計(jì)算流體動(dòng)力學(xué)和動(dòng)態(tài)耦合熱力學(xué)畢業(yè)論文中英文資料外文翻譯文獻(xiàn).doc

計(jì)算流體動(dòng)力學(xué)和動(dòng)態(tài)耦合熱力學(xué)軟件在頂吹轉(zhuǎn)爐中的應(yīng)用Mikael ERSSON, Lars HGLUND, Anders TILLIANDER,Lage JONSSON and Pr JNSSON應(yīng)用程序冶金部，皇家技術(shù)學(xué)院（KTH）SE-10044，瑞典首都斯德哥爾摩。（2007年11月8日收到，2007年12月10日接受）一種新的建模方法被提出，這種建模方法是使用計(jì)算流體力學(xué)軟件相連結(jié)熱力學(xué)數(shù)據(jù)庫(kù)以獲取動(dòng)態(tài)模擬冶金過(guò)程的現(xiàn)象。這種建模方法已被應(yīng)用在一個(gè)基本的氧氣頂吹轉(zhuǎn)爐模型。通過(guò)各種氣體之間的反應(yīng)研究。 結(jié)果表明,大量的表面氣體的流通是完全受對(duì)流控制的。此外，在這個(gè)過(guò)程中大量產(chǎn)生的CO脫碳可能會(huì)放慢從浴缸噴出的液滴的脫碳率。在目前的模擬反映實(shí)驗(yàn)室的實(shí)驗(yàn)條件下，這點(diǎn)也被證實(shí)在這個(gè)過(guò)程中所產(chǎn)生的爐渣（FeO和/或SiO2）接近于零，即只產(chǎn)生的氣體（二氧化碳CO2）就好比是氧氣射流擊中鋼液。它也說(shuō)明如何從幾秒鐘的采樣推算脫碳速度， 只要是含碳量足夠的高可以在后期的時(shí)候做含碳量的模擬，從而得到的碳含量的粗略估計(jì)?？偟慕Y(jié)論是，通過(guò)Thermo-Calc的數(shù)據(jù)庫(kù)和CFD軟件的動(dòng)態(tài)耦合來(lái)達(dá)到冶金動(dòng)態(tài)模擬是有可能的。關(guān)鍵詞：轉(zhuǎn)爐;計(jì)算流體力學(xué)，熱力學(xué)建模;爐渣和動(dòng)態(tài)模擬。介紹在許多涉及氧氣噴射撞擊到鋼液面的冶金過(guò)程中，為了優(yōu)化涉及動(dòng)力學(xué)的部分，如脫碳，底層流體動(dòng)力學(xué)是需要的?，F(xiàn)在對(duì)于這個(gè)問(wèn)題已經(jīng)幾個(gè)實(shí)驗(yàn)報(bào)告和一些數(shù)值或計(jì)算流體動(dòng)力學(xué)（CFD）的報(bào)告。Szekely and Asai已經(jīng)介紹了一種將液體的沖擊射流表面的計(jì)算模型。Ngyen and Evans通過(guò)使用這種方法計(jì)算溶池噴嘴直徑比液體表面所造成變形的沖擊射流的影響，張等人模仿了一種同時(shí)使用頂吹和底吹復(fù)合吹煉的情況。Odenthal等人展示了一種頂吹轉(zhuǎn)爐多相CFD模型，在這種頂吹轉(zhuǎn)爐中由于沖擊射流以及底部和頂部轉(zhuǎn)換混合時(shí)存在飛濺現(xiàn)象。Nakazono等人描述了鐵液表面的超音速氧氣噴射沖擊時(shí)的含碳量的兩階段的數(shù)值分析。通過(guò)計(jì)算表明在真空和表面處理?xiàng)l件下天然氣和鋼鐵之間的變化。該模型采用穩(wěn)態(tài)方法無(wú)飛濺等。在其他文獻(xiàn)中還其他非頂吹CFD模型介紹，瓊森等。提出了硫精煉?cǎi)詈嫌?jì)算流體力學(xué)和熱力學(xué)模型熱力學(xué)是成立的在CFD程序中作為一個(gè)自定義的子程序，尤其是專門(mén)為調(diào)查系統(tǒng)所寫(xiě)的子程序。圖中1可以看到這樣的做法一個(gè)示意圖。圖1。合并計(jì)算流體力學(xué)和熱力學(xué)建模與數(shù)值模型方法的示意圖。由文獻(xiàn)（14）最近包含頂吹系統(tǒng)CFD模型已經(jīng)出現(xiàn)并和實(shí)驗(yàn)數(shù)據(jù)進(jìn)行比較，這里提出，這個(gè)模型是包括氣/液/渣的流體體積（VOF）等反應(yīng)擴(kuò)展的一個(gè)多相流模型，這個(gè)模型適用于頂吹系統(tǒng)。這個(gè)模型以及各個(gè)階段的擴(kuò)展已經(jīng)獲得批準(zhǔn)使用這一方法所建的裝備使得終于有一個(gè)可以說(shuō)明基本的頂吹轉(zhuǎn)爐模型結(jié)果。2。數(shù)值模型目前的建模方法如圖2所示。圖2。合并數(shù)值模型方法的示意圖為了解決新的研究可以輕易的合并到這個(gè)模型的問(wèn)題建立了以模塊化的方式，這也意味著，當(dāng)從一個(gè)系統(tǒng)變到另一個(gè)系統(tǒng)是只需要一個(gè)很小的重編程程序，只要是熱力學(xué)數(shù)據(jù)在目前的熱力學(xué)數(shù)據(jù)庫(kù)中是存在的以及不超過(guò)CFD軟件的運(yùn)算能力。這個(gè)模擬過(guò)程已經(jīng)在包含6個(gè)節(jié)點(diǎn)的集群的Linux PC上執(zhí)行?，F(xiàn)實(shí)生活中的模擬時(shí)間是和運(yùn)算系統(tǒng)的數(shù)量相關(guān)的，所以沒(méi)有固定和典型的模擬時(shí)間;它可能會(huì)在一小時(shí)和10天的實(shí)時(shí)變化亦或是10秒的時(shí)間。在圖3中可以看出其物理域和數(shù)值域的原理。圖3。頂吹轉(zhuǎn)爐示意圖。 a）物理域b）數(shù)值域。所涉及的邊界條件為入口速度，出口壓力，無(wú)滑墻壁和對(duì)稱軸。所有的墻壁都用標(biāo)準(zhǔn)壁面函數(shù)表示，合理的ke模型已使用在所有的例子中。域的寬度為0.075米，高度是0.13米。最開(kāi)始，1500C的15.6公斤距頂槍0.01米以上的鋼熔液用來(lái)試驗(yàn)，大量的氣體從入口吹入相當(dāng)于25升/分鐘的純體積流量氧氣。用于模擬的表1中的各種參數(shù)可以看出和表2中的初始濃度的不同。表1.不同階段密度和擴(kuò)散系數(shù)表2.初始濃度2.1。差價(jià)ANSYS軟件同時(shí)也被使用，這是一個(gè)為計(jì)算求解流體體積、質(zhì)量的有限元分析軟件，這樣動(dòng)量守恒方程中所涉及的質(zhì)量、體積都得到了解決。根據(jù)湍流模型同時(shí)使用了一些額外的守恒方程作為補(bǔ)充,例如湍流動(dòng)能守恒,k,和動(dòng)蕩能量耗散,e,都是用標(biāo)準(zhǔn)的k-e 模型，下面的公式用來(lái)計(jì)算任何形式的這里r是密度,u是指速度矢量,當(dāng)基于雷諾茲平均使用湍流模型,G是擴(kuò)散系數(shù),正如從表3中看到的一樣方程(1)和表3描述了質(zhì)量、動(dòng)量、湍流動(dòng)能,動(dòng)蕩能量耗散、能量、物質(zhì)和體積分?jǐn)?shù)。