Alex Stéphane

Bongo Njeng

Stéphane Vitu

Marc Clausse

Jean-Louis Dirion

Marie Debacq

A S Bongo Njeng

J.-L Dirion

Effect of lifter shape and operating parameters on the flow of materials in a pilot rotary kiln: Part II. Experimental hold-up and mean residence time modeling

Keywords: Rotary kiln, Rotary dryer, RTD, MRT, Hold-up, Lifters, Lifting ights

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Rotary kilns are gas-solid reactors widely used in mineral process applications and other processes applied to specic granular materials. Due to their extensive use in industry, there have been several studies intending to model the solids transport through the kiln cylinder, usually equipped with lifters. Most of these studies attempted to understand and predict key parameters such as the hold-up, the mean residence time (MRT) or, as shown in Part I of this study, the residence time distribution of solid particles.

Most of the substantial earlier body of scientic literature that exists in the eld has assumed void axial dispersion through the kiln, such that the time of passage τ was analyzed instead of the mean residence time t. Other simply confused and supposed the mean residence time to be equal to the time of passage. Indeed the time of passage is very easy to determine; it results from the ratio of the weight of the kiln hold-up to the mass ow rate. However, it should not be forgotten that the time of passage might fail to reect the ow of solids, especially when there is some axial dispersion, which is increased when using lifters.

One of the earliest equations was developed by Sullivan et al. [START_REF] Sullivan | Passage of solid particles through rotary cylindrical kilns[END_REF] for the calculation of the time of passage of particles in rotary kilns which do not have lifters, as follows:

τ = 1.77L √ θ SDN × f actor ( 1
)
where θ is the angle of repose, S is the kiln slope, N is the rotational speed, L and D respectively the length and internal diameter of the kiln, f actor is a parameter accounting for the operating conditions, it is unity for a simple kiln without obstructions or constrictions.

Latter, Chatterjee et al. [START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part I. Eect of some operational variables[END_REF] used a semi-empirical correlation to predict the mean residence time of solid particles.

Their model was built on a dimensional analysis taking into account parameters inuencing the ow of materials.

However, some parameters were missing such as the exit dam height, which does not appear in the list of parameters, though its eect has been studied in their experimental matrix. By applying conditions of dimensional homogeneity, they deduced the following correlation:

t = k L 3 F θ S a L 3 N F e L D -c (2) 1 INTRODUCTION 2
where F is the volumetric feed rate, k is a constant equal to 0.1026 and exponents {a,e,c} are evaluated as {1.054,-0.981,-1.1} [START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part II. Eect of kiln geometry[END_REF]. It can be noted in this correlation that the eect of the kiln slope and the angle of repose of solid particles are strongly linked.

Models for the mean residence time or time of passage, developed for kilns equipped or not with lifters in literature range from relatively simple empirical equations to fully mechanistic models. However, we will focus in the coming lines on some of the simple empirical models developed for kilns equipped with lifters since the so-called mechanistic models are not suitable for control purposes [START_REF] Shahhosseini | A simple dynamic model for solid transport in rotary dryers[END_REF].

Among the earliest models developed for rotary kiln equipped with lifters is the relation of Prutton et al. [START_REF] Prutton | Factors Inuencing the Performance of Rotary Dryers[END_REF] to predict the time of passage:

τ = kL SDN + mV f (3)
where V f is the volume of solids inside a lifter, k is a constant depending on the number and shape of lifters, and m is a constant which depends on the gas ow direction and the materials properties. This model does not consider eect of any changes in solids and/or gas ow rates through the rotary kiln. Moreover the constants k and m must be determined by tting the model to experimental data from the rotary kiln in use, thus making the model impossible to use for design purposes.

Certainly the most commonly used is the Friedman and Marshall [START_REF] Friedman | Studies in rotary drying part I-holdup and dusting[END_REF] relation which is derived from Sullivan et al.

[1] model with an additional term to allow for air drag on the solid particles; the following equation was obtained through the study of hold-up of a range of materials under overloaded conditions:

τ = L 0.3344 SDN 0.9 ± 0.6085G d 0.5 p F (4)
where d p is the average particle diameter, F and G are respectively the solids feed rate and the gas ow rate.

The second term in this equation expressed the air drag, thus the negative sign is used for counter-current ow and the positive sign is used for co-current ow. Compared to Sullivan et al. [START_REF] Sullivan | Passage of solid particles through rotary cylindrical kilns[END_REF] model, this one may account for variations of solids and gas feed rates, however by increasing the solids and gas feed rate by proportional amounts the predicted residence time will remain constant, and the geometric features of lifters are not taken into account in this formulation.

Shahhosseini et al. [START_REF] Shahhosseini | A simple dynamic model for solid transport in rotary dryers[END_REF] modied Friedman and Marshall [START_REF] Friedman | Studies in rotary drying part I-holdup and dusting[END_REF] model in order to better represent the dynamic of the system, the main objective being to determine the hold-up through the use of the retention time of sugar in the rotary kiln. An additional term was introduced to account for changes in solids ow rate under zero gas ow rate conditions:

τ = L 8.5 tan(S)DN 0.8 + 0.41(G + 0.14)

d 0.5 p F (5)
Even if this model attempted to address some of the shortcomings of Friedman and Marshall [START_REF] Friedman | Studies in rotary drying part I-holdup and dusting[END_REF] model, it still does not consider internal xtures of the kiln.

Alvarez and Shene [START_REF] Alvarez | Experimental Determination of Volumetric Heat Transfer Coecient in a Rotary Dryer[END_REF] presented an empirical relationship for residence time estimation. It was derived from experimental data recovering biological and mineral origin solid particles. This relation requires up to six constants and ve other exponents, leading to a total of 11 parameters to determine:

τ = αd 0.032 p ρ 0.956 bulk N F (βS + 1) + γd -0.065 p ρ 0.002 bulk δS + 1 - G 0.5 εS + 1 (6)
where ρ bulk is the density of the bulk materials. This formulation allows prediction of residence times even when the kiln is horizontal and may apply to a wide range a solid materials. However, due to the large number of model parameters there is a need to t the model with the system experimental data prior to its utilization.

More recently Thibault et al. [START_REF] Thibault | Modeling the Mean Residence Time in a Rotary Dryer for Various Types of Solids[END_REF] proposed two empirical models for the prediction of the mean residence time.

The models consist of three factor as follows:

t = ρ p f 1 (1/FN )f 2 (S )f 3 (G) (7)
The three factors f 1 , f 2 and f 3 account for the inuence of the product FN, the slope of the rotary kiln, and the impact of the gas ow rate on the mean residence time. Denition of f 2 and f 3 as rst order equations in models allows calculation for horizontal kiln with no gas ow rate. The main dierence between the two models proposed is the denition of the factor f 1 either as a second-order polynomial with the inverse of FN or as a simple function with F and N each with an exponent. This paper is concerned with the study of the eects of usual operating conditions, shape of lifters, and type of materials on the mean residence time of solids particles as well as on the kiln hold-up. A semi-empirical model obtained from dimensional consideration for the mean residence time of solid particles is also presented. Compared to the other published correlations, this new one should be applicable to a wide range of kilns and operating conditions, and could be also useful for design purposes. Therefore comparisons of the predictions, calculated with this model when using some published experimental conditions, versus the experimental MRT results from the corresponding published data are given.

Materials and methods

Apparatus and materials

The apparatus and materials have been described in Part I of this work. Therefore only their main characteristics are given here. The rotary kiln is a 0.101 m diameter and 1.95 m long tube, which can be tilted to a maximum angle of 5°. Its rotational speed can be adjusted by a driven motor between 2 and 12 rpm. The solids ow rate was adjusted by regulating the rotational speed of a screw feeder. Dierent dam heights were used as given in Table 1.

In order to study the eect of internal ights, 4 straight one-section lifters of 10 mm referred to as straight lifters (SL) and 4 two-section lifters of 10 mm each, with a right angle cross section referred to as rectangular lifters (RL)

as shown in Fig. 1, were used.

Quartz sand with a narrow distributed size fraction and broken rice were employed as experimental materials.

The physical properties of these materials are listed in Table 2.

Experimental technique

The experimental mean residence time was determined from the residence time distribution (RTD) measurement data. The MRT τ is dened by [START_REF] Levenspiel | Chemical reaction engineering[END_REF]:

t = ´∞ 0 tC(t)dt ´∞ 0 C(t)dt ∼ = N S i t i C(t i )∆t i N S i C(t i )∆t i (8)
where C(t i ) represents the tracer concentration at the kiln exit end at the discrete time t i , i={1, 2, 3,..., N S }, and ∆t i the associated sampling time.

The kiln hold-up was obtained after the RTD measurement. The feeding system was disabled, and then the solid materials within the kiln were discharged into the recovery tank and weighed. It was also possible to assess the time of passage of particles in the rotary kiln by dividing the weight of solid materials measured by the mean ow rate at steady state.

Part I of this work provides further details on the whole experimental procedure.

Results and discussion

Table 3 gives the results of the mean residence time and the hold-up for a number of experiments where sand and broken rice were operated, with either straight, rectangular or no lifters. The details of these runs are also given. It must be pointed out that the average mass ow rate measured was within a margin of ±0.05 kg.h -1 of the reported values. Repeated experiments are not reported. In this part of the study will be discussed the eects of kiln rotational speed, kiln slope, mass ow rate, exit dam height, lifters shape and bulk materials properties on the fractional volumetric hold-up and the mean residence time. And then a model for the prediction of the MRT will be presented.

