Sanjay Chandra

An alternative fixed grid method for solution of the classical one-phase Stefan problem

In this paper, an alternative fixed grid method based on explicit finite difference technique has been presented to solve the classical one-phase Stefan problem. The most popular fixed grid method developed by Murray and Landis, which utilises fictitious temperature for the grid containing the fusion front, has been revisited. The concept of a fictitious temperature for the grid-containing interface, as proposed by Murray and Landis, has been eliminated and an alternative equation has been developed for the energy balance of grid point neighbouring the interface. Identical results have been obtained by the alternative fixed-grid and by the Murray-Landis fixed-grid method. Though the paper deals with explicit finite difference schemes only, the alternative method can also be applied to implicit formulation for one-phase as well as two-phase moving boundary problems.

X-ray diffraction and Mossbauer spectroscopy studies of cementite dissolution in cold-drawn pearlitic steel

Cementite dissolution in cold-drawn pearlitic steel (0.8 wt.% carbon) wires has been studied by quantitative X-ray diffraction (XRD) and Mössbauer spectroscopy up to drawing strain 1.4. Quantification of cementite-phase fraction by Rietveld analysis has confirmed more than 50% dissolution of cementite phase at drawing strain 1.4. It is found that the lattice parameter of the ferrite phase determined by Rietveld refinement procedure remains nearly unchanged even after cementite dissolution. This confirms that the carbon atoms released after cementite dissolution do not dissolve in the ferrite lattice as Fe-C interstitial solid solution. Detailed analysis of broadening of XRD line profiles for the ferrite phase shows high density of dislocations (∼1015/m2) in the ferrite matrix at drawing strain 1.4. The results suggest a dominant role of ⟨1 1 1⟩ screw dislocations in the cementite dissolution process. Post-deformation heat treatment leads to partial annihilation of dislocations and restoration of cementite phase. Based on these experimental observations, further supplemented by TEM studies, we have suggested an alternative thermodynamic mechanism of the dissolution process.

A robust statistical method to evaluate unit operation in coal washery

Abstract The effect of the change of an operating parameter on the washing performance is conventionally evaluated through a direct comparison of the average clean coal yields obtained under normal and trial conditions. Sometimes, in an apparent refinement to the analysis, the clean coal yields are normalized for their ash levels before such a comparison is carried out. This paper illustrates how such simplistic analytical methods can often be misleading and lead to erroneous conclusions. Another method of analysis involves the comparison of two data sets on the basis of their separation efficiencies. The method is not effective in plant conditions, where the fluctuation of several process variables leads to generation of noisy data. An alternative, statistically robust method has been proposed, where a simple linear relationships is established between the response variable and the independent variable during a normal and a trial conditions. These two regression lines are then tested for their equality of slopes using analysis of covariance (ANCOVA). The separation between the regression lines, as measured by the difference of their intercepts, quantifies the change in the process performance. Unlike other methods, this method is the least affected by variables that are not of intrinsic interest and hence is more reliable. This method can be used in a two-stage two-product system and also in a multi-stage multi-product system. Although the recommended method of analysis is not as efficient as one involving a formal design of experiments using analysis of variance (ANOVA), it is nevertheless of significant practical merit for analysis of plant data or where the design of experiments would be too time consuming or difficult.

Microstructures and Mechanical Properties of as-Drawn and Laboratory Annealed Pearlitic Steel Wires

Near eutectoid fully pearlitic wire rod (5.5 mm diameter) was taken through six stages of wire drawing (drawing strains of 0 to 2.47). The as-drawn (AD) wires were further laboratory annealed (LA) to re-austenitize and reform the pearlite. AD and LA grades, for respective wire diameters, had similar pearlite microstructure: interlamellar spacing (λ) and pearlite alignment with the wire axis. However, LA grade had lower hardness (for both phases) and slightly lower fiber texture and residual stresses in ferrite. Surprisingly, essentially identical tensile yield strengths in AD and LA wires, measured at equivalent spacing, were found. The work hardened AD had, as expected, higher torsional yield strengths and lower tensile and torsional ductilities than LA. In both wires, stronger pearlite alignment gave significantly increased torsional ductility.

Effect of recalescence on microstructure and phase transformation in high carbon steel

Abstract This paper deals with the effect of recalescence on the microstructure of high carbon steels. Controlled experiments are conducted with varying cooling rates and different specimen geometries in a thermomechanical simulator to completely or partially suppress the transformation enthalpy. Different amounts of recalescence obtained from various experiments are then correlated with the final microstructures. The results clearly indicate the importance of recalescence and also show the limitations of using thermomechanical simulators in predicting the characteristics of γ→pearlite transformation in high carbon steels. A mathematical model has been developed to predict the phase transformation in high carbon steels under continuous cooling conditions incorporating the influence of recalescence. The newly developed model gives better prediction of microstructure than currently available models in high carbon steels under higher cooling rates.

