modeling of oxidation process of coal tar pitch in...

Research ArticleModeling of Oxidation Process of Coal Tar Pitch inRotating Kilns

Jun Xie1 Wenqi Zhong 1 Yingjuan Shao 1 and Kaixi Li2

1Key Laboratory of Energy ermal Conversion and Control of Ministry of Education School of Energy and EnvironmentSoutheast University Nanjing 210096 China2Institute of Coal Chemistry Chinese Academy of Sciences China

Correspondence should be addressed to Wenqi Zhong wqzhongseueducn

Received 17 May 2019 Accepted 23 June 2019 Published 7 July 2019

Guest Editor Xizhong An

Copyright copy 2019 Jun Xie et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this paper a three-dimensional numerical model has been developed to study the process of oxidative weight increment of coaltar pitch in a rotating kiln Based on the two-fluid method the gas phase is modeled by realizable k-120576 turbulent model and thesolid phase is modeled by kinetic theory of granular flow The dense gas-solid flow heat transfer and oxidation reaction for thebed and freeboard regions are simultaneously solved The model is applied to a rotating kiln with a cylinder of 075 m length and04 m diameter in the front and circular truncated cone on exit side The detailed verification of model is firstly performed bycomparisons with the available experimental data The particle velocity profiles product gas compositions and various forms ofsolid motion in rotary kilns are contrastively analyzed Afterwards simulations are carried out to obtain the primary hydrodynamicand reactive characteristics in the rotary kiln At the steady state the particle velocity peak is located at the active layer surface whilethe velocity has the opposite direction in the passive layer The bed region generally has a higher temperature than the freeboarddue to the large thermal capacity The concentrations of product gas compositions such as CO2 CO and CH4 and solid productof oxidation increase sharply near the surface and then keep on the steady values inside the bed The effects of rotational speed ofthe rotary kiln and flow rate of air are also studied The increasing rotational speed significantly accelerates the particle movementof the active layer and raises the final oxidative yield of coal pitch spheres By contrast increasing the flow rate of air has little effecton the particle motion and oxidation yield of coal pitch

1 Introduction

The spherical activated carbon has the unique morphologyhighwear resistance and good hydrodynamic characteristicswhich plays an important role in some special applicationssuch as air purification blood purification catalyst supportschemical protective clothing and others [1 2] Traditionalrawmaterials of activated carbon are mostly raw coal but thereducing quantity of high-rank coal needs to expand the newproduction materials

As a residue left by the distillation a lot of coal tarpitch is produced during coal tar processing The maincomponents include polycyclic aromatic hydrocarbons andtheir derivatives In recent years coal tar pitch attracts moreattention as a new rawmaterial of the production of sphericalactivated carbon due to its advantages of high carbon lowash and good plasticity [3]

The preparation of coal pitch-based spherical activatedcarbon consists of four processes pitch modulation pelletiz-ing oxidation stabilization and carbonization-activationOxidation stabilization is the core among the four processeswhich can be further categorized into four stages namelylight component pyrolysis preliminary oxidation oxida-tive weight increment and constant temperature oxidativeweightlessness respectively [4] Through dozens of hoursof low-temperature oxidation the unstable components incoal pitch are decomposed into small molecular gases orcondensed into stable macromolecules The softening pointis thereby improved to ensure that the sphere of coal tarpitch will not melt and deform during the subsequentcarbonization-activation process [5] The oxidation stabi-lization process consumes a lot of time and energy anddramatically impacts the capability of products thus it iscritical to choose the appropriate manufacturing technology

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 1953156 21 pageshttpsdoiorg10115520191953156

2 Mathematical Problems in Engineering

Rotary kilns are widely applied in modern industry suchas cement metallurgy chemicals and energy field due totheir good mixing performance high heat transfer efficiencyand large handling capacity [6 7] In addition the relativelylow particle motion velocity in rotary kilns results in thesmall collision force between particles and between particleand wall Considering the friability of pitch spheres and thedemand of high heat capacity in the oxidation process thefeatures of rotary kilns are very applicable for the oxidationstabilization of coal tar pitch spheres In the past decadesmodeling and numerical simulation have been used to pro-vide a detailed insight and quantitative guidelines for reactordesign and optimization However existing work for rotarykilns focuses on the flow field [7ndash9] mixingsegregation [10ndash13] and heat transfer performance [6 14 15] simulation ofchemical processes in a rotary kiln is still in its infancy dueto the complexity of coupling of dense gas-solid flow heattransfer and reactions [16] There are only few modelingresearches concerning the reacting flow for rotary kilnswhich can be categorized two typesThe first one is modelingthe motion and chemistry under steady condition and theother one is separately modeling the processes for bed regionand freeboard region respectively Montagnaro et al [17]presented a 15-dimensional (15D) model for oxy-pyrolysisof sewage sludge at the steady state in a rotary kiln Babler etal [18] developed a modular numerical model for biomasspyrolysis in a rotary kiln which considered the solid bedregion and gas phase domain at steady state Mujumdar andRanade [16] developed separate but coupled computationalmodels for bed and freeboard regions for rotary cementkiln The reactions in the bed region were modeled throughsingle-phase pseudo fluid and combustion of coal particlesin the freeboard region was modeled by Eulerian-Lagrangianapproach Du et al [19] studied the combustion of pulverizedcoal in the airflow of cement rotary kiln using Eulerian-Lagrangian method which belonged to the dilute particleflow During the chemistry of rotary kilns the reactionprocess is dynamic and complicated due to the dense particlesmotion gas turbulence and multicoupling between the gasand solid phases Therefore the simultaneous modeling ofdense gas-solid flow heat transfer and chemical reactionsfor the whole rotary kilns is of the pressing need at presentbut relevant researches have not been found in the availableliterature In addition the characteristics derived from the 2Dor quasi-3D cross section might not be applicable to the 3Dsystem due to the wall and geometry impacts on the flow fieldand reactive characteristics The real 3D modeling is criticalto acquire the complete information inside the rotary kiln

The present work develops a comprehensive 3Dmodel tostudy the key oxidation process oxidative weight incrementin a rotating kiln Based on the two-fluid method themodel simultaneously solves the dense gas-solidmotion heattransfer and chemical reaction for the entire regions of arotary kiln The rotary kiln has a cylinder of 075 m lengthand 04 m diameter in the front and circular truncated coneson exit side The detailed verification of model is firstlyperformed by comparisons with the available experimentaldata Afterwards the solid flow field profiles of velocityand temperature the concentrations of gas compositions

(O2 CO2 CO and CH4) and the oxidized coal pitchinside the rotary kiln are analyzed Finally the effects ofair flow rate and rotating speed of the rotary kiln on theprimary particle movement and reactive characteristics areemphatically studied

2 Model Descriptions

Based on the Eulerian-Eulerian (two-fluid) method andkinetic theory of granular flow the conservation equationsof continuity momentum energy and species are solvedfor gas and solid phases respectively In consideration ofthe particularity of gas-solid motion in rotary kilns the gasphase is modeled by realizable k-120576 turbulent model andJohnson and Jackson model is used for the frictional stressThegoverning equations are briefly presented in the followingsections the details of which can be found in literatures[20 21]

21 Governing Equations Themass equations of gas and solidphases are written as [21]

120597 (120572119892120588119892)120597119905 + nabla sdot (120572119892120588119892V119892) = 119878119892119904 (1)

120597 (120572119904120588119904)120597119905 + nabla sdot (120572119904120588119904V119904) = 119878119904119892 (2)

where 120572 120588 and V are the volume fraction density andvelocity vector respectively The mass source term S fromheterogeneous reactions is expressed as

119878119892119904 = 119872119888sum120574119888119903 = minus119878119904119892 (3)

whereM 120574 and r represent molecular weight stoichiometriccoefficient and chemical reaction rate respectively

The species transport equations for two phases are [21]

120597 (120572120588119884119894)120597119905 + nabla sdot (120572120588119884119894V) = nabla sdot 120572119869119894 + 119877119894 (4)

where Yi and Ri are mass fraction and the net rate of speciesi The diffusion flux Ji takes the form

119869119894 = minus(120588119863119894 + 120583119905119878119888119905)nabla119884119894 (5)

where Sct is the Schmidt number and D is the coefficient ofturbulent mass diffusion

The momentum equation for gas phase is expressed as[21]

120597 (120572119892120588119892V119892)120597119905 + nabla sdot (120572119892120588119892V119892V119892)= minus120572119892nabla119901119892 + 120572119892120588119892119892 minus 120573 (V119892 minus V119904) + nabla sdot (120572119892120591119892)+ 119878119892119904119906119904

(6)

where p 120591119892 and u119904 represent the gas pressure gas stresstensor and the particle mean velocity respectively The term

Mathematical Problems in Engineering 3

119878gs119906s indicates the momentum exchange between the gas andsolid phases

Thegas-solid interphase drag coefficient120573 is derived fromGidaspow model [22]

120573 =

34120572119904120572119892120588119892 10038161003816100381610038161003816119907119892 minus 11990711990410038161003816100381610038161003816119889119904 119862119863120572119892minus265 120572119892 gt 08

15012057221199041205831198921205721198921198892119904 + 175120588119892120572119904 10038161003816100381610038161003816119907119892 minus 119907s10038161003816100381610038161003816119889119904 120572119892 le 08

(7)

119862119863 = 044 Re119904 gt 100024119877119890119904 [1 + 0151198771198901199040687] Re119904 le 1000 (8)

119877119890119904 = 12057211989212058811989210038161003816100381610038161003816119907119892 minus 11990711990410038161003816100381610038161003816 119889119904120583119904 (9)

The viscous stress tensor for the gas phase is expressed as[20]

120591119892 = 120583119892 (nablaV119892 + nablaV119879119892) minus 23120583119892 (nabla sdot V119892) 119868 (10)

120583119892 = 120583119892119897 + 120583119892119905 (11)

where the 120583g is gas shear viscosity and 120583gl is the laminarviscosity The turbulent viscosity 120583gt can be provided byturbulence kinetic energy k and dissipation rate 120576

120583119892119905 = 120588119892119862120583 1198962120576 (12)

where 119862120583 is the model constantThe realizable k-120576 turbulence model has exhibited the

significant improvements over the standard k-120576model wherethe flow features consist of strong streamline curvaturevortices and rotation Therefore the realizable k-120576 model isused to simulate the turbulent motion of gas and solid in therotary kiln

Considering the complication of expressions of realizablek-120576 model for each phase only the fundamental transportequations are given here Detailed expressions can be foundin literature [23]

120597120597119905 (120588 119896) + nabla sdot (120588 V119892119896)= nabla sdot ( 120583119905120590119896nabla sdot 119896) + 119866119896 + 119866119887 minus 120588 120576

(13)

120597120597119905 (120588 120576) + nabla sdot (120588 V 120576)= nabla sdot ( 120583119905120590119896nabla sdot 120576) + 1205881198621205761119864120576 minus 1205881198621205762

