Elsevier

Powder Technology

Volume 168, Issue 3, 18 October 2006, Pages 111-124
Powder Technology

Modelling the impaction of a micron particle with a powdery layer

https://doi.org/10.1016/j.powtec.2006.06.013Get rights and content

Abstract

The interaction of an incoming micron particle with already deposited particles is an important factor in particulate fouling of heat exchangers. A numerical model was developed based on the discrete element method to simulate this interaction. The contact forces between the colliding particles are based on the concept of contact mechanics, which takes plastic deformation of particles into consideration. The numerical model predicts the critical sticking and removal velocities, which are important parameters in determining the fouling rate of heat exchangers. Very detailed information of the bed dynamics can be extracted from the numerical model. It appears that the time required for a particle to be ejected out of a bed of particles due to an incident particle impact is proportional to the interacting particles diameter and to the square root of the number of bed layers. The maximum indentation in an incident particle hitting a bed of particles is proven theoretically and numerically to be directly proportional to the velocity and diameter of the incident particle if plastic deformation occurs. Experiments were carried out in a vacuumed column to validate the numerical model. In the experiments, incident particles dropped onto a bed of particles and the sticking, bouncing and removal behaviour were measured as a function of the incident particle impact speed. Both the numerics and the experiments showed that there are velocity regimes at which the incident particle sticks, bounces off or removes particles from the bed of particles. The regimes overlap due to the impact angle effect. The numerical model predictions regarding the critical sticking and removal velocities are in agreement with the measured values.

Introduction

Particulate fouling is defined as the accumulation of particles on a heat exchange surface that forms an insulating powdery layer. Particulate fouling is a major problem in biomass gasifiers that may lead to inefficient operation [1]. The fouling rate is determined by the difference between the deposition and the removal rate of particles on and from the fouling layer [2]. The incident particle velocity at which the particle sticks to the fouling layer, bounces off the surface or removes particles from the fouling layer are important parameters in determining the fouling rate. The objectives of this work are to model the interaction between a micron particle hitting a bed of particles and to predict the above mentioned velocities as a function of the physical properties of the incident particle and the deposit.

Konstandopoulos [3] and van Beek et al. [4], [5] modelled the interaction between an incident particle and a deposit as a two-body collision. In the simulation, the target particle incorporated in the deposit is given an effective mass meff, relative to its actual mass, arising from the fact that the target particle is in contact with a number of other bed particles. The assumption that the interaction between the incident and the target particles can be decoupled from the reaction of the entire deposit and described as a binary collision using an effective inertial mass for the target particle, is proposed by Werner [6] based on his 2D discrete element simulations. Konstandopoulos [7] reports that the above assumption breaks down when the kinetic energy of impact becomes sufficiently high to induce appreciable re-arrangements or erosion of pre-deposited particles.

Werner [8] and Tanaka et al. [9] modelled the dynamic response of a two-dimensional bed of particles subjected to an impact of a spherical projectile using the discrete element method (DEM) developed by Cundall and Strack [10]. In the DEM, particles are treated as discrete entities, which interact at their interfaces when they are in contact. Werner [8] and Tanaka et al. [9] used an approximate model, the spring-damper model, to model the contact forces between colliding particles. The disadvantage of the spring-damper model is that the resulting coefficient of restitution is constant [9], [11], independent of the colliding particles velocities, which is not the case as found by many researchers, e.g. Gorham and Kharaz [12] and Wu et al. [13]. In other words, the spring-damper model will result in a constant ratio between the amount of energy lost during collision and the incident kinetic energy, irrespective of the colliding particles velocities and the plastic deformation taking place.

Particulate fouling layers in biomass gasifiers are composed mainly of sulphates, chlorides [14], [15] and carbon particles of micron size where plastic deformations can happen at low colliding speeds of around 1 m/s [16]. Plastic deformations are likely to occur during collisions of fouling particles in biomass gasifiers due to the operating gas speeds, which may range from 2 m/s to 10 m/s. The Rogers and Reed model [17] is used to validate that plastic deformation needs to be taken into account. The model describes the adhesion of a particle to a massive plate following an elastic-plastic impact based upon consideration of the energy losses during impact. The energy balance is as follows for a particle of mass m impacting normally a stationary massive plate with a velocity Vi,n12mVi,n2+QA=Qe+Qp,with the left hand side of the equation the energy at the beginning of the collision and the right hand side the energy at the end of the approach phase. QA is the adhesive energy due to the attractive forces between the incoming particle and the surface, Qe is the stored elastic energy and Qp is the energy loss due to plastic deformation. If the stored elastic energy Qe is larger than the adhesive energy QA required to separate the particle from the surface then the particle will rebound otherwise it will stick to the surface. The mentioned energy terms are described in detail in [16], [17], [18]. The normal rebound speed Vr,n is calculated from12mVr,n2=QeQA.

