D E S I G N AND C O N S T R U C T I O N O F M A C H I N E R Y AND E Q U I P M E N T

SLURRY

DISCHARGE

COMBUSTION V.

S.

SYSTEM

FOR

SUBMERGED

EVAPORATORS Babich

and

G.

I.

Volov

UDC 66.048.59

D i r e c t contact submerged combustion e v a p o r a t o r s a r e used to concentrate c o r r o s i v e and c r y s t a l l i z ing solutions. Discharge of solutions containing salt c r y s t a l s from the lower part of such equipment is difficult and the use of air lifts is not economical. The best scheme available in industrial equipment is the use of a special solution circulation loop which c r e a t e s the conditions required for continuous d i s c h a r g e of solution f r o m the bottom of the apparatus by a special pulsed valve [1]. A specially constructed valve (Fig. 1) with a pneumatic o p e r a t o r (M[M) and impulse drive is used. The impulse drive (Fig. 2) is a s s e m b l e d using m a s s produced elements of a universal s y s t e m of c o m m e r c i a l pneumatic automation h a r d w a r e . It operates by t r a n s f o r m i n g the input signal f r o m the cont r o l l e r (0.2-1.0 k g / c m 2) into proportional pulses varying f r o m 0 to T c, where T e is a p r e d e t e r m i n e d cycle time [2]. selector relay 1RS c o m p a r e s the input signal Pin and the time variable signal Pvar" Pvar e n t e r s a c c u m u l a t o r PE (Fig. 2a) ~'~ through throttle valve D and tracking c h a m b e r SK at a constant weight flow. If the amplitude of Pvar r e a c h e s that of the control signal Pcont of controller 2ZU, the output signal of 1RS switches relay 1RP and 2RP to a position so that a c c u m u l a t o r p r e s s u r e is reduced to the value of the base signal Pbase (output of c o n t r o l l e r 1ZU). When the base and variable signals a r e equal relay 1RS r e t u r n s to its original position. The time for the variable signal to reach its upper limit (or the cycle time) is fixed using the constant differential throttle valve. The variable signal is also applied to relay 2RS which fixes the impulse duration during the p r e s e t cycle, if Pin > Pvar the output signal of relay 2RS will result in the valve opening. If Pin = P v a r t h e output signal will be z e r o and the valve will be closed until Pvar = Pbase. The duration tou t of the output impulse, established by throttling valve D within the limits of the given cycle, is e x p r e s sed as a linear function of the input pneumatic signal amplitude by: 9t o u t

= a + bp in:'

where a and b are constants. The impulse duration as a function of input signal amplitude and cycle time is determined from the following expression: tout =

ai +

O1Tc + (ci + g, re)Pir r,

where T c is the p r e s e t cycle time, secs, and al, bl, c 1 and gl are constants. When T c = 30-240 secs and Pin = 0.2-1.0 k g / c m 2, a i = 0.941, bl = 0.124, c 1 = 2.01 and gl = 1.155. The a v e r a g e e r r o r is 0 . 2 - 5 secs within the range Pin = 0.3-1.0 k g / c m 2 and T e = 30-240 sec. F~.g. 1. Pulsed valve: 1) bottom discharge valve, 2) valve column, and 3) positioner.

The pneumatic output Pout is a step signal of 1 k g / c m 2 a m p l i tude. The t i m e during which the valve is open is not equal to the d u r ation of the d r i v e r impulse since t r a n s i e n t behavior o c c u r s in the

T r a n s l a t e d from Khimicheskoe i Neftyanoe Mashinostroenie, No. 1, pp. 6-8, January, 1971. O 1971 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.

12

Supply

p, kg/cm z 1ZU

" .

i1R8

SK ~

k2 ]

i

I

I

I

I

I

b

Fig. 2. Valve drive: a) schematic; b) switching d i a g r a m ; 1ZU, 2ZU) c o n t r o l l e r s ; 1RS, 2RS) s e l e c t o r elements; 1RP, 2RP) u n i v e r s a l r e l a y s ; P) P - I S r e p e a t e r with bias; PE) pneumatic a c c u m u l a t o r ; D) DPSH v a r i a b l e throttle valve with a g r a d u a t e d scale; SK) tracking c h a m b e r ; F) filter; U) c o a r s e r e p e a t e r ; M1, M2, M3) MT-4 p r e s s u r e gauges. pneumatic t r a n s m i s s i o n lines and the volume of the a c t u a t o r . The duration of the t r a n s i e n t p r o c e s s (signal v a r i a t i o n in the actuator) is different f o r opening and closing the valve (Fig. 3b). The a i r p r e s s u r e v a r i a tion in the a c t u a t o r during opening and closing of the valve is d e s c r i b e d by f i r s t o r d e r differential equations:

Pc=Pit l - e

ru

);

