Convective heat transfer analysis in aggregates rotary drum reactor

Applied Thermal Engineering 54 (2013) 131e139

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Convective heat transfer analysis in aggregates rotary drum reactor Laurédan Le Guen, Florian Huchet*, Jean Dumoulin, Yvan Baudru, Philippe Tamagny Univ. Nantes, LUNAM, IFSTTAR, Route de Bouaye, BP 4120, 44341 Bouguenais Cedex, France

h i g h l i g h t s < A thermal and flow experimentation is performed on a large-scale rotary drum. < Four working points is chosen in the frame of asphalt materials production. < Evaluation of the convective transfer mechanisms is calculated by inverse method. < The drying stage is performed in the combustion area. < Wall/aggregates heat exchanges have a major contribution in the heating stage.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 3 September 2012 Accepted 15 January 2013 Available online 9 February 2013

Heat transport characterisation inside rotary drum dryer has a considerable importance linked to many industrial applications. The present paper deals with the heat transfer analysis from experimental apparatus installed in a large-scale rotary drum reactor applied to the asphalt materials production. The equipment including in-situ thermal probes and external visualization by mean of infrared thermography gives rise to the longitudinal evaluation of inner and external temperatures. The assessment of the heat transfer coefficients by an inverse methodology is resolved in order to accomplish a fin analysis of the convective mechanism inside baffled (or flights) rotary drum. The results are discussed and compared with major results of the literature. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: Flighted rotary drum Cascading dryer Asphalt plant Hot-mix asphalt Materials processing

1. Introduction Rotary kiln process is one of the most current industrial stages applied to many products of chemical, food and materials industry including mineral, metallurgical or waste processing. The capability to treat large amount of materials makes the rotary drum as a convenient gas/solid reactor with intensive heat and mass transfer. The rotary kiln can operate by external heating in the case of organic matter treatment [1], or by internal heating for mineral materials processing. Usually, this latter is designed as a classical furnace where a burner is located at the inlet in order to release sufficient energy for heat treatment. The drying process consists in extracting the moisture content of these materials involving many technologies (atomization, flash dryer, fluidized bed) used in many important manufacturing sectors (minerals, polymers, paper). For road industry, the rotary drum dryer is the most appropriated

* Corresponding author. Tel.: þ33 2 40 84 57 75. E-mail address: fl[email protected] (F. Huchet). 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.01.025

continuous process in order to reach high aggregates feed rate, and to accomplish successive operations of drying, heating, mixing and coating with bitumen binder for asphalt concrete production. Academic problem persists in tumbler such as the prediction of particle motion [2] including effect of cohesion, the heat and mass transfer rates [3], and the global internal heat exchanges. These phenomena are crucial in order to enhance heat and mass transfer and globally improve the performance of the rotary drum dryer. Important points were focused upon the interfacial heat transfer phenomena inside particulates rotary kiln. Thammavong et al. [4] described the many experimental results existing in the literature dedicated to the evaluation of the gas/wall transfer coefficient, hgw, and the solid/wall transfer, hsw. Based on the penetration model, many equations have been identified in order to predict solid/wall transfer coefficient in rotary kiln in laboratory tumbler with sand materials. Wes et al. [5] were the first to introduce a semi-empirical equation from a large amount of data. Schlunder [6] introduces the thickness film gas, c, to the penetration modelling in order to determine precisely heat transfer through fluidized and porous media. Recently, these approaches have been studied and

