Parametric study of flow field and mixing characteristics of TiCl₄ jet injected into O₂ crossflow in oxidation reactor for titanium pigment production by chloride process

Highlights

• Numerical investigation of TiCl₄ jet and O₂ crossflow mixing in oxidation reactor.

• Studied effect of geometrical and flow parameters on mixing characteristics.

• Distinctive kidney‒shaped structure formed at specific distances from jet holes.

• Penetration depth depended on dimensionless quantity relating all parameters.

• Mixing non‒uniformity and quality follow the same trend.

Abstract

A parametric study of the flow field and mixing characteristics of a TiCl₄ jet injected into an O₂ crossflow in an oxidation reactor for titanium pigment production is numerically investigated. A three-dimensional computational fluid dynamics (CFD) simulation of the turbulent gas mixing model is performed. The effect of geometrical (reactor diameter, jet nozzle number n, jet nozzle diameter, jet nozzle spacing S) and flow parameters (momentum flux ratio J) on the penetration depth (h/R) and mixing quality of the gases is examined. The results are validated with available experimental data and a good agreement is obtained. We show that three stages: under-, optimum, and over-penetration, occur sequentially in the oxidation reactor with increasing J. The kidney-shaped structure, characteristic of a jet-in-crossflow is formed, which is blurred when the mixture of TiCl₄ and O₂ moves into the downstream fluid. The h/R value at a minimum temperature difference is 0.683 and 0.604 for n = 32 and 16, respectively, which are within industrial production data range of 0.56–0.72. The optimum range of S is between 3.25 and 7.35. h/R strongly depends on the only dimensionless parameter J/n² expressed in terms of the geometrical and flow parameters via the relation: h/R = 0.7274 + 0.20228 ln (J/n²+0.04587). The TiCl₄ concentration profile changes from a quasi-sine to quasi-cosine distribution with increasing J/n². Both the mixing non-uniformity and the time to attain the optimum mixing quality of TiCl₄ and O₂ decrease first and then increase with increasing J/n².

Introduction

Titanium pigment (hereafter referred as TiO₂) is a very important white inorganic pigment [1]. It is widely used in coatings, plastics, rubber, papermaking, chemical fibres, metallurgy, pharmaceutical, cosmetics, and other industries [[2], [3], [4], [5], [6], [7], [8]]. With the development of the coatings industry, demand for TiO₂ has increased in recent years [9]. Currently, methods to manufacture TiO₂ include the sulphate process and the chloride process [[10], [11], [12]]. In comparison with the sulphate process, the chloride process offers advantages such as short process flow, ease of expanding production capacity, high quality product, low pollution, and high automation [13]. Therefore, it is attractive to manufacture TiO₂ with the chloride process instead of the sulphate process.

The chloride process consists of three main steps: chlorination, oxidation, and post-processing. Oxidation of TiCl₄ is the key technology, which is conducted in an oxidation reactor. TiCl₄ and O₂ are injected into the oxidation reactor from radial and axial directions, respectively. The rate of the oxidation reactions is rapid when the heat is provided, and the reactions are completed in milliseconds [14]. This clearly indicates that the oxidation of TiCl₄ in the oxidation reactor is controlled by a transport process, which is affected substantially by two contributions: a short range one (molecular diffusion) and a long range one (convection). In particular, convection is controlled by the fluid dynamics in the oxidation reactor. As a result, preferential fluid paths or rolls or stagnation regions have a dramatic effect on the growth rate of TiO₂ particles and an even greater effect on the uniformity of TiO₂ production. Therefore, it is very clear that the role of mixing of O₂ and TiCl₄ is really important for the behaviour of the overall process in terms of the productivity and quality of TiO₂ production. It has been reported that a jet-in-crossflow (JIC) is usually used to increase the mixing rate [15]. A JIC is typically employed to enhance mixing of the reactants and accelerate the reaction rate in an oxidation reactor in many applications such as chemicals, burners, and engines [[16], [17], [18]]. The mixing quality is improved because the gas is positioned further from the injection points; however, one must note that for industrial purposes, the chamber must be built as small as possible [19]. Therefore, reactants should be mixed rapidly and intensively in a minimum downstream distance. The optimum mixing quality depends both on the application and the downstream distance, and for the abovementioned industrial applications usually a distance < twice the chamber diameter is considered as practical downstream distance [20].

