CFD Simulation of Heat Transfer in Fluidized Bed Reactor.
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Publishing Edit or Wohlbier , T.
Send m ail
105 Springdale Lane, Millersville, USA, PA 17551;
Xu , X.P.
Send m ail
Huaqiao Universit y, Minist ry of Educat ion Engineering Research Cent er for Brit t le Mat erials
Machining; Xiam en, China, 361021;
Edit or ia l Boa r d
Cheng , Y.S.
Send m ail
Harbin I nst it ut e of Technology, School of Mat erials Science and Technology; P.O. Box 435,
Harbin, China, 150001;
Lucas , M.
Universit y of Glasgow, Depart m ent of Mechanical Engineering; Glasgow, Unit ed Kingdom ,
G12 8QQ;
Pa pe r
Tit le Pa ge
Experim ent al I nvest igat ion on t he Use of Secondary Refrigerant in Freezer for Energy
Savings
Aut hors: Aries Prih Har yono, Edi Sukam t o, Sum eru, Farid Nasir Ani
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Mirsoheil
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Abst ract : Considering t he growing role of nat ural gas as an alt ernat ive fuel in st at ionary and
aut om obile engines and t he differences in it s...
239
Flow Charact erist ics around Four Circular Cylinders in Equispaced Arrangem ent near a Plane
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Abst ract : The flow charact erist ics around four circular cylinders in equispaced arrangem ent
locat ed near a plane wall were invest igat ed...
245
Experim ent al St udy on t he Perform ance of I n - Cabin Vent ilat ion Syst em
Aut hors: Abdul Lat iff Zulkarnain, Cheong Weng Soon, Bam bang Supriyo, Mohd Rozi Mohd Perang,
Henry Nasut ion, Azhar Abdul Aziz
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Abst ract : Parking a car under t he hot sun wit h all windows closed could increase in - cabin
t em perat ure as high as 70°C. For such sit uat ion, hu m an...
251
Reduct ion of Energy Losses in t he End Wall Junct ion Area t hrough t he Addit ion of Forw ard
Facing St ep Turbulent Generat or
Aut hors: H. Mirm ant o, Sut risno, H. Sasongko, D.Z. Noor
Chapt er 1: Energy Conv ersion
Abst ract : The research is conduct ed in order t o reduce energy losses caused by t he
secondary flow in t he endwall j unct ion. This phenom enon is caused...
256
Biogas Pot ent ial of Co- Subst rat es in Balinese Biogas Plant s
Aut hors: Daniel Net t , I . Nyom an Suprapt a Winaya, I . Made Agus Put rawan, Rolf Wart m ann, Werner
Edelm ann
Chapt er 1: Energy Conv ersion
Abst ract : This research aim s t o give an ov erview on how t o im prov e t he biogas y eild in
Balinese digest er plant s using various co- subst rat es which are...
262
CFD Sim ulat ion of Heat Transfer in Fluidized Bed React or
Aut hors: I . Nyom an Supr apt a Winaya, I . Made Agus Put rawan, I . Nyom an Gede Suj ana, Made Sucipt a
Chapt er 1: Energy Conv ersion
Abst ract : This st udy aim s t o predict heat t ransfer from a heat ed bed in a gas fluidized bed
using Syam lal- OBrien drag coefficient . Discret e part icles...
267
I nfluence of Bioet hanol- Gasoline Blended Fuel on Perform ance and Em issions Charact erist ics
from Port I nj ect ion Sinj ai Engine 650 cc
Aut hors: Bam bang Sudarm ant a, Sudj ud Darsopuspit o, Dj oko Sungkono
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Abst ract : Perform ance and em issions charact erist ics from port inj ect ion SI NJAI engine 650
cc operat ing on bioet hanol- gasoline blended fuels of 0% , 5% ,...
273
I m proved Energy Saving for R22 Building Air Condit ioning Ret rofit t ed wit h Hydrocarbon
Refrigerant , St udy Case: Civil Engineering Depart m ent of I TS
Aut hors: Widyast ut i, Ar y Bacht iar Krishna Put ra, Ridho Hant oro, Eky Novianarent i, Arrad Ghani
Safit ra
Chapt er 1: Energy Conv ersion
Abst ract : Sepuluh Novem ber I nst it ut e of Technology ( I TS) encourages t he ECO Cam pus
program . The program enables I TS t o syst em at ically ident ify,...
281
The Evaluat ion of a Rigid Sail of Ship Using Wind Tunnel Test
Aut hors: Aries Suliset yono
Chapt er 1: Energy Conv ersion
Abst ract : This paper described t he evaluat ion of rigid sail perform ances by using t he wind
t unnel t est . The rigid sail m odels were dev eloped in t he...