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experimentally compared by Herz et al. [7], from several model of the literature [5,8,9]. Presented in Table 1, it appears that the model of Wes et al. (1976) [5] is compatible at low rotational speed (n < 6 rpm) while model of Tscheng and Watkinson (1979) [8] is more appropriated at upper rotational speed. The specific experimental conditions applied to the rotary drum of asphalt plants deserve to reconsider the literature for this kind of application. 2. Hot-mix asphalt reactor: position of the problem The process consists of mixing mineral aggregates, of mass fraction generally equal to 0.95, and bitumen binder, of mass fraction equal to 0.05, to produce the asphalt mix, which is also called “asphalt concrete”. However, the aggregates must be dried and heated prior to mixing in order to obtain satisfactory fluidity (workability) of the concrete. The rotary drum dryer including Lbaffle, features a long rotating cylindrical shell slightly inclined to the horizontal, is the most popular equipment in the asphalt industry. In a direct heat rotary dryer, hot gases are supplied by a burner operating in turbulent flow regime through the dryer. These hot combustion gases in turn provide the heat required for vaporization of the water and heating of the aggregates. At the end of the drying and heating steps, the aggregates are in an appropriate condition to be successfully mixed with bitumen until reaching a temperature of asphalt concrete roughly equal to 440 K. To the best of our knowledge, except few numerical works based on a global analysis [10] or a CFD tool [11], very few previous studies [12] have treated of the heat transfer analysis inside large-scale rotary drum dryer. Despite the size difference between particles and aggregates, the work of Leguen et al. [13] show that the granular mixing in the bulk flow (see Fig. 1) appears similar than particulates laboratory tumbler of the literature [14]. Fernandes et al. [12] used a simplified drying model from an overall coefficient of heat transfer proposed by Miller et al. [15]. Results of this model conduce to a deviation corresponding to 20% compared to the experimental measurements. A better estimation of the heat transfer coefficients would improve this type of drying model. The present paper proposes to apply an experimental methodology in order to assess the local heat transfer coefficients in largescale rotary drum dryer during hot-mix asphalt production. Mass flow rates, aggregates/gases temperatures measurements and humidity contents of the aggregates are simultaneously acquired along the tumbler. The external temperature is measured by infrared thermography that is recognized as a promising technique in the non-destructive thermal analysis [16,17]. A physical model based on the heat balance is solved through the wall in order to reach the heat transfer coefficients inside the aggregates rotary drum reactor. This approach is made possible since the thickness of the stainless steel (e ¼ 8 mm) is thin enough, satisfying a lumped system analysis, and so the criteria based on the Biot number (Bi ¼ h.e/l << 1).

Wes et al. (1976) [5] Tcheng and Watkinson (1979) [8]

Heat transfer coefficient hsw

Validity domain Particles diameter dp

dS ¼ 2p$ri $dz

(1)

It can be written according to the following budget:

d4int ¼ d4cond ¼ d4sh

(2)

B d4int corresponds to the heat transfer between the multiphases system (including aggregates and freeboard gases) and the inner wall according to the following expression:


d4int ¼ hi $ Tiw  Tg $dS

B d4cond corresponds to the heat transfer in the thickness of the drum dominated by the axial conductive transfer according to the following expression:

d4cond ¼

l$ðTew  Tiw Þ ln ðre =ri Þ

$dS

(4)

where l is the thermal conductivity of the steel shell, ri, the internal radius, re, the external radius and Tew the external wall temperature of the rotary drum. B d4sh corresponds to the heat loss of the wall, given by the following expression:

  4 d4sh ¼ Phe $ðTe  Tew Þ$re þ εsh $s$ Te4  Tew R$dS

(5)

with he, the external transfer coefficient of the rotary drum, Te the ambient temperature and εsh the emissivity of the shell. The external transfer coefficient exerted upon the circumferential length of the drum, Lc, is calculated by a correlation of Kays cited by Labraga and Berkah [18] and given by:

Nu ¼

he $Lc

l

 1=3 ¼ 0:135$ 0:5$Re2w þ Re2N þ Gr

(6)

with Reu ¼ u$r2 =na , with u, the angular velocity of the drum, and na, the kinematics viscosity of the ambient air. The heat balance conservation through the shell, (1) ¼ (3) and (2) ¼ (1), leads to the elimination of the unknown, Tiw, to form a fourth degree polynomial such as: 4 a$Tew þ b$Tew þ c ¼ 0

a ¼ ε$s$A$ð1 þ hi $BÞ

Assumptions

137 < dp (mm) 3.5 < u (rpm) < 6 hsw ¼ 2kb(2n/ab40)0.5 Nu ¼ 22Pe0.5 < 1260 2 0.3 3.5 < u (rpm) < 10 hsw ¼ 11.6kb(nR /ab40) /lw Nu ¼ 11.6Pe0.3