Hold-up, volume fraction

As shown in Table 2, the particulate solids used as bulk materials have varying properties. It was convenient to use the fractional volumetric hold-up (or elsewhere the degree of lling) for the analysis of the results. This latter is dened as the ratio of the volume of the working content to the volume of the kiln cylinder. The eects of operating parameters on the volumetric hold-up are illustrated in Fig. 2. At given operational conditions, experiments processing broken rice lled a higher volume than those with sand, even though the values of the hold-up weight were very close. This is a direct consequence of the materials diering bulk density properties. Another remark is about the eect of the lifters: the experimental results showed that the presence of lifters signicantly increases the hold-up (see Table 2). It was also observed that the use of rectangular lifters slightly increases the hold-up within the kiln compared to the use of straight lifters. This may be related to the lifters hold-up capacity, which is higher in the case of rectangular lifters. Hence the loading of a kiln will be partly dependent on the presence, size and shape of the lifters as previously suggested by Prutton et al. [START_REF] Prutton | Factors Inuencing the Performance of Rotary Dryers[END_REF] and Afacan and Masliyah [START_REF] Afacan | Solids hold-up in rotary drums[END_REF].

The classical operational parameters also signicantly inuence the volumetric hold-up. The fractional volumetric hold-up sharply decreases at smaller rotational speed values before slowing down at higher speed values, as if a bottom was to be reached (see Fig. 2a). Indeed the hold-up must be at the lowest when the motion is starting centrifuging.

This usually happened at very high speed. The fractional volumetric hold-up gradually goes down as the kiln slope increases (see Fig. 2b). On the contrary, the volumetric hold-up steadily increases with the feed rate (see Fig. 2c). This is not obvious but still can be understand if one extrapolates the work of Saeman [START_REF] Saeman | Passage of solids through rotary kilns. Factors aecting time of passage[END_REF] followed by Descoins et al.

[12] on the bed depth proles. These studies showed that in a kiln without lifters any increase of the feed rate will result in an increase in the bed depth and so an increase in the fractional volumetric hold-up. Even if their models are not directly applicable to kilns equipped with lifters, the results remain the same in regard to the eect of the ow rate on the volumetric hold-up. Eventually, it has been observed that the volumetric hold-up increases slightly with increasing exit dam height (see Fig. 2d). The higher the dam height, the higher the kilning bed depth, which explains the obtained results.

Time of passage

The hold-up measurements allow the calculation of the time of passage. This latter is calculated as follows:

τ = HU Ṁ (9)
Most of the previous studies focus on this simple relation to investigate the solids transport through a rotary kiln, sometimes on behalf of the MRT, as previously stated. Therefore a comparison is made between the time of passage and the MRT results over the whole experimental campaign as shown in Fig. 3. It must be said that, not surprisingly there are quite good agreements between the MRT and corresponding time of passage in general. This is because the dispersion coecients observed in the system are very low, as showed in Part I of this work. However some deviations are still observable because contrary to the MRT, this method does not oer an insight in the dispersion related issues which are linked to the solids residence time distribution. The time of passage estimates the mean residence time only with a certain degree of accuracy.

Mean residence time 3.2.1. Inuence of operating conditions

The mean residence times of sand particles were found to be higher than those of the broken rice particles mainly due to the eect of gravity and their diering angle of repose. For a given type of materials and xed operating parameters, the MRT obtained while using rectangular lifters was higher than that obtained while using straight lifters, due to the diering hold-up capacity of the lifters. These trends as shown in Fig. 4 were previously discussed in detail by Bongo Njeng et al. [START_REF] Bongo Njeng | Eect of Lifters Shape and Operating Parameters on the Flow of Materials in a Pilot Rotary Kiln : Part I[END_REF].

The MRT signicantly decreases by about 69% as the rotational speed is increased 6 times, as shown in Fig. 4a.

These results also agreed well with Abouzeid et al. [START_REF] Abouzeid | The inuence of operating variables on the residence time distribution for material transport in a continuous rotary drum[END_REF] ndings while varying the rotational speed over a wide range of values. He found that the MRT declines with increasing speed and then reaches a bottom at approximately 20 rpm, from which it follows a plateau before rising. Fig. 4b and Fig. 4c show that the MRT also decreases with the kiln slope and the mass ow rate. But it must be further specied in the case of the inclination that there is a sharp decrease between 2 and 4 degrees followed by a slow decrease for higher slope, whereas the MRT slowly decreases when the mass ow rate increases from 0.68 to 2.5 kg.h -1 (see Fig. 4c). This tendency is similar to the one observed by some other researchers [START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part I. Eect of some operational variables[END_REF][START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part II. Eect of kiln geometry[END_REF][START_REF] Abouzeid | The inuence of operating variables on the residence time distribution for material transport in a continuous rotary drum[END_REF][START_REF] Hehl | Longitudinal mixing in horizontal rotary drum reactors[END_REF]. When increasing the exit dam height the MRT slightly increases (see Fig. 4d) as observed previously by Chatterjee et al. [START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part I. Eect of some operational variables[END_REF]. However, in our experiments, a maximum increase of only 5% was observed on the MRT by using a 13.5 mm exit dam height compared to the case where no exit dam was tted at the kiln outlet end. It has been observed that these two experimental conditions, all in all, led to similar bed proles.

The only dierence which can be mentioned is that the bed depth was kept constant till the outlet end with the use of the dam, while it started displaying a slope assumed to be close to the angle of repose approximately 20 mm to the exit with no dam. Hence the design of a kiln and its exit dam should give careful consideration to the singular aspects pointed out here to be optimal with regard to the production objectives. For a dam to have a signicant impact on the materials transport characteristics, its height must be higher than the bed depth observed when the kiln has a clear exit.

Model

The main purpose of this model is to come up with a prediction of the MRT of solid particles dened as a function of operating parameters, namely the kiln rotational speed, the kiln slope, the mass ow rate and the exit dam height, as well as the kiln design and the bulk materials properties. For the purpose of application to other kiln design and operating conditions, and thus to meet scaling-up issues, the model for the prediction of the MRT is based on a dimensional analysis as described below.

Dimensional analysis. In dimensional analysis, a certain functional form is assumed, to relate the varying parameters.

All the possible parameters are commonly present with their own exponent. In this study the main operating, geometrical, and physical parameters which can aect the MRT are listed below along with their dimensions:

LT -2 t = k ρ bulk LD 2 Ṁ N 2 D g α Dopen D β (θ) γ (S) δ Ṁ ρ bulk N LD 2 4S lif t πD 2 ε ρ bulk ρ tapped ζ L D η (13)
It is convenient to rewrite Eq.10 so that the dependent variable t appears directly. Whatever the function F may be, Eq.10 can be written in the form:

F (N, Ṁ , S, Dopen, S lif t , L, D, ρ bulk , ρ tapped , θ, g)

• t = 1 (11)
Assuming that Eq.11 is dimensionally homogeneous, parameters of the function F must be subject to the power dependence, as previously stated. According to the Buckingham's theorem, the formula connecting the set of parameters can be expressed as a function of dimensionless arguments. And each of these arguments is a dimensionless product of a combination of the original parameters raised to integer power. Having in Eq.11 a number of variables r=12 and a number of fundamental units n=3, the number of dimensionless groups p is, according to Buckingham's second theorem:

p = r -n = 12 -3 = 9
A collection of 9 dimensionless groupings formed from the parameters in Eq.11 were found as follows:

t Ṁ ρ bulk LD 2 = F N 2 D g , Dopen D , θ, S, Ṁ ρ bulk N LD 2 , 4S lif t πD 2 , ρ bulk ρ tapped , L D (12)
Some of these dimensionless expressions are already famous such as the Froude number, the length-to-diameter ratio, or the (inverse of ) Hausner ratio. Dopen D

is the fractional open diameter at the kiln outlet end, 4S lif t πD 2 estimates the fraction of solids held in lifters, where S lif t = πD 2 4 -

n lif t -1 2
S horlif t with n lif t the total number of lifters and S horlif t the section of materials in a lifter at horizontal position. The two dimensionless groupings t Ṁ ρ bulk LD 2 and Ṁ ρ bulk N LD 2 are very similar to those found by Chatterjee et al. [2] in their correlation. However, in this work, contrary to what Chatterjee et al. [START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part I. Eect of some operational variables[END_REF] proposed, the bulk materials angle of repose and the slope of the kiln are taken as separate factors rather than gathered as an angular ratio (see Eq.2). Eq.12 can be written as specied by Buckingham's theorem so that an expression of the MRT is obtained from the dened dimensionless numbers as given in Eq.13.

The variables in Eq.13 are expressed in the International System of units, therefore the mean residence time obtained is in seconds. The exponents α, β, ..., ζ and the constant k are to be determined with the use of experimental data. The length-to-diameter ratio has not been varied in our experimental matrix, therefore the exponent η was xed to the value of 1.1 which has been determined by Chatterjee et al. [START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part II. Eect of kiln geometry[END_REF] when varying the dimensionless group L D from 3.3 to 16. To determine the other exponents and the constant k, a MatLab script was written. More specically the program sought to determine the parameters by minimizing the sum of square error between the experimental and predicted values of the MRT. The program was rst run with the whole experimental data matrix, i.e. resulting from the ow of both sand and broken rice, then it was run with sand and broken rice experimental data separately.

The angle of repose and the (inverse of ) Hausner ratio are strongly dependent on the materials properties; for this reason, when determining the parameters with either sand or broken rice experimental data, γ and ζ were xed to the values obtained from the whole experimental data matrix . Thus, three sets of parameters tting the best the experimental data using the presented model are obtained as given in Table 4.

It should be noted that the aforementionned correlation for the MRT is applicable in the case of inclined rotary kilns, equipped or not with lifters, and tted or not with dam at the outlet end.

Predictive performance of the model. The performance of the model was assessed using the three sets of optimal parameters separately on the experimental results. For reasons of clarity, a criterion in performance assessments J was dened as follows: (b) Experiments with broken rice Fig. 5: Comparison of the experimental MRT while using a) a bulk of sand and b) a bulk of broken rice with predicted values from Eq.13 using the 3 sets of parameters as given in Table 4. Solid lines are ±20% margins.

J = 1 N T i=N T i=1 tiexp -ti calc 2 tiexp ( 14
)
This criterion can be dened as the sum of the relative square error between predicted and experimentally determined values of the MRT divided by the number of experiments. It will be used to determine which one among the three sets of optimal parameters gives the best predictions. The lower is the value of this criterion the better are the predictions.

The performance of the proposed model was rst tested on the experimental data from this study as given in Fig. 5.