I--r

PO =Pi e

i'd

w h e r e Pc and Po a r e the p r e s s u r e v a r i a t i o n s in a c t u a t o r volume c o r r e s p o n d i n g to opening and closing the valve, k g / c m 2, Pi is the amplitude of the control impulse; r is the t r a n s m i s s i o n lag t i m e of the i m p u l s e through the pneumatic lines; T u and T d a r e the t i m e constants of the valve, a c t u a t o r , and pneumatic lines during the upstroke and the downstroke of the valve, sec; e is the b a s e of natural logarithms; and t is t i m e . The values of Tu and T d a r e d e t e r m i n e d by c o n s i d e r a t i o n of data in [3], the c o n s t r u c t i o n of the valve and a p p a r a t u s , and the p a r a m e t e r s of the technological p r o c e s s . The t r a n s p o r t lag of the pneumatic line is d e t e r m i n e d by the e x p r e s s i o n L

I+

1 . 4 d "r R T

~E

330,8 where L and d a r e the length and inner d i a m e t e r of the pneumatic line, m; 3/is the density of a i r , kg/m3; R is the gas constant for a i r , m / d e g r e e ; T is the absolute a i r t e m p e r a t u r e , ~ 5 is the pneumatic pipe wall thickness, m; and E is the modulus of e l a s t i c i t y of the pneumatic pipe, k g / m 2. T h e t i m e constant of the pneumatic o p e r a t o r during upstroke of the valve is

(=,,,L

r~ = k - - g T - - \ - - U -

+ --g-

pd-pf-pp-6 +ed ed-pf-e,,-6

"

-s~p

ssp

/

where k is a c o r r e c t i o n coefficient (k • 2); tz is the dynamic v i s c o s i t y of air; D, is the d i a m e t e r of the c a s ing of the pneumatic a c t u a t o r , m; F d is the effective d i a p h r a g m a r e a ; Pf = 1.5 • 0.025 ds/ is the f r i c t i o n f o r c e of the valve packing in kg; ds is the valve s t e m d i a m e t e r , cm; L is the length of the stern inside the packing, cm; Fp = F2(H3"1 + Papp) is the f o r c e pushing the s t e m down, kg; F 2 is the a r e a of the valve seat, m2; H is Lhe liquid height in the a p p a r a t u s , m; 3'1 is the density of the solution in the a p p a r a t u s , kg/ma; Papp is the a p p a r a t u s p r e s s u r e , kg/mZ; and 8sp is the stiffness of the s p r i n g s of the pneumatic a c t u a t o r . The t i m e constant of the valve during closing T o is a p p r o x i m a t e l y equal to (0.1-0.15) T u. T h i s can be neglected.

13

t o, sec

Actual duration of the impulse to the valve stem is adequately described by the following expression:

~out, kg/cmz

r i = t i - - r u (l--e--Tu). I

The time to open the valve considering the p a r a m e t e r s of the impulse drive equals

I I////////.'~///X2~.

T i = a , - - b , T e + (c, + &To)Pin --- Tu (1 -- e - r U ) . o2

Q,#

a

(1)

The flowrate of concentrated solution f r o m the apparatus is equal to

Q,8 Pin, kg/cm2

Fig. 3. Static c h a r a c t e r i s t i c and impulse diag r a m of the generator and valve.

apR' a = ~o D C r ~1 kl V / 2gi4 + 2gp -C1

(2)

where #0 = ( 1 / v ~ + Z~) ~0 is the flow coefficient; X~ is the sum of the local r e s i s t a n c e s of the valve, including impact r e s i s tance of flow around the stem, change of direction and valve body d i a m e t e r r e s i s t a n c e s , ~o is the c o m p r e s sion coefficient of the stream; D = 3600 is the c o n v e r s i o n factor for flow f r o m m a / s e c to ma/h; C = T i / T c is the relative time the valve is open; F is the a r e a of the valve opening, m2; kso 1 is the coefficient which accounts for the solid phase in the slurry; k 1 is the coefficient which c o r r e c t s for the specific gravity of the fluid under operation conditions (water - 1); and g is the a c c e l e r a t i o n of gravity. The p a r a m e t e r s of the pulsating drive to give the d e s i r e d flow can be selected by a n u m b e r of methods. The method of s u c c e s s i v e approximations is the simplest. It r e q u i r e s that C be 0.3-0.6. Substituting the known p a r a m e t e r s of the concentrated solution and the apparatus into formula (2) we find the value of p0 F. Using the standard nominal valve bore we determine >~ F v. The valve diameter m u s t yield a minimal value of F#0 - Fv/%' (#0 and Fv a r e the flow coefficient and valve a r e a opening for the nominal bore selected). We substitute this value of F v #0' for F#0 in the original formula. Then we determine the value of T c / T i -- C m o r e a c c u r a t e l y . Based on the operating conditions of the apparatus and the valve the maximum number of switchings is fixed at n = 3600/~c = 10-60 per hour. The required cycle time is determined from this expression using the assigned value of n. The time during which the valve m u s t be open T i = CT c. The time constant of the s y s t e m is d e t e r mined to select the valve p a r a m e t e r s considering the construction of the valve and the apparatus and solution p r o p e r t i e s . Substituting values of Ti, T c and T u into (1) and solving it for pin we determine the m a s t e r a i r p r e s s u r e for the impulse drive. Substituting Pin (0.2-1.0 k g / c m 2) we determine the flow through the valve. Then we determine the flow c h a r a c t e r i s t i c of the valve. This method does not consider the effect of valve operation on the basic p a r a m e t e r s of the technological p r o c e s s . Let us examine the sequence of calculation for the operation of an apparatus in which liquid level must be maintained within • Ah of the nominal when X 1 m a / s e c of concentrated solution is discharged. The flow rate of feed solution is X 2 m a / s e c and that of evaporated water is X 3 m a / s e c . As a f i r s t approximation the change in solution level during the variation in flow within the operating range can be r e p r e sented by dht a-7 = -

