DISTRIBUTION PHASE

IN

OF A

GAS-

THE LIQUID

VELOCITY FLOW

A . P~ B u r d u k o v , B . K. a n d V. E. N a k o r y a k o v

PROFILES WITH

Koz'menko,

SMALL

OF GAS

THE

LIQUID CONTENTS UDC 532.529.5

Artilce [1] gives the results of m e a s u r e m e n t of the friction at the wall of a channel under bubble conditions, in a wide range of Reynolds numbers. It is shown that the concept of l a m i n a r flow conditions has no meaning when it is applied to the flow of a two-phase mixture, since, even with v e r y small Reynolds numbers, the level of the pulsations of the f r i c tion is high, and the s p e c t r u m of the pulsations of the friction is continuous. In this ease, the mean friction is much g r e a t e r than the calculated; here the value of the r e s i s t a n c e coefficient is not a single-valued function of the Reynolds number. The p r e s e n t article gives the results of m e a s u r e m e n t of the velocity profiles of the liquid phase, c a r r i e d out using an e l e c t r o diffusion method. It is shown that, with Reynolds numbers corresponding to turbulent flow conditions, the profile of the velocity in a two-phase mixture is close to turbulent and does not depend on the gas content.

With Reynolds numbers corresponding to l a m i n a r flow conditions, the velocity profile of a two-phase flow differs strongly from the c h a r a c t e r i s t i c l a m i n a r velocity profile of a one-phase liquid. It is fuller, close to turbulent, and, in this sense, depends on the gas content. This result is in complete a g r e e m e n t with the data of [1]. The determination of the phase velocities in a g a s - l i q u i d flow is of undoubted interest from the point of view of constructing calculating models and methods for such flows. At the p r e s e n t time, with m e a s u r e m e n t of the velocity of the liquid with a t h e r m o a n e m o m e t e r , f i l m type pickups a r e usually used. It is obvious that, in a g a s - l i q u i d flow with dimensional gaseous inclusions m e a s u r i n g less than 1 mml the dimensions of the sensing element and the bubbles of gas are c o m m e n s u r a t e , and it is p r a c t i c a l l y impossible to m e a s u r e the velocity of the liquid without breaking down the s t r u c t u r e of the flow. In addition, the use of the t h e r m o a n e m o m e t r i c method in the investigation of g a s - l i q u i d flows is complicated to a considerable degree by unavoidable e r r o r s brought about by evaporative cooling of the pickup with the p a s s a g e of the bubbles of gas. The electrodiffusion method [2] has a n u m b e r of undoubted advantages from this point of view, since the sensing element in such a pickup has a dimension of less than 100 pro. There is no effect of evaporation. The e s s e n c e of the method consists in m e a s u r i n g the rate of an o x i d a t i o n - r e d u c t i o n reaction, taking place under diffusional conditions. The sensing elements, a m i c r o c a t h o d e and an anode, considerably g r e a t e r in s u r f a c e area, a r e a r r a n g e d in the flow of the electrolyte and, together with the electrolyte, make up an e l e c t r o c h e m i c a l cell. The reaction takes place under diffusion conditions; the value of the saturation c u r r e n t I s is a function of the velocity of the liquid in the neighborhood of the micropickup cathode and does not depend on the voltage V. Under these c i r c u m s t a n c e s , the concentration of working ions at the cathode is close to Zero, i.e., the cathode is polarized. We used a (0.1-1110 -2 N solution of potassium f e r r i e y a n i d e and f e r r o c y a n i d e K3Fe(CN) 6 and K4Fe(CN) ~ in a 0.5 N background solution of NaOH in distilled water. Under diffusion conditions, the following r e a c tion takes p l a c e at the cathode: Fe (CN)~- -4- e --->Fe (CN)~Novosibirsk. Translated f r o m Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 2932, N o v e m b e r - D e c e m b e r , 1975. Original a r t i c l e submitted D e c e m b e r 10, 1974. 019 76 Plenum Publishing Corporation, 22 7 West 17th Street, New York', N. Y. 10011. No part o f this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission o f the publisher. A copy o f this article is available from the publisher for $15.00.

