-
Journal of Materials Processing Technology 214 (2014) 334
346
Contents lists available at ScienceDirect
Journal of Materials Processing Technology
jou rn al h om epage : www.elsev ier .com/
Numer mheated
MauricioResearch Cente arian
a r t i c l
Article history:Received 13 MReceived in re15 SeptemberAccepted
18 SAvailable onlin
Keywords:CFDNumerical simAluminum melting furnacePhase
change
protmer
alum and snducd zonhe siSeverompffect.
solving the conjugated problem comprising refractory walls and
heated load. Secondly, thermal inter-action with air cavities seems
to determine the convective movement of the molten load and
thereforeinner-load temperature patterns and their time evolution.
Nevertheless, this comprehensive simulationconsumes 3.6 times the
computational resources of a simplied model, where the momentum
equationsare not solved for the air cavity and overall furnace
parameters are still reasonably predicted (e.g., with
1. Introdu
Recoverperformed is the geneto be treatbeing develof
lesseningexamples aarc furnace
Traditionempirical minvolved, wbased on rand shortcocal
simulatiand scalingphysical mofurnace tec
CorresponE-mail add
(C. Corts).
0924-0136/$ http://dx.doi.oan error in fusion time less than
7.3%). 2013 Elsevier B.V. All rights reserved.
ction
y of aluminum from dross or light-gauge scrap is usuallyin
furnaces using salt uxes. The main inconvenienceration of a
sub-product that contains salt and needsed before its nal disposal.
Alternative processes areoped in which oxidation of the load is
avoided by means
the oxygen potential inside the furnace. Noteworthyre the
heating by a plasma torch and oxyfuel and electrics.al design of
melting furnaces has been based on semi-ethods due to the
complexity of the phenomena
hich has limited the use of computational techniquesst
principles physics. However, the inherent difcultymings of
experimental measurements make numeri-ons an attractive alternative
for aided design, operation-up. Furthermore, they can assist in the
development ofdels, or serve as a pre-evaluator of
non-conventional
hnologies and multi-unit systems.
ding author. Tel.: +34 976762954; fax: +34 976732078.resses:
[email protected] (M. Carmona), [email protected]
The core of such a simulation must include a model for the
phasechange of the load material, that in the general case depends
ontime and space and originates a phase-separating boundary mov-ing
within the medium during the process. Transport propertiesvary
considerably between phases, resulting in totally differentrates of
energy, mass and momentum transfer from one phaseto the other. The
position of this moving boundary cannot beidentied in advance, but
has to be determined as a essential con-stituent of the solution.
In order to appreciate the complexity of thefundamental physics and
understand the method adopted in thiswork, the explanation of
phase-change theory given by Alexiadesand Solomon (1993) is
recommended. As a complement, Hu andArgyropoulos (1996) present an
excellent review of typical analyt-ical implementations.
These evidently entail important simplications, related
togeometry and physical properties of the distinct phases, that
pre-vent their use in almost all practical problems of solidication
andmelting. Numerical techniques are therefore adopted, based on
twobroad classes of approximations: variable- and xed-grid
methods.
Most widespread variable-grid methods use dynamical grids,where
some nodes move with the phase change boundary andothers are
dynamically reconstructed at every time step. Trans-port equations
are solved for each phase separately. This is themost direct
approximation to the underlying physics, having the
see front matter 2013 Elsevier B.V. All rights
reserved.rg/10.1016/j.jmatprotec.2013.09.024ical simulation of a
secondary aluminum by a plasma torch
Carmona , Cristbal Cortsr for Energy Resources and Consumption
(CIRCE), CIRCE Building Campus Ro Ebro, M
e i n f o
ay 2013vised form
2013eptember 2013e 30 September 2013
ulation
a b s t r a c t
Tests carried out in an experimentalare numerically simulated
with a comand temperature distributions in thecalculating tool to
assist in the designmetric and take into account heat
cointeractions between gasliquidsolimodeled with the enthalpy
method. Ta reasonable computational expense. tional economy and
their accuracy in cgasliquidsolid have an important elocate /
jmatprotec
elting furnace
o Esquillor Gmez, 15, 50018 Zaragoza, Spain
otype of crucible melting furnace heated by a plasma torchcial
CFD code, in order to calculate melting time, heat lossesinum load
and refractory parts. The objective is to develop acaling-up of
industrial furnaces. Models used are 2D axisym-tion in solid parts,
convection in air and molten aluminum,es and radiation heat
transfer. Fusion of solid aluminum is
mulation is able to predict temperatures and melting times atal
calculation strategies are tested concerning their computa-uting
different key parameters. Results show that interactions
Firstly, a proper account of heat transfer and losses
requires
-
M. Carmona, C. Corts / Journal of Materials Processing
Technology 214 (2014) 334 346 335
inherent shortcoming of a large computational expense related
togrid calculations, which adds up to (and usually is larger
than)the approximation and resolution of transport equations
them-selves. Samarskii et al. (1993) give an exhaustive review of
differentvariable-griities of this(1990).
In xed-domain, mainstead of sreview meris a subclasused in
phatemperaturarticial forcomputatio(1987a, 198hensive andthe
enthalpare summa
In additical phenomto model aheat diffusthe
moltenAccordinglylations are forcibly briapproximatthe followiing
of alumtreating thestant thermempirical d(1995) presmodel for
tconsideringprediction Abbassi andstudy of a nace.
A relatedto Phase ChSimulationshandle buoconsider simtechniques
ing advantause distinctAssis et al. the most cosolve a conviscosity
ingated problorder to coural convecpresent an edominated
In this furnace for prehensive principle ofnal purponaces.