表3守恒方程參數(shù)2.2熱計(jì)算為了獲得準(zhǔn)確描述了熱力學(xué)特征，軟件Thermo-Calc被使用使用。這是一個(gè)通用的軟件方案的多組分的相平衡計(jì)算。它使用一種技術(shù),它允許非常靈活的設(shè)置條件的平衡狀態(tài),從而適用過(guò)程模擬。問(wèn)題的解決方法是以下。第一,質(zhì)量和熱量含量分別計(jì)算每個(gè)階段。然后,總質(zhì)量和熱量的內(nèi)容是總結(jié)。該系統(tǒng)是氫原子核裝備中的。最后,程序?qū)⒂?jì)算各階段溫度,新的成分和含量。能與熱力學(xué)的軟件應(yīng)用程序編程接口使用TQ操作。這個(gè)接口是一個(gè)接口Thermo-Calc中可用的軟件包,使其能要推廣實(shí)施不同系統(tǒng)(例如組件和元素,該系統(tǒng)由),而無(wú)需更改代碼。2.3. 耦合和假設(shè)其目在于CFD-package和Thermo-Calc數(shù)據(jù)庫(kù)軟件兩個(gè)軟件的耦合,是創(chuàng)建一個(gè)通用的計(jì)算模型,包括化學(xué)反應(yīng)冶金系統(tǒng)。在下面的文本描述的耦合。主要的假設(shè)是局部均衡、每個(gè)時(shí)間步可以到達(dá)每個(gè)計(jì)算單元的過(guò)程中,。軟件之間的接口CFD-package和熱力學(xué)數(shù)據(jù)庫(kù)分別被編碼在C和FORTRAN。2.4多相考慮所有的散裝階段的建模為不可壓縮;有統(tǒng)一的密度,見(jiàn)表1。與一個(gè)精化的模型應(yīng)該有可能使用一個(gè)理想氣體定律假設(shè)對(duì)氣態(tài)和一些溫度對(duì)鋼密度模型的依賴。簡(jiǎn)要地說(shuō)明一些細(xì)節(jié)的功能假設(shè)一摩爾的氧和碳反應(yīng)形成的融化2摩爾的一氧化碳。在計(jì)算單元在考慮將會(huì)有一個(gè)擴(kuò)張的氣相到約兩倍于原體積。這反過(guò)來(lái)將很可能意味著氣體向外擴(kuò)張的計(jì)算單元。如果再加上CFD,擴(kuò)張將發(fā)生在以下步驟中,作為額外的氣體質(zhì)量被添加到細(xì)胞源項(xiàng)。經(jīng)過(guò)計(jì)算細(xì)胞已經(jīng)達(dá)到平衡它也將會(huì)有一個(gè)特定的溫度平衡溫度。3.結(jié)論3.1.基本頂級(jí)吹轉(zhuǎn)爐在圖5顯示氣體射流向量的情況,正如水落在鋼鐵溶液中所顯示的那樣。這是看到射流失去其軸向沖擊就好像其滴落在剛?cè)芤罕砻?。從射流中?lái)的低流量給出了一個(gè)相對(duì)較小的滲透率在鋼鐵溶液中。圖6說(shuō)明了流場(chǎng)的鋼鐵浴引起碰撞射流。目前的最高速度的射流沖擊的鋼液面和面積。流體措施阻止了滲透區(qū)向墻壁,然后進(jìn)入到鋼液中。一個(gè)大型的循環(huán),循環(huán)中形成的沖擊流(即軸和墻之間)和幾個(gè)小的循環(huán)回路。應(yīng)該指出的是,在更大的循環(huán)級(jí)速度是非常小的。這是由于低流量來(lái)自高層的射擊流。更高的流率呈現(xiàn)較大的滲透和較強(qiáng)的循環(huán)。圖5.在氣體速度矢量。矢量有固定長(zhǎng)度;他們是由色彩反映速度級(jí)(m / s)。圖6.速度向量在鋼液中的變現(xiàn)，矢量有固定長(zhǎng)度;他們速度級(jí)有色彩反映圖7展示了碳在1、2、3和5s時(shí)在鋼液里的濃度。首先氣體的射流量應(yīng)該注意,只有在相當(dāng)狹窄的范圍內(nèi)才能看到的結(jié)果。這是故意為了使少量濃度的差異在一定范圍內(nèi)可見(jiàn)。同時(shí)可以看到圖7(a),碳濃度梯度存在于一個(gè)小區(qū)域接近自由面面積以及在一個(gè)更大的地區(qū)的右邊的滲透區(qū)當(dāng)仔細(xì)觀察圖7時(shí)。7(a)-7(d),它的變化就會(huì)更明顯,規(guī)模更大的向爐壁發(fā)展混合,且隨著時(shí)間變得更大。從圖之間可以看到碳濃度在不斷地減小。從7(a)-7(d)看來(lái),鋼液實(shí)在表面混合運(yùn)動(dòng)(參見(jiàn)圖6),隨后由于循環(huán)模式出現(xiàn)在中下部出現(xiàn),而且呈現(xiàn)紊流的混合。碳濃度高的鋼的深度只有幾毫米的滲透區(qū);然而真正的大梯度出現(xiàn)在一個(gè)更薄的地區(qū)靠近自由表面。漸漸地,隨著流場(chǎng)的發(fā)展,再循環(huán)趨向爐壁。圖7a.鋼中碳的質(zhì)量分?jǐn)?shù).1 s模擬時(shí)間圖7 b.鋼中碳的質(zhì)量分?jǐn)?shù).2 s模擬時(shí)間圖7 c.鋼中碳的質(zhì)量分?jǐn)?shù).3s模擬時(shí)間圖7 d.鋼中碳的質(zhì)量分?jǐn)?shù).5s模擬時(shí)間圖8.CO的質(zhì)量分?jǐn)?shù)5s模擬時(shí)間。圖8展示了在氣相中CO氣體濃度呈現(xiàn)的規(guī)律。射流所覆蓋的鋼液的表面幾乎完全充滿氧氣所以幾乎沒(méi)有CO的存在,除了一個(gè)薄層旁邊的鋼液表面。CO氣體數(shù)量則會(huì)變得更明顯的逐漸減少距離爐壁附近。4.結(jié)論一個(gè)新的建模方法,提出了采用CFD軟件已經(jīng)耦合熱力學(xué)數(shù)據(jù)庫(kù)(Thermo-Calc)使用自定義子例程獲得動(dòng)態(tài)模擬冶金過(guò)程的現(xiàn)象。gas-steel之間的反應(yīng),gas-slag,steel-slag和gas-steel-slag一直被認(rèn)為在一個(gè)基本的模型頂吹轉(zhuǎn)爐。 最后的結(jié)論是,它可能是一個(gè)動(dòng)態(tài)的耦合Thermo-Calc數(shù)據(jù)庫(kù)和CFD軟件進(jìn)行動(dòng)態(tài)模擬的冶金過(guò)程如頂吹轉(zhuǎn)爐。具體的結(jié)論來(lái)自高層的吹轉(zhuǎn)爐模擬包括:(1)紊流擴(kuò)散的氣體中不可忽視的要考慮射流沖擊面積的影響。(2)大量一氧化碳脫碳期間可能會(huì)減慢鋼液中鋼的脫碳速度。(3)可以使用脫碳速度的推斷,對(duì)一個(gè)幾秒鐘的仿真,得到的粗略估計(jì)碳含量在隨后階段過(guò)程中只要碳含量相對(duì)較高(比較下一點(diǎn))。(4)對(duì)當(dāng)前系統(tǒng)來(lái)說(shuō)，大約3%碳在鋼的初始的渣中。FeO或二氧化硅了接近于零即只要?dú)怏w(COCO2)在鋼液中的含量足夠的多。