(70c) Characteristics of Fluid Deformation Induced By a Rotationally Reciprocating Impeller

Although poorly mixed regions or stagnant regions in a mixing vessel are avoidable in turbulent mixing condition due to velocity field fluctuation, effective mixing performance is achieved by an intentional change in velocity field or unsteady flow field even at a laminar mixing condition. For example, some researchers already have reported that the mixing operation with periodic changes in rotational speed or rotational direction improved mixing performance. However, most of them have employed the impeller motion with comparatively high rotational speed and long period of operational condition change. Therefore, unsteady velocity field appeared only in the moment around the operational condition change and the unsteady impeller operation will not play significant role on the enhancement of overall mixing is relatively small. On the contrary, the impeller motion with continuous change in rotational speed from negative to positive has a possibility to make the most of unsteady velocity field for improving mixing performance. In this study, this mixing operation was named “rotationally reciprocating mixing” after the impeller motion with rotating back and forth. Since the mixing process with unsteady velocity field is usually three dimensional and complicated, it is difficult to describe the mixing mechanism induced by the unsteady velocity field. Therefore, we have firstly chosen two-dimensional mixing process in r-qplane of a cylindrical vessel in order to neglect the effect of vertical fluid motion on the mixing mechanism. Since Inoue reported that a streak line should be a template of laminar mixing process (Inoue et al, 1999,2000), streak line was numerically and experimentally visualized in this study to elucidate the mixing process.

   In our previous study, we have already experimentally and numerically clarified that the rotationally reciprocating plate impeller generates several pairs of vortices in the r-qplane of the cylindrical vessel and realizes an excellent fluid deformation process especially at the reciprocating condition of large amplitude and long period (Komoda et al, 2012). These vortices alternately generate suction and discharge flows in radial direction. A fluid lump was dragged inward due to the suction flows and then pushed outward due to the discharge flow. Therefore, a fluid lump is effectively transported in radial direction in spite of rotational impeller motion. Additionally, a fluid lump discharged from the impeller tip was effectively stretched behind the impeller plate and then folded due to the inverse motion of fluid flow after the impeller counterturn. The mixing process was clearly observed by the development of streak line. As a result, we found that the vortex generated plays a significant role on the deformation and transportation of fluid in a mixing vessel.

   In the case of a typical unidirectional rotational impeller, various characteristics in the mixing process are characterized by mixing Reynolds number. At the condition of the same dimensions of mixing equipment with the same test fluid, the rotational speed becomes the only one parameter which affects the mixing process. Similarly, in the rotationally reciprocating impeller, the mixing process should be drastically changed with reciprocating period. At least, the flow regime must be changed from laminar to turbulent with the decrease in reciprocating period, and the mixing mechanism must change as well. Therefore, in the present study, we have investigated the two-dimensional fluid deformation process in a cylindrical vessel induced by a plate impeller rotationally reciprocating at different period from the view point of experimental visualization and numerical simulation.

Firstly, we have experimentally visualized the development of streak line. A flat-bottomed cylindrical vessel made of transparent acrylic resin having the inner diameter of 0.08 m was filled with an aqueous starch solution with the liquid height of 0.07 m. Flat plate impeller having the width of 0.06 m and the height of 0.08 m was rotated back and forth at the center of the vessel just above the bottom. Since the impeller height is larger than the liquid height, the velocity field can be considered as 2-dimensional in the r-θ plane far above the vessel bottom. The impeller motion was preciously controlled by a stepping motor via a mixing shaft (o.d. = 8 mm). The orientation of the impeller is expressed by j = A [1-cos(2πt/T)], where A and T represent the amplitude and period of rotational reciprocation of the impeller. In this study, the reciprocating amplitude was constant at π/2 where the impeller sweeping region corresponds to a circle, and the reciprocating periods were 0.5, 1, 2, 4s. The density and viscosity of the aqueous starch solution used were 1220 kg/m³ and 0.1 Pa∙s, respectively. After attaining periodically stable velocity field by reciprocating the impeller for several cycles, we have started injecting the tracer fluid, which is the starch solution containing a fluorescent dye (Rhodamine B), into the starch solution in the mixing vessel at the point 1 cm below the liquid surface and 8 mm from the vessel wall. By using a planar laser light source (532nm), the track of the tracer fluid in the r-θcross-section was visualized. The streak line thus obtained was observed from the vessel bottom via a mirror.

We also have numerically carried out the visualization of streak line under the same reciprocating condition with experiments. Periodically stable sets of 2-dimensinal velocity fields in the r-qplane have been obtained for each reciprocating condition under laminar flow regime using CFD software RFLOW. Tracer particles put at the tracer injection point one after another for each calculation time step, and then they were moved according to the corresponding velocity field. In the course of the calculation, another tracer particles were inserted at the middle point of two tracer particles in case of too large particle separation in order to obtain smoothly deformed streak lines, which can be drawn by connecting all adjacent tracer particles.

   In the velocity profile obtained in CFD simulation, the generation of vortices behind the impeller tip just after the impeller counterturn still has been observed for each reciprocating period investigated. However, the development process of the vortices significantly differed with reciprocating condition. At the short reciprocating periods of T = 0.5 and 1s, the shape of vortices deformed in circumferential direction, their center were released from the impeller tip, and they remained at the next impeller counterturn. At the period longer than 2s, the vortices have already disappeared at the next impeller counterturn and their center always stayed at the impeller tip at the longest period condition.

After the start of tracer fluid injection at t= 0, the development of the streak line was observed by means of experimental and numerical methods. As already reported, the tracer fluid was dragged inward and then strethced along the vessel wall at the case of T = 2s. As a result, the corss sectional area of the vessel was almost filled with the deformed streak line because the streak line was effectively stretched and folded due to developed vortices. However, the central region near the mixing shaft remained without the instrusion of streak line because the fluid lump near the shaft stretched along the impeller plate but eventually pushed outward from the impeller tip after many cycles of reciprocation. At a shorter period of T = 1s, the deformation of the streak line proceed rapidly but was similar to that of T = 2s with the generation of poor mixing regions. On the other hand, at the longest period of T = 4s, the streak line was mainly stretched and folded along the vessel wall around the impeller tip because vortices were not separate from the impeller tip. The characteristic behavior of the deformed streak line has been successfully expressed in the numerical simulation at the period longer than 1s. However, at the shortest period of T = 0.5s, the definitely different deformed streak lines were obtained in numerical and experimental observations. The numerical streak line was still similar to that at T = 1s and 2s, and poor mixing regions remained near the shaft. In the experiment, however, the streak line was initially stretched and folded in the similar manner with numerical simulation but was observed to be split into several deformed streak lines. As the small deformed streak lines spread all over the vessel, poor mixing regions were disappeared. Additionally, a regular deformation of stretching and folding of streak line have not been performed anymore. That is to say, the velocity field contained terrible fluctuation and showed three-dimensionality. From these experimental results, turbulent flow was generated in the mixing vessel at this condition and the velocity field obtained in CFD simulation under a laminar flow condition is not appropriate.

At the condition of equipment dimensions and fluid properties investigated in this study, a significant enhancement in fluid deformation and an elimination of poor mixing regions have not been achieved as far as in a laminar flow condition. Additionally, at the longest reciprocating period, the fluid deformation was localized around the impeller tip. On the other hand, under a turbulent flow regime at the shortest reciprocating period, poor mixing regions immediately disappeared.