Expemethodologwith experi
2. Experimental conguration
2.1. Principle of operation and test protocol
er thary withg memined wogra
maion, coent efurna
rsty a preratig frhe p
alumthe fontaort-cted; e aluthe sentl
re is en veeral ounted f
easu
R thempeper
, is me. Con th
at aenteple iis uses m
inpust of unde
paras eles andeat linedomp
del d
nera
ericLUEN
algn. Ad schemes, whereas a general appraisal of the peculiar-
kind of techniques is presented by Lacroix and Voller
grid methods, a single equation is solved for the wholede up of
solid, mushy (for alloys) and liquid regions,eparated equations for
each phase. Voller et al. (1990)its and demerits of this scheme.
The enthalpy methods of xed-grid models that is in fact the most
widelyse change problems. In it, evolution of latent heat ande are
accounted for by phase enthalpy, constituting anm to track the
variable interface with a much reducednal cost. First formulation
was developed by Voller et al.7b); these contributions constitute
the most compre-
recommendable account of the subject. In this work,y method is
used; for a full appreciation, their equationsrized in Section
3.5.ion to phase change, several other complex phys-ena occur in
industrial furnaces that are difcult
nd couple within an unied simulation. Conjugateion through solid
and uid volumes, movement of
load and radiation heat transfer are some of them., works
dealing with realistic, comprehensive simu-rather scarce in the
literature, so that a review isef and encompasses very different
applications andions. As direct antecedents of the work presented
here,ng can be quoted. Zhou et al. (2006) simulate melt-inum scrap
in a rotary furnace under a salt layer,
solidliquid region as a conducting solid with con-al properties
and adjusting the overall simulation withata, which are difcult to
obtain a priori. Wu and Lacroixent a two-dimensional time-dependent
heat transferhe melting of scrap metal in a circular furnace
without
radiation heat transfer. The model was limited to theof the
temperature distribution in the axial direction.
Khoshmanesh (2008) undertake a three dimensionalgas-red,
regenerative, side-port glass melting fur-
class of problems that have been widely studied referange
Materials (PCM) at near-ambient temperatures.
typically use the enthalpy formulation and logicallyyancy via
the Boussinesqs approximation, but oftenplistic 2D geometries. Also
experimental visualization
are used to validate the detailed numerical results, tak-ge of
the transparency of the liquid phase. A few authors
properties for liquid and solid phases. The works of(2007) and
Scanlon and Stickland (2004) are amongmplete studies in this eld.
Faraji and El Qarnia (2010)jugate problem in a simplied form using
an innite
solid regions. Jones et al. (2006) also simulate a conju-em and
use the method of Volume Of Fluid (VOF) innsider the volume
expansion. Trp (2005) ignores nat-tion in the molten phase and
Vidalain et al. (2009)nhanced thermal conduction model for the
convection-change of phase.work, experimental tests in a prototype
of cruciblemelting aluminum are reproduced numerically. A
com-simulation is attempted, aimed at representing the
operation and validating the models used, with these of
acquiring a design tool for industrial-size fur-rimental
facilities, models used and main assumptions,y of the simulation,
results obtained and comparisonmental data are discussed.
Undsecondtaken heatinthe aluconna photing theinjectisuremof
the
Thecible bthe opcrackintests, tload ofinside be in cis a
shseparaheat thinput, is frequperatuhas be
Sevand amis selec
2.2. M
An Iface tegas temspherethe pipature ilocatedat the cmocoumetal
includenergy
Motaken in solidwhereweightever, hdetermwhen c
3. Mo
3.1. Ge
Numcode FSIMPLEpolatioe general objective of developing an
innovative type ofaluminum melting furnace, experiments were
under-
a reduced-size prototype (ca. 50 kg max. load). Theans is a
transferred plasma torch that supercially heatsum load, which acts
as a conducting body. The load isithin a crucible made of
refractory material. Fig. 1(a) isph of the practical experimental
rig, externally show-n elements: graphite electrodes, plasma gas
(nitrogen)oling system of the electrodes and electrical and
mea-quipment. For clarity, Fig. 1(b) shows a sectional viewce.
stage of the experimental test is preheating the cru-opane gas
burner for 2 h approximately, until it reacheson temperature. This
is done to avoid damage due toom thermal expansion; the lid is not
heated. For thereheated crucible temperature was set at 658 C.
Theinum is weighed before the test and then it is placed
urnace. At the initial instant, both electrodes have toct
through the metallic load, so that the starting pointircuit. The
plasma gas is injected and the cathode isat this moment the plasma
torch starts and begins tominum surface. In order to maintain a
constant powereparation distance between the cathode and the loady
adjusted. After the theoretical time for melting, tem-measured in
the aluminum; once fusion of the materialried, it is poured into a
mold.tests were carried out for different congurations, typets of
load and power input. A single representative caseor the
simulations.
rement equipment
rmograph camera is used to produce a map of outer sur-rature of
different components of the furnace. Exhaustature, which is
indicative of that of the inner atmo-easured through a thermocouple
probe installed in
ntact thermocouple probes are used to record temper-e wall of
the crucible; the measurement point (Pm) is
height of 245 mm from the bottom of the crucible andr of the
wall thickness. An assembly made up of a ther-n a steel tube that
the operator shoves in the moltened to measure its temperature. The
electrical systemeasurement of instantaneous power and
accumulatedt.the measurements related to thermal magnitudes arer
industrial conditions. Measurement of temperaturests and fused
metal has an estimated accuracy of 2 C,ctric power supply is
measured to within 0.1 kW. Load
times can be considered exact in practical terms. How-osses to
ambient and initial preheat of the crucible are
only indicatively, which is to be taken into accountaring with
numerical results.
escription
l assumptions and boundary conditions
al simulation is undertaken with the commercial CFDT.