287
Applied Mechanics and Materials Vol. 493 (2014) pp 267-272
© (2014) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMM.493.267
CFD Simulation of Heat Transfer in Fluidized Bed Reactor
I Nyoman Suprapta Winaya1, a, I Made Agus Putrawan2,b ,
I Nyoman Gede Sujana2, Made Sucipta4,c
1,4
2,3
Mechanical Engineering Department, Udayana University, Bali-Indonesia
Magister Program of Mechanical Engineering, Udayana University, Bali-Indonesia
a
[email protected], [email protected], [email protected]
Keywords: CFD, heat transfer, fluidized bed, Syamlal-O’Brein drag coefficient, Eulerian
Abstract
This study aims to predict heat transfer from a heated bed in a gas fluidized bed using
Syamlal-O’Brien drag coefficient. Discrete particles model with the Navier-Stokes equation and
Eulerian multiphase are used to approach heat transfer simulation. Coefficient of heat transfer which
is related to Nusselt Number and volume fraction are calculated using Gunn model which was
compiled from C++ program language. The effect of fluidization velocity variation on the heat
transfer coefficient comes to the fore, indicating the heat transfer and solid volume fraction at the bed
height are very dependent. Contour of solid volume fraction and temperature distribution are also
presented.
Introduction
Fluidization is defined as the contacting techniques through which fine solids are transformed
into a fluid using either gas or liquid. In fluidization contact between the gas and solid particle occurs
appropriately because its wide range of contact surface. Using wastes as a fuel in fluidized bed
system needs a deep understanding on fluidization phenomena. In this study, a Fluent Computational
Fluid Dynamics (CFD) program was applied to simulate fluid flow that is expected to provide
information about the feasibility of the utilization of solid waste as a fuel
Simulation of CFD has been widely developed recently, and it is one of the popular tools used
in simulating the fluidization [1]. The program could provide the flexibility to change the design
parameters without much cost, providing faster time of the trial, and also able to provide a detailed
information about the flow field especially in the area of measurement which is difficult or impossible
to obtain [2]. Armstrong and Luo [3] developed a model approach Syamlal-O'Brien drag coefficient
which showed more local fluctuations on the basis of particle terminal velocity with slight sensitivity
to the microscopic scale. Tasirin, et al. [4] conducted an experimental study as well as modeling and
it was found for a higher in gas velocity the fluidization process could be improved. Fluidization
behavior involves three important phases namely: the particle-dominated, predominantly gas and a
mixture of both.
CFD Model
Eulerian model in Fluent program is an important tool to study the solid particulate phase
which involves the complex inter-phase momentum. Therefore, it is important to use the correct drag
law to predict the early onset of fluidization occurred. Syamlal O’Brien model has been successfully
applied to predict hydrodynamic phenomena on fluidized bed compares to the experimental data. The
kinetic theory of granular flow (KTGF) applied with a two-fluid Eulerian-Eulerian model carried out
to heat transfer mechanism due to complexity problem from multiphase flow. Standard-setting
Syamlal O'Brien is as follows [5]:
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,
www.ttp.net. (ID: 36.86.237.235-08/01/14,05:40:01)
268
Advances in Applied Mechanics and Materials
=
3
4
,
−
,
1
Where Ksg, α, Res , CD, vs, vg and vr,s are the momentum exchange coefficient between solid and gas
phase, volume fraction, Reynold number of solid phase, drag coefficient, velocity of solid and gas,
the coefficient of terminal velocity for the solid phase respectively.
In the gas phase, Eulerian model is treated as a continuum, which can be described by a set of
volume average Navier-Stokes equations. For global mass balance is in the form of conservative as:
+ ∇.
= 0 2
and
is the fraction of each space, the density of the gas, and the gas phase velocity
Where ,
respectively. Thus, balance equation for the individual in the gas phase can be written as follows:
+ ∇.
=
+ ∇.
+
+
.
.
(3)
Here Yα is a mass fraction in the gas phase, . , is the net production rate due to gas-phase reactions.
Gas-phase momentum equation is written as follows:
+ ∇.
+
∇ +
+
∇.
∇.
=
+
(4)
=
(5)
Where; p, ,g, e,
and Igs are indicated as pressure, voltage, gravity, energy, energy rate and
momentum exchange term between the gas phase and particulate phases respectively.
In this study, the heat transfer is determined only in the zone of solid concentration. The heat
energy transfer is simplified as the two difference temperatures of gas-solid phase as Eq. 6. The heat
transfer coefficient with related to Nusselt Number and volume fraction from both phase is calculated
using Eq. 7.