There are very good agreements between the experimental MRT obtained while processing sand and the predictions in general, however as one may expect the best predictions are obtained with the sand-tted parameters which displayed the lowest value of the criterion J as shown in Fig. 5a. Similar remarks can be made when looking at the experiments processing broken rice. There as well, good agreements are found between the experimental and predicted values of the MRT, and the rice-tted parameters give the least deviations from experimental values according to the criterion value (see Fig. 5b). In both cases the sand & rice-parameters give some good results, with values of the criterion sometimes very close to the minimum observed.

The predictive capacity of the proposed model was then tested on some experimental data from the literature.

Kilns of dierent geometries and processing a range of materials at varying conditions were chosen. Only few researchers investigating the residence time of particles through rotary kiln have published their experimental data along with sucient details on the bulk materials properties. This is even more true for kilns equipped with lifters.

The results from the work of Debacq [START_REF] Debacq | Etude et modelisation des fours tournants de deuoration et reduction du diuorure d'uranyle[END_REF] are used in this case. The results from kilns equipped with dams and no lifters were also tested. These latter are from the work of Sai et al. [START_REF] Sai | Residence time distribution and material ow studies in a rotary kiln[END_REF] and Chatterjee et al. [START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part I. Eect of some operational variables[END_REF]. The results from the kiln used by Colin et al. [START_REF] Colin | Torrefaction en four tournant: etude de l'ecoulement de plaquettes de bois[END_REF], which was not equipped with lifters nor exit dam, are also used in this study. The experimental results of the mentioned kilns were used to evaluate the predictive performance of the model for kilns of varying geometries with diering types of materials properties and operating conditions. Details about the kilns geometry and materials properties are specied in AppendixA. However it should be pointed out that the mass ow rates achieved in most of these experiments extracted from the literature are (between 2 to 300 times) higher than those in the present study. Fig. 6: Comparison of experimental MRT from Debacq [START_REF] Debacq | Etude et modelisation des fours tournants de deuoration et reduction du diuorure d'uranyle[END_REF] with predicted values from Eq.13 using the 3 sets of parameters as given in Table 4. Solid lines are ±20% margins. [START_REF] Colin | Torrefaction en four tournant: etude de l'ecoulement de plaquettes de bois[END_REF] with predicted values from Eq.13 using the 3 sets of parameters as given in Table 4. Solid lines are ±20% margins. (b) Chatterjee et al. [START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part I. Eect of some operational variables[END_REF] Fig. 8: Comparison of experimental MRT from a) Sai et al. [START_REF] Sai | Residence time distribution and material ow studies in a rotary kiln[END_REF] and b) Chatterjee et al. [START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part I. Eect of some operational variables[END_REF] with predicted values from Eq.13 using the 3 sets of parameters as given in Table 4. Solid lines are ±20% margins.

parameters are revealed to be the best set of parameters with the lowest value of the criterion. The results are even better knowing that this industrial kiln was equipped with six rectangular lifters and processed high mass ow rate of cohesive particles .

The correlation was then used to calculate the MRT of beech particles owing through the kiln used by Colin et al. [START_REF] Colin | Torrefaction en four tournant: etude de l'ecoulement de plaquettes de bois[END_REF], and operating without any internal xtures or exit dam. It should be mentioned that this kiln is twice as big than the one use in the present study, so that these kilns have similar length-to-diameter ratio. The comparisons of predicted and experimental values of the MRT are given in Fig. 7. Results show good agreements between the experimental and calculated MRT regardless of the set of parameters used. However, it should be noted that results while using the sand-tted parameters give the lowest value of the performance criterion followed by the rice-tted parameters.

Other tests were carried out with data from rotary kilns equipped with dams of dierent height at their outlet end. These rotary kilns were those used by Sai et al. [START_REF] Sai | Residence time distribution and material ow studies in a rotary kiln[END_REF] and Chatterjee et al. [START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part I. Eect of some operational variables[END_REF] as previously mentioned. Fig. 8 shows the results of the comparison of the experimental and predicted values of the MRT. Looking at the results obtained with the data from Sai et al. [START_REF] Sai | Residence time distribution and material ow studies in a rotary kiln[END_REF], the correlation gives good predictive performance when using either the rice-or sand & rice-tted parameters, but revealed an even better agreement with the experimental MRT with the sand-tted parameters, which gives a signicant low criterion compared with the other results. Chatterjee et al. [START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part I. Eect of some operational variables[END_REF] achieved a huge experimental matrix including 5 types of dam, but their correlation for the MRT was not adapted for kilns tted with a dam (see Eq.2). The comparisons of the predicted and experimental values of the MRT show some deviations. In this case the predictive performance of the model seems to be somehow diminished, as suggested by the elevated values obtained for the criterion J. But still about 30 to 50% of the results are within reasonable margins of the MRT experimentally measured. These latter poor results of the model can be attributed to (i) the diculties in extrapolating to kilns of rotational speed lower than 2 rpm, leading most of time to small Froude numbers characteristic of beds in slipping motion [START_REF] Mellmann | The transverse motion of solids in rotating cylinders-forms of motion and transition behavior[END_REF], or perhaps (ii) the wide range of variation of the eective exit open diameter achieved by Chatterjee et al. [START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part I. Eect of some operational variables[END_REF] even if the results obtained in the case of Sai et al. [START_REF] Sai | Residence time distribution and material ow studies in a rotary kiln[END_REF] experiments were quite acceptable.

It appears, in accordance with the results of the present study, that the correlation proposed in this work for the MRT is also valid when applied to kilns with materials and operating conditions dierent from those used in the study. This conrms the excellent predictive capacity of Eq.13 compared to similar semi-empirical models which are often limited to a small range of conditions and operating variables. Regardless of the set of parameters, the predictions of the correlation are usually within reasonable margins of the experimental MRT. For that reason the authors recommend the use of the sand & rice-tted parameters.

Conclusions

The eects of operating parameters, namely, the rotational speed, the kiln slope, the mass ow rate, the exit dam height, the type of materials and shape of lifters, on the hold-up and mean residence time have been investigated.

As far as these parameters are concerned, in this work it was observed that:

Increasing either the rotational speed or the kiln slope increased the kiln hold-up and the MRT of the charge.

Increasing the feed rate tended to increase the hold-up while the MRT of particles decreased. With an increase in the exit dam height these two latter gently increased.

The use of rectangular lifters slightly increased the kiln hold-up and the MRT of particulate solids compared with straight or no lifters. Sand and broken rice bulks have close Hausner ratio though they have dierent bulk and tapped density and dierent particle size. Their MRT were relatively close but the sand MRT were always higher whereas the rice hold-ups were usually higher.

A semi-empirical model was developed in order to predict the mean residence time of solid materials in inclined rotating kiln equipped or not with lifters and exit dam under steady state conditions, as follows:

t = k ρ bulk LD 2 Ṁ N 2 D g α Dopen D β (θ) γ (S) δ Ṁ ρ bulk N LD 2 4S lif t πD 2 ε ρ bulk ρ tapped ζ L D η
The correlation consists of dimensionless factors accounting for (i) the kiln basic operational parameters, (ii) the bulk solids properties, (iii) the kiln geometry, (iv) the number, shape and presence of lifters, (v) the height of the exit dam. The parameters, namely k, α, β, . . . ., ζ have been determined from experimental data. Authors recommend the use of the sand & rice-tted parameters as given in Table 4, which give good agreements with experimental data from this study and published data as well. However, the sets of parameters presented here are only applicable to beds in cascading (tumbling) motion as dened by Mellmann [START_REF] Mellmann | The transverse motion of solids in rotating cylinders-forms of motion and transition behavior[END_REF]. Therefore, possible directions for further work could be (i) to extend the validity of the model to other types of bed motion with adequate set of parameters, (ii) to enrich the experimental data matrix with results from the use of new types of solid materials for a better condence in the set of parameters determined.

List of symbols AppendixA. Geometrical characteristics and operating conditions of some kilns Table A.5 gives the characteristics of dierent kilns from the literature, along with the range of their operating conditions and characteristics of the materials used. For some materials the tapped density was missing in the published papers (those marked with * in Table 2). For these cases a literature review was done to determine the ability of the solid particles to ow. The ow ability is inuenced by the particle size; ne particles (< 0.1 mm) tend to be more cohesive and thus less free-owing, whereas larger, denser particles tend to be free-owing. It was decided to used a Hausner ratio of 1.05, characteristic of a free owing bulk, for both Ilmenite and Iron ore.

Fig. 1 :

 1 Fig. 1: Experimental Rotary kiln equipped with lifters: a) Rectangular lifters b) Straight lifters. The bulk materials are broken rice.

  Fig.2: Inuence of operating parameters (N, S, Ṁ and exit dam height) on the hold-up volume fraction for the ow of sand and broken rice, when the kiln is equipped with either straight or rectangular lifters.

Fig. 3 :

 3 Fig. 3: Comparison of experimental MRT and time of passage of solid particles. Solid lines are ±20% margins.

Fig. 4 :

 4 Fig.4: Inuence of operating parameters (N, S, Ṁ and exit dam height) on the MRT for the ow of sand and broken rice, when the kiln is equipped with either straight or rectangular lifters.

2 L

 2 length of the kiln L D internal diameter of the kiln L ρ bulk bulk density of materials ML -3 ρ tapped tapped bulk density of materials ML -3 θ angle of repose of the bulk materials g gravitational acceleration

Fig. 6

 6 Fig.6shows a comparison of Debacq[START_REF] Debacq | Etude et modelisation des fours tournants de deuoration et reduction du diuorure d'uranyle[END_REF] experimental MRT with corresponding predictions. The model predictions are very good and the values of the criterion are very close for the three sets of parameters, but the rice-tted

Fig. 7 :

 7 Fig.7: Comparison of experimental MRT from Colin et al.[START_REF] Colin | Torrefaction en four tournant: etude de l'ecoulement de plaquettes de bois[END_REF] with predicted values from Eq.13 using the 3 sets of parameters as given in Table4. Solid lines are ±20% margins.