The Rogers and Reed model was solved for a copper particle of diameter 50 μm hitting a massive steel plate at different impact speeds and the results are depicted in Fig. 1. The copper particle was chosen to represent the soft fouling particles in biomass gasifiers and the steel plate to represent the heat exchangers tubes. The plastic energy loss Qp, the stored elastic energy Qe and the ratio between them are shown in Fig. 1 where the significance of the plastic energy loss in comparison to the stored elastic energy, which is transformed into rebounding kinetic energy during the restitution phase can be clearly seen. It can be concluded that for velocities relevant in biomass gasifiers, plastic deformation of colliding particles plays an important role in the particles postcollision behaviour. Therefore, plastic deformation should be taken into account when using the methodology of Werner [8] and Tanaka et al. [9] to model the interaction between a particle hitting a bed of soft particles.

A numerical model is presented in the present article to simulate the interaction between a particle hitting a bed of particles. The incident particle and the bed particles are soft particles of micron size. The numerical model is based on the discrete element method. The contact forces between colliding particles are based on the concept of contact mechanics [19], [20] taking into account plastic deformation of colliding particles. The numerical methodology is presented in Section 2. The numerical code was tested for a spherical particle hitting a massive flat surface and the results are compared to the literature in Section 3. The interaction between a single particle hitting a bed of particles was simulated using the numerical code and the results are presented in Section 4. Special attention was given to the maximum indentation of the bed and the so-called ejection time. An experimental set-up was developed to study the interaction between a particle hitting a bed of particles. Impaction experiments were carried out to study sticking, bouncing and removal of particles from powdery layers due to an incident particle impact and these are described in Section 5. The experimental results are compared to the numerical simulations and conclusions are drawn about the validity of the numerical model and the method adopted.

Section snippets

Numerical methodology

The numerical method adopted is the discrete element method (DEM), which is based on Newton's second law of motion. For the translational motion of a spherically symmetrical particle, Newton's second law has the formF=mr¨,where F is the sum of the forces exerted on the particle by other particles and by gravity. r¨ is the acceleration vector of the particle and m its mass. Integrating Eq. (3) over a time step Δt yields the velocity of the particler˙=r˙o+FmΔt,where r˙o and r˙ are the

Numerical simulation of a particle hitting a flat surface

The numerical model was tested for spherical copper and steel particles of diameter 50 μm hitting a massive steel plate at a normal speed of 0.1 m/s and the results are shown in Fig. 3. The material properties of the copper and the steel particles used in the simulations are shown in Table 1. An important parameter in the numerical code, which determines the accuracy of simulation, is the integration time step Δt. The integration time step was selected to be much smaller than the actual contact

Sticking, bouncing and removal velocity limits

The numerical model was used to simulate the interaction between a copper particle of diameter 50 μm hitting a bed of particles. The incident particle and the bed's particles were of the same material and diameter. The bed consisted of 20 × 20 × n particles, where n was the number of bed layers and was equal to 1, 2, 3, 5 or 10 layers. The particles in the bed were arranged in an orthorhombic structure with a porosity of 0.4 [34].

An orthorhombic bed of particles of a porosity 0.4 was considered to

Experimental procedure

An experimental set-up has been built to determine the impact speed at which an incident particle sticks, bounces off or removes particles out of a bed of particles. The set-up consists of a vacuumed column in which particles are released from a particle feeder onto a bed of particles. The particle feeder is installed in the top-segment of the column as shown in Fig. 12a. The vacuumed column is optically accessible by two windows. The trajectory of the particles is recorded using a digital

Sticking, bouncing and removal velocity limits

The interaction between a particle hitting a bed of particles was modelled numerically and measured experimentally and the results are summarized in Fig. 7, Fig. 14 respectively. Both the numerics and the experiments show that there are velocity regimes at which the incident particle sticks, bounces off or removes particles from the bed of particles. The regimes overlap due to variation in the angle of impact of the incident particle. A comparison was made between the numerical model results

Conclusions

A numerical model was developed to simulate the interaction between a particle hitting a bed of particles, which was based on the discrete element method pioneered by Cundall and Strack [10]. The numerical model can predict the critical velocity at which an incident particle starts to stick, rebound or remove other particles from a bed of particles. The time taken for a particle to be ejected out of a bed of particles due to an incident particle impact is found to be proportional to the

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