S. Müller, H. Pries, K. Dilger inštitut za spajanje in varjenje, Braunschwkigska tehnološka univerza/ Braunschweig, Nemčija / Institute of Joining and Welding, Braunschweig University of Technology, Braunschweig, Germany Izboljšanje procesa načrtovanja hladilnih sistemov pri kokilah za tlačno litje -občuten prispevek h kakovosti in življenjski dobi Enhancing the Design Process of Cooling Systems for Die-Casting Dies - A Significant Contribution to Quality and Lifetime Izvleček Pri visokotlačnem kokilnem litju nastopajo velike ciklične temperaturne in mehanske obremenitve. Cikli segrevanja in ohlajanja povzročajo toplotne raztezke in skrčke materiala, ustvarjajo napetostna polja, kar vodi do občutne plastične deformacije. Kopičenje plastičnih deformacij pogosto pripelje do nepričakovanih poškodb površine kokil za tlačno litje. Izbira, kakovost in obdelava (npr. toplotna obdelava) orodnih jekel za vroče preoblikovanje so parametri, o katerih se razpravlja v znanstveni literaturi. Vendar je krmiljenje temperature kokil za tlačno litje dodaten pomemben parameter, da se doseže primerna življenjska doba. Prispevek osvetljuje, kako se lahko značilne lastnosti klasičnih notranjih hladilnih sistemov (npr. koeficient prestopa toplote na steno in zmanjšanje tlaka) izračunajo s CFD-simulacijo (CFD - computational fluid dynamics - računalniška dinamika fluidov, op. prevajalca) (ANSYS CFX) in preverijo eksperimentalno. Izračunane specifične vrednosti zmanjšanja tlaka in koeficienta za prenos toplote na steno so bile obdelane in uporabljene za tehnične specifikacije. S tem znanjem je proces načrtovanja hladilnega sistema natančnejši kot pri ocenjevanju, ki sloni na dobljenih praktičnih izkušnjah. Vendar smo zaradi omejitev pri delovanju klasičnih hladilnih sistemov razpravljali o alternativni metodi, kako določiti usklajene hladilne kanale: razdelitev tlačne kokile na segmente. Da bi prikazali možnosti, prednosti in omejitve te metode, smo uporabili vložek iz obstoječe tlačne kokile. Prispevek se konča s kratkim povzetkom in pregledom pristopov za nadaljnje izboljšave. Ključne besede: tlačno litje, proces načrtovanja, krmiljenje temperature, CFD-analiza, usklajeni hladilni kanali Abstract High-pressure die-casting dies are subjected to high cyclic temperatures and mechanical loads. Heating and cooling cycles cause thermal expansion and contraction of the material, generating strain fields which lead to a significant plastic deformation. An accumulation of plastic deformations often leads to unexpected failures at the surface of the die-casting die. The selection, quality and the pro-cessing (e. g. heat treatment) of hot work tool steels are parameters that are often discussed in scien-tific literature. However, the temperature control of the die-casting die is another important parameter for the achievement of reasonable lifetimes. The article illustrates, how characteristic properties of conventional internal cooling systems (e. g. the wall heat transfer coefficient and the pressure drop) can be calculated by CFD simulation (Ansys Cfx) and verified Livarski vestnik, letnik 61, št. 3/2014 135 by experimental investigations. The calculated specific values for the pressure drop and the wall heat transfer coefficient were processed and transformed into engineering specifications. Using this knowledge, the design process of the cool-ing system is more accurate than an estimated guess based on gained practical experience. However, due to restrictions in the performance of conventional cooling systems, an alternative method to estab-lish conformal cooling channels is discussed: the segmentation of the die-casting tool. In order to demonstrate the potential, advantages and restrictions of this method, an existing die-casting tool insert is used. The article finishes with a brief summary and an outlook on further improvements to the approaches. Keywords: die-casting, design process, temperature control, CFD analysis, conformal cooling channels 1 Uvod Notranji hladilni