Multiphysics Simulation of Microwave Sintering in a Monomode Cavity

Transcription

1 Multiphysics Simulation of Micowave Sinteing in a Monomode Cavity Didie Bouvad, Sylvain Chamond and Claude P. Cay Laboatoie SIMAP, Genoble INP, Saint Matin d Hèes, Fance The simulation of sinteing of a ceamic powde in a monomode micowave cavity has been caied out with COMSOL finite element softwae. At a given time, a stationay calculation povides the electomagnetic field in both the cavity and the compact when we assume an incident powe, and when we suppose that dielectic pemittivity and themal paametes depend on elative density and tempeatue. Fom the electic field in the compact, the value of the geneated heat is deduced, and a tansient themal calculation is then un with this value as a heat souce and with adiating losses at the boundaies of the compact. The density of the compact is updated though a pescibed densification law, and finally, tempeatue and density kinetics ae obtained. The developed tool is used to analyze the influence of the insulation device on heating. The effect of intoducing a suscepto in the cavity fo the pupose of hybid heating is also investigated. Intoduction Micowave heating of dielectic mateials esults fom the absoption by molecule polaization of pat of the enegy tanspoted by an oscillating electic field. As compaed to conventional heating, it esults in shote heating times and thus may slow down unwanted micostuctual changes aising duing sinteing, such as gain gowth in fine gain ceamics. Howeve, micowave sinteing is a complex pocess, and is much moe difficult to contol than conventional sinteing. Even such a basic issue as measuing the tempeatue of the mateial undegoing sinteing is a poblem. Also, insulation and positioning of a compact may be citical. Compute models epesenting the pocess as a whole would be of geat help in the effot of undestanding the micowave sinteing pocess and binging it to an industial scale. Micowave sinteing involves seveal phenomena that ae stongly coupled to each othe: electomagnetism, heat tansfe and sinteing. Fo example, electomagnetic enegy absoption that contols heating (and thus also contols sinteing) depends on tempeatue-dependent mateial paametes and on the electomagnetic field, which changes as the sinteing pogesses. Taking into account such coupling effects is necessay fo ealistic modeling of micowave sinteing. Macoscopic scale simulations of micowave sinteing, coupling electomagnetism and heat tansfe, have been pesented in the liteatue [1-3]. These models ae mainly based on eithe the finite element method o finite diffeence time domain techniques, and most of these studies do not intoduce densification. Notable exceptions ae the model by Binboim and Camel [4], who calculated density gadients in complex shape components, and the model by Riedel and Svoboda [5], who found density and gain size distibutions in a cylindical compact suounded by a suscepto inside an axisymmetic esonant cavity. We pesent in this pape seveal esults of a 3D finite element simulation of micowave sinteing in the monomode cavity funace designed at Genoble INP. This simulation takes into account electomagnetism, heat tansfe and densification, as well as, in pat, coupling of these 21

2 phenomena. The simulation pocedue is fist descibed. Next, to demonstate the inteest of modeling, seveal examples of calculation ae shown, including a simulation of sinteing of a compact of ziconia, a dielectic mateial that absobs micowave enegy modeately at oom tempeatue but significantly at sinteing tempeatue. Emphasis is put on the influence of the insulation on tempeatue and density fields, and the question of hybid heating is also discussed. Moe simulations can be found in [6]. Model Desciption The model attempts to closely epesent the conditions of a monomode cavity micowave funace simila to the one developed at Genoble INP by Chamond et al [7]. In this equipment, a ectangula waveguide tanspots micowave adiation to a ectangula TE 10p cavity of 86 x 43 mm coss-section. Located at one end of this cavity is a movable shot-cicuiting piston (an electic conducto) to eflect the adiation and ceate a standing wave; at the othe end of the cavity (on the same side as the waveguide) is a movable iis consisting of a coppe sheet with a vetical slot. When the distance between the shot-cicuiting piston and the iis is set coectly, backwad adiation is eflected by the iis, and the stacking of fowad and multiply-eflected micowaves esults in an incease of the electomagnetic enegy in the cavity (a esonance phenomenon). When the cavity is empty, the pope distance between the iis and the piston is a multiple of the half-wavelength in the waveguide. When the cavity contains a dielectic sample, the wavelength is modified, and thus this distance changes depending on mateial pemittivity and sample dimensions. In this study, we simply simulate a standing wave in the cavity with a value of electomagnetic enegy adjusted so that the sample eaches a pescibed tempeatue in the steady state; we do not intoduce the coupling iis. The iteative simulation pocess is descibed is as follows. At a given time, a stationay calculation povides the electomagnetic field eveywhee in the cavity, including within the compact, and uses the electic field within the compact along with the imaginay pat of the mateial pemittivity to calculate the enegy absobed by the compact. This enegy is consideed as an intenal heat souce; taking into account heat flux out of the compact accoding to the assumed bounday conditions, we then calculate the esulting heteogeneous tempeatue vaiation fo the next time incement. As a consequence of local tempeatue, a coesponding change in mateial density esults; this change is calculated by integating a known densification equation. This incease obviously esults in a defomation of the compact howeve, fo the sake of simplicity, we assume that the dimensions of the compact do not change duing the pocess. This means that the elative density is a local paamete that descibes the micostuctue of the mateial but does not affect the geomety of the sinteing compact. We do not calculate the stesses and stains esulting fom heteogeneous density vaiation. This calculation pocedue has been caied out in 3D with COMSOL Multiphysics finite element softwae. Thee models have been used: Electomagnetics Waves (COMSOL model efeence ( fw ) in hamonic popagation, Heat Tansfe by Conduction ( ht ) in tansient analysis (in the compact only), Patial Diffeential Equations, Geneal Fom ( g ) in tansient analysis with the elative density as a vaiable. We suppose that the complex pemittivity in the compact is a function of tempeatue, T, and that the themal conductivity of the compact is a function of the elative density, ρ. The 22