(3)

with hi, the heat transfer coefficient of the particulates system. Tiw and Tg being respectively the inner wall temperature and the gases measured temperature.

with:

Table 1 Wall to solid heat transfer coefficient used in rotary kiln. Author

Fig. 2 presents the physical model corresponding to the assessment of convective transfer coefficient inner the drum. Its evaluation is calculated from the heat balance in an elementary surface, dS, of length dz of the drum and equal to:

b ¼ he $A þ hi $B þ he $hi $A$B   c ¼ ð1 þ hi $BÞ$  he $A$Te  ε$s$A$Te4  hi $B$Ti and

(7)

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133

Fig. 1. Solid cascading inside rotary drum dryer. Left [16] e Right: [17].

ln ðre =ri Þ ln ðre =ri Þ A ¼ re $ ; B ¼ ri $

l

average fraction of the wall covered by the aggregates clusters and can be determined by the following expression:

l

The algorithm of assessment of hi is based on the resolution of Eq. (7) by the FerrarieCardan polynomial method leading to the evaluation of Tew. Compared to the experimental value, TewIR, measured by infrared camera, the best evaluation of hi corresponds to the minimization of a cost function, f, given by:

f ¼ ½Tew ðhi Þ  TewIR 2

(8)

As mentioned above, global internal heat exchange is composed by two heat transfer mechanisms. In the studied case, d4int couples the gas/wall transfer and the solid/wall transfer as represented in Fig. 3. The ratio of each transfer depends on each exchange area and can be interpreted in the same way than the renewal model applied to the fluidized beds [19] under certain consideration linked to the size of the particles and suspension density [20]. Spread out to the aggregates rotary drum, the convective mechanisms are alternatively dominated by aggregates cluster where friction phenomena are predominant and then by a convective transfer type between the gases and the wall satisfying an undeveloped hydrodynamics boundary layer. If the heat exchanges between the wall and the aggregates cluster located in the baffle are neglected, d4int can be expressed by the following expression:


dfint ¼ Pa$hsw $ðTiw  Ts Þ þ ð2$p  aÞ$hgw $ Tg  Tiw R$dS

(9)

where a is the angle defining the granular bed width (see Fig. 2). This parameter, classically defined by the angle of repose, is also the

d

sh

a  sin a ¼

8 ð1  aCT Þ$ma $rapp $ va D2

with ma the granular mass flow rate, (1  aCT) the ratio of granular particles in the bed determined experimentally, rapp the apparent density of the granular bed due to the flights mixing, and va the axial aggregates velocity in the drum. If we assume that aggregates/wall transfer obeyed to a known semi-empirical correlation as those presented in Table 1, consequently, hgw can be expressed by:

hgw ¼

  1 Ts  Tiw $ 2$p$hi  a$hsw $ Tg  Tiw 2$p  a

d

cond

int

he

α

hi

(11)

3. Experimental set-up 3.1. Temperature measurements An industrial mix asphalt processing unit (TSM XL-17) has been monitored. Fig. 4 presents the dimension of the drum, the position of the temperature capture for the characterization of the aggregates and the gases during the manufacturing process. Four areas can be distinguished. The combustion zone (A-A), 3 m of length, corresponding to the flame area provided by a burner (Oertli e MIBSM452N-VL450) working with natural gas that

T exterior

inboard

d

(10)

Ti Tiw

e= (ri-re) (Thickness of the drum)

Tew Te 0

ri

ω=11 rpm Fig. 2. Heat transfer through the rotary drum dryer.

re

r

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Aggregates/gases flows along a wall

Wall Cluster of aggregates Near-wall region dominated by friction phenomenon with aggregates clusters

