Bohumil Sekanina

An Original Numerical Model Of Heat AndMass Transfer In A Concasting Machine

The solidification and cooling of a continuously cast billet or slab (generally a concasting) and simultaneous heating of the crystallizer is a very complicated problem of transient heat and mass transfer. The solving of such a problem is impossible without numerical models of the temperature field, not only of the concasting itself, while it is being processed through the concasting machine (CCM), but of the crystallizer as well. This process is described by the FourierKirchhoff equation. An original three-dimensional (3D) numerical model of the temperature field of a CCM has been developed. It has graphical input and output automatic generation of the net and plotting of temperature fields in the form of color isotherms and iso-zones, and temperature-time curves for any point of the system being investigated. This numerical model is capable of simulating the temperature field of a CCM as a whole, or any of its parts. Simultaneously, together with the numerical computation, experimental research and measuring have to take place not only to be confronted with the numerical model, but also to make it more accurate throughout the course of the process. This analysis was conducted using a program devised within the framework no. 706/P&/02P6 < 20. 1 An original numerical model Solidification and cooling of a casting and simultaneous heating of the mold is, from the point of view of heat transfer, a case of transient spatial, or 3D, heat and mass transfer in a system comprising the casting, mold and surroundings. This is Advances in Fluid Mechanics III, C.A. Brebbia & M. Rahman (Editors)

A Numerical Model of the Crystallization of Pure Aluminium

The model was originally designed to confirm and enhance the capabilities of experimental research in the crystallization of pure aluminium (99.99% Al), specifically to determine the zone of the occurrence of columnar and equiaxed crystals and the positions of the transition interface. The character of primary crystallization was investigated on a simple cylindrical sample, crystallizing in a cast-iron mould pre-heated to various temperatures. The experimental research comprised the measurement of temperatures using thermocouples, the evaluation of the experimentally acquired temperature gradients G, and the shift rate of the phase transition interface R. The numerical model had been developed to expand the limited experimental capabilities of the evaluation of G and R to every point of the longitudinal section, based on the investigation of the 3D transient temperature field within the system comprising the casting, the mould and ambient. This enabled the prediction of the character of the crystallization in greater detail.Copyright

Calculation of the Temperature Field of the Solidifying Ceramic Material EUCOR

EUCOR, a corundo-badelleyit material, which is not only resistant to wear but also to extremely high temperatures, is seldom discussed in literature. The solidification and cooling of this ceramic material in a non-metallic mould is a very complicated problem of heat and mass transfer with a phase and structure change. Investigation of the temperature field, which can be described by the three-dimensional (3D) Fourier equation, is not possible without the employing of a numerical model of the temperature field of the entire system—comprising the casting, the mould and the surroundings. The temperature field had been investigated on a 350×200×400 mm block casting—the so-called “stone”—with a riser of 400 mm, and using a numerical model with graphical input and output. The computation included the automatic generation of the mesh, and the successive display of the temperature field using iso-zones and iso-lines. The thermophysical properties of the cast, as well as the mould materials, were gathered, and the initial derivation of the boundary conditions was conducted on all boundaries of the system. The initial measurements were conducted using thermocouples in a limited number of points. The paper provides results of the initial computation of the temperature field, which prove that the transfer of heat is solvable, and also, using the numerical model, it is possible to optimise the technology of production of this ceramic material, which enhances its utilisation. The results are complemented with an approximated measurement of the chemical heterogeneity of EUCOR.Copyright

Numerical Optimization of the Method of Cooling of a Massive Casting of Ductile Cast‐Iron

An original application of ANSYS simulating the forming of the temperature field of a massive casting from ductile cast-iron during the application various methods of its cooling using steel chills. The numerical model managed to optimize more than one method of cooling but, in addition to that, provided serious results for the successive model of structural and chemical heterogeneity, and so it also contributes to influencing the as solidified microstructure. The file containing the acquired results from both models, as well as from their organic unification, brings new and, simultaneously, remarkable findings of causal relationships between the structural and chemical heterogeneity and the local solidification time in any point of the casting. Therefore the determined relations enable the prediction of the local density of the spheroids of graphite in dependence on the local solidification time. The calculated temperature field of a two-ton (500 × 500 × 1000) mm casting of ductile cast-iron with various methods of cooling has successfully been compared with temperatures obtained experimentally. This has created a tool for the optimization of the microstructure with an even distribution of the spheroids of graphite in such a way so as to minimize the occurrence of degenerated shapes of graphite, which happens to be one of the conditions for achieving good mechanical properties of castings of ductile cast-iron.

