© Strojni{ki vestnik 48(2002)9,472-481 © Journal of Mechanical Engineering 48(2002)9,472-481 ISSN 0039-2480 ISSN 0039-2480 UDK 004.94:536.2:621.762.5 UDC 004.94:536.2:621.762.5 Izvirni znanstveni ~lanek (1.01) Original scientific paper (1.01) Analiza prenosa toplote v postopku sintranja feritov A Heat-Transfer Analysis of the Ferrite Sintering Process Zlatko Rek - Matja` Perpar - Iztok @un Obravnavana je analiza prenosa toplote v postopku sintranja feritov v komorni peči. Izvedeni sta bili meritev in numerično simuliranje časovnega razvoja temperaturnega polja. Zaradi zahtevnosti problema je simuliranje potekalo v dveh delih. V prvem delu je obravnavana celotna peč, v drugem delu pa je analiziran samo pladenj s feriti. V prispevku je opisan postopek meritve temperature, numerični model (enačbe prenosa toplote) in generacija mrežastega modela peči za izbrano računsko območje, tj. notranjost peči z grelniki, pladnji, feriti, nosilci in podstavki. Narejena je analiza rezultatov numerične simulacije in njihova primerjava z izmerjenimi vrednostmi. Ujemanje numerične rešitve in izmerjenih vrednosti je dobro. © 2002 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: sintranje feritov, prenos toplote, simuliranje numerično, modeli sevanja) The paper deals with a heat-transfer analysis of the process of sintering ferrites in a furnace. Experimental measurements and a numerical simulation of the time development of the temperature field were performed. Due to the complexity of the problem the simulation had to be performed in two steps. The first step takes into consideration the whole furnace, while in the second step only a single ferrite plate is analyzed. The experiment, the numerical model (the heat-transfer equations) and the generation of the discretized model of the furnace for the chosen computational domain, e.g. furnaces with heaters, plates, ferrites, bearers and supports, are described. The results of the numerical simulation are analyzed and compared with experimental data. The agreement between the numerical results and the experimental data was good. © 2002 Journal of Mechanical Engineering. All rights reserved. (Keywords: ferrite sintering, heat transfer, numerical simulations, radiation models) 0 UVOD Prispevek predstavlja opravljeno delo v okviru raziskovalnega projekta L2-0784: Izboljšave postopkov pri sintranju feritov v peči, pri katerem sta sodelovala Fakulteta za strojnišvo - Laboratorij za dinamiko fluidov in termodinamiko, Ljubljana in Iskra Feriti, Podjetje za proizvodnjo feritov in navitih komponent, d.o.o., Ljubljana. V postopku sintranja feritov je natančen časovni potek temperature, poleg drugih parametrov, ključnega pomena za kakovost izdelka, to je njegove elektromagnetne in reološke lastnosti. Da bi bolje razumeli dogajanje pri prenosu toplote v postopku sintranja, skušamo narediti numerični model peči ([1] in [2]). Tako lahko proučujemo vpliv posameznih parametrov na kakovost izdelka. Ker je treba numerični model preveriti, smo v prvi fazi izvedli meritve temperatur [3]. Namen je bil dvojen: 0 INTRODUCTION This paper presents work done in the framework of research project L2-0784 – Improvement of ferrite sintering in furnaces – in collaboration of the Faculty of Mechanical Engineering, Laboratory for Fluid Dynamics and Thermodynamics, Ljubljana with Iskra Feriti, Company of ferrite materials and wound components production Ltd., Ljubljana. In the process of ferrite sintering, an accurate time-dependent temperature distribution (among other parameters) is of key importance for achieving a high-quality product, i.e. a material with good electromag-netic and rheological properties. To understand better the heat transfer during the sintering process a nu-merical model of the furnace has to be made ([1] and [2]). In this way the influence of the process parameters on the quality of the product can be studied. Because the numerical model has to be veri-fied, in the first step the temperature measurements [3] are performed. The purpose is twofold: VH^tTPsDDIK stran 472 Rek Z., Perpar A., @un I.: Analiza prenosa toplote - A Heat-Transfer Analysis 1. Izmeriti časovni potek temperatur na notranji steni peči in na grelnikih, ki jih potrebujemo za robne pogoje pri numeričnem simuliranju. 