sistem v kokili za tlačno ulivanje aluminija je namenjen predvsem za ustvarjanje toplotne bilance na določeni temperaturni ravni. [MEN99] je ugotovil, da je stroškovna učinkovitost proizvodnega procesa v veliki meri odvisna od dejstva, ali je orodje za litje učinkovit toplotni menjalnik. Ta trditev se je prvotno nanašala na vbrizgovalno ulivanje polimerov. Vendar so naraščajoči stroški dela, stroški energije in zahteve po kakovosti upravičili, da se ta trditev lahko uporabi tudi za tlačno litje. V osnovi ima hladilni sistem v kokili za tlačno litje vpliv na naslednje tri glavne vidike tlačnega litja: • čas cikla pri tlačnem litju: učinkovit hladilni sistem omogoča, da se iz kokile za tlačno litje odstrani velika količina toplote. Rezultat tega je skrajšan čas strjevanja, kar predstavlja dodatno skrajšanje časa cikla; • kakovost tlačno ulitih delov: krmiljenje temperature in s tem krmiljeno strjevanje tlačno ulitega dela zmanjšuje na minimum tveganja za krčilne napake, ki se pojavijo, kadar ni na razpolago materiala za napajanje, da kompenzira krčenje, ko se kovina strjuje. Učinkovit hladilni sistem ima vlogo, da pospeši ohlajanje nestrjenih 1 Introduction The internal cooling system of an aluminum die-casting die primarily serves to establish a heat bal-ance at a defined temperature level. [MEN99] stated that the cost effectiveness of the production process strongly relates to the question of whether the casting tool is an efficient heat exchanger. This statement was related to the injection moulding process originally. However, increasing labour costs, energy costs and demanding requirements in terms of quality justify the fact that this statement can also be seen in the context of the die-casting process. Basically, the cooling system of a die-casting die has an impact on the following three major aspects of the die-casting process. • The cycle time of the die-casting process: An efficient cooling system enables the die-casting die to remove a high amount of heat. This results in a shortened solidification time which in turn implies a reduction of the cycle time. • The quality of the die-casting parts: A temperature control and thus a controlled solidifica-tion of the die-casting part enable the minimization of the risk of shrinkage defects that occur when feed metal is not available to compensate 136 Livarski vestnik, letnik 61, št. 3/2014 136 območij. Alternativno se lahko uporabi tudi za segretje lokalnih območij, da bi se zagotovil material za napajanje pri upočasnitvi strjevanja; • življenjska doba tlačno ulitega materiala: predhodne raziskave so navadno osredotočene na kakovost orodnega jekla za vroče preoblikovanje. V tem oziru sta metalurška sestava in obdelava (tj. tehnologije obdelave staljene kovine, toplotna obdelava, razvoj površinskih prevlek) orodja za vroče preoblikovanje glavna kriterija. Cilj je ustvariti visokokakovostne materiale, da bi se povečala življenjska doba tlačno ulitega materiala. Zato je velika ciklična obremenitev zaradi toplotnih šokov neizogibno dejstvo. Glavna prednost učinkovitega hladilnega sistema je doseči zmanjšanje temperaturne razlike (in s tem zmanjšanje nateznih napetosti, ki jih povzroča toplota) med kokilo za tlačno litje in mazivom kokile na vodni osnovi na minimum. Vsota vseh teh vidikov kaže, da se hladilni sistem lahko obravnava kot bistveni parameter pri zagotavljanju gospodarnosti tlačnega litja. Kljub temu obstaja več težav, ki jih je treba razčistiti. Dimenzioniranje hladilnega sistema često sloni na pridobljenih izkušnjah konstruktorja kokile in tu manjka sistematični postopek načrtovanja [LIN03],[LI05]. Navadno imajo kokile za tlačno litje omejeno odvajanje toplote in omejene toplotne izgube zaradi neusklajenih hladilnih kanalov z omejenimi površinami ter slabo možnostjo krmiljenja temperature kokile. Dodatno so se v zadnjem času razvile in vpeljale tehnologije, pri katerih se uporablja minimalna količina pršil [MUE 12]. Čeprav ima ta metoda pršenja zanemarljiv vpliv na toplotno bilanco