let. - vol. 48 (2002) {t. - no. STROJNIŠKI VESTNIK JOURNAL OF MECHANICAL ENGINEERING strani - pages 471 - 518 ISSN 0039-2480 . StrojV . STJVAX cena 800 SIT 1. 2. 3. 4. 00 ¦* CO o Analiza prenosa --in--tranja feritov A Heat-Transfer Ferrite Sintering toplote v postopku Analysis of the rocess naliza vezanega prenosa toplote v hladilniku elektronskega ~ipa ------- An Analysis of Conjugate Heat Transfer in the Heat Sink of an Electronic Chip Nekateri vidiki terenskih preskusov Peltonovih turbin v HE “Peru}ica” ------- Some Aspects of the Research Carried out on the Power Generation Units at the Peru}ica Hydroelectric Power Plant tru`enje navarov Walter ------- The Turning of Ove orodji podjetja Produced g of Overlays Using Tools by the Company Walter z © Strojni{ki vestnik 48(2002)9,471 Mese~nik ISSN 0039-2480 © Journal of Mechanical Engineering 48(2002)9,471 Published monthly ISSN 0039-2480 Vsebina Contents Strojni{ki vestnik - Journal of Mechanical Engineering letnik - volume 48, (2002), {tevilka - number 9 Razprave Rek, Z., Perpar, M., Žun, I.: Analiza prenosa toplote v postopku sintranja feritov 472 Horvat, A., Catton, I.: Analiza vezanega prenosa toplote v hladilniku elektronskega čipa 482 Mrkič, M., Culafič, Z.: Nekateri vidiki terenskih preskusov Peltonovih turbin v HE “Peručica” 491 Brožek, M.: Struženje navarov z orodji podjetja Walter 501 Osebne vesti Navodila avtorjem Papers Rek, Z., Perpar, M., Žun, I.: A Heat-Transfer Analysis of the Ferrite Sintering Process Horvat, A., Catton, I.: An Analysis of Conjugate Heat Transfer in the Heat Sink of an Electronic Chip Mrkič, M., Culafič, Z.: Some Aspects of the Research Carried out on the Power Generation Units at the Peručica Hydroelectric Power Plant Brožek, M.: The Turning of Overlays Using Tools Produced by the Company Walter 516 Personal Events 517 Instructions for Authors stran 471 glTMDDC © 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 electromagnetic and rheological properties. To understand better the heat transfer during the sintering process a numerical 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 verified, 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(š)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 between the conventional true and the calculated values were within the range of correction, therefore, we considered the calculated values suitable. 1.2 Measuring procedure The thermocouples were inserted into the furnace 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 chamber. 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 thermocouple “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, p gostota, X 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.502-10 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'/ 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 directions ([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 particles 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 equation (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 computed 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 somewhat worse deviation also appears at the heating phase, where the maximum error is 12%. This is understandable, 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 cooling 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^sfcflMiscsD ^BsfTTWHIK | 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 ooooooooooo 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 laboratory 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^OtJJlMISCSD 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: © Strojni{ki vestnik 48(2002)9,482-490 ISSN 0039-2480 UDK 62-714:621.565:536.2 Izvirni znanstveni ~lanek (1.01) © Journal of Mechanical Engineering 48(2002)9,482-490 ISSN 0039-2480 UDC 62-714:621.565:536.2 Original scientific paper (1.01) Analiza vezanega prenosa toplote v hladilniku elektronskega ~ipa An Analysis of Conjugate Heat Transfer in the Heat Sink of an Electronic Chip Andrej Horvat - Ivan Catton Prispevek opisuje razvoj algoritma za izračun vezanega prenosa toplote z namenom izbire najugodnejše geometrijske oblike za hladilnik elektronskega čipa. Struktura hladilnika je bila modelirana kot homogena porozna snov z uporabo teorije prostorninskega povprečenja (TPP - VAT). Geometrijska oblika simulacijskega območja in robni pogoji so bili povzeti po eksperimentalni napravi v laboratoriju za prenos toplote “Morrin-Martinelli-Gier” na Univerzi Kalifornije v Los Angelesu. Primeri numeričnih simulacij so bili izvedeni za izotermno testno sekcijo kakor tudi za toplotno prevodno testno sekcijo iz aluminija. Primerjava koeficienta upora celotne proge Cd kot funkcije Reynoldsovega števila Reh razkriva dobro ujemanje z objavljenimi rezultati, medtem ko primerjava porazdelitev Nusseltovega števila Nu kaže večje razlike. Končna toplotna prevodnost trdnine zmanjša koeficient prestopa toplote in Nusseltovo število Nu. Vpliv toplotne prevodnosti na rezultate se zvečuje s povečevanjem Reynoldsovega števila. © 2002 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: prenosniki toplote, hladilniki čipov, prenos toplote, razvoj algoritmov) This paper describes the construction of an algorithm for conjugate heat-transfer calculations in order to find the most suitable form for the heat sink of an electronic chip. Applying volume averaging theory (VAT) to a system of transport equations, a heat-sink structure was modeled as a homogeneous porous medium. The geometry of the simulation domain and the boundary conditions followed the experimental setup used in the Morrin-Martinelli-Gier Memorial Heat Transfer Laboratory at the University of California, Los Angeles. The example numerical simulations were performed for the test section with an isothermal structure as well as for the heat-conducting aluminum pin-fins. A comparison of the whole-section drag coefficient Cd as a function of Reynolds number Reh reveals good agreement with existing data, whereas the comparison of the Nusselt number Nu distributions shows larger discrepancies. The finite conductivity of the solid decreases the heat-transfer coefficient and Nusselt number Nu. The influence of conductivity becomes larger with increasing Reynolds number. © 2002 Journal of Mechanical Engineering. All rights reserved. (Keywords: heat exchangers, heat sinks, heat transfer, algorithms) 0 UVOD Prenosniki toplote so ena od osnovnih komponent ne samo v termoenergetski in procesni industriji ampak tudi v proizvodnji elektronske opreme. Navkljub pomembni vlogi, je v konstrukcijski postopek prenosnikov toplote še vedno vpleteno mnogo izkustvenih spoznanj. V preteklosti sta se namreč razvoj in uporaba prenosnikov toplote razvijala ločeno na številnih, največkrat nepovezanih področjih, zlasti v avtomobilski in letalski industriji, v kriogeni in hladilniški tehniki. Pri tem so se tehnologije, dobro znane v enem področju, le počasi širile na druga področja [1]. Zaradi tega lahko skupen način izbire in optimizacije konstrukcije prenosnikov toplote pomembno zmanjša stroške v industriji. 