- 3 τ

 3 Time of passage min

Table 1 :

 1 Details of the circular dams at the kiln outlet end

	Exit Dam	Open	Diameter	Area
	Height	Diameter	Covered	Covered
	[mm]	[mm]	[%]	[%]
	0	101.3	0.00	0.00
	13.5	74.3	13.33	46.20
	23.5	54.3	23.20	71.27
	33.5	34.3	33.07	88.54

Table 2 :

 2 Physical properties of materials

	Materials	Shape	ρ bulk	ρ tapped	dp	θ
			[kg.m -3 ]	[kg.m -3 ]	[mm]	[°]
	Sand	Nodular	1422	1543	0.55	39
	Broken rice Cylindrical	889	934	3.8×1.9 36

Table 4 :

 4 Calculated values of exponents and constant k for the MRT dimensional correlationThe analysis involves the fundamental dimensions MLT: mass, length and time. It follows from the above that the relation being sought can be summarized as: F ( t, N, Ṁ , S, Dopen, S lif t , L, D, ρ bulk , ρ tapped , θ, g)

	Exp. data	k	α	β	γ	δ	ε	ζ	η [3]
	Sand	0.1363 0.0508 -0.4008 0.8749 -0.9814 0.8115 -4.5285 0.7723	1.1
	Rice	0.0792 -0.0218 -0.3387 0.8749 -1.2277 0.8184 -8.0175 0.7723	1.1
	Sand & Rice 0.2611 0.0842 -0.3649 0.8749 -1.1243 0.8350 -5.5283 0.7723	1.1

Table A .

 A 5: Characteristics of diering kilns with their operating parameters range of variation as given in literature.

			L	D	L/D	Materials	Size	θ	ρ bulk	ρ tapped	N	S	Ṁ	h	S lif t
			[m]	[m]	[-]	[-]	[mm]	[°]	kg.m -3	kg.m -3	[rpm]	[°]	kg.h -1	[mm]	m 2
	Bongo Njeng et al. [13]	1.95	0.10	19.50	Sand Rice	0.4-0.8 1.8-4.4	39 36	1422 889	1543 934	2-12	2-5	0.69-2.5	0-33.5	0-0.008
	C Debacq [16] Tracer concentration, 6.85 0.75	g/g, 9.13	UO 2 F 2 U 3 O 8	0.02-0.5 0.01-0.05	42 33	400 1000	500 1300	1.6-2.1	1.43	508-895	0	0.438
	sample conductivity Colin et al. [17] 4.2 0.21	µS.cm -1 20.00 Beech	5-15	42	260	284	2-4	1-2	4-8	0	0
	Dopen Eective exit open Sai et al. [18] 5.9 0.15	m 39.33	Ilmenite	1.1	27.4	4200	4410*	1-3	0.78-1.37	6-36	15-28	0
	diameter Chatterjee et al. [2]	2	0.3	6.67	Iron ore	3-6	35	2500	2625*	0.3-0.7	1-3	15-60	0-75	0
	dp	Average particle size	mm
	D	Kiln internal diameter	m
	F , α,β,γ, δ, ,ε, f 1 ,f 2 ,f 3 F ζ,η	Function Solids feed rate		-kg.s -1
	f actor Fitting parameters G Gas ow rate	-kg.s -1
	g	Gravitational		m.s -2
		acceleration
	HU	Hold-up			kg
	k	Fitting parameters	-
	J	Performance criterion	min
	L	Kiln Length		m
	Ls	Area occupied by solid	m 2
		particles contained in
		loading lifters
	Ṁ	Mass ow rate		kg.h -1
	MRT Mean residence time	min
	N	Kiln rotational speed	rpm
	NL	No lifters			-
	n lif t	Total number of lifters	-
	NS	Total number of		-
		samples
	N T	Total number of		-
		experiments
	RL	Rectangular lifters	-
	rpm	Rotation per minute	-
	RTD Residence Time		-
		Distribution
	S	Kiln slope			degrees
	SL	Straight lifters		-
	S lif t	Area covered by solid	m 2
		particles in a lifter at
		horizontal position
	S horlif t Area covered by solid	m 2
		particles in a lifter at
		horizontal position
	t	Time			min
	t	MRT			min
	V f	Volume of solids inside	m 3
		a lifter
	X	hold-up volume fraction -
	Greek letters


A S Bongo Njeng

S Vitu

M Clausse

J.-L Dirion

M Debacq

Effect of lifter shape and operating parameters on the flow of materials in a pilot rotary kiln : Part III. Up-scaling considerations and segregation analysis

Keywords: Rotary kiln, RTD MRT, Filling degree, Axial Dispersion, Lifters, Particle segregation

Up-scaling tracer experiments were carried out in a pilot-scale rotary kiln twice as big as the kiln used in the first two Parts of this study. Internal fixtures such as grid, or lifter structure arranged in 3 and 6 rows of single throughout lifters were used. The effects of these removable fixtures and other usual operating conditions, namely, mass flow rate of granular biomass materials, rotational speed and slope of the kiln on the residence time distribution (RTD), the mean and variance of residence time (MRT and VRT), the hold-up (HU), the Peclet number (Pe) and corresponding axial dispersion coefficient (D), were investigated. Scaling-up rules were derived for the MRT, HU volume fraction and D from the results of a comprehensive experimental work. Good agreement was found between the experimental data and the calculated values. The wide size distribution of the beech chips used in the present study allows analysis of particle segregation, which may further increase understanding of the flow characteristics of granular materials, notably within flighted rotary kilns. The results show that while significantly increasing the dispersion, ipso facto, enhancing the mixing, the lifters limit the extent of particle segregation.

Introduction

Rotary kilns have become over the years among the most commonly used gas-solid reactors in a variety of applications in metallurgical and chemical manufacturing, but also in the waste disposal. They are equally applicable to a wide range of materials ranging from granular solids to sludge and slurry. In the processing of solids, the particle size distribution is only a function of the handling capacity of the feeding system.

The focus of this study, initiated in [START_REF] Bongo Njeng | Effect of lifter shape and operating parameters on the flow of materials in a pilot rotary kiln: Part I. Experimental RTD and axial dispersion study[END_REF][START_REF] Bongo Njeng | Effect of lifter shape and operating parameters on the flow of materials in a pilot rotary kiln: Part II. Experimental hold-up and mean residence time modeling[END_REF], is the characterization of solids transport within flighted rotary kilns. If there have been several studies in that field up-to-date, most of these studies have generally focused on the bare kiln [START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part I. Effect of some operational variables[END_REF][START_REF] Bandopadhyay | Mathematical modelling of charge movement in rotary kiln for spong iron making[END_REF][START_REF] Sai | Residence time distribution and material flow studies in a rotary kiln[END_REF][START_REF] Chen | Residence time and mass flow rate of particles in carbon rotary kilns[END_REF] to model through empirical or mechanistic correlations some of the main solids transport variables such as the hold-up, mean residence time or the bed depth profile. A few studies have characterized effect of the lifters on the flow of solids particles [START_REF] Miller | Factors Influencing the Performance of Rotary Dryers[END_REF][START_REF] Kelly | Dynamics of granular material rotary dryers and coolers[END_REF][START_REF] Kelly | Flight design in rotary dryers[END_REF][START_REF] Hatzilyberis | An Rtd Study for the Flow of Lignite Particles Through a Pilot Rotary Dryer Part II: Flighted Drum Case[END_REF][START_REF] Ablitzer | A Phenomenological Analysis of Particulate Solids in the Operation of Rotary Reactors[END_REF].

The correlations developed by Hwan [START_REF] Hwan | Heat transfer mechanisms in an indirectly heated rotary kiln with lifters and its role in scaling[END_REF] for horizontal flighted rotary kilns can be mentioned. They are based on dimensional analysis similar to the correlation by Chatterjee et al. [START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part II. Effect of kiln geometry[END_REF], which was adjusted using residence time distribution (RTD) measurements conducted in an inclined rotary kiln without lifters but equipped with an exit dam. Hwan [START_REF] Hwan | Heat transfer mechanisms in an indirectly heated rotary kiln with lifters and its role in scaling[END_REF] performed systematic experiments carried out in horizontal rotary kilns of different length-to-diameter ratios (between 5 and 10), using segmented lifters and different solid materials. From these the same way for the identified set of dimensionless groups, only differing by a multiplication factor.

To further understanding of the flow of materials in inclined flighted rotary kiln units started in Parts I and II, in the present work , granular materials (biomass) of wider size distribution, and a rotary kiln of larger scale were used. As will be presented in the following sections, the present study aims at investigating the effects of lifter shape and configurations, kiln rotational speed and slope, and mass flow rate on:

the RTD of solid particles, determined from experimental stimulus response test; and the corresponding mean and variance of residence time (MRT and VRT); -the hold-up (HU) of solid particles;

the Peclet number (Pe) as well as the corresponding axial dispersion coefficient (D); -the segregation of solid particles.

A set of models are proposed for the prediction of the MRT, HU (volume fraction) and D. These models, established on the basis of dimensional considerations, can be used either for design or control purposes.

Materials and methods

Apparatus and materials

The pilot scale rotary kiln considered to carry out this study consists of a tube made of an nickel-chromium alloy. The tube, supported on rollers, is 4.2 m in length and 0.21 m in diameter. It can be tilted from 0°and downward to an angle of 7°. The kiln tube can be rotated between 0.5 and 21 rpm through chains and sprockets coupled to a variable speed motor. At the upper end of the tube, the feeding system comprising a 30 L hopper and a vibrating cylindrical conveyor is set up. At the lower end, it is possible to install (in a sealed manner, if necessary) a tank (30 L) for storage. Notice that the feed rate is adjusted by regulating the vibration frequency of the conveyor on the basis of continuous weight measurements of the feeding system by an electronic balance.

A second electronic balance is installed at the kiln end, so that both inlet and outlet mass flow rates can be continuously determined.