2. Izmeriti časovni potek temperatur ob feritih, v feritih na robu pladnja in v feritih na sredini pladnja. Te izmerjene vrednosti so namenjene za primerjavo oz. overitev numeričnega modela. 1 MERITEV TEMPERATUR V komornih pečeh je sintranje pod nadzorom računalnika, ki vodi postopek glede na vstavljen program obratovalnih parametrov. Za (iz)gradnjo ter testiranje modela prenosa toplote je poleg vstopnih parametrov potrebno poznavanje temperatur znotraj peči, še posebej ob samem sintrancu. Izmerjen je bil časovni potek temperatur na različnih mestih v peči, na zunanji steni peči in v okolici. Temperature v snovi so bile izmerjene s termopari tipa S in K, na zunanji steni peči pa z merilnikom temperature na infrardeče zaznavalo. 1.1 Izvedba meritev Za merjenje temperatur v peči so bili uporabljeni termopari tipa S (Pt-10%Rh/Pt) in K (Ni-Cr/Ni-Al). Tip S so bili iz neoplaščenih žic debeline 0,5 mm, vodenih skozi keramične cevi, tip K pa so bili iz žic debeline 0,8 mm, oplaščenih s temperaturno odporno tkanino. Termopar S je omogočal meritve temperatur do 1700 °C, termopar K pa meritve do 1200 °C stalno ter do 1400 °C kratkotrajno. Pripravljena je bila merska veriga termopar - podaljševalni vod - referenčna točka hladnega spoja (0 °C) - priključni kabel - preklopno stikalo - digitalni voltmeter. Temperatura zunanje stene peči je bila izmerjena z infrardečim digitalnim merilnikom. Temperatura ob zunanji steni (25 mm od stene) in temperatura okolice sta bili izmerjeni z digitalnima termometroma z zaznavali tipa K. Izmerjene vrednosti so bile zapisane v računalnik. Merska veriga je bila umerjena za vsak tip termoparov Termopar tipa S je bil umerjen v območju 170,0 °C do 1123,2 °C, največja vrednost poprave je bila -2,6 °C. Termopar tipa K je bil umerjen v območju 170,0 °C do 1086,0 °C, največja vrednost poprave je bila -2,4 °C. Relativna napaka kazanja merila (razmerje med vsoto absolutnih vrednosti poprave in merilne negotovosti ter dogovorno pravo vrednostjo temperature) za temperature, večje od 170 °C ni presegla 0,5%. Ocenjeno je bilo, da je bila točnost merske verige zadostna, torej poprava izmerjenih temperatur ni bila potrebna. Vrednosti temperatur, ki so bile izmerjene z digitalnim voltmetrom, so bile izračunane z znižanima polinomoma po ameriškem standardu NBS (9. stopnje za tip S in 8. stopnje za tip K). Za testiranje izračuna so bili uporabljeni rezultati kalibracijske meritve. Razlike med 1. To determine the time-dependent temperature of the furnace’s internal wall, which is used as a boundary condition for the numerical simulation. 2. To measure the time-dependent temperature profile near the ferrites, in the ferrites at the edge, and in the plate centre. 1 TEMPERATURE MEASUREMENTS The process of sintering in the furnace is controlled by computer with an operation schedule. Besides input parameters, the development and testing of the heat-transfer model requires temperatures inside the furnace, especially near the ferrite. A time history of the temperatures at different locations in the furnace, on the outer wall, and in the surroundings was measured. Thermocouples (types S and K) and an infrared (IR) thermometer were used for the medium and outer-wall temperatures, respectively. 