1205762119896 + radicV120576+ 1198621120576 1205761198961198623120576119866119887

(14)

where Gk is the generation of turbulence kinetic energyand Gb is the generation of turbulence kinetic energy due

to buoyancy 1198621205762 1198621120576 and 1198623120576 are the constants and the120590119896 and 120590120576 are the turbulent Prandtl numbers The relevantexpressions are listed as follows [23]

119866119896 = 120583119892119905ΔV119892sdot [ΔV119892 + (ΔV119892)119879 minus 23ΔV119892 (120583119892119905ΔV119892 + 120588119892119896)]

(15)

119866119887 = 120581119892119894 120583119905119875119903119905120597119879120597119909119894 (16)

C1205761 = max [043 + 120578120578 + 5] (17)

120578 = (2119864119894119895119864119894119895)12 119896120576 (18)

119864119894119895 = 12 ( 120597119906119894120597119909119895 +120597119906119895120597119909119894 ) (19)

Themomentum equation for solid phase is written as [21]

120597 (120572119904120588119904V119904)120597119905 + nabla sdot (120572119904120588119904V119904V119904)= minus120572119904nabla119901 + 120572119904120588119904119892 minus 120573 (V119904 minus V119904) + nabla sdot (120572119904120591119904) + 119878119904119892119906119904

(20)

where 120591s is the solid phase stress tensor and takes Newtonianform [21]

120591119904 = [(minus119901119904 + 120582119904nabla sdot V119904) + 120583119904 [nablaV119904 + (nablaV119904)119879]minus 23 (nabla sdot V119904)] 119868

(21)

120582119904 = 431205721199041205881199041198891199041198920 (1 + 119890)radicΘ119904120587 (22)

120583s = 4512057221199041205881199041198891199041198920 (1 + 119890)radicΘ119904120587 +10120588119904119889119904radic120587Θ11990496 (1 + 119890) 1205721199041198920 [1

+ 451205721199041198920 (1 + 119890)]2 + 119901119904 sin 1206012radic1198682119863

(23)

The granular temperature of solid phase Θ can bederived from the following equations [21]

32 [ 120597120597119905 (120572119904120588119904Θ119904) + nabla sdot (120572119904120588119904Θ119904119906119904)]= minus (119901119904119868 + 120591119904) nabla119906119904 + nabla sdot (119896119904nablaΘ119904) minus 120574 minus 3120573Θ119904

(24)

119896119904= 150120588119904119889119904radicΘ119904120587384 (1 minus 119890) 1198920 [1 +

651205721199041198920 (1 + 119890)]2

+ 212058811990412057221199041198891199041198920 (1 + 119890)radicΘ119904120587

(25)


120574 = 3 (1 minus 1198902) 1205722119904120588119904Θ119904 ( 4119889119904radicΘ120587 minus nabla119906119904) (26)

1198920 = [1 minus ( 120572119904120572119904max)13]

minus1

(27)

The solid pressure 119901119904 is written as [23]

119901119904 = 119901119896119894119899119890119905119894119888 + 119901119891119903119894119888119905119894119900119899 (28)

The kinetic pressure pkinetic indicates the normal force ofcollision between particles and the Lun model is used [20]

119901119896119894119899119890119905119894119888 = 120572119904120588119904Θ[1 + 21198920120572119904 (1 + 119890)] (29)

In the bed region of the rotary kiln solid volume fractionis very high and instantaneous particles collision is lessimportantThe frictional stress needs to be taken into accountwhen the solid concentration exceeds a critical value Thefrictional pressure model proposed by Johnson and Jackson[24] is used in this simulation

119901119891119903119894119888119905119894119900119899 = 119865119903 (120572119904 minus 120572119904min)119899(120572119904max minus 120572119904)119875 (30)

where the coefficients n = 2 and p = 5 [25] The value of120572smin is normally set to 05 for the 3D flow and the maximumpacking limit 120572smax is 063 The coefficient Fr is a function ofthe critical solid concentration

119865119903 = 01120572119904 (31)

The frictional viscosity is expressed as

120583119891119903119894119888119905119894119900119899 = 119901119891119903119894119888119905119894119900119899 sin 120601 (32)

where 120601 is the angle of internal frictionThe enthalpy equations are used to describe the energy

conservation for gas phase and solid phase Heat conductionheat convection and heat exchange between two phases aretaken into account [21]

120597120597119905 (120572119892120588119892119867119892) + nabla sdot (120572119892120588119892V119892119867119892)= nabla (120582119892nabla119879119892) + ℎ119892119904 (119879119892 minus 119879119904) + 119878119892119904119867119904

(33)


(34)

where H 120582 and h represent the specific enthalpy mixturethermal conductivity and convective heat transfer coefficientrespectively The SsgHs is the heat exchange because ofheterogeneous reactions

The convective heat transfer coefficient between the twophases is given by

ℎ119892119904 = ℎ119904119892 = 61205821198921205721198921205721199041198731199061199041198892119904 (35)

TheNusselt number correlation is provided byGunn [20]

119873119906119904 = (7 minus 10120572119892 + 51205722119892) (1 + 07Re02119904 Pr13)+ (133 minus 24120572119892 + 121205722119892)Re07119904 Pr13

(36)

where Pr is Prandtl number of each phase

22 Chemical Reactions The oxidation stabilization processof coal tar pitch sphere can be categorized into four stageswhich are briefly described as follows In the first stage thetemperature is mainly in the range of 20sim140∘C The lightcomponents of coal pitch are released and weight loss isabout 5sim15 at this stage The coal pitch sphere reaches themaximum weight loss rate at the midpoint of the segmentThe second stage is from 140 to 200∘C where preliminaryoxidation of the pitch happens and the mass reductionrate slows down with weight loss about 3 In this stagewith the increase of temperature the oxidation reaction rateincreases Although there exists volatiles release the loss ofweight is small and the loss rate is slow The third stage islocated in the range of 200sim300∘C The significant oxidativeweight increment of coal pitch takes place gaining weightabout 3 At this stage the pyrolysis is basically completedand the oxidation rate significantly increases due to thehigher temperature The combination of oxygen makes upfor the quality loss caused by the dehydrogenation of theside chain of pitch molecule The coal tar pitch reaches themaximum weight gain rate at the midpoint of the segmentThereafter with the increase of temperature the growth rategradually decreases Stage four is the period of constanttemperature oxidative weightlessness at about 300∘C Theoxidative reaction rate is basically stable and the cross-linkedpolymerization of aromatics alkylation and dehydrogenationof the medium-temperature pitch take place at this stage

As the most key oxidation process oxidative weightincrement of coal tar pitch at the temperature range of 200sim300∘C is modeled in this paper The primary assumptionsintroduced for the simplification of calculation process arelisted as follows

(1) the gaseous products of oxidation process are CO2CO CH4 H2O and tar the other small moleculehydrocarbons generally present in insignificantamounts and hence are neglected

(2) the equivalent formulae of the coal pitch and oxidizedcoal pitch are derived from the ultimate analysis of therelevant species as shown in Table 1

(3) the radiative heat transfer is not taken into accountbecause the attribution of radiation in a rotary kiln isless than 3 at the temperature of 300∘C [26]

Based on the above assumption the solid phase consistsof two species coal pitch (before oxidation) C762H344O0243and oxidized coal pitch (after oxidation) C719H31O0581 thegas phase involves seven components oxygen O2 nitrogenN2 carbon dioxide CO2 water vapor H2O carbonmonoxideCO methane CH4 and tar Because of minor amount offormation the nitrogen oxide and sulfur oxide are not takeninto account


Table 1 Ultimate analyses of coal tar pitch spheres before and after oxidative stabilization

Stage C H O N SInitial state 91437 3526 3722 0876 0439Before oxidation 91383 3436 3895 0845 0440After oxidation 86271 3098 9303 0966 0361

Table 2 The typical measured data of the experiments

200 Time CO2 CO CH4 300 Time CO2 CO CH4∘C s ppm ∘C s ppm Test 1 00057 0 73 0 Test 1 00012 09 1971 01Test 2 00128 0 86 0 Test 2 00042 1 2261 01Test 3 00158 0 74 0 Test 3 00112 12 2636 02Test 4 00229 0 72 0 Test 4 00143 1 2468 02Test 5 00259 0 76 0 Test 5 00213 1 2211 01Test 6 00329 0 68 0 Test 6 00243 1 2211 01Test 7 00400 0 76 0 Test 7 00314 09 2197 01Test 8 00430 0 90 0 Test 8 00344 1 2347 01Test 9 00500 0 68 0 Test 9 00414 11 2609 02

During the process of oxidative weight increment thecoal pitch sphere is oxidized and volatile components arereleased into the rotary kiln The composition balance of theoxidation reaction is considered as follows

Coal pitch + 1198991O2 997888rarr1198981Oxidized coal pitch + 1198992CO2 + 1198993CO + 1198994CH4+ 1198995H2O + 1198996Tar

(R1)

In (R1) the stoichiometric coefficient of oxidized coalpitchm1 is determined based on the previous experimentaldata of oxidation stabilization [4] and ultimate analysisshown inTable 1The coefficient of tar is derived fromanotherthermogravimetric experiment [27]TheTGandDTGcurvesof the pitch fractions under N2 and air atmosphere showedthat the weight loss of tar between 200sim300∘C is about 3The coefficients of gas compositions n1 sim n5 are obtainedby the current experimental results in Table 2 and the massbalance calculation

Guo et al [4] experimentally studied the oxidation stabi-lization process of coal pitch spheresThe kinetic parameterssuch as activation energy and preexponential factor andreaction mechanism function 119891(120594) under four reactionstages were deduced which were of different values andexpressions Based on the results the equation of reaction rateand the relevant mechanism expression of oxidative weightincrement are given as follows

119903 = 119860 exp( minus119864119877119879119904)119891 (120594) (37)

119891 (120594) = 13 (1 minus 120594) [minusln (1 minus 120594)]minus2 (38)

120594 = 1198980 minus 1198981199051198980 minus 119898infin (39)

where m0 mt and 119898infin are the initial instantaneous andultimate amounts of coal pitch sphere respectively Thereaction kinetics parameters in this simulation are derivedfrom experimental data [4] lnA=12024 and E=53384 kJmol