kokile, obstajajo nadaljnji izzivi za razvoj notranjih hladilnih sistemov. for shrinkage as the metal solidifies. An effi-cient cooling system possesses the function of an increased cooling of non-solidified areas. As an alternative, it serves to heat local areas in order to assure the feeding of material by decelerating the solidification process. • The lifetime of the die-casting material: Preliminary research work commonly focused on the quality of the hot work tool steel. In this context, the metallurgical composition and the processing (e. g. molten metal processing technologies, heat treatment, development of surface coatings) of the hot work tool was regarded as a major criterion. The aim was to establish high-quality materials in order to strengthen the lifetime of the die-casting material. Conse-quently, the high cyclic loading due to thermal shocks was seen as an inevitable factor. The main advantage of an efficient cooling system is found in the minimization of the temperature difference (and thus in a reduction of thermally induced tensile strains) between the die-casting die and a water-based die lubricant. The sum of all aspects indicates that the cooling system can be regarded as an essential parameter for ensuring an economicdie-castingprocess.Nevertheless, there are several problematic issues that can be identified. The dimensioning of the cooling system is often based on the gained experience of the die-designer and lacks a systematic design process [LIN03], [LI05]. Usually die-casting dies exhibit a limited heat output and heat losses due to non-conformal cooling channels with limited surfaces and a poor controllability of the die temperature. In addition, the application of minimum quantity spraying technologies were developed and qualified recently [MUE12]. Since this spraying method has Livarski vestnik, letnik 61, št. 3/2014 137 Da bi spoznali preje omenjene izzive, je bil na Inštitutu za spajanje in varjenje pripravljen raziskovalni projekt. Strategija rešitve raziskovalnega projekta se je razdelila na dva pristopa: optimiranje z bolj učinkovitim dimenzioniranjem hladilnih kanalov in razdelitev kokile na segmente, da bi prišli do usklajenih hladilnih kanalov. 2 Osnove 2.1 Prenos toplote Podrobne podatke o prenosu toplote med fluidom in trdnino lahko najdemo v številnih virih [BAE 12], [VDI06]. Da bi se osredotočili na glavno težavo, bomo v tem delu obravnavali vpliv osnovnih parametrov v enodimenzijskem modelu prenosa toplote. S tem bomo prikazali, kako optimirati prenos toplote in njegove učinke. Gostoto toplotnega toka v trdnini zaradi prevajanja toplote lahko opišemo z enačbo 2-1 [BAE12]. Temu ustrezno enačba 2-2 opisuje gostoto toplotnega toka zaradi konvekcije fluida [BAE12]. Oba člena se lahko po pravilu o ohranitvi energije izenačita. Tako se lahko neznana temperatura stene (Twall) izloči, s čemer smo izpeljali enačbo 2-3. Oznake spremenljivk v enačbah 2-1 do 2-3 prikazuje slika 2-1. Enačba 2-3 je dobra osnova za razpravo o parametrih, ki imajo vpliv na toplotni tok. Tako slika 2-2 a-d ilustrira spreminjanje parametrov. Vsak diagram kaže spreminjanje ene spremenljivke; druge spremenljivke so pri tem konstantne. Vidi se, da linearno povečanje toplotne prevodnosti povzroči eksponentno povečanje toplotnega toka. Orodna jekla za vroče preoblikovanje (npr. H11 ali H13) imajo navadno majhno toplotno prevodnost, kot prikazano na sliki 2-2a. Povečanje toplotne prevodnosti na vrednost 100 W/m.K občutno poveča toplotni tok. a negli-gible impact on the heat balance of the die, further challenges exist for the development of internal cooling systems. In order to face the challenges mentioned above, a research project was conducted at the Institute of Joining and Welding. The solution strategy of the research project was split into two approaches: the optimization by a more efficient dimensioning of the cooling channels and the segmentation of the die in order to achieve conformal cooling channels. 