INVESTIGATION POROUS

OF METALS

S. O.

V. G.

AT

Belov, M. Kartuesov,

HYDRAULIC LOW E.

PROPERTIES

OF

TEMPERATURES

Lebedev, and A. Yu.

UDC 6 6 9 - 1 3 8 : 5 3 2 . 5 8 . 0 0 1 . 2 Popov

The h y d r a u l i c r e s i s t a n c e of p o r o u s m e t a l s a t low t e m p e r a t u r e s h a s to be d e t e r m i n e d in o r d e r to u t i l i z e t h e m a s f i l t e r m e d i a i n c r y o g e n i c e n g i n e e r i n g . N o r m a l l y h y d r a u l i c p r o p e r t i e s of p o r o u s m e t a l s a r e i n v e s t i g a t e d d u r i n g f i l t r a t i o n of l i q u i d o r g a s a t 15-20 ~ C. E x p e r i m e n t a l v e r i f i c a t i o n i s r e q u i r e d to c o n f i r m t h e p o s s i b i l i t y of e x t r a p o l a t i n g t h e s e h y d r a u l i c p r o p e r t i e s to o p e r a t i n g t e m p e r a t u r e s o u t s i d e t h e 15-20~ r a n g e . L a r g e d e v i a t i o n s of f i l t e r e d f l u i d a n d p o r o u s m e t a l t e m p e r a t u r e s f r o m t h i s r a n g e c a n c a u s e d i f f e r e n t p r e s s u r e d r o p s due to c h a n g e s in v i s c o s i t y and d e n s i t y of t h e f i l t e r e d f l u i d a s w e l l a s c h a n g e s in the p o r o u s m e d i u m p r o p e r t i e s due to i t s t h e r m a l e x p a n s i o n . I n v e s t i g a t i o n s [1-3] of the e f f e c t of h e a t i n g t h e p o r o u s m e d i u m on i t s h y d r a u l i c p r o p e r t i e s h a v e b e e n c a r r i e d out by f i l t e r i n g a i r a n d oil a t 20-250~ T h e s e s h o w e d that t h e c h a n g e i n h y d r a u l i c r e s i s t a n c e of p o r o u s m e t a l l i c m e d i a c a n b e d e t e r m i n e d , w i t h s u f f i c i e n t p r a c t i c a l a c c u r a c y , by c o n s i d e r i n g o n l y t h e v a r i a tion in p h y s i c a l c o n s t a n t s of t h e f i l t e r e d fluid. It is r e c o m m e n d e d t h a t t h e p h y s i c a l c o n s t a n t s s h o u l d b e t a k e n at t h e a r i t h m e t i c m e a n t e m p e r a t u r e of the f i l t e r e d f l u i d i n t h e p o r e s . H o w e v e r , d a t a p u b l i s h e d in [4] i n d i c a t e t h a t t h e h y d r a u l i c r e s i s t a n c e of p o r o u s m e t a l s ( b r o n z e , b r a s s , n i c k e l , c o p p e r , a n d t u n g s t e n ) , p r e p a r e d b y s i n t e r i n g s p h e r i c a l p a r t i c l e s , u n d e r g o e s a g r e a t e r c h a n g e in h e a t i n g f r o m 15 to 60~ t h a n do t h e p h y s i c a l p r o p e r t i e s of t h e f i l t e r e d fluid. T h i s r e s u l t s f r o m a s t r u c t u r a l c h a n g e of the p o r o u s m e t a l a s it u n d e r g o e s t h e r m a l e x p a n s i o n . V N I I k r i o g e n m a s h , in c o n j u n c t i o n with t h e N. 1~. B a u m a n M o s c o w T e c h n i c a l C o l l e g e , h a s c a r r i e d out w o r k to d e t e r m i n e t h e e f f e c t of c o o l i n g p o r o u s m e t a l s on t h e i r h y d r a u l i c r e s i s t a n c e . T h e c h a n g e in p o r e s i z e on c o o l i n g and h e a t i n g s h o u l d r e s u l t in c o r r e s p o n d i n g i n c r e a s e s and d e c r e a s e s of h y d r a u l i c r e s i s t a n c e . A s m a l l c h a n g e in t h e r e l a t i v e l o c a t i o n of p r o j e c t i o n s on t h e p o r e s u r f a c e due to t h e r m a l e x p a n s i o n of p o r o u s m a t e r i a l can r e s u l t in a s u b s t a n t i a l c h a n g e in s i z e of p o r e p a s s a g e s . V i s c o s i t y a n d d e n s i t y of t h e f i l t e r e d f l u i d v a r y w i t h i t s t e m p e r a t u r e r e s u l t i n g i n c h a n g e s in p r e s s u r e d r o p t h r o u g h p o r o u s e l e m e n t s . L e t us e x a m i n e a n i d e a l p o r o u s m e d i u m (Fig. 1) with p o r e s of d i a m e t e r d n a n d l e n g t h l to t h e o r e t i c a l l y e v a l u a t e the e f f e c t of t h e s e f a c t o r s on t h e h y d r a u l i c r e s i s t a n c e of the m e d i u m . W e w i l l a s s u m e u n i d i r e c t i o n a l d e v e l o p e d g a s flow in t h e p o r e s . T h e i n t e g r a l f o r m of t h e e q u a t i o n of g a s flow in the p o r e s c a n b e w r i t t e n a s I

