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Numerical Analysis Group

Numerical Modeling of GranularFlows in Rotary Kilns

M. A. Romero Valle

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Numerical Modeling of Granular Flowsin Rotary Kilns

Literature Survey

M. A. Romero Valle

Supervisor: Dr. Domenico Lahaye

May 4, 2012

Faculty of Electrical Engineering, Mathematics and Computer ScienceDelft University of Technology

The work in this literature survey was supported by Almatis, Inc. Their cooperation is herebygratefully acknowledged.

Copyright c© Faculty Electrical Engineering, Mathematics and Computer Science (EEMCS)All rights reserved.

Abstract

Literature usually presents two approaches for numerical modeling of granular material, adiscrete approach and a continuum approach [38]. The purpose of the current document isto explore both approaches with respect to the numerical modeling of a rotary kiln.

First numerical experiments were done using open source software, LIGGGHTS [21] for a La-grangian model and OpenFOAM [30] for an Eulerian model, in order to explore the feasibilityof a rotary kiln numerical model.

As simplified models exist, which are also briefly discussed in the present document, thequestion left to answer is whether a full granular flow model is necessary in order to have asufficiently accurate description of the granular material properties.

Literature Survey M. A. Romero Valle

ii

M. A. Romero Valle Literature Survey

Table of Contents

1 Introduction 11-1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-2 Rotary Kilns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-3 Solids Phase: Granular Bed of a Kiln . . . . . . . . . . . . . . . . . . . . . . . . 2

1-3-1 Transverse Bed Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-3-2 Axial Bed Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41-3-3 Heat Transfer Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . 6

1-4 Modeling of a Rotary Kiln: Previous Approaches . . . . . . . . . . . . . . . . . . 61-5 Calcium Aluminate Cement Kiln . . . . . . . . . . . . . . . . . . . . . . . . . . 81-6 Granular Flow Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Euler-Lagrange Approach: Discrete Element Modeling 112-1 Description of the Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112-2 Applicability to Current Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 122-3 Experimental Setup and Results . . . . . . . . . . . . . . . . . . . . . . . . . . 132-4 Discussion: Advantages and Disadvantages . . . . . . . . . . . . . . . . . . . . 14

3 Euler-Euler Approach: Two-Fluid Model 173-1 Description of the Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173-2 Applicability to Current Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 193-3 Experimental Setup and Results . . . . . . . . . . . . . . . . . . . . . . . . . . 193-4 Discussion: Advantages and Disadvantages . . . . . . . . . . . . . . . . . . . . 20

4 Summary: Euler-Lagrange and Euler-Euler 234-1 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234-2 Heat Transfer and Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . 24


iv Table of Contents

5 Open Questions and Conclusions 255-1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

6 Further Work: Project Goals 27

Bibliography 31


List of Figures

1-1 Cement Kiln . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-2 Different modes of operation in the transversal mixing plane of a rotary drum [5] 31-3 Characteristic curve for a 0.40 diameter rotary drum [5, 15] . . . . . . . . . . . . 41-4 Rolling mode with an active top part and a passive lower part [5] . . . . . . . . . 41-5 Kiln fill geometry [5] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51-6 Kiln basic heat transfer paths: 1) Freeboard gas to exposed bed, 2) Freeboard gas

to exposed wall, 3) Exposed wall to exposed bed, 4) Exposed wall to exposed wall,5) Covered wall to covered bed, 6) Loss to surroundings [7]. . . . . . . . . . . . 6

2-1 Spring and dampener contact force model . . . . . . . . . . . . . . . . . . . . . 122-2 Number of Particles vs CPU Time . . . . . . . . . . . . . . . . . . . . . . . . . 14

3-1 Solids phase glyph plot of the lower part of the cylinder . . . . . . . . . . . . . . 20


vi List of Figures


List of Tables

4-1 Summary of advantages and disadvantages for the discussed modeling approachesto granular flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24


viii List of Tables


Chapter 1

Introduction

1-1 Motivation

The main motivation for the present document is to give insight into the phenomena thatoccur inside a cement kiln in order to make its operation more efficient.The present project deals with the consequences on the granular material bed in the kiln dueto changes of its operating conditions. Different approaches for granular flow modeling willbe presented.

1-2 Rotary Kilns

Rotary kilns are employed to carry out a wide range of operations such as the reductionof oxide ore, the reclamation of hydrated lime, the calcination of petroleum coke and thereclamation of hazardous waste. However, they are much more widely known for their placein the cement industry as the main stage for the manufacture of cement.A rotary kiln is a pyro-processing device used to raise materials to high temperatures. It isa long horizontal cylinder with a certain inclination with respect to its axis. Material withinthe kiln is heated to high temperatures so that chemical reactions can take place. A rotarykiln is therefore fundamentally a heat exchanger from which energy from a hot gas phase istransferred to the bed material [5].There are several types and configurations for rotary kilns. The rotary kiln in question [33]is a counter-current gas direct fired Calcium Aluminate Cement rotary kiln.As it can be observed in Figure 1.1, a rotary kiln is a long, narrow cylinder. It should beinclined 2 to 5 degrees to the horizontal and should rotate at 0.25 to 5 rpm. The length/di-ameter should range from 10 to 35, depending on the reaction time needed [32].Rotary kilns can also be seen as a solid-solid chemical reactor, in which one has mainly heattransfer interactions with a gas phase. The phenomena in the solids phase will be addressedwith a certain level of detail as it will be the focus of the present project.


2 Introduction

Figure 1-1: Cement Kiln

1-3 Solids Phase: Granular Bed of a Kiln

Rotary kilns are used to process granular material. Granular material is a collection of solidparticles, in which every particle is in contact with at least some of the neighboring particles.This granular material has transport properties similar to both liquids and solids [38].

The heat transfer within the granular bed of a rotary kiln occurs with the same mechanismsin any packed bed [5]. However the momentum transfer, or movement of particles, within thebed is unique due to the rotary motion and geometry of the kiln.

There are two mixing mechanisms in a rotary kiln, an axial and a transversal component [5].The axial mixing component is attributed to overall convection; one can assume that thereis an average velocity equal to the plug flow velocity. However for the transversal or radialmixing, one has mechanisms that result in velocity components in both axial and transversaldirections.

Both are dependent on the rotation, inclination, filling percentage of the kiln and rheologi-cal properties of the material to be processed. Both mixing mechanisms increase with kilnrotational speed [5].

As it can be inferred from above, movement of the particle bed inside the rotary kiln has twocomponents: the axial component that determines the residence time and the transverse planecomponent that determines most of the transport processes such as, mixing, heat transfer andreaction rate.

1-3-1 Transverse Bed Motion

There are various studies that describe the motion of particles in a rotating cylinder. Theyshow that the motion depends on the dimensionless Froude number [14, 15].