Pressurevelocity coupling is implemented by the
orithm, with the standard scheme for pressure inter- rst-order
upwind scheme is adopted for spatial
-
336 M. Carmona, C. Corts / Journal of Materials Processing
Technology 214 (2014) 334 346
Fig. 1. (a) Pilo ; 4, canitrogen pipe;
discretizatiis to achievcontinuity athe absolutical techniq
In ordersimplied tand sectionThe load coformly fromis closed:
ga
Heating lar heating at the centeplexity of thheat transfepower
transthe fractioning on arc leexperimentto the load assumed
heassumptionmeans and and losses. incorporateabsence of earc
geometanted at thi
Gas and sity differenas 2 108 ato the critic
199ar, lanallyt lost melting furnace. (b) Sectional view (1,
crucible/ladle; 2, top of furnace; 3, anode 8, transport hook; 9,
temperature measurement sensor; 10, load).
on. The criterion of numerical convergence by time stepe a
decrease of 1 103 in the absolute residuals of thend momentum
equations, and a decrease of 1 106 ine residual of the energy
equation. Details of the numer-
(Mills,not cleadditio
Hea
ues are given in the users manual (ANSYS, 2012).
to reduce the computational cost, the real geometry iso a 2D
axisymmetric model; details such as the anodes of gas outlet and
temperature probes are thus ignored.nsisting in 10 kg of metal is
assumed to ll the ladle uni-
the bottom up to a specic height. The whole domains inlet and
outlets and air inltrations are neglected.from the plasma torch is
represented by a small, circu-area of equal diameter as the
electrode, 50 mm, locatedrline on the top surface of the load. Due
to the com-e phenomenon, there are no simple, reliable models ofr
from thermal plasmas. Hur et al. (2001) measure theferred to the
load in a similar application and show that
of energy transferred ranges from 45 to 60% depend-ngth. In our
case, adopting a value of 55%, and a typicalal measurement of 30 kW
input electricity, input power(Winput) is 16.3 kW. This is
uniformly distributed on theating area and imposed as a boundary
condition. The
is intended as a rst approach to represent the heatingfocus the
calculation on material fusion, temperaturesObviously, better
models of the plasma torch can bed under the same general scheme.
However, given thexperimental observations regarding e.g.,
electrode and
ry or plasma temperature, these are possibly not warr-s
stage.molten aluminum move due to thermally induced den-ces.
Corresponding Rayleigh numbers can be estimatednd 106,
respectively. Although the rst is relatively closeal value of 109
usually given for external ows in air
roundings aperfectly innatural conheat transfaccording tDe Witt,
19perature debut only an cient hconvvertical cylimula givingBoth
coefassumed untively, are typical avedistributionnon-polishehrad
11.7 W
3.2. Geome
Main dimand the geoin Fig. 2(b)Material usalumina, wcal
propertiof molten aremaining thode; 5, exhaust gas pipe; 6, cooling
system of electrodes; 7, inlet
2), whereas turbulence transition for liquid metals isminar ow
is considered for both sub-domains, which
simplies the problem.ses from the external surface of the
crucible to the sur-
re approximated as follows. The bottom is consideredsulated. In
the remaining external walls, heat transfer byvection and radiation
takes place. A constant, averageer coefcient hav = hconv + hrad
[W/(m2 K)] is estimatedo elementary heat transfer calculations
(Incropera and90). It should be noted that, since the major part of
tem-crease occurs in the refractory parts, not a precise
valueindicative gure is needed here. For the convective coef-, an
empirical correlation for the ideal geometry of ander is applied.
Radiation is estimated through the for-
the losses to a large (thus, black) radiative environment.cients
depend on surface and ambient temperatures,iform and known. Values
of 250 C and 18 C, respec-used, the former conrmed as
representative of therage of numerical results for the surface
temperature. Total emissivity used is a typical value of 0.7 ford
surfaces. Calculation results in hconv 7.2 W/(m2 K),/(m2 K), and
thus hav 18 W/(m2 K).
try and materials
ensions of the melting furnace are shown in Fig. 2(a),metry
adopted for numerical computations is shown, detailing the
different computational sub-domains.ed for the refractory parts
(crucible and top lid) is highhereas load is made up of alloy
AlSi9Cu3. Thermophysi-es are given in Tables 1 and 2, respectively.
Only densityluminum is considered variable with temperature;
themagnitudes are (reasonably) assumed constant. Gas
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M. Carmona, C. Corts / Journal of Materials Processing
Technology 214 (2014) 334 346 337
Table 1Thermophysic
Density (kg/Specic heatThermal con
Table 2Thermophysic
Density (kg/
Specic heatThermal conViscosity (kgLatent heat oSolidus
tempLiquidus tem
a Assael et ab Brandt (19c Zeiger and
inside the lpressure, an
3.3. Simula
The phyappropriateinvolved. Onvation (Navand air llias stated
abslip, or veloother handair, which iFig. 2. (a) Main dimensions of
melting furnace and (b) geometry
al properties of refractory (Carbosanluis, 2007).
m3) 2150 (kJ/(kg K)) 0.850ductivity (W/(m K)) 1.5
al properties of aluminum load.
m3)a 2700 T < 873 K3.873T + 5992 873 K < T < 933.15
K0.3116T + 2668 T > 933.15 K
(kJ/(kg K))b 0.900ductivity (W/(m K))b 237/(m s))a 0.001f fusion
(kJ/kg)b 397erature (K)c 873perature (K)c 933.15
l. (2006).84).
Nielsen (2004).
adle is represented by standard dry air at atmosphericd
calculated as an ideal gas.
tion of gas cavity
sical model consists in the numerical solution of the
differential conservation equations for all domains
the one hand, mass continuity and momentum conser-ierStokes
equations) are solved for liquid aluminumng up the ladle, which
takes into account buoyancy;ove, solid parts are considered
incompressible. Non-city continuity, is imposed on all interfaces.