3 densification ate is expessed as a function of tempeatue and elative density, and we suppose that it supposed oughly descibes the behavio of submiconic ziconia powde. The calculations pesented in this pape have been un on a standad PC with 1.8 GHz CPU and 2 GB RAM. The computing time fo the late calculations that involve all the phenomena and coupling was aound 5 min. Pocess and Mateial Paametes The following paametes have been intoduced in the simulation. Some of them have been taken fom the liteatue, while othes have been estimated intuitively. It should be emphasized that such dielectic paametes as pemittivity ae vey pooly known: indeed, values with diffeent odes of magnitude can be found in the liteatue. This, of couse, is a seious issue fo modeling and should be consideed in futue wok, when we seek a quantitative desciption of micowave sinteing. Electomagnetic paametes: Relative pemittivity of the ai in the cavity: ( T 293) Relative pemittivity of the compact: ε = 10 i0.1e, i.e., the eal pat of ε is constant and the imaginay pat inceases fom 0.1 to 1.0 when the tempeatue inceases fom oom tempeatue to 1,700 K. Input powe in the cavity enty section is constant in evey simulation, adjusted by tial and eo to each a pescibed tempeatue. Cavity walls ae pefectly conducting. Heat tansfe paametes: Conductivity: k = 30ρ W/(mK) Weight density: ρ = 6,000ρ kg/m 3 Heat capacity: C p = 900 J/(kg K) Initial tempeatue: T 0 = 293 K Bounday conditions: adiative loss with emissivity equal to 0.1 o 0.9 (see below) Densification paametes: Densification law: dρ dt densification aound 1,700 K. Initial density: ρ 0 = 0.65 Pocess and Mateial Paametes 1 ρ = 200 e T 1 ρ 0.64 ρ 2, descibing significant Figue 1 pesents the electic field distibution in the cavity containing a 1 mm tall cylindical sample of diamete 1 mm. Fo this simulation, a constant elative pemittivity, ε = 10 i0.3, has been assumed. Pio simulation of the empty cavity showed egula nodes and antinodes along the wave diection, as expected; the compact has been positioned at one of these peaks so that it absobs as much enegy as possible. Pesence of the compact does not significantly change the positions of nodes o antinodes, but the electic field inside the compact is vey low (about 15% 23

4 Fig. 1. Electic field nom distibution in the plain cavity containing a cylindical compact. The electic field anges fom 0 to V/m. of the field found in the empty cavity) due to the high elative pemittivity of ziconia compaed to that of ai, and to the stong gadient obseved in the ai below and above the compact. This means that the enegy absobed by the compact will be much lowe than fom the enegy absobed in an empty cavity situation; thus, a highe electomagnetic powe will be equied in the cavity to heat the compact, which is pactically obtained due to the esonance. The gadient may also lead to detimental phenomena, such as plasma fomation. Next, we will show esults of multiphysics simulations. We investigated the effect of compact insulation on tempeatue and density gadients. In the fist case, the 1 mm height, 1 mm diamete cylindical compact is insulated on evey side (an emissivity of 0.1 is assumed), wheeas in the second case it is insulated eveywhee except on its uppe suface (an emissivity of 0.9 is assumed). The second case coesponds to expeiments of Chamond et al. [7], duing which the tempeatue in the uppe suface is measued by an infaed camea. The input powe in evey expeiment is adjusted so that the aveage tempeatue afte 30 min is about 1,680 K. Figue 2 shows the tempeatue on the suface of the compact in both cases. With full insulation, the tempeatue at the cente of the compact is found to be highe by 16 K than the tempeatue of the edges of the uppe and side sufaces. With patial insulation, the tempeatue distibution is asymmetical, with the maximum tempeatue in the lowe pat of the compact being 57 K highe than the minimum in the uppe pat. This second case has been moe deeply investigated. We plotted in Figue 3 the changes of tempeatue and elative density duing sinteing in thee points of the compact: the cente of the lowe section (called bottom ), the cente of the compact ( cente ), and the cente of the uppe section ( top ). It can be obseved that the heating ate is about 200 K/min and the tempeatue eaches a peak befoe a slight decease. This vaiation esults fom the assumed constant input powe, and could be contolled by adjusting this powe thoughout the simulation. Figue 3 shows that the bottom and cente tempeatues ae about equal, and the tempeatue at the top sepaate aound 1,300 K. This diffeence leads to a vaiation of about 1% in density. 24