Fr = ω2R

g, (1-1)

where ω is angular velocity in [s−1], R is the radius of the kiln in [m] and g is the gravity in[m/s2].

Henein and Boateng noted six different transversal motion modes for rotary drums[5, 14]:


1-3 Solids Phase: Granular Bed of a Kiln 320 Chapter 2 Basic Description of Rotary Kiln Operation

Slumping RollingSlipping

Cataracting CentrifugingCascading

Fr (=ω2R/g) at φ = 35°Fr < 1.0 × 10–5

1.0 × 10–5 < Fr < 0.3 × 10–3

0.9 × 101 < Fr < 1Fr > 1.0

0.5 × 10–3 < Fr < 0.2 × 10–1

0.4 × 10–1 < Fr < 0.8 × 10–1

Mode1. Slipping2. Slumping3. Rolling4. Cascading5. Cataracting6. Centrifuging

Figure 2.3 Bedmotion in cross sectional plane. Froude numbers (Fr) are givenfor each of the different modes. (Henein, 1980.)

drying applications take advantage of the high particle-to-heat transferfluid exposure associated with the cascading mode and the separa-tion effect caused by the centrifugal force component. For example,starting at the other extreme, that is, at very low rates of rotationand moving progressively to higher rates, the bed will typically movefrom slipping, in which the bulk of the bed material, en masse, slipsagainst the wall; to slumping, whereby a segment of the bulk materialat the shear wedge becomes unstable, yields and empties down theincline; to rolling, which involves a steady discharge onto the bed sur-face. In the slumping mode, the dynamic angle of repose varies in acyclical manner while in the rolling mode the angle of repose remainsconstant. It has been established (Rutgers, 1965) that the dynamic

Figure 1-2: Different modes of operation in the transversal mixing plane of a rotary drum [5]

one then can describe them from low to high Froude number as follows:

Slipping: occurs when the bulk material, as a whole, slips against the wall; Slumping: occurswhen a segment of bulk material at the shear wedge becomes unstable, yields and emptiesdown the incline;

Rolling: occurs when there is a steady discharge onto the bed surface causing its renewal;

Cascading: occurs at high rates of rotation, where the particles cascade or shower down thefree surface;

Cataracting: occurs in between cascading and centrifuging mode;

Centrifuging: occurs at critical and high speeds, all the material rotates with the drum wall.

Henein in his research developed graphs with experimental data in order to characterizethe mode of operation depending on operating parameters and geometry aspects of rotarydrums[15].

Rotary kilns usually operate with a rolling mode, as in the mode the mixing is maximized [5].For the kiln to be analyzed, the Froude number is in the range of 10−4. It can be inferred fromthe data obtained by Henein that the kiln to be analyzed is in a transitional mode betweenslumping and rolling mode [15]. However one must make the distinction that the particlesizes and properties from the study are not the same as in the case of the particular rotarykiln to be analyzed.

When a kiln is operating in rolling mode there are two areas that can be described: an activelayer near the top where a surface renewal occurs from the rolling motion of the particlesfalling down, and a passive layer, which is beneath the active layer and assumed to have aplug flow behavior.


4 Introduction24 Chapter 2 Basic Description of Rotary Kiln Operation

Rotational speed, rpm1 10 100

5

Slipping0.05

0.15

0.25Slumping

1! 10–4 1! 10–2 1

Rolling

Cataracting

Cen

trifu

ging

Cascading

Froude number

20

% F

ill

Bed

dep

th, m

Figure 2.6 Bed behavior diagram. Mapping of bed behavior regimes for dif-ferent operation conditions. (Henein, 1980.)

2.4 Experimental Observations of TransverseFlow Behavior

The key step in almost all particulate processing applications is solidsmixing. Mixing is primarily used to reduce the non-uniformity in thecomposition of the bulk to achieve uniform blending or as a firststep to improve the convective/advective and diffusion componentsassociated with heat transfer to a particulate bed in thermal processing.Some of the observed flow and transport phenomena in rotary kilnsthat have provided insights into particulate flow behavior, which leadto accurately stating the mathematical problem or modeling the rotarykiln transport phenomena, are described. Dependent upon the beddepth and the operational conditions, the flow behavior constrainedin the transverse plane can be purely stochastic, purely deterministic,or a hybrid of both; hence mixing can either be modeled by a randomwalk for very shallow beds (Fan and Too, 1981) or by a well-definedbulk velocity profile estimated by shear flows similar to boundarylayer problems (Boateng, 1993). Early workers used tracer particles toobserve and characterize mixing (Zablotny, 1965; Ferron and Singh,1991; and others). Lately, such works have been extended to the use ofnonintrusive techniques, such as nuclear magnetic resonance (NMR;Nakagawa et al., 1993) and positron emission particle tracking (PEPT;Parker et al., 1997).

Figure 1-3: Characteristic curve for a 0.40 diameter rotary drum [5, 15]

2.3 Transverse Bed Motion 21

similarity of the rotary drum behavior, and hence the type of trans-verse bed motion that occurs during powder processing, is dependentupon the rotational Froude number, Fr, defined as

Fr = !2R/g (2.2)

where the critical condition for centrifuging implies Fr = 1. The rangesof Froude numbers for the various modes are shown in Figure 2.3.

In the rolling mode (Figure 2.4), where rotary drum mixing is max-imized, two distinct regions can be discerned, the shearing region,called the active layer, formed by particles near the free surface, andthe passive or plug flow region at the bottom where the shear rate iszero. The particular mode chosen for an operation is dependent uponthe intent of the application. A survey of various rotary drum typeoperations (Rutgers, 1965) has indicated that most operations are inthe 0.04–0.2 range of N-critical, which is well below the centrifugingmode and probably the cascading mode as well.

The geometric features of a typical rolling bed are depicted inFigure 2.5. The bed is subtended at the continuous angle of repose ".The free surface is subtended at 2#. Hence the bed cross section occu-pied by material can be defined by this angle. The chord length, Lc, thelongest distance traveled by particles on the free surface (path of steep-est decent), can also be defined in terms of this angle. The fraction ofthe cross sectional area occupied by material is the kiln loading. Thisis usually defined as the volume percent occupied by material in the

Figure 2.4 Rolling bed.Figure 1-4: Rolling mode with an active top part and a passive lower part [5]

Most of the mixing in the kiln cross section occurs in the active region. Taking into accountthe surface renewal in the active layer, one can infer that by increasing the rotational speedof the kiln one can get better mixing. However, this will decrease residence time as axialspeed increases with increasing rotational speed. Thus, it is important to know the criticalresidence time to achieve the sufficient product quality in order to have a balance betweenmixing and residence time [5].

1-3-2 Axial Bed Motion

Boateng [5] mentions that the best way to define axial bed motion is by using empiricalrelationships based on geometric considerations. One can then consider the following figure.