On the
, energy conservation is solved in refractory, load ands
equivalent to a problem of heat conduction in solids
and heat coenforces tethrough intin terms of is used to m
Aluminuthermal radbut air llimodel of hthermal radfaces of thean
amountadded comphase chan
Howevethe input eof the gas by consideand less rethe
differenputational calculated, plest one; the uids. Tent
schemeindustrial scomputatio
3.3.1. Case This is t
ity, which iradiation isradiation mmentation o for the numerical
simulations.
nvection in air and liquid aluminum. The method usedmperature
continuity and conservation of heat uxerfaces. Energy conservation
in the load is formulatedtotal enthalpy, to serve to the enthalpy
method, whichodel the phase change of the metal.m in solid and
liquid phases is practically opaque to
iation in the spectral range corresponding to T < 700 C,ng up
the ladle is transparent. Therefore, an accurateeat losses must
incorporate the transfer of energy byiation between the surface of
the load and inner sur-
ladle. Such a mechanism is expected to contribute in comparable
to heat convection in the gas. This is anplexity to the already
complex model of heating andge.r, since heat losses are actually
only a small fraction ofnergy, it is reasonable to consider
simplied modelscavity. The idea is to develop a simplied
simulationring successively simpler and thus more economicalliable
models. Aside from estimating the accuracy oft simulation results,
the progressive reduction in com-workload is also monitored. Five
different cases areas described below from the more complex to the
sim-the latter even disregard movement of one or two ofhe objective
is to assess the applicability of the differ-s to the comprehensive
simulation of realistic, complexystems, which often requires a
judicious use of limitednal resources.
1: Thermal radiation and air convection fully modeledhe more
precise and expensive model of the gas cav-s taken as a reference
for the remaining cases. Thermal
calculated by the so-called surface-to-surface (S2S)odel of
FLUENT (ANSYS, 2012). This is a built-in imple-f the net radiation
method (Mills, 1992), coupled to the
-
338 M. Carmona, C. Corts / Journal of Materials Processing
Technology 214 (2014) 334 346
diffusive term of surface energy balances. It relies on the
calculationof geometric view factors between pairs of surface
elements, onlydependent on discretization, and assumes diffuse-gray
radiation,which is reasonable for the problem.
3.3.2. Case Radiatio
mine the efreduction o
3.3.3. Case augmented,
An apprlosses fromall heat tranestimated ftions. This losses
fromthe reducedcavity surfaference betwof the inner
Howeve(load) and priori, resuof the matcavity woucalculated
domains. Ua scheme, thof Tcav woulwould be co
Given thobviously vInstead of acavity is allprocess. Trethen
allowsat once is mation.
Now, sinby a Nusseby convectian augmening the cavand height and
500 C are estima(Incropera hrad 29.5 Wductivity is
Finally, interface suthere a freemolten alum
3.3.4. Case Invoking
lated surfacload only ltouches it. over-/undeetc. Howeveis
equivalenit. As in casea free-slip t
3.3.5. Case 5: Cavity not modeled and load heated by
pureconduction
In addition to the assumptions of the previous case, density
ofsolid and liquid aluminum is taken as a constant, load = 2400
kg/m3,
ragercula
of co. Thise is
the the p
umer
ulati profcumoured ad in ex thspect
vern
worhalpferen
the Stok
writ
(
(2), tding alueg vale mor be
acco
Au
A in decrell-kropos, is t
1 3 +
C isy; vst coh (19ent
ene et a
+ 2: Radiation no modeledn is simply not taken into account, in
order to deter-fect of this rough approximation both on the
ctitiousf heat losses and on the economy of the calculation.
3: Purely diffusive transfer in the gas, with an effective
thermal conductivityoximate way of handling convective and
radiative heat
the top surface of the load is to adopt a constant, over-sfer
coefcient [W/(m2 K)], heff = hconv + hrad, that can beor typical
temperature differences and idealized condi-is of course completely
similar to the consideration of
the outer surface of the ladle, and can be justied given
magnitude of the term. Heat uxes [W/m2] from/toces are then
calculated as q = heffT, where T is the dif-een the local surface
temperature and the temperature
atmosphere of the cavity Tcav.r, the value of Tcav, intermediate
between maximumminimum (lid) surface temperatures, is unknown
alting from the balance of energy input, heat of fusionerial and
external losses. An energy balance to theld allow to calculate Tcav
coupled to the numericallytemperature distributions in load and
refractory sub-nfortunately, FLUENT does not implement directly
suchus rendering it iterative. A too-high/low guessed valued lead
to an articial heat source/sink in the cavity thatrrected by
lowering/raising the guess.e complexity of the numerical solution,
this would beery costly, but a better alternative can be
implemented.ssuming a uniform Tcav, the inner temperature of
theowed to vary spatially according to a purely diffusiveating
losses in the gas cavity as pure heat conduction
to improve on the assumption of a constant Tcav, anduch cheaper
than calculating gas convection plus radi-
ce heat conduction in a at layer of thickness t is givenlt
number Nu = ht/k = 1, the fact that real heat transferon and
radiation is more intense can be represented byted thermal
conductivity given by keff = hefft. Consider-ity as a cylinder with
the inner diameter of the ladlet = 0.5 m, and uniform surface
temperatures of 660, 100in load, lid and lateral wall,
respectively, coefcientsted according to basic heat transfer
calculationsand De Witt, 1990). Results are hconv 3.4 W/(m2 K),/(m2
K), heff = hconv + hrad 33 W/(m2 K), so that con-
taken as keff = 16.5 W/(m K).although gas is considered still in
this approach, therface with the load is allowed to move by
imposing-slip boundary condition. In this way, movement ofinum is
predicted.
