The  physical  phenomena  occurring  inside  a  rotary  kiln  can  be  separated  in  two  parts:  gas  phase  (freeboard)  phenomena  and  granular  bed  phenomena.    In  the  freeboard  the  main  phenomena  are:  •  Turbulent  non-­‐premixed  combus?on  •  Heat  Transfer  including  Radia?on    On  the  granular  bed  the  main  phenomena:  •  Heat  Transfer  •  Chemical  Reac?ons  •  Phase  changes    Due  to  the  complexity  of  the    physical  phenomena  of  a  rotary  kiln,  one  can  divide  the  model  in  two:  

•  Freeboard  CFD  model  •  Granular  Bed  model        

Turbulent  combus?on  results  from  the  two-­‐way  interac?on  of  chemistry  and  turbulence.  When  a  fame  interacts  with  a  turbulent  flow,  turbulence  is  modified  by  combus?on  because  of  the  strong  flow  accelera?ons  through  the  flame  front  induced  by  heat  release,  and  because  of  the  large  changes  in  kinema?c  viscosity  associated  with  temperature  changes.      •   Reynolds  stress  tensor:  Realizable  k-­‐epsilon  model  (Turbulence  Model)  •   Turbulent  scalar  flux:  Eddy  diffusivity  model  •   Mean  source  term:  Eddy  break-­‐up  model  (EBU)  •   RadiaFon:  ParFcipaFng  Media  RadiaFon  Model  (DOF)  •   NOx:  Zeldovich  Model    The  grid  was  done  using  polyhedral  elements:  2.8  Million  elements                

A  rotary  kiln  is  a  pyro-­‐processing  device  used  to  raise  materials  to  high  temperatures.  It  is  a  long  horizontal  cylinder  with  a  certain  inclina?on  with  respect  to  its  axis.  Material  within  the  kiln  is  heated  to  high  temperatures  so  that  chemical  reac?ons  can  take  place.  A  rotary  kiln  is  therefore  fundamentally  a  heat  exchanger  from  which  energy  from  a  hot  gas  phase  is  transferred  to  the  bed  material.  The  energy  originates  from  the  combus?on  of  hydrocarbon  fuels  via  a  main  burner  at  the  hot  end.                      The  rotary  kiln  in  ques?on  is  a  counter-­‐  current  gas  direct  fired  Calcium  Aluminate  Cement  rotary  kiln.      •   Increasing  market  demand  for  high  purity  cement    •   Unscheduled  shutdown  due  to  ring  forma?on  •   Restric?ve  emission  regula?ons  (i.e.:  NOx)  have  triggered  the  industrial  partner’s  management  to  increase  its  knowledge  base  on  kiln  processes.  The  model  is  a  plaRorm  to  understand  and  op?mize  the  opera?on  of  the  process.  

Numerical  Modeling  of  Rotary  Kilns  M.A.  Romero  Valle,  M.  Pisaroni  ,  D.  van  Puyvelde  and  D.  J.  P.  Lahaye,  Scien?fic  Compu?ng  Group,  DelX  Ins?tute  of  Applied  Mathema?cs,  Faculty  of  Electrical  

Engineering,  Mathema?cs  and  Computer  Science,  DelX  University  of  Technology,  The  Netherlands    

Objec?ves  

Physical  Phenomena  

CFD  Freeboard  Model   Industrial  Case  Results  

Further  Work  

References  CounteracFng  Ring  FormaFon  in  Rotary  Kilns,    Accepted  for  publica?on  in  Mathema?cs  with  Industry.  M.  Pisaroni,  D.  J.  P.  Lahaye  and  R.  Sadi.    Numerical  Modeling  of  Rotary  Kilns,  in  prepara?on  M.A.  Romero  Valle,  M.  Pisaroni,  D.  van  Puyvelde,  and  D.  J.  P.  Lahaye.  

The  developed  one-­‐dimensional  granular  bed  model  encompasses  two  phenomena  in  the  kiln:  the  axial  heat  transfer  and  the  sintering  reac?ons  occurring  in  the  bed.  A  one-­‐dimensional  axial  heat  transfer  model  was  developed  and  validated  with  data  from  the  literature.  The  sintering  reac?on  kine?cs  model  was  developed  taking  as  basis  informa?on  found  in  literature  and  experimental  XRD  (X-­‐Ray  Diffrac?on)  data  handed  by  the  industrial  partner.      •  Energy  balance  for  Granular  Bed:        •  3-­‐D  diffusion  controlled  sintering  reacFon  model:    •  Correla?ons  coming  from  literature  were  used  to  determine  the  Heat  Transfer  Coefficients  for  the  different  

heat  transfer  paths  that  exist  in  the  granular  bed  system.    •  The  model  uses  results  from  the  CFD  freeboard  model  as  input.  •  ValidaFon  was  done  by  modeling  an  inert  bed  and  comparing  the  model  with  exis?ng  data  from  the  literature.    Valida?on  Results:                      

                                         *Experimental  data  taken  from  Barr  et  al.  and                                                XRD  Data  from  industrial  partner.  

 

Granular  Bed  Model  

3-2 Radiative Heat Transfer 25

mscp,sdTs = qdA [W ], (3-1)

where the left hand side denotes the heating of the bulk material and the right hand side theheat transferred to the material at position z. It is to be noted that the heat transfer pathsare the same as described in Chapter 1.

By rearranging the terms one gets the following:

mscp,sdTs

dz= qLcrd = QLcrd

A= Q

LK[Js≠1m≠1], (3-2)

where ms is the mass flow rate, cp,s the heat capacity of the solids, Ts the temperature ofthe bulk solids, q the heat flux into the bulk solids, Q the heat transfer rate, Lcrd the chordlength for calculating the area of heat exchange, A the heat exchange area between freeboardand granular bed, and LK the total kiln length.