The definition of kiln load is the percentage of cross sectional area of the cylinder occupiedby the granular material. Boateng also mentions that one can make a distinction between alightly and a heavily loaded kiln. This is due to the fact that there are different theoreticaland empirical models for the residence time, volumetric flow and velocity profiles of the axialcomponent of the flow of particles in the kiln. The kiln from Almatis is a lightly loaded kiln,operating with 5% loading. This means that the degree of fill can be taken constant within


1-3 Solids Phase: Granular Bed of a Kiln 522 Chapter 2 Basic Description of Rotary Kiln Operation

R

y(=H)

Lc/2

r

ro

φ ψ

θ

ξ

Figure 2.5 Rolling bed fill geometry.

vessel. Granted that the kiln length is constant, the degree of fill is thepercent of the cross sectional area of the cylinder occupied by material(% Fill). The fraction filled defining the bed depth, and based on thegeometry, relates the angles at any transverse section as follows:

fc =12!

!2cos!1

!R

R!H

"! sin

#2cos!1

!R

R!H

"$"(2.3)

Seaman (1951) developed an approximation for the theoretical res-idence time of a shallow bed (lightly loaded kiln) and a theoreticalrelationship for the kiln volumetric flow rate for deep beds (heavilyloaded kilns). Nonetheless, no clear definition has ever been given forthe range of operation encompassed by the two cases of kiln loadings.Seaman’s approximations led to the conclusion that kilns should beconsidered heavily loaded when the fractional cross sectional fill ofsolids exceeds approximately 5 percent.

As shown in Figure 2.4, two regions of the transverse plane can bediscerned: (i) the active region near the top of the bed where surfacerenewal occurs, and (ii) the passive region beneath the active region.The active region is usually thinner than the passive region becauseparticles there are not restricted and they move faster. Because the bedis constrained within the cylinder’s geometrical domain, the laws of

Figure 1-5: Kiln fill geometry [5]

the length of the kiln, in other words, in the previous Figure (5) Ψ = 0 [5]. Ψ represents theangle between the surface of the bed material and kiln axis.

Boateng then presents the following relationships based on geometry using the nomenclatureobserved in Figure 1.5:

uax = 2πrn(

φ

sin θ

), (1-2)

where uax is the solids axial velocity, r the radius, n the number of revolutions [1/s], φ thekiln slope in angular measure and θ angle subtended by bed material at cylinder center. Thenfor the residence time depending on geometric considerations one has:

τ = L sin ξ2πrnφ = Lθ sin ξ

Lcω tan ξ , (1-3)

where L is the kiln length, ξ the dynamic angle of repose, r the radius, n the number ofrevolutions [1/s], φ the kiln slope in angular measure, θ the angle subtended by bed materialat cylinder center, Lc the distance from apex of bed cross-section to mid-chord and ω theangular velocity.

Boateng recommends to use this expressions in industrial kilns as long as there are no truegranular flow models to predict the bed behavior on the axial direction [5].


6 Introduction

1-3-3 Heat Transfer Phenomena

Brimacombe [6, 7] explains that there are three basic paths of heat transfer into the particlebed:Freeboard gas to exposed bed;Exposed wall to exposed bed;Covered wall to covered bed;where for the first point there are two mechanisms, the radiative heat transfer from the flameand the convective heat transfer from the gases to the bed. For the second point there isonly one mechanism, the radiative heat reflected from the wall to the bed. And lastly, themechanism is given by conductive heat transfer from the wall to the particle bed.From all the mechanisms, Boateng [5] mentions that the main path is the radiative heattransfer from flame to the bed. In Figure 1.6 the basic paths for the heat transfer of a kilncross section are presented.

(9 F r e e b o a r d gas to e x p o s e d b e d | F r e e b o a r d gas to e x p o s e d wa l l | E x p o s e d wa l l to e x p o s e d b e d | E x p o s e d wa l l to e x p o s e d w a l l | C o v e r e d wa l l to c o v e r e d b e d | S t e a d y - s t a t e loss to s u r r o u n d i n g s

Fig . 1 - - B a s i c p a t h s a n d p roces se s fo r hea t t r a n s f e r at a k i ln c ross - sect ion.

Part of the reflected energy is reabsorbed by the gas, and the residue is incident on the freeboard surfaces, where this cycle begins anew. Part of the energy which is absorbed at the exposed wall surface is lost through the kiln wall, but some may be transferred into the bed during the time that the wall surface is covered by the bed. This regenerative action of the wall, under some circumstances, can operate in reverse; i .e . , heat transfer can be from the bed to the covered wall. Although heat transfer within the wall is by conduction only, this is not the case for the bed where conduction, convection, radiation, and advection (due to the motion of the bed particles') operate simultaneously. An adequate heat-transfer model for a rotary kiln would account for all of these paths and processes, as well as allow for their interaction. Before pro- ceeding with a description of the model developed in this study which meets these requirements, it is useful to review the accomplishments of other investigators.

The high freeboard temperatures of most kiln operations ensure that radiative heat transfer is significant. Therefore, a model for the radiative exchanges occurring among the exposed wall and bed surfaces is an essential component of any kiln model. The freeboard region of the kiln forms an enclosure filled with the emitting/ absorbing mixture of gases resulting from the combustion process and, in many instances, the chemical reaction within the bed material. In the absence of luminous flames, the calculation of radiative heat transfer within

the freeboard involves adequately simulating the emis- sive/absorptive characteristics of the gas mixture and incorporating the results into a realistic geometric model. For the solution of enclosure problems, Hottel and Cohen I41 developed the zone method, for which the radiative characteristics of the actual gas mixture are matched closely by a weighted summation of several hypothetical gray gases.

<5

e = E e. {1 - e x p ( - K . p L ) } [11 n=O

In order to account for the wavelengths which are not absorbed by the actual gas, one of the gray gas components included in Eq. [1] is radiatively clear, i . e . , has an extinction coefficient Ko = 0. Emissivity models for- mulated in this manner are referred to as clear-plus-N- gray-gas models, where N is the number of absorbing gray gases (K > 0) which are incorporated. Although developed as part of the zone method, Eq. [1 ] provides a convenient form for simulating gas emission and absorption in other radiation models. In addition to gas emission, Eq. [1] also can be utilized to simulate emission from luminous particles, e .g . , Johnson and Be6r, lSj and can be adapted to account for nonuniform gas com- position within the enclosure, e .g . , Pieri et al. t6J

For the most general case, when the gas temperature field in the enclosure is unknown, application of the zone method requires a knowledge of both the flow and combustion fields in order to solve for the unknown temperatures and attendant radiative exchanges. Lacking abundant data for the flow and combustion fields, Jenkins and Moles t71 applied the zone method to the rotary kiln by assuming plausible values for each. Good agreement was obtained between predicted and measured wall temperatures in a 1.7 m I.D. by 47 m cement kiln. The regenerative action of the inside refractory surface was not included in the model, an omission which can be justi- fied retrospectively by the minor role of the covered wall to bed heat transfer in the pilot kiln. [q However, regen- eration has not been proven to be unimportant under all circumstances, and its exclusion from any kiln model can be regarded as a deficiency.

