LFOM Initial Concept generation

By Dave Railsback, Melina Dianconis, Mike Blazejewski in Fall 2007.

Abstract

We found that alum flow can be automatically regulated to a nearly-constant dose when dealing with a changing plant flow rate using simple, non-electric means.  Using a system of orifices in the grit chamber outflow, the head in the chamber is linearly corresponded to the plant flow rate.  A float in the tank can then be used to pull the alum outflow pipe up and down, thereby increasing or decreasing the alum flow rate and keeping the dose constant.

Introduction

The purpose of our project is to design a mechanism to regulate the flow of alum into the rapid mixer according to changes in flow rate. Currently the existing plants require manual adjustment of the alum flow rate when the plant flow gets too high or too low. Correct alum dose is very important to the performance of the flocculation and sedimentation processes, and as it exists the job of keeping a constant alum dose is left open to human error. Automation of this process would improve the performance and efficiency of the plant and simplify the operator's responsibilities. Basic goals for the final design:

• Keep alum dose as close to constant as possible.
• Be able to install device into existing plants.
• Include a simple way for the plant operator to change the dosage. As we developed our design for this regulated alum feed system, we came upon various questions that guided the directions of our designs. For instance, our design will be based around taking a relative measurement of the plant flow rate and using that to regulate the alum flow into the rapid mixer.  But how will this information be transferred automatically using simple, non-electronic means? Secondly, what is the best way to accurately regulate the alum flow without using valves or pumps?

The method used to keep track of the plant flow rate is a measurement of the water level in the grit chamber. This showed itself to be a major complicating factor, as the head in a tank and the flow rate into that tank are not linearly related.  The main equation used to model this is the orifice equation:

The equation shows how flow rate is related to the square root of the change in head. It would arise several times during design experiments as a challenge to the goal of connecting head in the tank to alum flow rate.
The design process went through several stages, each improving on the last in precision and simplicity. Each stage is discussed separately in the following sections.

Design

The Bucket System

The bucket system would improve alum dose consistency, but the design is fairly complicated to build.We experimented with a second design
which used the grit chamber's head level to determine flow rate.This system incorporated a tall and thin cylindrical float in the chamber.
This is then connected to the same alum outflow pipe design as before, redesigned as a see-saw lever on a central pivot. A counterweight
is used to keep the float wire taut as the water rises. In this sketch, the alum drips out of the right end of the pipe:

Figure 2: System with float and weights

The non-linear relationship between head and flow rate must be accounted for in this design as well. This is done using weights similar to
those in the bucket design. When the head reaches a certain level, the wire leading to the first weight in a series of weights becomes taught.
The first weight will remain in place as the water level rises around the float until the change in buoyant force is great enough to allow
the counterbalance to lift the first weight. Keep in mind that the buoy does not actually lift the weight. When wire to the first weight is
taught, but the weight is not yet lifted, the float will not be moving, and so the alum flow will be constant. This is represented in the
figure below by the blue line's horizontal regions. Once the head raises enough, and the buoyant forces overcome the weight, the float will
again rise with the water level. In the figure below, this is when the blue line has a vertical slope. This pattern repeats for every weight
in the sequence.
This would theoretically provide a more linear response than the step function created by the bucket design. So, along with being simpler to build, this design would more accurately deliver the correct alum dosage.
The design, however, is complex. First, each additional weight corresponds to an added flow rate which remains constant. We find this "flow step" by subtracting the minimum flow from the maximum and dividing by the desired number of weights. We can then find the specific tank head at which each weight will be lifted.
The goal of the weight system is to force the float to rise linearly with flow rate, even while the tank head rises non-linearly. So, the head which lifts up the first weight is multiplied to create a linear array of float heights. By doing this we are developing a target line which we can then match as closely as possible by using the proper weights.

Figure 3: Target Linear Relationship

The next step is to find out how much weight needs to be added at each flow step to achieve the linear result. We know that the result of the design on the flow/head graph will be a wave-like pattern; there will be flat areas where the next weight holds down the float, and then the height will increase at the same squared rate as the water level.