The smooth inner wall of the kiln tube can be equipped with a grid or a lifter structure. These features are illustrated in Figure 1. The grid consists of 16 rows of thin rods (5 mm in diameter) equally distributed in the periphery as shown in Figure 1a. The lifter structure can hold, depending on the desired configuration, a maximum of 36 one-section lifters (30 mm), referred to as straight lifters (SL). The lifters can be longitudinally arranged in a maximum of six rows equally distributed in the periphery: either as single throughout lifters or segmented lifters. The configurations used in this study are represented in Figure 1b: 3 and 6 rows of single throughout lifters. The main characteristics of the rotary kiln and the order of magnitude of operating conditions investigated in the present work are summarized in Table 1.

Biomass materials are selected to run the experiments; specifically, beech chips are chosen. A characterization of the size distribution of these particles is achieved using 250 particles randomly chosen among tracer particles used for the RTD experiments. The size distribution of these free flowing parallelepiped chips is quite wide as illustrated in Figure 2: 5-17 mm in length, 2-8 mm in width and 1-4 mm in thickness. In addition, as shown in Table 2, the materials used are characterized by a bulk density, ρ bulk , about 260 ± 30 kg.m -3 and a repose angle, θ, about 42 ± 1°measured through the fixed cone method [START_REF] Woodcock | Bulk Solids Handling Unit, Bulk solids handling: an introduction to the practice and technology[END_REF].

A comparison with the rotary kiln used in [START_REF] Bongo Njeng | Effect of lifter shape and operating parameters on the flow of materials in a pilot rotary kiln: Part I. Experimental RTD and axial dispersion study[END_REF][START_REF] Bongo Njeng | Effect of lifter shape and operating parameters on the flow of materials in a pilot rotary kiln: Part II. Experimental hold-up and mean residence time modeling[END_REF] shows that the two pilot-scale rotary kilns share a very similar length-to-diameter ratio. However, looking at their dimension ratio, there is a factor about two. The particles size used in the present study is an order of magnitude higher and of a wider distribution compared to those of the sand (0.55 mm) and broken rice (3.8 mm × 1.9 mm) particles used in the first Parts [START_REF] Bongo Njeng | Effect of lifter shape and operating parameters on the flow of materials in a pilot rotary kiln: Part I. Experimental RTD and axial dispersion study[END_REF][START_REF] Bongo Njeng | Effect of lifter shape and operating parameters on the flow of materials in a pilot rotary kiln: Part II. Experimental hold-up and mean residence time modeling[END_REF].

Experimental procedure

The experiments conducted in the present study were performed at ambient temperature and atmospheric pressure. The RTD measurement procedure was kept as close as possible to the one presented in Bongo Njeng et al. [START_REF] Bongo Njeng | Effect of lifter shape and operating parameters on the flow of materials in a pilot rotary kiln: Part I. Experimental RTD and axial dispersion study[END_REF]. However, the feeding systems of these units being different, the impulse injection was carried out differently. In order to characterize the flow of beech chips, stimulus response tests are performed using dyed beech chip tracers as emphasized above, following the procedure outlined below:

Step 1: The desired internal fixture is installed at the inner wall, if necessary. The kiln tube is then tilted to the desired angle value. Then the rotational speed and mass flow rate are indicated on the user interface of the operating unit. The rotary kiln is then started and the feed hopper regularly filled with biomass materials to keep it topped up, when needed.

Step 2: Steady-state conditions of the flow are reached, usually after 2-4 hours. The steady-state conditions are assumed to be reached when: the slopes of the lines obtained by plotting the mass variations with time at inlet and outlet, are equal. In addition, the measured inlet and outlet mass flow rates must be equal within a margin of ±0.05 kg.h -1 .

Step 3: The unit is then run until emptying the hopper. The kiln tube inlet end is not readily accessible. Hence, when the vibrating conveyor was empty, the system was stopped to perform the tracer injection. A known amount of dyed beech chips is injected at the kiln inlet end through the hopper and the vibrating conveyor, while the system is stopped. The feed hopper is then refilled with the beech chips and the whole unit is started again at an arbitrary zero time.

Step 4: Samples are then continuously collected at the kiln outlet end with a sampling time of 30 s until all tracer materials are (visually) discharged. The sample time was reduced to 15 s when the tracer particles tended to exit the kiln in a very short time.

Step 5: Then, the kiln rotation is stopped and the vibrating conveyor disabled at the same time. Only the kiln rotation is started again and the solids are discharged. The collected solids which constitute the kiln hold-up are weighed.

Step 6: Lastly, the tracer concentration in each sample is determined by weighing on the one hand the collected sample and on the other hand the dyed tracer, manually extracted from the sample. While analyzing the collected samples, the number of dyed tracer particles extracted from each sample is also determined.

It is important to assess the amount of tracers required to provide sufficient accuracy for the RTD analysis. Therefore, preliminary experiments were performed using amounts of dyed beech chips varying from 5 g to 30 g. It was found that amounts of 20 and 30 g of tracers are enough to get a good accuracy. To shorten the sampling analysis time, 20 g of tracers (about 720 particles) are used to perform the RTD measurements.

Data processing

Data evaluation

The RTD curve or E-curve, E(t), the mean residence time (MRT), t, and the variance of residence times (VRT), σ 2 , are determined as follows [START_REF] Levenspiel | Chemical reaction engineering[END_REF]:

E(t i ) = C(t) ´∞ 0 C(t)dt ∼ = C(t i ) N S i C(t i )∆t i (4) t = ´∞ 0 tC(t)dt ´∞ 0 C(t)dt ∼ = N S i t i C(t i )∆t i N S i C(t i )∆t i (5)
σ 2 = ´∞ 0 (t -t) 2 C(t)dt ´∞ 0 C(t)dt ∼ = N S i t i 2 C(t i )∆t i N S i C(t i )∆t i -t2 (6)
where t is the time, C(t) represents the tracer concentration at the kiln exit end, the time integral of C(t)

represents the total tracer concentration, and ∆t i is the sampling time with i={1, 2, 3,..., N s }, N s is the total number of collected samples.

The presented E(t) function and VRT can also be expressed in dimensionless form using the dimensionless time, θ = t t , as follows: E(θ) = tE(t), and σ 2 θ = σ 2 t2 .

Axial dispersion model

As shown in [START_REF] Bongo Njeng | Effect of lifter shape and operating parameters on the flow of materials in a pilot rotary kiln: Part I. Experimental RTD and axial dispersion study[END_REF], the axial dispersion model can be used to represent the time dependent E-curves. This model is used to fit the RTD measurements assuming open-open boundary condition. In dimensionless form, the model is given as follows [START_REF] Levenspiel | Chemical reaction engineering[END_REF]:

E(θ) = 1 2 P e πθ exp - P e(1 -θ) 2 4θ (7)
The variance of this distribution is defined as:

σ 2 θ = 2 P e + 8 P e 2 (8)
The Peclet number, Pe, is then determined by a fitting method that consists in minimizing the deviation between the experimental E-curve and the prediction. The fitted Peclet numbers obtained, and the theoretical Peclet numbers determined from Eq.8, are compared in Figure 3. Except in isolated cases (2 in total), where the least-square algorithm used failed to find the actual Peclet number that represents the experiment, it was found that the theoretical Peclet Number underestimates the actual Peclet number. A similar observation was previously made in [START_REF] Bongo Njeng | Effect of lifter shape and operating parameters on the flow of materials in a pilot rotary kiln: Part I. Experimental RTD and axial dispersion study[END_REF] while processing sand and broken rice; however in this case the discrepancy observed is smaller. Nevertheless, for the analysis, only results obtained from the fitting method are considered.

Figure 3 also displays a comparison of the experimental MRT from Eq.5 versus the fitted MRT, which is obtained when fitting the experimental data using the dimensional form of Eq.7, i.e., E(t) = 1 2 P e π tt exp -P e( t-t) 2

tt

.

Very good agreement is found. Lastly, in Figure 3 is presented a comparison of the axial dispersion determined from the theoretical and fitted Peclet number using the following expression: D = uL/P e, where u = L/ t estimates the solids axial velocity. D is inversely proportional to Pe, so that the observed discrepancies show this time an overestimation of the actual axial dispersion coefficient by the theoretical coefficient.

Results and discussion

The experimental matrix was derived from a set of benchmark values of the operating parameters defined as follows: a rotational speed of 3 rpm, a kiln slope of 2°and a mass flow rate (MFR) of 5 kg.h -1 (±0.05 kg.h -1 ).

While using the grid, the straight lifters, or even without any internal fixtures, the operating conditions were set to the given values except the one whose effect is being evaluated on the beech chips flow. Note that no exit dam was fitted at the kiln exit end, unlike the kiln used in Parts I and II of this study. Moreover, compared with preceding Parts, the benchmark value of the mass flow rate is doubled, so that the actual kiln can be operated design-loaded or over-loaded depending on the other operating conditions. In addition, the present paper investigates in particular effect of the configuration of lifters, arranged as 3 or 6 rows of single throughout lifters; effect of the grid on the flow behavior is also considered. Effect of the operating parameters on the flow characteristics of materials are qualitatively and quantitatively studied through: (1) the residence time distribution (RTD), (2) the mean residence time (MRT), (3) the variance of residence time (VRT), (

the hold-up (HU), [START_REF] Sai | Residence time distribution and material flow studies in a rotary kiln[END_REF] the Peclet number (Pe) and axial dispersion coefficient (D), and (6) the segregation of solids. For this purpose, 28 different runs are performed. The detailed results of the experimental campaign are summarized in Table 5 in the Appendix 5.1.

3.1.

Influence of operating variables on the experimental RTD, MRT, VRT and HU

Effect of lifters configuration

Effect of the lifter shape has been previously established while comparing the flow characteristics in a smaller kiln operated with 4 straight and 4 rectangular lifters equally spaced around the kiln tube internal wall periphery. The lifters with higher hold up capacity were found to generate more dispersion and longer residence times. Here the lifters used are similar but two configurations are tested: 3 and 6 rows of single throughout straight lifters. In addition, the effects of a grid are also considered. Figure 4 presents the variations of the residence time distribution when operating at the given benchmark values with and without internal fixtures;

the replicated runs are plotted. The RTD curves overlap; in particular, those corresponding to 3SL and 6SL are nearly superimposing. Notice that in the absence of internal fixtures the flow behaves as a plug flow as suggested by the narrow RTD obtained.

