ТЕОРЕТИЧЕСКИЕ ОСНОВЫ ХИМИЧЕСКОЙ ТЕХНОЛОГИИ, 2013, том 47, № 4, с. 410-421
УДК 66.011
COMPARISON OF FLOW PATTERNS OF DUAL RUSHTON
AND CD-6 IMPELLERS © 2013 г. T. T. Devi, B. Kumar
Indian Institute of Technology, Guwahati, India bimk@iitg.ernet.in Received 06.02.2012
The flow patterns (parallel, merging and diverging) of dual CD-6 impeller has been modeled using computational fluid dynamics simulation in FLUENT software compared with dual Rushton impeller. Simulated results have been verified with experimental observations on Rushton impeller. Comparison of simulated and experimental results of Rushton impeller has been observed similar flow patterns, whereas CD-6 impeller exhibits different flow pattern from the Rushton impeller in merging flow pattern. Analysis has shown that formation of flow patterns of Rushton impeller and CD-6 impeller is different in the case of merging flow pattern.
DOI: 10.7868/S0040357113040040
INTRODUCTION
Mixing tanks are extensively used in the industrial process to carry out many different operations like dispersion of gases, suspension of solids, heat transfer, chemical reactions and blending of miscible liquid. The efficiency of these operations is greatly influenced by the flow characteristics developed inside by the rotating component of mixing tanks (impellers). The study of the hydrodynamics of the turbulent flows field generated in stirred vessels makes possible to improve the performances of the agitators and the vessels by the development of the geometrical and operational conditions [1]. Several designs of impellers are available based on shape of blades and their operating conditions to achieve different mixing operations producing different flow patterns. The formation of flow patterns is caused by the interaction of recirculating turbulent flow produced by the periodic movements of impellers with the stationary tank walls and baffles. These flow patterns are very complex and highly swirling in nature. Complex flow pattern with strong swirling nature is the indication of proper mixing in case of dispersion of gases, breaking down of solids into liquids, blending of miscible liquids, etc. The number of impellers used and their types made variation in the characteristics of flow patterns. Dual impellers are more efficient than the single impeller as the flow pattern generated by dual impeller is stronger and swirling in nature than the flow pattern produced by single impeller. Shape and size of the impeller blades have a profound impact on the generated flow. The other parameters like impeller clearance, proximity of the vessels walls, baffle can also dramatically affect the generated flow [2]. Use of dual impeller is common where the tall mixing tanks
are to be adopted in process industries. In this situation single impeller is not able to generate uniform mixing throughout the entire vessel; it requires two or more impellers mounted with their specific intervals. Because of this impeller spacing and their clear off distances from the bottom and top of the tank, the nature of flow characteristics is also different. The discharge flow of the impeller is characterized by the formation of coherent vortex structures induced by the blade motion and called trailing vortex [3]. The formation of trailing vortex is common in disc blade shape Rushton impeller in both the cases of singular and doubles impeller, one above the blade and another behind the blade. These different fluid characteristics generated in case of dual Rushton impellers are stable and also define as parallel, merging and diverging flow depending upon the off-bottom clearance of lower impeller and spacing between two impellers. Other type of impeller like CD-6 impeller has concave blade shape and study on this type of impeller is found very less in literature. Gimbun et al. [4] studied single Rushton and CD-6 impeller for modeling of mass transfer in gasliquid stirred tanks and found that CD-6 impeller is more efficient than the Rushton impeller. The comparison of Rushton and CD-6 impeller was performed by Devi and Kumar [5] in singular impeller; analyzed the flow hydrodynamics (mean velocity, turbulent kinetic energy and dissipation rate) produced by these two impellers and observed more efficiency in case of CD-6 impeller. Many studies have been done on same combination of dual impeller systems with Rushton impeller [6-12]. Some few studies based on different combination of dual impeller systems were also performed like by Bouaif and Roustan [13], Ja-
Combinations of flow patterns with different axial height and corresponding grid sizes
Case Flow Sb S2> S3 Rushton impeller CD-6 impeller
pattern cells faces nodes cells faces nodes
1 Parallel 51 = 0.407" 52 = 0.487 53 = 0.67 261687 548485 56260 468833 1016420 125575
2 Merging 51 = 0.407 52 = 0.3157 53 = 0.67 225507 469592 46369 443088 961011 118745
3 Diverging = 0.157 52 = 0.407 53 = 0.857 231140 481855 47956 459177 984254 113683
hoda et al. [14] and Woziwodzki and Jedrzejczak [15] with Pitched blade turbine and a standard Rushton turbine. And it has also been verified by many researchers that using impeller more than one gives more enhancing efficiency in the performance of stirred tanks. The multiple impeller system provides better gas utilization, higher interfacial area and narrower residence time distribution in the flow system compared to a single impeller system [8].