0 INTRODUCTION Heat exchangers are one of the basic installations, not only in power and process industries, but also in the production of electronic equipment. Despite their crucial role, there is still a great deal of empiricism involved in the design procedure of heat exchangers. The development and application of heat exchangers and their surfaces has taken place in a piecemeal fashion in a number of rather unrelated areas, principally those of the automotive, aerospace, cryogenic and refrigeration sectors. A lot of detailed technology, familiar in one sector, progressed only slowly over the boundary into another sector [1]. Therefore, a unifying approach to select and to optimize a heat-exchanger design can bring significant cost reduction to industry. VH^tTPsDDIK stran 482 Horvat A. - Catton I.: Analiza vezanega prenosa toplote - An Analysis of Conjugate Heat Transfer Prispevek je del širših prizadevanj za razvoj znanstvenega prostopa k problemu optimizacije geometrijske oblike prenosnikov toplote. Opisuje gradnjo algoritma za hiter izračun vezanega prenosa toplote z namenom izbire najugodnejše geometrijske oblike za hladilnik elektronskega čipa. Struktura hladilnika je bila modelirana kot homogen porozen medij z uporabo teorije prostorninskega povprečenja (TPP) ([2] do [4]) sistema prenosnih enačb. Medsebojni vpliv tekočine in strukture je bil opisan s koeficienti lokalnega upora Cd in prestopa toplote h, ki so bili prevzeti iz razpoložljive literature ([7] do [9]) in vstavljeni v računalniški program. Izračunani koeficient upora celotne proge Cd, toplotna učinkovitost Q/W in Nusseltovo število Nu so bili primerjani z razpoložljivimi eksperimentalnimi podatki [5]. Primerjava kaže dobro ujemanje s preskusi kljub poenostavitvam predstavljenega modela. 1 MODELNI PRISTOP Zračni tok skozi hladilnik čipa lahko opišemo z osnovnimi enačbami prenosa snovi, gibalne količine in energije [6]. Zaradi zahtev po kratkem računskem času modela, je treba prenosnim enačbam izračunati povprečje po periodični nadzorni prostornini (za podrobnosti glej [4]). To prostorninsko računanje povprečja vodi do problema sklenitve sistema enačb, pri katerem je treba prenos gibalne količine in toplote med tekočino in trdnino opisati z empiričnimi razmerji, npr. s koeficientoma lokalnega upora Cd in prestopa toplote h. Da bi še nadalje poenostavili simuliran sistem, smo predpostavili tok tekočine le v vzdolžni smeri z nespremenljivim znižanjem tlaka (sl. 1). Zaradi tega se profil hitrosti spreminja le prečno na smer toka. To pomeni, da je tlačna sila čez celotno simulacijsko območje v ravnovesju s strižnimi silami. Tako je mogoče enačbo prenosa gibalne količine zapisati v diferencialni obliki kot: 2 m ff d uf d u dy2 dz2 kjer so: af delež tekočine, Cd koeficient lokalnega upora, S specifična površina porozne snovi, Dp padec tlaka čez simulacijsko območje in L dolžina simulacijskega območja. Temperaturno polje v tekočini se oblikuje pod vplivom ravnovesja med toplotno konvekcijo v smeri toka, toplotno difuzijo in toploto, ki se prenese s trdnine na tekočino. Iz tega izhaja diferencialna oblika energijske enačbe za tekočino: dT afrfcfuf ox aflf d2T kjer sta: Tf temperatura tekočine in T temperatura trdnine. Prenos toplote med trdnino in tekočino je This paper is part of a broader effort to develop a scientific procedure for optimization of heat-exchanger geometries. It describes the construction of an algorithm for fast calculations of conjugate heat transfer in order to find the most suitable form for an electronic chip heat sink. Applying volume averaging theory (VAT) ([2] to [4]) to a system of transport equations, a heat-sink structure was modeled as a homogeneous porous media. The interaction between the fluid and the heat-sink structure was described with local drag and heat-transfer coefficients, which were taken from the available literature ([7] to [9]) and inserted into a computer code. The calculated whole-section drag coefficient Cd , thermal effectiveness Q/W and Nusselt number Nu were compared with available experimental data [5]. The comparison shows a good agreement with the experimental data despite model simplifications. 1 MODEL APPROACH The airflow through a chip-cooler structure can be described with basic mass, momentum and heat-transport equations [6]. Due to the requirement for the model to have short computing times, the transport equations have to be averaged over a periodic control volume (see [4] for details). This volumetric averaging leads to a closure problem, where an interface exchange of momentum and heat between a fluid and a solid has to be described with additional empirical relations, e.g. a local drag coefficient Cd and a local heat-transfer coefficient h. To further simplify the simulated system, fluid flow was taken as unidirectional with a constant pressure drop in the streamwise direction (Fig. 1). As a consequence, velocity only changes transverse to the flow direction. This means that the pressure force across the entire simulation domain is balanced with shear forces. Thus, the momentum equation can be written in differential form as: Cdrfu2fS Dp (1), L is the fluid fraction, Cd the local drag where a coefficient, S the specific surface of porous media, Dp the pressure drop across the simulation domain and L the simulation domain’s length. The temperature field in the fluid is formed as a balance between thermal convection in the streamwise direction, thermal diffusion, and the heat that is transferred from the solid to the fluid. Thus, the differential form of the energy equation for the fluid is: d2Tf d2Tf dx2 dy2 dz2 h (Tf -Ts) S (2), where Tf and Ts are the fluid and solid temperatures, respectively. The heat transfer between the solid and the | IgfinHŽšlbJlIMlIgiCšD I stran 483 glTMDDC Horvat A. - Catton I.: Analiza vezanega prenosa toplote - An Analysis of Conjugate Heat Transfer modeliran kot linearna odvisnost temperatur obeh faz, kjer je h koeficient lokalnega prestopa toplote. V vsaki nadzorni prostornini je struktura hladilnika le šibko povezana v vodoravni smeri (sl. 1). Zaradi tega je le toplotna difuzija v navpični smeri v ravnovesju s toploto, ki odteka skozi stično površino kapljevine in trdnine, medtem ko lahko toplotno difuzijo v vodoravni smeri zanemarimo. To poenostavi energijsko enačbo trdnine: fluid is modeled as a linear relation between both phase temperatures, where h is a local heat-transfer coefficient. The chip-cooler structure in each control volume is only loosely connected in the horizontal directions (see Fig. 1). As a consequence, only the thermal diffusion in a vertical direction is in balance with the heat leaving the structure through the fluid-solid interface, whereas the thermal diffusion in horizontal directions can be neglected. This simplifies the energy equation for the solid to: 0 = asls 2zT2s + h Tf-Ts S (3), kjer je a delež trdnine. Enačbe (1) do (3), ki so zapisane s povprečenimi veličinami, so enačbe ravnovesnega prenosa gibalne količine in toplote skozi homogeno porozno snov. Zanesljive podatke za dva dodatna parametra, to sta koeficienta lokalnega upora Cd in prestopa toplote h, smo poiskali v [7] do [9]. 2 SIMULACIJSKO OBMOČJE Geometrijska oblika simulacijskega območja kakor tudi robni pogoji enačb (1) do (3) sledijo geometrijski obliki eksperimentalne testne sekcije, ki je bila uporabljena v laboratoriju za prenos toplote “Morrin-Martinelli-Gier” na Univerzi Kalifornije v Los Angelesu za pridobitev eksperimentalnih podatkov, opisanih v [5]. where as is the solid fraction. Equations (1) to (3), written with the phase averaged variables, are equations for the steady-state transport of momentum and heat through homogeneous porous media. The reliable empirical data for two additional parameters, a local drag coefficient Cd and heat-transfer coefficient h, were found in [7] to [9]. 