Cooling of a Massive Casting of Ductile Cast-Iron and Its Numerical Optimization

The numerical models of the temperature field of solidifying castings often observe two main goals: directed solidification and optimization of the technology. These goals can be achieved only if the deciding factors which either characterize the process or accompany it are analysed and their influence controlled. An original application of ANSYS, based on the numerical finite-element method, is applied. The numerical model simulated the forming of the temperature field of a two-ton 500×500×1000 mm casting from ductile cast-iron during the application of various methods of its cooling using steel chills. This model managed to optimize more than one method of cooling but, in addition to that, provided results for the successive model of structural and chemical heterogeneity, and so it also contributes to influencing the pouring structure. The file containing the acquired results from both models, as well as from their organic unification, brings new and, simultaneously, remarkable findings of causal relationships between the structural and chemical heterogeneity and the local solidification time in any point of the casting. This has established a tool for the optimization of the structure with an even distribution of the spheroids of graphite in such a way so as to minimize the occurrence of degenerated shapes of graphite, which is one of the conditions for achieving good mechanical properties of castings of ductile cast-iron.© 2009 ASME

Pilot Calculation Of The Temperature Field Of The Ceramic Material EUCOR

EUCOR, a corundo-badelleyit material, which is not only resistant to wear but also to extremely high temperatures, is seldom discussed in literature. The solidification and cooling of this ceramic material in a non-metallic mold is a very complicated problem of heat and mass transfer. The investigation into the temperature field, which can be described by the 3D Fourier equation, is not possible without the engagement of a numerical model of the temperature field of the entire system — comprising the casting, the mold and the surroundings. The temperature field was investigated on a 350x200x400 mm block casting of stone with a riser of 400 mm using an original model with graphical input and output. The computation included the automatic generation of the network, and the successive display of the temperature field using iso-zones or iso-lines. The thermophysical properties of the cast as well as the mold materials were gathered and the initial derivation of the boundary conditions was conducted on all boundaries of the system. The initial measurements were conducted using thermocouples in a limited number of points. The paper provides results of the initial computation of the temperature field, which prove that the transfer of heat is solvable, and also that using the numerical model it is possible to optimize the technology of production of this ceramic material, which enhances its utilization. The results are complemented with an approximated measurement of the chemical heterogeneity of EUCOR. This analysis was conducted using a program devised within the framework of the GA CR projects no. 106/01/1464, 106/01/1164 and 106/99/0728, of the COST-OC.P3.20 and COSTOC 526.10, of the KONTAKT. Introduction Corundobaddeleyit Material (CBM) is a modern electrically cast heatand wear-resistant material. It is resistant to corrosion and to wear even at very high temperatures. This material belongs to the not too well known area of the Al2O3-SiO2-ZrO2 system. This material is produced in several plants throughout the world under different trademarks, in three different types, differing mainly in the ZrO2 content. EUTIT s.r.o. in Stara Voda, which is the initiator of this grant proposal, produces this material with 32-33% ZrO2 under the name of EUCOR. During production, mainly the waste from dismantled glass furnaces is processed here. All customers place the requirements on the properties of CBM which are determined: a) for the internal walls of glass furnaces: the resistance to liquid glass and the creation of bubbles when in contact with liquid glass. b) for the production of wear-resistant products: resistance to wear, low porousness, crystalline structure, and resistance to temperature shocks. CBMs are applied mainly in the construction of glass furnaces, in certain steel-works aggregates, especially within heating furnaces, etc. They have a high resistance to glass as METAL 2001 15. 17. 5. 