A numerical analysis of the hydrodynamic mixing characteristics of a rectangular versus a cylindrical mixing crystallizer tank for a membrane distillation apparatus

Abstract

A membrane distillation crystallization (MDC) experimental setup was designed, constructed and commissioned with rectangular mixing crystallizer tanks. The advantages and disadvantages of a rectangular mixing tank are compared to the traditional cylindrical mixing tank with baffling by means of a computational fluid dynamic (CFD) analysis in Ansys Fluent. The effect of tank configuration and geometry on the hydrodynamic and mixing characteristics for efficient momentum, solid suspension, heat and mass transfer were investigated. The hydrodynamic conditions in a crystallizer-mixing tank determine the quality of fluid mixing essential for optimal crystallization. Forty-five degree pitched blade turbines (PBT) were used to provide the agitation in the stainless steel rectangular jacketed tanks. Clear polycarbonate replicas of the rectangular tanks were manufactured to visually observe the mixing process in the tanks. Silica particles were used to represent the calcium carbonate crystals in the experiment. The data gathered from these experiments showed that the tanks should be operated between 600 to 750 rpm in the CFD simulations to simulate partial to complete suspension. In the numerical simulations a rectangular tank was compared to a cylindrical tank with baffling of the same volume. The partial differential equations solved in the numerical simulation were the conservation of mass (continuity), conservation of momentum and additional turbulence equations. In order to solve the turbulent fluid flow characteristics, the industry standard two-equation model, namely the K-epsilon model was used. This model was refined by the addition of the Wen-Yu drag model, the Simonin turbulent dissipation and the Simonin et al. turbulence interaction models. The RANS based RNG (k-ε), derived from the instantaneous Navier-Stokes equation was selected as the preferred model to analyse the hydrodynamic flow fields in the tanks. The 3D sliding mesh method was used to compute a time accurate solution. The Eulerian-granular multiphase model was used to predict the degree of solids suspension in the tanks. The efficiency of mixing within the tank was measured by the tank’s ability to keep the crystals in suspension and preventing any particle from settling at the bottom for more than 1-2 second(s). The mixing tanks were initially loaded with 5% v/v, which equates to a loaded height of approximately 10 mm. The simulations were done with the use of the volume fraction function to visually observe the cloud height and gauge the homogeneity and distribution of the particulates within the fluid flow fields. The results from the experimental setup were compared to the CFD simulations to qualify the use of CFD simulations for the comparison of the geometrically different tanks. Lastly, the findings from the CFD simulations were used to compare the tanks and determine if the rectangular tank built for the MDC experiment perform satisfactorily to replace a standard cylindrical tank with baffling for this application.