23 Experiment System and Computational Conditions Theexperimental setup and simulation schematic diagram of therotary kiln are shown in Figure 1 The experiments wereconducted for the oxidation stabilization of coal tar pitchsphere at Institute of Coal Chemistry Chinese Academy ofSciencesThe rotating kiln has a cylinder of 075m length and04 m inner diameter in the front and circular truncated coneof 02 m top diameter on right side which is made of heat-resistant steel and insulated with insulation material insidethe enclosureThe rotary kiln is heated by the electric heatersand the temperature rise is regulated through the subsectioncontrol program at room temperature to 140∘C the settingtime is 1 h 140 sim 200∘C the setting time is 5 h 200 sim 300∘Ctime is set to 10 h constant temperature at 300∘C the timelasts 1 h The air is continuously introduced to the rotarykiln from four small pipes at the left side As a batch reactorthis rotary kiln is horizontal and the particles of oxidizedcoal tar pitch are extracted at the end of the reaction Atthe monitoring temperature range of 200 sim 300∘C the fluegas compositions at the exit of rotary kiln such as O2 CO2CO and CH4 are measured by gas analysis instrument inreal-time monitoring For the sake of simplicity the typicalmeasured data at 200 and 300∘C are given in Table 2The measurements are repeated nine times for averaging ateach temperature point The oxidized coal pitch spheres aresampled for elemental analysis at intervals of 10∘C and theelemental composition before and after oxidative stabiliza-tion is presented in Table 1 The results obtained from theexperiments will be used for the kinetic data and comparativebasis


(a)

750mm

350 mm

200 mm

Φ 4

00 m

m

Φ20

0 m

m50 mm

Φ10 mm

Air

Flue gas

Z

Y

X

Heat flux

(b)

Figure 1 The setup and schematic diagrams of rotary kiln (a) setup diagram (b) schematic diagram

In this paper the 3D Eulerian-Eulerian model is appliedto simulate the oxidation process in a rotating kiln The basecase is built in accordance with the setting of experimentsInitially the particles of coal tar pitch are located at thebottom of the kiln with solid volume fraction of 055 andthe packing limit is set as 06 The air is introduced intothe kiln through four gas inlets at a specified velocity Atthe right outlet the boundary condition of pressure-outletwith atmosphere is adopted At the walls the no-slip andmovingrotational condition is set and the fixed heat fluxis specified The second-order upwind discretization schemeis used for momentum term while other convective termsadopt first-order upwind The constant time step of 1times10minus4 sis set for the calculation Detailed modeling conditions andparameter settings are given in Table 3 The simulation wasconducted based on 8 processes parallel on an Intel w5580workstation

The sliding mesh model is used to simulate the rotatingmovement of kilns The cylindrical section is divided byhexahedral mesh and the circular truncated cone is dividedby tetrahedral mesh Four different grid domains are testedto perform the validation of the mesh independence whichcontain 222 342 398 468 618 327 and 788 361 grid cellsrespectively The profiles of the particle velocities along thebed depth and bed surface at x=0375mare shown in Figure 2With the increase of grid number the velocity profilesgenerally reduce first and then increase but the variation ofsimulation results is much little when the grid cells increaseto 618 327 Therefore in terms of the computation time and

Table 3 Summary of relevant parameters of simulations

Description ParametersParticle diameter ds (mm) 10Particle density 120588s (kgm3) 1435Particle viscosity 120583s (Pasdots) 018Particle thermal conductivity 120582s(WmsdotK) 2000

Inventory of particles Gb (kg) 8

Air flow rateVa (Nm3h) 10 25 375 50

625Air temperature Ta (

∘C) 25

Rotational speed of kiln 120596 (rpm) 033 095 143191 239

Heat flux hw (Wm2) 150Temperature of rotary kiln Tb (

∘C) 200sim300

calculation accuracy the computational domain containing618 327 mesh cells is selected for the following work

3 Results and Discussions

31 Model Validation With the purpose of verification ofthe established 3D model the hydrodynamic and reactivecharacteristics in rotary kilns are compared with experimen-tal data Considering the lack of data of particle motion inour experiments the results from the Boateng et al [28]


00 minus02 minus04 minus06 minus08 minus10minus006

000

006

012

018

024

030

Grid number222342398468618327788361

ＰＭ(m

s)

ＳH

Ｔ

Ｓ

LH

0

(a)

00 02 04 06 08 10

000

004

008

012

016

020

Grid number222342398468618327788361

ＴL

ＰＭ(m

s)

Ｔ

Ｓ

LH

0

(b)

Figure 2 Variations of particle velocity profiles with grid number (a) depth velocity (b) surface velocity

00 02 04 06 08 10

00

01

02

03

04

05

06

SumulationExperiment

0 LH

ＴL

ＰＭ(m

s)

Ｔ

Ｓ

(a)

ＰＭ２

ＳH

Ｔ

Ｓ

LH

2015100500minus05minus10

02

00

minus02

minus04

minus06

minus08

minus10

0


(b)

Figure 3 Particle velocity profiles along the bed surface and depth (a) surface direction (b) depth direction

are used to validate the present model The selected particlematerial is the polyethylene pellet with uniformly sphericalshapeThe rotary drum comprises a 964 mm inside diameterand 1000 mm axial length According to the experimentaldata the flow field at an axial distance of 220 mm from theend-piece belongs to the undisturbed region For the sakeof simplification the simulated rotary kiln length is reducedto 500 mm The polyethylene pellets with 363 mm size and960 kgm3 density are loaded at 33 fill and operated at therotational rates of 3 and 5 rpm Detailed particle propertiesand operating parameters can be found in literature [28]Representative results including particle velocities along the

bed surface and depth in the midsection are shown inFigure 3 The surface velocity presents a parabolic profileskewing towards the bottom The depth velocity at the mid-chord position presents the maximum value at the bedsurface and the velocity conforms to the tangential velocityat the wall position Generally the predicted results along thebed surface and depth compare well with experimental data

Subsequently a base case of the oxidation stabilization ofcoal tar pitch is applied to evaluate the predictive ability oftwo-fluid model coupled with chemical reaction As listed inTable 3 the experiments of the base case are operated at theair flow rate with 10 Nm3h and rotational speed with 033


470 480 490 500 510 520 530 540Temperature (K)

00

01

02

03

04

Mol

e fra

ctio

n (

)

CO

Experiment

2

（4

Figure 4 The component concentrations of product gas versus temperature

rpm The molar fractions of main gas compositions at theexit are shown in Figure 4 In the process of oxidative weightincrement the elevating particle temperature from the wallheat conduction and the heat release of reaction gives riseto the increase of concentrations of exit gas compositionsIt can be observed that the predicted values of three kindsof product gas such as CO2 CO and CH4 are basically inagreement with experimental results

In order to further verify the range of application ofthe built model the simulations are performed with a largerange of rotation rates 0095sim95 rpm which take on variousforms of solid motion in the rotary kiln The three represen-tative flow patterns in transverse section and the transitioncriteria (Froude number and filling degree) characterizedby Mellmann [29] are given in Table 4 as the baselineThe contours of predicted solid concentration and particlevelocity vector as well as the criteria number are illustratedin the last five rows in Table 4 With regard to the threerotation rates (0095 095 and 95 rpm) the relevant Froudenumbers Fr are the 204times10minus6 204times10minus4 and 204times10minus2respectively and the filling degree 119891 is about 011 Accordingto the transition criteria the rotary kiln is operated atsurging rolling and cascading modes respectively The flowcharacteristics revealed by solid volume fraction and velocityvector are consistent with those of reference modes

In conclusion the developed 3D numerical model hassuccessfully predicted the hydrodynamic and reaction char-acteristics as well as various motion modes for the typicalrotary kilns Therefore it can be applied to the further studyon oxidation stabilization process of coal tar pitch in a rotarykiln

32 Particle Motion Characteristics Because the oxidativeweight increment is a slow oxidation reaction the simulationof whole temperature rising process consumes consider-able computation time The base case might cost about

eight months under the current computational conditionsTherefore air flow rate and rotating speed are substan-tially increased to accelerate the oxidation reaction in thesensitivity analysis of parameters The key parameters ofthe following simulation are air flow rate 50 Nm3h androtational speed 143 rpm

In the rotary kiln the particles located at the bottommovewith the kiln wall by viscous friction force between particlesand internal wall and then the inner particles start moving byviscous force among particles With the rotation of the kilnparticles on the bed top slide down to the bottom and anothercircle will begin when these particles move with the kiln wallOverall the variation of particle distribution in the rotarykiln slows after a period of time In the present simulationthe particle movement reaches the quasi-stable state 5 s afterthe initial computation Figure 5 illustrates the profiles ofparticle volume fraction in the cross and vertical sections ofthe kiln (t =10 s) It can be observed that particles assemble ina specific region namely bed region which has a local highconcentration The bed surface takes on a typical wave formrather than flat plane in the cross section

To better display the simulation results inside the kilnpostprocessing coordinate is applied for the data processingFigure 6 is the coordinate schematic of the cross section ofthe rotary kiln used in present simulations The origin ofCartesian coordinate is located at the center of the plane Thez-axis and y-axis of postprocessing coordinate are paralleland perpendicular to the particle bed surface at steady staterespectively As the nomenclature shown in Figure 6 vs isthe actual velocity of particles V119911

1015840 is the velocity componentparallel to the surface and V119910

1015840 is the velocity componentnormal to the surface L indicates the full chord of the bedand H denotes the central thickness of the particle bed

Figure 7 illustrates the velocity vector of particles atsteady state The color and arrow represent the magnitudeand direction of the velocity respectively The magnitude


Table 4 The motion forms of particles in rotary kiln

Motion form Surging Rolling Cascading

Schematic

Froude number Fr119865119903 = 1205962119877119892 0 lt Fr lt 10minus4 10minus4 lt Fr lt 10minus2 10minus3 lt Fr lt 10minus1Filling degree f119891 = 120576 minus sin 120576 cos 120576 f gt 01 f gt 01 f gt 01Rotation rate (rpm) 0095 095 95

Contours of simulatedsolid concentration

Contours of simulatedparticle velocity vector

Froude number Fr 204times10minus6 204times10minus4 204times10minus2Filling degree f 011 011 011

increases from the blue to red From the vector contour andpartial enlargement in the middle it can be seen that twoparticle layers with opposite direction of velocity exist in thebed The downward velocity in the upper layer is obviouslylarger than in the lower layer improving the performancesof mixing and heat transfer between gas and particle phasesThis thin layer is called the active layer [6] The particles inthe lower layer are stacked and move upward with the kilnby the friction The small relative velocity in this thick layerleads to the weak particles mixing and heat transfer which iscalled the passive layer [6] As displayed in left and middledrawings of partial enlargement the particle velocity vectorat the bed surface is at an angle rather than being parallel tothe surface Because of the particles collision the particles inthe outer layer bounce from the surface and drop by gravityresulting in the velocity component normal to the surfaceIn the bottom region of bed surface (enlarged figure on theright) some particles could bounce off after their collisionwith kilnwallThese simulation results are in accordancewiththe data in [30]

The variation of particle velocity with the bed depthis presented in Figure 8(a) Owing to similarity of profileshapes irrespective of the position along the chord length thedetailed analysis focuses on the results at mid-chord position