2 Basics 2.1 Heat Transfer Detailed information about the heat transfer between fluid and solid can be found in numerous sources [BAE12], [VDI06]. In order to focus on the main problem, only the influence of the basic parameters on a one-dimensional heat transfer model shall be considered in this section. This shall serve to point out the targets for a heat transfer optimization and its effects. The heat flux density in a solid due to heat conduction can be described according to equation 2-1 [BAE12]. Accordingly, equation 2-2 describes the heat flux density due to fluid convection [BAE12]. Both terms can be equated, based on the rule of energy conservation. Thus, the unknown wall temperature (TwaN) can be eliminated and equation 2-3 is derived. The designation of the variables for the equations 2-1 to 2-3 can be obtained from Figure 2-1. Hence, equation 2-3 is a good base for a discussion of the parameters that have an influence on the heat flux. For that purpose, Figure 2-2 a-d illustrates the variation of parameters. Each graph depicts the variation of one variable; the other variables were set constant. 138 Livarski vestnik, letnik 61, št. 3/2014 138 litje / casting kokila za tlačno litje / die-casting die toplotna prevodnost / , thermal conductivity — koeficient prenosa toplote na steno / h wall heat transfer coefficient hladilna tekočina / cooling fluid ï'walj) enačba / Eg. 2-1 die surface površina kokile / die surface stena / wall celoten / total <1 - h(Twall - Tt cooling fluid ) enačba / Eg. 2-2 h ■ X q ~ À + h ■ d prostorninski tok hladilne tekočine / volume flow of cooling fluid Slika 2-1. Shematični prikaz enodimenzijskega sistema toplotnega toka Figure 2-1. Schematic description of a one-dimensional heat flux system ■A Ttr enačba / Eg.2-3 Vendar se učinek zmanjšuje z večjimi vrednostmi toplotne prevodnosti. V osnovi je toplotna prevodnost jekel za vroče preoblikovanje omejena iz metalurških vidikov. A če razdelimo kokilo za tlačno litje na segmente, je razumno uporabiti materiale z boljšo toplotno prevodnostjo. Vpliv koeficienta prenosa toplote na steno (slika 2-2b) kaže enako obnašanje kot toplotna prevodnost. Poleg tega se lahko ugotovi še dodatno pomembno dejstvo. Če pogledamo obliko krivulje, postane očitno, da mora biti glavni poudarek pri procesu načrtovanja na povprečnih vrednostih toplotnega prenosa. Nadaljnja optimiranja, kar se tiče prenosa toplote, bodo tudi povečala toplotni tok, vendar se bo njegov učinek občutno zmanjšal. Poleg tega se velike vrednosti koeficienta prenosa toplote na steno lahko dosežejo samo z velikimi hitrostmi toka. Vpliv temperaturne razlike se lahko ugotovi iz slike 2-2c. Kot se vidi, povzroča naraščajoče spreminjanje temperature ustrezno konstantno spreminjanja toplotnega toka. Zato je ustrezneje, da uporabljamo nizke temperature hladilnega sredstva. Poleg tega višja temperatura tudi povzroča večja napetostna nihanaj na površini. Glede na želeno daljšo življenjsko dobo materiala za It becomes obvious that the effect of a linear increasing thermal conductivity results in an exponential increase of the heat flux. Hot work tool steels (e. g. H11 or H13) usually only possess a poor thermal conductivity as illustrated in Figure 2-2a. An increase of the thermal conductivity to a value of 100 W/m K would enhance the heat flux significantly. However, the impact decreases with higher values for the thermal conductivity. Basically, the thermal conductivity of hot work tool steels is restricted, due to metallurgical aspects. Nevertheless, in terms of the segmentation of a die-casting die, it is reasonable to use materials with a high thermal conductivity. The influence of the wall heat transfer coefficient (Figure 2-2b) exhibits an identical behaviour, compared to the thermal conductivity. In addition, further important information can be derived here. When examining the development of the graph, it becomes obvious that the main focus for the design pro-cess should be on ensuring the common values for the heat transfer. Further optimizations regarding