Low Cycle and Ratchetting Fatigue Behavior of High UTS/YS Ratio Reinforcing Steel Bars

Cyclic deformation behavior of high UTS/YS rebars has been studied employing both symmetric strain-controlled and asymmetric stress-controlled cycles in an attempt to understand the influence of UTS/YS ratio on fatigue life. While strain-controlled cyclic deformation did not exhibit a pronounced influence of UTS/YS ratio, a substantial life enhancement is noted for the asymmetric stress-controlled cycle. Reasons for life enhancement were found to be due to the ratchetting strain development and the associated hardening behavior. An equivalent stress-based model has been used to predict both the symmetric and asymmetric fatigue lives of rebars.

Numerical treatment of diffusional phase transformation through fully implicit control volume method

Abstract Solid state, diffusion controlled phase transformation kinetics with a moving boundary has been quantified using a fully implicit, fixed grid, finite difference method based on the control volume approach. In a departure from the usual modeling techniques for phase change problems, the region undergoing phase change has also been considered as a control volume. A new equation for the interface flux balance has been obtained that minimises the mass balance error that normally plagues the numerical solution of moving boundary problems. The model has been validated with the calculated phase thickness based on binary equilibrium diagram and available experimental data in the literature for the Cu–Zn system and a good match has been obtained. The results obtained by the present formulation are compared with those obtained from the other models. In addition to the improved accuracy of the prediction because of elimination of the mass balance error, the proposed method has the usual advantages of a fully implicit scheme.

Thermodynamic study of evolution of sinter phases at different alumina level

Though sintering is controlled by kinetics of various reactions and is far from equilibrium, a thermodynamic analysis can provide useful inputs on melt formation and helps understand deviation from actual process conditions. The thermodynamic software ‘FACTSAGE™’ was used for this study. The general sequence of reactions during the heating cycle is as follows: decomposition of calcium carbonate to calcined lime; formation of calcium ferrites/silicates; decomposition of calcium ferrites, reduction of haematite to magnetite and formation of spinel and silicates; assimilation of ferrites, silicates, spinel and magnetite into the melt. During the cooling stage, the amount of melt decreased with subsequent precipitation of phases such as magnetite, ferrites, silicates, spinel and formation of haematite. It is very much clear that the sinter made by using higher alumina levels generate fewer amounts of oxides and more slag phase compared to its low alumina counterpart.

A Mathematical Model to Optimise Aluminium Wire Injection in Steel Melts

A mathematical model was developed at the R&D Division of Tata Steel to simulate the process of aluminium wire injection into steel melts and utilised to assess the influence of various operating parameters on the efficiency of aluminium wire injection and, thereby, arrive at an optimum operating condition. The present paper deals, in detail, with the mechanism of heat transfer at the interface between the aluminium wire and the steel shell which is formed on the original wire. The present work revealed that a secondary shell could also be formed based on the operating parameters. This secondary shell delays the melting of the wire until it reaches deeper into the ladle, thereby increasing the residence time of the released aluminium. The model was applied to the on-line purging station of the steel melting shop producing slabs at Tata Steel and based on the model outputs, recommendations made to enhance the utilisation of aluminium injection. An improvement of 10% in the average utilisation of aluminium was obtained during the trial period.

Thin-slab casting: New possibilities

Changes in the IT industry are known to proceed at a scorching pace. In sharp contrast, the rate of development in the steel industry is generally slow. Nonetheless, the unpact of recenr technical development on the steel industry has been quite significant. The production chain from iron ore to final rolled steel is a long one and the shortening of this length has long been the endeanvour of scientists and engineers. The initial development came in the form of speeding up the process of steelmaking by reducing the slow open-hearth process (8 h tap-to-tap time with the 45 min tap-to-tap time of the Basic Oxygen Furnace (BOF) process. Significant development thereafter have been in the process of continuous production of billets and blooms from liquid steel thereby doing away with the large blooming mills needed for rolling ingots.For a fairly long time after the stabilition of continuous casting, hot rolling involved reheating thick (200–250mm) slabs and reducing them in a hot strip mill. The advent of thin-slab casters has made even these large hot strip mills redundant. The new installations produce thin slabs (50–70mm) that are directly nil led hin strip without the need of an intermediate furnace for raising the stock temperature; the so-called cunnel furnace prior to the rolling stands serving only to equalise stock temperatures. Additionally, what started as a step for reducing investment in hot rolling has in fact, given new opportunity for direct hot rolling of thickneses that were, for long, considered to be feasible only through the cold-rolling route.This article discusses the slow but steady encroachment of hot-rolled sheets into the domain of strip thicknesses hitherto produced by cold rolling and tries to show how the development of thin-slab casters has allowed this process to be accelerated. A techno-economic analysis of thin-slab casting: been presented along with the benefits that arise when a thin-slab caster is linked to the blast furnace and basic oxygen route of steel making.