2 SIMULATION DOMAIN The geometry of the simulation domain as well as the boundary conditions for Eqs. (1-3) follow the geometry of the experimental test section used in the Morrin-Martinelli-Gier Memorial Heat Transfer Laboratory at the University of California, Los Angeles, where the experimental data described in [5] were taken. m " II \ J _f \ d=0.125" v / ; Sl. 1. Eksperimentalna testna proga Fig. 1. Experimental test section VH^tTPsDDIK stran 484 z y x Horvat A. - Catton I.: Analiza vezanega prenosa toplote - An Analysis of Conjugate Heat Transfer Splošna razporeditev palčnih reber hladilnika je podana na sliki 1. Premer palčnih reber je znašal d = 0,003175 m (0,125"). Razmerje medpalčnega razmika in premera v smeri toka je bilo px /d = 1,06 in v smeri prečno na tok py /d = 2,12. Simulacijsko območje je zajemalo 34 vrst palčnih reber v smeri toka in 17 vrst prečno na smer toka. Dolžina hladilnika L kakor tudi širina W sta znašali 0,1145 m , medtem ko je višina H znašala 0,0381 m. Robni pogoji trdne stene brez zdrsa so bili uporabljeni za enačbo prenosa gibalne količine (1) na vseh štirih stenah, ki so vzporedne s smerjo toka: The general arrangement of the heat-sink pin-fins is given in Fig. 1. The diameter of the pin-fins was d = 0.003175 m (0.125"). The pitch-to-diameter ratio in the streamwise direction was set to px /d = 1.06, and in the transverse direction to py /d = 2.12. The simulation domain consisted of 34 rows of pin-fins in the streamwise direction and 17 rows of pin-fins in the transverse direction. The length L as well as the width W of the heat sink were 0.1145 m, whereas the height H was 0.0381 m. The no-slip boundary conditions for the momentum equation (1) were implemented for all four walls, which are parallel to the flow direction: uf(0,z)=0, uf(W ,z)=0, uf( y ,0)=0 , uf( y,H )=0 (4). Kot gonilna sila toka je bil podan tlačni padec vzdolž celotnega simulacijskega območja. Absolutne vrednosti so zbrane v preglednici 1. Pri enačbi prenosa energije v tekočini (2) smo predpostavili izotermni vtok tekočine kot tudi izotermno spodnjo steno: As a flow driving force, the whole-section pressure drop Dp was prescribed. The absolute values are summarized in Table 1. For the fluid energy equation (2), the simulation domain inflow and the bottom wall were taken as isothermal: Tf (0,y,z)=Tin , Tf (x,y,0)=Tg (5), medtem ko so bile druge stene adiabatne: 8Tf dTf ( ) -(L,y,z)=0, -x,0,z =0, ox oy Pri enačbi prenosa energije v trdnini (3) je bila spodnja stena privzeta kot izotermna, medtem ko je bila zgornja stena adiabatna: whereas the other walls were considered as adiabatic: (6). 8Tf 8Tf (x,W,z) = 0 J(x,y,H) = 0 cy oz For the solid energy equation (3), the bottom wall was prescribed as isothermal, whereas the top wall was assumed to be adiabatic: dT Ts(x,y,0)=Tg , Ts(x,y,H )=0 dz (7). Predpostavka o izotermnosti spodnje stene (5) in (7) se pomembno razlikuje od eksperimentalne postavitve [5], pri kateri so palčna rebra spojena s toplotno prevodno bazno ploščo. Kljub vsemu bodo rezultati pokazali, da sedanji model daje zadovoljiv približek izmerjenih vrednosti. Absolutne temperature robnih pogojev za različne simulirne primere so zbrane v preglednici 1. 3 NUMERIČNE METODE Prenosne enačbe (1) do (3) in robni pogoji (4) do (7) so bili preoblikovani v brezdimenzijsko obliko in diskretizirani, upoštevajoč načela metode končnih Preglednica 1. Robni pogoji - izbrane vrednosti Table 1. Boundary conditions - preset values The assumption about the isothermal bottom wall (5) and (7) significantly differs from the experimental set-up [5], where the pin-fins were joined with a conductive base plate. Nevertheless, as the results will show, the presented model still gives a satisfactory approximation to the measured values. The absolute temperatures in different simulation cases are summarized in Table 1. 3 NUMERICAL METHODS The transport equations (1) do (3) and boundary conditions (4) to (7) were transformed into the dimensionless form and then discretized following Št. No. Dp Pa Tin oC Tg oC 1 5,0 23,00 54,90 2 10,0 23,00 43,43 3 20,0 23,00 37,20 4 40,0 23,00 33,00 Št. No. Dp Pa Tin oC 74,7 23,02 30,30 175,6 23,02 27,90 266,5 23,04 27,30 368,6 22,85 26,64 Tg oC | IgfinHŽšlbJlIMlIgiCšD I stran 485 glTMDDC Horvat A. - Catton I.: Analiza vezanega prenosa toplote - An Analysis of Conjugate Heat Transfer prostornin ([6] in [10]). Pri vseh izvedenih numeričnih simulacijah smo uporabili 34x17x70 končnih prostornin v smereh x, y in z. Zaradi robnih pogojev (4) do (7), sta bili hitrost uf in temperatura trdnine T zapisani kot dvodimenzionalno skalarno polje, medtem ko je bila temperatura tekočine Tf zapisana kot tridimenzionalno skalarno polje. Zaradi diskretizacijskega postopka je nastal, v primeru dvodimenzionalnih skalarnih polj, pet-diagonalni matrični sistem in, v primeru tridimenzionalnega skalarnega polja, sedem-diagonalni matrični sistem. Za učinkovito obračanje matričnega sistema enačb je bila za ta poseben primer privzeta metoda spremenjenih vezanih gradientov (MSVG - PCGM), ki je podrobneje opisana v [11]. 4 REZULTATI IN RAZPRAVA Rezultati izračunov za primer aluminijastega (Al) hladilnika so predstavljeni na slikah 2 in 3. Tlačni padec Dp = 368,6 Pa povzroči zračni tok z Reynoldsovim številom Reh = 1904, pri čemer je Reynoldsovo število definirano na podlagi hidravličnega premera dh hipotetičnega kanala porozne snovi: Reh=d vf Slika 2 prikazuje temperaturno polje v Al strukturi v Celzijevi skali, medtem ko slika 3 razkriva temperaturno polje v zračnem toku. Kakor prikazuje slika 2, ima Al struktura najvišjo temperaturo blizu izotermne spodnje stene in najnižjo je struktu temperatu segreva o Spodnji d intenzivno ima za po prehajajoč the principles of the finite-volume methods ([6] and [10]). In all the performed numerical simulations, 34x17x70 finite volumes were used in x, y and z directions, respectively. Due to the boundary conditions (4) to (7), the velocity uf as well as the solid temperature Ts were described as two-dimensional scalar fields, whereas the fluid temperature Tf was described as a three-dimensional scalar field. This resulted in a non-symmetric five-diagonal matrix system for the two-dimensional scalar fields and a seven-diagonal matrix system for the three-dimensional scalar field. In order to invert the matrix systems efficiently, the preconditioned conjugate gradient method (PCGM), as described in [11], was adopted for this specific problem. 