Hybrid Particle Laden Flow Modelling

Table of Contents

1 Introduction and motivation

1.1 Numerical simulation of particle-laden flow

1.1.1 Numerical modelling of dilute flows

1.1.2 Numerical modelling of dense flows

1.1.3 Numerical modelling of intermediate dilute/dense particle-laden flows

1.2 Aim of this thesis

1.3 Organization of this thesis

2 Eulerian granular phase modelling

2.1 Continuity equation

2.2 Momentum balance

2.3 Granular temperature

2.4 Radial distribution function

2.5 Drag coefficient and interphase momentum exchange

2.5.1 Wen and Yu

2.5.2 Gidaspow

2.5.3 Huilin and Gidaspow

2.6 Solids Stresses

2.6.1 Kinetic and collisional stresses

2.6.2 Frictional stresses

2.7 Turbulence modelling

2.8 Boundary Conditions

2.8.1 Johnson and Jackson

2.8.2 Li and Benyahia

2.8.3 Jenkins and Louge

2.8.4 Schneiderbauer et. al.

3 Lagrangian discrete phase modelling

3.1 Force balance and torque balance

3.2 Forces on a particle

3.2.1 Drag force

3.2.2 Particle rotation and Magnus force

3.2.3 Saffman force

3.2.4 Additional forces

3.3 Torque

3.4 Turbulent fluctuations

3.5 Particle wall collisions

3.5.1 Restitution coefficient model

3.5.2 Rough wall-particle collisions

4 The hybrid model EUgran+Poly

4.1 Motivation and overview

4.2 Coupling and exchange forces

4.3 Coupling forces on the Eulerian granular phase

4.3.1 Magnus force

4.3.2 Particle-wall interaction

4.3.3 Modified drag law for poly-dispersity

4.4 Coupling forces on the Lagrangian tracer particles

4.4.1 Collisional particle-solid force

4.4.2 Granular pressure force

4.4.3 Collisional torque

4.5 Simulation sequence and implementation

5 Agglomeration

5.1 Simple models

5.1.1 Agglomerated filling

5.1.2 Linear agglomeration

5.2 Particle population balance equation

5.2.1 Assumptions

5.2.2 Collision rates

5.2.2.1 Kinematic collision rate

5.2.2.2 Brownian collision rate

5.2.2.3 Turbulent collision rate

5.2.2.4 Comparison of collision rates

5.2.3 Effective collision rate

5.2.4 Sticking probability

5.3 Bus stop model

5.3.1 Implementation

5.4 Volume population balance model

6 Validation by lab-scale experiments

6.1 Dilute poly-dispersed flow in a duct

6.1.1 Boundary conditions and simulation setup

6.1.2 Results and discussion

6.2 Mono-dispersed flow in a medium laden duct

6.2.1 Boundary conditions and simulation set up

6.2.2 Results and discussion

6.3 Agglomeration of poly-dispersed particulate flow in a vertical pipe

7 Application to cyclone separation

7.1 Hybrid Model

7.1.1 Boundary conditions and simulation setup

7.1.2 Results and discussion

7.1.3 Results and discussion for separation of limestone material

7.1.4 Discussion of computational efficiency

7.2 Agglomeration

8 Conclusions and Outlook

Research Objectives and Core Themes

The primary research objective of this thesis is to develop a hybrid modeling framework that accurately simulates particle-laden flows characterized by locally and time-dependent variations in flow density. By integrating Eulerian and Lagrangian modeling approaches, the work aims to overcome the computational limitations of conventional methods and enhance the simulation of poly-disperse particulate systems, specifically within industrial environments like preheating towers and cyclones.

• Development of a coupled hybrid modeling approach (EUgran+Poly) for poly-disperse granular flows.
• Implementation of sophisticated particle-wall boundary conditions to account for sliding and non-sliding collisions.
• Integration of a novel population balance equation (Bus stop model) to capture agglomeration phenomena within Lagrangian tracking.
• Validation of the hybrid model against experimental data for various particle load conditions and duct geometries.
• Optimization of computational efficiency for industrial-scale cyclone separation simulations.