2001, Ostrava, Czech Republic 2 well as liquid metal, they are also suitable for great temperature changes. Slabs from this material are therefore very suitable for the walls and floors of melting aggregates, linings, pouring filters, isolation plates and for a number of other uses which can be accessible after mastering the optimising of the technology of their production and utility properties. From the foundry viewpoint it is possible to compare the properties of EUCOR with those of commonly cast metals, especially steels and cast steel. For example, the solidification coefficient of steel when cast into a sand mould is approximately 0.07, here EUCOR is 0.065 and the solidification coefficient of steel when cast into a cast-iron mould is 0.13, here EUCOR is 0.163 [m.h], etc. This relationship can not be assumed generally. The proposed investigation will either confirm or disprove this. An original numerical model of solidification, cooling, and heating An original and universal mathematical model of solidification, cooling and heating has been developed in order to be capable of analyzing a oneto three-dimensional steady or unsteady temperature field of a system comprising a casting, the mold and surroundings, namely the system as a whole or any of its parts during any industrial technological processes whose individual sub-processes can be solidification, cooling, heating, refrigerating and others in any sequence or singly. The model enables the simulation of traditional and also non-traditional technologies of casting in foundries, metallurgical plants, forging operations, heat treatment processes, etc.[3,4] Solidification (crystallization) and cooling rank among the most important technological processes. It is the case of general, up to the 3D (spatial) transfer of not only heat but also mass. In the system of the casting, mold and surroundings, all three kinds of heat transfer take place. In such a case, the problem is unable to be solved accurately. It is not exactly solvable in the case when mass transfer is not under consideration and from the three kinds of heat transfer in the system the conduction is considered decisive. Thus neither the Fourier equation (1) (the melt does not flow) nor the Fourier-Kirchhoff equation (2) (the flowing melt) is exactly solvable. Both are partial differential equations of the 2nd order. The chance of their successful solution lies in the outdated analogue and numerical methods. 2 2 2 2 2 2 Q d t t t t S O U R C E d c c x y z λ δ δ δ τ ρ ρ δ δ δ     = + + +   ⋅ ⋅   (1) . x y z Q dt t t t SOURCE a t w w w d x y z c τ ρ   ∂ ∂ ∂ = ∆ + + + +   ∂ ∂ ∂ ⋅   (2) From these the explicit difference method has been chosen. It will allow the most elegant way of simulation of the development of latent heat of the phase or structural changes that in both of the mentioned equations appear as a member of the so-called heat flow from the internal source. For the proper simulation of latent heat development the thermodynamic function of enthalpy is introduced. The entalphy function and its dependence on temperature must be known for relevant metallic material (Fig.1). The authors of this paper have used it in the Czech Republic as the first. The assignment and preparation for simulation The aim of the research was to investigate a 3D transient temperature field of a EUCOR casting, solidifying in a mold made from a CT mixture. The final layer of the bottom of the mold comprises a CT mixture of crushed magnesite. Figure 2 illustrates the assembled mold. METAL 2001 15. 17. 5. 2001, Ostrava, Czech Republic 3 The riser comprises an oblique four-sided prism, where the upper end is 150 x 270 mm, the base is 123 x 250 mm and the height 300 mm. The actual EUCOR casting has a size of 400 x 350 x 200 mm. Three frames are used during the molding procedure—two being 690 x 600 x 400 mm and one 690 x 600 x 200 mm. The method of casting, which is being considered, therefore, is vertical pouring. It is also possible to use the horizontal arrangement, where it is necessary to design the circular riser mounted in the geometrical center within the upper, i.e. larger, wall of the casting. This approach ties on to experimental research into the temperature field of the same material—EUCOR—mentioned at last year’s METAL 2000 Symposium [1]. The pouring temperature is 2300 °C, the initial mold temperature is 20 °C. The liquidus temperature is estimated to be 1775 °C and the solidus 1765 °C. The dependence of the heat capacity c, heat conductivity λ and density ρ of EUCOR on temperature is illustrated in Figures 3-5. The values of the same properties for the mold material are taken from other literature and exacted via measurement [2]. The mean density of the discretization network is 20 mm. A scheme of the 3-D computational network of the solved systemted casting(riser) mold surroundings can be see in Figure 6. The selected time step is 10 s. Heat transfer by convection and radiation is considered in the direction from the upper base of the mold and casting (from the level) and from the surface of the frame of the mold to the surroundings αtotal = αconvection + αradiation . Heat transfer coefficients on these boundaries were estimated. It was presumed that there is ideal physical contact between the casting and mold, and the riser and mold. It is necessary to state that this is merely a preliminary calculation of the temperature field of a solidifying casting of EUCOR. Results of numerical analysis The results attained from the analysis of the temperature field of a solidifying casting and the heating of the mold represent only one quadrant of the system in question. The thermokinetics of the phenomenon was monitored over a five-day period when the casting was kept inside the mold in order to cool completely. Figures 7-10 display the temperature field after periods of 5 minutes; 2 hours; 4 and 9,9 hours. Figure 9 shows the system after 4 hours—shortly before complete solidification. Figure 11 shows the temperature curves of the points along the heat and geometrical axis of the system illustrated in Figure 6.

