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The main objective of this paper is to establish a mathematical framework to analyze the complex thermal economic performance of the calcination process. To find the factors affecting exergy efficiency loss, different exergy destruction is investigated in detail. Furthermore, the exergy flow cost model for exergy cost saving has also been developed. The results show that the vertical shaft furnace is a self-sufficiency equipment without additional fuel required, but the overall exergy destruction accounts for 54.11% of the total exergy input. In addition, the energy efficiency of the waste heat recovery boiler and thermal deaerator are 83.52% and 96.40%, whereas the exergy efficiency of the two equipment are 65.98% and 94.27%. Furthermore, the import exergy flow cost of vertical shaft furnace, waste heat recovery boiler and thermal deaerator are 366.5197 RMB per MJ, 0.1426 RMB per MJ, and 0.0020 RMB per MJ, respectively. Based on the result, several suggestions were proposed to improve the exergoeconomic performance. Assessing the performance of suggested improvements, the total exergy destruction of vertical shaft furnace is reduced to 134.34 GJ per hours and the exergy efficiency of waste heat recovery boiler is raised up to 66.02%. Moreover, the import exergy flow cost of the three different equipment is reduced to 0.0329 RMB per MJ, 0.1304 RMB per MJ, and 0.0002 RMB per MJ, respectively.

A walking beam type reheating furnace with advanced control technology has been evaluated by combined energy and exergy analysis. In order to gain insight into the performance of the present furnace, the results of energy analysis are compared with those in published papers and the irreversibility of the furnace is analyzed via exergy destruction calculation. The results show that slabs preheated before charged into the furnace can save fuel and improve energy utilization. The structure and material of the wall and roof show good thermal insulation. However, the oxidized scale is a little more and the temperature of flue gas is high in the present reheating furnace. The energy efficiency of the furnace is 71.01%, while exergy efficiency is 51.41%, indicating a potential for energy-saving improvements of the present furnace. The exergy destruction of the furnace accounts for 28.36% of total exergy input which is mainly caused by heat transfer through a finite temperature difference (14.71%), fuel combustion (11.66%) and scale formation (1.99%).

Size-induced particle segregation in rotating drums has been investigated using an Eulerian continuum approach (ECA). The mixing process of a binary mixture were respectively predicted in an unbaffled drum, a drum with a “+” shaped central baffle and a drum with a “-” shaped central baffle. Qualitative comparisons with DEM results showed that ECA works well for describing the mixing process of binary mixtures. A mixing index based on sampling information from the computational grids was developed and used for quantitative analysis. Compared with a base case which uses equal-sized particles, the results showed that ECA can separate the effects of mixing from the effects of segregation. However, the rate of mixing were over-estimated and the improvement effects of “+” shaped baffle and “-” shaped baffle were hard to distinguish quantitatively in the ECA. The drag model was modified for improving the ECA. The final segregation was found independent on the initial particle distribution using ECA.

Discrete element method (DEM) has been used to investigate the effects of particle contact parameters, sliding friction coefficient (SFC), rolling friction coefficient (RFC) and restitution coefficient (RC), in a rotating drum. Their effects were examined in terms of mean power draw, mean collision energy and collision frequency employing response surface method (RSM) in conjunction with analysis of variance (ANOVA) to perform significance analysis for the effects of single factors and factor combinations. Various rotational speed was also considered in the present work. The results revealed that sliding friction coefficient was a determining factor for mean power draw and mean collision energy, and restitution coefficient had the greatest impact on collision frequency. Additionally, sliding friction coefficient and restitution coefficient showed interaction effects on both mean collision energy and collision frequency over the range of rotational speed. Moreover, the sensitivity of particle contact parameters varies with the rotational speed of the drum.

In continuum-based models, the kinetic theory of granular flow (KTGF) provides a model for calculating solids stresses but has limitations in densely packed regions such as mills, kilns and rotating drums. The Eulerian-Eulerian multiphase model coupled with KTGF is evaluated in the present work. An additional frictional stress models were added, and their suitability evaluated. For the evaluation, a rotating drum at three rotational speeds (20 rpm, 42 rpm and 65 rpm) was analyzed. Compared with Positron Emission Particle Tracking (PEPT) measurement data from literature, Johnson and Jackson's model and Schaeffer's model for the frictional stress both showed a lower angle of repose regardless of the wall boundary condition used. Thus, a new frictional viscosity model based on granular pressure was proposed. By adjusting the specularity coefficient of wall boundary condition, results of the present model agreed well with the PEPT measurements in terms of angle of repose and spatial velocity fields. In addition, considering that the actual Johnson and Jackson model for boundary condition includes two parts, collisional and frictional part, a discussion was made about boundary condition. The results showed that the validation of the proposed frictional viscosity model with experimental results could be completed at different rotational speeds by considering only the collisional part of the boundary condition with different specularity coefficients or only the frictional part of the boundary condition with different angles of friction or both parts with the same specularity coefficient and angle of friction. Nevertheless, when the complete Johnson and Jackson model of boundary condition was applied, the same specularity coefficient and angle of friction are used at different rotational speeds which is more physically meaningful. Moreover, it is found that the frictional contribution has greater influence on dynamic angle of repose than collisional contribution of the boundary condition in the current rotating drum.

As an excellent reducing agent, lime has an important role in the steel production process. Annular Shaft Kiln (ASK) has been widely used in the lime production industry for its low cost, low footprint, high chemical activity, easy construction, and easy maintenance. Due to the high temperature generated inside ASK during operation, it is hard to observe the limestone decomposition process and the field distribution in the lime kiln. The simulation analysis of temperature field, velocity field and decomposition field in the limestone calcination process by CFD provides practical guidance for future lime product quality control, ASK design and operation parameters’ control. This study is based on an ASK that was put into production. Based on the finite volume method, this paper combines the porous medium model and the shrinking core model to establish a set of mathematical models that can describe the temperature and flow field distribution inside the ASK, as well as the limestone decomposition process and the heat and mass transfer process inside the ASK. According to the feedback from the production site, the mathematical model is in good agreement with the production results.