, = ℎ
−
(6)
ℎ
=
6
7
Where; qs,g, Kg, Tg , Ts, dp, Nus, , are indicated as heat flux, gas thermal conductivity,
temperature each phase, diameter particles, Nusselt number and volume fraction of gas-solids
respectively. Hence, the Nusselt number is calculated using Gunn model as follows [6]:
= 7 − 10
g
+5
g
. 1 + 0.7
.
8
Where; Res and Pr are indicated as Reynold and Prandtl number respectively.
Numerical Set-Up and Grid Study
In order to reduce the computation time, the reactor system is designed as 5.08 cm and 70 cm
for diameter and height of reactor respectively with static bed height of 10 cm as seen in Fig. 1. Air
fluidization velocity is varied at 0.05, 0.09 and 0.13 cm/s with waste particle size of 0.03 cm.
The next entry on the stage is determining boundary conditions of the reactor section which is
divided as: the bottom is assumed as velocity inlet of the gas (side entrance), wall on each side and
pressure side outlet is assumed as side exit, and conditioning circumstances in the face is the fluid
mesh. For the initial condition, it is assumed to be adiabatic wall in which the gas phase is not going to
Applied Mechanics and Materials Vol. 493
269
slip along the wall while allowing for the solid phase of contact that refers to the Syamlal-O’Brien
drag coefficient. Eulerian granular iteration process is used for the gas phase and dense granules in
modeling of fluidized bed volume fraction. This model allows the processing issues in two different
phases of the volume control in the grid. Granular phase is assumed to have a uniform diameter and
solid-gas phase is completed individually with the mass and momentum equations (Eq. no. 3).
Simulation of heat transfer is carried out in Two-Dimension (2D) grid model and analyzed
using a model of Eulerian multiphase. Computation domain 2D discretized using rectangular cells
(Quad) with mesh total size of 0.41 and 0.29 cm for vertical and horizontal side respectively, and
terminated in steps of 0.005 s with 2000 iterations. The program can replace the partial differential
equations of continuity, momentum, and energy with algebraic equations which is an approximation
of the original continuum problem into a particle discrete model.
The process of selection menu which include the equation solver can be used to complete the
calculation in the simulation process. However, in some special case containing custom equations
such as heat transfer model is not included in the program. Heat transfer analysis on the fluidized bed
system simulation is affected by initial parameters such as material properties, flow rate, operating
temperature, density and the flow multiphase model equations. Hence, the C++ language program is
used to compile the mechanistic heat transfer model (eq. 7) into CFD program. The wall temperature
from reactor is set at 300 K (ambient temperature) and the solids phase is conditioned at combustion
mode temperature as high as 973 K. The initial determination of the parameters that used in the
simulation process can be seen from tables 1 and 2.
Exit side
Solid wall
70 cm
Entry side
5.08 cm
Fig. 1. Outline of a typical numerical setup
Table 1. Fluent Model using in simulation
Model
Settings
Space
2D
Solver time
Unsteady
Viscous
k epsilon
Wall Treatment
Multiphase Model
Standard Wall Functions
Solid fluid
270
Advances in Applied Mechanics and Materials
Table 2. Parameter properties of gas and waste particles
Gas
Properties
Unit
gas velocity
0.05; 0.0 9; 0.13 [cm/s]
g
gas density
1.225 [ kg/m3]
g
viscosity
1.79x10-5 [kg/m.s]
g
g
gravity acceleration
9.81 [m/s]
P
freeboard pressure
1.01 x 105 [Pa]
Particles
hbed
height bed static
10 [cm]
dp
particle diameter
0.03 [cm]
particle density
328 [kg/m3]
s
Specific heat
2000 [J/kg.K]
s
solids conductivity
0.08 [W/m.K]
s
Velocity magnitude (m/s)
Result and Discussion
Variations of air velocity flow into the reactor certainly have an important role on the
characteristics of bed hydrodynamic. As the velocity increased the gradient of fluidization velocity
also increased as shown in the Fig. 2 as the red colour. The domination between solid and gas can be
well visualized using CFD simulation.
0.0 5 m/s
0.09 m/s
0. 13 m/s
Fig. 2. Contour of fluidization characteristic for different velocity at 10 s
Fig. 3 shows the contour of temperature along the bed reactor at fluidization velocity of 0.05
m/s at the time step of 0 to 10 s. It was observed the heat flux continuously flowed as the velocity was
just started. The degradation of the red colour was found to change as the solid fraction decreased
mostly until the maximum bed height of 18 cm. The similar behavior was found for different
fluidization velocity in which the higher velocity resulted in longer contour temperature distribution.