4: Cavity not modeled again the small value of heat losses,
perfectly insu-es (heff = 0) can be specied for the cavity, so that
theosses heat by conduction to the refractory where itThis is
obviously a rough approximation, which willrestimate energy
efciency, temperatures, fusion times,r, it amounts to a large
computational economy, since itt to treat the cavity as a vacuum,
i.e., to avoid modeling
3, movement of the fused load is allowed by imposingop
surface.
an aveural cimodelfusionexpenssolvingtion of
3.4. N
Simchangevery diof parais assuresultecomplare, re
3.5. Go
It isthe entthe dif
ForNaviercan be
t
+
t
u +
In Eq. depenlarge vlimitinuid. Thalloys can be
Su =
wheretion 0. A wbeen pregion
A = C(
wherephologfor moPrakasto prev
The(Voller
(h)t of the values shown in Table 2. This suppresses nat-tion in
the material, which amounts to the simplisticnsidering inner heat
transfer driven exclusively by dif-
is obviously another reference case: the computationalthe
minimum that can be imagined, amounting only to
heat conduction equation everywhere, with the addi-hase change
model in the load.
ical time step
ons are carried out for a transient process. In phaseblems,
convergence of the numerical iteration can belt to reach;
therefore, selection of a suitable time step isnt importance. In
this approach, iterative convergencet each time step. Different
values were tested, whichthat the required maximum value should be
lower thee problem solved. Values nally adopted for cases 15ively:
0.0005, 0.00075, 0.01, 0.1, 1 s.
ing equations of the enthalpy method
th to give more detail about phase-change modeling byy method,
which it is realized here by briey discussingtial
equations.convective motion of the molten load (cases 14), thees
equations corresponding to a uid of variable densityten as:
u) = 0 (1)
(uu) = P + ( ) + g + Su (2)
he source term (Su) modies the momentum balanceon the completion
of the phase change. It varies from a
imposing complete rest of a solid material, down to aue of zero
when the material becomes completely liq-ushy zone in between can
have a physical existence for
made conveniently thin for pure metals. This behaviorunted for
by dening:
(3)
creases from zero to a large value as the liquid frac-eases from
its liquid value of 1 to its solid value ofnown format, derived
from the Darcy law, which hassed as a general model for ow in
metallurgical mushyhe CarmanKozeny equation:
)2
q(4)
the mushy zone constant, that depends on its mor-alues between 1
104 and 1 107 are recommendedmputations. is the local liquid
fraction. Voller and87) introduce the constant q as a small number
(0.001)division by zero.rgy equation is rewritten in terms of the
enthalpy h asl., 1987a, 1987b):
(uh) = (
k
ch)
+ Sh (5)
-
M. Carmona, C. Corts / Journal of Materials Processing
Technology 214 (2014) 334 346 339
In this case, the relation thermal conductivity/specic heat,k/c
is approximated as a constant. Evolution of the latent heat
isaccounted for by dening the source term Sh as:
Sh =(h
t
where
H = h + H
and H = Lfraction bei
=
0,
T Tl 1,
The comthis set of e
In case 5not neededconservatioi.e., as a pur
3.6. Meshin
Due to tmentation computatioout a grid cois used in thferent
sub-dload (825 cecases 4 and
4. Preheat
As descrconditions bing on its icontent andand both shheating
proone for the
The rathimated as surfaces of losses to thnot simulatrefractory
mume duringbe estimateature and laadequate fo
Results abe discusseture distribtemperaturthickness o
Temperafor the inneThese estimtions, in
whtemperaturtemperatur
Fig. 3. 2D axisymmetric grid for the numerical simulation.
emperature distribution [K] in the crucible at the end of the
preheating
emperature along the thickness of the refractory wall at the end
of theng process.) + (uH) (6)
=
c dt + H (7)
, with L denoting the latent heat of fusion and the liquidng
dened as:
T < Ts solidphase
TsTs
, Ts < T < Tl solid/liquidphase
T > Tl liquidphase
(8)
mercial code Fluent has a built-in implementation ofquations, so
that no UDFs are required.
(no movement of the material), equations (1)(4) are. The
enthalpy method is implemented via the energyn equation, written as
Eqs. (5)(8) with a zero velocity,ely conductive problem.
g scheme
he diverse complex phenomena involved, the imple-of the
numerical simulations is very expensive innal terms. Therefore,
currently it is not feasible to carrynvergence study, and only a
single mesh of 18,116 cellse present work. The number of cells
allotted to the dif-omains is as follows: ladle (5749 cells), lid
(2522 cells),lls) and air (9020 cells). These last cells are not
used in
5. Fig. 3 shows the grid used for the simulations.
ing of the refractory ladle
ibed in Section 2.1, the process does not start from coldut
rstly the ladle is preheated by a gas burner imping-nner surface.
This imposes an initial internal energy
a temperature distribution in the refractory material,ould be
taken into account. Therefore, rstly the pre-cess is simulated, and
its nal state is taken as the initialensuing simulation of the
fusion of the aluminum load.er complex and uncontrolled actual
process is approx-a constant and uniform heat ux entering the
innerthe ladle, with the remaining area subjected to heate
environment. Load, top lid of the furnace and air areed at this
stage. Assuming that the temperature of theaterial is increased 500
C in average for all the vol-
a time interval of 2 h, a heat ux of 15,000 W/m2 cand. The
preheating process starts from ambient temper-sts for 7200 s. A
large numerical time step of 5 s is used,r simple heat conduction
problems.nd comparison with experimental measurements cand as
follows. Fig. 4 shows the calculated nal tempera-ution in the ladle
material, as well as the position of thee measurement point Pm.
Final temperature along thef the crucible wall at the same height
is shown in Fig. 5.tures numerically predicted are 1050, 775 and
625 Kr wall, measurement point and outer wall, respectively.ations
agree reasonably with experimental observa-ich inner wall
temperature ranges from 950 to 1180 K,e of the measurement point Pm
is 750 K, and outer walle ranges from 509 to 600 K.
Fig. 4. Tstage.
