Micro and Macro Mixing: Analysis, Simulation and Numerical Calculation

✍ Scribed by Henning Bockhorn; Dieter Mewes; Wolfgang Peukert; Hans-Joachim Warnecke

• Publisher: Springer
• Year: 2010
• Tongue: English
• Leaves: 345
• Category: Library

✦ Synopsis

The homogenization of single phase gases or liquids with chemical reactive components by mixing belongs to one of the oldest basic operations applied in chemical engineering. The mixing process is used as an essential step in nearly all processes of the chemical industry as well as the pharmaceutical and food ind- tries. Recent experimentally and theoretically based results from research work lead to a fairly good prediction of the velocity fields in differend kinds of mixers, where as predictions of simultaneously proceeding homogeneous chemical re- tions, are still not reliable in a similar way. Therefore the design of equipment for mixing processes is still derived from measurements of the so called “mixing time” which is related to the applied methods of measurement and the special - sign of the test equipment itself. The cooperation of 17 research groups was stimulated by improved modern methods for experimental research and visualization, for simulations and nume- cal calculations of mixing and chemical reactions in micro and macro scale of time and local coordinates. The research work was financed for a six years period within the recently finished Priority Program of the German Research Foundation (DFG) named “Analysis, modeling and numerical prediction of flow-mixig with and without chemical reactions (SPP 1141)”. The objective of the investigations was to improve the prediction of efficiencies and selectivities of chemical re- tions on macroscopic scale.