Models for calculating radiative exchange within en- closures are constructed by subdividing the enclosure (including the gas contained within) into numerous zones and then formulating the expressions for radiative exchange among the zones. When detailed knowledge of radiative heat transfer is required, a l~ge number of zones are necessary, and the model becomes computationally intractable. In the particular case of the rotary kiln, where the length of the freeboard space is long relative to the inside diameter, radiative exchanges occurring at one axial position will be influenced little by conditions far upstream or downstream as a result of the combined effects of gas absorption and geometry. In such instances, it may be computationally inefficient to consider the entire enclosure in order to calculate local radiative exchange. In recognition of this fact, Gorog et al. [21 developed a model for radiative exchange at a transverse cross-section of kiln. Rather than considering the entire kiln freeboard, the model was extended only a short distance upstream

4 0 4 - - V O L U M E 20B, JUNE 1989 METALLURGICAL TRANSACTIONS B

Figure 1-6: Kiln basic heat transfer paths: 1) Freeboard gas to exposed bed, 2) Freeboard gasto exposed wall, 3) Exposed wall to exposed bed, 4) Exposed wall to exposed wall, 5) Coveredwall to covered bed, 6) Loss to surroundings [7].

As mentioned in previous sections heat transfer mechanisms within the bed are the same asin packed beds. This means that it is mainly given by particle to particle conduction [5].This makes the heat transfer modeling within the particle bed relatively simple in discrete orcontinuum models.

1-4 Modeling of a Rotary Kiln: Previous Approaches

There are various approaches in the literature for the simulation of a rotary kiln. However,all of them make the distinction between 2 distinct phenomena in the kiln, the freeboard partwhich consists of the combusting gases phase, and the granular bed.Most of the approaches presented in literature deal with a CFD approach for the freeboardand a model for the granular bed which deals with chemical reactions and heat exchange


1-4 Modeling of a Rotary Kiln: Previous Approaches 7

[27, 5, 16, 41, 28, 29, 43, 18].

One then can divide the simulation into two different parts based on this observation:

• Simulation of the Freeboard: work done by M. Pisaroni [33];

• Simulation of the Granular Bed: focus of the present project.

The simulation of the granular material bed usually uses input data from the freeboard simu-lation in a coupled or uncoupled way, depending on the influence of exothermic or endothermicchemical reactions in the bed and the thermal properties of the material.

There are several ways of modeling the characteristics of the granular bed. The simplest wayis to assume that the material bed is perfectly mixed and use the temperature profile of thefreeboard simulation in order to use it as input for a one dimensional simulation of chemicalreactions of the following or similar form.

dCidz

= f(T,Cj), (1-4)

where z is the axial direction of the kiln, and Ci is the concentration of the ith species. Thisapproach is used by Mastorakos [28] and similarly by Kääntee [18]. This is equivalent to havea 1-D model of a Plug Flow Reactor (PFR) in the solids phase.

The main advantage for this approach is that one only needs to solve a system of ordinarydifferential equations with data from a freeboard model. It treats the granular bed as if itwas a packed bed reactor. This type of reactor is extensively studied in the field of chemicalengineering [11, 24, 22] and by using this approach and reaction kinetics from experimentaldata one can get good qualitative results [18]. If an energy balance is included, one can couplethe energy exchange between the particle bed and the freeboard due to chemical reactions[28].

The main disadvantage of this approach is that the particle bed is usually not very well mixed,thus results could differ greatly from reality. This is normally the case, as this approach isused primarily for the finding of qualitative trends on changes of parameters or feed of arotary kiln such as Kääntee does in her paper [18]. It is interesting to note, that Käänteeuses Aspen Plus [2] to simulate the chemical reactions involved in the freeboard and particlebed, contrary to Mastorakos [28] who couples a CFD solution for the combusting gases in thefreeboard with a bed model based in the solution of mass and energy conservation equations.By using Aspen-plus she also assumes a PFR behavour on the freeboard.

There is not much information on coupled simulations for the granular bed of a rotary kiln.However there are various publications that describe models for hydrodynamics and heattransfer in the transversal plane for the kiln. Heydenrich proposes in his PhD thesis [16] someinteresting models in the transversal plane for heat and mass transfer in rotary kilns with arolling mode, however there is no indication that it could be useful in a practical sense as it isnot presented as a full 3-D model. Boateng presents an interesting model for the transversalplane hydrodynamics based on kinetic theory of gases applied for dense granular flow in a twofluid approach [5]. He makes the distinction between the plug flow layer and the active layer


8 Introduction

and defines a transfer coefficient between the layers. The main downside is that his modeldoes not work well with kilns with low loading such as the kiln in question with 5% and it isalso not proved to be extendible to 3-D.

Boateng does give a simplified kiln model in his publications by taking advantage of symmetryassumptions. It is worth noting that the symmetry simplifications are probably not valid forthe present problem, as Pisaroni notes in his paper [33, 5].

1-5 Calcium Aluminate Cement Kiln

The rotary kiln to be modeled is not a typical Portland Cement kiln, thus it has differentchemical reactions and operating conditions to most of what is presented in literature. Infact, it is a Calcium Aluminate Cement kiln. In the current section a small overview of itsoperating conditions will be given1.

Operational Aspects:

• Rotational Speed: 1.5 - 2.0 RPM

• Residence time: 1 - 1.5 hours

• Kiln Load: 5%

• Particle Size at the Feed: 50 microns

• Particle Size at the Discharge: 5000 microns

For its operational aspects one can add that the Froude number is of the order of Fr = 10−4.Then by comparing the operating conditions and Froude number with the figures presentedby Henein [14] similar to Figure 1.3, it can be inferred that the operation of the kiln lies ina region between slumping and rolling mode. This is supported by the fact that rotary kilnsare designed to operate in rolling mode in order to maximize mixing.

1Information given by Ir. Rudy Sadi from Almatis. URL: http://www.almatis.com/


1-6 Granular Flow Modeling 9

1-6 Granular Flow Modeling

As it can be observed in the previous section there are no such thing as an exact or per-fect model for a lightly loaded rotary kiln such as the one described in the present project.However, due to advancements in the study and modeling of granular flows, one can inferthat using recent approaches for granular flow can bring better results in the modeling andsimulation of the granular bed of the rotary kiln in question.