Fig. 5. Tpreheati
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340 M. Carmona, C. Corts / Journal of Materials Processing
Technology 214 (2014) 334 346
The temperature distribution shown in Fig. 4 is taken as
theinitial one in the refractory material for the transient
simulationof aluminum melting. Top lid, air and load are added at
ambienttemperature to complete this initial state.
5. Results and discussion
5.1. Melting time
An approximate melting time (tm) can be calculated by assum-ing
heat is communicated to the load at a constant rate. Total
heatneeded for melting is
Q = mCT + mL (9)
where T = Tm T0 is the increment from ambient to fusion
tem-peratures. Thus,
tm = QWinput= 560 s (10)
Fig. 6. Liquid fraction in the load throughout simulation time
for ve study cases.
Melting time predicted by the simulation is measured by a
mon-itor of the melting fraction, dened as total amount of
moltenaluminum divided by the initial solid load. For cases 15,
predictedmelting times are 625, 603, 622, 614, 584 s, respectively.
Experi-mental value is 671 s, although this includes some
overheating ofthe fused aluminum. In conclusion, numerically
predicted times
c) case 3, (d) case 4 and (e) case 5.Fig. 7. Liquid fraction at
t = 150 s: (a) case 1, (b) case 2, (
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M. Carmona, C. Corts / Journal of Materials Processing
Technology 214 (2014) 334 346 341
agree reasonably, both with approximate guesses and with
mea-surement.
Fig. 6 shows total liquid fraction in the load throughout the
sim-ulation time for the ve cases studied. Behavior of the melting
rateis roughly the same for the two models including radiation
(cases1 and 3), that correspondingly predict similar melting times.
Com-pared with them, simulation without radiation (case 2) and
withoutthe whole gas cavity (case 4) exhibit a similar melting rate
for, say,the initial ve sixths of the process, but clearly
accelerate duringthe last sixth. This is an indication that
radiative losses logicallypredominate at latter stages, under
increased load temperatures;the effect is more pronounced for case
4 than for case 2, which is alsocoherent. Finally, case 5
overpredicts load temperature and leadsto a shorter melting time.
Difference with case 4, and the lack of itbetween cases 2 and 4,
clearly show that inuence of heat convec-tion inside the load
surpasses that of losses through the gas cavity.
5.2. Distribution of liquid fraction
Figs. 7 and 8 show liquid fraction distribution for cases 15
attimes 150 and 480 s, respectively. The gas cavity sub-domain is
notcolored in these drawings.
The shapes clearly suggest that melting is initially controlled
byheat conduction, and at a certain time, effects of natural
convectioninside the load become important. In the last gure,
differencesbetween cases 1 and 2 on the one hand, and cases 3 and 4
on theother pinpoint the effect air movement has on movement of
themolten load. Input heat seems to extend supercially more, butto
a lower depth, when surface is assumed free, not subjected tothe
shear stress needed to drag air along. Similarity between cases3
and 4 indicates that this is unaffected by heat losses from
thesurface of the load. Finally, a pure heat conduction situation,
for avery conductive material, is clearly observed for case 5.
c) caseFig. 8. Liquid fraction at t = 480 s: (a) case 1, (b)
case 2, ( 3, (d) case 4 and (e) case 5.
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342 M. Carmona, C. Corts / Journal of Materials Processing
Technology 214 (2014) 334 346
5.3. Temper
Figs. 9 ature for cas
For comouter surfacas well as tand electroinside the c
Outer sFigs. 9 and550 K for t =images pres478512 K fpoint Pm
rant = 480 s, whIt is interestuously decrto the procand losses Fig.
9. Temperature [K] at t = 150 s: (a) case 1, (b) case 2, (c)
cas
atures
nd 10 show color maps of calculated domain tempera-es 15 at
times 150 and 480 s, respectively.parison purposes, Fig. 11 shows
thermal images of thee taken during the experiment at times 150 and
480 s,he values estimated at specic points on the ladle, liddes.
Fig. 12 shows the evolution of temperature of gasavity and wall of
the crucible.urface temperatures predicted by the simulation,
10, range from 500 to 600 K for t = 150 s and 450 to 480 s.
These values agree reasonably with the thermalented in Fig. 11,
that show 483517 K for t = 150 s andor t = 480 s. Temperature
predicted in the measurementges from 750 to 850 K for t = 150 s,
and 700 to 800 K forich agrees with experimental values shown in
Fig. 12.ing to note that the temperature of the crucible
contin-eases, which means that it supplies a part of the energyess,
that it is subsequently distributed for load heatingto the
environment. Gas cavity temperature predicted
by the full msame order
Experimshown in Fiof the test, from 700 tomations.
Final loa950 K, withat which allture at the efurther sho
5.4. Molten
Fig. 14 s14 at the ecentric recionly one isdifferencese 3, (d)
case 4 and (e) case 5.
odel (case 1) ranges from 500 to 700 K, which is of the than the
experimental value in Fig. 12.ental measurements of the inner wall
temperature areg. 13, as estimated by thermal images taken at the
endwhen the top lid of the ladle is removed. Values range
950 K, which is also in agreement with numerical esti-
d temperature predicted in case 1 ranges from 933 to hot spots
of 1200 K. This value corresponds to the time
the metal load is in liquid phase, t = 627 s. Load tempera-nd of
the experimental test, for t = 671 s is 1030 K, whichws that
calculation and experiment agree reasonably.
load movement
hows velocity vectors in the liquid aluminum for casesnd of the
melting process. It is observed that four con-rculation zones are
predicted in cases 1 and 2, whereas
formed in cases 3 and 4. This is coherent with the observed in
Fig. 8, and points out the fact that a full
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M. Carmona, C. Corts / Journal of Materials Processing
Technology 214 (2014) 334 346 343
Fig. 10. Temperature [K] at t = 480 s: (a) case 1, (b) case 2,
(c) case 3, (d) case 4 and (e) case 5.
