Rapid Mix Tube

Abstract

During the fall 2009 semester, the main focus of the Rapid Mix Tube subteam was the development and design of a rapid mix tube system to provide adequate large and small-scale mixing of alum with the raw water source entering the plant. The system developed in the fall 2009 semester is designed for the Agalteca plant, but the ultimate design can be modified to fit into future AguaClara plants and even fit into existing plants to improve rapid mix . The design of the system evolved multiple times throughout the semester, and the current system was developed to improve upon the main problem of those initial designs: access to the small scale rapid mix orifice to clean it in case of clogging. The design of the tube was thus tailored to fix this problem, and a MathCAD file calculating orifice sizes and head loss through the system was developed.

Figure 1. Overview of the plant flow from the entrance tank through the rapid mix tube, out into the flocculation tank.

Rapid Mix Tube Design Process

Initial Rapid Mix Design

The initial rapid mix system proposed for the Agalteca plant was much different than the system designed this semester. As can be seen in Figure 2, water from the entrance tank flows into a pipe that carries it into the flocculation tank.

Figure 2. Initial Rapid Mix system design and integration into the plant. As indicated, the Rapid Mix Orifice in this design is completely submerged and accessed through the flocculation tank.

Rapid mix is achieved in this system when the water flows through an orifice at the end of the pipe leading into the flocculation tank, allowing small-scale mixing of the aluminum sulfate with the raw water to occur before reaching the flocculation tank. One of the main problems with this system is the location of the rapid mix orifice; it is submerged in the bottom of the flocculation tank, making it very difficult to reach or remove. Flow to the plant would have to be stopped and the flocculation tank drained at least partially to remove and clean this orifice if it ever clogged or needed to be replaced or exchanged. Another problem with this design is that the exit tube taking water from the entrance tank to the flocculation tank is flush with the side wall of the entrance tank and is located quite deep in the tank. Thus, for flow to the plant to be stopped, the entrance tank would have to be emptied completely.

Current Rapid Mix Tube Design Deveopment

The current design for the rapid mix tube was developed to address the problems created by the initial design. A schematic of the new design is shown in Figure 3. This new rapid mix tube system consists of two separate 'stages,' a large-scale mixing process in the first portion of the system, and small-scale mixing process in the second portion. The tube protrudes up into the entrance tank to help regulate flow through the plant-flow through the plant will cease once the water level in the entrance tank reaches the top of the rapid mix tube, allowing the water already in the tank to be stored if there is low source flow or the plant needs to be cleaned.

Figure 3. Schematic of the current Rapid Mix Tube system.

Large-Scale Mixing Orifice Design

Water enters the top of the tube through the large-scale mixing orifice, where it is dosed with the aluminum sulfate and begins the rapid mix process. This orifice is in place to create large scale mixing in the first section of the tube. The design of this orifice size is based on the exit loss coefficient through the orifice, K. The target K value for this orifice is 2, which provides the best mixing in the first section of the tube for large-scale rapid mix. To calculate the necessary area and diameter of the large scale mixing orifice, the following equation was used:

Solving for A.in, which will be the area of the stream of water entering the tube through the orifice, we obtain:

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In this equation, A.in is taken to be the area of contracted flow through the orifice, which is the area of the large-scale mixing orifice multiplied by the vena contracta coefficient, which accounts for the contraction of flow through an orifice. The equation the describes this is as follows:

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Figure 4 illustrates the effect of the water contraction flowing through an orifice.

(Good explanation surrounding your equations, but can you insert the equations as objects in mathtype and then also label the variables present in your equations?)

Figure 4. Diagram showing the area used for A.in in the Exit loss coefficient equation.

A.out in the above equations is taken to be the area of the pipes used in the system since the water is allowed to outlet freely into these pipes.

Water flows down the pipe after entering through the large-scale mixing orifice, then flows down the length of the pipe, which should be at least as long as several diameters of the pipe to provide adequate mixing. The Agalteca plant will be using 0.152 m (6-in.) diameter PVC pipes, and thus the length of the large-scale rapid mix tube will be between 0.457 m and 0.762 m (18-in. to 30-in.) to provide enough diameters of length for large scale mixing.