Pl --P2 = 1~".(v2-- v~)

g

2I

+ ~-

,f ca ~ dx,

(1)

0

w h e r e Pl a n d P2 a r e t h e g a s p r e s s u r e s a t t h e i n l e t a n d o u t l e t of the p o r e s ; j i s t h e unit w e i g h t flow t h r o u g h a p o r e , j = ptvl = P2v2 = c o n s t ; v 1 a n d v 2 a r e the g a s v e l o c i t i e s at the i n l e t a n d o u t l e t c r o s s s e c t i o n s of the p o r e s ; Pl and P2 a r e t h e g a s d e n s i t i e s a t t h e i n l e t a n d o u t l e t c r o s s s e c t i o n s of t h e p o r e s ; g i s the a c c e l e r a t i o n of g r a v i t y ; ~d i s t h e h y d r a u l i c r e s i s t a n c e c o e f f i c i e n t of t h e c h a n n e l f o r m e d by t h e p o r e s w i t h l a m i n a r g a s flow t h r o u g h t h e p o r e s ; a n d v x i s the g a s v e l o c i t y in t h e p o r e a t c r o s s s e c t i o n x. T h e f i r s t t e r m of t h e r i g h t hand s i d e of t h e e q u a t i o n r e p r e s e n t s t h e p r e s s u r e d r o p A p m due to t h e c h a n g e in m o m e n t u m of t h e g a s w h i l e the s e c o n d t e r m i s the p r e s s u r e d r o p A p f due to f r i c t i o n in t h e p o r e s . T r a n s l a t e d f r o m K h i m i c h e s k o e i N e f t y a n o e M a s h i n o s t r o e n i e , No. 11, pp. 13-14, N o v e m b e r , 1971.

9 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without permission of the publisher. A copy of this article is available from the publisher for $15.00.

966

I

,_.

2

T

5

%.,

)

!x[

~= f5

Fig.

1

t5

/4

4 5 7 t0

,

ZO 50 40 6~ fQ~2 200 500 f00 Re~

Fig. 3

Fig. 2

Fig. I. Calculation diagram

F'fl

of an ideal porous medium.

Fig. 2. Sche:matic of the experimental

apparatus

for pore filtration of cold gaseous

nitrogen.