1 7 7 x,;

dh2 at -

1 Pl x~;

dh a at = -

1 el x , ,

where hl, h2 and h3 are the changes in level due to variationsin flow rates of XI, X2, and X3, respectively and F I is the area of the apparatus, m2. The time when the valve is shut during a level change within the limits 2A h is equal to t=

2Ah 1

?i

14

When

the valve is open the time for the level to change from the upper to the lower limit is equal to tl=

1

cycle time is Tc =t+tl;

(3)

and the flow during the time the valve is open is

VTc___

x1= v~L _

3690 (Tc-- t)'

tl

w h e r e V 1 and V a r e t h e v o l u m e s of d i s c h a r g e d s o l u t i o n d u r i n g one c y c l e a n d d u r i n g 1 h, r e s p e c t i v e l y . S u b s t i t u t i n g the v a l u e s of t1, t, a n d X 1 into e q u a t i o n (3) a n d s o l v i n g f o r Tc, we d e t e r m i n e t h e r e q u i r e d cycle time for these conditions: 2ah36oo

To=

1 1 -r~ ( x~ - x , ) - 2 ~ h v T ,

I 3600 (X2-- Xa) - - (X2 -- Xs) Y - -

pf

S i n c e T c = tt, t h e r e l a t i v e d u r a t i o n of t h e v a l v e b e i n g s w i t c h e d on i s e q u a l to c-

tl

to

S u b s e q u e n t c a l c u l a t i o n s a r e c a r r i e d out in an a n a l o g o u s m a n n e r . T h e s e q u e n c e of c a l c u l a t i n g p a r a m e t e r s of a p u l s a t i n g v a l v e when s o m e o t h e r p a r a m e t e r i s c o n t r o l l e d o r t h e d y n a m i c c h a r a c t e r i s t i c s a r e r e p r e s e n t e d by a p e r i o d i c c h a i n s i s s i m i l a r to t h a t d e s c r i b e d a b o v e . T h i s s y s t e m of s o l u t i o n d i s c h a r g e f r o m a s u b m e r g e d c o m b u s t i o n e v a p o r a t o r u s i n g a s p e c i a l v a l v e w a s e x p e r i m e n t a l l y t e s t e d on a c o m m e r c i a l s c a l e . R e s u l t s of p r o l o n g e d t e s t s d e m o n s t r a t e d t h a t t h i s d i s c h a r g e s y s t e m i s w o r k a b l e . T h e p u l s e d v a l v e r e q u i r e s s o m e i m p r o v e m e n t in c o n s t r u c t i o n to i n c r e a s e r e l i a b i l i t y and c o r r o s i o n r e s i s t a n c e . The t y p e M P - 2 5 p n e u m a t i c a c t u a t o r h a d a low o p e r a t i n g r e l i a b i l i t y due to t h e l a c k of a l u b r i c a t i n g d e v i c e f o r t h e s t e m . N o r m a l o p e r a t i n g of t h e p u l s e d v a l v e d u r i n g t h e d u r a t i o n of the t e s t s ( m o r e t h a n 3 m o n t h s ) w a s p r o v i d e d by t h e p n e u m a t i c d r i v e m e c h a n i s m .

LITERATURE i.

2. 3.

CITED

K. D. Losievskii, et al., Khim. i Neft. Mashinostr., No. 5 (1968). T. K. Berends, et al., Elements and Circuits of Pneumatic Automation [in Russian], iV[ashinostroenie, Moscow (1968). N. F. Broide, Universal System Pneumatic Instruments in Automated Circuits [in Russian], Mashgiz, Moscow (1963).

15