" section.

3t Continuous tunnels

3.1 Direct-drive return flow

A sketch of a typical tunnel layout is shown in Fig.1. The tunnel is driven by an electric motor through a speed-up gear box to an axial or centrifugal compressor. The former is preferable owing to the aimplified geometry of the ducting.

A cooler is required to remove the heat of compression but may at the same time serve as an efficient honeycomb. The working

section has glass sides for flow observation (schlieren or shadowgraph),

changing the supersonic liners.

Table I gives the pressure ratio and approximate horse-power required by a tunnel with 2 in. sq. working section over a range of Mach n\fflibers. The results are plotted in Pigs. 8 and 9. The difficulty involved in matching a compressor to drive the tunnel efficiently over a wide range of Mach nxanber is apparent.

3,2 Direct flow ' straight-through' t\annel

A diagrammatic layout of a typical form of this tunnel is sho"vn in Pig. 2. The txinnel is supplied with air fr^rn a ^^'-iprocating compressor via an after cooler, oil separator and reservoir.

The main advantage of this scheme over the retm'n flow turmel is that the performance of the compressor need not necessarily be closely matched to that of the tunnel. The compressor discharge pressiire must, hovrever, be greater than the minimim operating pressure (p, min), given in Table 2, and the air tloif (w lb/sec) must also eqiial at least the values quoted. The electric motor b.h.p, v/ill be greater, for a corresponding Mach number, than the value quoted in Table I as the compressor efficiency will be lov/er.

3.3 Induction, continuous, return flow tunnel

A typical layout is shovm in Pig,3. The main advantage over scheme 3*1 is that the compressor and tunnel characteristics need not be closely matched, but this is gained at the expense of extra power required by.-the compressor. In general the induction principle is applied when relatively small supplies of high pressure air or gas are available. A disadvantage is that Mach nianbers above 2.0 have as yet not been

attained Y/hen the induction principle is used, although fiirther development and research may help to raise the limit. The remarks in the f ollov/ing paragraph relating to ejector slots apply here.

3.4 Induction, continuous, straight-through tunnel

The scheme is shoirm in Pig.4* The important design feature of this tunnel is that of the ejector slot. To obtain maximum operating efficiency at any given Mach number the ratio of ejector slot area to working section area must be matched to the required blowing presstire. The ejector slot is usually designed to give at the slot a Mach number of unity. This condition is dependent only on the blowing pressure and is independent of tunnel operating conditions.

Typical design curves can be obtained from Reference 1, '#hile Table 3 gives the quantity of high prassvire air required by a 2 in. sq. tvinnel when the blowing pressure is 100 Ib./sq, in^ above atmospheric.

Recently this tjrpe of txinnel has been driven by a jet engine of 5,000 lb. static thrust placed dovmstream of the working section. Tfith this arrangement. Mach numbsrs up to 0.9 can be obtained.with working section areas of about 10 sq.ft.

4» Intermittent Tunnels

4."1 ' Straight-through' intermittent with high pressiire reservoir

A diagrammatic layout of the tunnel is sho7m in Pig.5»

Table 4 gives the size of reservoir required for a 2 in.sq. working section when i^ is 100 Ib./sq.in. absolute and p, is equal

to p, . (see Table 2). ' The time of running is 30 sees.

b m m ^

4.2 ' Straight-through' intermittent with vacuum tank at exit

A diagrammatic layout of the tunnel is shown in Pig.6.

In order to run the tunnel at constant subsonic speeds, a throat at the end of the working-section must be fitted. It is essential for efficient tunnel operation to use a quick acting valve with a minimum time lag. The main advantage of this scheme is that Mach numbers up to 4«5 can easily be obtained provided that efficient

vacuum p\mips are used.

Table 5 gives the volume V of the vacuimi tank for a 2in. sq. working-section when the time of running is 30 sees. The initial pressure in the vacuum tank is assumed, to be 0.44 Ib./sq.in. absolute.

4.3 ' Straight-through' intermittent induction t\mnel

The layout of this txonnel is similar to that shown in Fig. 4 except that a storage cylinder must be provided between the compressor and ejector box.

Table 6 gives the necessary storage volume V for a 2in. sq. tunnel running for 30 sees. The initial reservoir pressure is

100 lb,/sq.in. and the constant blowing pressure 55 Ib./sq,in.

The advantage of using the induction type intermittent tunnel Y/ill be seen to lie in the relatively small volume of reservoir required.