It is to be noted that implicit in the heat transfer rate Q shown above are the heat transferpaths described in Chapter 1. By noting this, one can observe that Equation 3-2 can also beseen as the governing equation of the axial heat transfer model.

In the following sections expressions for the heat transfer paths described in Chapter 1 willbe shown. It is to be noted the following adjustments in nomenclature with respect to Figure1-6 and the present chapter:

Qgæeb = Qradiation,gæs + Qconvection,gæs,

Qgæew = Qconvection,gæw,

Qewæeb = Qradiation,wæs.

On the left hand side one can observe the nomenclature given in Figure 1-6 and on the righthand side one can observe the nomenclature used in the present chapter.

One should note as well that the nomenclature used in the present chapter will be in accor-dance to mechanical and chemical engineering texts where a heat transfer coe�cient is used.We note that the heat transfer rate can be written as [4]:

Q = hA�T,

where Q is the heat flow [W], h the heat transfer coe�cient [W/m2K], A the heat transfersurface area [m2] and �T the temperature di�erence between two materials [K].

3-2 Radiative Heat Transfer

In the present section models considering radiative heat transfer within the kiln will be pre-sented.

Master of Science Thesis M. A. Romero Valle

3-2 Radiative Heat Transfer 25

mscp,sdTs = qdA [W ], (3-1)

where the left hand side denotes the heating of the bulk material and the right hand side theheat transferred to the material at position z. It is to be noted that the heat transfer pathsare the same as described in Chapter 1.

By rearranging the terms one gets the following:

mscp,sdTs

dz= qLcrd = QLcrd

A= Q

LK[Js≠1m≠1], (3-2)

where ms is the mass flow rate, cp,s the heat capacity of the solids, Ts the temperature ofthe bulk solids, q the heat flux into the bulk solids, Q the heat transfer rate, Lcrd the chordlength for calculating the area of heat exchange, A the heat exchange area between freeboardand granular bed, and LK the total kiln length.

It is to be noted that implicit in the heat transfer rate Q shown above are the heat transferpaths described in Chapter 1. By noting this, one can observe that Equation 3-2 can also beseen as the governing equation of the axial heat transfer model.

In the following sections expressions for the heat transfer paths described in Chapter 1 willbe shown. It is to be noted the following adjustments in nomenclature with respect to Figure1-6 and the present chapter:

Qgæeb = Qradiation,gæs + Qconvection,gæs,

Qgæew = Qconvection,gæw,

Qewæeb = Qradiation,wæs.

On the left hand side one can observe the nomenclature given in Figure 1-6 and on the righthand side one can observe the nomenclature used in the present chapter.

One should note as well that the nomenclature used in the present chapter will be in accor-dance to mechanical and chemical engineering texts where a heat transfer coe�cient is used.We note that the heat transfer rate can be written as [4]:

Q = hA�T,

where Q is the heat flow [W], h the heat transfer coe�cient [W/m2K], A the heat transfersurface area [m2] and �T the temperature di�erence between two materials [K].

3-2 Radiative Heat Transfer

In the present section models considering radiative heat transfer within the kiln will be pre-sented.

Master of Science Thesis M. A. Romero Valle

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1300

400

500

600

700

800

900

1000

1100

1200

Axial Position (m)

Te

mp

era

ture

(K

)

Bulk Temperature

Wall Temperature

Gas Temperature

Gas Temperature (Barr et al., 1989)

Bed Temperature (Barr et al., 1989)

•  The  freeboard  CFD  model  was  used  to  evaluate  how  by  having  an  excess  air  one  could  reduce  the  peak  temperature  of  the  kiln.  The  model  was  used  to  determine  that  a  120%  air  excess  would  reduce  the  peak  temperature  to  avoid  ring  forma?on.  The  result  was  validated  in  situ.  

•  The  granular  bed  model  was  used  to  analyze  the  plant  observa?ons  regarding  the  product  quality  altera?ons  with  respect  to  the  opera?ng  changes  derived  with  the  freeboard  model.  It  is  concluded  that  the  proposed  opera?ng  changes  increase  product  quality  due  to  a  slower  conversion  of  Alumina.  

                           100%  Base  Air  (ring  blockage)                                120%  Excess  Air  (no  rings)  

0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (min)

Conve

rsio

n

Conversion of Alumina (Al2O3)

A = 14500, Ea=205 Kj/mol, f(alpha)=D4(alpha)

Experimental Values XRD

Transversal  Granular  Flow  +  Heat  Transfer  Model    •  Discrete  Element  Modeling  •  Con?nuum  Approach  •  Energy  Balance  

          !0.6 !0.4 !0.2 0 0.2 0.4 0.6

!1.25

!1.2

!1.15

!1.1

!1.05

!1

!0.95

!0.9

!0.85

!0.8

1900

1905

1910

1915

1920

1925

1930

1935

1940

1945

!0.6 !0.4 !0.2 0 0.2 0.4 0.6

!1.25

!1.2

!1.15

!1.1

!1.05

!1

!0.95

!0.9

!0.85

!0.8

2000

2050

2100

2150

2200

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

Normalized Kiln Length (!)

Conve

rsio

n / F

ract

ion

Al2O3 Conversion / Liquid Fraction

Al2O3 Conversion

Liquid Fraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

Normalized Kiln Length (!)

Conve

rsio

n / F

ract

ion

Al2O3 Conversion / Liquid Fraction

Al2O3 ConversionLiquid Fraction