[28] It can be observed that the greatest velocity and velocitygradient appear on surface of the active layer As the bedthickness (1199101015840119891 distance from surface) increases the particlevelocity dramatically decreases and reaches zero when thedimensionless thickness of the layer |1199101015840119891H| approaches 045As the bed thickness increases to more than 45 of thetotal thickness (|1199101015840119891H| gt 045) the particles start movingin the opposite direction and the velocity gradient graduallyreducesWhen the bed thickness is larger than 80 (|1199101015840119891H| gt08) the particle velocity is basically the same as the wallrotational speed (vs 120596R= 1)The reason for this is the particlesin near-wall region move with the kiln wall due to frictionThe variation of particle velocity with different axial lengthsof kiln can also be seen in Figure 8(a) With the increase ofaxial length the particle velocity gradually decreases but thechange is very smallThe slightly larger velocity at x=005m ison account of the little effect of particles on the far left side ofthe kiln The minimum velocity on the far right side (x=075m) might be ascribed to impact of particles in the regionof circular truncated cone The profiles of particle velocityon bed surface are illustrated in Figure 8(b) Along the z1015840direction the particle velocity first gradually increases andthen decreasesThe peak velocity is located at z1015840L=07 whichis the synergy of gravity and solid friction force Meanwhile


05505225049504675044041250385035750330302502750247502201925016501375011008250055002750

(a)

(b)

Figure 5 Profiles of solid concentration (a) cross section (b) longitudinal section

The coordinate of post-processing

Ｉ

Ｉ

Ｓ

Ｓ

Ｔ

ＳＩ

Ｔ

Ｔ

ＳＭ

Ｓ

ＴＩ

Ｔ

L

H

Figure 6 The postprocessing coordinate in the rotary kiln

the particles at the larger axial length have higher velocity inthe upper surface region while are of smaller velocity in thelower region

33 Oxidation Reaction Characteristics Figure 9 showsthe temperature profile of gas phase in the different

cross-sections The temperature contours in the cross sectionof x=0375 m and in the longitudinal section of z=0 m areillustrated in Figures 9(a) and 9(b) respectively It can beobserved that the bed region generally has a higher temper-ature due to the large thermal capacity The central region isthe freeboard where the inlet air with low temperature mainly


Figure 7 Velocity vector contour of particles

x = 005 mx = 0375 mx = 075 m

ＰＭ

２

ＳHminus10minus08minus06minus04minus0200

2

0

minus2

minus4

minus6

minus8

minus10

(a)

x = 005 mx = 0375 mx = 075 m

030

025

020

015

010

005

000

00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)

Figure 8 Particle velocity along different directions (a) depth direction (b) surface direction

gathers so the gas temperature is relatively low Close to thebed surface the temperature increases sharply and reachespeak value at bed surface That is because oxidation reactionfirstly takes place in this region In the passive layer regionthe temperature remains stable and then slightly increasesnear the cylindrical wall of the rotary kiln due to the wall heatflux For the different axial positions because the entering airwith low-temperature gathers in the cylindrical region thegas temperature in the front of the kiln is lower than in therear

The distributions of solid temperature in the cross sectionand in the longitudinal section are illustrated in Figures10(a) and 10(b) respectively The temperature profiles ofsolid phase are generally in accordance with those of gasphase except for the peak value The solid temperatureat the bed surface is lower than gas temperature and noobvious peak exists for the solid phase The discrepancyof physical property gives rise to the higher temperaturerise for the gas phase It is worth noting that the par-ticles with solid volume fraction of less than 001 are


600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)

Figure 9 Temperature profiles of gas phase (a) cross section (b) longitudinal section

neglected so the bed surface in the figure is not verysmooth

Figures 11ndash14 illustrate the concentration profiles of fourmain gas compositions namely O2 CO2 CO and CH4 Asshown in Figure 11 O2 primarily gathers in the freeboardregion and decreases suddenly at the bed surface due tooxidative reaction When entering the bed region the O2concentration almost approaches zero because high concen-tration of coal pitch sphere leads to the huge consumptionof O2 Along the axial direction the O2 concentrationsin the cylindrical region (xlt075 m) are apparently higherthan in the back of the kiln (xgt075 m) as a result of thegas diffusion and oxidative reaction The middle sectionof cylinder has highest O2 concentration in the freeboardregion as a result of the inlet air gathering As a productof oxidation reactions CO2 concentration takes on a nearlyopposite profile of the reactant of O2 as shown in Figure 12That is CO2 molar fraction has a low value in freeboardregion and then increases sharply close to bed surface andfinally remains stable inside the bedThe CO2 concentrationsin the cylindrical region of the kiln are apparently lowerthan in the back and the middle of cylinder is of minimalCO2 concentration in the freeboard In Figures 13 and 14the concentration profiles of CO and CH4 have the similarvariation trends with that of CO2 the only difference existingin the magnitude of concentration As can be seen from

Figures 11ndash14 a circular truncated cone is located at rightside (x=075sim095 m) and connected to a cylinder with 02m diameter (xgt095 m) The product gas such as CO2 COand CH4 tends to concentrate in the exit section while theair is of lower concentration in this region However sincethe coal pitch particles are concentrated at the bottom of thereactor (Figure 5(b)) the locally uniform distribution of gascomponents caused by the geometry has little impact on theoxidation process

The contours of concentration profile for oxidized coaltar pitch in the cross section and longitudinal section areshown in Figure 15 It should be noted that the color in thefigure presents the mass fraction of the oxidized coal pitch Ingeneral the higher concentration of oxidized coal pitch existsat the top of the bed because of the elevated temperature andplenty of oxygen Since the coal tar pitch sphere assemblesin the bed region the mass fraction of oxidized coal pitchapproaches to zero in the freeboard regionAt the bed surfacethe concentration of the oxidized yield of coal tar pitchincreases suddenly and keeps on a steady value in the passivelayer region The profiles of solid concentration along theaxial position are similar to those of gas phase Consideringthe high concentrations of O2 in the middle region and theO2 consumption along the axial distance due to oxidationreaction the mass fraction of oxidized coal pitch in the frontof the kiln is larger than in the rear


600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)

Figure 10 Temperature profiles of solid phase (a) cross section (b) longitudinal section

0210201901801701601501401301201101009008007006005004003002001

(a)

(b)

Figure 11 Concentration profiles of O2 (a) cross section (b) longitudinal section


0016001550015001450014001350013001250012001150011001500100095000900085000800075007000650006

(a)

(b)

Figure 12 Concentration profiles of CO2 (a) cross section (b) longitudinal section

0002700026400025800025200024600024000234000228000222000216000210002040001980001920001860001800017400016800016200015600015

(a)

(b)

Figure 13 Concentration profiles of CO (a) cross section (b) longitudinal section


0001350001320001290001260001230001200011700011400011100010800010500010200009900009600009300009000087000084000081000078000075

(a)

(b)

Figure 14 Concentration profiles of CH4 (a) cross section (b) longitudinal section

34 Effects of Air Flow Rate and Rotational Speed To investi-gate the effects of operating parameters on the gas-solid flowand oxidation reaction characteristics flow rate of air androtational speed are changed within a relatively wide rangeThe particle velocity profiles temperature profiles of gas andsolid the product gas and oxidized yield of coal tar pitch areanalyzed in the following section

341 Effects on Particle Motion The simulations are per-formed with air flow rates as 25 375 50 and 625 Nm3hwhile the rotating speed remains a constant value of 143 rpmFigure 16 shows the particle velocity profiles along the beddepth and bed surface As can be seen from Figure 16(a)when |y1015840H| gt 07 the four curves with the different airflow rates basically coincide and the particle velocity ofthe passive layer approaches the rotation speed of the kilnThe profile shapes of particle velocity on the bed surfaceare roughly the same under different air flow rates Thesecurves in Figure 16(b) present slightly skewed parabola andthe maximum velocity occurs at about z1015840L=075 In generalthere is no definite tendency for the particle velocity withthe increasing air flow indicating that air flow rate has littleimpact on the particles motion

Figure 17 shows the variations of particle velocities withvarious rotating speeds The kiln is rotated with the speeds of095 143 191 and 239 rpm and the flow rate of air is kept at

50 Nm3h It is evident from Figure 17(a) that the rotationalspeed has a significant impact on the particle velocity alongthe depth direction When the rotational speed increasesfrom 095 to 239 rpm the particle velocity of the active layerincreases from eight times the tangential wall velocity (120596119877)to thirteen times the velocity and the thickness of the activelayer is also found to increase correspondingly The increasein the rotational speed encouragesmore particle participationin the circular reciprocating movement of the outer layer perunit time and accelerates the update frequency of surfaceparticles Figure 17(b) shows that the particle velocity alongthe bed surface also increases with the increasing rotationalspeed When the speed increases within the range of 095sim239 rpm the maximum particle velocity at bed surfacegradually increases until it reaches 065 ms In addition theincreasing rotational speed gives rise to the profile of surfacevelocity shift towards the center of the chord (z1015840L=05)and the parabolic shape is more symmetric In conclusionthe increase of rotating speed can significantly increase themovement speed of particles and thicken the active layerwhich is conducive to themixing and replacement of particlesin the kiln

342 Effects on Gas and Solid Temperature Figure 18 showsthe distributions of gas and particle temperature along thenegative y1015840 axis and central cross section of the rotary kiln


09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)

Figure 15 Concentration profiles of oxidized coal pitch (a) cross section (b) longitudinal section

minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２

Va = 25 Ｇ3ＢVa = 375 Ｇ3ＢVa = 50 Ｇ3ＢVa = 265 Ｇ3Ｂ

00 minus02 minus04 minus06 minus08 minus10ＳH

(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)

Figure 16 Particle velocity profiles at various air flow rates (a) depth direction (b) surface direction

(x=0375 m) under different air flow rates with a constantrotational speed of 143 rpm It can be found that the gastemperature is lower in the freeboard region and higher inthe bed region The temperature gradient is obviously largenear the active layer region where oxygen is well mixed

with the coal pitch sphere promoting the oxidation reactionThe gas temperature is rapidly heated by releasing heat andthe maximum value appears in this region By contrastthe temperature profile of the particle phase remains stablethroughout the bed surface where the particle temperature is


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)

Figure 17 Particle velocity profiles at various rotational speeds (a) depth direction (b) surface direction

000 005 010 015 020Radial position (m)

Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)

Figure 18 Profiles of gas and particle temperatures at various air flow rates (a) gas phase (b) solid phase

lower than that of gas phase The slightly higher temperatureof solid phase lies in the wall region of the rotary kiln dueto wall heat flux which also takes on for the gas phaseUnder different air flow rates the temperature profiles ofgas and particles basically overlap in the passive layer onlyslight differences existing in the freeboard and the activelayer It shows that air flow rates have no obvious influenceon the temperature distributions of gas and particles inrotary kiln Although the increasing inlet air introducesmore low-temperature gas the higher oxygen concentration

facilitates the oxidation reaction which means more heatreleased from the reaction compensates for the effects of coldair

Figure 19 shows the temperature distributions of gas andparticle phases along the negative y axis at different rotationalspeeds with the same air flow rate of 50 Nm3h It can befound that the rotational speed also has no definite effect onthe temperature profile in the freeboard while some tendencybeing in the active layer and near-wall regions With theincrease of rotational speeds the temperature of gas and solid



Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)

