COMMUNICATIONS
Automated Variable Flow for Pilot Plants Walter K . Johnson University of Minnesota, Minneapolis, Minn. 55455
A device was developed for use with continuous flow pilot plants whereby the input rate of flow was varied continuously and automatically. The equipment was used on a pilot scale to simulate the sinusoidal flow patterns normally encountered in municipal waste water treatment plants. With the particular equipment used and commercially available, average flow rates ranging from 13 to 3800 ml./min. were used. The motion and pumping rates of the equipment are described mathematically and compared with the discharge rates from the actual installation.
T
he operation of continuous flow pilot plants for waste water treatment offers many unique problems. When the objective is to simulate operation of a prototype plant. both the flow rate and input waste water solids concentration must vary continuously. One phase of a research project on nitrogen removal by denitrification conducted at the University of Minnesota Sanitary Engineering Laboratories has been to investigate the effect of variable flow on the process. A device for continuously varying the flow rate was developed and used both in the laboratory and as part of a pilot plant located a t a municipal treatment plant. Because a synthetic waste water was used in the laboratory application, the composition of the waste was constant. However, in the field application using a municipal waste water, the composition varied continuously. Pumping Equipment Feed pumps selected for use were Sigmamotor pumps driven by electric motors through Zero-Max speed reducers. These reducers operate with a lever such that small angular changes in lever settings produce approximately linear responses in speed change. Since a Sigmamotor pump output varies linearly with input speed, the pumping rate in this application varied approximately as a linear function of the angular movement of the lever on the speed changer. Adaptation to Variable Flow Using the above equipment, a sinusoidal flow pattern was achieved by using a disk rotating once every 24 hours. A simple 24-hour timer was used for this purpose. By pinconnecting one end of an operating arm a t an experimentally determined distance from the center of the rotating disk and the other end to the operating lever of the speed reducer, the pumping rate was controlled as desired. The arrangement of the equipment is shown graphically in Figure 1. Using the notation in Figure 1: 68 Environmental Science & Technology
Figure 1. Schematic diagram of speed control linkage
+ 0, - = d2 (x + + y 2 = r2
(x -
y1)2
x,)2
x1 =
c cos 0
y1 = c sin 0
(1)
(2)
(3)
+b
(4)
By substituting Equations 3 and 4 in Equation 1 and solving Equations 1 and 2 simultaneously, Equation 5 is obtained as: x(2u
+ 2c cos 0) + (2c sin 0 + 2 b ) ~ ' r -~ (x + a12 = 2 bc sin 0 - m ( 5 )
+ +
where: m = b 2 c ? r 2 - u 2 - d2 The lengths a, b, c, d, and r a r e all characteristic lengths of the particular control system utilized. A further inspection of Equation 5 will indicate that with reasonable values for the constants, a simplification of the equation shows the distance x to be essentially a function of sin 0. Because the distance x establishes the position of the control lever it also establishes the pumping rate. Since x is a function of sin 0, the pumping rate also is a function of sin 0 in view of the linear relationship between the angular position of the speed control lever and the pumping rate. Equation 5 may be solved by graphical methods or, as in this case, by an iterative process using a digital computer. An example of the use of this concept is given below.
Table I. Pump Discharge Rates as Functions of Disk Rotatiow 0
x
Degrees 1 0 30 60 90 120 150 180 210 240 270 300 330
Inches 2 5.9 5.8 5.6 5.4 5.2 5.0 5.0 5.1 5.3 5.5 5.8 5.9
For identification of
8 , x;a,
s f a - sin ~-
39.4-CY
Degrees
Degrees
4 37.2 36.6 35.4 34.3 33.2 32.0 32.0 32.6 33.7 34.8 36.6 37.2
5 2.2 2.8 4.0 5.1 6.2 7.4 7.4 6.8 5.7 4.6 2.8 2.2
3 ,604 ,596 ,579 ,563 ,547 ,530 .530 .538 ,555 ,571 ,596 604
r , and
I
CY
a, see
I
d = 5.5"
b
=
12.5"
r =
12.25"
c
=
0.5"
In
-274
Then Equation 5 becomes: x (cos 8 - 3.0)
6 10.5 13.5 19.2 24.5 29.8 35.5 35.5 32.6 27.3 22.0 13.5 10.5
Pump Discharge ml./min. 7 6.3 8.1 11.5 14.7 17.9 21.3 21.3 19.6 16.4 13.2 8.1 6.3
The use of 39.4 degrees in obtaining the data for column 5 is simply to convert the angular positions to a convenient scale characteristic of the speed reducer. The data in column 5, together with a manufacturer's curve showing the Zero-Max output speed as a function of the degrees of movement of the control lever, were used to obtain the R P M data of column 6. In this example, a in. I.D. tubing was used in a Model T-8 Sigmamotor pump to give a discharge of 0.6 ml./min. RPM. The discharge data for these conditions are shown in column 7 of Table I and plotted o n Figure 2 together with actual discharge data. The pattern of flow in Figure 2 shows a centinuously varying flow pattern as one might normally encounter at municipal waste treatment plants. The maximum and minimum rates are approximately 50% above and below the average rate, respectively. Equipment was used to obtain average flow rates of as low as 13 ml. :min. and as high as 3800 ml.,'min. For the latter rate, the largest Sigmamotor pump (Model T-4) with a 1-inch I.D. tubing was used and powered by a Model QXI Zero-Max power block assembly. Because this pump was the largest available, this pumping rate was a controlling factor in sizing the pilot plant which it was to serve.
Geometry measured and related to Figure 1 :
=
RPM
Figure 1.
I
a = - l._s"
Pump
+ (sin 8 + 2 5 ) d 1 5 0 - (x - lS)*= 12.5 sin 8
Acknowledgment
+ 274
Values for x corresponding to selected values of 8 are presented in Table 1 . Columns 3, 4. and 5 in Table I are a conversion of the data into angular positions ( a ) of the speed reducer control arm.
This work was part of an FWPCA sponsored research project (WP-01028). Loren Leach, Student Engineering Assistant, was employed part time on the project and assisted in the development of the equipment. Receiwd for reciew April 2 , 1969. Accepted October 16, 1969.
Volume 4,Number 1, January 1970 69