Excerpt from the Book

Summary of Chapters

1 Introduction and motivation: This chapter contextualizes particle-laden flows in industrial and environmental settings, identifying the need for efficient numerical models, and outlines the thesis goals and structure.

2 Eulerian granular phase modelling: This section details the theoretical foundation of the Eulerian-Eulerian granular model, focusing on the definition of continuity, momentum balance, granular temperature, and stresses for solid phases.

3 Lagrangian discrete phase modelling: This chapter describes the Lagrangian modeling approach, focusing on force and torque balances for individual particle tracking and the inclusion of turbulence and wall interaction effects.

4 The hybrid model EUgran+Poly: This chapter introduces the core development of the thesis, a hybrid model that combines Eulerian and Lagrangian frameworks to efficiently simulate poly-disperse particulate flows.

5 Agglomeration: This chapter covers various agglomeration mechanisms and proposes the "Bus stop model" as a novel approach to solve the population balance equation within a Lagrangian context.

6 Validation by lab-scale experiments: This section presents the performance evaluation of the hybrid and agglomeration models by comparing simulation results against established experimental data from various test setups.

7 Application to cyclone separation: This chapter applies the developed hybrid model to industrial-scale cyclones, evaluating its capability to predict separation efficiency, pressure drop, and the impact of agglomeration in realistic scenarios.

8 Conclusions and Outlook: This chapter summarizes the key scientific contributions of the thesis and provides recommendations for future research, including model extensions and software integration.

Keywords

Particle-laden flow, Eulerian-Lagrangian hybrid model, Computational Fluid Dynamics (CFD), Pneumatic conveying, Cyclone separation, Particle agglomeration, Population Balance Equation (PBE), Granular temperature, Particle-wall collisions, Poly-dispersity, Turbulent flow, Bus stop model, Numerical simulation, Solid stress, Industrial applications.

Frequently Asked Questions

What is the core purpose of this dissertation?

The research focuses on the development of a numerically efficient "hybrid" model that combines Eulerian and Lagrangian simulation methods to accurately capture the physics of poly-disperse, particle-laden flows across diverse concentration regimes (dilute to dense).

What are the central thematic fields covered?

The work covers granular phase modeling, Lagrangian particle tracking, the development of specialized hybrid coupling techniques, agglomeration modeling, and the validation of these models for pneumatic conveying and cyclone separation.

What is the primary research question or goal?

The goal is to provide a computationally feasible simulation framework that can handle industrial-scale problems, such as those found in cement preheating towers, where flow regimes change locally and particle-particle interaction is critical.

Which scientific methods were employed?

The author uses Computational Fluid Dynamics (CFD) involving multi-phase Navier-Stokes equations, kinetic theory for granular flows, and specialized User Defined Functions (UDF) for the ANSYS FLUENT software to integrate the hybrid logic.

What is covered in the main section of the thesis?

The main part encompasses the mathematical derivation of the Eulerian and Lagrangian sub-models, the formulation of the new "Bus stop model" for agglomeration, and the detailed validation of these models using lab-scale duct experiments and cyclone simulations.

How would you characterize this thesis using key terms?

The work is defined by the terms: Hybrid Modeling, Poly-disperse Granular Flow, Computational Fluid Dynamics (CFD), Particle Agglomeration, and Industrial Cyclone Separation.

How does the "Bus stop model" differ from traditional population balance methods?

Unlike standard methods that might require complex scalar transport equations across the entire domain, the Bus stop model discretizes the population balance directly into the Lagrangian tracer trajectories, making it highly efficient for implementation.

What unique challenges does the preheating tower present for simulations?

The preheating tower involves a massive number of small, poly-disperse particles experiencing highly variable flow regimes, ranging from dilute transport to dense agglomeration zones, which traditional models struggle to compute simultaneously without extreme resource usage.