271
Temperature (K)
Applied Mechanics and Materials Vol. 493
18 cm
Fig. 3. Contour of temperature distribution at velocity of 5 cm/s from 0 to 10 s
0,45
800
0,4
700
0,35
600
0,3
500
0,25
400
0,2
300
0,15
0,1
200
0,05
100
0
0
0,0
0,1
0,2
0,3
0,4
0,5
Heat transfer coefficient,htc (W/m2K)
Volume of solid fraction, vof
Fig. 4 shows the correlation between volumes of solid fraction to heat transfer coefficient (htc)
along reactor bed height after 10 s steps of iteration. It is observed that the initial bed height of 10 cm
increases until 18 cm at air velocity of 0.05 m/s (vof) with heat transfer coefficient of 500 - 650
W/m2K. It is clearly found that the solid volume fraction has a major effect on heat transfer
coefficient. In this study, the heat transfer coefficient above the bed height was not calculated.
vof
htc
0,6
Horizontal bed height (m)
Fig. 4 Volume of solid fraction and heat transfer coefficient at air velocity of 5 cm/s.
A similar behavior was observed when the fluidization velocity was increased. The increased
in velocity resulted in an increased the solid expansion of 21 and 30 cm at velocity of 9 and 13 cm/s
respectively. The increased in solid volume fraction was found between 0.22 – 0.33. The heat transfer
phenomenon tends to follow the behavior of the solid volume fraction and it was found at average of
655 W/m2K with the maximum of 710 W/m2K at velocity of 0.13 m/s. Fig. 5 shows that the higher
gas velocity resulted in the higher heat transfer coefficient.
272
Advances in Applied Mechanics and Materials
Fig. 5 Heat transfer coefficient along bed height at different velocity
Summary
Discrete particles model with Syamlal_O’Brien drag coefficient was used to predict heat transfer
from a heated bed in a 2-D bubbling fluidized bed. The two fluid simulation using energy balance and
momentum shows a good value to visualize the phenomenom into the bed. The heat transfer
coefficient is closely linked to the solids volume fraction in which the dominance of the particles
cause the high heat transfer coefficient. It seems that the mechanistic of Gunn model can be well
recommended to use in CFD simulation.
Acknowledgement: This study was kindly supported by Directorate of Higher Education-The
Indonesia’s Ministry of Education and Culture through Hibah Desentralisasi Pascasarjana of
Udayana University: No. 175.62/UN14.2/PNL.01.03.00/2013
References
[1] S. Kallio, M. Gulden, A. Hermason., Experimental study and CFD Simulation of a 2D
Circulating Fluidized Bed. Proceedings of the 20th International Conference on Fluidized Bed
Combustion, pp. 818 (2009).
[2] Amit Kumar., CFD Modeling of Gas-Liquid-Solid Fluidized Bed. Department of Chemical
Engineering National Institute of Technology Rourkela pp.769, Orissa (2008).
[3] L.M. Armstrong, S. Gu dan K.H. Luo. , Study of Wall-to-Bed Heat Transfer In a Bubling
Fluidized Bed Using the Kinetic Theory of Granular flow. International Journal of Heat and Mass
Transfer 53, pp. 4949-4959, (2010).
[4] S.M. Tasirin, S.K. Kamarudin dan A.M.A. Hweage, Mixing Behavior of Binary Polymer
Particles in Bubbling Fluidized Bed. Journal of Physical Science, Vol. 19 (1), pp. 13–29 (2008).
[5] M. Syamlal., D. Gidaspow, Hydrodynamics of fluidization: prediction of wall-to-bed heat transfer
coefficients, AIChE J, Vol. 31, pp. 127–135(1985).
[6] D.J. Gunn, Transfer on heat or mass to particles in fixed and fluidized beds, International Journal
of Heat and Mass Transfer, Vol. 21, pp. 467-476 (1978).
Applie d M e cha nics a nd M a t e r ia ls
I SSN :
1662- 7482
Abou t :
Applied Mechanics and Mat erials publishes only com plet e volum es on given t opics,
proceedings and com plet e special t opic volum es. Thus, we are not able to publish stand-alone
papers.
Applied Mechanics and Mat erials specializes in t he rapid publicat ion of proceedings of
int ernat ional conferences, w orkshops and sym posia as well as st at e- of- t he- art volum es on
t opics of current int erest in all areas of m ech anics and t opics relat ed t o m at erials science.
Aut hors ret ain t he right t o publish an ext ended, significant ly updat ed version in anot her
periodical.
I n de x in g: I ndex ed by Elsevier: SCOPUS w ww.scopus.com and Ei Com pendex ( CPX)
www.ei.org/ . Cam bridge Scient ific Abst ract s ( CSA) www.csa.com , Chem ical Abst ract s ( CA)
www.cas.org, Google and Google Scholar google.com , I SI ( I STP, CPCI , Web of Science)
www.isinet .com , I nst it ut ion of Elect rical Engineers ( I EE) www.iee.org, et c.