There are two typical ways of modeling granular flow [38, 35]:

• Discrete Method: Euler-Lagrange approach (Coupled DEM)

• Treat the material as a collection of particles. Newton′s laws of motion are appliedto each particle.

• Continuum Models: Euler-Euler approach (Two fluid modeling)

• Particles are modeled as a continuous medium where all the quantities are assumedto be smooth functions of position and time.

Both of them are valid and have advantages and disadvantages.

In the following section both approaches will be explained and referrals to its validity forrotary drums will be given.


10 Introduction


Chapter 2

Euler-Lagrange Approach: DiscreteElement Modeling

2-1 Description of the Method

With this approach each particle is simulated by applying Newton′s laws of motion and arefollowed in time [38, 37]. For particle tracking one then has the following governing equations,

dxp,idt

= up,i (2-1)

dup,idt

= 1mp

∑F (2-2)

where xp,i is the position of the particle, up,i the velocity of the particle, mp the mass of theparticle and

∑F the sum of forces exerted on the particle, respectively.

This set of equations is also known in the literature as the Basset-Bousinesq-Oseen equations[9, 35] when fluid-particle interactions are taken into consideration.

The sum of forces depend on various factors such as drag, lift, gravity, buoyancy, contact,friction and so on. Usually one can make assumptions in order to include or not certain forcesdepending on the type system to be modeled.

The method consists of calculating the F forces and then solving the set of ordinary differentialequations described above. By adding other equations per particle, such as an energy andmaterial balance, one can have particle properties included in the ODE set and calculate fora certain time the position, velocity, temperature and mass, concentration or diameter of theparticle [37, 35].

One of the main points to be considered is the computation of the contact forces. For granularflows a soft sphere approach is used. This consists in letting the simulated particles overlap.


12 Euler-Lagrange Approach: Discrete Element Modeling

This overlap can be seen as the displacement of a spring. Then one can use a relation similarto Hooke′s law in conjunction with a dampener model, used to model energy dissipation dueto contact, to compute the contact forces.

Figure 2-1: Spring and dampener contact force model

The soft sphere approach is also known as the spring and dampener model which can beobserver in Figure 2.1. Usually one uses a non-linear spring model. This means solving anadditional set ODE per particle as one have to have into account contact on all neighboringparticles. For this models, one needs certain physical properties of the particles such as therestitution coefficient. We refer to Radjai′s book [37] for more information on the modelingof contact forces.

2-2 Applicability to Current Problem

There are various papers that deal with discrete element simulations for rotating cylinders[23, 42, 10, 36, 39, 44]. However there is no paper which describes a full model for a rotarykiln. All of them agree within a certain degree that a DEM (discrete element method)approach is valid for the type of granular flow exhibited in a rotary kiln. Kwapinska [23] forinstance, validates the transversal mixing of a DEM approach with data from Van Puyvelde[42], whose experimental results are cited for its value within the characterization of mixing ofrotating drums. Kwapiska then concludes that the DEM approach, with certain tweaks, canbe much better than the existing continuum models for rotary drums with respect to mixingand hydrodynamics in the transversal plane [23].

In a more recent paper from Van Puyvelde [36], the author insists in using data existing inliterature [42, 14, 15] for the calibration of the DEM method with respect to this specificproblem. Refer to Radjai [37] for information on the parameters for the calibration of theDEM for dense granular flow.

These publications indicate that a discrete approach is valid for a rotary kiln. This then bringus to consider the size of the problem. It is well known from the literature that this kind ofmodel is computationally expensive for a high number of particles. Therefore, experimentswere made in order to determine whether the approach is feasible for a simulation of thewhole rotary kiln in question.


2-3 Experimental Setup and Results 13

2-3 Experimental Setup and Results

Experiments were done with an open source DEM implementation named LIGGGHTS whichstands for ’LAMMPS Improved for General Granular and Granular Heat Transfer Simula-tions’ which is based on LAMMPS (Large Atomic and Molecular Massively Parallel Simu-lator) which is an open source code by Sandia National Laboratories for solving moleculardynamics, the main motivation for the Discrete Element Method [34, 37]. The main featuresof LIGGGHTS are, wall contact laws, linear and nonlinear granular potentials (springs),moving mesh, heat transfer for particles and that it can run in parallel [21].

A rotating cylinder model was built using the ’moving mesh’ 3-D test case from LIGGGHTS.A Hertzian (non-linear spring) contact model with a low coefficient of restitution was chosen.The physical properties of the particles were taken from CaO and the rest of the parameterswere left unchanged from the test case. This was done due to the fact that the experimentswere not done to recreate accurately the transversal motion, but to check for the feasibilityand computational time of the current problem due to the potential high number of particlesinvolved.

The goal of the experiment was that given a slice of the kiln, vary the number of particlesand record the execution time in order to subsequently extrapolate and have a prediction ofthe total execution time for a complete kiln.

Experiment setup:

• Cylinder: 0.10 m long with a 2.1m diameter.

• Particle diameter: 2.5 mm

• Experiment time: 3 s

• 2 RPM

• Time-step: 10−5

• Single core simulation

• Periodic B.C.

The number of particles was varied from 15,000 to 180,000. For the upper limit, a 5%loading for the cylinder was calculated by taking the packing to be 50% which is lower thanthe theoretical maximum 64% [24, 38] due to the movement of particles while the kiln isin operation. With this packing the number of particles for this particular cylinder slice isaround 180,000.

It is to be noted that there was an overhead because of the writing of data every 1000 timesteps. By using the same packing as above, one gets that for the whole 42 meter kiln there are1.1 billion particles. Then by assuming that the CPU time grows linearly with respect to thenumber of particles, one can say that 1 processor can simulate 3 seconds of experimental timeof 2,800 particles per hour. So with 1 processor the total execution time would be around400,000 hours, which is around 35 years of CPU time.



0 20 40 60 80 100 120 140 160 180−10

0

10

20

30

40

50

Number of Particles (Thousands)

Tim

e (

hou

rs)

Experiment

linear

Figure 2-2: Number of Particles vs CPU Time

2-4 Discussion: Advantages and Disadvantages

As seen in the previous section, DEM simulations can turn out to be computationally expen-sive. They do however have the following advantages:

• Simple to model and easy to understand physics

• Relatively easy to implement and there are already a number of commercial and opensource implementations: Star CCM+, OpenFOAM, LIGGGHTS/LAMMPS, MFIX [8,30, 21, 40]

• All of the implementations presented above can run in parallel

The first point is proved on the previous sections. On the second point a short research onsoftware capabilities was done. From the options presented, all have DEM, coupled CFD-DEM capabilities and can run in parallel. This desirable because one then has to care abouttweaking and not so much about coding.