✦ Table of Contents

Title Page
Preface
Contents
Part 1: Quality of Mixing
The Variance as Measured Variable for the Evaluationof a Mixing Process or for the Comparison of Mixtures and Mixers
Introduction
Total Mixture
Mixedness
Measurable Properties
Definition of Mixedness
Choice of the Sample Size (Theoretical Variance $σ^2_N$ with Finite Sample Size)
Empirical Variances
Definition of the Empirical Variance $s^2$
Chi-Square Distribution
Confidence Intervals
Choice of the Number of Samples
Representative Controlled Sampling
Conclusion
Evaluating the Quality of a Mixture: Degree of Homogeneity and Scale of Segregation
Introduction
Homogeneity of a Mixture
Scale of Segregation
An Example: Mixing in a T-Shaped Micro-mixer
Concluding Remarks
References
Part 2: Experimental Methods for Visualization and Measurements in Macro- and Micro-Scale Dimensions of Mixing
Time-Resolved Measurement of Concentrations in Mixing Processes Using Raman Spectroscopy
Introduction
Demands on the Measurement System
Comparison of Different Optical Approaches
IR-Absorption
Laser Induced Fluorescence
Spontaneous Raman Scattering
Comparison of LIF and SRS
Experimental Set-Up
Selection of the Laser
Selection of the Recording System
Multi-line vs. Multi-point
Experiments
Course of Measurement
Typical Measurements of the T-Mixer and Taylor-Couette Reactor
Outlook
Summary
Acronyms
References
Measurements of Macro- and Micro-scale Mixing by Two-Colour Laser Induced Fluorescence
Introduction
Micro and Macro Mixing- the Degree of Deviation
Fluorescent Dyes
Experimental Set-Up
Experimental Results
Conclusions
References
Analysis of Macro- and Micromixing in Laminar Stirred Mixing Vessels Using Laser Optical and Numerical Methods
Introduction
Experimental Setup
Macro- and Micromixing
Numerical Calculations
Results and Discussion
Conclusions
References
Experimental Investigation of the Mixing-Process in a Jet-in-Crossflow Arrangement by Simultaneous 2d-LIF and PIV
Introduction
Experimental Setup
Flow Arrangement
2d-LIF-PIV Measuring System
Results and Discussion
Influence of a Swirled Jet with Respect to the Mixing between Jet and Crossflow
Influence of the Reynolds Number on the Mixing Process
Turbulent Mass Transfer
Conclusions
References
Characterization of Micro Mixing for Precipitation of Nanoparticles in a T-Mixer
Introduction
Optical Methods to Characterize Mixing
Particle-Image Velocimetry (PIV)
2D-Laser Induced Fluorescence (2D-LIF)
HR-Laser Induced Fluorescence (HR-LIF)
Nanoparticle Precipitation in a T-Mixer
Experimental Investigations
Modelling
Conclusion
References
Mixing in Taylor-Couette Flow
Introduction
Experimental Set-Up
Experimental Results
Macromixing
Mixing Inside the Vortex Cell
Micromixing
Conclusions
References
Part 3: Theoretical Methods for Modelling and Numerical Calculations of Mixing Processes
Direct Numerical Simulation, Analysis and Modelling of Mixing Processes in a Round Jet in Crossflow
Introduction
A Database for Mixing and Chemical Reactions in a Jet in Crossflow Obtained by DNS
Characteristics of the Present DNS Database for Mixing and Chemical Reactions
Geometry, Parameters and Boundary Conditions
Numerical Method
Sensitivity of the Jet Trajectory with Respect to the Velocity Ratio
Analysis of Mixing Based on Present DNS Results
Laminar-Turbulent Transition, Scalar Fields
Assessment of the Mixing Process by Means of Streamlines
Apriori Testing of Mixing Models Based on the Present DNS-Results
The Wavelet Approach to LES Modelling (WALES)
The Wavelet Basis Employed
WALES Subgrid-Scale Models Developed
WALES Modelling Applied to Plane Channel Flow
Results with the WALES Applied to the JICF
Conclusions
References
Analysis of Mixing Processes in Jet Mixers Using LES under Consideration of Heat Transfer and Chemical Reaction
Introduction
Methods of Investigation
Experimental Setup and Measurement Procedure
Numerical Models
Mixing in Jet Mixers
Performances of Mathematical Models for Simulation of Turbulent Mixing
Influence of Various Parameters on Mixing
Self-sustained Oscillations in Jet Mixers
Structure of the Scalar Field in Jet Mixers
Dissipation Rate Field
Chemical Reactions in Jet Mixers
Measurement of Flow with Neutralization Reaction
RANS and LES Computations of Neutralization Reaction
RANS Computation of Competitive-Consecutive Reactions
Conclusions
References
Formulation and Validation of an LES Model for Ternary Mixing and Reaction Based on Joint Presumed Discrete Distributions
Introduction
Biased, Multi-variate Mixing Modes
Variance Adjustment
Covariance
Transport Equations
Closure for the Scalar Dissipation Rate
Closure for the Covariance
DNS Simulations for a Priori Validation
Results
Distributions
Reaction Rates
Conclusion
References
Mixing Analysis and Optimization in Jet Mixer Systems by Means of Large Eddy Simulation
Introduction
Mathematical Models and Numerical Procedure
Model Package for SGS Scalar Transport Description
Numerical Procedure
Configurations, Results and Discussion
Non-reacting Jet in Channel Flow (Water)
Confined Impinging-Jets Reactor (CIJR)
Conclusions
References
Experimental Investigation of a Static Mixer for Validation of Numerical Simulations
Introduction
Experimental Set-Up and Measurement Methods
Results
Simultaneous PIV-PLIF Measurements
Experimental Characterization of Macro- and Micro-Mixing
First Comparisons with Numerical Simulations
Modeling Numerically Micro-Mixing
Conclusions
References
Simulation of Flow and Transport in a Static Mixer Using Adaptive and Higher Order Numerical Methods
Introduction
Mathematical Model
Discretization
Finite Volume Method
Discontinuous Galerkin Method
Numerical Results
Driven Cavity
Static Mixer
Concluding Remarks
References
Part 4: Macro- and Micro-Mixing in Micro Channel Flow
Computational Analysis of Reactive Mixing in T-Microreactors
Introduction
Computational Approach
Computational Analysis of the Mixing Zone
Hydrodynamics
Energy Dissipation
Passive Mixing
Intensity of Mixing and Specific Contact Area
Computational Analysis of the Reaction Zone
Reactive Mixing with Instantaneous Reactions
Parabolised Species Equation
Validation of the Parabolised Species Equation
Scale Effects
Variation of the Reynolds Number
Conclusions
References
Experimental Analysis and Modeling of Micromixing in Microreactors
Introduction
Experimental Methods
Results and Discussion
Conclusion
References
A Numerical Approach for Simulation of Turbulent Mixing and Chemical Reaction at High Schmidt Numbers
Introduction
Direct Numerical Simulation of the Flow and Mixing Inside a T-Mixer at Low $Sc$
Flow Field Inside the T-Mixer
Turbulent Mixing at $Sc$ = 1
Precipitation along Lagrange Paths
Semi Direct Numerical Simulation of the Mixing Inside a T-Mixer at High $Sc$
ADM Model for the Turbulent Mass Flux
Mixing at High Sc Inside a T-Mixer
Direct Numerical and Filtered Density Function Simulation of the Flow and Mixing Inside a T-Mixer at High Sc
The FDF-DNS Method
Formulation of a Model for the Micro Mixing
Small Scale Mixing at High Sc Inside a T-Mixer
Precipitation Simulation at High Sc Inside a T-Mixer
Conclusions
References
Theoretical and Experimental Investigations of Convective Micromixers and Microreactors for Chemical Reactions
Introduction
Characteristic Mixing Properties
The Mixing Quality α
The Mixing Potential Φ
Stoichiometry of Mixing
Flow and Mixing Regimes in T-Mixers
Static Flow Regimes
Periodic Vortex Shedding
Chaotic Regime with Transition to Turbulence
Summary of the Mixing Regimes
Improved Mixing Structures
Experimental Characterization
Flow Visualization with Fluorescent Dye
Measurement of Mixing with Color Reactions
Iodide-Iodate Reaction
Convective Lamination Model
Wall Contact vs. Mixing in Microreactors
Simulations and Optimization of Wall Contact
Quantification of Wall Contact with a Luminol Reaction
Conclusion
References
Author Index