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Introduction

    The term “Mixing”, when related to fluids, can have several different definitions depending upon the requirements of the application.  The mixing application can have one or a combination of the following requirements;

• Blending of one or more fluids together which are partially or completely miscible
• Maintaining settleable solids within the fluid
• Promoting cohesion of solids within the fluid
• Dissipating heat from one fluid into another fluid

    Determining which of these criteria applies to the application is the first step in deciding which mixing method should be applied.  There are three main types of mixing methods that the majority of devices can be classified under;

• Mechanical / Turbine
• Hydraulic Recirculation / Pumping
• Diffused Aeration / Pneumatic

    The specific application may also have additional process requirements such as oxygen demand, anoxic states, chemical dissipation, etc. which will influence the selection along with the geometry and construction materials of the mixing vessel.   When all of these criteria have been evaluated to be able to select the most feasible mixing method (or rule out methods which are not desirable to the process) an economic analysis can be conducted for each manufactured mixing system in terms of operational power cost, maintenance and expected life.

  The design method applied can vary significantly for each of the three mixing methods because many of the formulas utilized are empirical associations which have been generalized and do not allow for adjustment in variances of the fluid properties or constituents contained (i.e. Horsepower per volume of fluid, flowrate per volume of fluid, airflow per volume of fluid).  This only allows for comparison of the mixing alternatives in association with “rule of thumb” design values and not the effectiveness of each method to produce the desired level of mixing.  This also requires that a different design basis be defined for each of the alternatives making it difficult to have a benchmark for comparison.

The Velocity Gradient Analysis

  The effectiveness of a system to achieve a desired level of mixing can be determined by calculating the work done on the fluid body and the resulting velocity gradient produced.  A mixing value requirement can be assigned for each type of process regardless of the type of mixing mechanism applied.  The power produced by any specific device can be applied within this equation to satisfy the required mean velocity gradient standard for the specific process.

G = SQRT[ P / (μ * V)]

G = Mean Velocity Gradient, 1/sec

µ = Dynamic Viscosity, lb-sec/sqft

V = Liquid Volume, cuft

P = Power, ft-lbs/sec

    The standard Mean Squared Velocity Gradient equation can be adjusted for each type of mixing method or technology in association to the power or work produced by the mechanism.

Mechanical / Turbine

    For mechanical mixers, the rate of work produced will vary depending on the revolution rate of the mixer, the geometry of the impeller and whether the resulting flow condition is laminar or turbulent.  For turbulent conditions, the development of a vortex must be eliminated to apply these formulas.

G = Mean Velocity Gradient, 1/sec

The Mean Velocity Gradient is a factor of the following variables;

- Dynamic Viscosity

- Liquid Volume

- Power

- value specific to Impeller Geometry

- revolutions per second

- diameter of Impeller

Hydraulic Recirculation / Pumping

    For pumping recirculation systems, the rate of work produced is dependant on the total recirculation rate and the resulting velocity head across the discharge nozzles.

G = Mean Velocity Gradient, 1/sec

The Mean Velocity Gradient is a factor of the following variables;

- Dynamic Viscosity

- Liquid Volume

- Power

- Velocity Head across each diffuser

- Fluid Density

- Flowrate per Diffuser

- Diffuser Discharge Velocity

Diffused Aeration / Pneumatic

    For diffused aeration systems, the rate of work done is a result of the net weight of the fluid displaced by the volume of the gas within the fluid.  The power produced by a diffused aeration system can be substituted into the equation to produce a standard equation for aeration systems in reference to the velocity gradient,

G = Mean Velocity Gradient, 1/sec

The Mean Velocity Gradient is a factor of the following variables;

- Dynamic Viscosity

- Liquid Volume

- Power

- Atmospheric Pressure Head

- Volumetric Airflow Rate

- Submergence Depth of Bubble

Validation of Design Values

    All mixing systems generate directional velocities which produce resulting momentums within the fluid mass.  These velocities are associated to a portion of the fluid which is forced at a higher rate through the ambient fluid body producing a discharge plume effect which follows the properties associated to Gaussian plume physics.  Mechanical mixers produce a plume from the discharge of the impeller, pump recirculation systems produce a plume from the diffuser discharge, and diffused aeration systems produce a vertical plume from the rising bubble mass.  The basic principal of the Gaussian plume is that it will expand dimensionally as it travels through the fluid and also generate a shearing plane where ambient fluid is educted into the discharge plume resulting in blending of the fluids.  The mass of the fluid within the plume and it’s associated discharge velocity produce momentum which continues through the entire fluid volume resulting in continued mixing.

    To determine the extent and effectiveness of the plume(s) and momentum on the entire fluid body computer modeling can be applied.  The most utilized is Computational Fluid Dynamics (CFD) where the geometry of the fluid body is generated in a three dimensional mesh and a finite analysis is integrated throughout from the initial point of the plume generation and the reactions occurring as the plume extends through the fluid body.  CFD modeling is important with fluids and tank geometries that have characteristics where Velocity Gradient design may not address such as suspension of higher density particles (grit and sand), density or temperature differentials (stratifications), and interferences which dampen momentum (square corners, columns, etc.).

Design Summary

    The Velocity Gradient value provides a benchmark for the required energy (work) to be applied to a specific fluid and process so that various types of mixing methods and systems can be evaluated as well as providing a standard scale for the energy required to produce the rate of mixing desired.  Computational Fluid Dynamics modeling provides information relating to equipment orientation, quantity of initial mixing points, specific velocity enhancements required, and a time based projection of the duration required to achieve a complete mix state.

    Tideflex Technology provides four different types of systems for mixing potable water, process wastewater (aerobic), process wastewater (anoxic), and wastewater effluent.  These systems are designated by the following product / system names:

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Hydraulic Recirc Systems Anoxic Mixing	Aeration Systems Aeration & Mixing Systems	(TMS) Mixing Systems Systems for Water Storage	Effluent Diffusers Effluent Mixing Systems