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Modelling of Heat Treatment of Steel Elements with the Movement of Coolant
A mathematical and numerical model of hardening process using the generalized finite difference method for the movement of fluid and heat transport have been proposed in this paper. To solve the Navier-Stokes equation the characteristic based split scheme (CBS) has been used. The solution of the hea...
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| Published in: | Archives of metallurgy and materials 2011-01, Vol.56 (2), p.345-357 |
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| cites | cdi_FETCH-LOGICAL-c354t-7225a1c8466fb9fb757719926df411e6623aca0d2d624a8abbdeb8024f4c61493 |
| container_end_page | 357 |
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| container_start_page | 345 |
| container_title | Archives of metallurgy and materials |
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| creator | Kulawik, A. Bokota, A. |
| description | A mathematical and numerical model of hardening process using the generalized finite difference method for the movement of fluid and heat transport have been proposed in this paper. To solve the Navier-Stokes equation the characteristic based split scheme (CBS) has been used. The solution of the heat transport equation with the convective term has been obtained by a stabilized meshless method. To determine of the phase transformation the macroscopic model built on the basis of CCT diagrams for continuous cooling of medium-carbon steel has been used. The temporary temperature fields, the phase transformation, thermal and structural strains for the heat treated element and the fields of temperature and velocity for the coolant have been determined. The comparative analysis of the results of calculations for the model without taking into account movement of coolant has been carried out. The effect of the notch in the shaft on the cooling rates and fields of the kinetics of the phase transformations has been presented.
W pracy zaproponowano model matematyczny i numeryczny zjawisk termicznych oraz ruchów chłodziwa zbudowany z wykorzystaniem uogólnionej metody różnic skończonych. Do rozwiązania równania Naviera-Stokesa wykorzystano metodę rzutowania (CBS). Rozwiązanie równania przewodzenia ciepła z członem konwekcyjnym uzyskano na podstawie stabilizowanej bezsiatkowej metody różnic skończonych. Do modelowania przemian fazowych wykorzystano makroskopowy model zbudowany na podstawie analizy wykresów ciągłego chłodzenia CTPc dla stali średniowęglowej. Dla elementu obrabianego cieplnie określono chwilowe pola temperatury, udziały fazowe, odkształcenia termiczne, strukturalne oraz pala temperatury i prędkości cieczy chłodzącej. Przeprowadzono analizę porównawczą z wynikami obliczeń z ruchem i bez ruchu chłodziwa. W pracy przedstawiono także wpływ wycięcia (rowka na wałku) na pola prędkości chłodziwa oraz na kinetykę przemian fazowych. |
| doi_str_mv | 10.2478/v10172-011-0037-5 |
| format | article |
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W pracy zaproponowano model matematyczny i numeryczny zjawisk termicznych oraz ruchów chłodziwa zbudowany z wykorzystaniem uogólnionej metody różnic skończonych. Do rozwiązania równania Naviera-Stokesa wykorzystano metodę rzutowania (CBS). Rozwiązanie równania przewodzenia ciepła z członem konwekcyjnym uzyskano na podstawie stabilizowanej bezsiatkowej metody różnic skończonych. Do modelowania przemian fazowych wykorzystano makroskopowy model zbudowany na podstawie analizy wykresów ciągłego chłodzenia CTPc dla stali średniowęglowej. Dla elementu obrabianego cieplnie określono chwilowe pola temperatury, udziały fazowe, odkształcenia termiczne, strukturalne oraz pala temperatury i prędkości cieczy chłodzącej. Przeprowadzono analizę porównawczą z wynikami obliczeń z ruchem i bez ruchu chłodziwa. W pracy przedstawiono także wpływ wycięcia (rowka na wałku) na pola prędkości chłodziwa oraz na kinetykę przemian fazowych.</description><identifier>ISSN: 1733-3490</identifier><identifier>EISSN: 2300-1909</identifier><identifier>DOI: 10.2478/v10172-011-0037-5</identifier><language>eng</language><publisher>Warsaw: Versita</publisher><subject>continuous cooling ; heat treatment ; liquid coolant ; meshless method</subject><ispartof>Archives of metallurgy and materials, 2011-01, Vol.56 (2), p.345-357</ispartof><rights>Copyright Versita Jun 2011</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c354t-7225a1c8466fb9fb757719926df411e6623aca0d2d624a8abbdeb8024f4c61493</citedby><cites>FETCH-LOGICAL-c354t-7225a1c8466fb9fb757719926df411e6623aca0d2d624a8abbdeb8024f4c61493</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/1321088643?