Fig. 3. Experimentally determined hydraulic resistance coefficient ~d of porous metals as a function of Reynolds number Re d determined during filtration of nitrogen at 15-20~ i) bronze; 2) stainless steel; 3) Nichrome; 9 e, A) experimental data obtained during filtration of nitrogen at temperatures as low as II0~

TABLE 1 [~viaterial pae~ &veragepore ticle size Porosity ;ize dnav, /t d part. av, P

Material

0,340 0,266

Kh20NS0 Nichrome

0.864 0,297

231 211 293 933

Khl8N9T stainless steel[

o.312 0,345

67,4 74,1

Br. OF-10-1 bronze

0,343 0,334 0,390 0,380

62,9 52,9 62,6 61,9

I

Let us e v a l u a t e the r e l a t i v e m a g n i t u d e s of t h e s e two pressure drops, Apm/Apf

A pf _ a Pm

815--500

l 2 .( Cd Vx dx o dn (v2 - - v~)

(2)

We a s s u m e that ~d const a n d v x = (v~ + v 2 ) / 2 const. E q u a t i o n (2) can t h e n be w r i t t e n a s

~.00--815

Apf Pm

126--160

~d(Vl + v2)l dn (v~ - - v l )

T h e g r o u p of p o r o u s m e t a l s i n v e s t i g a t e d had the f o l l o w i n g t y p i c a l g e o m e t r i c d i m e n s i o n s : l 2-3 m m a n d d n = 50-300 #. The h y d r a u l i c r e s i s t a n c e c o e f f i c i e n t Cd >- 8 u n d e r c o n d i t i o n s of l a m i n a r flow (Reyn o l d s n u m b e r < 5) in the p o r e s . T h e r e f o r e a s s u m i n g that v 2 >> v 1 we find TM

h p f _ >~ 50. '~Pm

T h u s the f r i c t i o n l o s s e s in t h e p o r e s in t h i s e a s e a r e a l w a y s m u c h g r e a t e r t h a n l o s s e s r e l a t e d to the c h a n g e i n gas m o m e n t u m . T h e r e f o r e i n e v a l u a t i n g gas p r e s s u r e d r o p s i n p o r e f i l t r a t i o n we c a n l i m i t our a n a l y s i s to the f r i c t i o n c o m p o n e n t of the l o s s . F r o m Eq. (1) we c a n w r i t e (vl + v~)~p

l

9

dn

w h e r e p i s the gas d e n s i t y at the a v e r a g e gas t e m p e r a t u r e a n d p r e s s u r e i n the p o r e s . A s s u m i n g that i n l a m i n a r flow i n the p o r e s Cd = C R e d (where C is a c o n s t a n t , R e d = (v 1 + v2)dnP / 2 ~ i s the R e y n o l d s n u m b e r ; p is the v i s c o s i t y of the f i l t e r e d gas) we f i n a l l y get ~Pf

Cl(v~ + v~) ~,.

(3)

4 E q u a t i o n (3) shows that c h a n g e s i n f r i c t i o n a l l o s s e s d u r i n g l a m i n a r flow a n d c o n s t a n t gas v e l o c i t y a r e d e t e r m i n e d by v a r i a t i o n s i n v i s c o s i t y of the f i l t e r e d gas a n d g e o m e t r i c d i m e n s i o n s of the p o r e s . Let us e x a m i n e the r e l a t i v e v a r i a t i o n i n f r i c t i o n l o s s e s f r o m e a c h of t h e s e c a u s e s a s s u m i n g that gas t e m p e r a t u r e v a r i e s f r o m 293 to 110~ a n d that the p o r o u s m e t a l i s N i c h r o m e . T h e n

967

n

(~]7 f )29~

~t293

p~ -- (Ap~ f ),1o

~11o

-A Pcl =

(hpdf).'293 (Apdf )l~O --

=2.7;