862

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16 !

ttl Flow

i I

i

~

if . u

j

~2

8

4

i 4

8

I2

I

,

',6

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o

Fig. 1

o,z

o,~

0,6

o,8 ,,,u/R

Fig. 2

and the w o r k i n g ions a r e the ions Fe(CN)~-; at the anode t h e r e is a r e v e r s e r e a c t i o n with the f o r m a t i o n of Fe(CN)]-. The p o l a r i z e d p i c k u p - c a t h o d e c o n s i s t s of a p l a t i n u m w i r e with a d i a m e t e r d =50 pro, s o l d e r e d into a g l a s s shell; the o v e r a l l d i a m e t e r of the pickup is ~ 100/~m. The end is ground in such a way that the working p l a t i n u m e l e m e n t is flush with the g l a s s s h e l l . The pickup is o r i e n t e d in the flow as shown in Fig. 1. Under diffusion conditions, t h e r e is a m a s s - t r a n s f e r p r o c e s s between the flow and t h e p o l a r i z e d p i c k u g - c a t h o d e , obeying the laws of h y d r o d y n a m i c s and m a s s t r a n s f e r in the neighborhood of the f r o n t a l point of the end of a c y l i n d e r around which longitudinal flow is taking p l a c e , and, in a c c o r d a n c e with [3], Nu=0,753Prl/3Rel/2, w h e r e Nu = B R / D ; P r = v / D ; Re = W R / v ; the pickup; @ is the F a r a d a y constant;

(1)

W is the v e l o c i t y of the liquid; R is the r a d i u s of the g l a s s s h e l l of B--

I

C~F

(2)

is the m a s s - t r a n s f e r coefficient; F is the a r e a of the p l a t i n u m e l e c t r o d e ; v is the k i n e m a t i c v i s c o s i t y ; D is the diffusion coefficient; I is the value of the limiting diffusion current; Coo is the concentration of Fe(CN)Iions in the solution. The value of the current, not measured in the experiments, can be calculated using (1), (2), the mass-transfer coefficient, and the velocity of the liquid.

After fabrication, each pickup was calibrated in special test ~tands. The calibration of one of the pickups is shown in Fig. 1. The final calculating dependence for all the pickups has the form of formula (1) with a coefficient determined during the process of calibration. For the pickup, the results of whose testing are shown in Fig. 1, the coefficient is equal to 0.8. The concentration and the dimensions of the gaseous inclusions are very small, the frequency of the pulsations of the current in the pickup, as experiment has shown, is rather low, and the velocity can be calculated on the assumption that the process is quasi-steady-state. The method used for investigating the spectral characteristics of the friction is given in [2]. At the present time, we are doing work on the study of the spectral characteristics of the velocities of the liquid in such flows. The v e l o c i t y of the liquid p h a s e was m e a s u r e d in a unit which is d e s c r i b e d in d e t a i l in [1]. The e l e c t r i c a l s i g n a l f r o m the p o l a r i z e d p i c k u p - c a t h o d e and the anode was fed through an e l e c t r o d i f f u s i o n a l a m p l i f i e r to the input of an e l e c t r o n i c c o m p u t e r o r to a r e c o r d i n g i n s t r u m e n t (an a u t o m a t i c - r e c o r d i n g p e t e n t i o m e t e r or a loop o s c i l l o g r a p h ) . In the e x p e r i m e n t s , the value of the diffusion c u r r e n t was m e a s u r e d . The e x p e r i m e n t s w e r e m a d e u n d e r b u b b l e - f l o w conditions with v o l u m e t r i c m a s s flow r a t e s of the gas contents f l = 0 . 0 1 - 0 . 1 . In a c c o r d a n c e with v i s u a l o b s e r v a t i o n s and p h o t o g r a p h s , the d i m e n s i o n s of the bubbles h e r e v a r i e d within the l i m i t s 50-500 pro, depending on the m a s s flow r a t e of the gas and the liquid. It is shown in [1] that, in the above r a n g e of gas contents, in the r e g i o n of s m a l l Reynolds n u m b e r s (Re< 3000) t h e r e a r e flow conditions with high values of the s h e a r s t r e s s e s at the solid s u r f a c e c o m p a r e d with c a l e u !ated v a l u e s . In s p i t e of the fact that the Reynolds n u m b e r s c o r r e s p o n d e d to l a m i n a r flow conditions, the l e v e l of the p u l s a t i o n s of the f r i c t i o n in the e x p e r i m e n t s was v e r y high; the r a t i o of the m e a n - s q u a r e p u l s a t i o n a l