Fig. 11. Thermal images of the outer crucible surface: (a) t =
150 s and (b) t = 480 s.
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344 M. Carmona, C. Corts / Journal of Materials Processing
Technology 214 (2014) 334 346
Fig. 12. Evolution of measured temperatures of crucible wall and
gases.
model of air movement and coupling at the interface are neededto
adequately predict natural circulation of the molten metal.
Frompreceding results, it is clear that differences in local
temperatureand liquid fraction are important, but not so overall
gures, such asmelting time and overall liquid fraction (Fig.
6).
5.5. Energy balance
Table 3 presents the energy balance of the transient processfor
the ve cases computed, along with estimated data for
theexperimental assay. The energy balance reduces to the
statementthat estimated input thermal energy (55% of measured
electricalinput) plus heat given away by the preheated refractory
ladle equalsheating and fusion energy of the aluminum load, plus
heatingof the crucible lid, heating of the air inside the cavity
and accu-mulated heat losses to ambient. It should be noted that
some ofthese terms can be determined experimentally only with a
verylarge uncertainty. This is the case of losses from crucible
walls
Fig. 13. Thermal image at the end of the test.
and internal energy supplied by the refractory material, that
arebased (as discussed) on indicative surface temperatures or
verylocalized inner material temperatures. The simulation
developedachieves very good accuracy in all terms, but the relative
characterof empirical data should be taken into account, since
computationalmethods are logically adapted to empirical input, as
it has beenexplained.
5.6. Computational resources
Table 4 presents the consumed computational resources foreach
model, taking the cheapest case 5 as the basis for compari-son.Fig.
14. Velocity vectors [m/s] for the molten aluminum at the end of
the melting process: (a) case 1, (b) case 2, (c) case 3 and (d)
case 4.
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M. Carmona, C. Corts / Journal of Materials Processing
Technology 214 (2014) 334 346 345
Table 3Terms of the energy balance (kJ) and time (s) for each
computational case and experimental data.
Case 1 Case 2 Case 3 Case 4 Case 5 Experimental
internal e 106.5 103.4 NA internal e internal e internal eInput
thermLateral wall Top wall losTotal time o
NA: not availa
Table 4Consumed com
Case 1 Case 2 Case 3 Case 4 Case 5
The mosputational r(case 3). Theffects of ra4 present vtion
temperfraction anding that thethan that ofor estimatof ow in
Although sicase 4, inaccwhich do ncalculation.
5.7. Conclu
Numericaprototypesider heatmolten alphase cha
In order expense ausing suc
Results semeasuremof the reaexperimetheir timeload and d
The advanspecic aparameteplied treinner conDifferencpurpose
aconsiderediscussed
wled
s invwork. E
plishxperledg
nces
A., Khof an459.s, V., Sesses.012. .J., K
s, K.C.,ity anical
Katsmelting790J.L., 19ertiesnluis, ., El Q
rete p.rgyro
a revi396.
Hwanrimenitionsnergy top 1517.6 863.9 1596.6 nergy ladle 3543.3
3108 3904.7 nergy load 10,082 10,081 10,311.1 nergy air 19.4 18.6
20 al energy 10,211.3 9934.5 10,129.9 losses 2124.8 2070.8 2095.1
ses 10.8 8.2 11.8 f the process 627 610 622
ble.
putational resource for each computational case.
Relative time to case 5
2160135060021.81
t accurate model (case 1) consumes 3.6 times the com-esources of
the simplied case by effective coefcientsis latter is thus a good
option to take into account thediation in this kind of furnaces.
However, cases 3 andery similar results in basic parameters, such
as opera-ature and melting time, and similar proles for liquid
velocity in the molten load. In this sense, consider- time of
calculation for case 3 is signicantly higher
f case 4, the use of the latter should be recommendedes in
industrial problems where detailed calculationthe molten load or
radiation losses are not needed.mulations in case 5 are 20 times
less demanding thanurate results are obtained even for overall
magnitudes,ot make advisable such strong simplications of the
sions
l simulations that reproduce experimental tests in a aluminum
melting furnace are presented. Models con-
Ackno
ThiFrameEDEFUaccomwith eacknow
Refere
Abbassi,ysis 450
AlexiadeProc
ANSYS, 2Assael, M
MilldensChem
Assis, E.,of m50, 1
Brandt, Prop
CarbosaFaraji, M
disc1275
Hu, H., Aing:371
Hur, M.,expecond conduction in solid parts, convection effects
in gas anduminum, interactions between gasliquidsolid zones,nge and
radiation heat transfer.to determine the reduction in both
computationalnd accuracy of the simulation, ve computational
casescessively simplied models are studied.em generally reasonable
and agree well with empiricalents, showing the capacity to estimate
diverse featuresl furnace, many of them very difcult to
determinentally, such as load and refractory temperatures and
evolution, patterns of movement inside the moltenistribution of
heat losses.tage of simplied models must be considered for
eachpplication. Reasonable prediction of overall furnacers (e.g.,
melting time) is possible even when using a sim-atment of the air
cavity. However, a detailed account ofvection and radiative losses
demands a complete model.e in computational times is very
signicant, so thatnd number of simulations required should be
alwaysd. Predictions and cost of the simplied simulations are
and compared, which could assist in this respect.
Films 390,Incropera, F.P.
edition. JoJones, B., Sun, D
of melting2724273
Lacroix, M., Vchange proB: Fundam
Mills, A.F., 199Samarskii, A.A
Numericalreview. In4106.
Scanlon, T.J., Sing and fr436.
Trp, A., 2005. technical thermal en
Voller, V.R., Branalysis ofat the conf378390.