2

dnll 0 l.',93 =0.998. d~293 t11o

The calculated r e s u l t s show that friction l o s s e s related to v i s c o s i t y changes d e c r e a s e by a factor of 2.7 while the changes in g e o m e t r i c dimensions of an ideal pore i n c r e a s e the friction loss only by 0.2%. Experiments were c a r r i e d out using the porous samples described in Table 1 to confirm the calculated r e salts. Two sets of apparatus were used in the experiments. The f i r s t was designed for pore filtration of c o m p r e s s e d air at 15-20~ while the second (Fig. 2) was designed to investigate the filtration of gaseous nitrogen in pores at 300-110~ Gaseous nitrogen f r o m cylinder 1 flows through shutoff valve 2 and p r e s sure reducing valve 3 into f r e e z e r 4 where it is Cooled down to r e m o v e m o i s t u r e and carbon dioxide (carbon dioxide is precipitated as crystals). After the f r e e z e r the nitrogen p a s s e s through heat exchanger 6 and flows to the porous testpiece installed in housing 9. The testpiece was installed in a ring whose inner diameter was 0.2 m m less than the outer d i a m e t e r of the testpiece and the a s s e m b l y was placed in housing 9. Epoxy r e s i n with a hardening agent was poured between the c i r c u m f e r e n t i a l s u r f a c e of the test piece and the ring. The p r o c e d u r e permitted m o r e a c c u r a t e m e a s u r e m e n t of the filtering s u r f a c e and eliminated leaks along the edges of the testpiece. After passing through the testpiece the nitrogen flows to heater 10 and r o t a m e t e r 13 (for flow m e a s u r e m e n t ) and is d i s charged to atmosphere. Reduced nitrogen p r e s s u r e is m e a s u r e d by p r e s s u r e gauge 5. P r e s s u r e Pl at the inlet to the testpiece is m e a s u r e d by calibrated p r e s s u r e gauge 16. P r e s s u r e drop a c r o s s the testpiece is m e a s u r e d by a type DM differential p r e s s u r e t r a n s m i t t e r 14 and is r e c o r d e d on a type DSR r e c o r d e r 15. T e m p e r a t u r e at the inlet to the testpiece is m e a s u r e d by c o p p e r - c o n s t a n t a n t h e r mocouple 8 and is r e c o r d e d in an E P P - 0 9 electronic potentiometer 7. Nitrogen t e m p e r a t u r e at the r o t a m e t e r is m e a s u r e d by c o p p e r - c o n s t a n t a n thermocouple 11 and r e c o r d e d on KSP-06 12. Experimental r e s u l t s in dimensionless f o r m a r e shown in Fig. 3. It shows that the hydraulic r e s i s tance of porous metals in filtering gaseous nitrogen at 300-110~ can be calculated using dimensionless functions obtained during filtration of nitrogen under n o r m a l conditions (15-20~ The effect of variation in physical p r o p e r t i e s of the gas and the porous m a t e r i a l with changing t e m p e r a t u r e on p r e s s u r e drop in the pores can be adequately c o r r e l a t e d by determining the v i s c o s i t y and density, which appear in the dim e n s i o n l e s s functions, at a v e r a g e gas t e m p e r a t u r e and p r e s s u r e in the pores. The a v e r a g e pore dimension was used in c o r r e l a t i n g experimental data for actual porous media hydraulic r e s i s t a n c e e x p r e s s e d in dimensionless form. This a v e r a g e dimension was d e t e r m i n e d by the m e t h od of displacing liquid f r o m the pores. The velocity in the p o r e s was taken as the governing velocity in the correlation. LITERATURE 1.

2. 3. 4.

968

A. R. A. D.

S. N. M. B.

CITED

Berkman, Porous P e r m e a b l e C e r a m i c s [in Russian], Gostoptekhizdat, Moscow (1959). Mullokandov, Zh. Tekh. Fiz., 18, No. 8 (1948). Sycheva and N. N. Egorov, Khim. iTekhnol. Topliv i Masel, No. 8 (1963). Greenberg and E. Weger, Chem. Eng. Sci., 12, No. 1 (1960).