Publishing edit or: Thom as Wohlbier, TTP USA, t .wohlbier@t t p.net
Su bscr ipt ion :
I rregular: approx. 80- 100 volum es per y ear.
The
subscript ion
rat e
for web
access
is
EUR
St anding order price: 20% discount off list price
I SSN print 1660- 9336 I SSN cd 1660- 9336 I SSN web 1662- 7482
1089.00
per
year.
Pe r iodica l:
APPLI ED M ECH AN I CS AN D M ATERI ALS
I SSN : 1 6 6 2 - 7 4 8 2
Edit or ia l boa r d:
Edit or s
Publishing Edit or Wohlbier , T.
Send m ail
105 Springdale Lane, Millersville, USA, PA 17551;
Xu , X.P.
Send m ail
Huaqiao Universit y, Minist ry of Educat ion Engineering Research Cent er for Brit t le Mat erials
Machining; Xiam en, China, 361021;
Edit or ia l Boa r d
Cheng , Y.S.
Send m ail
Harbin I nst it ut e of Technology, School of Mat erials Science and Technology; P.O. Box 435,
Harbin, China, 150001;
Lucas , M.
Universit y of Glasgow, Depart m ent of Mechanical Engineering; Glasgow, Unit ed Kingdom ,
G12 8QQ;
Pa pe r
Tit le Pa ge
Experim ent al I nvest igat ion on t he Use of Secondary Refrigerant in Freezer for Energy
Savings
Aut hors: Aries Prih Har yono, Edi Sukam t o, Sum eru, Farid Nasir Ani
Chapt er 1: Energy Conv ersion
Abst ract : This st udy present s an experim ent al st udy on a freezer which has sm all cooling
capacit y. Typically a freezer uses prim ary refrigerant ...
233
I nv est igat ion of Nat ural Gas Com posit ion Effect s on Knock Phenom enon in SI Gas Engines
Using Det ailed Chem ist ry
Aut hors: Ahm ad Javaheri, Vahid Esfahanian, Ali Salavat i- Zadeh, Mehdi Darzi, Seyyed Moj t aba
Mirsoheil
Chapt er 1: Energy Conv ersion
Abst ract : Considering t he growing role of nat ural gas as an alt ernat ive fuel in st at ionary and
aut om obile engines and t he differences in it s...
239
Flow Charact erist ics around Four Circular Cylinders in Equispaced Arrangem ent near a Plane
Wall
Aut hors: A.Grum m y Wailanduw, Triyogi Yuwono, Wawan Aries Widodo
Chapt er 1: Energy Conv ersion
Abst ract : The flow charact erist ics around four circular cylinders in equispaced arrangem ent
locat ed near a plane wall were invest igat ed...
245
Experim ent al St udy on t he Perform ance of I n - Cabin Vent ilat ion Syst em
Aut hors: Abdul Lat iff Zulkarnain, Cheong Weng Soon, Bam bang Supriyo, Mohd Rozi Mohd Perang,
Henry Nasut ion, Azhar Abdul Aziz
Chapt er 1: Energy Conv ersion
Abst ract : Parking a car under t he hot sun wit h all windows closed could increase in - cabin
t em perat ure as high as 70°C. For such sit uat ion, hu m an...
251
Reduct ion of Energy Losses in t he End Wall Junct ion Area t hrough t he Addit ion of Forw ard
Facing St ep Turbulent Generat or
Aut hors: H. Mirm ant o, Sut risno, H. Sasongko, D.Z. Noor
Chapt er 1: Energy Conv ersion
Abst ract : The research is conduct ed in order t o reduce energy losses caused by t he
secondary flow in t he endwall j unct ion. This phenom enon is caused...
256
Biogas Pot ent ial of Co- Subst rat es in Balinese Biogas Plant s
Aut hors: Daniel Net t , I . Nyom an Suprapt a Winaya, I . Made Agus Put rawan, Rolf Wart m ann, Werner
Edelm ann
Chapt er 1: Energy Conv ersion
Abst ract : This research aim s t o give an ov erview on how t o im prov e t he biogas y eild in
Balinese digest er plant s using various co- subst rat es which are...
262
CFD Sim ulat ion of Heat Transfer in Fluidized Bed React or
Aut hors: I . Nyom an Supr apt a Winaya, I . Made Agus Put rawan, I . Nyom an Gede Suj ana, Made Sucipt a
Chapt er 1: Energy Conv ersion
Abst ract : This st udy aim s t o predict heat t ransfer from a heat ed bed in a gas fluidized bed
using Syam lal- OBrien drag coefficient . Discret e part icles...
