MSc. Thesis Project Simulation of a Rotary Kiln MSc. Cand.: Miguel A. Romero Advisor: Dr. Domenico Lahaye 1
Problem Description What is a Rotary Kiln? A Rotary Kiln is a pyroprocessing device used to raise materials to high temperatures in a continuous process. 2
Problem Objectives Abstract Accurately calculate the Temperature Profile of the Granular bed of the Rotary Kiln. This will lead to an accurate analysis on where hot spots could appear and a sensibility analysis in conjunction with M. Pisaroni s work by varying parameters, such as G/Air ratio, inclination and RPM, in order to homogenise the profile and reduce hot spots. If reaction kinetics are known, a more accurate description of the process can be made and concentration profiles can be incorporated into the Simulation. 3
Simulation Set-up Rotary Kiln simulation The Problem can be divided into two sub problems: Simulation of the Combusting Gases Work done by M. Pisaroni Simulation of the Granular Bed To be the focus of the present project The the simulation of the Granular Bed will use data from the Combusting gases as input 4
What is Granular Flow? Granular material is a collection of solid particles or grains, such that most of the particles are in contact with at least some of their neighboring particles. Examples: sand, gravel, food grains, seeds, sugar coal and cement, (Kesava & Prabhu, 2008) We call granular flow to the displacement of granular material Granular materials exhibit characteristics similar to both solids and liquids 5
Modeling Approaches There are two typical ways of modelling granular flow: Discrete Method: Euler-Lagrange approach (Coupled DEM) Treat the material as a collection of particles. Newton s laws of motion are applied to each particle Continuum Models: Euler-Euler approach (Two fluid modeling) Particles are modeled by a continious medium where all the quantities are assumed to be smooth functions of position and time (local averaging) 6
Euler-Lagrange: Discrete Element Method Consists of an ODE system: Particle Motion / Particle Tracking dx i dt = u p,i du p,i dt = 1 m p F p With contact forces using the soft-sphere approach (suitable for multiple contacts), spring and dampener model. Then we solve a new ODE system with linear or non-linear spring. 7
Euler-Lagrange: Discrete Element Method Advantages Relatively simple model, easy to understand physics Easy to implement, there are also a number of Commercial and Open Source software implementations: Star CCM+, OpenFOAM, LIGGGHTS/LAMMPS, MFIX. Implementations are in parallel/parallelizable Disadvantages May still need some empirical adjustments because of the nonsphericity of particles. Still needs validation of certain parameters. Very computationally expensive -> in 3-D one needs for particle motion 6 ODEs per particle, in our problem we have ~1.5 billion particles 8
Euler-Lagrange: Discrete Element Method Experiments were done with LIGGGHTS in order to investigate feasibility because of the size of the problem What is LIGGGHTS? Open Source discrete element method particle simulation software based on LAMMPS (molecular dynamics simulator from Sandia National Laboratories from the US DoE) Highly scalable parallel DEM Simulator (uses MPI) 9
Euler-Lagrange: Discrete Element Method Experiment Setup Simulation of a rotating cylinder Diameter: 2.1 m Number of particles: ~15,000-200,000 Cylinder Length: 0.1 m Simulation time: 3 s Timestep: 0.00001 s 1 core 2 RPM 5% loading by volume *Test for visualization. NOT an experiment run. 10
Euler-Lagrange: Discrete Element Method 80 Np vs t 70 60 50 40 30 Np vs t 20 10 0 0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000 11
Euler-Lagrange: Discrete Element Method Notes about the simulation There was overhead because of writing of data every 1000 time steps Not yet parallelized Only 3 s of simulation time There is maybe a cheaper way of incorporating the rotation of the cylinder No Heat Transfer or Chemical Reactions were incorporated By taking the packing limit of 0.5 and a loading of 5% with particles of 2.5 mm, one gets ~1.1 billion particles. 12
Euler-Lagrange: Discrete Element Method Possible set up for the Simulation Using fixed temperature profile/radiation from the flame data already available Having a Coupled simulation of the Combustion and Particle flow using the model already available Data needed: Mass and Energy balances for set up and validation Reaction kinetics or simplified kinetics in order to calculate accurately the T profile of the particle bed 13
Euler-Lagrange: Discrete Element Method Open Questions Mass and Energy balance data Reaction Kinetics Questions on implementation of solid-solid reactions with respect to the Discrete Element Method (opposed to a much easier implementation of solid-fluid reactions) How will the performance be affected by the Heat Transfer/ Chemical Reactions and Parallelization on the simulation? 14