4 RESULTS AND DISCUSSION The results of an example calculation for an aluminum (Al) heat sink are presented in Figs. 2 and 3. The imposed pressure drop Dp = 368.6 Pa causes airflow of the Reynolds number Reh = 1904, where the definition of the Reynolds number is based on a hydraulic diameter dh of a hypothetical porous media channel: (8). Fig. 2 shows the temperature field in the Al structure in degrees Celsius, whereas Fig. 3 reveals the temperature field in the airflow. In Fig. 2, the Al structure has its highest temperature close to the isothermal bottom, and the here the e inflow. ted from the right ield also al bottom thermal 1 2 3 4 5 6 7 8 910 24.6 24.8 25.0 25.2 25.4 25.6 25.8 26.0 26.2 26.4 /^ J J J I ^ J : j& - ^-^ ^^^ ^^'^ ^^ -""""^ ^^-—~~" — -"-"""^ ^-" ^--^ ^6^^ ___-1' — ^^~~—" ^——^' ^^—-^6" ^—----- ^-~~~V~~ ———" ^^9- _-----7 — ^^—^^^^ ____—--------- __——------~~~ —----—~~~~~~ __—— i-r-rrtrTT II «h-.T-1+r , , i 0.03 0.02 0.01 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 x[m] Sl. 2. Temperaturno polje v trdnini pri Reh = 1904, Tin = 22,85 oC, Tg = 26,64 oC Fig. 2. Temperature fields in the solid at Reh = 1904, Tin = 22.85 oC, Tg = 26.64 oC VBgfFMK stran 486 0 0 Horvat ansfer 1 2 3 4 5 6 7 8 9 1011 23.3 23.6 23.9 24.2 24.5 24.8 25.1 25.4 25.7 26.0 26.3 0.03 0.02 0.01 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 x[m] Sl. 3. Temperaturno polje v zraku pri Reh = 1904, Tin = 22,85 oC, Tg = 26,64 oC Fig. 3. Temperature fields in the air at Reh = 1904, Tin = 22.85 oC, Tg = 26.64 oC Poleg vzorčnega izračuna sta bili opravljeni še dve seriji izračunov pri osmih različnih tlačnih padcih. Pri izračunih uporabljeni robni pogoji so zbrani v preglednici 1. V obeh serijah smo za tok hladiva vzeli snovske lastnosti zraka. Pri prvi seriji izračunov smo za hladilnik vzeli snovske lastnosti aluminija, medtem ko je bila v drugi seriji predpostavljena izotermičnost strukture. Kakor je običajno pri tovrstnih simuliranjih, sta bila izračunana koeficient upora Cd (9) in Nusseltovo število Nu (10) za celotno sekcijo, dobljene vrednosti pa primerjane z eksperimentalnimi rezultati [5]. Besides the example calculation, two other series of calculations with eight different pressure drops were performed. The boundary conditions for these calculations are summarized in Table 1. In both series the air material properties were taken for coolant flow. For the first set of calculations the Al material properties were taken for the heat sink, whereas in the second set the heat sink was considered as isothermal. As is usually the case in such calculations, the whole-section drag coefficient Cd (9) and Nusselt number Nu (10) were calculated and compared with the experimental results [5]. C 2 Dp Nu = rfuf2L Qdh S DTAg l gf (9), (10), kjer sta: A = L- W površina gretega dna in DT = T -Tin temperaturna razlika med greto spodnjo steno in vtokom zraka. Pri definiciji Nusseltovega števila Nu je konvektivni toplotni tok definiran kot: Q = UfPfcfuf Primerjava na sliki 4 kaže koeficient upora celotne proge Cd kot funkcijo Reynoldsovega števila Reh . Slika kaže dobro ujemanje z že objavljenimi rezultati. Kljub temu pa se pri večji vrednosti Reynoldsovega števila Reh zaradi naraščajoče turbulence, ki ni bila zajeta v model, pokaže razlika v velikosti nekaj odstotkov. Primerjava porazdelitev Nusseltovega števila celotne proge Nu na sliki 5 prikazuje večje odstopanje. Zaradi razlike v toplotnih robnih pogojih kažejo izračuni za 20 odstotkov večji toplotni tok od eksperimentalnih vrednosti [5]. Nadalje je razvidno, da končna toplotna prevodnost aluminijaste strukture (na slikah 5 in 6 označeno z Al) znižuje koeficient prestopa toplote in Nusseltovo število Nu v primerjavi s strukturo z neskončno toplotno where = LW is the area of the heated bottom and DT = T -Tin is Ag the temperature difference between the heated bottom and the inflow air. In the Nusselt number Nu (10) definition, the convective heat-flow rate is defined as: (Tout -Tin ) (11). where A^=H-W. The comparison in Fig. 4 shows the whole-section drag coefficient Cd as a function of Reynolds number Reh . It reveals good agreement with already published data. Nevertheless, at a higher Reynolds number a difference of a few percent appears due to increasing turbulence, which was not taken into account in the model. The comparison of the Nusselt number Nu distributions in Fig. 5 shows larger discrepancies. Due to the difference in the thermal boundary conditions, the calculated data reveal up to 20 percent higher heat-transfer rate than the measured values [5]. Furthermore, it is evident that the finite thermal conductivity of the Al structure (in Figs. 5 and 6 marked with Al) decreases the heat-transfer coefficient and the Nusselt number Nu in comparison | IgfinHŽšlbJlIMlIgiCšD I stran 487 glTMDDC 0 0 Horvat A. - Catton I.: Analiza vezanega prenosa toplote - An Analysis of Conjugate Heat Transfer ¦a------ Simulacije ¦ Rizzi in sodelavci (2001) -S------ Simulations + Rizzi et al. (2001) 600 500 400 300 Simulacije (Al) Simulacije (Nesk) Rizzi in sodelavci (2001) Simulations (Al) Simulations (Inf) Rizzi et al. (2001) Re Sl. 4. Koeficient upora celotne sekcije kot funkcija Reynoldsovega števila Fig. 4. Whole-section drag coefficient as a function of Reynolds number prevodnostjo (na slikah 5 in 6 označeno z Nesk). Ta vpliv končne toplotne prevodnosti trdnine se z večanjem vrednosti Reynoldsovega števila še povečuje. Konstrukcija prenosnikov toplote mora upoštevati tako vrednosti toplotnega toka kakor tudi mehanskega dela, ki je potrebno za premagovanje trenja tekočine in za premikanje le-te skozi samo strukturo. V tem pogledu je glavni cilj konstrukcije povečati toplotni tok Q (11) pri najmanjši močičrpanja: Re Sl. 5. Nusseltovo število celotne sekcije kot funkcija Reynoldsovega števila Fig. 5. Whole-section Nusselt number as a function of Reynolds number with the infinite thermal conductivity case (in Figs. 5 and 6 marked with Inf). This influence of finite thermal conductivity of the solid becomes larger with increasing Reynolds number. The design of a heat sink involves consideration of the heat-transfer rate and the mechanical pumping power expended to overcome fluid friction and move the fluid through a structure. Thus, the main design goal is to maximize the heat-transfer rate Q (11) for the minimum pumping power: W = a f Dp A^ u ^ f (12). Slika 6 prikazuje toplotno učinkovitost prenosa toplote, ki je definirana kot razmerje med toplotnim tokom Q in mehansko močjo W. Razvidno je, da so eksperimentalni in numerični rezultati blizu skupaj. Pri padajoči toplotni učinkovitosti Q/W se vpliv toplotne prevodnosti poveča in povzroči 35 odstotkov razlike pri vrednosti Reynoldsovega števila Reh = 1904. 104 103 102 101 Fig. 6 shows the thermal effectiveness of the heat-transfer process, which is defined as the ratio between the heat-transfer rate Q and the mechanical power W. It is evident that the experimental and numerical results are close. With decreasing thermal effectiveness Q/W, the influence of the structure’s thermal conductivity increases and causes a 35 percent difference at the Reynolds number Reh = 1904. Simulacije (Al) Simulacije (Nesk) Rizzi in sodelavci (2001) Simulations (Al) Simulations (Inf) Rizzi etal. (2001) Re Sl. 6. Toplotna učinkovitost hladilnika v odvisnosti od Reynoldsovega števila Fig. 6. Heat-sink effectiveness as a function of Reynolds number VBgfFMK stran 488 200 20 16 14 12 1000 2000 3000 1000 2000 3000 1000 2000 3000 Horvat A. - Catton I.: Analiza vezanega prenosa toplote - An Analysis of Conjugate Heat Transfer Kakor je prikazano, se toplotna učinkovitost QW hladilnika zmanjsuje z vecanjem vrednosti Reynoldsovega števila Reh (8). Kljub temu, da manjše vrednosti Reynoldsovega števila Reh prinašajo večjo toplotno učinkovitost, pa morajo biti rezultirajoči majhni toplotni tokovi nadomeščeni z večjo površino in zaradi tega z večjimi dimenzijami samega hladilnika V nekaterih prime to ni mogoče zaradi gospodarnosti in omejitev velikosti. 