5 Continuous and intermittent t\innels using gases other than air

5.1 Tunnels in YJhich the gas in the working-section is not air

A considerable saving in power could be obtained by using a gas lighter than air, but having the same value of y* However, this advantage is offset by the added complications of the operating plant. Most schemes considered have been concerned v/ith gases such as freon

that have a much smaller speed of sound than air, and thus a given Mach nioraber is obtained using less power. For freon, however, the

value of Y is smaller than that for air.

5-2 Induction tunnels using steam in place of high pressure compressed air as the ejecting fluid

This type of tunnel is similar to that shovm in Fig.4 except that superheated steam is supplied to the ejector box in place of the compressed air. This scheme offers distinct advantages in establishments where a steam boiler plant is already in existence.

Typical operating characteristics can be obtained from Ref.2.

6. Conclusions

The performance of a variety of small high speed wind tunnels have been discussed with brief references to the advantages and

disadvantages of each.

A number of simple calculations, needed for the preliminary design of such tunnels, are described briefly in the Appendix,

REFERENCES

N\jmber Author Title

Holder, D.W. An estimation of the riinning time

of an induction type high speed tunnel driven from compressed air storage. A.E.C. 9902 T.P.160 August, 1946. Lilley, G.M. and Holder, D.¥.

Experiments on an induction type high speed tunnel driven by low pressure steam.

October, 1948.

(TO be published shortly in the College of Aeronautics series).

Lukasiewicz, J. Supersonic diffusers.

R.A.E. Report No. Gas 8 A.R.C. 10,110 T.P.173

TABLE I

Performance of a 2in.sq. direct-drive return flow tunnel Mach number (working section) M. 0.5 0,7 0.9 1.0 1.25 1.50 2,00 2,50 3.00 4,00 ^3 1.03 1,07 1,27 1.28 1.29 1.58 1.99 2.89 4.46 10.95 Mass flow W lb./sec. 1.03 1.25 1.36 1.37,

I.31J

1.17^ 0.81 0.52 0.32, 0.13" Actual Adiabatic h.p.

2^52

3.72 8.65 19.60 19.0 23.50 30.8 32.4 30.4 22.5' h.p. required (approx.) 10.0 18.5 38.5 78.5 78.5 78.5 47.5 47.5 43.5 43,5

P, is the static pressure upstream of the compressor.

P, is the static pressure downstream of the compressor.

Notes Mass flow calculated for atmospheric stagnation pressiore and temperature upstream of working-section.

The actual horse-power required is based on average compressor efficiencies for a compressor rated at a pressure ratio of 4 t 1»

TABLE 2 Continuous Working-section Mach number M. 0.5 0.7 0.9 1.0 1.25 1.50 2.0 2.5 3.0 4.0

direct flov/ , 2in.sq.

Blowing pressure 'straight-through' tunnel ^b min. Ib/sq.in. absolute. >/*— 15.1. 15.73 18.65 18.8 I8.93 23.2 29.23 42.5 65.6 161.0 ^^\

-l^?'

Mass Plow W lb./sec. 1.06 1.35 1.723 1.76 1.693 1.843 1.61 I.5O3 1.45 1.42. •L TABLE 3 Continuous i n d u c t i o n ' s t r a i g h t - t h r o u g h ' t u n n e l W o r k i n g - s e c t i o n 2 . 0 i n . s q . Blowing p r e s s u r e 100 I b . / s q . i n . above a t m o s p h e r i c . Working-section Mach number M. 0.5 0.7 0.9 1.4 Area Ejector Slot Area Working-section 0.006 0.009 0.012 0.037 Mass flow ratio, m 15.5 12.5 9.5 • 3.0 High pressure air required lb./sec. 0.07 0.10 0.14 0.41

TABLB 4

' Straight-through' intermittent tunnel with high pressure reservoir at entry. Working-section 2.0 in.sq. Initial reservoir pressure 100 Ib./sq.in. absolute*

Time of running 30.0 sees.

W o r k i n g - s e c t i o n Mach number M. 0 . 5 0 . 7 0.9 1.0 1.25 1.50 2.00 2.50 3.00 4 . 0 0 ' s t r a i g h t - t h r o u g h ' Blowing p r e s s u r e •^b m i n I b / s q . i n . a b s o l u t e 15.13 15.73 18.6^ 5 1 8 . 8 I 8 . 9 3 23.2 29.23 4 2 . 5 65.6 161.0. I^\v^' TABLE 5 i n t e r m i t t e n t t u n n e l w i t h vacuum Volijme of R e c e i v e r V c u . f t . 89.0 114.0 151.0 154.5 149.0 171.0 161,0 181.5 264,0 t a n k a t e x i t

Working-section 2in.sq. Time of running 30 sees. pressure in tank is 0.2^4 Ib./sq.in. absolute.