Near-wall region dominated by convective gases flow in non established regime

Fig. 3. Mechanistic model of the aggregates cluster and gases contact with the wall.

releases the heat required for the drying and the heating of the aggregates. One is 1.7 m of diameter and contains fourteen L-baffle in order to mix the aggregates and increase the heat exchange between hot gases and particles (B-B). The other insulated recycled ring, with a 1.3 m diameter, is situated at the middle part of the drum (C-C) corresponding to the introduction of recycled aggregates. In our experiments, no recycled aggregate has been added. The last area (D-D) corresponds to the mixing between the injected bitumen upon the heated aggregates in order to ensure proper coating.

Among the temperature capture, we used seven temperature probes, located on a rod and implemented in the longitudinal axis along the drum in order to measure gases temperature, Tg. As reported in Fig. 5, the probes support is located within the drum. The temperature sensors are protected against granular flow by means of a steel semi-shell; they were insulated from the support in order to avoid heat transfer conduction. K-thermocouples were chosen due to a temperature range varying between 400 K and 1500 K. The aggregates temperature, Ta, has been measured by four inner wall probes (Taiw) inserted within the drum during stop of the manufacturing. Two others flaps (Taf) have been machined in order to capture several samples of aggregates so that they can measure respectively their temperature and their humidity. Several parameters are monitored at the same time including solid feed rate, initial aggregates moisture content, gases temperature and wall temperature (Fig. 6). The wall temperature, TewIR, was monitored by two infrared camera. The FLIR A320 being necessary for a large-scale view and the FLIR E30 has been used at each position corresponding to the in-situ thermal probes and for the aggregates samples picking up at the opening flap. 3.2. Flow rates balance Furthermore, the heat transfer characterization requires studying its mass balance and the flow regime. The specific geometry of the rotary furnace gives rise to a particular distribution of gases mass flow rate since the equipment is a balanced draft system in

Fig. 4. Sketch of the aggregates rotary drum dryer.

L. Le Guen et al. / Applied Thermal Engineering 54 (2013) 131e139

135

Fig. 5. In-situ thermal probes.

order to maintain the internal pressure below the atmospheric pressure in order to avoid leakage. Consequently, the flaps located at the inlet for aggregates feed up and at the middle of the drum for the reclaimed asphalt pavement ring, become inlets for the air ambient, leading to refresh the particulates system flowing into the drum. The gases velocities are measured from several Pitot systems at three locations of the drum in order to establish the mass flow rates qout, q2 and q3 (Fig. 7). The combustion gases issued from the burner, q1, are calculated from the measured mass flow rate of the natural gas considering a complete combustion with an excess air equal to 4%. Its variation depends on the experimental conditions. Thus, the mass balance is established according to the following relationship:

The second and the third experiments are distinguished according to their difference of average humidity of the aggregates at constant solid feed rate roughly equal to 110 T h1. The four application cases studied are detailed in Table 2.

qout ¼ q1 þ q2 þ q3

The gases velocities are measured at three locations into the drum, providing an estimation of the flow rate distribution for each production (Fig. 9). The air mass flow rate caused by the aggregates inlet, q2, represents a ratio equal to 4% of the whole gases mass flow rate in the reactor. The air mass flow rate caused by the recycled asphalt pavement ring is substantial. Its ratio is equal to 62% of the whole gases mass flow rate. This additional mass flow rate induces aerothermal modifications. The gas/wall transfer coefficient depends on the gases flow rate in the rotary dryer. The analysis of the flow regime (Fig. 10) is carried out from the calculation of the Reynolds number, based on the drum diameter, DT, and the measured gases velocity and given by:

(12)

with q2 the air mass flow rate caused by the aggregates inlet, and q3 the air mass flow rate caused by the flap of the reclaimed asphalt pavement ring. 3.3. Asphalt concrete formulation and processing The formulation of the asphalt concrete is governed by the origin and the amount of aggregates. Fig. 8 shows the characteristics of the materials and the thermal fields of a sample picked during the experimental campaign. The heterogeneity of the measured temperature is noticeable into the sample. Four experimental conditions have been chosen from two mains manufacturing parameters including the solid feed rate and the humidity average of the aggregates. They play a crucial role on the heat provided by the burner at the inlet. The first and the fourth experiments are distinguished according to their solid feed rate corresponding respectively to 93.89 T h1 (either 25.67 kg s1) and 124.3 T h1 (either 33.98 kg s1) at constant aggregates humidity.