Figure 19 Profiles of gas and particle temperatures at various rotational speeds (a) gas phase (b) solid phase

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)

Figure 20 Concentrations of product gas and solid versus air flow rate (a) product gas and solid (b) radial concentration of solid

phases gradually increases at the bed surface and near thewall but only to a small extent

343 Effects on Product Gas and Oxidized Coal Pitch Thevariations of product gas and solid with air flow rate areshown in Figure 20(a) The flow rates of air increase between25 and 625 Nm3h while the rotational speed remains thesame value of 143 rpm The calculated results of gas molarfraction adopt the form of area average at the outlet whilethe mass fraction of oxidized coal tar pitch is the value of thewhole kiln With the increase of air flow rate more O2 takes

part in the reactionThe accelerated rate of oxidation reactiongives rise to the increase of quantities of generated gas andsolid Therefore the mass fraction of oxidized coal pitchslightly increases with the increasing air flow rate Howeverthe increasing flow rate of air introduces a large amountof N2 which has a dilution effect on the product gas andcounteracts the effect of accelerated oxidation reaction It canbeen seen from Figure 20(a) concentrations of three productgas compositions such as CO2 CO and CH4 present adropping trend to various degrees when the air flow rateincreases


00

02

04

06

08

10

10 15 20 25Rotational speed (rpm)

40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)

Figure 21 Concentrations of product gas and solid versus rotational speed (a) product gas and solid (b) radial concentration of solid

The effects of air flow rate on radial concentration profilesof the oxidized yield of coal tar pitch are illustrated inFigure 20(b) Along the radial position the mass fraction ofoxidized coal pitch has an abrupt increase and reaches itspeak near the bed surface because of the higher temperatureand O2 concentration As the flow rate of air increasesmore oxidation reaction takes place and the oxidized yield ofoxidized coal pitch gradually increases in the bed region

Figure 21 shows the variations of product gas and solidwith rotating speed The kiln is rotated with the speeds of095 143 191 and 239 rpm and the flow rate of air is keptat 50 Nm3h As the rotating speed increases the contactarea and time between air and coal pitch sphere increasewhich effectively enhances the oxidation reaction Thereforethe final oxidative yield of coal pitch spheres increaseswith the increasing rotating speed The concentrations ofmain product gas including CO2 CO and CH4 are almostthe same because the gas dilution offsets the acceleratedoxidation

The radial concentration profiles of oxidized coal pitchat different rotational speeds are presented in Figure 21(b)When the rotational speed increases the oxidized yield ofcoal tar pitch in the bed region and the peak value on thebed surface gradually increase due to the enhanced oxidationreaction Because fewer discrete particles appear above thebed surface and bed thickness reduces with the increasingrotational speed the radial position of abrupt increase ofoxidized coal pitch slightly moves backward

4 Conclusions

In this paper the two-fluid method and kinetic theory ofgranular flow are combined with heat transfer and reactionwhich is applied to simulate the process of oxidative weight

increment of coal tar pitch in a rotating kiln The dense gas-solid motion heat transfer and chemical reaction for theentire regions of the kiln are simultaneously solved Based onthe model validation the simulations are carried out to givethe detailed particle movement and reactive characteristics inthe 3D spaceThe effects of air flow rate and rotating speed onthe profiles of particle velocity and gas-solid temperature theexit gas composition and oxidized coal pitch are also studiedThe primary conclusions can be drawn as follows

(1) The developed 3D numerical model has successfullypredicted the hydrodynamic and reaction charac-teristics as well as various motion modes (surgingrolling and cascading mode) for the typical rotarykilnsThe calculated results are consistent with exper-imental data

(2) After reaching a steady state a wave shape forms onthe bed surface Due to the particles collision theparticle velocity vector is not parallel to the surfaceThe particle velocity peak is located at the activelayer surface and dramatically decreases along the bedthickness after that the particle velocity turns intoopposite direction in the passive layer

(3) The bed region generally has a higher temperaturethan the freeboard due to the large thermal capacityThe highest gas temperature exists at the bed surfaceand the temperature remains stable in the passivelayer region No obvious peak of temperature existsfor the solid phase Meanwhile the gas and solidphases have slightly higher temperatures near the wallof the rotary kiln

(4) The main compositions of product gas include CO2CO and CH4 and the generated solid species is the


oxidized coal pitchThe concentrations of gas productand oxidized coal tar pitch increase sharply near thesurface and then keep on a steady value in the passivelayer region

(5) There is no definite tendency for the particle velocitywith the increasing air flow rate By contrast theincrease of rotating speed can significantly acceleratethe particle movement and increase the thickness ofactive layer which is conducive to the mixing andreplacement of particles in the kiln

(6) The air flow rate has no obvious influence on thetemperature profiles of gas and particles inside therotary kiln With the increase of rotational speedsthe temperatures of gas and solid phases have anincreasing trend at the bed surface and near the wallbut only to a small extent

(7) The increasing rotational speed effectively enhancesthe oxidation reaction The final oxidative yield ofcoal pitch spheres increases with the rotational speedwhile the concentrations of product gas composi-tions such as CO2 CO and CH4 are almost the samebecause of the gas dilution In comparison increasingthe flow rate of air has little effect on the particlemotion and oxidation yield of coal tar pitch

Nomenclature

119860 Preexponential constant119862119863 Drag coefficient119889119904 Particle diameter mm119863119892119904 Diffusion coefficient for gas (m2s)119864 Activation energy1198920 Radial distribution functionℎ Heat transfer coefficient (Wm2sdotK)ℎ119908 Wall heat flux (Wm2)119867 Specific enthalpy (Jkg)119869119894 The diffusion flux (kgm2sdots)119896 Turbulent kinetic energy (1m2 sdot s2)119898 Mass (kg)119873119906 Nusselt number119901 Pressure (Pa)Pr Prandtl number119876f Fuel feed rate (kgh)119903 Reaction rate (kmolm3 sdots)119877 Universal gas constant (JkmolsdotK)119877119890 Reynolds number119878 Mass source term119878119888119905 Schmidt number119879 Temperature (K)119881119886 Volume flow rate of air (m3h)V Gas velocity (ms)119884119894 Mass fraction

Greek Letters

120572 Volume fraction120573 Gas-solid interphase drag coefficient120594 Instantaneous mass fraction of weight increment

120574 Dissipation of fluctuating energy (Wm3)120576 Dissipation rate of turbulent kinetic energy(1m2 sdot s3)120582 Thermal conductivity (Wm2sdotK)120583 Viscosity (kgmsdots)120588 Density (kgm3)120591 Stress tensor (Pa)120596 Rotational speed (rpm)

Subscripts

119892 Gas phase119894 The 119894th species119897 Laminar flow119904 Solid phase119905 Turbulent flow

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declared that there were no conflicts of interestregarding the publication of this paper

Acknowledgments

Financial supports from key project of NSFC-Shanxi coalbased and low carbon joint fund (no U1510204) NSFC(no 51606039) and Natural Science Foundation of JiangsuProvince (no BK20160684) are sincerely acknowledged

References

[1] M Li W Li and S Liu ldquoHydrothermal synthesis character-ization and KOH activation of carbon spheres from glucoserdquoCarbohydrate Research vol 346 no 8 pp 999ndash1004 2011

[2] A J Romero-Anaya M Ouzzine M A Lillo-Rodenas and ALinares-Solano ldquoSpherical carbons synthesis characterizationand activation processesrdquo Carbon vol 68 pp 296ndash307 2014

[3] J Fernandez A Figueiras M Granda J Bermejo and RMenendez ldquoModification of Coal-Tar Pitch by Air-Blowing 1Variation of PitchComposition andPropertiesrdquoCarbon vol 33no 3 pp 295ndash307 1995

[4] Y Guo Y Shao W Zhong and K Li ldquoCharacteristics ofoxidation stabilization process of coal pitch based spheresrdquoCiesc Journal 2018

[5] Y Wang X Liu Z Li and W Qiao ldquoOxidative stabilization ofpitch spheres in fluidized bed and their carbonization behaviorrdquoCarbon Techniques vol 6 p 3 2010

[6] H Liu H Yin M Zhang M Xie and X Xi ldquoNumericalsimulation of particlemotion and heat transfer in a rotary kilnrdquoPowder Technology vol 287 pp 239ndash247 2016

[7] Q Zheng and A Yu ldquoModelling the granular flow in arotating drum by the Eulerian finite element methodrdquo PowderTechnology vol 286 pp 361ndash370 2015


[8] R Maione S Kiesgen De Richter G Mauviel and G WildldquoDEM investigation of granular flow and binary mixture seg-regation in a rotating tumbler Influence of particle shape andinternal bafflesrdquo Powder Technology vol 286 pp 732ndash739 2015

[9] R Yang A Yu LMcElroy and J Bao ldquoNumerical simulation ofparticle dynamics in different flow regimes in a rotating drumrdquoPowder Technology vol 188 no 2 pp 170ndash177 2008

[10] Y Ding R Forster J Seville and D Parker ldquoSegregation ofgranular flow in the transverse plane of a rolling mode rotatingdrumrdquo International Journal of Multiphase Flow vol 28 no 4pp 635ndash663 2002

[11] P Liu R Yang and A Yu ldquoDEM study of the transverse mixingof wet particles in rotating drumsrdquo Chemical EngineeringScience vol 86 pp 99ndash107 2013

[12] S Jiang Y Ye Y Tan et al ldquoDiscrete element simulationof particle motion in ball mills based on similarityrdquo PowderTechnology vol 335 pp 91ndash102 2018

[13] S Jiang Y YeMHe et al ldquoMixing uniformity of irregular sandand gravel materials in a rotating drum with determination ofcontact model parametersrdquo Powder Technology 2019

[14] B Chaudhuri F J Muzzio and M S Tomassone ldquoModelingof heat transfer in granular flow in rotating vesselsrdquo ChemicalEngineering Science vol 61 no 19 pp 6348ndash6360 2006

[15] N Gui J Yan W Xu et al ldquoDEM simulation and analysisof particle mixing and heat conduction in a rotating drumrdquoChemical Engineering Science vol 97 pp 225ndash234 2013

[16] K S Mujumdar and V V Ranade ldquoCFD modeling of rotarycement kilnsrdquo Asia-Pacific Journal of Chemical Engineering vol3 no 2 pp 106ndash118 2008

[17] F Montagnaro C Tregambi P Salatino O Senneca and RSolimene ldquoModelling oxy-pyrolysis of sewage sludge in a rotarykiln reactorrdquo Fuel vol 231 pp 468ndash478 2018

[18] M U Babler A Phounglamcheik M Amovic R Ljunggrenand K Engvall ldquoModeling and pilot plant runs of slow biomasspyrolysis in a rotary kilnrdquo Applied Energy vol 207 pp 123ndash1332017

[19] D Wenjing B Wang and L Cheng ldquoExperimental researchand numerical analysis on thermal dynamic characteristics ofrotary kilnrdquoeCanadian Journal of Chemical Engineering vol97 no 4 pp 1022ndash1032 2019