找出濃度的結(jié)合,流動(dòng)速率和溫度下,呈現(xiàn)最高效脫碳,未來(lái)會(huì)有更進(jìn)一步的參數(shù)研究。確認(rèn)這個(gè)工作是由瑞典財(cái)政支持戰(zhàn)略研究基金會(huì)(SSF)和瑞典鋼鐵行業(yè)通過(guò)熱力學(xué)計(jì)算中心(CCT)進(jìn)行的。參考文獻(xiàn)1) E. 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Jnsson: Proc. 5th European Oxygen Steelmaking conf., Aachen, Germany, (2006), 519.Dynamic Coupling of Computational Fluid Dynamics and Thermodynamics Software: Applied on a Top Blown ConverterMikael ERSSON, Lars HGLUND, Anders TILLIANDER, Lage JONSSON and Pr JNSSONDivision of Applied Process Metallurgy, Royal Institute of Technology (KTH), SE-100 44 Stockholm, Sweden.(Received on November 8, 2007; accepted on December 10, 2007)A novel modeling approach is presented where a computational fluid dynamics software is coupled to thermodynamic databases to obtain dynamic simulations of metallurgical process phenomena. The modeling approach has been used on a fundamental model of a top-blown converter. Reactions between gassteel, gasslag, steelslag and gassteelslag have been considered. The results show that the mass transport in the surface area is totally controlled by convection. Also, that a large amount of CO produced during the decarburization might slow down the rate of decarburization in droplets ejected from the bath. For the present simulation conditions reflecting laboratory experiments, it was also seen that the amount of slag (FeO and/or SiO2) created is close to zero, i.e. only gas (CO_CO2) is created as the oxygen jet hits the steel bath. It was also illustrated how an extrapolation of the decarburization rate, sampled from a few seconds of simulation, could be done to get a rough estimate of the carbon content at a later stage in the process as long as the carbon content is relatively high. The overall conclusion is that it is possible to make a dynamic coupling of the Thermo-Calc databases and a CFD software to make dynamic simulations of metallurgical processes such as a top-blown converter.KEY WORDS: BOF; CFD; thermodynamics; modeling; slag and dynamic simulations.1. IntroductionIn many metallurgical processes involving an oxygen-jet impinging onto a steel bath surface, a good understanding of the underlying fluid dynamics is desirable in order to optimize the involved kinetics such as decarburization. There have been several experimental reports on the subject for instance17) and also some numerical or Computational Fluid Dynamics (CFD) reports.813) Szekely and Asai8) presented a computational model of a jet impinging onto a liquid surface. Ngyen and Evans investigated the effect the nozzle-to-pool diameter ratio had on the deformation of the liquid surface caused by an impinging jet, using a computational model.9) Zhang et al. modeled a combined blown case where a top jet as well as a submerged jet was employed. 