The Influence of Thermophysical Properties on a Numerical Model of Solidification

Solidification and cooling of a (con)casting, with the simultaneous heating of the mold, is a case of transient spatial heat and mass transfer. This paper introduces an original and universal numerical model of solidification, cooling and heating, of a one-to-three-dimensional stationary and transient temperature field in a system comprising the casting, the mold and its surroundings. This model simulates both traditional as well as non-traditional technologies of casting conducted in foundries, metallurgical plants, forging operations, heat-treatment processes, etc. The casting process is influenced not only by the thermophysical properties (i.e. heat conductivity, the specific heat capacity and density in the solid and liquid states) of the metallic and non-metallic materials, but also by the precision with which the numerical simulation is conducted. Determining these properties is often more demanding than the actual calculation of the temperature field of the solidifying object. Since the influence of individual properties should be neither under- nor over-estimated, it is necessary to investigate them via a parametric study. It is also necessary to determine the order of these properties in terms of their importance.© 2002 ASME

HEAT TRANSFER UNDER AN AIR-WATER COOLING JET

The solidification and cooling of a continuously cast billet, slab or cylinder—generally a concasting—and the simultaneous heating of the crystallizer is a very complicated problem of three-dimensional (3D) transient heat and mass transfer. The solving of such a problem is impossible without numerical models of the temperature field of the concasting itself while it is being processed through the concasting machine (CCM). Experimental research and measurements have to take place simultaneously with numerical computation, not only to be confronted with the numerical model but also to make it more accurate throughout the process. An important area of the CCM is the so-called secondary cooling zone, which is subdivided into thirteen sections, where the first section uses water jets from all sides of the concasting and the remaining twelve sections engage air-water cooling jets positioned only on the upper and lower sides of the concasting. A great number of experiments had also been conducted on an experimental laboratory device simulating the surface of a concasting in order to determine the intensity of the cooling jets. A real CCM contains a total of 8 types of jets and geometrical layouts. All of these jets had been measured individually on the actual laboratory device, which allows the measurement of temperatures beneath the surface of the slab, and which also simulates the movement of the slab. The measured temperatures are converted to cooling intensities by means of an inverse task, which, in turn, are converted to the courses of the heat transfer coefficients. These coefficients are used as the main input data of the numerical model of the temperature field. The numerical model serves also to determine the effect of radiation. The course of the reduced heat transfer coefficient will be illustrated. It is obvious that radiance is dependent on the surface temperature. The results of numerical simulation of the temperature field of a

The temperature field of a gravitationally cast ductile-cast-iron roller and its chemical and structural heterogeneity

The quality of the working rollers from ductile-cast-iron used for rolling rails is determined by the chemical and structural composition of the material of the rollers and the production technology. The requirements of the quality cannot be ensured without perfect knowledge of the course of solidification, cooling and heat treatment of the cast rollers as well as the kinetics of the temperature field of the casting and mould. An original application of ANSYS simulated the forming of the temperature field of the entire system. In the experimental investigation of temperature field, an original methodology for the measurement of the distribution of temperatures and heat flows in the roller-mould system had been developed and verified in the operation. The kinetics of the solidification has a measurable and non-negligible influence on the chemical and structural heterogeneity of the investigated type of ductile-cast-iron. Tying on to the results of the model of the temperature field of the cast rollers, an original methodology was developed for the measurement of chemical microheterogeneity. The structure of this cast-iron is created by a great amount of the transition form of graphite and small amount of globular graphite and also lamellar graphite and cementite, whereas the structure of the metal matrix is perlitic. The chemical and structural heterogeneity of the cast roller is therefore a significant function of the method of melting, modification and inoculation and the successive procedures of risering, casting and crystallization after cooling.

Temperature Field and Solidification Structure of a Ductile-Cast-Iron Roller

The quality of the working rollers from ductile-cast-iron used for rolling rails is determined by the chemical and structural composition of the material of the rollers and the production technology. The requirements of the quality cannot be ensured without perfect knowledge of the course of solidification, cooling and heat treatment of the cast rollers as well as the kinetics of the temperature field of the casting and mould. An original application of ANSYS simulated the forming of the temperature field of the entire system comprising the casting, the mold and ambient. In the experimental investigation of temperature field, an original methodology for the measurement of the distribution of temperatures and heat flows in the roller-mould system had been developed and verified in the operation. The kinetics of the solidification has a measurable and non-negligible influence on the chemical and structural heterogeneity of the investigated type of ductile-cast-iron. Tying on to the results of the model of the temperature field of the cast rollers, an original methodology was developed for the measurement of chemical microheterogeneity. The chemical and structural heterogeneity of the cast roller is therefore a significant function of the method of melting, modification and inoculation and the successive procedures of risering, casting and crystallization after cooling.