1.1 Obtaining the measurements The temperatures in the furnace were measured by types S (Pt-10%Rh/Pt) and K (Ni-Cr/Ni-Al) thermocouples. The S type thermocouple was made of uncoated 0.5-mm-thick wire led through a ceramic tube. The type K wire was 0.8-mm thick and shielded with a high-temperature-resistant textile. Thermocouple S was suitable for measurements up to 1700 °C, while thermocouple K was suitable for permanent measurements up to 1200 °C, and for a short duration up to 1400 °C. The composition of the measuring chain was: thermocouple - extension wire - cold reference point (0 °C) - connecting cable - switch contact - digital voltmeter. The temperature of the outer furnace wall was measured with a IR digital thermometer. The temperature near the outer wall (25 mm from the wall) and the temperature of the surroundings were measured by digital thermometers with type K sensors. The measured values were recorded with a computer. The measuring range was calibrated for each thermocouple. The type S thermocouple was calibrated in the range 170.0 °C to 1123.2 °C, the highest correction was -2.6 °C. The type K thermocouple was calibrated in the range 170.0 °C to 1086.0 °C, the highest correction was -2.4 °C. The relative error of the instrument readouts (the proportion between the sum of the absolute correction values and of the measurement uncertainty and the conventional true value of the temperature) for temperatures higher than 170 °C did not exceed 0.5%. The accuracy of the measuring chain was estimated to be sufficient, therefore, a correction of the measured temperatures was not necessary. Temperature values measured with a digital voltmeter were calculated using polynomial regression following the NBS standard (9th order for type S and 8th order for type K). The results of the calibration measurement | lgfinHi(s)bJ][M]lfi[j;?n 02-9______ stran 473 I^BSSIfTMlGC Rek Z., Perpar A., @un I.: Analiza prenosa toplote - A Heat-Transfer Analysis dogovornimi pravimi in izračunanimi vrednostmi so bile istega reda velikosti kot vrednosti poprav pri kalibraciji, zato smo menili, da so bile temperature ustrezno izračunane. 1.2 Potek meritev Termopari so bili v peč vstavljeni skozi obstoječe odprtine. Za postavitev zaznaval pri sintrancih je bil uporabljen endoskop, ker se zapiranje peči izvaja z dvigom pladnjev v komoro. Na sliki 1 je shematsko prikazana namestitev zaznaval v peči. Temperaturni zaznavali na steni (st1 in st3) sta bili nameščeni na izolacijo. Feriti so bili razvrščeni na treh pladnjih.V vsaki plasti je bilo nameščeno po eno zaznavalo 10 mm od sintranca (fsp, fsr, fzg). Eno zaznavalo je bilo položeno na grelnik (gre), eno pa je bilo nameščeno pod grelnikom (amb). Termopar “st3” je bil tip K, vsi drugi pa tip S. were used to test the calculation. The differences be-tween the conventional true and the calculated values were within the range of correction, therefore, we con-sidered the calculated values suitable. 1.2 Measuring procedure The thermocouples were inserted into the fur-nace through existing holes. An endoscope was used to position the sensors near the ferrites because the furnace is closed by lifting the ferrite trays into the cham-ber. The locations of the sensors in the furnace are shown schematically in Fig.1. The thermocouples on the wall (st1 and st3) were placed onto the insulation. The ferrites were arranged on three trays. In each level the sensor was placed 10 mm from the ferrite (fsp, fsr, fzg). One sensor was put on the heater (gre) and one was placed in the area under the heater (amb). The ther-mocouple “st3” was type K, the others were type S. Sl. 1. Shema eksperimentalne komorne peči za sintranje feritov in merilna mesta v komorni peči Fig. 1. Schematic of the experimental furnace for sintering of ferrites and measuring locations in the furnace 2 NUMERIČNO SIMULIRANJE 2.1 Prenosna enačba energije Temperaturno polje v komorni peči za sintranje feritov je opisano z enačbo ohranitve energije [4]: 2 NUMERICAL SIMULATION 2.1 Energy transport equation Temperature field in the furnace for ferrites sintering is governed by the equation for energy conservation [4]: P^=V.