[20] J XieW Zhong B Jin Y Shao andH Liu ldquoThree-dimensionaleulerian-eulerian modeling of gaseous pollutant emissionsfrom circulating fluidized-bed combustorsrdquoEnergyampFuels vol28 no 8 pp 5523ndash5533 2014

[21] W Zhong A Yu G Zhou J Xie and H Zhang ldquoCFD simu-lation of dense particulate reaction system Approaches recentadvances and applicationsrdquo Chemical Engineering Science vol140 pp 16ndash43 2016

[22] D Gidaspow Multiphase Flow and Fluidization ContinuumAnd Kinetic eory Descriptions Academic Press 1994

[23] A Fluent Release 150 Theory Guide November 2013[24] P C Johnson andR Jackson ldquoFrictional-collisional constitutive

relations for granular materials with application to planeshearingrdquo Journal of Fluid Mechanics vol 176 pp 67ndash93 1987

[25] R Ocone S Sundaresan andR Jackson ldquoGas-Particle flow in aduct of arbitrary inclination with particle-particle interactionsrdquoAIChE Journal vol 39 no 8 pp 1261ndash1271 1993

[26] L Le Guen M Piton Q Henaut F Huchet and P RichardldquoHeat convection and radiation in flighted rotary kilns AminimalmodelrdquoeCanadian Journal ofChemical Engineeringvol 95 no 1 pp 100ndash110 2017

[27] T Guan G Zhang J Zhao J Wang and K Li ldquoInsight intothe oxidative reactivity of pitch fractions for predicting andoptimizing the oxidation stabilization of pitchrdquo Fuel vol 242pp 184ndash194 2019

[28] A A Boateng and P V Barr ldquoGranular flow behaviour in thetransverse plane of a partially filled rotating cylinderrdquo Journalof Fluid Mechanics vol 330 pp 233ndash249 1997

[29] J Mellmann ldquoThe transverse motion of solids in rotatingcylindersmdashforms of motion and transition behaviorrdquo PowderTechnology vol 118 no 3 pp 251ndash270 2001

[30] Y Demagh H Ben Moussa M Lachi S Noui and L BordjaldquoSurface particle motions in rotating cylinders Validation andsimilarity for an industrial scale kilnrdquo Powder Technology vol224 pp 260ndash272 2012

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of


Mathematical Problems in Engineering

Applied MathematicsJournal of


Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of



Engineering Mathematics

International Journal of


Operations ResearchAdvances in

Journal of


Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


Rotary kilns are widely applied in modern industry suchas cement metallurgy chemicals and energy field due totheir good mixing performance high heat transfer efficiencyand large handling capacity [6 7] In addition the relativelylow particle motion velocity in rotary kilns results in thesmall collision force between particles and between particleand wall Considering the friability of pitch spheres and thedemand of high heat capacity in the oxidation process thefeatures of rotary kilns are very applicable for the oxidationstabilization of coal tar pitch spheres In the past decadesmodeling and numerical simulation have been used to pro-vide a detailed insight and quantitative guidelines for reactordesign and optimization However existing work for rotarykilns focuses on the flow field [7ndash9] mixingsegregation [10ndash13] and heat transfer performance [6 14 15] simulation ofchemical processes in a rotary kiln is still in its infancy dueto the complexity of coupling of dense gas-solid flow heattransfer and reactions [16] There are only few modelingresearches concerning the reacting flow for rotary kilnswhich can be categorized two typesThe first one is modelingthe motion and chemistry under steady condition and theother one is separately modeling the processes for bed regionand freeboard region respectively Montagnaro et al [17]presented a 15-dimensional (15D) model for oxy-pyrolysisof sewage sludge at the steady state in a rotary kiln Babler etal [18] developed a modular numerical model for biomasspyrolysis in a rotary kiln which considered the solid bedregion and gas phase domain at steady state Mujumdar andRanade [16] developed separate but coupled computationalmodels for bed and freeboard regions for rotary cementkiln The reactions in the bed region were modeled throughsingle-phase pseudo fluid and combustion of coal particlesin the freeboard region was modeled by Eulerian-Lagrangianapproach Du et al [19] studied the combustion of pulverizedcoal in the airflow of cement rotary kiln using Eulerian-Lagrangian method which belonged to the dilute particleflow During the chemistry of rotary kilns the reactionprocess is dynamic and complicated due to the dense particlesmotion gas turbulence and multicoupling between the gasand solid phases Therefore the simultaneous modeling ofdense gas-solid flow heat transfer and chemical reactionsfor the whole rotary kilns is of the pressing need at presentbut relevant researches have not been found in the availableliterature In addition the characteristics derived from the 2Dor quasi-3D cross section might not be applicable to the 3Dsystem due to the wall and geometry impacts on the flow fieldand reactive characteristics The real 3D modeling is criticalto acquire the complete information inside the rotary kiln

The present work develops a comprehensive 3Dmodel tostudy the key oxidation process oxidative weight incrementin a rotating kiln Based on the two-fluid method themodel simultaneously solves the dense gas-solidmotion heattransfer and chemical reaction for the entire regions of arotary kiln The rotary kiln has a cylinder of 075 m lengthand 04 m diameter in the front and circular truncated coneson exit side The detailed verification of model is firstlyperformed by comparisons with the available experimentaldata Afterwards the solid flow field profiles of velocityand temperature the concentrations of gas compositions

(O2 CO2 CO and CH4) and the oxidized coal pitchinside the rotary kiln are analyzed Finally the effects ofair flow rate and rotating speed of the rotary kiln on theprimary particle movement and reactive characteristics areemphatically studied

2 Model Descriptions

Based on the Eulerian-Eulerian (two-fluid) method andkinetic theory of granular flow the conservation equationsof continuity momentum energy and species are solvedfor gas and solid phases respectively In consideration ofthe particularity of gas-solid motion in rotary kilns the gasphase is modeled by realizable k-120576 turbulent model andJohnson and Jackson model is used for the frictional stressThegoverning equations are briefly presented in the followingsections the details of which can be found in literatures[20 21]

21 Governing Equations Themass equations of gas and solidphases are written as [21]

120597 (120572119892120588119892)120597119905 + nabla sdot (120572119892120588119892V119892) = 119878119892119904 (1)

120597 (120572119904120588119904)120597119905 + nabla sdot (120572119904120588119904V119904) = 119878119904119892 (2)

where 120572 120588 and V are the volume fraction density andvelocity vector respectively The mass source term S fromheterogeneous reactions is expressed as

119878119892119904 = 119872119888sum120574119888119903 = minus119878119904119892 (3)

whereM 120574 and r represent molecular weight stoichiometriccoefficient and chemical reaction rate respectively

The species transport equations for two phases are [21]

120597 (120572120588119884119894)120597119905 + nabla sdot (120572120588119884119894V) = nabla sdot 120572119869119894 + 119877119894 (4)

where Yi and Ri are mass fraction and the net rate of speciesi The diffusion flux Ji takes the form

119869119894 = minus(120588119863119894 + 120583119905119878119888119905)nabla119884119894 (5)

where Sct is the Schmidt number and D is the coefficient ofturbulent mass diffusion

The momentum equation for gas phase is expressed as[21]

120597 (120572119892120588119892V119892)120597119905 + nabla sdot (120572119892120588119892V119892V119892)= minus120572119892nabla119901119892 + 120572119892120588119892119892 minus 120573 (V119892 minus V119904) + nabla sdot (120572119892120591119892)+ 119878119892119904119906119904

(6)

where p 120591119892 and u119904 represent the gas pressure gas stresstensor and the particle mean velocity respectively The term




120573 =

34120572119904120572119892120588119892 10038161003816100381610038161003816119907119892 minus 11990711990410038161003816100381610038161003816119889119904 119862119863120572119892minus265 120572119892 gt 08

15012057221199041205831198921205721198921198892119904 + 175120588119892120572119904 10038161003816100381610038161003816119907119892 minus 119907s10038161003816100381610038161003816119889119904 120572119892 le 08

(7)

119862119863 = 044 Re119904 gt 100024119877119890119904 [1 + 0151198771198901199040687] Re119904 le 1000 (8)

119877119890119904 = 12057211989212058811989210038161003816100381610038161003816119907119892 minus 11990711990410038161003816100381610038161003816 119889119904120583119904 (9)



120583119892 = 120583119892119897 + 120583119892119905 (11)


120583119892119905 = 120588119892119862120583 1198962120576 (12)





(13)


1205762119896 + radicV120576+ 1198621120576 1205761198961198623120576119866119887

(14)




(15)

119866119887 = 120581119892119894 120583119905119875119903119905120597119879120597119909119894 (16)

C1205761 = max [043 + 120578120578 + 5] (17)

120578 = (2119864119894119895119864119894119895)12 119896120576 (18)

119864119894119895 = 12 ( 120597119906119894120597119909119895 +120597119906119895120597119909119894 ) (19)



(20)



(21)

120582119904 = 431205721199041205881199041198891199041198920 (1 + 119890)radicΘ119904120587 (22)

120583s = 4512057221199041205881199041198891199041198920 (1 + 119890)radicΘ119904120587 +10120588119904119889119904radic120587Θ11990496 (1 + 119890) 1205721199041198920 [1

+ 451205721199041198920 (1 + 119890)]2 + 119901119904 sin 1206012radic1198682119863

(23)



(24)

119896119904= 150120588119904119889119904radicΘ119904120587384 (1 minus 119890) 1198920 [1 +

651205721199041198920 (1 + 119890)]2

+ 212058811990412057221199041198891199041198920 (1 + 119890)radicΘ119904120587

(25)



1198920 = [1 minus ( 120572119904120572119904max)13]

minus1

(27)


119901119904 = 119901119896119894119899119890119905119894119888 + 119901119891119903119894119888119905119894119900119899 (28)


119901119896119894119899119890119905119894119888 = 120572119904120588119904Θ[1 + 21198920120572119904 (1 + 119890)] (29)




119865119903 = 01120572119904 (31)


120583119891119903119894119888119905119894119900119899 = 119901119891119903119894119888119905119894119900119899 sin 120601 (32)




(33)


(34)



ℎ119892119904 = ℎ119904119892 = 61205821198921205721198921205721199041198731199061199041198892119904 (35)



(36)















(R1)



119903 = 119860 exp( minus119864119877119879119904)119891 (120594) (37)






(a)

750mm

350 mm

200 mm

Φ 4

00 m

m

Φ20

0 m

m50 mm

Φ10 mm

Air

Flue gas

Z

Y

X

Heat flux

(b)









∘C) 25



∘C) 200sim300






000

006

012

018

024

030

Grid number222342398468618327788361

ＰＭ(m

s)

ＳH

Ｔ

Ｓ

LH

0

(a)

00 02 04 06 08 10

000

004

008

012

016

020

Grid number222342398468618327788361

ＴL

ＰＭ(m

s)