4. Results and discussion The results are divided in three subsections including the flow regime analysis, the thermal results and finally the assessment of the convective heat transfer inside the rotary drum reactor. 4.1. Flow regime analysis

Re ¼

U$DT

na

(13)

with na the kinematic viscosity of the gases depending on the measured temperature. The calculation of U is based on the gas density by means of its volume flow rate.

Fig. 6. Large-scale view of the rotary drum with the infrared caméra FLIR A320.

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Gas outlet chimney

Induced draught fan Natural gas supply

qout Burner

qout

q3

q1

bitumen

q2

Outlet flag for hot mix asphalt concrete

Flag for aggregates inlet Introduction of reclaimed asphalt pavement Fig. 7. Distribution of the flow rates.

The evolution of the mass flow rate and the gases velocity into the rotary drum dryer is distinguished by two areas, separated by the reclaimed asphalt pavement ring flap at z ¼ 5.5 m. In the first area and for all the production, the velocity decreases from 6 m s1 to 3.5 m s1 due to the diminution of the gas density caused by a fall of its temperature. After the reclaimed asphalt pavement ring, the gas velocity grows up to a value equal to 8.5 m s1 because of the ambient air infiltration across the flag. Thereby, the Reynolds number varies from 80,000 to 450,000. This range of value corresponds to a turbulent flow regime into the drum, satisfying a homogenization of the gas flow in the transversal section of the drum. 4.2. Temperature and moisture contents Fig. 11 presents the temperature profiles of the gases, the aggregates and the external wall along the rotary drum dryer. The aggregates humidity has been measured afterward, weighted at each position corresponding to the opening flap. In the four cases, the humidity is evaporated at the position z ¼ 4.1 m. Thus, the drying is located in the combustion area where the aggregates are instantaneously heated by the flame front governed by radiation and convection phenomena. Whatever the studied case, the gases temperature decrease sharply in the longitudinal axis from z ¼ 3.86 m to z ¼ 4.86 m, the temperature varying, according to the production, between 1050 K until about 800 K. A large diminution is noticed at the insulated

Origin of the aggregates

Formulation

Filler (<90 µm)

0.94%

Sand rolled Loire (0.2/4 mm)

25.40 %

Aggregates from Noubleau (2/6.3 mm)

43.27%

Crushed Sand (0/2mm)

24.46 %

recycled ring (z ¼ 5.36 m) where the temperature falls down to 500 K. The infiltration of fresh air due to the opening flap is responsible of this diminution. Aggregates temperature increases from the ambient temperature (Ta z300 K) at the inlet of the drum to a value close to Ta ¼ 430 K from z ¼ 4 m. Besides, the aggregates are almost in proper condition to be mixed with hot bitumen. The external wall temperature measured at all position, except for the insulated area, varied in the temperature range between TewIR ¼ 485 K and TewIR ¼ 422 K according to the studied case. Finally, these curves show that the drying is performed in the first part of the drum (until about z ¼ 3.5 m) where radiation and convective mechanisms issue from the flame provided the necessary heat for evaporation. Between z ¼ 3 m and z ¼ 5 m, the aggregates mixing with L-baffle are subjected to forced convective phenomena inside the gases flow but also granular conduction and convection in the bed as reported by the literature.

