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The AguaClara team is revising a design for smaller flow rates (under 50 L/s). This page will document documents and describe the current changes in the Rapid Mix system. The rapid mixer system sizing algorithm is presented is here. We are working toward including AutoCAD images for the entrance tank and rapid mixer in our designs. In Figure 1 , shows a layout of the design is shown below.
Figure 1: Design Layout of Rapid Mix System. Chemical Doser Team
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Where:
L.k: Kolmogorov Length Scale
NUν: Kinematic Viscosity
EPSε: Energy Dissipation Rate
The two different orifices in the rapid mixer are for the two types of mixing that occur. One is for macro-mixing and the other is for 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 where molecular diffusion can finish the task.
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Where:
h: Head Loss
K: Minor Loss Coefficient
V: Velocity of Fluid
G g: Gravitational Constant
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In the case of macro-mixing, we are setting the minor loss coefficient to 1.3. This value is assumed to be adequate to allow for macro-mixing. The total head loss through the rapid mixer is set to 20 - 50 cm accounts for a total head loss of 40 cm throughout the entire plant, with most of the head loss in the rapid mix system belonging to the micro-mixer. This will be needed for the dose controller that will be integrated into the system. The dose controller uses a flow measurement device which relates head loss to flowrate (See Lectures on Rapid Mix). From the equation for a submerged orifice, it can be seen with the design assumption of K = 1.3, each pipe size will allow for one macro-mixing orifice size.
A A pipe size/macro-mixing combination can be used for a range of flow-ratesflowrates. An increase in flow-rates flowrates will result in a higher head loss for the macro-mixing orifice. This can actually result in the macro-mixing orifice having a higher head loss than the micro-mixing orifice. Due to this, the user can select a constraint value for head loss (usually 2 to 10 cm, currently set at 5 cm) that will cap how high the macro-mixing head loss can be. This is done by selecting a larger pipe size and larger macro-mixing orifice. In figure 2, the results for head loss through the macro-mixer are shown below. At high flow-rates, macro-mixing head loss becomes higher than micro-mixing head loss.
With the head loss of the entire plant and the entire system accounted for the constraint on the macromixer headloss (MacroMHConstraint = 5 cm) the size of the nominal diameter of the pipe, the diameter of the macromix orifice and the size and number of micromix orifices can be determined.
Figure 2: Rapid mix sizing algorithm for lower flow rates with 20 cm through micro-mixer and no constraints
The 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-ratesflowrates, maximum pressure drop (20 to 50 cm). , total minor loss coefficients, and the available pipe sizes. The user also sets a constraint or limit for the macro-mixing orifice head loss.
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4. Use the assigned total head loss value (20-50 cmcalculated to provide 40 cm of loss in the entire system) 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. The number of orifices that can fit the area of the micro-mixing interface is returned based on the micro-mixing diameter.
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 macomacro-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 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.
Figure 6: Rapid mix sizing algorithm for lower flow rates with 40 cm maximum head loss throughout plant and 5 cm constraint on macro-mixer
Figure 7: Number of micro-mixing orifices for lower flow rates with 40 cm maximum head loss throughout plant and 5 cm constraint on macro-mixer
Figure 8: Head loss in macro and micro-mixing orifices for lower flow rates with 40 cm maximum head loss throughout plant and 5 cm constraint on macro-mixer
The next task is to use this code in developing an AutoCAD image of the entrance tank and rapid mixer.