the heat transfer will also result in an increase of the heat flux, but the significance is substantially reduced. In addition to this Livarski vestnik, letnik 61, št. 3/2014 139 tlačno litje se je treba temu na vsak način izogniti in zato ta parameter ni uporaben za optimiranje. Zadnji parameter, ki ga prikazuje slika 2-2d, je razdalja od površine kokile. Jasno se vidi, da zmanjšanje razdalje vodi do občutno večjega toplotnega toka zaradi eksponentne odvisnosti. To jasno potrjuje učinkovitost in uporabo fact, high values for the wall heat transfer coefficient can only be obtained by very high values for the flow velocity. Information about the influence of the temperature difference can be derived from Figure 2.2c. As illustrated, increasing temperature changes lead to a corresponding constant change of the heat flux. Consequently, it is 100 1 ? konstantne vrednosti: razdalja od površine = 25 mm celotna temperaturna razlika = 50 °C koeficient prenosa toplote = 200 W/m2K constant values: distance from surface = 25 mm total temperature difference = 50 °C heat transfer coefficient = 2000 W/m2-K 0 25 50 75 100 125 150 175 200 toplotna prevodnost / thermal conductivity (W/mK) 200 160 — 120 — 80 — * "0 constant values: heat transfer coefficient = 2000 W/m?-K thermal conductivity - 25 W/m»K distance from surface = 25 mm konstantne vrednosti: r koeficient prenosa toplote = 200 W/m2K toplotna prevodnost = 25 W/mK razdalja od površine = 25 mm "T" —i—i—|—i—r 50 100 150 200 celotna temperaturna razlika / total temperature difference (°C) 100- 80 — a 60- -S 40- £ 20- B konstantne vrednosti razdalja od površine = 25 mm celotna temperaturna razlika = 50 °C toplotna prevodnost = 25 W/mK splošno območje vode common range of water constant values: distance from surface = 25 mm total temperature difference = 50 °C thermal conductivity = 25 W/m-K 100 80 60 li 20 — -§ I ' I ' I ' I 2000 4000 6000 8000 10000 koeficient prenosa toplote / heat transfer coefficient (W/m2K) constant values: heat transfer coefficient = 2000 W/m2-K thermal conductivity = 25 W/nvK total temperature difference = 50 °C konstantne vrednosti: koeficient prenosa toplote = 200 W/m2K toplotna prevodnost = 25 W/mK" celotna temperaturna razlika = 50 °C T t~ T t~ 0 10 20 30 40 50 60 70 80 razdalja od površine / distance from surface (mm) Slika 2-2. Spreminjanje parametrov glede na enačbo 2-3 Figure 2-2: Variation of parameters according to equation 2-3 140 Livarski vestnik, letnik 61, št. 3/2014 140 usklajenih hladilnih kanalov. Optimizacija tega parametra je omejena le z življenjsko dobo kokile, omejitvami pri konstruiranju (npr. pomanjkanje prostora) in posebnimi težavami, povezanimi z izdelavo. Upoštevati je potrebno, da površina za menjavo toplote v tem primeru ni ovrednotena, ker delamo samo z enodimenzijskim modelom. Pri dvo- ali tridimenzijskih modelih je vpliv odvisen od velikosti in geometrije površin. Podatke o tem vplivu lahko najdemo v virih [BAE12], [VDI06]. Navadno povzroča večanje površin za menjavo toplote občutno večje toplotne tokove. 2.2 Zmanjšanje tlaka Poglavje 2-1 je odkrilo, da je zelo pomembno ustvariti ustrezno hitrost toka v hladilnih kanalih, da bi se zagotovil dovolj velik koeficient prenosa toplote na steno. Vendar je tok skozi hladilne kanale povezan z zmanjšanjem tlaka. To zmanjšanje tlaka je posledica trenja ob stenah in trenjskih sil v hladilnem sredstvu [SIG12]. Slika 2-3 ilustrira to težavo za preprost sistem hladilnih kanalov v vložku kokile za tlačno litje. Enačbi 2-4 in 2-5 slonita na Bernouillijevi enačbi, z njima pa se zmanjšanje tlaka opisuje analitično [SIG12]. Da bi se dobilo preprosto rešitev, smo uporabili več predpostavk. Kot se lahko izpelje iz enačbe 2-6, se celotno zmanjšanje tlaka lahko razdeli na tri posamezne dele [NOG10]. Enačba 2-7 opisuje, da je celotni koeficient trenja hladilnega sistema posledica treh delnih zmanjšanj tlaka [NOG10]. Celoten koeficient trenja je tudi posledica dveh mehanizmov: člen 1 opisuje vpliv koeficienta trenja ob steni; člen 