W o r k i n g - s e c t i o n Mach number M, 0 . 5 0 . 7 0.9 1.0 1.25 1.50 2 . 0 2 . 5 3.0 4 . 0 Volume of tank V c u . f t . 600.0 7 6 5 . 0 9 8 6 . 0 1005.0 982,0 1065.0 9 4 0 , 0 903.0 920.0 808.0 Initial «7

. v ^ ^ ^

-TABLE 6

' Straight-through' intermittent induction tunnel

Working-section 2in.sq. Time of running 30 sees. Initial reservoir pressure 100 Ib./sq.in. above atmospheric. Constant blowing pressure

P-v - 55 Ib./sq.in. absolute. Working section Mach number M. 0.5 0.7 0.9 1.4 A-rea Ejector Slot Area Working-section 0.013 0.022 0.030 0.080 Mass Plow ratio . 14.0 11.0 8.5 3.0 Volume of V. cu.ft 9.6 14.8 20.9 52.5 /

APPENDIX

1• The mass flow through the working-section

The mass flow in unit time through the working-section is,

H = pSU • A 1.1

The isentropic change of pressure from the settling chamber to the working-section is given by,

^ = / ; , ï z i M^v-^

_{.A 1.2}

p

If we combine equations A 1.1 and A 1.2 together vdth the relations, a^ = ÏH ' ..A 1.3 P •^ = constant A 1.4 PY

|i = p^ a^ SM M + ^ M^J ....*i,^..,A 1.5

2. The pressure ratio required by the compressor of a direct-drive return flow wind tunnel

The pressvire rise through the compressor (refei to Pig.l),

Zk. ^ Zh 12. £_ c-',. r ..-,.. ^-,.-. .A 2o1 P3 p^ p P3

where, p, - p is the pressiire drop across the cooler.

/ Y-1

2\

^/^"^

P /P = 11 + -"-T— M 1 see equation A 1.2

P3/P

=f^

+ ^

\ ' ^ l

and r\ is the overall efficiency of the return circuit diffuser.

If we make the necessary substitutions,

p ^ _ p ^ ; 1 + 2 M'^

^3 ^o I , Y d . M2

2. <y

A 2 . 2

The v a l u e of P , / p i s a p p r o x i m a t e l y ixnity and we t h e n w r i t e ,

•4 1 + ^ M^

Y / Y - 1

1 + ^ ri M^ 2 cr

A 2 . 3

3. The adiabatic horse-power required by the compressor of a

direct-drive ret\irn flov/ tunnel

r

The adiabatic h.p,

(1 G J T, _{'^ P 3} 550

ïzi

Y • 4 A 3.1

I f vre s u b s t i t u t e t h e v a l u e of Vi/v-z ^ound f r a n e q u a t i o n A 2 , 3 , t h e a d i a b a t i c h . p . =

u C J T,

P 3

550

^ M 2

b-^cr)

Y-1 2

1 + -n^ ^ M''

.... A 3.2

4. Limiting values for the diffuser efficiency

T]

IVhen M ^ 1 . 0 the limiting conditions for

r\

are,

(a) A normal shock exists at the end of the v/orking-section and is

followed by isentropic compression in the diffuser. This is

equivalent to T] , = 1 . 0 where \

cr

sub. \

Ti , is the efficiency of a subsonic diffuser.

(b) A normal shock exists at the end of the working-section and is

followed by constant pressure in the diffuser. This is

equivalent to T) , = 0 ,

cr sub.

Por (a) it can be shovm that.

Y+1 /

Y + 1 V1/Y

(n

0" sub

cr

= 1)

^~'' »

2 Y M ^

- Y+i

(Y-1 )M' • « « • • • • * « f « « i->- H-» I

/For ...

For (b) it can be shovm that,

"H,

2 Y M^ - Y

Y+1

^) ' -

j

_{A 4.2}

^

M2

5. The energy ratio of a return flov/ tunnel

T-, , . rate of flov/ of kinetic energy at working-section Energy ratio = ^,. , -„.. ^ 2

power input

If Y/e use the adiabatic horse-power then,

E.R. = r.„ Y-1

(i C J T,

^ P 3

_U3/

Y _{- 1}

A 5.1

I f v/e s u b s t i t u t e the value of P./p-z from equation A 2.3 and

assume t h a t T, = T then,

3

0

'

E.R. =

(l+Tl^^M^j

A 5.2

The energy ratio for small values of M, i,e,, M~>0 is, 1

E.R. = M-^0

A 5.3

1-ri

and for large values of M,

E.R. = 1-Tl

5.4

But from equations A 4.1 and A 4» 2 it can be shown that as

M-^00, Ti -^0. Therefore equation A 5.4 becomes,

E.R. = 0 M-=> CO

A

5.5

6. To calculate the time of running of an intermittent ' straight-through' tunnel operated from compressed air storage

If the high pressure reservoir is pumped up to a pressure pu then the following analysis gives the time of running until the

pressiore in the reservoir falls to the constant blowing pressure p, .

(it is not essential to maintain constant blov/ing pressure but if this is not done the pressure will fall continuously in the working-section and the temperature and density Td.ll also vary during the run).

If V is the volijme of the reservoir then in time dt the mass of air in the reservoir falls by Vdp. The air flowing through the tunnel in time dt is (i dt, where |i is the mass flow through the tionnel in unit time. Hence,

^ - _ Ü . A 6 1

If we assime that no heat interchange exists betv/een the reservoir, the v/alls of the tunnel and the atmosphere, then the heat energy given in time dt to the atmosphere by the air leaving the tunnel is,

ji C T dt T/here T is the temperature of air in the reservoir at time t.

The change in time dt of the internal energy of the air inside the reservoir is,

V C^ d (pT)

hence,

u C T dt = -V C d (pT) A 6.2

If we combine equations A 6.2 and A 6.1 then v/e obtain for pressure changes in the reservoir the isentropic law,

•^ = constant ... A 6,J)

PY

It can be shoYvn that provided no losses occur in throttling between pressures p,. and p , the mass flow through the tunnel is given by, ^ = p,^ a^ S M |l + J ^ M^ A 6,4 where Pb % = P b i R T - ^ ^-5 /

But T the temperature of air in the reservoir varies with time, therefore p, must vary v/ith time,

If v/e neglect frictional losses in the expansion from the settling chamber, at pressure p, , to the v/orking-section, it can be

shovm that, ,

^ =1 1 A 6.6

vdiere p is- the almospheric pressure a t the e x i t from the diffuser, v/hose efficiency i s "n ,

Prom equations A 6 . 1 , A 6 . 3 , A 6.4> and A 6.5 i t follov/s t h a t ,

A t

/_2_\ % V ^ / M

1 ^ ^R

l + i

2Y

A 6.7

where, ^ t = time of running in sees.

Tp = initial temperature of air in reservoir

|i. , the initial mass flow bj

RT SM

•R

|1 + ^ M 2

Y+1

• " 2 ( Y - 1 )

7. To calculate the time of running of an intermittent ' straight-througli' tunnel operated from a vacuimi tank at exit

If 'V is the volume of the vacuum tr-nk and |i the constant mass flow through the tunnel then,

~- = ^ = constant A 7.1

The change of internal energy in the tank in time dt is

V C^ d (pT)

and the heat energy extracted from the atmosphere at temperature T , in time dt is,

fj, C T dt '^ p a

hence,

ti Cp T^ dt = V C^ d (pT) A,7.2

• If v/e integrate equation A 7.2 we find that,

. . . 0 . A. f * J

/where, ...

At =

PYRT a

where, /\t is the time of rimning

^ p is ^the pressure rise in the vacuum tank.

If v/e substitute the value of p. found from equation A 1.5,

(1 + ^ M ^ 2 ( ? H r )

P« S _{Y a} A 7.4

The pressure rise

^ P = P R - Pi

where p. is the initial pressure in the vacuum tank Y/Y-I

and • %

1 + ^ M 2

A 7.5

A 7.6

8. To calculuate the time of running of an intermittent ' straight-through' induction tunnel

I t can be sho\m t h a t ,

dp |i

dt " " Vm A 8.1

where m = mass of air flov/ing through the tunnel working-section

mass of air from the high pressure cylinder

Let pu and T„ be the initial reservoir pressure and temperature respectively and p, the constant blov/ing pressure. If similar

assimiptions to those stated in Appendix 6 are used, then

A^

{^)

l l ^

(i R T R 1

-I+i

2Y A 8.2

where m. = initial mass flov/ ratio.

1

9 . The a d i a b a . t i c horse-pov/er r e q u i r e d by t h e compressor i n an i n d u c t i o n type txmnel I f t h e compressor h a s s s t a g e s t h e a d i a b a t i c h . p . =

ïzi

- 1

550

\H

^2\ ^"^ '^. A 9c1

v/here JJ, mass of air discharged per sec.

Pp exit pressure

p. inlet pressure

T, inlet tempers.ture.

10. The time required to pump up a high pressure reservoir

Let a reservoir of volume V at pressure p

be supplied v/ith a mass flow \x at tempcrat\ire T then the change of density dp inside the reservoir in time dt is given by

dt

V

A 10.1

hence,

At = T

V

_{Ii Y R T .} •a ^ - 1 A 10.2

where Pp is the final reservoir pressure.

11, The time required to evacuate a tank

The volvimetric e f f i c i e n c y of a vacttum p\jmp

•n = Effective suction volume per stroke

swept volume per stroke

and r\ = f (p).

If the piamp runs at N r.p.m. and the swept volume per stroke is V then the volvime of air removed in unit time from a tanlc, volume V, connected to its inlet is

T] s N

60

A 11.1

But the change of mass of air in the tank in time dt is Vdp, hence

, p T) V N

dp ^ s A 11.2

dt _{60 V}

If the operation takes place at constant temperatiore,

V 60 I d£

1 ^ t = - ^ ^ ^ A 11.3 s ^p ^

where p is the initial pressure in the vacuum tank, p is the

final pressure and j^t is the time taken.

In an efficient vacuum pump r\ approximately equals unity, In this case,

A t = ^ ^ log P A 11.4

N V °

s

DtPWSCT-DRIVE. « E T U R N FU3W WIND T U N N C L

FIG

I.

COMPRCSSOQ \NAT»R OUT AFTGLR C O Ó L C n TANK TO R E O U C e PUUSATIONS IfSl AIR F B O M C O M P Q E S S O Q .

A U T O M A T I C T H R O T T L I N G V A L V E S T R A I G H T - T H R O U G H I N T E R M I T T E N T P R E S S U R E T U N N E L F I G . 5 .

C ^

C^UICK A C T I N G V A L V E VS/ORKINC S E C T I O M I V T H R O A T 2 "i^ T H R O A T TO VACUUM P U M P S I N I T I A L . ^R.e6suae. V A C U U M T A N K S T R A I G H T - T H R O U G H I N T E R M I T T E N T ' V A C U U M ' T U N N E L . P I G . G .

o

m

jo m

l

Z O r9 (M l O

2 0

3 0

4 0

5 0

WOaKiNO SECTION MACH NÜM&ER M i

3]

N

D I F F U S E R E F F I C I E N C V FOR SUB - AND S U P E R S O N I C .

E t 4 T R V V E L O C I T I E S ( F O R A I R J = | • 4-)

Q A R A T I O A C R O S S C O M P R E S S O R

r

•^

P3.

18 O IfrO l 4 o 12 o lOO 8 0 GO 4 - 0 2 0 l O < D I R E C T - D R I V E R E T U R N F L O W 1 1 P R E t\ — - = ^ ^ ' '

V |.

S S U R E R A I j

V ^ ^ j ^ j ^

0 2

'lO F O Q C > /

/ y

/ / y yT y ^r ^ O 3 O M P R E S S C / / / / / / / / / / / / / 1 /

f

•O 4 W I N D T U N N a » 1 R . /

1

/

N

•o

f

/ / r • •PRESSURE CONSTANT IN R E T U R N C I R C U I T 7o'SUB = 0 ^ I F F I I J S E R EFFY FOUMD FROM P R A C T I C A L CURVE ( S E E F I G . 5-T ) O M A C H . N U M B E R I N W O R K I N O - S C C T l O N l .

FIG. 8.

P

- y = C O M P R E S S O R P R E S S U R E R A T I O 4 0 3 0 S O 1 0 W - F L O W O F A I R . tJB / S E C - T U N N E L R E X a U l R E M E N T C O M P R E S S O R R . P M ' T 3 AMD P 3 T E M P E R A T U R E A N D » R ^ T O C O M P R E S S O R O 0 0 2 O 0 0 4 - O OOC» 0 0 0 0 O O i O 0 0 1 2 0 0 1 4

v/>J^

T V P l C A L COMPRESSOR, P E R F O R M A N C E CUR.VEÖ OF C O N S T A N T OOKÓ C O M P R E S S O R C H A R A C T E R I S T I C S F O R A D I R E C T D R j V E R E T U R N F U . O W

s

z

10 to Oi W I N D T U N N E L ,