Figure 6 presents the variations of mean residence time, filling degree and variance of residence time with the kiln operating conditions for different internal fixtures or without. From the latter, it is clear, except when varying the mass flow rate, that the following order can apply to the experiments considering uncertainties as presented later on:

tNL < tG < t3SL t6SL , σ 2 N L < σ 2 G < σ 2 3SL σ 2 6SL and HU N L < HU G < HU 3SL HU 6SL .
It must be specified that very little or no significant differences were observed in the results obtained with the 3SL and 6SL. However, using lifters significantly increased the kiln hold-up and thus the filling degree, but also the MRT and VRT, as shown in Figure 6. Still, unlike what might be expected, the results are more or less equal with small discrepancies, especially when the kiln was over-loaded in both 3SL and 6SL configurations.

The kiln was over-loaded usually for filling degree higher than 8-10%. In fact, it appears that in the latter condition the amount of solids lifted out of the bulk bed by the lifters is virtually the same while using 3SL or 6SL, and probably would have not been increased much even with 12SL as illustrated in Figure 5. Hence, it is not so much the number of rows of lifters that will affect the flow characteristic but rather the overall hold up capacity of these lifters. Using lifters of (1) higher holding capacity and (2) higher angular position at the end of discharge, such as rectangular lifters, theoretically must have shown greater differences between the lifters configurations mainly because of the overall hold up capacity.

Aside from the evident benefit of increasing the friction at the kiln smooth wall, using a grid helps to promote rolling motion into the bulk bed. This latter motion, well characterized by Henein et al. [START_REF] Henein | Experimental study of transverse bed motion in rotary kilns[END_REF], is most commonly found in kiln operation. It is observed that in runs where no internal fixtures are installed at the kiln internal wall, the bulk bed is in the slipping mode as described by [START_REF] Henein | Experimental study of transverse bed motion in rotary kilns[END_REF][START_REF] Mellmann | The transverse motion of solids in rotating cylinders-forms of motion and transition behavior[END_REF], especially when the filling degree is lower than 8%. Experiments show that using a grid at similar operating conditions will set a rolling motion within the bulk bed. In fact, the grid can be considered as a structure of small flights, which continuously scrape off the solids from the bottom of the bulk bed to the upper part of the bed surface. Therefore, the grid imposes a motion en masse at the bottom part of the bed at the kiln rotational speed and generates at the bed surface a steady discharge of solids. This has a significant impact on the HU, MRT and VRT, which are all increased compared to the case of a smooth internal wall. However, this is still a moderate increase compared to the large increase induced by the use of lifters because of differences in size and holding capacity.

Effect of operating parameters: rotational speed, kiln slope and mass flow rate

Figure 7 shows the influence of the operating parameters on the residence time distribution of beech chips when the kiln is equipped with 6 rows of single throughout lifters. A general remark that can be made on the obtained RTD curves over the whole experimental campaign is the presence of small peaks extending the tail of the distributions. This can be due to some particle segregation phenomena occurring in the bulk bed as discussed later. The results presented in the following sections are also analyzed in the scope of previous observations made on the flow characteristics of sand and broken rice.

Kiln rotational speed. Similar to previous observations, there is a sharp decrease of the MRT by about 70% as the rotational speed is increased from 2 to 6 rpm (see Figure 6a). That increase is also suggested by the shifting of the RTD curves toward lower residence times (see Figure 7). However, unlike previous observations, the shape of the curves significantly changes from a spread distribution with a low peak to a very narrow distribution with a high peak. This is confirmed by the sharp decrease in the VRT (see Figure 6c). Finally, the kiln hold up is also decreased, actually divided by 3 to 4, when the kiln rotational speed varies from 2 to 6 rpm (see Figure 6b). Indeed with higher rotational speed the solids flow in the kilning bed or through lifters is faster, so that the accumulation of solids in the burden is reduced.

Kiln slope. The kiln slope has a similar effect to that of the kiln rotational speed on the flow of beech chips.

The same trends were previously observed while operating sand or broken rice. When increasing the kiln slope, whether the motion within the bulk bed is slipping or rolling, the forward axial displacement of solids is significantly increased due to gravity. In the first case, it is observed that the bed adheres to the rotating wall, up to a certain angle of deflection as described by Mellmann [START_REF] Mellmann | The transverse motion of solids in rotating cylinders-forms of motion and transition behavior[END_REF], and then en masse, the bed slides back and forward along the kiln slope. In the second case, when rolling motion is achieved, the particles thrown off the apex of the bed flow down along the bed inclination but also forward following the kiln slope. The higher the kiln slope, the higher the particles forward displacement. As a result an increase in the kiln slope reduce the MRT and filling degree, as illustrated respectively in Figures 6a and6b. As shown in Figure 7, the RTD shapes also vary much from widespread distribution to narrow distribution with increasing kiln slope, as indicated by the decrease of the VRT in Figure 6c.

Mass flow rate. Surprisingly, the mass flow rate has little effect on the flow of beech chips, as implied by the quasi overlapping RTD curves (see Figure 7 ). Even if a similar trend was observed previously while using broken rice, the rate of increase of the MRT with flow rate was higher than that of the present materials (see Figure 6a). In addition, significant changes in the shape of RTD curves were reported for the flow of sand and broken rice. The observed divergence can be related to the materials properties, rather than a difference in the tracer pulse experiment procedure, or even the amount of tracer with regard to the bulk burden. Notice that the VRT is strongly influenced by the type of motion of the bulk bed (see Figure 6c). Large discrepancies can be observed with regard to runs in slipping mode (without lifters or grid). When operating in rolling motion, if the MRT and VRT remain almost constant, the filling degree significantly increases linearly with the mass flow rate (see Figure 6b). This latter results are important for kiln operation, since they imply that the bulk burden can be significantly increased, without, this requiring much more residence time within the kiln.

Influence of operating variables on the experimental Pe and D

Figure 8 represents the variations of the Peclet number and resulting axial dispersion coefficient with the kiln operating conditions, when equipped with internal fixtures. The runs without internal fixtures, which display slipping motion, are not represented in order to focus only on the results referring to the rolling motion.

The Peclet numbers, determined by fitting the RTD curves, are large and comprise between 200 and 800 for runs in rolling motion, and even higher in case of slipping motion (see NL in Table 5). Indeed the higher the Peclet number, the smaller the dispersion, which thereby promotes plug flow. The Peclet number and axial dispersion have been previously investigated by several authors [START_REF] Sai | Residence time distribution and material flow studies in a rotary kiln[END_REF][START_REF] Rutgers | Longitudinal mixing of granular material flowing through a rotating cylinder: Part II[END_REF][START_REF] Abouzeid | The influence of operating variables on the residence time distribution for material transport in a continuous rotary drum[END_REF][START_REF] Sudah | Quantitative characterization of mixing processes in rotary calciners[END_REF], concluding most of the time that the Peclet number increased with rotational speed and slope of the kiln, and remained constant with the flow rate. However the present results do not all agree with these previous findings. Among the internal fixtures, the grid, which induces lower filling degree, shows higher Peclet number, and thus generates lower longitudinal back-mixing compared to the 3SL and 6SL configurations. It can be seen that when using the grid, the Peclet number decreases with the rotational speed, but that it remains fairly constant within the experimental error for the 3SL and 6SL configurations. A previous analysis of the flow of sand and broken rice shows, in accordance with the actual results, that the Peclet number increases with the mass flow rate; but unlike previous results, it is observed in this case while investigating the flow of beech chips that the Peclet number increases with the kiln slope.

The values reported in the present study for the axial dispersion coefficient are in the order of magnitude of those reported for the sand and broken rice in Part I, but also with those reported by Wes et al. [START_REF] Wes | Solids mixing and residence time distribution in a horizontal rotary drum reactor[END_REF] (4 • 10 -5 m 2 .s -1 ) or Sai et al. [START_REF] Sai | Residence time distribution and material flow studies in a rotary kiln[END_REF] (2 • 10 -5 m 2 .s -1 ). Furthermore the observed trends are similar to those previously described: the axial dispersion coefficient is found to increase with rotational speed and slope of the kiln, but to decrease with the mass flow rate. It can be added that higher dispersion coefficient values are obtained for the 3SL and 6SL configurations, as expected. Note that the axial dispersion coefficient increases as the filling degree decreases for a given internal fixture. Indeed, the mixing effect is much more powerful in a lower bulk burden than in a large one.

Modeling: MRT, HU and D

In this section are presented some scale-up rules for flighted rotary kilns. Models are determined from dimensional considerations for the prediction of the mean residence time, the filling degree and the axial dispersion. The dimensionless groups presented in the following sections may not account for inter-particle forces that may occur between cohesive particles. They may primarily be appropriated for free-flowing particles whose size may vary between 0.4 and 15 mm. In addition, they may likely be applicable to the rolling mode. The following scale-up rules are derived from previous findings in the literature as well as from experimental results

obtained in this study while processing sand, broken rice and beech chips. The main operating parameters, geometrical characteristics and physical properties, that may affect the MRT, the HU volume fraction and D are listed as follows: the rotational speed (N), the mass flow rate ( Ṁ), the kiln slope (S), the exit diameter (D ex ), the cross section of materials in lifters (S lift ), the length of the kiln (L), the internal diameter of the kiln (D i ), the bulk density of materials (ρ bulk ), the tapped density of materials (ρ tapped ), the angle of repose of the bulk materials (θ), the particle equivalent size (d p ), and the gravitational acceleration (g). Note that:

(1)

S lif t = πD 2 i 4
-

n lif t -1 2
S horlif t with n lif t the total number of lifters and S horlif t the section of materials in a lifter at horizontal position, which can be determined using the materials angle of repose and lifters dimensions [START_REF] Van Puyvelde | Modelling Transverse Segregation of Particulate Solids in a Rolling Drum[END_REF][START_REF] Sunkara | Modeling the discharge characteristics of rectangular flights in a flighted rotary drum[END_REF][START_REF] Debacq | Transverse motion of cohesive powders in flighted rotary kilns: Experimental study of unloading at ambient and high temperatures[END_REF], (2) d p = 3 √ l l l w l t with l l , l w and l t respectively the particles average length, width and thickness.