For the disadvantages a list is also presented:

• Very computationally expensive

• Still needs some small empirical adjustments

As seen before, the experimental results are not encouraging. They show that the method isprobably unfeasible for the whole kiln by using LIGGGHTS. Also, some adjustments mustbe done in order to correctly model the particulate flow in a rotating cylinder, which wouldbe done by comparing results from literature, as proposed by Van Puyvelde in his 2006 paper[36].


2-4 Discussion: Advantages and Disadvantages 15

The disadvantages presented does not mean that the approach is not useful. There are anumber of ways that the DEM approach could be used for the present problem such as forvalidation of rotary bed motion modes.




Chapter 3

Euler-Euler Approach: Two-FluidModel

3-1 Description of the Method

Two-phase hydrodynamic models treat the fluid and the solids phase as two interpenetratingcontinua. They also use an averaging approach where equations are derived by space, time orensemble averaging of the local instantaneous balances of each of the phases. They basicallyuse a Reynolds-Averaging Navier-Stokes approach.

These models appear due to the increase of interest for the scale up for operations involvingfluidized beds, packed beds, and so on [40, 12]. They use analogies from kinetic theory ofgases in order to model the solids phase. One of the classical text books with applications forfluidization is written by Gidaspow [12]. The same approach could be used in order to modelthe rotary kiln, thus a description of the governing equations will be done.

The following description will be based on the MFIX Theory Guide written by Syamlal whichis basically a review and a general overview of the Euler-Euler Approach [40]. The documentis usually referred in online tutorials for the understanding of the theory behind Euler-EulerApproach. The equations presented next are the most important from the described docu-ment.

First of all, due to the averaging of variables one must assume that the point variables areaveraged over a region that is large compared with the particle spacing, but smaller than theflow domain. One then introduces new variables, the volume fractions of the phases whichare assumed to be continuous functions of space and time:

∑α∈P

εα = 1, (3-1)

where P is the set of phase indices. For simplicity only two phases will be considered, a solidsphase s and a gas phase g. One then has:


18 Euler-Euler Approach: Two-Fluid Model

εg + εs = 1. (3-2)

Then by considering the conservation of mass in the gas and solids phase:

∂

∂t(εgρg) +∇ · (εgρg−→vg) = Rg, (3-3)

∂

∂t(εsρs) +∇ · (εsρs−→vs) = Rs, (3-4)

where the ρ denotes the bulk density of the phases, −→v the phase velocity vector, and Rthe rate of production of the phase (or mass transfer between the phases). These are thecontinuity equations for the gas and the solids. One needs an additional equation of state forthe gas. This could be the ideal gas law or any other equation of state for real gases.

For the conservation of momentum one gets the following:

∂

∂t(εgρg−→vg) +∇ · (εgρg−→vg−→vg) = ∇ · ¯Sg + εgρg

−→g −−→I g, (3-5)

∂

∂t(εsρs−→vs) +∇ · (εsρs−→vs−→vs) = ∇ · ¯Ss + εsρs

−→g +−→I g. (3-6)

It can be observed that the balance of momentum presented above is exactly the same as theone presented in literature for basic fluid dynamics [3]. The first term in the left hand sideis the rate of increase of momentum per unit volume, the second is the rate of momentumaddition by convection per unit volume where −→vs−→vs denotes the dyadic product of two vectors.On the right hand side the first term is the rate of momentum by molecular transport perunit volume given by the stress tensor ¯S. The second and third term are the external forceson fluid, where the gravity vector can be observed given by −→g and the by the interactionforces (momentum exchange) between phases given by −→I .

The interaction forces between phases can be modeled in the same way as in the Euler-Lagrange approach using drag, buoyancy and mass transfer:

−→I g = −εs∇Pg − Fg (~vs − ~vg) +R0~v, (3-7)

where R0~v is the momentum transfer due to mass transfer, ∇Pg is the pressure gradient ofthe gases and Fg describes the drag forces caused by the gas. Numerous expressions exist forthese interaction terms, these can be seen in the document by Syamlal and the book fromGidespow [40, 12].

It can be noted that the stress tensors for the momentum equations are missing for bothphases. For the gas phase the stress tensor takes the form of a Newtonian Fluid, which onecan find in any fluid mechanics and transport phenomena book [3]. However for the solidsstress one needs an analogy to adopt theories for the description of granular flows. Granularflows can show characteristics from both solids and liquids, thus it has been proposed thatmost of its dynamic behavior has analogs in other systems [17, 38].


3-2 Applicability to Current Problem 19

Granular flows can be classified in two regimes, a plastic flow which is slowly shearing and aviscous flow which is rapidly shearing. This brings two different approaches to describe thesolid stresses. For the plastic flow, an empirical power law from soil mechanics is usually inplace. For the viscous flow, an analogy with the kinetic theory of gases is used, where thereis momentum transfer due to the kinetic energy in that comes from particle collisions. Inthis case the stress tensor would be dependent on a granular temperature, which comes froman additional PDE, and a bulk viscosity term which in the present case would be based onthe one presented by Lun et al. for dense granular flow. For the details on the solids phasestress tensor we refer to the publications from Gidaspow, Syamlal and Lun [40, 12, 26]. Foran introduction to the concept of granular temperature we refer to the paper from Goldhirsch[13].

3-2 Applicability to Current Problem

For the applicability of a two fluid approach on rotary kilns, one can consult the publicationsfrom Boateng [5, 4]. He develops a model for the transversal plane of a kiln taking as a basethe same governing equations as above. The model only solves for the active layer as thepassive layer is assumed to be non-shearing. He achieves success using his model for kilnloads higher than 10%. For kilns that are not as loaded, there is some discrepancy fromexperimental data.

From recent advancements in code and correlations for Euler-Euler multiphase modeling ofgranular flow one can assume that they could be valid for the transversal plane of a rotarykiln. This can be done by adopting models which are valid for slowly and rapidly shearinggranular flow or by switching to stress tensor correlations depending on the packing of thesolids phase [5, 40]. This makes a rotary kiln model possible as the plug flow layer is slowlyshearing and the active layer is rapidly shearing. However, as Lun [26] notes for Euler-Eulermodeling of granular flow, one usually needs empirical adjustments depending on the case tobe modeled.