Euler-Euler: Two Fluid approach Two-phase hydrodynamic models treat the fluid and the solids as two interpenetrating continua. One uses an averaging approach where equations are derived by space, time or ensemble averaging of the local, instantaneous balances of each of the phases. Basically a multiphase RANS code; implemented in almost any CFD software such as: Fluent, Star CCM+, OpenFOAM and MFIX. Extensive use for simulating Fluidised Beds and Slurry flows 15
Euler-Euler: Two Fluid approach t t Conservation of mass and momentum ( ε g ρ g ) + i ε g ρ g v g ε g ρ g v g ( ) = R g vg ( ) + i( ε g ρ g v g ) = i S g + ε g ρ g g I g ( ε s ρ s ) + i ε s ρ s v s t The interaction force (momentum transfer) between phases can be modeled in the same way as in the Euler-Lagrange approach, having Drag, Buoyancy and Mass Transfer. I g = ε s P g F g t ε s ρ s v s vs v ( g ) + R 0v ( ) = R s vs ( ) + i( ε s ρ s v s ) = i S s + ε s ρ s g + I g 16
Euler-Euler: Two Fluid approach The most difficult and interesting part is the modeling and definition of the Stress Tensors. For the fluid phase it takes the usual form: S g = P g I + τ g With the Pressure and the Newtonian Viscous Stress Tensor 17
Euler-Euler: Two Fluid approach For the solids, we can observe that granular flows can be classified with two distinct flow regimes Viscous flow which is rapidly shearing, where stresses arise because of collisions (momentum transfer) Plastic flow which is slowly shearing, where stresses arise because of enduring contact (coulomb friction) We then have two models for the Stress tensor in our Solids Momentum transfer Viscous flow is based on Kinetic theory of gases Plastic flow by an empirical power law depending on material properties 18
Euler-Euler: Two Fluid approach Advantages Less computational cost Chemical Reactions are easy to include (modeled as a PFR on the bed = as a series of CSTRs on the volumes along the axis of the bed) Easier integration with previous work Disadvantages Much more modeling required, more validation needed and not so easy to understand Never has been used for a 3-D rotary drum (at least not reported) but there are reported results on a 2-D rotary drum Boundary conditions are tricky; Rotating walls, inflow velocity 19
Euler-Euler: Two Fluid approach OpenFOAM was used to do a 2-D rotating cylinder full of particles in order to learn about the possible caveats on an euler-euler simulation for a rotary drum. Tutorials on two phase euler simulations for fluidised beds was followed with modifications in order to adapt it to my specific problem Arbitrary material properties were chosen and a kinetic theory description was used for the stress tensor of the solid phase (viscous flow) 20
Euler-Euler: Two Fluid approach There was some difficulty to get a stable solution, especially because the system is near the packing limit of the particles Steady state conditions not met; initial conditions are tricky An angle of repose can be seen but correct recirculation zones are not observed 21
Euler-Euler: Two Fluid approach Possible set up for the Simulation Define a flow rate on the particle bed on the direction of the axis of the kiln and make a coupled two phase simulation with chemical reactions included Data needed Mass and Energy balances for set up and validation Reaction kinetics Residence time of the particles due to inclination and rotation 22
Euler-Euler: Two Fluid approach Open Questions Mass and Energy balance data Reaction Kinetics Residence Time of particles with respect to current or possible configurations (inclination and rotational speed) How to create a good mesh for the calculations? Exactly how fast can it be? 23
Simulation Set-up Granular Bed Simulation Now What? The DEM approach can be almost readily set-up for use with Star CCM+ and sent to a computational cluster A Two-Fluid approach needs to be further investigated although first results look quite promising Further reading in Reaction Kinetics needs to be done in order to have a correct Temperature Profile An Euler-Lagrangian simulation will be set up and sent to a computational cluster with particle heat transfer Meanwhile the Euler-Euler approach will be investigated 24
Validation of the Simulation There are various papers by Boateng that describe the hydrodynamics of the particle flow on a rotary kiln, these are to be used to validate the flow patterns and the angle of repose of the simulations 25
Validation of the Simulation Mass Balances and Energy Balances of the actual Rotary kiln can be used to validate the Heat Transfer / Temperature Profile and the Concentration Profile if done 26
Conclusions From literature study Each simulation approach can be used for different goals Discrete Element Modelling: Particle Mean Residence time depending on angle and RPM Accurate Temperature profile to look at hot spots Two Fluid Approach: Because of the averaging nature of the approach, temperature profile is not as accurate Concentration profiles are easily incorporated if reaction kinetics are known 27