SECGNJ QUARTEPLY PROGWSS l?EPOZT ON

NSK 22-009-288

7,- L g &i.K 7 - 3 4 - 6 J

A Study of F lu id Dynamics of Gaseous Nuclear

A comprehensive review of t h e state of knowledge of vor tex flows

- \ and how such flows may o r may not be used for f l u i d dynamic containment

of a gaseous nuclear f u e l has Seen continued. Vork t h i s p a s t qua r t e r

h a s concentrated on empirical c o r r e l a t i o n s of experimental d a t a a v a i l a b l e

i n the l i t e r a t u r e . This work has been repor ted i n Ref. (1) and only t h e

N p r i n c i p a l r e s u l t s obtained i n i t w i l l be summarized here in .

Vortex experiments run a t high Reynolds numbers t y p i c a l l y have some di

(7.3 a tu rbulence assoc ia ted wi th them. This in t roduces an unce r t a in ty i n t o

t h e flow that cannot be removed by completely t h e o r e t i c a l means without

some advances i n t h e present knowledge of t h e b a s i c phenomena of turbulence.

It is t he re fo re c u r r e n t l y necessary t o r e l y on sone empir ica l information

i n any attempt t o p r e d i c t vor tex flow p a t t e r n s wi th high Reynolds numbers.

One method of approach is t o compare a laminar flow theory which U s

i nc ludes as many important features of t h e flow as poss ib l e with experi-

menta l ly obtained v e l o c i t y p r o f i l e s . The d i f f e r e n c e s between theory and

u)9 mod Mlll3Vd

experiment are then used t o i n f e r a d i f f e r e n c e between t h e e f f e c t i v e

t u r b u l e n t eddy v i s c o s i t y and t h e l a u i n a r v i s c o s i t y . The laminar flow

theo ry chosen i n Ref. (1) f o r use i n t h i s conparison is that by

Rosenzweig, Lewellen and Ross(2). Figure (1) shows a comparison of t h e

r e s u l t s of t h i s theory with an experimental v e l o c i t y p r o f i l e obtained by

Tra~ers '~) under w h a t h e believed t o be 1ai::nar flow condi t ions . The

agreement, a l though not p e r f e c i , a p w a r s 30 be q u i t e s a t i s f a c t o r y .

is concluded t h a t t h e theory is adequate t o p r e d i c t a completely laminar

It

https://ntrs.nasa.gov/search.jsp?R=19680026940 2018-06-16T11:37:42+00:00Z

* . 4 ? ..- , \

flow and thus i t is reasonable t o a t t r i b u t e d i f f e rences between theory

and experiment t o turbulence i n the case of high Reynolds number experi-

ments. *

The r a t i o of e f f e c t i v e eddy v i s c o s i t y p t o a c t u a l laminar v i s c o s i t y JJ,

which w a s deduced i n the manner described i n t h e preceding paragraph is

p l o t t e d i n Fig. (2) f o r d a t a ava i l ab le i n the bibliography given i n Ref.

(4).

(") 'I2 (D/L)o'28 where R e is t h e Reynolds number based t h e parameter Re t ;

on t angen t i a l ve loc i ty and t h e radius at t h e o u t s i d e of the vor tex ; u/v

The da ta appear t o c o r r e l a t e reasonably w e l l when p lo t t ed aga ins t

t

is t h e r a t i o of r a d i a l to t angen t i a l v e l o c i t y a t t h e ou te r r ad ius of t he

vortex; and D/L is the diameter-to-length r a t i o of t h e vor tex chamber.

The exponents i n t h i s parameter were chosen to o b t a i n t h e b e s t poss ib le

least squares f i t to a l l t he data.

i n t h e Table i n Appendix A.

The key t o t h e d a t a poin ts is given

This t a b l e a l s o inc ludes information on o the r

experiments no t included on Fig. (2) due to a l ack of s u f f i c i e n t information.

Figure (2), perhaps, over-emphasizes t h e role o f turbulence i n de te r -

mining the v e l o c i t y d i s t r i b u t i o n i n a vortex.

of 1.1 /p r e s u l t from r a t h e r s m a l l d i f f e rences between laminar theory and

I n some cases l a r g e values *

experiment. Figure (3) shows a p l o t of t h e c i r c u l a t i o n a t t h e edge of t h e

exhaust rad ius as a func t ion of a boundary-layer i n t e r a c t i o n parameter.

