In this paper, we consider the existence of least energy nodal solution and ground state solution, energy doubling property for the following fractional critical problemwhere k is a positive parameter, L K stands for a nonlocal fractional operator which is defined with the kernel function K. By using the nodal Nehari manifold method, we obtain a least energy nodal solution u and a ground state solution v to this problem when k 1, where the nonlinear function f : R 3 × R → R is a Carathéodory function.
The flow distribution and mixing performance of the laminar flow in the PBT impeller-stirred tank were investigated in this study. The variation along with mixing time of the flow distribution and concentration at the selected positions was visualized by means of the CFD and experiment methods. The CFD simulations results had a good agreement with the experimental results. In order to minish the Segregated Regions, the PBT impeller was optimally designed by means of orthogonal factorial experiment with selecting the θ 99 mixing time as evaluation criteria. With the aim to increase the mixing efficiency, the optimal design results were obtained with the geometrical parameters of impeller diameter of 0.084 m, discharge angle of 45º, blade width of 0.018 m, and clearance of 0.05 m, and the mixing time of the optimal impeller-stirred flow was about 180 s, so this optimal design PBT impeller is more proper for the agricultural industries.
The flow distribution and mixing performance of the laminar flow in the PBT impeller-stirred tank were investigated in this study. The variation along with mixing time of the flow distribution and concentration at the selected positions was visualized by means of the CFD and experiment methods. The CFD simulations results had a good agreement with the experimental results. In order to minish the Segregated Regions, the PBT impeller was optimally designed by means of orthogonal factorial experiment with selecting the θ 99 mixing time as evaluation criteria. With the aim to increase the mixing efficiency, the optimal design results were obtained with the geometrical parameters of impeller diameter of 0.084 m, discharge angle of 45º, blade width of 0.018 m, and clearance of 0.05 m, and the mixing time of the optimal impeller-stirred flow was about 180 s, so this optimal design PBT impeller is more proper for the agricultural industries.
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