10) Odenthal et al. showed a multiphase CFD model of a top blown converter where splashing phenomena due to the impinging jet was investigated as well as the mixing time in the converter due to bottom and top blowing.11) Nakazono et al. described a two-phase numerical analysis of a supersonic O2-jet impinging on a liquid iron surface containing carbon.12) The calculations were performed under vacuum and addressed surface chemistry between the gas- and the steel-phase. The model used a steady state approach without treatment of splashing, ripples etc. There are also other non top blowing CFD models presented in the literature that address chemical reactions in metallurgical systems, see for instance.14,15) Jonsson et al. presented a coupled CFD and thermodynamics model of sulfur refining in a gas-stirred ladle.14) The thermodynamics was incorporated in the CFD program as a custom subroutine specifically written for the investigated system. A schematic of such an approach can be seen in Fig. 1. Recently a CFD model consisting of a top blown system has been presented and compared to experimental data.13) Here an extension to this model is presented which includes reactions i.e. a gas/liquid/slag Volume of Fluid (VOF)17) multiphase model, for a top blown system. Reactions between all phases have been allowed as well as expansion/ contraction associated with the creation or destruction of phases in the computational cells. The methodology of the setup is shown and finally some illustrative results of a fundamental top blown converter model are presented.2. Numerical ModelThe current modeling approach is seen in Fig. 2. It is built in a modular fashion in order to ease the incorporation of new research into the model. This also means that very little reprogramming is necessary when changing from one system to another, as long as the thermodynamic data is present in the thermodynamic database and the capabilities of the CFD software is not exceeded. The simulations have been performed on a Linux PC cluster containing 6 nodes. The real-life simulation time has been highly dependent on the number of Thermo-Calc calls performed so no typical simulation time can be given; it varies between one hour and ten days real-time for a 10 sFig. 1. Schematic of a numerical model approach with combined CFD and thermodynamics modeling. From Ref. 14).Fig. 2. Schematic of a numerical model approach with combined CFD and thermodynamics modeling. Modular approach that uses databases from the Thermo-Calc software.Fig. 3. Schematic of top blown converter. a) Physical Domain b) Numerical Domain.simulation. In Fig. 3 a schematic of the physical and numerical domains can be seen. The boundary conditions used are velocity inlet, pressure outlet, no-slip walls and symmetry axis. Standard wall functions have been used for both walls.18,19) The realizable ke model20) has been used in all examples. The domain width is 0.075 m and the height is 0.13 m. Initially, a 15.6 kg steel-melt is introduced with a temperature of 1 500C. From the top lance, placed 0.01 m above the steel, a mass flow inlet was specified corresponding to a volumetric flow rate of 25 L/min of pure oxygen. In Table 1 various parameters used in the simulation can be seen and in Table 2 the initial concentrations of the different species are shown.2.1. CFDThe Ansys Fluent software has been used which is a commercial finite volume solver used for computational fluid dynamics.19) Conservation equations of mass, momentum, energy and species are solved. Depending on the turbulence model used some extra conservation equations are added, for instance conservation of turbulence kinetic energy, k, and turbulence energy dissipation, e , as prescribed in the standard ke model.18) The following form is used for transport of any property f :where r is the density, u is the mean velocity vector, when using a turbulence model based on Reynolds Averaging, G is the diffusion coefficient and Sf is the source term, as can be seen in Table 3. Equation (1) and Table 3 describes the transport of; mass, momentum, turbulence kinetic energy,turbulence energy dissipation, energy, species and volumefraction.2.2. Thermo-CalcIn order to obtain an accurate description of the thermodynamics the software Thermo-Calc21) is used. This is a general software package for multi-component phase equilibrium calculations. It uses a technique that allows for a very flexible setting of conditions for the equilibrium state thus being suitable for use with process simulations. The method of solution is the following. First, the massand heat content in each phase is calculated separately. Then, the total mass and heat content is summed up. The system is thereafter equilibrated. Finally, the program calculates the temperature, new compositions and amounts of the phases. To communicate with the thermodynamic software anapplication programming interface TQ21) is used. This interface is one of the interfaces available within the Thermo- Calc software package21) and makes it possible to generalize the implementation of different system (e.g. the components and elements that the system consists of) withoutchanging the code.2.3. Coupling and AssumptionsThe aim with the coupling of the two softwares, the CFD-package and the Thermo-Calc database software, is to create a general numerical model for metallurgical systems including chemical reactions. In the following text the coupling will be described. The major assumption is that localequilibrium can be reached in each computational cell during the course of each time step. The software interface between the CFD-package and the thermodynamic databases is coded in C and FORTRAN, respectively.2.4. Multiphase ConsiderationsAll bulk phases have been modeled as incompressible; having uniform density, see Table 1. With a refinement of the model it should be possible to use an ideal gas law as- sumption for the gas phase and some temperature and composition dependent density model for the steel and the slagphases. To briefly explain some specifics of the functionalityassume that one mole of oxygen reacts with carbon in the melt to form 2 mole of carbon monoxide. In the computational cell under consideration there will be an expansion of the gas phase to roughly twice the original volume. This in turn will most likely mean that the gas expands outsidethe computational cell. When coupled with CFD, the expansion will occur in the following time step, as the extra gas mass is added to the cell as source term. After a computational cell has reached equilibrium it will also have a specific temperaturethe equilibrium temperature. Assumptions:a) Thermodynamic equilibrium can be reached in each cell during any time step.b) The densities of gas/steel/slag are constant in time and space.c) Equilibrium needs only to be calculated in cells containing at least two phases. A schematic of the coupling and the solution procedure can be seen in Fig. 4.Fig. 5. Velocity vector plot in gas. Vectors have a fixed length; instead they are colored by velocity magnitude (m/s).Fig. 6. Velocity vector plot in the steel. Vectors have a fixedlength; instead they are colored by velocity magnitude(m/s).Fig. 7a. Mass fraction of carbon in steel. 1 s simulation time.Fig. 7b. Mass fraction of carbon in steel. 2 s simulation time.Fig. 7c. Mass fraction of carbon in steel. 3 s simulation time.Fig. 7d. Mass fraction of carbon in steel. 5 s simulation time.Fig. 8. Mass fraction of CO in the gas phase. 5 s simulation time.3. Results3.1. Fundamental Top Blown ConverterIn Fig. 5 vector plot showing the gas jet, as it impinges on the steel bath, is shown. It is seen that the jet looses its axial momentum as it hits the bath surface. The low flow rate from the lance gives a relatively small penetration in the steel bath. Figure 6 illustrates the flow field in the steel bath caused by the impinging oxygen jet. The highest velocities are present where the jet hits the bath and in the surface area. The fluid moves from the penetration zone towards the wall and then down into the bath. A large re-circulation loop is formed in the center of the bath (i.e. between the axis and the wall) and several small re-circulation loops are formed close to the surface. It should be noted that the velocity magnitude in the larger loop is very small. This is attributed to the low flow rate from the top lance. Higher flow rates render larger penetration and a stronger bath circulation.Figure 7 illustrates the carbon concentration in the bath at times 1, 2, 3 and 5 s. First of all the plotting limits should be noted, where it can be seen that the range of the plot is quite narrow. This is intentional in order to make the small concentration differences visible over the range of plottingcolors used. It can be seen from Fig. 7(a) that a carbon concentration gradient exists in a small region close to the free surface area as well as in a larger region to the right of the penetration zone. When examining Figs. 7(a)7(d) it becomes evident that the larger region moves towards the wallof the converter and that it also becomes larger with time. The carbon concentration in the moving region slowly decreases between Figs. 7(a)7(d). It seems that the decarburized steel is transported along the surface (see Fig. 6) and