863

7.12

1 O,8

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l

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+ ti o2

!

i

~5

-",4 •

0,4

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L

L__ 0,2

o,,r

O,2 o,6

I o,z

0,8 y/~,

Fig. 3

! o,4

o,6

0,8 .,u/R

Fig. 4

friction to the m e a n friction r o s e with a d e c r e a s e in Re. Under these conditions, the value of the r e s i s t a n c e coefficient is not a single-valued function of Re, but obviously depends to a considerable degree on the mean size of the bubbles in the zone n e a r the wall. The hypothesis has been advanced that, with small Re, a considerable role is played by the t r a n s v e r s e t r a n s f e r of momentum due to the chaotic motion of the bubbles, brought about by a different kind of hydrodynamic f o r c e . Such flow conditions, a r b i t r a r i l y called " m i c r o t u r b u l e n t " bubble conditions, a r e of definite interest, in view of which experiments were made on the m e a s u r e m e n t of the velocity profiles of the liquid phase in a two-phase mixture with small gas contents. Under these conditions, the bubbles do not accumulate at the electrodiffusional pickup and, in actuality, the velocity of the liquid phase is recorded. Figures 2-4, respectively, give the results of m e a s u r e m e n t s of the velocity profiles of the liquid phase f o r l a m i n a r (Re = 1920-2060), transitional (Re = 2400-2600), and turbulent (Re = 6400-6800) flow conditions for the gas contents (1 - fl = 0; 2 - fl = 0.0"05; 3 - fl = 0.025; 4 fl = 0.045; 5 - fl = 0.07). Here Re = (W' 0 +W"0)d/v; W' 0 and W" 0 a r e the reduced velocities of the liquid and gas phases; d is the d i a m e t e r of the tube; v is the viscosity of the liquid; u is the velocity at the axis of the channel. The s e p a r a t i o n of the conditions into laminar, transitional, and turbulent is a r b i t r a r y , and the bounda r i e s of the t r a n s i t i o n are taken for the conditions of one-phase flow. F r o m Fig. 4 it can be seen that, in the region of l a r g e Reynolds numbers, the profiles of the velocity in a two-phase liquid obey the usual laws for turbulent single-phase flows, i.e., W'0/u = (y/R) l/n, where 1/n = t / 6 . . . 1/7. With Reynolds numbers corresponding to the conditions of a t r a n s i t i o n f r o m l a m i n a r flow to turbulent (see Fig. 3), the velocity profiles differ considerably f r o m the profiles for a single-phase liquid. With a r b i t r a r i l y l a m i n a r flow p a r a m e t e r s (Re = 1920 o r less), the divergence of the results of the experiments f r o m data obtained for a s i n g l e - p h a s e liquid b e c o m e s very accentuated. On the velocity profile with a gas content equal to fl = 0.07, t h e r e appear c h a r a c t e r i s t i c sections with a velocity g r e a t e r than at the axis. With the remaining gas contents, the profile is fuller than with the flow of a single-phase liquid; this deformation is v e r y appreciable, even with negligibly small concentrations of the gas phase. The results presented a r e in complete a g r e e m e n t with the data obtained in [1] on the mean and pulsational c h a r a c t e r i s t i c s of friction at the wall. Thus, the results of [1] and of the p r e s e n t work argue the need for a review of the concepts with r e spect to the m e c h a n i s m of the flow of a g a s - l i q u i d mixture under bubble conditions in the region of small Reynolds n u m b e r s . LITERATURE le

2.

3.

864

CITED

A. P. Burdukov, N. V. Valukina, and V. E. Nakoryakov, "Special c h a r a c t e r i s t i c s of the flow of a g a s liquid bubble-type mixture with small Reynolds n u m b e r s , " Zh. Prikl. Mekh. Tekh. Fiz., No. 4 (1974). V. E. Nakoryakov, A. P. Burdukov, B. G. Pokusaev, V. A. Kuz'min, V. A. Utovich, V. V . K h r i s t o f o r o v , and Yu. V. Tatevosyan, Investigation of Turbulent Flows of T w o - P h a s e Media, [in Russian], Izd. Inta Teplofiz. Sibirsk. Otd. Akad. Nauk SSSR (1973). H. Matsuda and J. Yamada, "Limiting diffusion c u r r e n t in hydrodynamic v o l t a m e t r y , " J. Electroanal. Chem., 30, 261-270 (1971).