Table 2 Experimental process conditions. Studied case

1

2

3

4

Solid feed rate (kg s1) Angle of repose, a (rad) Humidity contents into the aggregates (%) Supplied energy (MJ kg1)

25.67 1.906 1.56 0.213

29.55 2.021 3.06 0.215

30.79 2.041 1.54 0.194

33.98 2.121 1.57 0.197

Fig. 8. Left: origin of the aggregates e Right: infrared analysis of a sample (FLIR E30).

L. Le Guen et al. / Applied Thermal Engineering 54 (2013) 131e139

137

Mass gas flow rate (Nm3.h-1)

35,000 qout = 22,902 Nm3.h-1

qout = 25,751 Nm3.h-1

qout = 25,984 Nm3.h-1

qout = 28,127 Nm3.h-1

30,000 25,000

q1

20,000

q2

15,000

q3

10,000 5,000 0

1

3

2

4

Experimental conditions

500,000

12

400,000

10 8

300,000 6 200,000

Experimental conditions 1 : circle ; 2 : triangle 3 : diamond ; 4 : square

100,000

4 2

0

U (m/s) / Empty symbol

Re/ Full symbol

Fig. 9. Flow rates distribution for each studied case.

0 3

4

5

6

7

8

9

The curves exhibit an inflection point for the minimal value of f corresponding to the true value of hi. The results are very sensitive to the lesser modification of the physical modelling of the heat transfer. The increase of hi coincides with the increase of z. This trend is insufficient to make any conclusion upon the transfer phenomena including gas/wall transfer and solid/wall transfer. 4.3.2. Convective transfer coefficients analysis Based on existing data and correlation of literature, the present results can be mainly compared with two types of correlation:

z (m)

- In first approximation, one is based on the penetration theory where the solid to wall transfer coefficient, hsw can be expressed under certain assumption, to the more representative existent relationship which is the correlation of Tscheng and Watkinson [8] mentioned in Table 1, - gas/wall transfer, hgw, must be taken into account with existing correlations such as a turbulent flow for non-established tube tired of McAdams [21]:

Fig. 10. Reynolds number and gases velocities measured in the aggregates rotary drum dryer.

Above z ¼ 6 m and in the studied case which do not take into account aggregates recycled manufacturing, the temperature mixture is ideal for the mixing with bitumen. 4.3. Experimental evaluation of the heat transfer coefficient

l

This experimental evaluation of heat transfer coefficient is performed according to the method mentioned in Section 2. The gas-to-wall transfer, hgw, is deduced from the transfer coefficient, hi, which is obtained by minimisation of Eq. (8). The comparison between the present results and the literature is carried out. 4.3.1. Internal heat transfer coefficient Fig. 12 presents an example of the calculation of f and hi obtained in the first studied case.

1

hgw ¼ $0:023$Pr3 $Re0:8 L

(14)

For each infrared measurement location, hgw, the gas-to-wall transfer coefficient is obtained from Eq. (11). Fig. 13 is aimed to compare the present results with the existing correlation. In the heating part of the drum corresponding to a dry granular flow (3.85 < z(m) < 4.86), the values of the gas/solid heat transfer coefficients are obtained in an intermediate range between a pure solid/wall transfer and a heat transfer corresponding to a nonestablished turbulent flows in tube. The enhancement of the heat

1,200 1,100 1,000

Experimental conditions :

900

1:

T (K)

800

Empty symbol : gases Full symbol : external wall Grey symbols : aggregates

700

2: 3: 4:

600 500 400 300 200 0

1

2

3

4

5

6

7

8

z (m) Fig. 11. Experimental temperature profiles measured for several hot-mix asphalt production.