Ｔ

Ｓ

LH

0

(b)


00 02 04 06 08 10

00

01

02

03

04

05

06


0 LH

ＴL

ＰＭ(m

s)

Ｔ

Ｓ

(a)

ＰＭ２

ＳH

Ｔ

Ｓ

LH


02

00

minus02

minus04

minus06

minus08

minus10

0


(b)






470 480 490 500 510 520 530 540Temperature (K)

00

01

02

03

04

Mol

e fra

ctio

n (

)

CO

Experiment

2

（4















Schematic









05505225049504675044041250385035750330302502750247502201925016501375011008250055002750

(a)

(b)



Ｉ

Ｉ

Ｓ

Ｓ

Ｔ

ＳＩ

Ｔ

Ｔ

ＳＭ

Ｓ

ＴＩ

Ｔ

L

H







x = 005 mx = 0375 mx = 075 m

ＰＭ

２


2

0

minus2

minus4

minus6

minus8

minus10

(a)

x = 005 mx = 0375 mx = 075 m

030

025

020

015

010

005

000

00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)







600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)


0210201901801701601501401301201101009008007006005004003002001

(a)

(b)



0016001550015001450014001350013001250012001150011001500100095000900085000800075007000650006

(a)

(b)


0002700026400025800025200024600024000234000228000222000216000210002040001980001920001860001800017400016800016200015600015

(a)

(b)



0001350001320001290001260001230001200011700011400011100010800010500010200009900009600009300009000087000084000081000078000075

(a)

(b)








09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２



(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018











120573 =

34120572119904120572119892120588119892 10038161003816100381610038161003816119907119892 minus 11990711990410038161003816100381610038161003816119889119904 119862119863120572119892minus265 120572119892 gt 08

15012057221199041205831198921205721198921198892119904 + 175120588119892120572119904 10038161003816100381610038161003816119907119892 minus 119907s10038161003816100381610038161003816119889119904 120572119892 le 08

(7)

119862119863 = 044 Re119904 gt 100024119877119890119904 [1 + 0151198771198901199040687] Re119904 le 1000 (8)

119877119890119904 = 12057211989212058811989210038161003816100381610038161003816119907119892 minus 11990711990410038161003816100381610038161003816 119889119904120583119904 (9)



120583119892 = 120583119892119897 + 120583119892119905 (11)


120583119892119905 = 120588119892119862120583 1198962120576 (12)





(13)


1205762119896 + radicV120576+ 1198621120576 1205761198961198623120576119866119887

(14)




(15)

119866119887 = 120581119892119894 120583119905119875119903119905120597119879120597119909119894 (16)

C1205761 = max [043 + 120578120578 + 5] (17)

120578 = (2119864119894119895119864119894119895)12 119896120576 (18)

119864119894119895 = 12 ( 120597119906119894120597119909119895 +120597119906119895120597119909119894 ) (19)



(20)



(21)

120582119904 = 431205721199041205881199041198891199041198920 (1 + 119890)radicΘ119904120587 (22)

120583s = 4512057221199041205881199041198891199041198920 (1 + 119890)radicΘ119904120587 +10120588119904119889119904radic120587Θ11990496 (1 + 119890) 1205721199041198920 [1

+ 451205721199041198920 (1 + 119890)]2 + 119901119904 sin 1206012radic1198682119863

(23)



(24)

119896119904= 150120588119904119889119904radicΘ119904120587384 (1 minus 119890) 1198920 [1 +

651205721199041198920 (1 + 119890)]2

+ 212058811990412057221199041198891199041198920 (1 + 119890)radicΘ119904120587

(25)



1198920 = [1 minus ( 120572119904120572119904max)13]

minus1

(27)


119901119904 = 119901119896119894119899119890119905119894119888 + 119901119891119903119894119888119905119894119900119899 (28)


119901119896119894119899119890119905119894119888 = 120572119904120588119904Θ[1 + 21198920120572119904 (1 + 119890)] (29)




119865119903 = 01120572119904 (31)


120583119891119903119894119888119905119894119900119899 = 119901119891119903119894119888119905119894119900119899 sin 120601 (32)




(33)


(34)



ℎ119892119904 = ℎ119904119892 = 61205821198921205721198921205721199041198731199061199041198892119904 (35)



(36)















(R1)



119903 = 119860 exp( minus119864119877119879119904)119891 (120594) (37)






(a)

750mm

350 mm

200 mm

Φ 4

00 m

m

Φ20

0 m

m50 mm

Φ10 mm

Air

Flue gas

Z

Y

X

Heat flux

(b)









∘C) 25



∘C) 200sim300






000

006

012

018

024

030

Grid number222342398468618327788361

ＰＭ(m

s)

ＳH

Ｔ

Ｓ

LH

0

(a)

00 02 04 06 08 10

000

004

008

012

016

020

Grid number222342398468618327788361

ＴL

ＰＭ(m

s)

Ｔ

Ｓ

LH

0

(b)


00 02 04 06 08 10

00

01

02

03

04

05

06


0 LH

ＴL

ＰＭ(m

s)

Ｔ

Ｓ

(a)

ＰＭ２

ＳH

Ｔ

Ｓ

LH


02

00

minus02

minus04

minus06

minus08

minus10

0


(b)






470 480 490 500 510 520 530 540Temperature (K)

00

01

02

03

04

Mol

e fra

ctio

n (

)

CO

Experiment

2

（4















Schematic









05505225049504675044041250385035750330302502750247502201925016501375011008250055002750

(a)

(b)



Ｉ

Ｉ

Ｓ

Ｓ

Ｔ

ＳＩ

Ｔ

Ｔ

ＳＭ

Ｓ

ＴＩ

Ｔ

L

H







x = 005 mx = 0375 mx = 075 m

ＰＭ

２


2

0

minus2

minus4

minus6

minus8

minus10

(a)

x = 005 mx = 0375 mx = 075 m

030

025

020

015

010

005

000

00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)







600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)


0210201901801701601501401301201101009008007006005004003002001

(a)

(b)



0016001550015001450014001350013001250012001150011001500100095000900085000800075007000650006

(a)

(b)


0002700026400025800025200024600024000234000228000222000216000210002040001980001920001860001800017400016800016200015600015

(a)

(b)



0001350001320001290001260001230001200011700011400011100010800010500010200009900009600009300009000087000084000081000078000075

(a)

(b)








09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２



(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018










1198920 = [1 minus ( 120572119904120572119904max)13]

minus1

(27)


119901119904 = 119901119896119894119899119890119905119894119888 + 119901119891119903119894119888119905119894119900119899 (28)


119901119896119894119899119890119905119894119888 = 120572119904120588119904Θ[1 + 21198920120572119904 (1 + 119890)] (29)




119865119903 = 01120572119904 (31)


120583119891119903119894119888119905119894119900119899 = 119901119891119903119894119888119905119894119900119899 sin 120601 (32)




(33)


(34)



ℎ119892119904 = ℎ119904119892 = 61205821198921205721198921205721199041198731199061199041198892119904 (35)



(36)















(R1)



119903 = 119860 exp( minus119864119877119879119904)119891 (120594) (37)






(a)

750mm

350 mm

200 mm

Φ 4

00 m

m

Φ20

0 m

m50 mm

Φ10 mm

Air

Flue gas

Z

Y

X

Heat flux

(b)









∘C) 25



∘C) 200sim300






000

006

012

018

024

030

Grid number222342398468618327788361

ＰＭ(m

s)

ＳH

Ｔ

Ｓ

LH

0

(a)

00 02 04 06 08 10

000

004

008

012

016

020

Grid number222342398468618327788361

ＴL

ＰＭ(m

s)

Ｔ

Ｓ

LH

0

(b)


00 02 04 06 08 10

00

01

02

03

04

05

06


0 LH

ＴL

ＰＭ(m

s)

Ｔ

Ｓ

(a)

ＰＭ２

ＳH

Ｔ

Ｓ

LH


02

00

minus02

minus04

minus06

minus08

minus10

0


(b)






470 480 490 500 510 520 530 540Temperature (K)

00

01

02

03

04

Mol

e fra

ctio

n (

)

CO

Experiment

2

（4















Schematic









05505225049504675044041250385035750330302502750247502201925016501375011008250055002750

(a)

(b)



Ｉ

Ｉ

Ｓ

Ｓ

Ｔ

ＳＩ

Ｔ

Ｔ

ＳＭ

Ｓ

ＴＩ

Ｔ

L

H







x = 005 mx = 0375 mx = 075 m

ＰＭ

２


2

0

minus2

minus4

minus6

minus8

minus10

(a)

x = 005 mx = 0375 mx = 075 m

030

025

020

015

010

005

000

00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)







600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)


0210201901801701601501401301201101009008007006005004003002001

(a)

(b)



0016001550015001450014001350013001250012001150011001500100095000900085000800075007000650006

(a)

(b)


0002700026400025800025200024600024000234000228000222000216000210002040001980001920001860001800017400016800016200015600015

(a)

(b)



0001350001320001290001260001230001200011700011400011100010800010500010200009900009600009300009000087000084000081000078000075

(a)

(b)








09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２



(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018















(R1)



119903 = 119860 exp( minus119864119877119879119904)119891 (120594) (37)






(a)

750mm

350 mm

200 mm

Φ 4

00 m

m

Φ20

0 m

m50 mm

Φ10 mm

Air

Flue gas

Z

Y

X

Heat flux

(b)









∘C) 25



∘C) 200sim300






000

006

012

018

024

030

Grid number222342398468618327788361

ＰＭ(m

s)

ＳH

Ｔ

Ｓ

LH

0

(a)

00 02 04 06 08 10

000

004

008

012

016

020

Grid number222342398468618327788361

ＴL

ＰＭ(m

s)

Ｔ

Ｓ

LH

0

(b)


00 02 04 06 08 10

00

01

02

03

04

05

06


0 LH

ＴL

ＰＭ(m

s)

Ｔ

Ｓ

(a)

ＰＭ２

ＳH

Ｔ

Ｓ

LH


02

00

minus02

minus04

minus06

minus08

minus10

0


(b)






470 480 490 500 510 520 530 540Temperature (K)

00

01

02

03

04

Mol

e fra

ctio

n (

)

CO

Experiment

2

（4















Schematic









05505225049504675044041250385035750330302502750247502201925016501375011008250055002750

(a)

(b)



Ｉ

Ｉ

Ｓ

Ｓ

Ｔ

ＳＩ

Ｔ

Ｔ

ＳＭ

Ｓ

ＴＩ

Ｔ

L

H







x = 005 mx = 0375 mx = 075 m

ＰＭ

２


2

0

minus2

minus4

minus6

minus8

minus10

(a)

x = 005 mx = 0375 mx = 075 m

030

025

020

015

010

005

000

00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)







600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)


0210201901801701601501401301201101009008007006005004003002001

(a)

(b)



0016001550015001450014001350013001250012001150011001500100095000900085000800075007000650006

(a)

(b)