5 SKLEPI Prispevek opisuje delo, ki je bilo vloženo v razvoj računsko hitrega numeričnega algoritma za izračun prenosnikov toplote. Namen naloge je bil posvečen numerični raziskavi odvoda toplote iz elektronskega čipa. Pri tem je bila notranja struktura hladilnika, v obliki paličastih reber s premaknjeno postavitvijo, obravnavana kot homogena porozna snov. Vrednosti koeficientov lokalnega upora Cd in prestopa toplote h, ki so bile potrebne za zaprtje prenosnih enačb, smo prevzeli iz [7] do [9]. Razvite parcialne diferencialne enačbe so bile diskretizirane z upoštevanjem ohranitvenih lastnosti metode nadzornih prostornin. Sistem pol-linearnih enačb je bil nato rešen z metodo spremenjenih vezanih gradientov. Za preveritev postopka izračuna smo uporabili eksperimentalne podatke laboratorija za prenos toplote “Morrin-Martinelli-Gier”. Izvedeni sta bili dve seriji izračunov za hladilnik čipa, ki je bil hlajen z zračnim tokom. Izračunane vrednosti koeficienta upora celotne proge Cd kažejo dobro ujemanje z že objavljenimi podatki, medtem ko izračunane vrednosti Nusseltovega števila Nu celotne proge razkrivajo odstopanje zaradi razlik v toplotnih robnih pogojih. Prav tako smo raziskali vpliv končne toplotne prevodnosti trdne strukture. Izkazalo se je, da končna toplotna prevodnost aluminija zmanjša toplotno učinkovitost QJW za 35 odstotkov pri Reh = 1904. Prav tako je pričakovati večji vpliv toplotne prevodnosti pri večjih vrednostih Reynoldsovega števila. Prikazani rezultati potrjujejo ustreznost izbranega načina za preračun hladilnika, kjer je treba upoštevati toplotno prevodnost trdne strukture. Vzorčni izračuni prav tako potrjujejo, da razvit numerični program daje rezultate z zadostno natančnostjo za razširitev njegove uporabe na druge bolj zahtevne geometrijske oblike. Zahvala Prvi avtor se želi zahvaliti za finančno podporo skladu Kerze-Cheyovich in Ministrstvu za šolstvo, znanost in šport Republike Slovenije. The thermal effectiveness QW of the examined heat sink is reduced with increasing Reynolds number Reh. Although the lower Reynolds numbers Reh bring higher effectiveness, the resulting low-heat-transfer rates have to be compensated with a larger heat-transfer surface and consequently with a larger heat sink. In some cases this is not possible due to economics and size limitations. 5 CONCLUSIONS The present paper describes an effort to develop a fast-running numerical algorithm for heat-exchanger calculations. The purpose of the task was to numerically investigate heat removal from an electronic chip. The heat sink’s internal structure, in the form of a staggered arrangement of pin-fins, was treated as a homogenous porous media. The local values of drag coefficient Cd and heat-transfer coefficient h, which were needed to close the transport equations, were taken from [7] to [9]. The resulting partial differential equations were discretized using conservation properties of the finite-volume method. The system of semi-linear equations was solved with the preconditioned conjugate gradient method. To test the calculation procedure, experimental data obtained in the Morrin-Martinelli-Gier Memorial Heat Transfer Laboratory were used for the comparison. Two series of calculations were performed for the heat sink cooled with airflow. The calculated values of the whole-section drag coefficient Cd show a good agreement with already published data, whereas the calculated whole-section values of the Nusselt number Nu reveal some discrepancies due to differences in the thermal boundary conditions. Also, the influence of the finite thermal conductivity of the solid structure was examined. It was shown that the finite thermal conductivity of aluminum decreases the thermal effectiveness Q/W by 35 percent at Reh = 1904. Furthermore, it is expected that at a higher Reynolds number this thermal conductivity effect would increase. The presented results demonstrate that this approach is appropriate for heat-sink calculations where the thermal conductivity of a solid structure has to be taken into account. The example calculations also verify that the developed numerical code yields sufficiently accurate results to be also applicable for other more demanding geometries. Acknowledgements The first author’s financial support by the Kerze-Cheyovich scholarship and the Ministry of Education, Science and Sport of the Republic of Slovenia is gratefully acknowledged. | lgfinHi(š)bJ][M]lfi[j;?n 02-9______ stran 489 I^BSSIfTMlGC Horvat A. - Catton I.: Analiza vezanega prenosa toplote - An Analysis of Conjugate Heat Transfer [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] 6 LITERATURA 6 REFERENCES Hesselgreaves, J.E. (2001) Compact heat exchangers selection, Design and Operation, Pergamon Press. Whitaker, S. (1967) Diffusion and dispersion in porous media, AIChE Journal, Vol. 13, No. 3, 420-427. Travkin, V.S., I. Catton (1995) A two temperature model for fluid flow and heat transfer in a porous layer, J. Fluid Engineering, Vol. 117, 181-188. Travkin, V.S., I. Catton (1999) Transport phenomena in heterogeneous media based on volume averaging theory, Advans. Heat Trasfer, Vol 34, 1-143. Rizzi, M., Canino, M., Hu, K., Jones, S., Travkin, V., Catton, I. (2001) Experimental investigation of pin fin heat sink effectiveness, Procs. of the 35th National Heat Transfer Conference, Anaheim, California. Horvat, A., I. Catton (2001) Development of an integral computer code for simulation of heat exchangers, Procs. of the Conf “Nuclear Energy in Central Europe 2001”, Portorož, Slovenia, Sept. 10-13, No. 213. Launder, B.E., T.H. Massey (1978) The numerical prediction of viscous flow and heat transfer in tube bank. Trans, ASME J. Heat Transfer, Vol. 100, 565-571. Kays, W.M., A.L. London (1998) Compact heat exchangers, 3rd Ed. Krieger Publishing Company, Malabar, Florida, 146-147. Žukauskas, A.A., R. Ulinskas (1985) Efficiency parameters for heat transfer in tube banks, J. Heat Transfer Engineering, Vol.5, No.1, 19-25. Versteeg, H.K., W. Malalasekera (1995) An introduction to computational fluid dynamics, The Finite Volume Method, Longman Scientific & Technical: England, 103-1335. Ferziger, J.H., M. Peric (1996) Computational method for fluid mechanics, Chapter 5: Solution of linear equation systems, Springer Verlag: Berlin, 85-127. Naslova avtorjev: dr. Andrej Horvat Odsek za reaktorsko tehniko Institut “Jožef Stefan” Jamova 39 1111 Ljubljana prof.dr. Ivan Catton Morrin-Martinelli-Gier Memorial Heat Transfer Laboratory Department of Mechanical and Aerospace Engineering School of Engineering and Applied Science University of California, Los Angeles 420 Westwood Plaza, Eng. IV, 90095 Los Angeles, California, USA Author’s Addresses: Dr. Andrej Horvat Reactor Engineering Division Institute “Jožef Stefan” Jamova 39 SI-1111 Ljubljana, Slovenia Prof.Dr. Ivan Catton Morrin-Martinelli-Gier Memorial Heat Transfer Laboratory Department of Mechanical and Aerospace Engineering School of Engineering and Applied Science University of California, Los Angeles 420 Westwood Plaza, Eng. IV, 90095 Los Angeles, California, USA Prejeto: Received: 6.5.2002 Sprejeto: Accepted: 22.11.2002 VH^tTPsDDIK stran 490 © Strojni{ki vestnik 48(2002)9,491-500 © Journal of Mechanical Engineering 48(2002)9,491-500 ISSN 0039-2480 ISSN 0039-2480 UDK 621.311.21:621.224.1 UDC 621.311.21:621.224.1 Strokovni ~lanek (1.04) Speciality paper (1.04) Nekateri vidiki terenskih preskusov peltonovih turbin v HE “Peru}ica” Some Aspects of the Research Carried out on the Power Generation Units at the Peru}ica Hydroelectric Power Plant Milo Mrki} - Zoran Culafi} V delu so predstavljeni osnovni delovni parametri HE “Peručica”, prikazana je analiza delovnega procesa v Peltonovi turbini in eksperimentalno-analitična metoda za določitev pretočne karakteristike sob vgrajenih v HE “Peručica” pri obratovalnih pogojih. © 2002 