Rapid Mix Orifice Sizing Algorithm
Introduction
The AguaClara team is revising a design for smaller flow rates (under 50 L/s). This page will document and describe the current changes in the Rapid Mix system. The rapid mixer system sizing algorithm is presented is here. Currently, we are now developing an algorithm to plot the entrance tank and rapid mixer onto an AutoCAD drawing.
The suspended particles in the water are removed through a process known as sedimentation. The rate of sedimentation is increased by increasing the diameter of the particles through sticking them together. This is done in a process known as flocculation. Alum is the coagulant of choice used to cause the particles to undergo flocculation. This has to be done rapidly as to ensure the aluminum sulfate does not precipitate before it can be used by the particles. We also need even distribution of alum to the molecular level.
The rapid mix system is designed to accomplish this. The rapid mix design consists of piping leading from the entrance tank to the flocculator entrance. The piping contains two orifices. One orifice is for macro-mixing and the other orifice is for micro-mixing. The orifices decrease the cross sectional area of the flow allowing for a higher velocity and thus turbulence. Turbulence, measured in energy dissipation rate, is associated with the formation of eddies which mix the alum to the length scale at which viscosity overrides the formation of eddies with a larger energy dissipation rate being associated with a smaller eddies. The length scale at which the eddies can mix the alum to is known as the Kolmogorov length scale.
Where:
L.k: Kolmogorov Length Scale
NU: Kinematic Viscosity
EPS: Energy Dissipation Rate
There are two main forms of mixing. One is macro-mixing and the other is micro-mixing. Macro-mixing mixes the alum to the length scale at which micro-mixing can start. Micro-mixing distributes the eddies to the length scale that molecular diffusion can finish the task.
Design Algorithm
In the current design, we have two circular orifices on the same pipe segment. Originally, the micro-mixing orifice was after the first pipe bend. However we have decided to change that to allow facility of removal when cleaning is required. The micro-mixing orifice is two pipe diameters below the macro-mixing orifice. This ensures adequate mixing time for macro-mixing to take effect. The orifices for both equations are sized using the equations of minor loss coefficient for a submerged orifice.
Where:
K.e.orifice: Minor loss Coefficient
K.vc: Vena Contracta Coefficient
d.pipe: Pipe Inner Diameter
d.orifice: Orifice Diameter
The equation for head loss is shown below:
Where:
h: Head Loss
K: Minor Loss Coefficient
V: Velocity of Fluid
G: Gravitational Constant
The equation for minor loss coefficients for a submerged orifice shown above is used to find the orifice diameter needed.
Figure 1: Design Layout of Rapid Mix System
Research has estimated that for a macro-mixing orifice, we should have a minor loss coefficient of 1.3. Another design constraint from research is to have a 20-50 cm maximum head loss through both orifices with most of it going into the micro-mixing orifice. This will be needed for the dose controller that will be integrated into the system. In the case of a macro-mixing orifice, each pipe diameter allows for one orifice size. An increase in flow-rates will give the macro-mixing orifice a significant head loss. In the algorithm, if there is significant head loss above a certain limitation (2 cm or above), then the piping is upgraded to the next size. To accomplish this, the pipe sizing algorithm is modified to select pipe sizes that will meet this constraint. Another assumption is that the head losses through the entire plant (both micro-mixer and macro-mixer as well as flocculator) would be used to measure flow. Due to this, this algorithm will be set to allow the user to determine the constraint, if any they would like to put on the macro-mixer head. Having little or no constraints will allow for smaller pipe sizes.
If we run this algorithm with no constraints with a 20 cm head loss through the macro-mixer, we would obtain the following results.
Figure 2: Rapid mix sizing algorithm for lower flow rates with 20 cm through micro-mixer and no constraints 
The results show that above that with each pipe size and macro-mixing size, we have high head losses through the macro-mixing orifice which will increase to levels greater than 20 cm and hence give most of the head loss through the micro-mixing orifice.
The algorithm can be summarized in these following steps:
1. Determine the inner pipe size given the flow-rates, maximum pressure drop (20 to 50 cm). total minor loss coefficients, and the available pipe sizes.
2. Using the pipe size given, determine the orifice diameter of the macro-mixing orifice. This is determined using the equation for minor loss coefficients for submerged orifices
3. If the head loss through the macro-mixing orifice exceeds 2 cm, then move up to the next pipe available and recalculate the orifice size. This step is repeated until the head loss is 2 cm or less.
4. Use the assigned total head loss value (20-50 cm) and maximum flow rate to determine the minor loss coefficient needed for the micro-mixing orifice. Using the equation for minor loss coefficients for submerged orifices to determine the orifice diameter for the micro-mixing orifice.
Running this algorithm for flow-rates under 50 L/s gave the following results as shown below on Figure 3.
Figure 3: Rapid mix sizing algorithm for lower flow rates with 50 cm maximum head loss and 2 cm constraint on macro-mixer
We also did runs where the constraint was raised to 10 cm head loss through the maco-mixing orifice.
Figure 4: Rapid mix sizing algorithm for lower flow rates with 50 cm maximum head loss and 10 cm constraint on macro-mixer
With this lower constraint, we find much smaller pipe sizes used. The micro-mixing orifices are also larger. We can also change the results to see what happens when we want a 20 cm head loss through the rapid mixer with our 2 cm constraint through the macro-mixer.
Figure 5: Rapid mix sizing algorithm for lower flow rates with 20 cm maximum head loss and 2 cm constraint on macro-mixer
The results for the pipe sizing and and macro-mixer sizing are not changed but we have larger orifices.
The current work is now coding this onto the AutoCAD along with entrance tank.