267
I nfluence of Bioet hanol- Gasoline Blended Fuel on Perform ance and Em issions Charact erist ics
from Port I nj ect ion Sinj ai Engine 650 cc
Aut hors: Bam bang Sudarm ant a, Sudj ud Darsopuspit o, Dj oko Sungkono
Chapt er 1: Energy Conv ersion
Abst ract : Perform ance and em issions charact erist ics from port inj ect ion SI NJAI engine 650
cc operat ing on bioet hanol- gasoline blended fuels of 0% , 5% ,...
273
I m proved Energy Saving for R22 Building Air Condit ioning Ret rofit t ed wit h Hydrocarbon
Refrigerant , St udy Case: Civil Engineering Depart m ent of I TS
Aut hors: Widyast ut i, Ar y Bacht iar Krishna Put ra, Ridho Hant oro, Eky Novianarent i, Arrad Ghani
Safit ra
Chapt er 1: Energy Conv ersion
Abst ract : Sepuluh Novem ber I nst it ut e of Technology ( I TS) encourages t he ECO Cam pus
program . The program enables I TS t o syst em at ically ident ify,...
281
The Evaluat ion of a Rigid Sail of Ship Using Wind Tunnel Test
Aut hors: Aries Suliset yono
Chapt er 1: Energy Conv ersion
Abst ract : This paper described t he evaluat ion of rigid sail perform ances by using t he wind
t unnel t est . The rigid sail m odels were dev eloped in t he...
287
Applied Mechanics and Materials Vol. 493 (2014) pp 267-272
© (2014) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMM.493.267
CFD Simulation of Heat Transfer in Fluidized Bed Reactor
I Nyoman Suprapta Winaya1, a, I Made Agus Putrawan2,b ,
I Nyoman Gede Sujana2, Made Sucipta4,c
1,4
2,3
Mechanical Engineering Department, Udayana University, Bali-Indonesia
Magister Program of Mechanical Engineering, Udayana University, Bali-Indonesia
a
[email protected], [email protected], [email protected]
Keywords: CFD, heat transfer, fluidized bed, Syamlal-O’Brein drag coefficient, Eulerian
Abstract
This study aims to predict heat transfer from a heated bed in a gas fluidized bed using
Syamlal-O’Brien drag coefficient. Discrete particles model with the Navier-Stokes equation and
Eulerian multiphase are used to approach heat transfer simulation. Coefficient of heat transfer which
is related to Nusselt Number and volume fraction are calculated using Gunn model which was
compiled from C++ program language. The effect of fluidization velocity variation on the heat
transfer coefficient comes to the fore, indicating the heat transfer and solid volume fraction at the bed
height are very dependent. Contour of solid volume fraction and temperature distribution are also
presented.
Introduction
Fluidization is defined as the contacting techniques through which fine solids are transformed
into a fluid using either gas or liquid. In fluidization contact between the gas and solid particle occurs
appropriately because its wide range of contact surface. Using wastes as a fuel in fluidized bed
system needs a deep understanding on fluidization phenomena. In this study, a Fluent Computational
Fluid Dynamics (CFD) program was applied to simulate fluid flow that is expected to provide
information about the feasibility of the utilization of solid waste as a fuel
Simulation of CFD has been widely developed recently, and it is one of the popular tools used
in simulating the fluidization [1]. The program could provide the flexibility to change the design
parameters without much cost, providing faster time of the trial, and also able to provide a detailed
information about the flow field especially in the area of measurement which is difficult or impossible
to obtain [2]. Armstrong and Luo [3] developed a model approach Syamlal-O'Brien drag coefficient
which showed more local fluctuations on the basis of particle terminal velocity with slight sensitivity
to the microscopic scale. Tasirin, et al. [4] conducted an experimental study as well as modeling and
it was found for a higher in gas velocity the fluidization process could be improved. Fluidization
behavior involves three important phases namely: the particle-dominated, predominantly gas and a
mixture of both.
CFD Model
Eulerian model in Fluent program is an important tool to study the solid particulate phase
which involves the complex inter-phase momentum. Therefore, it is important to use the correct drag
law to predict the early onset of fluidization occurred. Syamlal O’Brien model has been successfully
applied to predict hydrodynamic phenomena on fluidized bed compares to the experimental data. The
kinetic theory of granular flow (KTGF) applied with a two-fluid Eulerian-Eulerian model carried out
to heat transfer mechanism due to complexity problem from multiphase flow. Standard-setting
Syamlal O'Brien is as follows [5]:
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Advances in Applied Mechanics and Materials
=
3
4
,
−
,
1
Where Ksg, α, Res , CD, vs, vg and vr,s are the momentum exchange coefficient between solid and gas
phase, volume fraction, Reynold number of solid phase, drag coefficient, velocity of solid and gas,
the coefficient of terminal velocity for the solid phase respectively.