0002700026400025800025200024600024000234000228000222000216000210002040001980001920001860001800017400016800016200015600015

(a)

(b)



0001350001320001290001260001230001200011700011400011100010800010500010200009900009600009300009000087000084000081000078000075

(a)

(b)








09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２



(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018









(a)

750mm

350 mm

200 mm

Φ 4

00 m

m

Φ20

0 m

m50 mm

Φ10 mm

Air

Flue gas

Z

Y

X

Heat flux

(b)









∘C) 25



∘C) 200sim300






000

006

012

018

024

030

Grid number222342398468618327788361

ＰＭ(m

s)

ＳH

Ｔ

Ｓ

LH

0

(a)

00 02 04 06 08 10

000

004

008

012

016

020

Grid number222342398468618327788361

ＴL

ＰＭ(m

s)

Ｔ

Ｓ

LH

0

(b)


00 02 04 06 08 10

00

01

02

03

04

05

06


0 LH

ＴL

ＰＭ(m

s)

Ｔ

Ｓ

(a)

ＰＭ２

ＳH

Ｔ

Ｓ

LH


02

00

minus02

minus04

minus06

minus08

minus10

0


(b)






470 480 490 500 510 520 530 540Temperature (K)

00

01

02

03

04

Mol

e fra

ctio

n (

)

CO

Experiment

2

（4















Schematic









05505225049504675044041250385035750330302502750247502201925016501375011008250055002750

(a)

(b)



Ｉ

Ｉ

Ｓ

Ｓ

Ｔ

ＳＩ

Ｔ

Ｔ

ＳＭ

Ｓ

ＴＩ

Ｔ

L

H







x = 005 mx = 0375 mx = 075 m

ＰＭ

２


2

0

minus2

minus4

minus6

minus8

minus10

(a)

x = 005 mx = 0375 mx = 075 m

030

025

020

015

010

005

000

00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)







600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)


0210201901801701601501401301201101009008007006005004003002001

(a)

(b)



0016001550015001450014001350013001250012001150011001500100095000900085000800075007000650006

(a)

(b)


0002700026400025800025200024600024000234000228000222000216000210002040001980001920001860001800017400016800016200015600015

(a)

(b)



0001350001320001290001260001230001200011700011400011100010800010500010200009900009600009300009000087000084000081000078000075

(a)

(b)








09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２



(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018










000

006

012

018

024

030

Grid number222342398468618327788361

ＰＭ(m

s)

ＳH

Ｔ

Ｓ

LH

0

(a)

00 02 04 06 08 10

000

004

008

012

016

020

Grid number222342398468618327788361

ＴL

ＰＭ(m

s)

Ｔ

Ｓ

LH

0

(b)


00 02 04 06 08 10

00

01

02

03

04

05

06


0 LH

ＴL

ＰＭ(m

s)

Ｔ

Ｓ

(a)

ＰＭ２

ＳH

Ｔ

Ｓ

LH


02

00

minus02

minus04

minus06

minus08

minus10

0


(b)






470 480 490 500 510 520 530 540Temperature (K)

00

01

02

03

04

Mol

e fra

ctio

n (

)

CO

Experiment

2

（4















Schematic









05505225049504675044041250385035750330302502750247502201925016501375011008250055002750

(a)

(b)



Ｉ

Ｉ

Ｓ

Ｓ

Ｔ

ＳＩ

Ｔ

Ｔ

ＳＭ

Ｓ

ＴＩ

Ｔ

L

H







x = 005 mx = 0375 mx = 075 m

ＰＭ

２


2

0

minus2

minus4

minus6

minus8

minus10

(a)

x = 005 mx = 0375 mx = 075 m

030

025

020

015

010

005

000

00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)







600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)


0210201901801701601501401301201101009008007006005004003002001

(a)

(b)



0016001550015001450014001350013001250012001150011001500100095000900085000800075007000650006

(a)

(b)


0002700026400025800025200024600024000234000228000222000216000210002040001980001920001860001800017400016800016200015600015

(a)

(b)



0001350001320001290001260001230001200011700011400011100010800010500010200009900009600009300009000087000084000081000078000075

(a)

(b)








09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２



(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018









470 480 490 500 510 520 530 540Temperature (K)

00

01

02

03

04

Mol

e fra

ctio

n (

)

CO

Experiment

2

（4















Schematic









05505225049504675044041250385035750330302502750247502201925016501375011008250055002750

(a)

(b)



Ｉ

Ｉ

Ｓ

Ｓ

Ｔ

ＳＩ

Ｔ

Ｔ

ＳＭ

Ｓ

ＴＩ

Ｔ

L

H







x = 005 mx = 0375 mx = 075 m

ＰＭ

２


2

0

minus2

minus4

minus6

minus8

minus10

(a)

x = 005 mx = 0375 mx = 075 m

030

025

020

015

010

005

000

00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)







600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)


0210201901801701601501401301201101009008007006005004003002001

(a)

(b)



0016001550015001450014001350013001250012001150011001500100095000900085000800075007000650006

(a)

(b)


0002700026400025800025200024600024000234000228000222000216000210002040001980001920001860001800017400016800016200015600015

(a)

(b)



0001350001320001290001260001230001200011700011400011100010800010500010200009900009600009300009000087000084000081000078000075

(a)

(b)








09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２



(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018











Schematic









05505225049504675044041250385035750330302502750247502201925016501375011008250055002750

(a)

(b)



Ｉ

Ｉ

Ｓ

Ｓ

Ｔ

ＳＩ

Ｔ

Ｔ

ＳＭ

Ｓ

ＴＩ

Ｔ

L

H







x = 005 mx = 0375 mx = 075 m

ＰＭ

２


2

0

minus2

minus4

minus6

minus8

minus10

(a)

x = 005 mx = 0375 mx = 075 m

030

025

020

015

010

005

000

00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)







600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)


0210201901801701601501401301201101009008007006005004003002001

(a)

(b)



0016001550015001450014001350013001250012001150011001500100095000900085000800075007000650006

(a)

(b)


0002700026400025800025200024600024000234000228000222000216000210002040001980001920001860001800017400016800016200015600015

(a)

(b)



0001350001320001290001260001230001200011700011400011100010800010500010200009900009600009300009000087000084000081000078000075

(a)

(b)








09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２



(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018









05505225049504675044041250385035750330302502750247502201925016501375011008250055002750

(a)

(b)



Ｉ

Ｉ

Ｓ

Ｓ

Ｔ

ＳＩ

Ｔ

Ｔ

ＳＭ

Ｓ

ＴＩ

Ｔ

L

H







x = 005 mx = 0375 mx = 075 m

ＰＭ

２


2

0

minus2

minus4

minus6

minus8

minus10

(a)

x = 005 mx = 0375 mx = 075 m

030

025

020

015

010

005

000

00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)







600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)


0210201901801701601501401301201101009008007006005004003002001

(a)

(b)



0016001550015001450014001350013001250012001150011001500100095000900085000800075007000650006

(a)

(b)


0002700026400025800025200024600024000234000228000222000216000210002040001980001920001860001800017400016800016200015600015

(a)

(b)



0001350001320001290001260001230001200011700011400011100010800010500010200009900009600009300009000087000084000081000078000075

(a)

(b)








09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２



(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018










x = 005 mx = 0375 mx = 075 m

ＰＭ

２


2

0

minus2

minus4

minus6

minus8

minus10

(a)

x = 005 mx = 0375 mx = 075 m

030

025

020

015

010

005

000

00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)







600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)


0210201901801701601501401301201101009008007006005004003002001

(a)

(b)



0016001550015001450014001350013001250012001150011001500100095000900085000800075007000650006

(a)

(b)


0002700026400025800025200024600024000234000228000222000216000210002040001980001920001860001800017400016800016200015600015

(a)

(b)



0001350001320001290001260001230001200011700011400011100010800010500010200009900009600009300009000087000084000081000078000075

(a)

(b)








09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２



(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018









600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)







600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)


0210201901801701601501401301201101009008007006005004003002001

(a)

(b)



0016001550015001450014001350013001250012001150011001500100095000900085000800075007000650006

(a)

(b)


0002700026400025800025200024600024000234000228000222000216000210002040001980001920001860001800017400016800016200015600015

(a)

(b)



0001350001320001290001260001230001200011700011400011100010800010500010200009900009600009300009000087000084000081000078000075

(a)

(b)








09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２



(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018









600Temperature (K)

585570555540525510495480465450435420405390375360345330315300

(a)

(b)


0210201901801701601501401301201101009008007006005004003002001

(a)

(b)



0016001550015001450014001350013001250012001150011001500100095000900085000800075007000650006

(a)

(b)


0002700026400025800025200024600024000234000228000222000216000210002040001980001920001860001800017400016800016200015600015

(a)

(b)



0001350001320001290001260001230001200011700011400011100010800010500010200009900009600009300009000087000084000081000078000075

(a)

(b)








09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２



(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018









0016001550015001450014001350013001250012001150011001500100095000900085000800075007000650006

(a)

(b)


0002700026400025800025200024600024000234000228000222000216000210002040001980001920001860001800017400016800016200015600015

(a)

(b)



0001350001320001290001260001230001200011700011400011100010800010500010200009900009600009300009000087000084000081000078000075

(a)

(b)








09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２



(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018









0001350001320001290001260001230001200011700011400011100010800010500010200009900009600009300009000087000084000081000078000075

(a)

(b)








09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２



(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018









09509025085508075076071250665061750570522504750427503803325028502375019014250095004750

(a)

(b)


minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２



(a)

00

01

02

03

04


00 02 04 06 08 10ＴL

ＰＭ(m

s)

(b)





minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018









minus15

minus12

minus9

minus6

minus3

0

ＰＭ

２


= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(a)

000

015

030

045

060

075

ＰＭ(m

s)

00 02 04 06 08 10ＴL

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)



Tem

pera

ture

(K)


475

500

525

550

575

600

(a)


Tem

pera

ture

(K)


572

573

574

575

576

577

578

(b)







Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018










Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

475

500

525

550

575

600

625

(a)


Tem

pera

ture

(K)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

572

573

574

575

576

577

578

(b)


Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

40

50

60

70

80

90

100

CO

Oxidized coal pitch

2

（4

30 40 50 60 7020Air flow rate (Ｇ3Ｂ)

00

02

04

06

08

10

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)


(b)






00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018









00

02

04

06

08

10


40

50

60

70

80

90

100

Mol

e fra

ctio

n (

)

Mas

s fra

ctio

n (

)

CO

Oxidized coal pitch

2

（4

(a)

0

20

40

60

80

100


Mas

s fra

ctio

n (

)

= 095 rpm = 143 rpm = 191 rpm = 239 rpm

(b)





4 Conclusions












Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018













Nomenclature


Greek Letters



Subscripts


Data Availability




Acknowledgments


References







































Journal of












Journal of







Volume 2018






Volume 2018







































Journal of












Journal of







Volume 2018






Volume 2018








modeling of oxidation process of coal tar pitch in...

Documents