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PSS Dynamics Model

Introduction

The current theory about the plate settlers predicts the failure for a certain sedimentation tank and plate spacing based on a failure mechanism called floc rollup. The floc roll up theory states that a floc hitting the bottom plate will experience a fluid velocity at its edge and a settling velocity. If the fluid velocity is higher than the settling velocity, then the floc will roll up the plate and will exit the plant without being captured.

This theory is based on the following assumptions:

  • The velocity profile at the edge of the particle is linearized,
  • Flocs are following straight lines,
  • Flocs are spheres,
  • There are no floc breakup or collision,
  • The presence of flocs do not affect the velocity profile,
  • The entrance region of a plate settler (where the velocity profile is not fully-developed) is ignored.

The current theory predicts failure by mean of a dimensionless ∏ ratio which is explained on this page: https://confluence.cornell.edu/download/attachments/87983632/WikiAppendix-Definitions_Equations_somevalues.pdf?version=1. When this ratio is less than one, then the turbidity should be above 0.25 NTU and this means that the spacing for a given flow rate is going to be above the maximum allowed turbidity.

Our firsts experimental results showed that this ratio is able to predict that the effluent turbidity will be above 0.25 NTU. But it is unable to predict the magnitude of the failure.

The PSS team therefore concluded that it needed to develop a numerical simulation taking more phenomenon into account in order to be able to better understand the failure mechanisms and maybe be able to assess the effluent turbidity.

Comments about how the code works

The code works on a Velocity-Verlet algorithm which computes all particles paths based on their experienced local velocities. The code takes particles sizes and the tube (or plate) geometry as well as the up flow velocity as an input. The figure below summarizes the steps taken by the algorithm.

 

Attachments

trajectory9.m ||The main file. Contains the input parameters as well as the velocity-Verlet algorithm

Vfluid.m || Function that computes the velocity profile as a function of the distance inside a tube or plate settler

Re.m || Function that computes the Reynolds number (required for modeling the entrance region)

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