In the gas phase, Eulerian model is treated as a continuum, which can be described by a set of
volume average Navier-Stokes equations. For global mass balance is in the form of conservative as:
+ ∇.
= 0 2
and
is the fraction of each space, the density of the gas, and the gas phase velocity
Where ,
respectively. Thus, balance equation for the individual in the gas phase can be written as follows:
+ ∇.
=
+ ∇.
+
+
.
.
(3)
Here Yα is a mass fraction in the gas phase, . , is the net production rate due to gas-phase reactions.
Gas-phase momentum equation is written as follows:
+ ∇.
+
∇ +
+
∇.
∇.
=
+
(4)
=
(5)
Where; p, ,g, e,
and Igs are indicated as pressure, voltage, gravity, energy, energy rate and
momentum exchange term between the gas phase and particulate phases respectively.
In this study, the heat transfer is determined only in the zone of solid concentration. The heat
energy transfer is simplified as the two difference temperatures of gas-solid phase as Eq. 6. The heat
transfer coefficient with related to Nusselt Number and volume fraction from both phase is calculated
using Eq. 7.
, = ℎ
−
(6)
ℎ
=
6
7
Where; qs,g, Kg, Tg , Ts, dp, Nus, , are indicated as heat flux, gas thermal conductivity,
temperature each phase, diameter particles, Nusselt number and volume fraction of gas-solids
respectively. Hence, the Nusselt number is calculated using Gunn model as follows [6]:
= 7 − 10
g
+5
g
. 1 + 0.7
.
8
Where; Res and Pr are indicated as Reynold and Prandtl number respectively.
Numerical Set-Up and Grid Study
In order to reduce the computation time, the reactor system is designed as 5.08 cm and 70 cm
for diameter and height of reactor respectively with static bed height of 10 cm as seen in Fig. 1. Air
fluidization velocity is varied at 0.05, 0.09 and 0.13 cm/s with waste particle size of 0.03 cm.
The next entry on the stage is determining boundary conditions of the reactor section which is
divided as: the bottom is assumed as velocity inlet of the gas (side entrance), wall on each side and
pressure side outlet is assumed as side exit, and conditioning circumstances in the face is the fluid
mesh. For the initial condition, it is assumed to be adiabatic wall in which the gas phase is not going to
Applied Mechanics and Materials Vol. 493
269
slip along the wall while allowing for the solid phase of contact that refers to the Syamlal-O’Brien
drag coefficient. Eulerian granular iteration process is used for the gas phase and dense granules in
modeling of fluidized bed volume fraction. This model allows the processing issues in two different
phases of the volume control in the grid. Granular phase is assumed to have a uniform diameter and
solid-gas phase is completed individually with the mass and momentum equations (Eq. no. 3).
Simulation of heat transfer is carried out in Two-Dimension (2D) grid model and analyzed
using a model of Eulerian multiphase. Computation domain 2D discretized using rectangular cells
(Quad) with mesh total size of 0.41 and 0.29 cm for vertical and horizontal side respectively, and
terminated in steps of 0.005 s with 2000 iterations. The program can replace the partial differential
equations of continuity, momentum, and energy with algebraic equations which is an approximation
of the original continuum problem into a particle discrete model.
The process of selection menu which include the equation solver can be used to complete the
calculation in the simulation process. However, in some special case containing custom equations
such as heat transfer model is not included in the program. Heat transfer analysis on the fluidized bed
system simulation is affected by initial parameters such as material properties, flow rate, operating
temperature, density and the flow multiphase model equations. Hence, the C++ language program is
used to compile the mechanistic heat transfer model (eq. 7) into CFD program. The wall temperature
from reactor is set at 300 K (ambient temperature) and the solids phase is conditioned at combustion
mode temperature as high as 973 K. The initial determination of the parameters that used in the
simulation process can be seen from tables 1 and 2.
Exit side
Solid wall
70 cm
Entry side
5.08 cm
Fig. 1. Outline of a typical numerical setup
Table 1. Fluent Model using in simulation
Model
Settings
Space
2D
Solver time
Unsteady
Viscous
k epsilon
Wall Treatment
Multiphase Model
Standard Wall Functions
Solid fluid
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Advances in Applied Mechanics and Materials
Table 2. Parameter properties of gas and waste particles
Gas
Properties
Unit
gas velocity
0.05; 0.0 9; 0.13 [cm/s]
g
gas density
1.225 [ kg/m3]
g
viscosity
1.79x10-5 [kg/m.s]
g
g
gravity acceleration
9.81 [m/s]
P
freeboard pressure
1.01 x 105 [Pa]
Particles
hbed
height bed static
10 [cm]
dp
particle diameter
0.03 [cm]
particle density
328 [kg/m3]
s
Specific heat
2000 [J/kg.K]
s
solids conductivity
0.08 [W/m.K]
s
Velocity magnitude (m/s)
Result and Discussion
Variations of air velocity flow into the reactor certainly have an important role on the
characteristics of bed hydrodynamic. As the velocity increased the gradient of fluidization velocity
also increased as shown in the Fig. 2 as the red colour. The domination between solid and gas can be
well visualized using CFD simulation.