(-*?r) + S (1), pri čemer so: c specifična toplota pri nespremenljivem tlaku, r gostota, l toplotna prevodnost in S viri toplote. Za temperaturno odvisnost toplotne where cp denotes the specific heat at constant pressure, r is the density, l is the heat conductivity and S are the heat sources. The dependence of the temperature on VH^tTPsDDIK stran 474 Rek Z., Perpar A., @un I.: Analiza prenosa toplote - A Heat-Transfer Analysis prevodnosti je uporabljen Sutherlandov zakon [5]: heat conduction is described by Sutherland’s law [5]: -J.5Ü2-IÜ JrIJ A = T ¦ hl.l (2). Natančnost približka je 2% na temperaturnem območju med 160 K in 1000 K. Ker imamo v našem primeru več različnih materialov (zrak, feriti, keramika), morajo na stiku veljati združljivostni pogoji: torej enakost temperatur in nasprotna enakost gostote toplotnih tokov. 2.2 Difuzijski model sevanja Sevalna temperatura T je določena z integralom intenzivnosti sevanja r/ po prostorskem kotu ([6] do [8]): The accuracy of the approximation is 2%, in the range between 160 K in 1000 K. Because there are different materials air, ferrites, ceramics – the compatibility conditions have to be satisfied: (3), (4), i.e. equality of the temperatures and the heat fluxes. 2.2 Diffusion model for radiation The radiation temperature Tr is defined with the integral of the radiant intensity i over all direc-tions ([6] to [8]): ' , JT (5). Po analogiji za gostoto sevalnega toplotnega toka pri difuzijski meji je gostota sevalnega energijskega toka definirana kot: By analogy with the radiant heat flux in the diffusion limit, the radiant energy flux is defined as: S = -^ (6). Difuzijska meja obstaja, če je dejanska absorpcija ^ velika, in je po Gibbu definirana kot: V našem primeru je^' -0, ker v zraku ni trdnih delcev. Ko enačbo (6) vstavimo v prenosno enačbo sevanja in integriramo po vsem območju valovnih dolžin, dobimo: A diffusion limit exists if the effective absorption^ is large, and was defined by Gibb to be: (7). In our case K’p=0, because there are no parti-cles in the air. When equation (6) is substituted into the radiation transport equation and integrated over all wavelengths we obtain: kjer je Tf temperatura zraka. Celoten energijski tok iz zraka na sevalno fazo je: (8), where Tf is the air temperature. The net energy transfer from the air to the radiant phase is: #,= 4^,(17-j;') (9). Ta člen je treba v prenosni enačbi toplotne energije (1) odšteti. Robni pogoj Ob predpostavki, da na steni sevanje prihaja in jo zapušča neodvisno od smeri, za robni pogoj na steni velja: This term is subtracted from the thermal energy equa-tion (1). Boundary conditions From the assumption that the radiant intensity arriving at and leaving from the wall are directionally independent, the boundary conditions at the walls are: *¦<• -m=Lt0) in fazo ohlajanja (dT/dt<0). S slik se jasno vidi, da so največji temperaturni gradienti v feritih na robu pladnja. To je tudi razumljivo, saj zunanji deli feritov prejmejo največ sevalne energije zaradi neposredne izpostavljenosti grelnikom. Temperaturno polje v notranjih feritih je bolj homogeno. 15 10 5 0 -5 -10 -15 2.5 Analysis of the results 2.5.1 Temperature in the furnace Figure 4 shows the difference between the com-puted and measured temperatures in the furnace at the monitoring point (fsp). The location of the monitoring point is close to the ferrites on the bottom plate. Agreement between the numerical results and the measured values is good. The largest relative error appears at the expulsion phase, and does not exceed 20%. A some-what worse deviation also appears at the heating phase, where the maximum error is 12%. This is understand-able, because the rate of change in temperature is very high. The differences in the sintering phase are minimal, the relative error is <0.1%. This also make sense because the conditions are steady (dT/dt=0). In the cooling phase the error again increases up to 12%. 