The s o l i d l i n e is t h e t h e o r e t i c a l curve obtained as the r a d i a l Reynolds

number based on r a d i a l mass flow becomes very large.

f a r e d i n t o f i t t h e da t a . The d i f f e rence between t h e two l i n e s is

The dashed l i n e is

assumed t o be caused by turbulence, although p a r t o f t h i s d i f f e rence

could a c t u a l l y be caused by approximations used i n the boundary-layer

theory used to generate t h e s o l i d l i n e .

probably provides as good an estimate of re/r The d i r e c t use of Fig. (3)

f o r any experiment as 0

,. 3 .

* does t h e more e l abora t e procedure of es t imat ing p

using t h i s i n t h e laminar theory of R e f . (2 ) .

The empir ica l c o r r e l a t i o n s of t h e p a s t q u a r t e r have been aimed a t

from Fig. (2) and

providing t h e information required t o p r e d i c t t h e flow p a t t e r n i n any

given vo r t ex tube. This e f f o r t w i l l be continued, s ince t h e degree t o

which one can do t h i s forms an e s s e n t i a l part of a comprehensive review

of t h e state of knobledge of vortex flows.

lii. S. Lewellen

Pro j ec t Supervisor

September 30, 1968

REFERENCES

1. Newton, W. H . , 111, "Correlation of Diss ipa t ion i n Confined Turbulent Vortices", S.M. Thesis , Dept. of Aero. and Astro., M.I.T. (August 1968).

2. Rosenzweig, M. L., Lewellen, W. S., and Xoss, D. H., "Confined Vortex Flows with Boundary Layer Interact ion", Aerospace Corporation ATN-64 (9227)-2 (1964).

3. Travers, A., "Experimental I w e s t i g a t i o n of Flow Pa t t e rns i n Radial-Outflow Vortexes Using a Rotating-Peripheral-Wall Water Vortex Tubel', United Aircraf t Research Laborator ies Report F-910091-10, prepared under Contract NASw-847 (February 1968).

4. Lewellen, W. S., "F i r s t Quarterly Progress Report on NSR 22-009-288" (July 1968).

5 . Wormley, D. N . , "An Analyt ical and Experimental Inves t iga t ion of Vortex-Type Fluid Pbdulators", Ph.D. Thesis, Department of Hechanical Engineering, M.I.T. (October 1967).

6 . Keyes, J. J., "An Experimental Study of Gas Dynamics i n High Veloci ty Vortex Flow", Proceedings of t h e 1960 Heat Transfer and Flu id Mechanics I n s t i t u t e , Stanford Universi ty (1960).

Kendall, J. t4., Jr., "Experimental Study of a Compressible Viscous Vortex", Report No. TR-32-290, Jet ?repulsion Laboratory, Pasadena, Ca l i fo rn ia ( 5 June 1962).

7.

8. Smith, J. L., "An Experimental Study of t he Vortex i n the Cyclone Separator", ASME Paper No. 61-bJA-189.

9. P i v i r o t t o , T. J . , "Binary Diffusion in a Compressible Three-Dimensional Turbulent Vortex", Space Program Summary 37-18, Jet Propulsion Laboratory, Pasadena, Cal i forn ia (31 December 1962), pp. 129-132.

10. Eins te in , H. A. and Li, H. L . , "Steady Vortex Flow i n a Real Fluid", Proceedings of t h e 1951 Heat Transfer and Fluid Mechanics I n s t i t u t e , Stanford Universi ty (1951).

11. Ragsdale, R. G., "A Mixing Length Cor re l a t ion of Turbulent Vortex Data", ASME Paper No. G1-WA-244.

12. Donaldson, C. duP. and Williamson, G. G., "An Experimental Study of Turbulence i n a Driven Vortex", Aeronautical Research Associates of Pr inceton, Report No. ARAP TII-64-2 (July 1964).

5 . 13.

14

15.

16.

17 .

18.

19.

20.

21.

22.

23.

24.

25.

Anderson, O., "Theoretical Solutions f o r t h e Secondary Flow on t h e End Wall of a Vortex Tube", UAC Research Laboratories Report R-2494-1, United Ai rc ra f t Corporation, East Hartford, Connecticut (November 1961).

Owen, F. S., Hale, R. W., Johnson, B. V., and Travers, A., "Experimental Inves t iga t ion of Charac t e r i s t i c s of Confined Jet- Driven Vortex Flows", United A i r c r a f t Research Laboratories Report R-2494-2, prepared under Contract AF 04(611)-7448 (November 1961).

Travers, A., and Johnson, B. V., "Measurements of Flow Characteristics i n a Basic Vortex Tube", United Ai rc ra f t Research Laboratories Report C-910091-2, prepared under Contract NASw-847 (September 1964).