0.0 5 m/s
0.09 m/s
0. 13 m/s
Fig. 2. Contour of fluidization characteristic for different velocity at 10 s
Fig. 3 shows the contour of temperature along the bed reactor at fluidization velocity of 0.05
m/s at the time step of 0 to 10 s. It was observed the heat flux continuously flowed as the velocity was
just started. The degradation of the red colour was found to change as the solid fraction decreased
mostly until the maximum bed height of 18 cm. The similar behavior was found for different
fluidization velocity in which the higher velocity resulted in longer contour temperature distribution.
271
Temperature (K)
Applied Mechanics and Materials Vol. 493
18 cm
Fig. 3. Contour of temperature distribution at velocity of 5 cm/s from 0 to 10 s
0,45
800
0,4
700
0,35
600
0,3
500
0,25
400
0,2
300
0,15
0,1
200
0,05
100
0
0
0,0
0,1
0,2
0,3
0,4
0,5
Heat transfer coefficient,htc (W/m2K)
Volume of solid fraction, vof
Fig. 4 shows the correlation between volumes of solid fraction to heat transfer coefficient (htc)
along reactor bed height after 10 s steps of iteration. It is observed that the initial bed height of 10 cm
increases until 18 cm at air velocity of 0.05 m/s (vof) with heat transfer coefficient of 500 - 650
W/m2K. It is clearly found that the solid volume fraction has a major effect on heat transfer
coefficient. In this study, the heat transfer coefficient above the bed height was not calculated.
vof
htc
0,6
Horizontal bed height (m)
Fig. 4 Volume of solid fraction and heat transfer coefficient at air velocity of 5 cm/s.
A similar behavior was observed when the fluidization velocity was increased. The increased
in velocity resulted in an increased the solid expansion of 21 and 30 cm at velocity of 9 and 13 cm/s
respectively. The increased in solid volume fraction was found between 0.22 – 0.33. The heat transfer
phenomenon tends to follow the behavior of the solid volume fraction and it was found at average of
655 W/m2K with the maximum of 710 W/m2K at velocity of 0.13 m/s. Fig. 5 shows that the higher
gas velocity resulted in the higher heat transfer coefficient.
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Advances in Applied Mechanics and Materials
Fig. 5 Heat transfer coefficient along bed height at different velocity
Summary
Discrete particles model with Syamlal_O’Brien drag coefficient was used to predict heat transfer
from a heated bed in a 2-D bubbling fluidized bed. The two fluid simulation using energy balance and
momentum shows a good value to visualize the phenomenom into the bed. The heat transfer
coefficient is closely linked to the solids volume fraction in which the dominance of the particles
cause the high heat transfer coefficient. It seems that the mechanistic of Gunn model can be well
recommended to use in CFD simulation.
Acknowledgement: This study was kindly supported by Directorate of Higher Education-The
Indonesia’s Ministry of Education and Culture through Hibah Desentralisasi Pascasarjana of
Udayana University: No. 175.62/UN14.2/PNL.01.03.00/2013
References
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Circulating Fluidized Bed. Proceedings of the 20th International Conference on Fluidized Bed
Combustion, pp. 818 (2009).
[2] Amit Kumar., CFD Modeling of Gas-Liquid-Solid Fluidized Bed. Department of Chemical
Engineering National Institute of Technology Rourkela pp.769, Orissa (2008).
[3] L.M. Armstrong, S. Gu dan K.H. Luo. , Study of Wall-to-Bed Heat Transfer In a Bubling
Fluidized Bed Using the Kinetic Theory of Granular flow. International Journal of Heat and Mass
Transfer 53, pp. 4949-4959, (2010).
[4] S.M. Tasirin, S.K. Kamarudin dan A.M.A. Hweage, Mixing Behavior of Binary Polymer
Particles in Bubbling Fluidized Bed. Journal of Physical Science, Vol. 19 (1), pp. 13–29 (2008).
[5] M. Syamlal., D. Gidaspow, Hydrodynamics of fluidization: prediction of wall-to-bed heat transfer
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[6] D.J. Gunn, Transfer on heat or mass to particles in fixed and fluidized beds, International Journal
of Heat and Mass Transfer, Vol. 21, pp. 467-476 (1978).