2.5.2 Temperature in the ferrites Figures 5 and 6 show the temperature field on the horizontal plane through the centre of the ferrites in the first layer, e.g. the ferrites near the ceramic ferrite base, during the heating phase (dT/dt>0) and during the cool-ing phase (dT/dt<0). It can be clearly seen that the largest temperature gradients appear in the ferrites at the plate edge. This is understandable because the outer parts of the ferrites receive the majority of the radiation heat due to direct exposure to the heaters. The temperature field in the other ferrites is more homogeneous. -20 ¦" A lfl *!>Vi- I / K^ J~~ ¦^ *m Ti* II / \f "S 1/ 1 I 0 0.2 0.4 0.6 time 0.8 Sl. 4. Razlika med izmerjeno in izračunano temperaturo Fig. 4. Difference between computed and measured temperatures grin^sfcflMISDSD ^BSfiTTMlliC | stran 478 1 Rek Z., Perpar A., @un I.: Analiza prenosa toplote - A Heat-Transfer Analysis ooooooooooo OOOOOOOOOO ) ooooooooooo ooooooooooo ooooooooooo T=0 T=1 Sl. 5. Temperaturno polje v feritih v fazi segrevanja Fig. 5. Temperature field in the ferrites during the heating phase coooooooooo ooooooooooo ooooooooooo ooooooooooo CO ^ %~~^ o T=0 T=1 Sl. 6. Temperaturno polje v feritih v fazi ohlajanja Fig. 6. Temperature field in the ferrites during the cooling phase 3 SKLEPI V prispevku je prikazan postopek numeričnega simuliranja temperaturnega polja v laboratorijski komorni peči za sintranje feritov in temperaturnega polja v feritih. Narejena sta bila dva mrežasta modela: peč z notranjimi telesi (feriti, pladnji, nosilci, podstavki) in pladenj s feriti za dve numerični simuliranji. Za preverbo numeričnega modela je bilo treba izvesti meritve temperatur. Za merjenje temperatur znotraj peči so bili uporabljeni umerjeni termopari tipa S in tipa K. Temperature zunaj peči so bile izmerjene z digitalnimi termometri. 3 CONCLUSIONS This article shows a numerical simulation of the development of the temperature field in a labora-tory furnace for sintering ferrites. Two discrete models were made, the furnace with CHT objects (ferrites, plates, bearers, supports) and a single ferrite plate, for two numerical simulations. Testing of the numerical model required temperature measurements. The temperatures inside the furnace were measured with calibrated type S and type K thermocouples. The temperatures outside the furnace were measured with digital thermometers. gfin^OtJJlMlSCSD 02-9 stran 479 |^BSSITIMIGC Rek Z., Perpar A., @un I.: Analiza prenosa toplote - A Heat-Transfer Analysis Ker postopek sintranja poteka pri visokih Due to the high temperatures of the sintering temperaturah, je glavni mehanizem prenosa toplote iz process the main heat-transfer mechanism from the grelnikov na ferite sevanje. Za reševanje sistema heaters to the ferrites is radiation. The system of dif- diferencialnih enačb v razliški obliki je bila uporabljena ferential equations in a discrete form is solved by the metoda nadzornih prostornin. Časovno odvisni robni control volume method (CVM). The time-dependent pogoji, ki so potrebni za rešitev tega sistema, so bili boundary conditions, which are needed to solve the dobljeni z meritvami. system, are obtained by measurement. Zaradi zahtevnosti problema je bilo narejenih A few simplifications are used because of the nekaj poenostavitev. Ker so feriti zelo majhni v complexity of the problem. Because the ferrites are very primerjavi s preostalimi telesi, jih ni mogoče razbiti small when compared to the other objects they could not na dele. V prvi fazi so bili obravnavani kot enoten be discretized. In the first step they are treated as a single del. Ker se med seboj ne dotikajo, med postopkom block. Because they are not touching each other, and sintranja pa se še skrčijo, je bilo treba zračne reže because they shrink during the sintering process, the air upoštevati pri izračunu koeficienta prevodnosti gap must be taken into account when computing the feritnega dela.V drugi fazi je bilo izvedeno heat conduction coefficient of the ferrite block. In the numerično simuliranje časovno spremenljivega second step a numerical analysis of the time-dependent