Inter-particle force and stress models for wet and dry particulate flow at the intermediate flow regime Xi Yu 1, Raffaella Ocone 3, Sotos Generalis 2, Yassir Makkawi 1 1 Chemical Engineering & Applied Chemistry, Aston University, Birmingham B4 7ET, UK 2 Mathematics, Aston University, Birmingham B4 7ET, UK 3 Chemical Engineering, Heriot-Watt University, Edinburgh EH14 4AS, UK
Outlines 1. Granular material and regime map of granular flow 2. Objectives and big picture 3. Dry particle flow 4. Slightly wet particle flow 5. Summary and Acknowledgement
What s granular material? Granular material -a collection of a large number of discrete solid particles may behave an elastic-solid or a fluid Some examples of granular materials are nuts, coal, sand, rice, coffee, corn flakes, fertilizer and ball bearings.
Regime map In granular flow Fluid-like behaviour Rapid flow regime Binary-collision KTGF (kinetic theory of granular flow) Intermediate regime of granular flow Coexistence of frictional and collisional stress in dry flow Less understood? Solid-like behaviour Particle packing- Enduring contact Coulomb frictional law
Regime map In granular flow Continuous shear field Friction ignored (Tardos er al, 2003) Three regimes are identified using a dimensionless shear rate In a sense, shear rate is gradient of velocity in granular material
Example of problems at intermediate dry flow Dense bubbling fludised bed Particle-particle friction leading to limited bed expansion, increased bubble size and solid slugging Pneumatic conveying Excessive particle-wall friction leading to pressure drop, wear and line blockage (Makkawi et al, 2006) Solid volume fraction (McGlinchey et al, 2012) Solid volume fraction
Example of problems at intermediate wet flow Coal/biomass gasification Surface oil/tar leading to agglomeration and sever Degradation and fludisation Fluidised bed coating Liquid presence leading to undesired Agglomeration and particles segregation Exothermic fludised reactor Temperature control by liquid injection leading to dead zones And overheating at various Parts Of the reactor Simple Gasification Process Graphic (Gas Technology Institute, Illinois, US) Schemes of fluidized bed spray granulator (Fries et al, 2011) Fluidized Bed Systems, hitachi Zosen Inova, Switzerland)
What s popular approach to model dense granular flow? Solid phase: continuity equation: momentum: Gas phase: continuity equation: momentum: Energy equation (granular temperature): Well developed KTGF (kinetic theory of granular flow)
Intermediate stress in CFD commercial codes solids shear viscosity No friction Particle packing- Enduring contact How to present friction shear stress in intermediate regime of granular flow?? Friction fluid shear resistance
Objective and big picture 1. How to incorporate shear stress in intermediate particle dry flow? 2. How to incorporate shear stress in intermediate and slightly wet particle flow? Formula user defined function (UDF) Fluent (platform) Experimental observation ECT Validate Predicted flow behavior (Solid concentration distribution)
Dry particle flow
Experiment results (ECT) in dry particle-flow (Makkawi et al, 2006) Solid volume fraction ECT (electrical capacitance tomography) is a diagnostic imaging tool in the medical field
Unified solid stress model- Tardos et al (2003) Average particle stress Standard deviation of the strain rate Simpler expression Energy dissipation Solid phase momentum: Energy equation (granular temperature): Specific shear stress(pascal)at the wall user defined function written in C language (approx. 600 lines)
Model setup for numerical experiment Diffusion of granular temperature Lun et al. Boundary/operating condition Value Drag Turbulence Syamlal and O Brian K-epsilon Gas inlet velocity, U g [m/s] 0.26,0.54,0.8 Gas density, ρ g [kg/m 3 ] 1.2 Particle-particle restitution 0.9 Particle-wall restitution 0.9 Frictional Viscosity Johnson et al Bulk viscosity Lun et al Solids pressure Lun et al Radial distribution function Lun et al Specularity coefficient 0.2 Gas dynamic viscosity [kg/(m.s)] 1.8x10-5 Gas outlet pressure, P go [Pa g ] 0 Apparent particle density, ρ P [kg/m 3 ] 2500 20 Particle size, D s [µm] 350 14.3-18.1
Tardos et al (2003) friction model 0.61 0 Time averaged Fluent friction model 0.61 Fluent KTGF without friction model 0.61 0 0 Time averaged Time averaged
Tardos et al (2003) friction model 0.61 0 Time averaged Fluent friction model Fluent KTGF without friction model 0.61 0.61 0 0 Time averaged Time averaged
Tardos et al (2003) friction model 0.61 Time averaged 0 Fluent friction model Fluent KTGF without friction model 0.61 0.61 0 0 Time averaged Time averaged
Prediction of bed height Tardos et al (2003) friction model Fluent friction model Fluent KTGF without friction model Experimental and simulated bed height of gas velocity
Slightly wet particle flow (on-going work)
In slightly wet and dense systems Figure: the different states of saturation of liquid-bound granules ( Newitt and Conway-Jones,1958; York and Rowe,1994) Liquid bridges liquid saturation higher merge continuous fluid network Frictional contact Fluid shear resistance Collisional contacts dissipate energy in both the liquid bridges and particles.
Experimental results(ect) in slight wet flow air conventional bubbling packed particles bubbles splitting slugging solid slugs Types of two-phase system 0 0.03 0.06 0.09 0.12 0.15 liquid weight % (kg/kg dry bed) three-phase system: slightly wet system
Solid concentration Particle-particle interactions in slightly In wet particles flow, direct solid-solid contacts are limited wet suspension Rapid flow Transient contacts dominated by collisional stresses Hypothesis Dense-intermediate flow Enduring contacts dominated by liquid viscous stresses Quasi-static flow Enduring contacts dominated by particle frictional stresses
Liquid bridge Stresses For this, we may start from the interparticle force at single particle level: F liquid Approach velocity 3 u 2 liquidd R p 8 h Interparticle gap h Normal stress For this, it is required to determine the force per unit area: P liquid 3 8 liquid d 2 u 6 p s 3 h d 2 3 Equivalent shear viscosity Analogue to Coulomb friction law wet 2 P liquid S lubrication coefficient
Conclusion and ongoing work An unified shear stress (Tardos et al, 2003) model in 3D has been implemented in numerically studying a bubbling fluidised bed and its predicted results (solid distribution, bed height) have been compared with experimental data (ECT) and two other stress models (Fluent friction model, Fluent KTGF without friction model). Ongoing work will be focused on developing a shear stress model for slightly wet particle flow. The validation of the model will be done using experimental data (ECT) in a fluidised bed.
Acknowledgement Aston University Dr Yassir T. Makkawi Dr Sotos Generalis Grant funding from The Leverhulme Trust Heriot Watt University Professor Raffaella Ocone
(Makkawi et al, 2006)