1-s2.0-s0924013613003014-main

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


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


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)


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


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, (


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.


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


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.


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.


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

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Abbassi,ysis 450

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ANSYS, 2Assael, M

MilldensChem

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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

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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.

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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