Orifice Size and the Dual Scale Design for the Nonlineary Alum Doser

Abstract:

During the fall semester of 2009, the 2009 Nonlinear Chemical Dosing Team developed the dual scaled orifice-based doser in order to deliver turbulent alum flow. This doser, once set for a specific dosage by the operator, must automatically increase or decrease the alum solution to maintain that target dosage as the plant flow changes. The two different scale provides the operator with additional precision through a low dosage (5-25 mg/L) and a high (20-100 mg/L) alum dosage range.

We have currently researched and identified the nonlinear relationship between plant flow rate and alum dosage and the movement of the lever arm. We utilized this relationship to develop the lever arm design to include the dual scale and the orifices. Attached is the Mathcad File.that contains the calculations for our dosing system.

Our current design consists of a 80cm long lever arm with equal lengths and two orifices of 3.175mm and 0.01587mm diameer, 9.525 mm pvc tubing, and other associated hydraulic components listed in our component list.

Theory:

Our first and key step in developing a dosage system that can deliver both turbulent and laminar flow of alum was the selection of the orifice to control the flow of alum. We increased the tubing size connecting the constant head tank to the orifice to 9.525mm which is wide and smooth enough to make the head loss from the tubing negligible compared to the head loss through each orifice, making the orifice the flow control component for the dosage system. The orifice equation, shown below, demostrates the nonlinear relationship between flowrate and the change in head loss. The flow rate(Q) is the result of the square root of the head loss(h), the area of the orifice(Aor), and the orifice constant,(Kvc).

Head loss occuring in the plant after the entrance tank including rapid mix, the flocculation tank, and the launders are all controlled by orifices. The only source of head loss not controlled by an orifice is the weir. Because the majority of the head loss is dominated by the orifice we can link the flow rate of the plant with the flow rate of alum required for the plant using the same square root relationship mentioned above. h5. Table 1: Head Loss Through the Plant

The lever arm dosing flow rate and plant flow rate are both governed by the same nonlinear relationship as a result of the mutual use of the orifice.

Below, we would demonstrate how the movement of the lever arm and the rise and fall of

where
Q_C = dosing flow rate
K_C = orifice coefficient
Q_P = the plant flow rate
K_P = the orifice coefficient.

The mass balance equation calculates the flow of alum needed based on plant flow rate and the concentration of the alum chemical stock tank.

Below, C_P is the target alum concentration for our plant while C_C is the alum solution concentration and Q_C

We substitute the dosing flow rate equation in and link the two heights with a lever and cancel out any duplicate variables. (Please label what each of these variables are, is L for level, C for chemical stock tank, and P for plant?)

The height of the water, or the flow rate to the plant via the entrance tank, is non-linearly related to the change in height of the scale. Because the relationship is defined by the orifice equation,the change in height gives us the change in flowrate required. Linking the different sets of heights to the scale, we generate a scale that an operator can use to adjust the dosage. Because the orifice equation that controls this relationship is nonlinear, the scale is nonlinear. An example of a nonlinear scale is shown below.

(Your scale is a good visual representation. I would include a table as well of these values and perhaps a sample calculation for what you described above.)

Method:

We utilized Mathcad to calculate our design parameters. The rest of this section illustrates our method in designing the orifice diameter and the dual scale for the plant.

The maximum movement of the water height in the entrance tank is determined by the sum of the the headloss from the flocculator, macro and micro mixer, weir, and launder orifices as shown in Table 1.

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This vertical distance of 33.5 cm establishes the upper and lower limit of flow to which our lever arm must be designed to respond.

In our calculations, we first define the applicable alum dose range of plant operation. Two different orifices handle two different scales of alum dosage: high (20-100 mg/L) and low (5-25 mg/L). They are offset to each other by a factor of four. Consequently, as dictated by the area portion of the orifice equation, the diameter of the larger orifice is twice the diameter of the smaller orifice.

(Please label and describe your mathcad screenshot)

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The operator of this program will change the diameter of the program until the dual scale utilizes maximum space on the lever arm (40 cm). This Mathcad program is designed to find the right size diameter through a series of trial and error iterations until we utilze the entire length of the scale which corresponds to the maximum and minimum height of the plant flow.

After we have input the tentative diameter for the larger orifice and the dual series of doses we conduct the calculations mentioned in the theory section to produce the nonlinear dual scale. We convert the dosage to the alum flow rate required by utilizing the mass balance equation.

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The above snap shot also shows how the maximum headloss dicatates the maximum angle that our lever arm will be operating around.

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We then calculate the necessary head loss in the dosage system to produced the required flow rates.

Utilizing the sine function we convert the head loss to points along the lever scale arm. (Show the equation if possible)

We can also calculate the dual scale through a quicker method by utilizing the orifice equation relationship governing this whole process by linking the dosage directly to the scale. The resulting scale is shown below with the rest of the results for comparison. (Did you compare your two methods here? I didn't see this.)

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We know that the governing equation for this system dictates that the flow is equal to square root of distance times a constant K. We solve for the K by dividing the maximum dosage by the square root of the maximum length (can you refer to an equation here?). We then utilize the K to solve for the dual scale.

The snapshot below shows us our final results. We manipulated the larger orifice size until we fully utilize the lever arm scale as shown below.

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Shown below is the scale that is generated from our calculations.

(Please connect the calculations you performed in MathCAD to some sort of diagram of the system and refer to it. Also, make sure that your mathcad screenshots and graphs are separate and that you have a caption for both figures and that you refer to your caption in the text.)

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Results and Discussions

Currently, our orifices are 0.310 cm for alum dosage of 20 to 100 mg/L offset by 10 mg/L and 0.0155 cm for alum dosage of 5 to 25 mg/L offset by 2.5 mg/L. Our lever arm is 80 cm in length with equal lengths on each side. Tubing is made up of PVC and of 3/8 inch diameter which is wide and smooth enough to produce negligible head loss on the alum flow. The scale developed by linking the dosage to the scale is very similiar to our dual scale developed via our longer Mathcad programs, validating that the nonlinear relationship dictated by the orifice equation governs plant flow rate, the change in head loss, and the dual scale.

For ease of operation, whenever this lever arm is used in the field, this lever arm can be delivered to the Aguaclara Plant with the dual scales already engraved on the arm. The operator simply has to calibrate the maximum dosage to the maximum flow rate and the lever arm will be ready for operation.

Our near goal is to build the [lever arm prototype] and set up our hydraulic components and engrave our dual scale. We also plan on conducting experiments to test our lever arm and find a solution to the clogging problem currently besetting actual alum dosers in Honduras.

Bibliography

• CEE4540 Flow Control Measurement Notes at https://confluence.cornell.edu/display/cee4540/Syllabus