Mathematical model and numerical solutions for the coupled gas–solid heat transfer process in moving packed beds

Highlights

• A mathematical model is proposed for a moving cooling packed clinker bed.

• Numerical solutions and temperature distributions of clinker cooling process are obtained.

• Optimal operating conditions for the cement production are discussed.

Abstract

A theoretical study was performed into the coupled gas–solid heat transfer process in a moving cooling packed clinker bed. A mathematical model for the clinker cooling process including effects from clinker movement is proposed. The aim is to predict through numerical methods the temperature distribution in the clinker layer and determine the optimal operating conditions. The equations and boundary conditions are discretized using the Taylor series expansion. The Jacobi iteration algorithm is employed to solve the difference equations to obtain temperature distributions for the clinker cooling process. The results are validated using industrial data. The relative errors are 7.0% and 1.1% for secondary and tertiary air temperatures, respectively. An analysis of the temperature difference distribution between clinker and cooling air confirmed the need to apply thermal non-equilibrium conditions in packed bed modeling. The different clinker speeds and thicknesses are also calculated. The results show that, with the same thickness of clinker layer, the most effective speed of the clinker is 0.008 m/s and ensures clinker cooling and heat recovery requirements. With the same clinker mass flow rate, operating with a thicker clinker layer can improve heat recovery and decrease the clinker outlet temperature; both can be used as a guiding framework in real cement production.

Introduction

Large quantities of high-temperature particle material, for example, sinter, cement clinker, and furnace slag, are usually formed in industrial production. They need to be cooled for utilization and transportation. A moving packed bed is commonly used during cooling although a considerable amount of high-temperature waste heat is generated. Studies on the gas–solid heat transfer enhancement process in the moving packed bed are significant for particle material cooling and waste heat recovery.

Cement production industry normally consumes a large amount of energy [1], [2], [3]. A typical type of packed bed equipment used is the cement grate cooler, which is crucial for rapid clinker cooling and exhaust heat recovery that includes secondary and tertiary air for the cement process and high-temperature air for cogeneration. High-temperature clinker generated in the rotary kiln falls onto a moving grate plate in the cooler and forms a clinker layer of a certain thickness. The cooling air flows vertically through the clinker layer (Fig. 1). In cement production, electricity accounts for 25% of the total energy; thermal energy accounts for 75%. Heat loss from cooling the clinker represents about 35–40% of the total heat loss [4]. The cement industry has been a key industrial emission sector in China and there is a large potential for reducing emissions [5], [6], [7]. Reducing the energy consumption of cooling fans during clinker cooling and improving the quality of waste heat are important ways for energy conservation and emission reduction. Therefore, it is of great importance to obtain temperature distribution of the heat transfer process in the grate cooler and improve the efficiency of the cooling system for energy conservation.

Forced convection is the major heat transfer mode for packed beds. Intensive research has been conducted using different thermodynamic theories. Liu et al. [8] proposed a two-dimensional transient numerical model for sintering beds with the Brinkman–Forchheimer model and thermal non-equilibrium model. Wen et al. [9], [10] established a three-dimensional mathematical model for cement clinker cooling process with a porous media seepage heat transfer theory and the model is verified by simulation. Yin and Zhu et al. [11], [12] simulated the heat transfer process in a grate cooler with FLUENT UDF (User-defined functions) and obtained the temperature distribution without considering the motion of the clinker. Shao et al. [13] obtained the temperature distribution in a grate cooler with a FLUENT porous media model and a dynamic mesh technique with the thermal equilibrium assumption. Ahmad et al. [14] proposed a heat transfer model by applying the first law of thermodynamic and gas–solid convective heat transfer theory. Touil et al. [15] established a clinker cooling heat transfer model via a convective heat transfer theory and conducted entropy generation analysis. Caputo et al. [16], [17] proposed a dynamic simulation method for cooling packed beds based on transient convection-conduction heat transfer methods and law of energy conservation. Zheng et al. [18] proposed a general three-dimensional mathematical model for heat transfer in high-temperature solid granule and obtained the solutions of one-dimensional conditions. Wang et al. [19] established a numerical model of a grille-sphere composite structured packed bed with A3-D model in Fluent software. Li et al. [20] investigated and analyzed the influence of packing form and particles shape on the mass transport behavior using the volume average method and numerical simulations. Peng et al. [21] conducted research on the heat storage performance of compressed air in a packed bed thermal energy storage and an unsteady continuous solid phase model was proposed to study the heat transfer in the packed bed. Barbour et al. [22] presented a thermodynamic analysis of an adiabatic compressed air energy storage system with packed bed and a numerical model was established for packed beds with energy rate balance. Ortega-Fernández et al. [23] proposed a packed bed thermal storage system for heat recovery and established the heat transfer model in packed bed system with local thermal equilibrium model. Cascetta et al. [24] presented a comparison between Fluent software results and experimental data obtained from a sensible thermal energy storage system based on alumina beads. A local thermal non-equilibrium model with the porous medium model was employed to model heat transfer behavior in the packed bed using separate energy equations. Anderson et al. [25] presented a model using a two-energy-equation model to predict the fluid and solid temperature in a thermal energy storage vessel packed with alpha-alumina beads. Almendros-Ibanez et al. [26] proposed a theoretical study of a moving bed cross-flow heat exchanger with general two-phase equations. Energy two-equation is used to simulated heat transfer in packed beds widely. However, the clinker cooling process in a grate cooler is a complicated convective heat transfer process with variable boundary conditions. Previous research mostly ignores the clinker movement and treats the clinker layer as stationary packed beds.

In this paper, we conduct theoretical research on the clinker cooling process on the moving packed beds using an improved energy equation. The aim is to establish a mathematical model taking into account the motion of the clinker and determine the optimal operating conditions. Effects of the movement of clinker will be qualified through adding a convective term into the solid-phase equation in an energy two-equation model. The heat transfer process will be characterized and compared with the industrial data. In addition, parametric studies on the clinker speeds and thicknesses will be performed for their effects on the heat recovery and clinker cooling process.