Voller, V.R., Ction/diffusEngineerin2828.3 2558.9 2781.910,455.8
9810.1 10,621
0 0 169999.6 9511 10,927.92257.4 2148.5 2802.1
8.2 7.9 NA614 584 671
gments
estigation has been partially funded by the EU 7th Program,
project NMP 2009 LARGE3 - No. 246335,xperimental facilities and
tests were provided anded by Corporacin Tecnalia, that kindly
provided usimental data. Help of Tecnalia personnel is kindlyed,
with special mention to Patxi Rodriguez.
oshmanesh, Kh., 2008. Numerical simulation and experimental
anal- industrial glass melting furnace. Applied Thermal Engineering
28,
olomon, A.D., 1993. Mathematical Modeling of Melting and
Freezing Hemisphere Publishing Corporation, United States of
America.ANSYS FLUENT 14.0 Users Guide.akosimos, K., Banish, R.M.,
Brillo, J., Egry, I., Brooks, R., Quested, P.N.,
Nagashima, A., Sato, Y., Wakeham, W.A., 2006. Reference data for
thed viscosity of liquid aluminum and liquid iron. Journal of
Physical andReference Data 35 (1), 285300.an, L., Ziskind, G.,
Letan, R., 2007. Numerical and experimental study
in a spherical shell. International Journal of Heat and Mass
Transfer1804.84. Properties of pure aluminum. In: Hatch, J.E.
(Ed.), Aluminum:
and Physical Metallurgy. ASM International, Ohio, pp.
124.http://www.carbosanluis.com.ar/REFRACT CSL-2007.pdfarnia, H.,
2010. Numerical study of melting in an enclosure with
rotruding heat sources. Applied Mathematical Modelling 34,
1258
poulos, S.A., 1996. Mathematical modelling of solidication and
melt-ew. Modelling and Simulation in Materials Science and
Engineering 4,
g, T.H., Ju, W.T., Lee, C.M., Hong, S.H., 2001. Numerical
analysis andts on transferred plasma torches for nding appropriate
operating
and electrode conguration for a waste melting process. Thin
Solid 186191., De Witt, D.P., 1990. Fundamentals of Heat and Mass
Transfer, thirdhn Wiley and Sons Inc., United States of America,
pp. 529585.., Krishnan, S., Garimella, S., 2006. Experimental and
numerical study
in a cylinder. International Journal of Heat and Mass Transfer
49,8.oller, V.R., 1990. Finite difference solutions of solidication
phaseblems: transformed versus xed grids. Numerical Heat Transfer,
Partentals 17, 2541.2. Heat Transfer. Richard D. Irwin, United
States of America.., Vabishchevich, P.N., Iliev, O.P., Churbanov
Alexiades, A.G., 1993.
simulation of convection/diffusion phase change
problemsaternational Journal of Heat and Mass Transfer 36 (17),
4095tickland, M.T., 2004. A numerical analysis of buoyancy-driven
melt-eezing. International Journal of Heat and Mass Transfer 47
(3), 429
An experimental and numerical investigation of heat transfer
duringgrade parafn melting and solidication in a shell-and-tube
latentergy storage unit. Solar Energy 79 (6), 648660.
ent, A.D., Reid, K.J., 1987a. Computational modeling framework
for the metallurgical solidication process and phenomena. Paper
presentederence for solidication processing. Ranmoor House,
Shefeld, UK, pp.
ross, M., Markatos, N.C., 1987b. An enthalpy method for
convec-ion phase change. International Journal for Numerical
Methods ing 24, 271284.
-
346 M. Carmona, C. Corts / Journal of Materials Processing
Technology 214 (2014) 334 346
Voller, V.R., Prakash, C., 1987. A xed grid numerical modelling
methodology forconvection-diffusion mushy region phase-change
problems. International Jour-nal of Heat and Mass Transfer 30 (8),
17091719.
Voller, V.R., Swaminathan, C.R., Thomas, B.G., 1990. Fixed grid
techniques for phasechange problems: a review. International
Journal for Numerical Methods inEngineering 30 (4), 875898.
Vidalain, G., Gosselin, L., Lacroix, M., 2009. An enhanced
thermal conduction modelfor the prediction of convection dominated
solidliquid phase change. Interna-tional Journal of Heat and Mass
Transfer 52, 17531760.
Wu, Y.K., Lacroix, M., 1995. Numerical simulation of the melting
of scrap metal ina circular furnace. International Communications
in Heat and Mass Transfer 22(4), 517525.
Zeiger, H., Nielsen, H., 2004. Constitucin y propiedades de los
materiales de alu-minio. In: Hufnagel, W. (Ed.), Manual del
aluminio, vol I, segunda edicin.Revert S.A., Spain, pp. 100122.
Zhou, B., Yang, Y., Reuter, M.A., Boin, U.M.J., 2006. Modelling
of aluminium scrapmelting in a rotary furnace. Minerals Engineering
19, 299308.
Numerical simulation of a secondary aluminum melting furnace
heated by a plasma torch1 Introduction2 Experimental
configuration2.1 Principle of operation and test protocol2.2
Measurement equipment
3 Model description3.1 General assumptions and boundary
conditions3.2 Geometry and materials3.3 Simulation of gas
cavity3.3.1 Case 1: Thermal radiation and air convection fully
modeled3.3.2 Case 2: Radiation no modeled3.3.3 Case 3: Purely
diffusive transfer in the gas, with an augmented, effective thermal
conductivity3.3.4 Case 4: Cavity not modeled3.3.5 Case 5: Cavity
not modeled and load heated by pure conduction
3.4 Numerical time step3.5 Governing equations of the enthalpy
method3.6 Meshing scheme
4 Preheating of the refractory ladle5 Results and discussion5.1
Melting time5.2 Distribution of liquid fraction5.3 Temperatures5.4
Molten load movement5.5 Energy balance5.6 Computational
resources5.7 Conclusions
AcknowledgmentsReferences