temperaturnega polja v feritih med postopkom temperature field in the ferrites during the sintering proc-sintranja. Obravnavan je bil keramičen pladenj, 220 ess was performed. It deals with a ceramic plate with 220 svitkov feritov, naloženih po štiri v stolpec in toroidal ferrites stacked in columns of four on a ceramic feritne ploščice za podlago feritom. Porazdelitev base. The temperature distribution is as expected. In the temperature v feritih je pričakovana. V fazah izgona expulsion and heating phase the temperature is higher in in segrevanja je temperatura višja v feritih, ki so na the ferrites at the edge of the plate and lower at the plate’s robu pladnja, na sredini pa nižja. Po fazi sintranja, centre. After the sintering phase, i.e. during the cooling tj. je v fazi ohlajanja, pa je slika obrnjena. Na sredini phase, the picture is reversed. The temperature is higher je temperatura višja kakor na robu. Zaradi at the centre and lower at the edge. Due to the geometry, geometrijske simetrije in simetrije robnih pogojev and the symmetry of the boundary conditions, the tem-je tudi temperaturno polje simetrično. perature field is also symmetrical. Iz primerjave meritev in rezultatov numeričnega From a comparison of the measurements and simuliranja lahko sklenemo, da je numerični model the numerical simulation results we can conclude that ustrezen in da z njim dovolj natančno opišemo the numerical model is appropriate and that the proc- dogajanje v komorni peči. ess in the furnace is well described. Zahvala Acknowledgements Avtorji se zahvaljujejo Računalniškemu The authors wish to thank the Computer centru na Institutu Jožef Stefan za uporabo Centre at the Jožef Stefan Institute for allowing us to programskega paketa TASCflow za numerično use the TASCflow software for the numerical simuliranje. Prav tako se zahvaljujejo g. Lepoldu simulation. We also thank Mr. Lepold Knez and Dr. Knezu in dr. Andreju Žnidaršiču iz Iskra Feriti, d.o.o. Andrej Žnidaršič from Iskra Feriti Ltd. for their review za pregled članka in pripombe. of the article and their valuable comments. 4 LITERATURA 4 REFERENCES [1] Rek, Z., I. Žun (1998) Numerična simulacija temperaturnega polja v komorni peči. Poročilo FERITI 02 - 97/98. Poročilo o raziskovalni nalogi. Fakulteta za strojništvo, Ljubljana. [2] Rek, Z., I. Žun (2000) Numerična simulacija temperaturnega polja v feritih Poročilo FERITI 03 - 00. Poročilo o raziskovalni nalogi. Fakulteta za strojništvo, Ljubljana. [3] Perpar, M., I. Žun, D. Petrič (1998) Meritve temperatur in deleža kisika v komorni peči. Poročilo FERITI 01 - 97. Poročilo o raziskovalni nalogi. Fakulteta za strojništvo, Ljubljana. [4] Isachenko, V.P, VA. Osipova, A.S. Sukomel (1977) Heat transfer. Mir Publishers, Moskva. [5] TASCflow (1996) Version 2.5 Documentation: User documentation. Advanced Scientific Computing Ltd., Waterlo, Ontario, Canada. [6] TASCflow (1996) Version 2.5 Documentation: Theory documentation - diffusion model for radiation. Advanced Scientific Computing Ltd., Waterlo, Ontario, Canada. [7] Siegel, R. and J.R. Howell (1972) Thermal radiation heat transfer . Mc Graw-Hill Book Company, New York. [8] Edwards, D.K. (1981) Radiation heat transfer notes. Hemisphere Publishing Corporation, New York. ^BSfiTTMlliC | stran 480 i Rek Z., Perpar A., @un I.: Analiza prenosa toplote - A Heat-Transfer Analysis Naslov avtorjev: dr. Zlatko Rek Author’s Address: Dr. Zlatko Rek, dr. Matjaž Perpar Dr. Matjaž Perpar prof. dr. Iztok Žun Prof. Dr. Iztok Žun Laboratorij za dinamiko fluidov in Laboratory for Fluid Dynamics termodinamiko and Thermodynamics Faculty of Mechanical Eng. Univerza v Ljubljani University of Ljubljana Aškerčeva 6 Aškerčeva 6 1000 Ljubljana SI-1000 Ljubljana, Slovenia zlatko.rek@fs.uni-lj.si zlatko.rek@fs.uni-lj.si matjaz.perpar@fs.uni-lj.si matjaz.perpar@fs.uni-lj.si iztok.zun@fs.uni-lj.si iztok.zun@fs.uni-lj.si Prejeto: 9.4.2002 Received: Sprejeto: 22.11.2002 Accepted: