| The rotating liquid film reactor is a new type of micro-chemical reactor consisting of two coaxial conical cylinders (frustum). The inner cone is a rotor and the outer one is a stator. The rotor can rotate at variable speed through adjustable speed motor. The gap between two conical cylinders can be adjusted by moving stator and is filled with reaction solution, which is, in general, an incompressible fluid. The rotating liquid film reactor (RLFR) has broad application in manufacturing nanomaterial. Experiment showed that the nanomaterials obtained using RLFR were smaller in particle size and narrower in particle size distributions than that prepared in conventional reactors. The experiment also showed that the precipitation process in the RLFR was strongly dependent on flow behavior and the chemical reactions. We have chosen the flow field in both RLFR and reverse RLFR as the main research object of this work.The effect of initial and boundary condition, as well as geometrical parameters of the RLFR on the flow pattern has been investigated using theoretical analysis and numerical simulation. Mathematical modeling for the reactor was carried out, and appropriate numerical simulation has been found. Comparison between the numerical results and experimental ones was made. The results of this research may provide guidance for further experimental study on preparation of nanomaterials in the RLFR.Firstly, a complete mathematical model for the flow in the rotating liquid film reactor was established. In order to reduce the dimension of the problem, a dimensional analysis was conducted on the system. Through dimensional analysis it is proved that the dimensionless quantity of pressure and velocity in the flow field is determined by parameters:Reynolds number Re, aspect ratio r, inclination angle θ and radius ratio η. In addition, the necessary and sufficient conditions for mechanical similarity has been obtained based on dimensionless analysis. The case of Γ12.5,θ=82° and η= 0.8 was selected to carry out the numerical simulation. The results showed that for small Reynolds numbers the flow was laminar and no Taylor vortex occurred. The flow became unstable at the largest radius, when the Reynolds number reached about 112.5, and the first Taylor vortex occurred. The gap was filled with six pairs of vortices at about Re=192.5. Increasing the aspect ratio to 25, the pairs of vortices in the gap increased from six to eleven, and the larger the aspect ratio, the greater the pressure and velocity in the flow field. In addition, the closer the inclination angle of the reactor to the right angle was, the more uniform the size of the vortex would be. If the inclination angle became smaller, the upper vortices would be larger than the bottom ones.An analytical solution of pressure distribution at small Reynolds numbers has been derived using pressure integration. It is found that the analytical results were well consistent with the numerical ones and the two results met better for a larger aspect ratio than for a smaller one. They agreed very well for the inclination angle close to the right angle. With increasing Reynolds number, the coincidence of the two results became worse. Owing to the influence of the no slip boundary at both end plate, the coincidence of the numerical and analytical solution is worse at the point near the upper and bottom.The streamline of the flow in the RLFR and the reverse RLFR were different due to different geometries. In the two reactors the basic flow became unstable at about Re= 112.5 and the first vortex occurred near the largest radius. With increasing the Reynolds number, new Taylor vortices were added towards the end of smaller radius and the gap was filled with vortices at approximately Re= 192.5.If the end plate at the top of the reverse RLFR bridged the gap only partly and the gap was connected to the gap of two coaxial rotating cylinders, in which the inner cylinder and the inner frustum rotated with same angular velocity, Wimmer found in the experiments that for the Reynolds number slightly greater than 192.5 the number of the vortices in the gap of reverse RLFR was no longer fixed and in pairs but periodic (alternating in odd and even). The numerical simulation reproduced the experimental phenomena. In addition, the article also continued to study the case of larger Reynolds number, which Wimmer’s experiments didn’t considered. The results showed that the period of vortex number alternating in odd and even increased with increasing Reynolds number and both the gap of two frustums and the gap of two cylinders were filled with vortices for Reynolds number of 300, the number of vortex no longer changed.The numerical investigation also found that the different acceleration of the inner frustum speed resulted in different flow behavior. For the dimensionless acceleration of the period of the vortex number in the gap was about 90 seconds, and the number of vortices was either 12 or 13; the period reached 148 seconds for and the number of the vortices was either 12,13 or 14. With an increase of the acceleration the period of the vortex number increased. These results were almost the same as Wimmer’s experimental results, which was analyzed using the definition of the Reynolds number.Finally, the instability boundaries of the flow in the RLFR for the inclination angles of 75°,80° and 85° were given by numerical simulation. The results showed that the flow in the RLFR was more likely unstable than that between cylinders, when the average radius of inner frustum and the outer one was equal to that of inner cylinder and the outer one, respectively. Moreover, the calculation also showed that the smaller the angle of inclination was, the easier the flow in the RLFR would become unstable. |
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