Modeling of Laminar Flow Static Mixers COMOL
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Transcript of Modeling of Laminar Flow Static Mixers COMOL
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Modeling of Laminar Flow Static Mixers
®
Nagi Elabbasi, Xiaohu Liu, Stuart Brown (Veryst Engineering)
Mike Vidal, Matthew Pappalardo (Nordson EFD)
COMSOL Conference 2012, Boston, MA
Veryst Engineering 47A Kearney Road Needham, Massachusetts 02494 phone 781.433.0433 [email protected] www.veryst.com
Excerpt from the Proceedings of the 2012 COMSOL Conference in Boston
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Veryst Engineering
Introduction
• Laminar flow static mixers are inexpensive and suitable for wide range of industrial applications
• There is very limited diffusion in between the mixed fluids
– Mixing must involve dividing and recombining fluids
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Image courtesy of Nordson EFD
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Veryst Engineering
Introduction
• Multiphase CFD simulation cannot be used by itself to predict mixing quality due to numerical diffusion
3
Size of fluid streaks too
small for detection with
multiphase CFD only
Experimental data
Is there a more
suitable approach?
Yes!
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Veryst Engineering
Multiphase CFD Example
• A 2D example demonstrating dispersion in multiphase flow
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Fluid 1
Fluid 2
Too much phase dispersion even with fine mesh and low numerical diffusion
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Veryst Engineering
Multiphase CFD Example
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Phase dispersion region too wide
If there is no diffusion between fluids this width should be zero
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Veryst Engineering
Modeling Approach
1. CFD analysis to predict overall mixer performance, flow pattern and pressure drop
2. Use streamlines or mass-less particle tracing to track motion of the fluid particles
3. Export streamline or particle tracing data for evaluation of mixing efficiency
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Veryst Engineering
Step 1: CFD Analysis
• CFD analysis to predict overall mixer performance, flow pattern and pressure drop
– May be a two-phase analysis if two fluids have different density or viscosity
– Very low Reynolds number flow
– Assumed Newtonian fluids
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Veryst Engineering
CFD Analysis
• Velocity and pressure drop for a specific mixer
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Pre
ssu
re
Velocity profile Pressure drop
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Veryst Engineering
Step 2: Streamlines/Particle Tracing
• Use streamlines or mass-less particle tracing to track the motion of fluid particles
– Limited numerical diffusion
– Large number of particles required
– Accuracy of time integration essential
– Insert streamlines in a uniform grid at any section
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Veryst Engineering
Streamlines Calculation
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• The same 2D example
Single-phase flow with streamlines
Two-phase flow
Unrealistic mixed region due to numerical diffusion
Distinct fluid boundary
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Veryst Engineering
Particle Tracing
• Generate grid of mass-less particles instead of streamlines
• Poincare sections generated by COMSOL provide useful visualization tool
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Veryst Engineering
Step 3: Mixing Algorithm
• Export streamlines or mass-less particle tracing data using COMSOL’s Java script feature
• Calculate coordinates where each streamline intersects different sections along static mixer
– Similar to Poincare maps
• Divide each mixer section into a suitable sized grid and calculate number of streamlines intersecting each grid
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Veryst Engineering
Mixing Algorithm
• Evaluate mixing using 2 metrics:
– Coefficient of variation
– Sectional images for detecting unmixed streaks
• Insert streamlines at multiple locations along mixer to increase accuracy and check level of numerical diffusion
– Find optimal settings for streamline calculation
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Veryst Engineering
Coefficient of Variation
• One number that measures the mixing quality at a mixer cross-section
• Has positive value (~1.0) for no mixing, and 0.0 for “complete mixing”
• Complete mixing means good mixing at a specific cell size
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Veryst Engineering
Coefficient of Variation
• Typical Coefficient of Variation result
Minimum
detectable value
for current settings
Local oscillations
function of cross-
sectional area of
mixer
Rate of CoV drop
indicative of mixer
efficiency
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Veryst Engineering
Coefficient of Variation
• Coefficient of variation predicts overall mixing quality. It is not ideal for detecting streaks.
• Streaks best detected by examining images of mixing at different cross-sections
A fluid streak. Easy
to detect visually,
not through CoV
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Veryst Engineering
Algorithm Validation
• Performed mixing experiments using two epoxy materials that solidify when mixed – a black and a white compound
• After solidification mixer sliced into about 40 sections to visually assess mixing progression
• Simulate same experiment with developed mixing algorithm and compare predictions
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Veryst Engineering
Algorithm Validation
• Experimental sectional images
– Images only shown for first half of mixer
– Exact entry angle of fluid into mixer not captured
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Veryst Engineering
Mixing Results
• Before first inverter
Good agreement between experimental and numerical predictions
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Experiment Simulation
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Veryst Engineering
• At end of first inverter
Mixing Results
Area of very slow flow/recirculation
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Experiment Simulation
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Veryst Engineering
• Before second inverter
Mixing Results
Ellipses show captured streaks
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Experiment Simulation
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Veryst Engineering
• After second inverter
Mixing Results
Simulation also captures flow patterns
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Experiment Simulation
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Veryst Engineering
Summary
• Developed algorithm for evaluating mixing quality in static mixers
– CFD simulation to predict overall fluid flow and pressure drop in mixer
– Streamline or particle tracing calculation to track fluid particles
– Sectional images at multiple sections along mixers
– Coefficient of variation that gives quantitative assessment of mixing quality
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Veryst Engineering
Summary
• Very good agreement obtained between experimental and simulation results
• Advantages of using COMSOL Multiphysics
– Accurate CFD simulation
• Single-phase and multi-phase flows
– Accurate streamline and particle tracing calculations with over 200,000 particles
– Ease of scripting with interfaces to Java and MATLAB
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Veryst Engineering
Current and Future Work
• Evaluating mixing quality for different fluid flow rates, viscosities and mixing proportions
– Mixed fluids are frequently non-Newtonian (shear thinning, shear thickening or thixotropic)
• Using developed tool to optimize static mixer designs for Nordson EFD and investigate radically different mixer designs
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