2 opisuje koeficient trenja kot posledico ovir (npr. sprememba smeri ali hladilni elementi) v območju toka. Primer je prikazan na sliki 2-3, kjer celoten koeficient trenja določa eligible to oper-ate with low temperatures of the cooling fluid. However, a higher temperature difference also leads to larger stress amplitudes at the die surface. With respect to a high lifetime of the die-casting material, this should be avoided by all means and therefore this parameter is not applicable for the optimization. The last parameter illustrated in Figure 2-2d is the distance from the die surface. As it can be seen clearly, a decrease of the distance leads to a substantial higher heat flux due to an exponential corre-lation. This clearly substantiates the effectiveness and application of conformal cooling channels. The optimization of this parameter is limited only by restrictions due to the lifetime of the die, design re-strictions (e. g. a lack of space) and especially problems associated with production. Note that the area of the heat exchanging surface is not evaluated in this example since this is only a one-dimensional model. For two or three-dimensional models, the influence depends on the surface area and the geometry of the surfaces. Information about this influence can be found in the literature [BAE12], [VDI06]. Usually, an increase of heat exchanging surfaces also leads to a significantly higher heat flow. 2.2 Pressure Drop Chapter 2.1 revealed that it is essential to establish an adequate flow velocity in the cooling channels in order to ensure a sufficient wall heat transfer coefficient. However, a pressure drop results from the flow through the cooling channels. This pressure drop originates from the wall friction and frictional forces within the cooling fluid [SIG12]. Figure 2-3 shall serve to illustrate this issue for a simple cooling channel system in a die-casting die insert. The equations 2.4 and 2.5 are based on Bernoulli's princi-ple and are used to Livarski vestnik, letnik 61, št. 3/2014 141 izstop / outlet f f vstop / inlet Pin , -it Pout , Uout Zrn ■ 0 + — + -T- = Zout ■ a + —— + -, Pin <- Pout ù enačba / Eg. 2-4 uin ~ llout ~ u Pin = Pout= P Zm.=W = 0 yield Pin - Pouf = Ap = li,,12 * P Yield - izkoristek Cooling lines - hladilni kanali Redirections - spremembe smeri Cooling element - hladilni elementi ? ? , , u u ^L, 12 V ^cooling lines t ^redirections ^ ^cooling elements J t enačba / Eg. 2-5 enačba / Eg. 2-6 Slika 2-3. Shematičen prikaz toka fluida in različnih odporov toku Figure 2-3. Schematic description of a one-dimensional heat flux system specifična površina hladilnega sistema, premer izvrtine, podatek o hrapavosti površine in specifični koeficient trenja za en hladilni element ter šest sprememb smeri. 'l 2 = A — + V t Aind St 1 dt ALr enačba / Eg. 2-7 k=1 re> člen 1 / term 1 člen 2 / term 2 kjer je Ai koeficient trenja ob steni Î skupna dolžina hladilnega kanala di premer izvrtine A f ref primerjalni prerez za izračun koeficienta trenja Ad ind posamezni primerjalni prerez hladilnega elementa Narejene so bile obsežne raziskave, da bi se lahko opisal koeficient trenja ob steni, podatki pa se lahko najdejo v literaturi [LAU09], [SIG12]. Enako velja za spremembe smeri toka v kokili za tlačno litje [NOG10], [MEN99], [VDI06], čeprav preiskane geometrije često komaj ustrezajo geometriji v kokili za tlačno litje (geometrija, ki je posledica križanja dveh izvrtin). Glavni poudarek bo dan hladilnim elementom, ker ti elementi navadno povzročajo največje zmanjšanje tlaka in zato zahtevajo natančno ovrednotenje. Vrednost koeficienta trenja describe the pressure drop analytically [SIG12]. In order to retrieve a straightforward solution, several assumptions were made. As it can be derived from equation 2.6, the pressure drop is divided into three individual losses [NOG10]. Equation 2-7 describes the total friction factor of the cooling system that originates from the three losses [NOG10]. The total friction factor results from two different