From the defined variables, following a procedure that can be found in [START_REF] Delaplace | Modélisation en génie des procédés par analyse dimensionnelle : Méthode et exemples résolus[END_REF], dimensionless groups are set to correlate the MRT, HU[%] and D as follows. Table 3 summarizes the values of the model parameters determined with the use of experimental data at the 95% confidence level, while Figure 9 presents the comparison of the calculated model predictions with experimental results.

MRT

The model established for the mean residence time is presented in Eq.9. This might be very similar to the previous proposition in Part II, but there are a few differences. In order to define the dimensionless groups, it is necessary to choose a set of parameters to represent the fundamental dimensions. In this study the involved dimensions are mass, length and time. To achieve the dimensional analysis in this paper ρ bulk , D i and g are selected, instead of ρ bulk , D i and N in Part II of this study. This allows the impact of the operating parameter N to be set in only one dimensionless group: the Froude number. The dimensionless parameters, θ and S, are gathered in one group. Finally, the model parameters presented in Table 3 are determined from experimental results obtained from the 3 granular materials used: sand, broken rice and beech chips. Notice that these parameters are determined within narrow confidence intervals.

t = k gL N 2 Di g α Dex Di β θ S γ Ṁ ρ bulk D 2 i √ gL δ 4S lif t πD 2 i ρ bulk ρ tapped ζ L Di η (9)
Unlike previous results in Part II [START_REF] Bongo Njeng | Effect of lifter shape and operating parameters on the flow of materials in a pilot rotary kiln: Part II. Experimental hold-up and mean residence time modeling[END_REF] or by Hwan [START_REF] Hwan | Heat transfer mechanisms in an indirectly heated rotary kiln with lifters and its role in scaling[END_REF] in the literature, it is found that the Froude number has a significant impact on the MRT. As illustrated in Figure 9a, the predictions from Eq.9 are in good agreement with the experimental data irrespective of the kiln or the materials used. For the calculations, the variables forming the dimensionless groups must be filled in SI units, therefore the unit of the obtained predictions for the MRT is second. Notice that in the present study the length-to-diameter ratio varies only slightly and could not be used for parameter fitting, therefore the value of η is set to 1.1, which has been previously determined by Chatterjee et al. [START_REF] Chatterjee | Flow of materials in rotary kilns used for sponge iron manufacture: Part II. Effect of kiln geometry[END_REF].

HU

The model defined for the filling degree is presented in Eq.10. It is very similar to the one proposed for the MRT. Indeed a direct correlation can be found between these two, especially when the dispersion is very negligible, the time of passage and the mean residence time are very close, yet the time of passage is defined as τ = HU/ Ṁ . This also explains why some parameters of both models are very close, such as α, β, and γ, as shown in Table 3.

HU [%] = k ρ bulk LπD 2 i 4 N 2 Di g α Dex Di β θ S γ Ṁ ρ bulk D 2 i √ gL δ 4S lif t πD 2 i ρ bulk ρ tapped ζ L Di η ( 10
)
Note that the model parameters were not only determined using the hold-up measurements from this hydrodynamic study; the hold-up measurements obtained while performing experiments at hot temperatures with sand were also used [START_REF] Bongo Njeng | Evaluation of the wall-to-solids and wall-to-gas heat transfer coefficients in flighted rotary kilns: Lumped system analysis[END_REF], as illustrated in Figure 9b. The model parameters were defined within narrower confidence intervals, and good agreements were found between the calculated and experimental filling degree. To obtain the filling degree, the variable parameters must be filled using SI units; the model directly produces a percentage. Note that the value of the parameter η is fixed to 0, since no fitting value was found in the literature that was defined with sufficient accuracy for the length-to-diameter ratio.

D

The proposed model for the axial dispersion coefficient is given in Eq.11. The materials physical properties have been reported to significantly affect the axial dispersion coefficient. They are represented in the given model by the Hausner ratio, as well as a ratio of the particle equivalent size to the kiln diameter. The model parameters are determined within reasonable confidence intervals as given in Table 3.

D = k D 2 i gL N 2 Di g α dp Di β (S) γ Ṁ ρ bulk D 2 i √ gL δ 4S lif t πD 2 i ρ bulk ρ tapped ζ L Di η (11)
Figure 9c shows that all experimental data do not agree well with the predicted value within the ±20% margins. However, as shown later on, these predictions are mostly within the experimental uncertainty which is about 30%. Except scarce cases in particular for beech chips, the experimental data obtained without internal fixture are not well predicted by the model, certainly because of a bed flowing in the slipping mode. Note that η is fixed to 0. Therefore the effect of the length-to-diameter ratio is taken into account within the value of the model parameter k.

Analysis of particle segregation

Segregation is a property of dry granular solids, which tend to separate spatially by size, shape or density under varying flow conditions [START_REF] Cantelaube | Kinetics of segregation of granular media in a two-dimensional rotating drum[END_REF][START_REF] Khan | Subdiffusive axial transport of granular materials in a long drum mixer[END_REF]. This phenomenon has been observed in industrial processing involving granular materials, and it has been widely studied within rotating drums.

In this study, there are a few elements that may indicate possible phenomena of segregation. Firstly, the wide size distribution of beech chips, as illustrated in Figure 2, indeed implies not only larger or smaller particles but also heavier and lighter particles. Generally, the larger the chip size, the heavier the chip weight. Secondly, while analyzing the beech chips RTD curves, an extended tail can be observed due to small peaks of tracer concentration, implying a possible higher concentration due to particle segregation.

Bensmann et al. [START_REF] Bensmann | Residence Time Distribution of Segregating Sand Particles in a Rotary Drum[END_REF] has been able to investigate the particle segregation through tracer experiments using several fractions of tracers particles. With such a straightforward approach, the effects of segregation can be easily observed and analyzed. However as previously demonstrated by Colin et al. [START_REF] Colin | Wood chips flow in a rotary kiln: experiments and modeling[END_REF] such experiments are not mandatory. Instead, a tracer of wide distribution size (see Figure 2) can be used to achieve this purpose.

As stated before, while analyzing the samples collected after the tracer injection, the number of tracer particles contained in each sample was determined. From the number of tracer particles collected and their weight, an average particle weight can be determined and is used for the analysis of particle segregation. The present analysis is therefore less in terms of particle size and more in terms of particle weight, due to the direct relationship. Note that there have been good tracer mass recoveries as follows, for NL experiments 99.5% ± 0.5, for G experiments 99.4% ± 0.7, for 3SL experiments 99.3% ± 0.6 and for 6SL experiment 99.9±0.6%. A more detailed look in Figure 10 demonstrates that when varying only one operating condition and keeping the other constant, the obtained weight distribution differed primarily in function of the filling degree as highlighted by Colin et al. [START_REF] Colin | Wood chips flow in a rotary kiln: experiments and modeling[END_REF]. Secondly it is also observed that the tracer average weight distribution varies depending on presence and type of internal fixtures.

In Figures 10a, b andc, where there is no internal fixtures, there is no significant effect of segregation at low filling degree (below 8%): distributions are more centered, with a tracer weight remaining nearly constant in spite of few lighter and heavier particles respectively at lower and larger residence times. Whereas at higher filling degree, the tracer average weight distribution is more dispersed and the heavier particles tend to have significantly lower residence time compared to lighter particles. This can be explained by the differing mode of motion observed at lower and higher filling degree, respectively, slipping motion and rolling motion. From the literature [START_REF] Cantelaube | Kinetics of segregation of granular media in a two-dimensional rotating drum[END_REF], it is well known that especially in the rolling motion, radial segregation may appear very quickly, causing concentration of smaller particles toward the core of the bed, while larger particles may roll in the active layer following the incline at the bed surface. Knowing that the axial transport is highly promoted by the continuous flow at the bed surface, this may explain the preceding observations.

When a grid is used as shown in Figures 10d, e andf, the tracer average weight decreases slowly with time, implying higher concentration of heavier particles at low residence time and higher concentration of lighter particles at high residence time as previously observed in case of rolling motion. It seems that the grid tends in a way to homogenize the bulk of particles. That homogenization can also be observed when using 3SL or 6SL.

In both latter cases, except at higher residence times, the weight distribution is not widespread, and there is no more a decrease in the tracer average weight. These observations may be related with Grajales et al. [START_REF] Grajales | Mixing and motion of rice particles in a rotating drum[END_REF] statements implying that straight lifters do not affect the flow regimes of the kilning bed but only reduce the area of the central core in the rolling motion. Hence, the concentration of small particles in the core at the bed center is reduced, and the small particles are allowed to flow with the bigger particles in the active layer. This reduces the time of residence of smaller particles, therefore lowering the tracer average weight at lower residence times, and by scarcity effect (of lighter particles) automatically increases the tracer average weight at higher residence times, as shown in Figures 10g,h and i when using 3SL, and in Figures 10j,k and l when using 6SL.

However, the presence of heavier particles at higher residence time can be possibly due to effect of axial segregation [START_REF] Khan | Subdiffusive axial transport of granular materials in a long drum mixer[END_REF], which unlike radial segregation is reported to develop after hundreds of kiln rotations. Therefore the axial segregation, happening after radial segregation, splits the existing core into periodic axial band along the kiln axis. This may also explained in some cases the extensive presence of heavier particles at higher residence time.

Reproducibility of experiments

Reproducibility of the experimental results was investigated through replicates of some runs. Table 4 shows the experimental hold-up, mean residence time, variance of residence time, Peclet number and axial dispersion coefficient determined. Figure 11 illustrates the reproducibility of the segregation of particles. Both Table 4 and Figure 11 gather the results of the replicates of some runs carried out at selected benchmark values for the operating conditions, when the kiln was equipped with 3 and 6 rows of straight lifters, and without internal fixture.