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: turbine Peltonove, parametri energetski, karakteristike procesov, metode eksperimentalne) This paper describes the basic power parameters of the “Peručica” HEPP Also included is an analysis of the work process in the Pelton turbine and an experimental-analytical method for determining the nozzle-flow characteristics under real working conditions. © 2002 Journal of Mechanical Engineering. All rights reserved. (Keywords: Pelton turbines, power parameters, process characteristics, experimental methods) 0 UVOD Hidroelektrarna “Peručica” ima moč 307 MW. Zgrajena je bila v treh fazah, prva faza se je začela leta 1960. Hidroelektrarna je derivacijskega tipa in ima skupaj sedem agregatov vodoravne izvedbe s Peltonovimi turbinami. Prvi avtor prispevka je delo začel kot hidroinženir v tej elektrarni leta 1964, zaposlen z reševanjem obratovalnih problemov. V dolgem času delovanja elektrarne so bila opravljena raziskovanja mnogih pojavov v dejanskih razmerah, da bi zagotovili pogonske stabilnosti. Pri neposrednem učenju pogonskega osebja so bila v raziskovanja vključene domače strokovne institucije. Avtor je pri vseh raziskovanjih sodeloval neposredno ali kot svetovalec. Glede na bogato znanje in izkušnje, pridobljene v času delovanja hidroelektrarne, je avtor v svojem delu podal vidike, pridobljene pri eksperimentalnih raziskovanjih v dejanskih razmerah in iz tega izhajajoče metode analitičnega določanja pretočnih karakteristik Peltonovih turbin, vgrajenih v obravnavani hidroelektrarni. 0 INTRODUCTION The Peručica hydroelectric power plant (HEPP) has an installation power of 307 MW. It was built in three phases, and the first phase began operating in 1960. It was built as a derivative type, and it has seven power-generation units of the horizontal type with Pelton turbines. One of the authors of this paper started work as a hydro engineer at this HEPP in 1964, when he was working on some problems concerning exploitation. During the long exploitation period of this HEPP a lot of research was conducted on many occurrences in stationary and non-stationary regimes under real conditions. In order to acquire operational staff, other qualified domestic and scientific institutions were engaged. In all this research the author participated directly or as a consultant. Having gained much experience during the exploitation period of this HEPP, from the very beginning to the present day, the author presents some aspects of the completed experimental research under real conditions, and the method of analytically determining the flowing exploitation characteristic of the Pelton turbines mounted in this HEPP. gfin^OtJJIMISCSD 02-9 stran 491 |^BSSITIMIGC Mrki} M. - Culafi} Z.: Nekateri vidiki terenskih preskusov - Some Aspects of Research 1 OSNOVNI ENERGETSKI PARAMETRI TURBIN V PRIMERU HE PERUČICA Za vsak hidroenergetski sistem so karakteristični osnovni delovni parametri bruto in čisti padec ter instalirani pretok. V že zgrajenih hidroelektrarnah obratujejo turbine pod določenimi energetskimi parametri, od katerih so nekateri lahko stalni, večina pa se jih spreminja glede na funkcijo delovnega režima. Med osnovne parametre vodnih turbin spadajo: moč (P), pretok (Q), specifična energija (Y), izkoristek (h) in število vrtljajev turbine (n). Specifični energiji vodnega toka (Y, Y) na gladini vode zgornje akumulacije V GNV (indeks g) in na gladini vode spodnje akumulacije VDNV (indeks d) sta za splošni primer hidroenergetskega sistema izraženi z enačbama: 1 BASIC POWER PARAMETERS OF THE PELTON TURBINES ON THE PERUČICA HEPP The basic characteristic working parameters of any hydroelectric power plant are the gross and the net fall and the installed flow On the hydroelectric power plants that are already built the turbines operate with certain power parameters, some of which can be permanent, whereas most of them change depending on the function of the working mode. The basic parameters of water turbines include the following: power (P), flow (Q), specific energy (Y), degree of efficiency (h) and the number of revolutions (n). The specific energies of the water flow (Yg, Yd) on the surface of the upstream reservoir V GNV (index g) and on the surface of the downstream reservoir V DNV (index d) on the Peručica hydroelectric power plant with Pelton turbine are: p c g r g g 2 2 r (1), (2). Razlika energij Y in Yd pomeni bruto specifično energijo hidroelektrarne (Ybr). The difference between the specific energies Yg and Yd represents the gross specific fall in the flow of the electrical power plant (Ybr). Sl. 1. Razporeditev hidroagregata s Peltonovo turbino, vgrajenega v HE “Peručica” Fig. 1. General arrangement of power generation unit with Pelton turbine in the Peručica HEPP VH^tTPsDDIK stran 492 Mrki} M. - Culafi} Z.: Nekateri vidiki terenskih preskusov - Some Aspects of Research V (1) in (2) so: pg in pd tlaka na nivojih (g - g) in (d - d), c in cd srednji hitrosti v prerezih, z in zd koti zgornjega in spodnjega nivoja vode hidroelektrarne, g je zemeljski pospešek. Za Peltonove (akcijske) turbine z eno šobo (agregati I do V v HE “Peručica”) je razpoložljiva specifična energija: The designations in (1) and (2) are as follows: pg and pd - absolute pressure at levels (g- g) and (d -d), cg and cd - mean velocities in the cross-sections, zg and zd - elevations of upstream and downstream water surface, g - acceleration due to gravity. For the Pelton (action) turbines with one nozzle (power generation units I–V) the available specific energy: pm c1 Y = g.H = ^ + 2 + g-(z1 + a-z2) (3), kjer so: z1 - kota vstopnega prereza turbine, a -oddaljenost kote težišča vstopnega prereza do kote vgradnje manometra, z2 - kota točke, kjer os šobe tangira osnovni krog turbinskega kolesa, p -manometrični tlak, H - neto padec. Hitrost c2 na izstopnem prerezu turbine (izhodni rob Peltonove turbine) je zanemarljiva (c << c1). V primeru, ko ima turbina dve šobi z enakim pretokom (agregati VI in VII v HE “Peručica”), se kota z2 določa kot srednja vrednost kot točk A in B (sl. 1). Vse hitrosti, podane v prejšnjih enačbah, so srednje hitrosti, ki se določajo s pretokom Q in pretočnim prerezom A, tj. po enačbi C= Q /Ai. i i Moč vodnega toka se določa z enačbo: where: z1 - the elevation of the turbine inlet cross section, a - the distance between the elevation of the centre of gravity of the inlet cross section and the elevation of the installation of the pressure gauge, z2 - the elevation of the point where the nozzle axis touches the basic circle of the turbine wheel, pm - the overpressure indicated by the pressure gauge, H - the net turbine fall. The velocity c2 at the turbine outlet cross section (outlet edge of the Pelton turbine) is low (c2 <%--------------------- N^v Xs"» nA» N. v * V- * ------*----------- -------*------- -^-------*---- NX NX 100 1000 rezalna hitrost / cutting speed vc / m/min WNMA 080404 WAK 10 WNMA 080412 WAK 10 WNMG 080412 WTA 13 Sl. 7. Odvisnost obstojnosti T od rezalne hitrosti vc (C 508, WALTER) Fig. 7. T - vc relationship (C 508, WALTER) Preglednica 7. Odvisnost obstojnosti T od rezalne hitrosti vc Table 7. T - vc relationship Izmenljiva ploščica / insert WNMA 080404 WAK 10 WNMA 080412 WAK 10 WNMG 080412 WTA 13 T - vc T = 3,5798.1012 .v-5.1525 (2) T = 6,7542.1012 .v-5.2149 (3) T = 1,1169.109 .v-3.4199 (4) Grafični rezultat izračuna optimuma je za IP WNMA 080404 WAK 10 naveden na sliki 8, za IP WNMA 080412 WAK 10 na sliki 9 in za IP WNMG 080412 WTA 13 na sliki 10; skupaj za vse tri preskušene IP pa na sliki 11. 