3-3 Experimental Setup and Results

A short experiment was done in order to try to build a rotating drum Euler-Euler model inOpenFOAM [30] to check feasibility. Tutorials on two phase euler simulations for fluidizedbeds were followed with changes being done to adapt it to a rotary drum simulation. Asummary of the parameters of the simuation is done next:

• A kinetic theory description with correlations from Lun (1984) [30, 26] for dense granularmaterials was used

• Material properties from CaO were used

• Most of the empirical values were defined for a fluidized bed (following the tutorial)

• A normal velocity with respect to the cylinder wall was defined as a boundary conditionfor the granular phase (depending on the revolutions per minute of the kiln)



• A non-uniform grid was used using BlockMesh from OpenFOAM

Figure 3-1: Solids phase glyph plot of the lower part of the cylinder

As it can be observed from the figure, the flow field calculated by the model does not describecorrectly the granular flow described by Boateng [5]. There is a hint that the inconsistenciesare due to inherent problems in two phase Euler modeling in OpenFOAM which are beingaddressed by Passalacqua in his paper from 2010 [31]. He states that there is a stabilityproblem with simulations with packings near the limit (as it is the case in the passive layerof a rotary kiln). This was confirmed by the experiments which were done above and by auser forum discussion in CFD Online about OpenFOAM and high packing two phase Eulermodeling. This draws the conclusion that a model on OpenFOAM is not possible at themoment until the problem is addressed by developers or academia. However, multiphaseEuler models are readily available in Fluent, StarCCM+ and MFIX which are arguably matureenough to handle the current problem 1.

3-4 Discussion: Advantages and Disadvantages

As with the DEM approach, a Two-Fluid model pose a number of advantages. The followingsummary can be done:

• Less computational cost than the DEM approach [35]

• Chemical reactions easy to include

• There are existing commercial and open source eulerian solvers such as: Star CCM+,OpenFOAM, Fluent, MFIX [1, 8, 30, 40]

For the first point one must note that solving a problem using a RANS code is equivalentto solving a system of coupled PDEs with the finite volume method. The speed depends onthe spatial discretization, more specifically the number of cells. It must be noted that thenumber of cells will be far less than the number of particles. As for the chemical reactions,because of the nature of the finite volume approach, this is equivalent to a number of CSTRs(Continuos Stirred-Tank Reactors) in series and parallel, which in turn is equivalent to aPFR/PBR (Plug Flow Reactor/Packed Bed Reactor) [11, 24]. This makes the inclusion ofchemical reactions easy if experimental data is in hand.

As for the disadvantages:1CFD Online discussion forums. URL: http://www.cfd-online.com/


3-4 Discussion: Advantages and Disadvantages 21

• Much more complicated to understand and to tweak

• No reported use for a 3-D model of a rotary drum

The first point can be made obvious by the length to the introduction of the theory of anEuler-Euler approach. As for the tweaking, this is usually discussed while presenting orexplaining the approach [35, 40, 14, 26]. Most of the authors coincide that it requires sometweaking based on experience and experimental observations. As for the second point, it isthe case that there is no indication of a 3-D model. This makes uncertain a full simulationof a rotary drum. However, this does not mean that the approach cannot be used.




Chapter 4

Summary: Euler-Lagrange andEuler-Euler

4-1 Comparison

In the previous chapters two approaches for the modeling of granular flow were presented.Both have some similarities and differences, as well as advantages and disadvantages.

Concerning similarities, the easiest to appreciate is given by the phase interactions. In theEuler-Lagrange approach one can observe in Equation (2-2) that the sum of forces exertedon the particle are given by drag, lift, gravity and buoyancy correlations. On the other hand,by carefully examining Equations (3-5) and (3-6) one can see that there is also an interactionterm given by the momentum transfer between phases. The interesting observation is thatthis interaction term is given by the same correlations for drag, lift, gravity and buoyancyforces that are used in the Euler-Lagrange approach [35, 9].

Other similarities reside in the fact that both approaches can be used either for dispersedmultiphase flow and dense granular flow [35, 9, 38].

For the differences, the most obvious is the fact that the Euler-Lagrange approach involves themodeling of every particle and the Euler-Euler approach involves the modeling of volumes of anumber of particles. These differences can be broken down into advantages and disadvantages.In Table 4.1 a summary of both approaches is presented.

It can be observed that that while both have its own advantages and disadvantages there isno clear indication which method is better for the numerical modeling of a rotary kiln. Thisis due to the particularity of the system to be modeled.

From an Euler-Lagrange perspective, the fact that the kiln has around 1 - 3 billion particleshighlights the fact that DEM simulations can turn out to be computationally expensive.However, as it is proven to work for granular flows in rotating cylinders, we expect it to workfor rotary kilns as well.


24 Summary: Euler-Lagrange and Euler-Euler

Advantages DisadvantagesEuler - Lagrange Relatively easy to set up, it

is proven to work for rotatingcylinders

Can turn out computationallyexpensive

Euler - Euler As it is a RANS code, it canrun as fast as any multiphaseCFD code, chemical reactionsare easily incorporated

Complicated to set up andtweak

Table 4-1: Summary of advantages and disadvantages for the discussed modeling approaches togranular flows

For an Euler-Euler model one has other challenges. The fact that such a model has neverbeen done for a rotary kiln, and the complications one gets to set up such model is a hugedetractor for the selection of a Two Fluid approach. However, because of the size of theproblem, it is not only desirable but also convenient to have a relatively unexpensive modelfor the understanding of the consequences of physical parameter changes.

4-2 Heat Transfer and Chemical Reactions

Modeling approaches for granular flow dynamics were presented in the previous sections.However the inclusion of heat transfer and chemical reactions was not discussed.

For the a discrete model, heat transfer within the bed is trivial by adding one equation perparticle [9, 35] coming from an energy balance and depending on material physical properties.The only difficulty is the addition of a radiative heat transfer term which has to be investigatedfrom literature and implemented. As for chemical reactions, there is no clear indication ofhow to implement solid-solid reactions with particle growth due to sintering.

For the continuum model, the addition of heat transfer within the bed is also trivial as itfollows the same mechanisms as in a packed be d[5]. The physical property correlations forpacked beds are easily found in literature on packed bed reactors [24]. As for the radiativeheat transfer from the freeboard, the same models used by Pisaroni [33] can be used. Forchemical reactions, due to its finite volume method of solution, an Euler-Euler approachmodels CSTRs (Continuous Stirred-Tank Reactors) in series. Thus chemical reactions arenaturally integrated if there is experimental data or reaction kinetics from literature.


Chapter 5

Open Questions and Conclusions

There are still some open questions regarding the applicability and set-up of both modelswith respect to the rotary kiln. These can be divided in questions for both approaches andquestions with respect to each approach.

Questions particular to the DEM approach will be presented:

• Correct tweaking of the model parameters,

• Implementation of solid-solid chemical reactions (sintering).

For the first bullet one can take experimental data from Henein [14] and try to reproduceit. However it is not clear exactly what parameters to adjust in order to have a more exactsolution. Secondly, solid-solid reactions are not commonly treated with a DEM approach. Asin a rotary kiln material is transformed by a sintering process, the particles should grow andadhere [19]. While the growth of particles with respect to time has been implemented in theDEM [21], it is not clear how to relate it to actual reaction kinetics or experimental data forthe rotary kiln in question.