Small-Scale Mixing Orifice Design

After water flows into the rapid mix tube and through the top section of the pipe to achieve large-scale mixing, it reaches the small-scale mixing orifice. The area of the small-scale mixing orifice is designed to achieve a target head loss, providing a mechanism to measure the level of water in the plant to assist in the correct dosing of the plant's raw water source with aluminum sulfate. The equation used to calculate the area of the small-scale mixing orifice is as follows:

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In this equation, Q signifies the flow rate of water through the plant, K.vc is the vena contracta coefficient as discussed above in the large-scale orifice design section, and Δh is the target head loss for which the plant is being designed; this design value can be varied based on the desired characteristics of each plant. K.vc is used here again because the flow of water through the small-scale mixing orifice is also a flow contraction, and the area of the water stream entering the pipe following is a fraction of the area of the orifice.

The area of the small scale orifice can be either cirucular or rectangular in shape, again depending upon the plant flow rate, desired energy dissipation rate, and desired head loss through the small-scale orifice. A diagram of some possbile orifice configurations is shown below in Figure 5.

Figure 5. Possible configurations for the small scale rapid mix orifice. Which is chosen depends upon the specific plant for which the rapid mix system is being designed.

Each of these designs is preferred in different cases depending on the plant flow rate, pipe diameter, desired head loss, and desired energy dissipation rate. Tentatively, the Agalteca plant will feature a small-scale orifice featuring the multiple round orifices, which will best serve this plant in evenly mixing the aluminum sulfate dosed to the raw waste, as well as achieving the desired energy dissipation rate through the orifice. To calculate the dimensions of the round orifices that will occur in the small-scale mixing orifice, the following equation in used:

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Here, ε is the value of the maximum energy dissipation rate for the plant, and the orifice is thus designed to achieve this value. Δh is the same target value for the head loss from the small-scale orifice design equation. This equation thus calculates the maximum minimum dimension of a rectangular orifice. This dimension can be adapted to the proposed Agalteca design with multiple small orifices, however, because of the presence of many small orifices in entire small-scale mixing orifice. The dimension calculated in this equation will then be used as the diameter of the multiple orifices that must be put into the small-scale mixing orifice. Figure 6 provides a schematic of the rapid mix tube as well as the placement of the two orifices and a detail of the multiple-orifice small scale mixing orifice that will likely be used in the Agalteca plant.

Figure 6. Proposed schematic for the rapid mix tube showing orifice placements and design for the small and large scale mixing orifices.

Headloss Calculations and Significance
The total headloss through the system is comprised of minor losses, caused by water flow through the orifices and through pipe fittings such as elbows, and major losses due to friction on the pipe walls. The equation used to calculate total headloss through the system is:

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Here, HL.LargeScaleMixing and HL.SmallScaleMixing refer to the minor losses through the large and small scale mixing orifices, respectively. HL.PipeFittings and HL.PipeFriction are caused by minor losses through the pipe fittings and major losses sue to shear along the pipe walls.

Flow through both the large and small scale orifices is modeled as an expansion; as the water flows through the orifices, the flow is contracted and then expands on the other side of the orifice. Thus, head loss can be calculated using the equation for head loss in a flow expansion:

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The calculation of the headloss through the system is important because the headloss through the rapid mix tube system partially determines the change in height of the water in the entrance tank when the plant flow changes. The nonlinear chemical doser is designed to change the flow rate of alum with the flow rate of the plant, and it is thus very important to calculate the headlosses through the rapid mix tube system and the sections of the plant following it in order to correctly design the chemical doser to maintain a constant concentration of alum in the raw water source despite changing flow rates.

(I would expand this section and include a graph of the relationship between head loss and plant flow rate.)

Future Work

Work throughout the rest of the fall 2009 semester will focus on finalizing the Agalteca plant rapid mix tube design. The rapid mix subteam will also build a full-scale model of the system in order to test the feasibility of the system as well as create a prototype tube on which to base future improvements to the tube. Experiments will also be carried out to test the flow of water through the system as well as the effectiveness of the orifices in creating rapid mix of chemical introduced to the water source flowing through the tube system.

Bibliography

• CEE 4540 [Rapid Mix Power Point|CEE4540:syllabus^Rapid Mix.pptx] Lecture
• CEE 4540 [Flow Control and Measurement Power Point|CEE4540:syllabus^Flow Control and Measurement.pptx] Lecture
• Expansion Losses Power Point

Deliverables

• MathCAD file detailing the Rapid Mix Tube design specifications including orifice sizes and head losses through the system
• Schematic drawing of the Rapid Mix Tube system as well as how it fits into the greater plant design
• A prototype of the Rapid Mix Tube system constructed of PVC piping and fittings to test the feasibility of the design as well as the effectiveness of the chemical mixing