4 RAZPRAVA Skupni rezultati optimizacije rezalnih razmer, izračunani na osnovi podatkov gospodarskih kazalnikov stružilnega obrata v pogojih Češke The result of the calculation is graphically represented in Fig. 8 for the insert WNMA 080404 WAK 10, in Fig. 9 for the insert WNMA 080412 WAK 10 and in Fig. 10 for the insert WNMG 080412 WTA 13, and a summary of all three tested inserts is in Fig. 11. 4 DISCUSSION The summary of the results of the cutting-conditions optimization calculated on the basis of the economic indexes of the turning shop for the WALTER WNMA 080404 WAK 10 N K1/n K2/n.T K 50 100 150 200 rezalna hitrost / cutting speed vc / m/min 250 Sl. 8. Grafična ponazoritev kriterija najmanjših stroškov obdelave Fig. 8. Graphical expression of minimum machining costs criterion ^vmskmsmm 02-9 stran 511 |^BSSITIMIGC Bro`ek M.: Stru`enje navarov z orodji - The Turning of Overlays WALTER WNMA 080412 WAK 10 4 3 2 1 0 ^K ^^—^^^ ¦- * + +¦ ^ * — * ** * *" N K1/n K2/n.T K 50 100 150 200 rezalna hitrost / cutting speed vc / m/min 250 Sl. 9. Grafična ponazoritev kriterija najmanjših stroškov obdelave Fig. 9. Graphical expression of minimum machining costs criterion WALTER WNMG 080412 WTA 13 4 3 *> —^^ ^___«_______ 2 1 *-" — mmm --.-'*"" » ¦¦ "" -- ^™ N K1/n K2/n.T K 50 100 150 200 rezalna hitrost / cutting speed vc / m/min 250 Sl. 10. Grafična ponazoritev kriterija najmanjših stroškov obdelave Fig. 10. Graphical expression of minimum machining costs criterion 2,8 2,6 2,4 2,2 ---------WNMA 080404 WAK 10 - - - -WNMA 080412 WAK 10 ---------WNMG 080412 WTA 13 100 120 140 160 180 200 rezalna hitrost / cutting speed vc / m/min 220 Sl. 11. Grafična ponazoritev kriterija najmanjših stroškov obdelave Fig. 11. Graphical expression of minimum machining costs criterion grin^sfcflMiscsD ^BsfTTWHIK | stran 512 Bro`ek M.: Stru`enje navarov z orodji - The Turning of Overlays republike, so navedeni na sliki 11. S slike je očitno, da ima odvisnost skupnih stroškov od rezalne hitrosti obliko črke “U”. Za stvarne razmere gospodarjenja torej vedno obstaja rezalna hitrost, pri kateri so skupni stroški za obdelavo najmanjši. Oblike krivulj za različne materiale orodij pa so različne. Iz oblike krivulje je prav tako očitno, da ima vsak odmik od optimalne rezalne hitrosti za posledico povečanje stroškov obdelave. Za obdelavo je torej najprimernejša uporaba modernih obdelovalnih strojev, ki omogočajo brezstopenjsko spremembo vrtljajev (rezalne hitrosti). Starejši stroji, ki so se do sedaj uporabljali v manjših delavnicah, te možnosti nimajo. Zato je treba v stroške za obdelavo vračunati tudi stroške zaradi neupoštevanja optimalne rezalne hitrosti. To povečanje je odvisno od oblike krivulje odvisnosti skupnih stroškov od rezalne hitrosti. Iz grafične ponazoritve rezultatov preskusov je očitno, da bo pri ravni krivulji stroškov to povečanje manjše kakor pa pri strmi krivulji stroškov. Rezultati matematične analize tega problema za preučevane materiale orodja so navedeni v preglednici 8. 5 SKLEPI V prispevku so objavljeni rezultati preskusov, ki so bili izvedeni z namenom, da bi določili uporabnost izbranih rezalnih materialov podjetja Walter za obdelavo navara, izdelanega s tehnologijo pulznega MIG/MAG varjenjažice C 508 v zaščitni atmosferi ogljikovega oksida V preskuse je bilo skupaj uvrščenih 6 tipov orodnih materialov. Po orientacijskih kratkoročnih preskusih so bili iz preskusov izločeni trije materiali. Preskusi dolgotrajne obstojnosti so bili izvedeni ob obdelavi navara z orodjem WAK 10 in WTA 13 v obliki IP tipa WNMA 080404 in WNMA 080412 oziroma WNMG 080412. Po obdelavi izmerjenih podatkov so bile izračunane enačbe odvisnosti obstojnosti T od rezalne hitrosti v . Na podlagi znanj teh odvisnosti je bila z uporabo računalniškega programa izvedena optimizacija rezalnih razmer za osnovne gospodarske kazalnike obrata in za cene, veljavne v Češki republiki. Rezultati vrednotenja izmerjenih vrednosti in optimizacije rezalnih razmer na osnovi kriterija najmanjših proizvodnih stroškov so navedeni v preglednici 9. Preglednica 8. Povečanje stroškov zaradi neupoštevanja optimalne rezalne hitrosti Table 8. Costs increase resulting from a less(more)-than-optimum cutting speed conditions of the Czech Republic are shown in Fig. 11. It is evident that the relationship between total costs and cutting speed has the shape of the letter U. For concrete economic conditions there always exists a cutting speed for which the total machining costs are at a minimum. However, the shape of the curve for different tool materials can vary. From the shape of the curve we can see, that any kind of elevation from the optimum cutting speed results in an increase in machining costs. Therefore, it is advantageous to use modern machine-tools with a stepless speed variation. Older machine-tools in use up to this time in smaller workshops do not have this possibility. Therefore, it is necessary to include the costs increase in the machining costs when the optimum cutting speed is not achieved. This increase depends on the shape of the curve of the relationship between total costs and cutting speed. The graphical representation shows that for a flat curve this increase will be less than for a steep one. The mathematical analysis of this problem for the tested inserts is shown in Tab. 8. 5 CONCLUSIONS In this paper we present test results on the usability of tool materials from the firm Walter for machining of the overlay made by pulsed carbon dioxide shielded surfacing technology using wire C 508. Six types of tool material were tested. After the short-term orientation tests three tool materials were eliminated. The long-term tests of the overlay machining were made using the tool materials WAK 10 and WTA 13 in the form of inserts of the type WNMA 080404, WNMA 080412 and WNMG 080412. After processing the data we calculated the equations of the relationship between tool-life T and cutting speed vc. On the basis of these equations, using a computer program, we calculated the optimum cutting conditions for the basic economic indexes of the workshop and the prices valid in the Czech Republic. The results of the evaluated measured values and the cutting-conditions optimization at the minimum machining costs criterion are shown in Tab. 9. IP / inserts rezalna hitrost cutting speed vcopt / m.min-1 vrtljaji revolutions nopt / min-1 vrtljaji revolutions n / min-1 povečanja stroškov costs increase DN / % WNMA 080404 WAK 10 130,00 752,4 710 + 0,5 1 000 + 19,3 WNMA 080412 WAK 10 138,10 799,2 710 + 2,1 1 000 + 11,1 WNMG 080412 WTA 13 168,75 976,6 710 + 8,5 1 000 + 0,1 gfin^OtJJIMISCSD 02-9 stran 513 |^BSSITIMIGC Bro`ek M.: Stru`enje navarov z orodji - The Turning of Overlays Preglednica 9. Rezultati preskusov Table 9. Test results IP / insert WNMA 080404 WAK 10 WNMA 080412 WAK 10 WNMG 080412 WTA 13 enačba obstojnosti T - rezalna hitrost vc T - vc equation T = 3,5798.1012 . v-5.1525 130,00 T = 6,7542.1012 . v-5.2149 138,10 T = 1,1169.109 . v-3.4199 168,75 rezalna hitrost cutting speed vcopt obstojnost orodja tool life Topt 45,9 46,6 27,0 stroški obdelave machining costs CZ NmOmm1 2,58 2,45 2,33 Pri preskusih je bila prav tako izmerjena hrapavost površine, dejansko parametra hrapavosti R in Rt. Iz vrednotenja izmerjenih vrednosti izhaja, da se s povečano obrabo (torej s povečanim časom delovanja stroja) oba parametra hrapavosti