5 Fig. 2. Tempeatue distibution in a vetical coss-section of the compact afte 30 min heating. The compact suounded by themal insulation on evey side (a), and on evey side except the uppe suface (b). The tempeatue anges fom 1,673 to 1,693 K in (a) and fom 1,628 to 1,685 K in (b). Tempeatue (K) Bottom Top Cente Time (min) Fig. 3. Tempeatue and elative density changes duing sinteing of the patially-insulated compact. The cuves coesponding to cente and bottom tempeatue and elative density coincide Relative density Finally, we pesent esults of simulating sinteing of a SiC cylindical suscepto (height: 15 mm, extenal diamete: 30 mm, thickness: 5 mm, elative pemittivity: 100 i100) suounding the compact. Such a configuation is fequently used in expeimentation to peheat mateials with low pemittivity at oom tempeatue, and to sinte mateials in case of poo coupling with micowaves in sinteing tempeatue ange. A elevant question is whethe the suscepto shields the compact fom the electic field, which would pevent hybid sinteing. Figue 4 shows that the electic field is lowe in the suscepto than in the compact due to the highe eal pemittivity of SiC. The dissipated powe in the suscepto is much highe than that in the compact (296 W vs. 2.3 W) due to the highe imaginay component of electic pemittivity of SiC. Ou calculation shows that the suscepto does not shield the compact fom the field. Thus the compact can undego hybid heating, i.e. adiation coming fom the suscepto and coupling with the micowaves. 25

6 Fig. 4. Distibution of the electic field nom in a plane nomal to wave popagation in the whole cavity (a), and in the compact and suscepto only (b). Range of electic field: V/m in (a) and V/m in (b). Conclusion Inteest in using finite element simulation to aid in bette undestanding micowave sinteing in monomode cavities has been demonstated. We fist calculated the distibution of electomagnetic field in the cavity containing a typical cylindical ceamic compact; next we showed the tempeatue and density gadients in a compact with complete o patial themal insulation, and finally, we investigated the electic field with a suscepto suounding the compact and found that the compact can successfully undego hybid heating. We ae cuently woking on simulating such hybid heating by taking into account adiation fom the suscepto to the compact. Refeences [1] M.D. Iskande and A.O.N.M. Andade, FDTD simulation of micowave sinteing of ceamics in multimode cavities, IEEE Tans. Micowave Theoy and Techniques, vol. 42, pp , [2] J. Lasi, P.D. Ramesh and L. Schächte, Enegy convesion duing micowave sinteing of a multiphase ceamic suounded by a suscepto, J. Am. Ceam. Soc., vol. 83, pp , [3] Y. Duan, D.C. Soescu, J.K. Johnson, Finite element appoach to micowave sinteing of oxide mateials, Poc. COMSOL Uses Confeence, Boston, [4] A. Binboim and Y. Camel, Simulation of micowave sinteing of ceamic bodies with complex geomety, J. Am. Ceam. Soc., vol. 82, pp , [5] R. Riedel and J. Svoboda, Simulation of micowave sinteing with advances sinteing models, In: Advances in Micowave and Radio Fequency Pocessing, M. Willet-Poada, Ed., Spinge, [6] D. Bouvad, S. Chamond and C.P. Cay, Finite element modeling of micowave sinteing, Advances in Sinteing Science and Technology, Ceam. Tans., vol. 209, pp , [7] S. Chamond, C.P. Cay, and D. Bouvad, Densification and micostuctue evolution of Y- Tetagonal Ziconia Polycystal powde duing diect and hybid micowave sinteing in a singlemode cavity, J. Eu. Ceam. Soc., vol. 30, pp ,