mechanisms: Term 1 describes the influence of the wall friction factor; Term 2 describes a friction factor that originates from obstacles (e. g. redirections or cooling elements) in the flow passage region. For the example given in Figure 2-3, the total friction factor is determined by a specific length of the cooling system, the diame-ter of the bore, information about the surface roughness and by a specific friction factor for one cooling element and six redirections. Ai wall friction factor i d accumulated length of the cooling channel bore diameter A f ref reference cross section of the calculated friction factor Aind ind individual reference cross section of the cooling element Extensive research has been conducted in order to describe the wall friction so 142 Livarski vestnik, letnik 61, št. 3/2014 142 za hladilni element mora biti odvisna od hitrosti toka. Ker hitrost toka v hladilnem elementu ni konstantna zaradi različnim prerezov, prerez primerjalnega premera nudi enak odpor kot celoten sistem odporov (v našem primeru Aind). Enačba 2-8, ki sledi, opisuje izračun koeficienta trenja in izkoristke iz preje omenjenih enačb 2-5 in 2-6. Ta enačba se uporablja, da pretvori rezultate izračuna zmanjšanja tlaka, ki smo jih dobili s preskusi in numeričnimi izračuni, v koeficient trenja. Ker hitrost toka znotraj hladilnega elementa ni konstantna, se uporabi primerjalna hitrost (ki se dobi na osnovi primerjalnega prereza). Ustrezna vrednost tega prereza bi bil prerez ostalih hladilnih kanalov, ki so izdelani z orodjem za globoko vrtanje izvrtin. enačba / Eg. 2-8 kjer je Ap P u tlačna razlika med vstopom in izstopom gostota fluida za hlajenje/prenos toplote hitrost fluida za hlajenje/prenos toplote 3 CFD-izračun parametrov hladilnega sistema Da bi dobili ustrezno zanesljive parametre, je bilo treba upoštevati naslednje pomembne vidike [ANS10b]: • podrobno modeliranje geometrije hladilnega kanala, • skrbna izbira modela fluida (npr. turbulenčnega modela), • združitev primernih lastnosti materiala in • izbira ustreznih robnih pogojev. Za analizo je bila uporabljena računalniška oprema ANSYS CFX. Prvi that further information can be found in the literature [LAU09], [SIG12]. The same applies to the redirections in the die-casting die [NOGIO] [MEN99] [VDI06], although the examined geometries often hardly correspond to the ge-ometry that exists in the die-casting die (a geometry that results from the crossing of two bores). The main emphasis shall be put on the cooling elements since the elements usually induce the highest pressure drop and hence require a precise evaluation. The value of the friction factor for the cooling element must be referred to a flow velocity. Since the flow velocity within the cooling element is not constant due to different profiles, the cross section of a reference diameter is integrated (here: Aind). The equation 2.8 stated below describes the calculation of the friction factor and yields from the equa-tions 2.5 and 2.6, mentioned above. This equation is used to transform the pressure drop results, de-rived from experimental and numerical investigations, to a friction factor. Since the flow velocity inside of the cooling element is not constant, a reference velocity (which results from a reference cross sec-tion) has to be used here. A reasonable value for this cross section would be the cross section of the remaining cooling channels that are manufactured by deep hole drilling tools. Ap P u pressure difference between inlet and outlet density of the cooling/ heat transfer fluid velocity of the cooling/ heat transfer fluid 3 CFD-BASED EVALUTION OF COOLING SYSTEM PARAMETERS In order to retrieve reliable results, the following major aspects necessarily should be considered [ANS10b]: ■ the detailed modeling of the cooling Livarski vestnik, letnik 61, št. 3/2014 143 korak je modeliranje geometrije hladilnega kanala. Ker to zahteva izračun prenosa toplote na steno, sta bili modelirani dve območji: območje fluida (geometrija hladilnega