In Table 4, the given values of the relative uncertainty for the hold up and MRT are lower than 6%, implying very good reproducibility of these two flow characteristics. The reported relative uncertainties for the VRT, Pe and D are higher, reaching 30% at maximum. For decision making in industry, even if these uncertainties are relatively high, they are sufficiently low to consider the experimental values as consistent. Note that the relative uncertainties derived from the replicates are determined at the 80% confidence level.

In Figure 11, the reproducibility of the experiments is very good in terms of uniform repartition of more and less dense tracer particles along the dimensionless time. This confirms also the reproducibility of RTD experiments as illustrated in Figure 4.

Conclusions

The flow characteristics of materials are significantly impacted by the internal fixtures. Therefore, in the design stage or for improvement purposes, the choice of lifters' configuration as well as their overall holding capacity, mostly dependent on the shape, must be carefully selected. The use of lifters increases the burden and the residence time of solid particles. They promote the mixing of particles as suggested by the increase of the axial dispersion coefficient. In regard to the flow of materials of wide size distribution, by their mixing effect, lifters reduce the segregation phenomena that may occur, causing different residence time for the different size fractions.

The flow characteristics of solids through flighted rotary kilns are also affected by the operating conditions as demonstrated by the experimental results:

-Increase in the mean residence time may result from a decrease of the rotational speed and slope of the kiln, but also to a lesser extent, from an increase in the mass flow rate of solids;

12

-The mass flow rate has a remarkable influence on the filling degree. As the flow rate is increased, or the kiln rotational speed and slope are decreased, the hold-up increased.

-The axial dispersion is increased with the kiln rotational speed and slope, but decreased with the mass flow rate. The higher the filling degree the smaller the axial dispersion.

Three models were developed for the prediction of the mean residence time, the filling degree, and the axial dispersion coefficient under steady-state conditions in inclined rotating kilns, whether equipped with lifters and exit dams or not, and operated in the rolling mode. These correlations consist of dimensionless factors accounting for (1) the basic operational parameters of the kiln, (2) the properties of the bulk solids, (3) the geometry of the kiln, (4) the overall lifters' holding capacity, (5) the height of exit dam. The model parameters, namely k, α, β, . . . , ζ as given in Table 3, have been determined from experimental data of the flow of sand, broken rice and beech chips, at varying operational conditions and through different rotary kilns. The predictions and experimental data were in good agreement.

The segregation analysis made on the flow of beech chips revealed a possible effect of radial segregation.

However, it was found that the segregation was lessened in some operating conditions, in particular when using lifters, depending on the filling degree of solids within the kiln. The experimental matrix achieved and the experimental hold up, mean residence time, and variance of residence time, the fitted Peclet number, and resulting axial dispersion coefficient are resumed in Table 5. Fig. 9: Comparison of the experimental MRT, HU[%] and D, while using sand (left), broken rice (middle), and beech chips (right), with the calculated values from Eq.9 using the sets of parameters given in l) 6SL -2˚C -3 rpm M=2.5 kg/h , f= 5.1% M=5.0 kg/h , f= 11.5% M=7.5 kg/h , f= 16.8% Fig. 10: Influence of operating parameters N (a-d-g-j), S (b-e-h-k) and Ṁ (c-f-i-l) on the tracer average weight (function of dimensionless time) for the flow of beech chips, when the kiln is equipped with: NL (1st row), G (2nd row), 3SL (3rd row) and 6SL (4th row). The dimensionless time is defined as θ = t/ t and so the red lines represent the time when t = t.

Figures

Figure 10

 10 Figure10presents the (dimensionless) time variations of the average tracer weight for a variety of operating conditions when using a grid, 3SL, 6SL and no internal fixtures. A first preliminary general observation concerns the unbalanced distribution of tracer around the mean residence time symbolized by the red line, which furthers understanding of the presence of an extended tail on the RTD curves. It is also observed that the average weight of tracer particles is mainly between 20 and 30 mg. Out of this interval the particles can be considered lighter or heavier and by extension smaller or larger. Assuming a beech chip of parallelepiped shape, about 10 mm × 4.5 mm × 2 mm, and a density of 279 kg.m -3 , the particle weight is about 25.1 mg.

5 . 1 .

 51 Experimental Results: HU, MRT, VRT, Pe, D

  (a) Grid, 16 rows. (b) Lifter structure and configurations: 3 rows of SL (left side) and 6 rows of SL (right side).

Fig. 1 :Fig. 2 :

 12 Fig. 1: Kiln internal fixtures: a) lifter structure and b) grid.

Fitted

Fig. 3 :Fig. 4 :

 34 Fig. 3: Comparison of experimental/theoretical and fitted values of the axial dispersion model parameters, i.e MRT, Pe, and resulting D. Solids lines are ±20% margins.

Fig. 5 :

 5 Fig. 5: Lifters hold-up for three configurations, from left to right side: 3SL, 6SL and 12SL.

Fig. 6 : 1 Fig. 7 :

 617 Fig.6: Influence of operating parameters (N, S and Ṁ) on the MRT, HU[%] and VRT, for the flow of beech chips, when the kiln is equipped without lifters, with a grid, or with 3 and 6 rows of straight lifters.

Fig. 8 :

 8 Fig.8: Influence of operating parameters (N, S and Ṁ) on the Pe and D, for the flow of beech chips, when the kiln is equipped with a grid, or with 3 and 6 rows of straight lifters.

Fig. 11 :

 11 Fig.11: Reproducibility of segregation of beech chips when the kiln is operated within the defined benchmark value for the operating parameter, and equipped with 3 or 6 rows of straight lifters or without lifters.

Table 3 .

 3 Solid lines are ±20% margins.

			a) NL -2˚C -5 kg.h -1		b) NL -3 rpm -5 kg.h -1		c) NL -2˚C -3 rpm
	Tracer av. weight [mg]	10 0 10 1 10 2	0.8	1 N=2 rpm, f= 12.4% 1.2 1.4 1.6 N=3 rpm, f= 7.7% N=6 rpm, f= 3.5%	10 0 10 1 10 2	0.8	1 S=1°C, f= 13.8% 1.2 1.4 1.6 S=2°C, f= 7.7% S=3°C, f= 5.1%	10 0 10 1 10 2	0.8	1 M=2.5 kg/h , f= 3.6% 1.2 1.4 1.6 M=5.0 kg/h , f= 7.7% M=7.5 kg/h , f= 12.4%
			d) G -2˚C -5 kg.h -1		e) G -3 rpm -5 kg.h -1		f) G -2˚C -3 rpm
	Tracer av. weight [mg]	10 10 2 1 10 0	0.8	1 N=2 rpm, f= 14.5% 1.2 1.4 1.6 N=3 rpm, f= 9.6% N=6 rpm, f= 4.8%	10 10 2 1 10 0	0.8	1 S=1°C, f= 16.9% 1.2 1.4 1.6 S=2°C, f= 9.6% S=3°C, f= 6.5%	10 10 2 1 10 0	0.8	M=2.5 kg/h , f= 4.7% M=5.0 kg/h , f= 9.6% 1 1.2 1.4 1.6 M=7.5 kg/h , f= 14.4%
			g) 3SL -2˚C -5 kg.h -1		h) 3SL -3 rpm -5 kg.h -1		i) 3SL -2˚C -3 rpm
	Tracer av. weight [mg]	10 10 10 0 1 2	0.8	1 N=2 rpm, f= 17.1% 1.2 1.4 1.6 N=3 rpm, f= 11.2% N=6 rpm, f= 5.2%	10 10 10 0 1 2	0.8	1 S=1°C, f= 22.4% 1.2 1.4 1.6 S=2°C, f= 11.2% S=3°C, f= 8.3%	10 10 10 0 1 2	0.8	M=2.5 kg/h , f= 5.1% M=5.0 kg/h , f= 11.2% 1 1.2 1.4 1.6 M=7.5 kg/h , f= 17.0%
			j) 6SL -2˚C -5 kg.h -1		k) 6SL -3 rpm -5 kg.h -1
	Tracer av. weight [mg]	10 0 10 1 10 2	0.8	1 N=2 rpm, f= 17.0% 1.2 1.4 1.6 N=3 rpm, f= 11.5% N=6 rpm, f= 5.6%	10 0 10 1 10 2	0.8	1 S=1°C, f= 20.9% 1.2 1.4 1.6 S=2°C, f= 11.5% S=3°C, f= 8.3%	10 0 10 1 10 2	0.8	1	1.2	1.4 1.6
				θ [-]			θ [-]			θ [-]

Table 5 :

 5 Results of the experimental matrix set for the RTD measurements.

		D	[m 2 /s]	0.1801	0.1549	0.0974
		Pe	[-]	318.3	394	394.3
	6SL	σ 2	[min²]	18.19	18.46	36.48
		t	[min]	51.78	48.81	77.26	24.76
		HU	[kg]	4.345	4.145	6.440	2.135
		D	[m 2 /s]	0.1745	0.1591	0.1095	0.3109
		Pe	[-]	349.6	377.8	344.8	418.8
	3SL	σ 2	[min²]	16.42	18.50	52.91	2.70
		t	[min]	49.06	49.84	79.56	22.71
		HU	[kg]	4.235	4.105	6.470	1.985
		D	[m 2 /s]	0.1258	-	0.0805	0.315
		Pe	[-]	541.4	-	557.5	437.5
	Grid	σ 2	[min²]	7.49	-	23.30	2.19
		t	[min]	43.54	-	66.52	21.47
		HU	[kg]	3.615	-	5.490	1.805
		D	[m 2 /s]	0.0484	0.0582	0.0853	0.0728
		Pe	[-]	1728	1467	590	2629
	NL	σ 2	[min²]	1.81	2.38	18.77	0.18
		t	[min]	35.20	34.64	59.07	15.34
		HU	[kg]	2.920	2.785	4.690	1.310
			]
	Operating conditions	N S Ṁ	[rpm] [°] [kg.h -1	3 2 5	3 2 5	2 2 5	6 2 5

List of symbols 7. Tables 471 Table 1: Geometrical characteristics of the rotary kiln and order of magnitude of operating conditions achieved in this study.

Subsets