Several research studies have been conducted via experiments and/or simulations to improve the mixing efficiency of a JIC. Holdeman [21] both experimentally and computationally examined a confined subsonic crossflow. He found that variations in momentum flux ratio, orifice size, and spacing have a significant effect on the flow distribution. He et al. [22] studied the effect of the Schmidt number on turbulent scalar mixing in a JIC utilizing the Reynolds-averaged Navier-Stokes equation with the standard k-ε turbulence model. Zhang [23] investigated the gas mixing and the reaction process via cold and hot experiments, and showed that a tangential inlet ring should be used to improve the gas mixing. Wegner et al. [24] conducted a comparative study of the mixing process for three configurations with different angles by performing a large eddy simulation. The results showed that the inclinations influence the characteristics of vertical structures and secondary motion, which in turn have an effect on the mixing process. Bazdidi-Tehrani et al. [25] performed a numerical simulation of a non-reacting flow inside a duct for predicting the temperature and flow fields. The penetration and mixing characteristics of a single row of coolant jets injected normally into a heated crossflow in a constant area duct were investigated. Cheng et al. [26,27] experimentally mixed gases via particle tracing and particle image velocimetry. They concluded that the main factors affecting the mixing condition were the momentum ratio and the crossing angle of the two flows. However, there is ambiguity regarding the appropriate momentum ratio, crossing angle, and jet ring opening position. Wang and Mujumdar [28] numerically examined the flow and mixing characteristics of multiple and multi-set three-dimensional confined turbulent round opposing jets in a novel in-line mixer. Li et al. [29] studied the crossflow and heat transfer characteristics in wall-bounded tube bundles. The results showed that the flow in wall-bounded tube bundles has an intrinsic transient flow feature of swaying similar to in free tube bundles, but the walls modify the flow and heat transfer significantly. Bhuiyan et al. [30] simulated the air-side turbulent thermal and hydraulic characteristics of a finned tube heat exchanger in a staggered tube arrangement using a commercial CFD code for turbulent flow regimes. Recently, Kartaev et al. [31] analysed the formation process of a counter jet as a result of impinging jets radially injected into a confined crossflow of a cylindrical duct. They obtained the point estimates of axial and radial mixing fractions in over-penetration mode with counter jet formation. Nada et al. [32] investigated the flow field and mixing behaviour of coolant radial jets injected radially from multiple nozzles rows of a centreline distributer into a heated non-reacting crossflow in a cylindrical chamber.

Several interesting results pertaining to gas mixing have been obtained by researchers over the past years. Injection of a single jet or a limited number of multiple jets normally into a crossflow has motivated a number of studies. Most of these studies examined JICs for circular ducts and some for rectangular ducts. Injection for specific values of control parameters has been performed in two-dimensions. However, this has not been reported in three-dimensions at present. Furthermore, a detailed parametric study of the effect of the geometric and flow parameters on mixing temperature characteristics, jet penetration depth, and mixing quality of TiCl₄ and O₂ for the production of TiO₂ via the chloride process is still being researched. There is also ambiguity regarding the appropriate momentum flux ratio and jet nozzle features (number, diameter, and spacing).

In this study, to obtain the optimum gas mixing conditions and reveal the flow hydrodynamics in the oxidation reactor, a three-dimensional CFD simulation of turbulent gas mixing of TiCl₄ and O₂ for the production of TiO₂ via the chloride process was performed. To this end, a comprehensive parametric study of the effect of the geometric (reactor diameter, number of jet nozzles, diameter of the jet nozzle, spacing between adjacent jets) and flow parameters (momentum flux ratio) on the mixing temperature characteristics, jet penetration depth, and mixing quality of TiCl₄ and O₂ was investigated. Developing dimensionless correlations between the penetration depth and geometric and flow parameters, mixing temperature features and penetration depth, and mixing quality and penetration depth is the other aim of the present study. The optimum penetration depth and mixing quality were also obtained in terms of the geometrical and operational parameters considered herein. We believe that the interesting results will provide a theoretical basis and guidance for the design and optimization of the uniform distribution of fluids in the oxidation reactor in the feeding torus.