kanala) in območje trdnine (kokila za tlačno litje). Materialne lastnosti materiala, odvisne od temperature, se lahko dobe za večino hladilnih tekočin in so bile integrirane v simulacijo. Ker se hladilne tekočine navadno uporabljajo v sorazmerno ozkem temperaturnem območju, so se za določene simulacije uporabile konstantne materialne vrednosti. Večina preiskanih tokov je turbulentnih [SIG12], [NOGIO]. Raje pa imamo za naš namen stacionarne simulacije, ker so krajše, naknadna obdelava je preprostejša, navadno pa nas zanimajo povprečne časovne vrednosti [EGG11]. Zato smo uporabili Reynolds-povprečni Navier-Stokesov model (RANS - Reynolds-Averaged Navier-Stokes (op.prevajalca)) in strižno-napetostni model prenosa (SST) kot turbulenčni model. Ta model združuje prednosti k-e modela in k-w modela ter se lahko obravnava kot industrijski standard za modeliranje turbulence, ker so ga številne aplikacije verificirale, njegovo delovanje je robustno za večino mrežnih topologij, ima dobro interoperabilnost z drugimi fizikalnimi modeli in prefinjeno obravnava steno [EGG11]. Pri vseh izračunih smo uporabili robne pogoje brez zdrsa. Hitrost fluida je ob steni nič, kar je dober približek realnemu toku fluida. Da bi bil izračun koeficienta prenosa toplote na steno zaupanja vreden, je bilo treba skrbno paziti na modeliranje mejnih plasti. Zato je bilo treba zagotoviti, da so bili hitrostni profil fluida in pojavi prenosa energije v območju sten pravilno modelirani [ANS10a], [ANS10b]. Slika 3-1 prikazuje tipični rezultat za zmanjšanje tlaka pri kaskadnem spoju vodnih kanalov s premerom izvrtine 5 mm. Kot robni pogoj je bilo postavljeno, da je channel geometry, • the careful selection of the fluid model (e. g. the turbulence model), • the integration of suitable material properties and • the selection of reasonable boundary conditions. The analyses were carried out by the software ANSYS CFX. The first step is the modeling of the cooling channel geometry. Since it is required for the calculation of the wall heat transfer, two domains are modeled: the fluid domain (the cooling channel geometry) and the solid domain (the die-casting die). Temperature dependent material properties of the major cooling fluids are accessible and were inte-grated into the simulation. Since the cooling fluid is usually operated at a rather narrow temperature range, constant material properties were used for a specific simulation setup. The majority of examined flows are turbulent [SIG12], [NOGIO]. Steady state simulations are preferred for this application because they exhibit a shorter simulation time, post-processing is simplified and usually only time-averaged values are of interest [EGG11]. Hence, a Reynolds-Averaged Navier-Stokes model (RANS) is applied. Accordingly, the Shear-Stress-Transport model (SST) was selected as a turbulence model. This model combines the advantages of the k-e mo an th k -w mo an can be regarded as an industrial standard for turbulence modeling since it has been validated for a broad range of applications, shows a robust performance on most of the mesh topologies, has a good interoperability with other physical models and exhibits a sophisticated treatment of the wall [EGG11]. For all of the conducted calculations, a no-slip boundary condition was applied. The fluid will have zero velocity relative to the boundary which is a good 144 Livarski vestnik, letnik 61, št. 3/2014 144 tlak / pressure ■ 150000 B 135000 ■ 120000 105000 90000 75000 «0000 J5ÎO0 30000 15000 0 [Pa] IZSTOP / ^ OUTLET VSTOP/ H INLET Slika 3-1. Zmanjšanje tlaka zaradi toka fluida pri kaskadnem spoju vodnih kanalov (hladilna tekočina: voda, povprečna temperatura: 50 oC, premer izvrtine: 5 mm, hitrost toka na vstopu: 2,5 l/min) Figure 3-1. Pressure drop due to a fluid flow in a cascade water junction (cooling fluid: water, averaged temperature: 50 °C, bore diameter: 5 mm, flow velocity at the inlet: 2,5 l/min koeficient prestopa toplote na steno / wall heat transfer coefficient h 3.500»» 003 ® 3.1sow