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Rapid Mix Orifice Sizing Algorithm

Introduction

The AguaClara team is making changes in the arrangement of the Rapid Mix system.  This page will document and describe the current changes in the Rapid Mix system and the algorithm for preparing an AutoCADD drawing of the Rapid Mix system. 

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:  Diameter of orifice


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.  This is what we are using for our design.  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 (2 cm or above), then the piping is upgraded to the next size. The reason for having a minimum flow-rate for macro-mixing is that we plan to use the macro-mixing orifice as a flow-measurement device which can handle 20-50 cm maximum head loss at maximum flow-rate.  The micro-mixing orifice is sized for a minor loss coefficient that allows for this type of flow and head loss.  The equation for minor loss coefficients for a submerged orifice shown above is used to find the orifice diameter needed. 

The algorithm can be summarized in these following steps:

  • 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. 
  •  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
  • 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. 
  • 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.

For a flow rate of 1 L/s with 50 cm maximum head loss, we obtained an inner pipe diameter of 1.89 in and macro-mixing and micro-mixing orifice diameters of 1.64 in and 0.94 in respectively. For the case of 2 L/s with 50-cm maximum head loss, we obtained an inner pipe diameter of 2.80 in and macro-mixing and micro-mixing diameters of 2.42 in and 1.33 in respectively.There will be changes made to make this algorithm more robust and they are in process.

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