povečujeta. Hrapavost površine se je v vsem obdobju trajanja gibala v sprejemljivih mejah, le na koncu vsakega preskusa so se izmerjene vrednosti naglo povečale. Na koncu lahko poudarimo, da je uporaba preskušenih orodnih materialov podjetja Walter, v obliki IP, za obdelavo navara žice C 508 primerna in ekonomsko utemeljena. Najboljši rezultati so bili doseženi z uporabo orodja WNMG 080412 WAT 13. ZAHVALA Prispevek je nastal ob podpori Ministrstva za šolstvo, mladino in teleseno vzgojo Češke republike v okviru rešitve raziskovalnega načrta J03/98:41300016. Along with the tests we measured the surface roughness and the parameters Ra and Rt. From the measured values it follows that with increasing wear (and so with increasing working time of the tool) both roughness parameters increase. During the tests the surface roughness was within acceptable limits, only at the end of each test did the measured values increase significantly. We can conclude that the use of the tested tool materials from Walter in the form of inserts is suitable for overlay machining of an overlay made from C 508 wire. The best results were achieved with using the insert WNMG 080412 WTA 13. ACKNOWLEDGEMENTS This paper has been supported by the Ministry of Education, Youth and Sports of the Czech Republic as part of research project J03/98:413100016. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] 6 LITERATURA 6 REFERENCES Brožek, M. (1995) Vybrane problemy navafovani [Habilitačni price]. (Selected problems of surfacing. Inaugural dissertation). Praha, 148. - CUA. Technical Fakulty. Brožek, M. (1997) Obribeni navaru dritu C 508 nastroji ze slinutych karbiduruznych firem. (Machining of overlay made by welding wire C 508 using sintered carbide tools of different firms). Collection of papers of International Conference DIDMATTECH'97, Nitra, PF UK 1997, 115 - 118. Brožek, M. (2001) Optimalizace feznych podminek pri soustruženi navafenych vrstev. (Optimization of cutting conditions with turning of overlays). Proceedings 1-st. International Congress of Precision Machining. Usti nad Labem, UJEP 2001, 95 - 100. Brožek, M. (2000) Soustruženi navaru dritu C 508 nastroji firmy WIDIA. (Turning of overlays made by welding wire C 508 using WIDIA firm tools). Strojirenskd technologie, V, Nr. 2, 25 - 33. Chasuj, A., O. Morigaki (1985) Naplavka i napylenie. (Surfacing technology). Moskva, Masinostroenie, 240. Kamenarov, G., U. Pankow (1981) Uber die Beeinflussung der Eigenschaften des Grundwerkstoffs bei der Instandsetzungsschweissung verguteter Einzelteile. (Affecting of basic materials properties at repair work of heat treated parts using surfacing). Agrartechnik, 31, Nr. 3, 120 - 121. Liemert, G, F. Dribek, J. Ondra, I. Vavfik (1974) Obribeni. (Machining). Praha, SNTL 1974, 352. Madl, J., I. Kvasnička (1998) Optimalizace obribeciho procesu. (Optimization of machining process). Praha, ČVUT 1998, 168. Repair and maintenance welding handbook. ESAB AB, 120. Firm literature. VH^tTPsDDIK stran 514 Bro`ek M.: Stru`enje navarov z orodji - The Turning of Overlays Naslov avtorja: prof. dr. Milan Brožek Tehnična fakulteta Češka univerza za kmetijstvo Kamycka129 165 21 Praga 6 - Suchdol Češka republika brozek@tf.czu.cz Authors’ Address: Prof. Dr. Milan Brožek Technical Faculty Czech University of Agriculture Kamycka129 165 21 Praha 6 - Suchdol Czech Republic brozek@tf.czu.cz Prejeto: Received: 6.5.2002 Sprejeto: Accepted: 22.11.2002 © Strojni{ki vestnik 48(2002)9,516 © Journal of Mechanical Engineering 48(2002)9,516 ISSN 0039-2480 ISSN 0039-2480 Osebne vesti Personal Events Osebne vesti Personal Events Magisteriji, diplome MAGISTERIJI Na Fakulteti za strojništvo Univerze v Ljubljani je dne 29. septembra 2002 Franc Rotar z uspehom zagovarjal svoje magistrsko delo z naslovom: “Razvoj generične strukture in programskih modulov elementarnega delovnega sistema”. S tem je navedeni kandidat dosegel akademsko stopnjo magistra tehničnih znanosti. DIPLOMIRALI SO Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 24. septembra 2002: Tadej AUER, Matej PEGAN, Sergij PLEŠNAR, Danjela PRINČIČ, Rok SUŠNIK; dne 27. septembra 2002: Aljaž ARNOLD, Rado BAJT, Andrej BIČEK, Danilo EKAR, Gašper GARANTINI, Goran KEZELE, Robert KOTNIK, Martin TERLEP, Andrej THALER, Silvester TOTH -POPE; dne 30. septembra 2002: Sebastjan GREGORŠANEC, Marko OBID, Tadej POŽAR Edvard SODNIK Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 2. septembra 2002: Vladan MLADENOVIČ; dne 26. septembra 2002: Franci JERENKO, Bojan RIZMAN, Andrej STARIČ. * Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva: dne 11. septembra 2002: Dejan ARBI, Marjan GOVEKAR Jernej JANŠKOVEC, Rudolf KRPIC, Mihec KUZMAN, Matjaž RAKUN, Miran ŠUŠTERŠIČ, Bojana WEBER; dne 12. septembra 2002: Branislav AVSEC, Florjan BEVC, Branko BIŠČAK, Simon OMAN, Rok STAVANJA; dne 13. septembra 2002: Jernej FABIJAN, Janez FAJDIGA, Anton FORTUNAT, Gregor GOVEKAR MatjažKOVIČ, Dušan KRŠTINC, Matjaž LAPORNIK, Marko LEMUT, Gregor PODOBNIK, Aljoša ŠINKOVEC, Damir ŠKROBOT, Martin TRAMTE; dne 16. septembra 2002: Matjaž COTAR, Janez KLJUN, Jurij KOS, Primož KRŽIČ, Slavko MARN, Zoran TURKALJ, Matej ZRIMŠEK; dne 17. septembra 2002: Marijan CER Bojan GANTAR, Janko MIKULETIČ, Matjaž RUPNIK, Branko ŠULER. Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva: dne 12. septembra 2002: Roman DEŽELAK, Mitja DOBRAVC, Robert FAŠNIK, Jože IVANČIČ; dne 25. septembra 2002: Boštjan GREGORC, Andrej JURIČ, Matej MEJAČ, Tonček PLEČKO, Marko PONGRAC, Drago SLANIC, Jože TOPIČ; dne 26. septembra 2002: Luka BERCKO, Boštjan CILENŠEK, Aleš DOLŽAN, Miroslav LOMBAR, Damir LUKEŽIČ, Urban UVERA; dne 27. septembra 2002: Stanko KRAJNC. * Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv inženir strojništva: dne 11. septembra 2002: Uroš BIZJAK Aleš HABICHT, Matej LOZAR; dne 12. septembra 2002: Rok POPOVIČ; dne 13. septembra 2002: Bojan REPNIK; dne 16 septembra 2002: Janez TOMAŽIN; dne 17. septembra 2002: Branko ŠULER. Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv inženir strojništva: dne 12. septembra 2002: Albin GREGORC, Mirsad HODA, Matjaž KNEZ, Simon KRAJNIK; dne 25. septembra 2002: Robert BROZ, Miran DETIČEK, Robert DOLER, Jurica JAGARINEC, Albert KEKEC, Štefan KOLTAJ, Aleš PEČAK Milan PETRAK, Bojan PUSTOSLEMŠEK, Andrej REBERNAK, Marjan SABO, Jasna ŠVAGAN, Nevenko VARŠIČ, Rajko VAVDI; dne 26. septembra 2002: Oliver ANTONIČ. 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Balič (1996) Rationale Gestaltung der organisatorischen Ablaufe im Werkzeugwesen. Proceedings of International Conference on Computer Integration Manufacturing Zakopane, 14.-17. maj 1996. [3] Oertli, PC. (1977) Praktische Wirtschaftskybernetik. Carl Hanser Verlag Minchen. Author information The following information about the authors should be enclosed with the paper: names, complete postal addresses, telephone and fax numbers and E-mail addresses. Acceptance of papers and copyright The Editorial Committee of the Journal of Mechanical Engineering reserves the right to decide whether a paper is acceptable for publication, obtain professional reviews for submitted papers, and if necessary, require changes to the content, length or language. Authors must also enclose a written statement that the paper is original unpublished work, and not under consideration for publication elsewhere. On publication, copyright for the paper shall pass to the Journal of Mechanical Engineering. 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