Travers, A. and Johnson, B. V., "Measureiients of Flow Charac te r i s t i c s i n an Axial-Flow Vortex Tube", United A i r c r a f t Research Laboratories Report C-91OOS1-3, prepared under Contract NASw-847 (September 1964).

Roschke, E. J. and P iv i ro t to , T. J. , "Simi la r i ty i n Confined Vortex Flows", Jet Propulsion Laboratory, Technical Report No. 32-789 (15 August 1965).

Rott , N. and Lewellen, W. S . , "Boundary Layers and Their In t e rac t ions i n Rotating Flows", Progress i n Aeronautical Sciences. Vol. 7, Edited by D. Kuchemann (1966).

Donaldson, C. duP. and Snedeker, 3.. S. , "Experimental Inves t iga t ion of t he S t ruc tu re of Vortices i n Simple c y l i n d r i c a l Vortex Chambers", ARAP Report 47 (December 1962).

Ross, D. H., "An Experimental Study of Secondary Flow i n Jet-Driven Vortex Chambers", Aerospace Corporation ATN-G4(9227)-1 (1964).

Savino, J. M. and Keshock, E. G . , "Experimental P r o f i l e s of Velocity Components and Radial Pressure Dis t r ibu t ions i n a Vortex Contained i n a Short Cyl indr ica l Chamber", Lewis Research Center NASA TND-3072 (1965).

Keyes, J. J., "Hydromagnetic S t a b i l i z a t i o n Experiments with Jet- Driven Vortex Flow", Oak Ridge National Laboratory, Oak Ridge, Tennessee.

Roschke, E. J., "Experimental Inves t iga t ion of a Confined, Jet- Driven Water Vortex", California I n s t i t u t e of Technology, Jet Propulsion Laboratory, Technical Report No. 32-982 (October 1966).

Nakamura, T., "Experimental Study of a Confined Vortex Flow", S.M. Thesis, Department of Aeronautics and Astronautics, M.I.T. (January 1966).

Hester, J. A., "The Effec ts of L/D and Mass Flow Rate on t h e Strength of a Confined Vortex", S.M. Thesis, Department of Aeronautics and Astronautics, M.I.T. (June 1966).

. 26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

6 . Pivirotto, T. J., "Binary Diffu;jon iu a Compressible, Three- Dimensional Vortex", Calif. Institute of Technology, Jet Propulsion Laboratory, Space Programs Summary 37-15, Vol. IV (1962).

Poplawski, R. and Pinchak, A. C., "Aerodynamic Performance of Reversed Flow Vortex Chambers", Aerospace Research Laboratories Report ARL-65-219 (October 1965).

Roschke, E. J., "tieat Transfer and Fluid Mechanics", California Institute of Technology, Jet Propulsion Laboratory, Space Programs Summary No. 37-20, Vol. IV (1963).

Pivirotto, T. J., "Radial Static Pressure Distributions in Confined Compressible Vortex Flow Fields", Jet Propulsion Laboratory, Technical Report No. 32-1076 (1 Piarch 1967).

Toomre, J., "Highly Swlr!€ng Flgws Through a Convergiq Diverging Nozzle", S.M. Thesis, Depjartient of Aeronautics and Astronautics, M.I.T. (Jiine 1963).

Mayer, E. A,, "Large-Signal Vortex Valve Analysis", The Bendix Corporation, Southfield, Michigan.

Kwok, C. C. K., "Vortex low ir, a Thin Cylindrical Chamber and Its Application in Fluid Ampliiier Technology", McGill University (Montreal) Department of Mechanical Engineering Report 66-80 (1966).

Lay, J. E., "An iixperimental and Analytical Study of Vortex-Flow Temperature Separation by Superposition of Spiral and Axial F l o w s , Parts 1 and 2, Transactions of ASHE (August 1959).

Savino, J. M. and Ragsdale, R. G., "Some Temperature and Pressure Measurements in Confined Vortex Fields", ASHE Paper No. 60-SA-4 (13 July 1960).

Hartnett, J. P., and Eckert, E. R. G . , "Experimental Study of the Velocity and Temperature Distribution in a High-Velocity Vortex- Type Flow", Transactions of the ASME (1957).

Kidd, G. J., Jr., "Confined Vortex Flow Hear a Stationary Disk", Oak Ridge National Laboratory (April 1966).

Keyes, J. J., J r . , and Dial, R. E., "An Experimental Study of Vortex Flow for Application to Gas-Phase Fission Heating", Oak Ridge National Laboratory (16 April 1960).

Royle, J. K. and Hassan, M. A., "Characteristics of Vortex Devices", Second Cranfield Fluidics Conference, Cambridge, England (January 1967).

Collins, J. C. and Stubbs, T. F., "Qualitative Experimental Vortex Tube Configurations", University of California, Lawrence Radiation Lab., UCRL 12045 (1964).

40. Gyarmathy, G., "Optical Measurement of Radial Density Distribution in a High-speed Confined Air Vortex", ARL 67-0234 (December 1967).

.. ..

Y 5

f M e c

4

.. .

.

1

-. . ....

7.

Experimental Curve

Theore t ica l Curve

Velocity used to begin Second I t e r a t i o n

De t c-mi i ned from F i r s t It er a t ion

c

Figure 1. Tangential Velocity Profilc? Showing f::cpcrir!:cntal Curve 2nd

Tlieoret.icrtl Curve Based on Countlary-Layer Intcr ,?ct ion Theory.

,

. . - ..

n

1000.

100

8.

I -2 -w-- 2,-.-.----~ 1 -.-+.----"..-.---' t I-- I-

c -pr )' a.2 ~ 0 0 0 0 0 3orom :eo.oo

5 0 3 0- S O 0 0 3 6 0 0 I b O O O

4

Ret (.+-I uoo

Figure 2.The Var ia t ion of t h e Ratio of L m i n n r R e d i a l Reynolds t o E f fec t ive u .50 D ?8 . Turbulent Radiai R e y n o l d s I!u;nber w i t h Re,(-) V (E) -

.

9.

Figure 3 . The Var i a t ion of t h e Ra t io of t h e C i r c u l a t i o n rt t h e Exit t o t h e

r C i r c u l a t i o n ' a t - r0 =, .8 wi th A \ I - s)

- Rer+c;Otheory (Ref. 2)

- - - b p i r i c a l F i t

1.0 '

re c

rf3

.8

' .6

-2

C I

. .

. 0 1 =03 . I . . 1.0 3 .0

.

. . 0.

.

APPENDIX A

. DATA TABULA'L'ION

,

. . Data used i n t h i s a n a l y s i s were obtained through a l i t e r a t u r e

sea rch from twenty-four t echn ica l r epor t s .

i n the form of nondirnenslonal p a r m e t e r s ob ta ined through t h e u s e of t h e

These results are t abu la t ed

d a t a reduct ion procedure descr ibed i n Appendix A.

A few conmaits regard ing t h e explana t ion of t l i i s t a b l e are i n

order .

The r e fe rence from which t h e data were obta ined , t h e symbol re-

p r e s e n t i n g t h e d a t a on the figures , dimensionless parameters , are

l i s t e d reading from l e f t t o r igh t . . /

Some of tKe parameters from va r ious re ferences could not be

. determined due t o lack of s u f f i c i e n t information, for example t h e area

ra t io from Reference 12, This is ind ica t ed on t h e c h a r t by t h e le t ters

"NA" neaning n o t a v a i l a b l e .

, determined before t h e r a d i u s . The c i r c u l a t i o n ra t io , - r . 8

c o r r e c t i o n (see Appendix A) was made.

re

' * I A l l r e p o r t s except where otherw3se noted had a s p e c i f i c hea t r a t i o /

of 1.4.

10.

. . o.

11.

k 2

p? 4

. -

I . 12.

. .

c %

4 ;4

4 x 4 2

4 2

4 z 4 %

-4 z

0 r( x h co

e 4

_ . c

L, L4 0 a 2

. .

x

u 2 >:

13.

e e . . . . .

In VI m o o r ( d X x e b N

r-4

o u o e a N

o r ( G f - 4

c\l ri

0 0 0 r-i o - ? b r-i

. .

t- N h w m

e .

m r- I. b Pi

co t-i N

\D 0 N

.

eJ a ri . ~ ~ ~ 0 0 0 0 0 0

7

14. .

. > r 4 u u w a *

X VI .- a 0 r - i u ) a u u 0 t n h U - i E o ~ o a o o 4 4 4 N u u ~ o o o o o o o o . z z z . . . . . . . . . & Pi Pi r i d

0 0 0 3 0 0 u u 'U u N N cu rJ

r( d Pi Pi r( Pi % z z Q m 0 u) m m rn m u) 0 u) u) 0 0 0 0 ~ 0 0 4 4 4 u u u 0 ~ u u u m m ~ m . . . . . .

. . e . . . . . . . ; . . I i

rd z o 5L

0 N . '

m u k 0 a al p:

. . . . .

U e7

r - i

03 u3 ri . u3 U U .

15.

\o m N

03 l-i r i . 9 w m .

.3 m ri .

m V M

e

a co .

W \o

l-i e

m \D c7 . VI \o

e

4 M

4 .

03 a m . vl N W .

W u3

ri .

W a r ) . m VI

9 CCL

N .

0 c.l N

03 0 m .

rn P'I

m

0 N N . vl V .

.a rcI

ri

0 Q m

h a

a c n t - l m N m . . \ o m

m m . . N ri

ovl W N m rr) . .

h c n Q b m m

. e

m o m v l * e

o m \ D m e . . . . .

m m m r r r l n m m m m m m ~ 0 0 0 m I n 0 0 0 0 0 0 0 0 '. r n v l v l m m m 0 0 0 0 0 .

0 d X z PI . vl

M

. (3

b 0 . cn VI ri

m m U

0

M N N

ri x rrr r-i rn . \D m

UJ rf M . ri m cv

rrr rrr U . * N N

rl x N 03 0 . \D h

b 9

d

e ch m

rrr m U . I- * N

N

\D m N . vl N . (v U u3 .

r( x Co V

rl .

M o\

0 b

4 .

N * rrr

CA rrr V . M I- N

N

U J rn (v . vl N . U u3 a .

4 x a 4 m . a U

N N

N . 0 h ri

VI m e . 03 03 N

ei

4 0

r-i

vl N ri . 0 V U .

r-l x m b a

U VI

N m ri .

i.1 VI N

VI vl * . h 9 N

e4

ri 0

4

m N d

.

. d a .

0 0 &i x Q 4 t-l . a\ N

0 M h

W N 4

Y, m U . 03 VI N

u3

N 0

0-l

m N ri

.

. m 9 .

r( x N h U . m V M

0 m m

m m N

m vl U . N 0 N

e

0

co 7! . W h

a m 9

03 03 N

m m U . h I- N

a

\D CA b . rn N

0 W

e

~

ri X U h . m m

03 4j

ri .

a3 m CCI

m m . a 0 N

N

4 0

ri

rrr W ri . m 0 h

e

ri X ' ri hI . rrr W 4 . 0 .;t . 0 ri ri

rrr rrr e . . .

ri 0 r(

0 4

N I-

(v . I- ri . I- 03 .

\o co . 0 u3

h N rl

N t-- V

vl Y, U

N 03 ri

ei

rl 0 4

rrr N d . h m 02

0

. . *

k 2

U O I J W N a

r i d

0 ri

(v I-

N . I- 4 . Pi U .

0 0 0 r l I 4 4

N e 4

m m

l n m N N r i d

9 9

0 0

N O 0 0 - . .

PIP . *O

i

. . 6 .

16.

2

c %

W U N .

I n - m m m m I n 0 in 0 0 0 0

m m m m ' 0 0 0 0

U

2

. . . . . . . . . . . . * e . . . d o .

k 2

P4

U e4 u4 al c4

17.

VI m o 0 6 4 4 % x u a .

m 0 4 x U co

c %

. . . . . . .

,

18. - .

a The r a t i o of s p e c i f i c heats, y , f o r thk f i r s t 3 po in t s from Ref. 2 is 1.67 (hellurn) and f o r ;he l a s t 3 p o i n t s 1.4 (ni t rogen) . The r a t i o of s p e c i f i c hea t s for R e f . 39 is 1.67 (hclium). Thc o t h e r r e p o r t s (i.e. Refs. lS, 16, 20) used water as the work.ing f l u i d f o r which t h e ratio of s p e c i f i c h e a t s is defined as one.

l

In t h e s e r e p o r t s a per iphe ra l bypass was employed which recioved p a r t of t h e flow from the vortex charuber during the experiments.

The value of * is, t he re fo re , i n qucst ioi i . A

*re

The vortex chamber gcoinetry used i n t h i s r epor t M R S unusual i n t h a t it hzd a maximum rad ius of r . = 1.875 inches (used h e r e as ro) at its c e n t e r and then tapered s l i g h t l y t o - ~ a r d both ends.

Even t1:oug'n t h e r e were insuf f ic ien t : d a t a i n these r e p o r t s t o apply t h e theory of R e f . 2 (i..e. except f o r t h e f i r s t en t ry under -Xef. 2 4 ) t h e s e p o i n t s a r e included because the boundary layer cor rec t io i l f a c t o r is of an o rde r of magnitude m a l 1 enough such t h a t resul ts obta ined h e r e w i l l not be a f f ec t ed .

d

. .

. .

..