Figure 4: In this figure, the blue line represents the theoretical path of the float, following closely with the target linear relationship.

The float is designed to rise higher at each flow step than the target line would suggest. This way, the alum flow will almost always be somewhat above or below what is optimal, but never so different that it affects the plant's performance.
At each step, the submerged volume of the float can be found and therefore so can the buoyant force. This is then matched with the proper countering torque on the lever arm which will hold the float to that level. This can subsequently be changed into a weight at each step, depending on the length of the lever and where the weights and float are located. The each weight will increase successively if all the weights are located at the same point on the lever arm.
The resulting design provides a more linear alum flow response to changing flow rate than the bucket's step function. The alternating rising and holding movement pattern of the float is difficult to model because the rate at which it rises changes with its height, but its effect is easy to imagine, and it would undoubtedly succeed in automating the alum feed. The lack of pulleys also makes the system easier to build than the bucket design. Importantly, unlike the bucket system, the float would provide some alum to the plant even at very low flows.
There are some issues that must be addressed, however, such as the assumption that the pipe we use as a lever arm will not bend under the increasing weight. Also, as with the bucket, the system would only be very accurate when many weights are involved. Any time several items are hanging in the air, it creates issues as to how they will be housed and kept from tangling. Not only that, but for the design to work well the weight of each object is defined down to the tenth of a gram. This would require specially made, accurate weights which may be difficult to come across in the global south.

Linear Orifice System

The main problem with the previous designs was that the relationship between head in a tank and flow rate into the tank is not linear. This occurs because flow is proportional to the square root of head.
But what if there was an orifice shape that did give a linear relationship? Some research into the subject brought out some interesting ideas. Victor Sutro developed the linear weir and it was patented in 1915. The image below shows the approximate shape of a Sutro Weir.

Figure 5: Linear Weir (Image: Cussons Technology)

Using this shape, we decided to construct our own analog using a series of orifices drilled into the grit chamber outlet pipe. Updating to this system would require replacement of the current pipe in existing plants.

Figure 6: A pattern of holes which mimics the effects of the Sutro Weir

For our program, the user inputs the size of the drill bit that he will use to make the orifices, thereby giving the area of each orifice. The program sets the flow rate through the first row of holes when the head is one orifice spacing above the holes. This is done by dividing the given maximum plant flow by the desired number of orifice rows. The orifice equation can be used to find the number of orifices needed in this first row.
We now have the total orifice area of the first row, allowing us to do a check to see if the given drill bit is too large or too small. We define too large as a diameter larger than our given orifice row spacing. An orifice diameter that is too small creates a situation where more than half the circumference of the pipe is taken up by holes, and we do not want to significantly weaken this pipe. If the bit size is increased, the number of holes would decrease.
The next element of the program is a function which gives the flow rate at any grit chamber head. This then allows us to find the number of orifices in each row which would generate our linear goal. For example, if flow through the first row is 10 L/min, then flow through the first two rows should be 20 L/min, and so on. The program finds the number of holes by first calculating Q is there were zero holes at the current level. If the total calculated flow is less than the desired flow, it adds a tenth of a hole. Once the linear goal is met, the number is rounded to the nearest whole number of orifices, and this repeats for each row on the pipe.
We can now find the expected flow out of the grit chamber using these orifice sizes, spacing, and numbers, but only when the head is exactly at the height of each row. Our last step, therefore, is to calculate the flow rate for intermediate heads. The resulting graph shows a dramatically more linear relationship than any we have yet seen.

Results and Mathcad files

Mathcad files

Float with Linear Head System
Float with Weights System
Bucket System
Alum Dosing System

The Results

The word document with the results for defined user inputs is on the attached page

Conclusions

The linear system of orifices proves to be the most useful innovation that was developed. Combined with the float and the unique alum distribution pipe, it allows us to accomplish our goals. The pipe design contains a simple way for the dose to be manually changed, the dose is kept almost constant through variations in flow rate, and the installation into existing plants would be inexpensive and fairly simple. Using this design, the plant operator's job of regulating alum dose would be great simplified.