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>315,786,790,25783,27957,27958,37047,44625</link.rule.ids></links><search><creatorcontrib>Kulawik, A.</creatorcontrib><creatorcontrib>Bokota, A.</creatorcontrib><title>Modelling of Heat Treatment of Steel Elements with the Movement of Coolant</title><title>Archives of metallurgy and materials</title><description>A mathematical and numerical model of hardening process using the generalized finite difference method for the movement of fluid and heat transport have been proposed in this paper. To solve the Navier-Stokes equation the characteristic based split scheme (CBS) has been used. The solution of the heat transport equation with the convective term has been obtained by a stabilized meshless method. To determine of the phase transformation the macroscopic model built on the basis of CCT diagrams for continuous cooling of medium-carbon steel has been used. The temporary temperature fields, the phase transformation, thermal and structural strains for the heat treated element and the fields of temperature and velocity for the coolant have been determined. The comparative analysis of the results of calculations for the model without taking into account movement of coolant has been carried out. The effect of the notch in the shaft on the cooling rates and fields of the kinetics of the phase transformations has been presented.
W pracy zaproponowano model matematyczny i numeryczny zjawisk termicznych oraz ruchów chłodziwa zbudowany z wykorzystaniem uogólnionej metody różnic skończonych. Do rozwiązania równania Naviera-Stokesa wykorzystano metodę rzutowania (CBS). Rozwiązanie równania przewodzenia ciepła z członem konwekcyjnym uzyskano na podstawie stabilizowanej bezsiatkowej metody różnic skończonych. Do modelowania przemian fazowych wykorzystano makroskopowy model zbudowany na podstawie analizy wykresów ciągłego chłodzenia CTPc dla stali średniowęglowej. Dla elementu obrabianego cieplnie określono chwilowe pola temperatury, udziały fazowe, odkształcenia termiczne, strukturalne oraz pala temperatury i prędkości cieczy chłodzącej. Przeprowadzono analizę porównawczą z wynikami obliczeń z ruchem i bez ruchu chłodziwa. 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To solve the Navier-Stokes equation the characteristic based split scheme (CBS) has been used. The solution of the heat transport equation with the convective term has been obtained by a stabilized meshless method. To determine of the phase transformation the macroscopic model built on the basis of CCT diagrams for continuous cooling of medium-carbon steel has been used. The temporary temperature fields, the phase transformation, thermal and structural strains for the heat treated element and the fields of temperature and velocity for the coolant have been determined. The comparative analysis of the results of calculations for the model without taking into account movement of coolant has been carried out. The effect of the notch in the shaft on the cooling rates and fields of the kinetics of the phase transformations has been presented.
W pracy zaproponowano model matematyczny i numeryczny zjawisk termicznych oraz ruchów chłodziwa zbudowany z wykorzystaniem uogólnionej metody różnic skończonych. Do rozwiązania równania Naviera-Stokesa wykorzystano metodę rzutowania (CBS). Rozwiązanie równania przewodzenia ciepła z członem konwekcyjnym uzyskano na podstawie stabilizowanej bezsiatkowej metody różnic skończonych. Do modelowania przemian fazowych wykorzystano makroskopowy model zbudowany na podstawie analizy wykresów ciągłego chłodzenia CTPc dla stali średniowęglowej. Dla elementu obrabianego cieplnie określono chwilowe pola temperatury, udziały fazowe, odkształcenia termiczne, strukturalne oraz pala temperatury i prędkości cieczy chłodzącej. Przeprowadzono analizę porównawczą z wynikami obliczeń z ruchem i bez ruchu chłodziwa. W pracy przedstawiono także wpływ wycięcia (rowka na wałku) na pola prędkości chłodziwa oraz na kinetykę przemian fazowych.</abstract><cop>Warsaw</cop><pub>Versita</pub><doi>10.2478/v10172-011-0037-5</doi><tpages>13</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | continuous cooling heat treatment liquid coolant meshless method |
| title | Modelling of Heat Treatment of Steel Elements with the Movement of Coolant |
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