(70c) Numerical Simulation of BaSO4 Precipitation in a Coaxial Pipe Mixer with Micromixing Effects

Numerical simulation of BaSO₄ precipitation in a coaxial pipe mixer with micromixing effects

A. A. Öncül[*]^,1, D. Thévenin¹, K. Sundmacher^2,3

¹ Institut für Strömungstechnik und Thermodynamik, Lehrstuhl für Strömungsmechanik und Strömungstechnik, Otto-von-Guericke-Universität-Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany

² Max-Planck-Institut für Dynamik komplexer technischer Systeme, Sandtorstr. 1, 39106 Magdeburg, Germany

³ Institut für Verfahrenstechnik, Lehrstuhl für Systemverfahrenstechnik, Otto-von-Guericke-Universität-Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany

Precipitation of various crystals has always been an important subject in chemical and process engineering. A huge amount of corresponding experiments can be found in the literature. These experiments have been used to develop and test numerical models, which have been then successfully coupled with Computational Fluid Dynamics (CFD) codes in recent years. The resulting numerical tools can predict crystal properties for various reactors and hydrodynamic conditions.

In this work, the precipitation of barium sulphate (BaSO₄) in a non-premixed coaxial pipe mixer is numerically investigated by considering explicitly the influence of micromixing. The global properties of this reactor and the macromixing have been examined by the authors in previous publications [1, 2]. Results are obtained by coupling the Population Balance Model (PBM) and two presumed Probability Density Function (PDF) methods within the commercial CFD code FLUENT^® 6.2 via external User-Defined Functions (UDF) and User-Defined Scalars (UDS). The Standard Method of Moments (SMM) has been used to solve the PBM for the initial simplified computations. Afterwards, the Direct Quadrature Method of Moments (DQMOM) [3], an improved version of the SMM, has been used when considering more complicated reaction kinetics. Moreover, the Mixture Fraction-PDF (MF-PDF) approach is applied to describe the mixing between two feed streams in the reactor whereas a Finite Mode-PDF (FM-PDF) method is implemented as the micromixing model. Here, the FM-PDF model is based on the multi-environment micromixing approach, which represents the scalars and their source terms as finite modes (or environments) in every computational cell by discretizing the composition space. Moreover, since the mixture fraction is also discretized by using the FM-PDF model, it is possible to obtain a set of moments for this scalar describing the mixing properties in the micro domain (i.e. at the subgrid level). In this respect, the FM-PDF model has been found quite efficient in comparison to full PDF methods by many authors [4, 5, 6].

In order to verify the implemented micromixing model, preliminary simulations have been performed based on three environments by using the same computational domain and model parameters as in [4]. Consequently, the obtained results are validated by the corresponding experimental and SMM-based numerical results presented in [4] (see Fig.1). The parameter α in the x-axis denotes the initial reactant concentration ratio (α = C_B0/C_A0) whereas the d₄₃ is related to the mean crystal size expressed in terms of third and fourth moments (µ₃ and µ₄) of the Crystal Size Distribution (CSD). The two cases in the experiments of [4] indicate two different configurations of the inlet streams through the inner and outer tubes. As can be seen in this figure, the implemented micromixing model reproduces well the reference data obtained from the literature. Here, it is worth noting that these RANS-based simulations have been performed in two dimensions with a standard k-ε turbulence model.

Figure 1. Validation of the implemented (three-environment) micromixing model with the corresponding reference experimental and numerical data obtained from literature.

In these preliminary simulations some parameters like variation of the activity coefficient [1], aggregation and breakage terms are ignored, as in [4]. Therefore, some discrepancies between the numerical and experimental results are observed. The more sophisticated and improved version of the model including these parameters will be validated and applied for different geometries and hydrodynamic conditions in the next step. In addition to these, a very recent and promising presumed-PDF method, the DQMOM-IEM model (IEM: Interaction by Exchange with the Mean), proposed by Wang and Fox [7] will also be implemented to describe more accurately micromixing and compared with the available numerical and experimental data.

References:

[1]       Öncül, A. A., Sundmacher, K., & Thévenin, D. Numerical investigation of the influence of the activity coefficient on barium sulphate crystallization. Chemical Engineering Science, 60:5395-5405, 2005.

[2]       Öncül, A. A., Sundmacher, K., Seidel-Morgenstern, A., & Thévenin, D. Numerical and analytical investigation of barium sulphate crystallization. Chemical Engineering Science, 61:652-664, 2006.

[3]       Marchisio, D. L., & Fox, R. O. Solution of population balance equations using the direct quadrature method of moments. Aerosol Science, 36:43-73, 2005.

[4]       Marchisio, D. L., Fox, R. O., Barresi, A. A., & Baldi, G. On the comparison between presumed and full PDF methods for turbulent precipitation. Industrial & Engineering Chemistry Research, 40:5132-5139, 2001.

[5]       Fox, R. O. On the relationship between Lagrangian micromixing models and computational fluid dynamics. Chemical Engineering and Processing, 37:521-535, 1998.

[6]       Fox, R. O. Computational models for turbulent reacting flows, Cambridge University Press, Cambridge-UK, 2003.

[7]       Wang, L., & Fox, R. O. Comparison of micromixing models for CFD simulation of nanoparticles formulation. AIChE Journal, 50:2217-2232, 2004.