Process Chemistry Toolbox - Mixing

Process Chemistry Toolbox - Mixing

Industrial diffusion flames are turbulent Laminar Turbulent

3 T s of combustion Time Temperature Turbulence

Visualization of Laminar and Turbulent flow http://www.youtube.com/watch?v=kqqtob30jws Laminar http://www.youtube.com/watch?v=nplrdarmdf8 Turbulent - Effective mixing

Characteristics of turbulence Effective mixing Eddy fluid parcel 3D Time-dependent Gustavo Assi

Turbulence - chemistry interaction Heat 1 = i Heat 2 Heat 3 Heat n Smallest eddies - most of dissipation - size limited by the Kolmogorov length scale Large eddies - receive kinetic energy from mean flow - size limited by the geometry of e.g. the furnace Eddy: transport of a parcel of fluid (for example fuel or oxidizer) Dissipation of kinetic energy to heat ε mixing on molecular level Reactions occur on molecular level!

Mixing considerations in industrial scale furnaces Example: black liquor recovery boiler ~85 m ~15 x 15 m

(m/s) >50 Mixing considerations in industrial scale furnaces Example: black liquor recovery boiler Combustion air - Staging - Distribution over cross section (O 2 vol-%) 20 m 3 m 0.2 m

Introduction to Computational Fluid Dynamics

Process Chemistry Toolbox - Mixing Computational Fluid Dynamics (CFD) - A tool for studying reactive flows in complex geometries ~85 m Example: Black Liquor Recovery Boiler ~15 x 15 m

Computational Fluid Dynamics (CFD) Boundary conditions and Predictions (m/s) Gas flow Fuel

Computational Fluid Dynamics (CFD) Boundary conditions and Predictions (%) O 2 concentration ( C) Temperature

The Computational Procedure (1) Technical Device (boundary conditions/ geometry known) Computational Domain with Computational Grid Computational Cell/ Control Volume (Mueller)

The Computational Procedure (2) Computational Cell/ Control Volume Balancing for: Mass Momentum Energy etc. Boundary Value Problem Iterative Process CFD-Result (complete description u, v, w, p, h, T) (Mueller)

Iteration towards a converged solution

Modeling conversion of char forming fuel

Modeling conversion of char forming fuel Drying Pyrolysis Char combustion H 2 O Volatiles Char-C as CO Heat transfer Heat transfer Mass transfer and kinetics (O 2, CO 2, H 2 O)

Modeling conversion of char forming fuel Drying Pyrolysis Char combustion

Modeling conversion of char forming fuel 6 mm initial diameter Drying Pyrolysis Char combustion

Modeling conversion of char forming fuel 2 mm initial diameter

Modeling conversion of char forming fuel Average initial diameter ( C) 4 mm 7 mm

Turbulent flow some modeling approaches

Pulverized coal flame photograph LES RANS (Courtesy of Phil Smith, U. Of Utah)

Turbulent flow some modeling approaches Computational expense increases DNS: - No turbulence model! - eq to analytical solution of turbulent flow (Hanjalic et al. Analysis and Modelling of Physical Transport Phenomena )

Visualization of Laminar and Turbulent flow http://www.youtube.com/watch?v=kqqtob30jws Laminar http://www.youtube.com/watch?v=nplrdarmdf8 Turbulent - Effective mixing

RANS - Conservation equations General property balance (conservation equation) / t ( U ) G ( 2 ) Applied to turbulence with instantaneous velocity U U U ' / t ( U ) ( ) [ G 2 ( U ' ' )] Same form as original equation Average properties Fluctuations Unknowns > Equations Closure problem Turbulence models

1-equation model 2-equation model - k-ε model - k-θ model Reynolds Stress Model (RSM) Some turbulence models isotropic turbulence representative stress (turbulent viscosity) modelled non-isotropic turbulence indiviual stresses in all directions modelled ' U ' Momentum ' ' [ ( U )] fluctuations ( ' U U ' ) '2 U x ' U yu ' U zu ' x ' x U U ' x U ' z '2 y U U ' y ' y U U U ' x ' y U U '2 z ' z ' z Reynolds stresses

The scalar variables k and calculated by scalar transport equations i j i j i j i S + x ~ x ~ ~ x ~ t u j Kinetic energy k: k Dissipation : k turb Pr i ~ i S Pr turb k P ~ c P k ~ c k ~ ~ 1 k 1 Standard k- turbulence model Turbulent viscosity

Mixing - Exercise Methane combustion with air, λ = 1.2 Air Methane Steps included in calculation - Chemical reactions - Calculation grid - Boundary conditions - Iterations

Mixing - Exercise Stoichiometric overall reaction CH 4 + 2 O 2 CO 2 + 2 H 2 O Chemical reactions considered in model 1: CH 4 + ½ O 2 CO + 2 H 2 2: CH 4 + H 2 O CO + 3 H 2 3: H 2 + ½ O 2 H 2 O 4: CO + H 2 O CO 2 + H 2 5: CO 2 + H 2 CO + H 2 O Turbulence-chemistry interaction Finite rate / Eddy-dissipation

Mixing - Exercise Calculation grid from 3D to 2D

Mixing - Exercise Calculation grid outer dimensions 100 m 40 m Outlet 50 cm 20 cm

Mixing - Exercise Calculation grid Cells - connected reactors Calculation procedure Boundary conditions Iterations Balancing for - momentum - mass - species - energy in + gen = out + acc Air Methane Steady-state (acc =0)

Mixing - Exercise At start of calculation Initial values are given 0 iterations - Velocity - Temperature - Species concentrations As calculation proceeds - Boundary conditions unchanged - Initial values inside reactor are updated toward converged solution

Mixing - Exercise

Example of CFD calculation (m/s) Velocity magnitude after 3000 iterations Contours Along symmetry axis

Example of CFD calculation O 2 mole fraction after 3000 iterations Contours Along symmetry axis

Example of CFD calculation CH 4 mole fraction after 3000 iterations Contours Along symmetry axis

Example of CFD calculation Gas temperature (K) after 3000 iterations Contours Along symmetry axis Heat released from CH 4 combustion is removed from gas

Example of CFD calculation Species mole fractions and T after 3000 iterations 0.4 2500 T 2000 (-) 0.2 CH 4 H 2 O 1500 1000 (K) H 2 0 CO CO 2 O 2 0 10 20 30 40 500 0 Position along Position symmetry (m) axis (m)