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L. Le Guen et al. / Applied Thermal Engineering 54 (2013) 131e139

100,000 10,000 1,000 z=3.86 m

100

z=4.36 m z=4.86 m

1.00

z=5.86 m z=6.86 m

f

10

0.10

z=7.86 m

0.01 0

20

40

60 -2

80

100

120

-1

hi (W.m .K ) Fig. 12. Minimization curves calculated at the temperatures probes location for the first studied case [asphalt concrete production: 25.67 kg s1].

h (W.m-2.K-1)

300 250

Experimental conditions 1 : circle ; 2 : triangle 3 : diamond ; 4 : square

200

Empty symbol : h from McAdams (1954) Grey symbol : h calculated Full symbol : h

from Tscheng and Watkinson (1979)

150 100 50 0

3

4

5

6

7

8

9

z (m) Fig. 13. Comparison of hgw with existing correlations along the rotary drum.

exchange can be easily attributed to the hydrodynamics structures generated by the dispersed phase. The heat transfer coefficient increases after the open flap to reach at z ¼ 6.85 m a value equal to 60 W m2 K1 for Re ¼ 400,000. This value is very close to the solid/wall transfer coefficient. From z ¼ 6.86 m, the heat transfer coefficients increase sharply up to reach values close to 100 W m2 K1. Outlet effects such as bitumen injection for mixing and coating tend to ensure a cohesive granular flow where the heat transfers are enhanced. 5. Conclusion The experimental gases/wall (hgw) and aggregates/wall (hsw) transfer coefficients have been determined in large-scale aggregates rotary drum reactor during asphalt concrete production. The inner heat transfer coefficient is obtained by an inverse methodology from a large range of measured data. Among them, energy consumption, temperature profiles, humidity contents of aggregates and mass flow rates are recorded for four experimental conditions. A global analysis for a point of view of the process gives rise to the important results: - Whole of the aggregates is dried in the combustion chamber where radiation and convection phenomena extract quasiinstantaneously the humidity content. - The flue gases show that the flap used for the reclaimed asphalt pavement gives rise to an infiltration into the drum. It corresponds to 62% of the total gases mass balance flowing through

the drum. The gases flow rate into the rotary drum is modified with a substantial increase of the Reynolds number from 80,000 to about 400,000. The gas/wall transfer coefficient values are ranged between 15 W m2 K1 and 60 W m2 K1 in the heating zone of the drum, located between the values derived from the McAdams [21] correlation and those derived from the Tscheng and Watkinson works [8]. This last correlation deserves to be verified by deeper experimental studies where particles diameter corresponds to the granular size of an aggregate (dp >> 1 mm). Thus, one can expect to a significant contact time between aggregates and wall that leads to reconsider the renewal theories from a friction law. Yet, the results of gas/wall heat transfer are reliable since they present a reasonable difference with a standard turbulent heat transfer in a tube. Finally, the aggregates-to-wall contact (aggregates in the bed and into the baffles) can be considered as an important convective transfer, similar to the gases-to-wall transfer. More investigations about convective mechanisms (aerothermal phenomena and aggregates-to-wall contact) are relevant to determine the wall thermal losses in order to design new equipments including power recovery for hot-mix asphalt processes. Acknowledgements The authors would like to express their thanks to Ermont-Fayat Group for the financial fund for the thermal rod instrumentation. The authors are grateful to the SEMR/CETE Normandie-Centre

L. Le Guen et al. / Applied Thermal Engineering 54 (2013) 131e139

department for the monitoring of the industrial mix asphalt processing unit. Appendix. Assessement of uncertainties The calculation of uncertainties is based on the measurements of the temperature carried out at the external wall by infrared thermography (DTew ¼ 2  C) and the temperature measured inside the drum (DTi ¼ 1%Ti). The relative errors on the heat transfer coefficient, hi, are estimated by:

Dhi hi

U0 ðTew  Ti Þ  1 1 DTew þ DT ¼ U U þ Tew  Ti i U þ Tew  Ti

with:

  4 þ he AðTe  Tew Þ U ¼ εsA Te4  Tew and: 3 U 0 ¼ 4εsATew  he A

The relative error on the heat transfer coefficient, hgw, is estimated by:

Dhgw hgw

¼

2pDhi þ ahsw DTi ðTs  Tiw Þ=ðTi  Tiw Þ2 DTi 2phi  ahsw DTi ðTs  Tiw Þ=ðTi  Tiw Þ

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