For the Two Fluid approach one has the following open questions:

• Correct stress tensor correlation and tweaking,

• Good boundary and initial conditions.

For the first point one must observe that there are hints of what correlations to use in thework by Boateng. However one of the biggest parameters is the packing limit, as it willdefine the depth of the active phase, thus the correct granular flow pattern depends greatlyon it. For a 3-D model the initial and boundary conditions will be similar as in a 3-D pipe.A prescribed pressure at the inlet and a pressure gradient equal to zero at the outlet. Aprescribed velocity field in the axial direction calculated by the correlation given by Equation


26 Open Questions and Conclusions

(2) and the residence time of the kiln. For the axial direction of the walls one has a Johnsonand Jackson [25] no slip condition for granular flow. For the rotating walls in the transversalplane, one has two ways of modeling the rotating behaviour of the kiln: with a prescribednormal velocity at the wall in the transversal direction and with a moving mesh condition.This will depend heavily on the software to be used.

The open questions for both approaches are:

• Mass and Energy balances of the actual process

• Reaction kinetics from experimental data or literature

The reason for information in the first bullet is to use it as validation of the model. Thisinformation is to be either collected from the literature, from a cement producing plant similarto the one in question or from the actual rotary kiln [33]. As for the reaction kinetics, thereare some reported reaction kinetics in the literature, but first a reasonable material balanceis needed. They can also come from experimental data from a laboratory as one can adjustthe data to an Arrhenius type equation or other existing models in literature [11].

5-1 Conclusions

As presented in the first sections, the key to the prediction of granular material properties isthe correct modeling of the granular flow behavior. This is because the material propertiesat the exit of the actual kiln are highly inhomogeneous 1.

However, one should not discard the possibility of using a 1-D PFR model for the granular bedby using the physical property correlations presented by Boateng or in literature for packedbeds. It could turn out to be sufficiently accurate in order to make design and operationdecisions for the kiln as it can be seen in previous approaches for Portland Cement Kilns.

This then brings the question: Is a model which takes into account the granular flow ofthe material in the kiln needed or is a simplified model sufficient for the case of a CalciumAluminate Cement kiln?

1Information given by Ir. Rudy Sadi from Almatis. URL: http://www.almatis.com/


Chapter 6

Further Work: Project Goals

Until recently there was practically no information of the chemical reactions that take placein the kiln in question. As of the time this chapter was written, there is recent non-isothermalexperimental data from Almatis1 available which can be used to propose a reaction kineticmodel. This then opens the possibility of proposing and setting up a simplified model similarto the ones presented earlier for Portland Cement Kilns with chemical reactions.

If the simplified model can predict the quality of the product along the axis of the kiln goodenough, it would be of great use to analyze the changes of the product when variables suchas the flame configuration are modified.

Then it is natural to state that the project goal is to develop a simplified kiln model and amuch more complete model involving granular flow. This in order to compare both modelsand judge whether a simplified model is enough or a more involved model is needed.

Then the following goals and intermediate goals are proposed.

Short Term Goals

• Migration of a DEM rotary kiln model to a parallel architecture

As it can be observed from the experiments done, it is probable that LIGGGHTS is not themost adequate DEM implementation for the present case. There are better reported resultson granular flow modeling with a DEM approach by using Star CCM+ which also includesa coupled motion-heat transfer model2. Thus it seems natural to to develop a model in thementioned software and migrating it to a parallel architecture.

This would aid the development of a granular flow model for the kiln including heat transfer,which then would account for the complexities of the flow and inhomogeneities of the presentkiln.

1Information given by Ir. Rudy Sadi from Almatis. URL: http://www.almatis.com/2Information from the CD-Adapco Users Meeting 2012


28 Further Work: Project Goals

• Development of reaction kinetics model based on experimental data

As some experimental data of mass fraction versus temperature is available, one can developa reaction kinetics model by taking Arrhenius type equations for solid reactions and makinga mass and energy balance for the experiment taking into account the operating conditions.There is already a hint on the reaction mechanisms by looking at the experimental data.The main factor is to get the correct operating conditions and set up of the experiment inorder to have the material and energy balances. The rest is selecting a viable solid kineticsmodel as the ones presented in the review paper from 2006 from Khawam [20] and optimizingparameters for the best fit with the data in hand. The main sources for more informationand hints for the proposal of reaction mechanisms are professors and colleagues involved withchemical reaction engineering, as they are acquainted with the development of kinetic modelsfrom experimental data for the design of chemical reactors.

Long Term Goals

• Development of a 1-D PFR type model for the granular bed

A one dimensional PFR model for the granular bed means supposing that the granular ma-terial is perfectly mixed, taking as input the a 1-D temperature profile calculated previouslyby Pisaroni [33] and then by using the reaction kinetics developed in the short term goals forcalculating the concentration profiles along the axis of the rotary kiln.

One can make this model a bit more complex by incorporating ideas from previous approachesfor Portland Cement Kiln modeling, such as calculating a 1-D temperature profile of thematerial based on the residence time and the previously calculated freeboard temperatureprofile. This also can be seen as a heat exchanger approach for the calculation of a 1-Dtemperature profile of the material.

• Development a granular flow model for the material bed

For the development of a model that takes into account the granular flow one has to use eitherof the approaches earlier discussed in the present document.

Using DEM simulations from Star CCM+ seem to be the next step to go. If it is provento be feasible, then there should not be much problems to set up a kiln model taking intoconsideration heat transfer to and within the granular bed. Furthermore, details for theimplementation the chemical reactions should be investigated and implemented.

As for an Eulerian model, apparently ANSYS Fluent seems to be the best software option asit has implemented a granular Eulerian flow model including Johnson and Jackson boundaryconditions for granular flow and solid stress correlations specific to dense granular flow3.However one still must do tweaking and validation with experimental data available.

One can conclude that as for the time being, a granular flow model using a discrete approachfor the material bed of the kiln seems closer than an Eulerian model. This is due to the fact

32012 ANSYS Fluent User Guide


29

that there are already some working heat transfer models available and that the Eulerianmodel arguably poses a greater challenge as for tweaking and setup.

General Goal

By developing a simplified model and a more complex granular flow model for a kiln, onecan compare results and judge whether a full granular flow model is needed for the particularcase of the discussed kiln. At the same time, this would bring insight to the granular materialproperties inside the kiln and by consequence it could be used as an aid to the design andoperation of Calcium Aluminate Cement kilns producing the same type of clinker as the onein question.


30 Further Work: Project Goals


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Documents

Literature Survey: Numerical Modeling of Granular Flows …ta.twi.tudelft.nl/nw/users/domenico/rotary_kiln/romero_litstudy... · Numerical Modeling of Granular Flows in Rotary Kilns