The numerical simulation (computational fluid dynamics) for modeling of the flow generated by the impellers inside the mixing tank under different governing parameters is increasing day by day because of the flexibility of this technique. An advantage of computational fluid dynamics (CFD) based methods is that the fundamental equations governing fluid flow are solved and thus the scaling up and scaling down problems are eliminated [14]. In CFD simulation, the main governing equations are the well known continuity and momentum equation. It is purely based on numerical solutions governing certain parameters like turbulence model (three families of k—s; large eddy simulation (LES); Reynolds stress model (RSM)), impeller model (multiple reference frame model (MRF); sliding mesh (SM); rotating model, snapshot model), discretization schemes (upwind, power law, quadratic upstream interpolation for convective kinematics (QUICK), etc.), grid sizes and convergence criteria. The success story of CFD simulation in the studies of stirred tanks is long list including the study done by Yapici et al. [16] to investigate the effects of type of impeller on flow characteristics with LES turbulence model and found good agreement with experimental results. Study based on the parameters of CFD simulation was performed by Deglon and Meyer [17] and defined the suitable grid, turbulence model and discretization schemes. Aubin et al. [18] also per-
formed CFD simulation based on modeling approach, turbulence model and numerical scheme.
The main objective of this study is to characterize and compare the numerically predicted flow patterns of dual CD-6 and Rushton impellers at different impeller spacing. Later these numerically predicted results are being verified with the experimental results of Chunmei et al. [7]. To assess the ability of CFD to represent the trailing vortices generated by Rushton impeller is also one of the main aims of this study.
MODEL GEOMETRY
The geometry of mixing tank simulated in this study is taken same with the dimensions of Chunmei et al. [7]. The clear off distances have been made same with their study to get the three stable flow patterns, i.e., parallel, merging and diverging. The axial height of lower impeller from tank bottom is denoted by S^ spacing between two impellers is by S2 and distance ofup-per impeller from top open tank is by S3. Figure 1 shows
(a) geometric dimensions of stirred tanks with notations,
(b) the grid of full tank ofRushton impeller and (c) CD-6 impeller. The diameters of tank T and impeller d are 48 and 19 cm, respectively, at the speed of 66.6 rpm. Working fluid is water at 20°C (p = 998.2 kg/m3; | = = 0.001003 Pa s) filled up to the height H of 1.4T (67 cm). In this study, three cases have been considered based on the combinations of S1, S2 and S3 (table). In Figs. 1b and 1c, the difference of Rushton impeller from CD-6 impeller can be revealed as in Rush-ton impeller, the blades are in straight manner; however, in CD-6 impeller, the shape of the blade is concave.
The size of grid generated in terms of cells, faces and nodes for each combination of impeller spacings is presented in table. In the generated grid of Rushton and CD-6 impeller, the area of impeller region is high-
Fig. 1. (a) Geometry of stirred tank used in this model; unstructured grid generated for full tank mounted by (b) Rushton and (c) CD-6 impellers.
er in the case of CD-6 impeller. This impeller region is the most efficient region of the whole part of stirred tank where the movements of fluid particles are significantly higher than the other regions of stirred tank. The sizes of grid for different flow patterns are different in both the cases of Rushton and CD-6 impellers. The number of cells, faces and nodes for CD-6 impeller is almost double from the Rushton impeller.
NUMERICAL MODELING
In numerical modeling of CFD simulation, certain parameters are involved as governing equations, turbulence model, impeller model, discretization scheme, etc. These parameters are discussed in brief in the following sections.
Governing equations. The basic equation in numerical simulation is continuity and momentum equation. Theoretical predictions were obtained by solving the two equations, e.g., conservation of mass and conservation of momentum (Reynolds-averaged Navier— Stokes equations) simultaneously.
The continuity equation is a statement of conservation of mass and is given as
+ (PU) = 0,
dt dxI
(1)
where U is the /th component of the fluid velocit
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