On the Coupled of NBEM and CFEM for an Anisotropic Quasilinear Problem in an Unbounded Domain with a Concave Angle

In this paper, based on the Kirchhoff transformation and the natural boundary element method, a coupled natural boundary element and curved edge finite element is applied to solve the anisotropic quasi-linear problem in an unbounded domain with a concave angle. By using the principle of the natural boundary reduction, we obtain the natural integral equation on the artificial boundary of circular arc boundary, and get the coupled variational problem and its numerical method. Then the error and convergence of coupling solution are analyzed. Finally, some numerical examples are verified to show the feasibility of our method.

Experimental study on gas–liquid dispersion and mass transfer in shear-thinning system with coaxial mixer

The effects of impeller type, stirring power, gas flow rate, and liquid concentration on the gas–liquid mixing in a shear-thinning system with a coaxial mixer were investigated by experiment, and the overall gas holdup, relative power demand, and volumetric mass transfer coefficient under different conditions were compared. The results show that, the increasing stirring power or gas flow rate is beneficial in promoting the overall gas holdup and volumetric mass transfer coefficient, while the increasing system viscosity weakens the mass transfer in a shearing–thinning system. Among the three turbines, the six curved-blade disc turbine(BDT-6) exhibits the best gas pumping capacity; the six 45° pitched-blade disc turbine(PBDT-6) has the highest volumetric mass transfer coefficient at the same unit volume power.

On the Coupled of NBEM and FEM for an Anisotropic Quasilinear Problem in Elongated Domains

In this paper, based on the Kirchhoff transformation, the coupling of natural boundary element method and finite element method are discussed for solving exterior anisotropic quasilinear problems with elliptic artificial boundary. By the principle of the natural boundary reduction, we obtain natural integral equation on elliptic artificial boundaries, the coupled variational problem and its numerical method. Moreover, the convergence and error estimate of the approximate solutions are obtained. Finally, some numerical examples are presented to illuminate the feasibility of the method.

Numerical study on solid suspension characteristics of a coaxial mixer in viscous systems

A coaxial mixer consisting of an anchor and a Rushton turbine was selected as the research object,whose solid suspension characteristics were studied with the help of Computational Fluid Dynamics(CFD)method.Based on the Eulerian–Eulerian method and modified Brucato drag model,the just-suspension speed of impeller was predicted,and the simulation results were in good agreement with the experimental data.The quality of solid suspension under different rotation modes was also compared,and the results showed the coaxial mixer operating under co-rotation mode could get the best performance,and a larger anchor speed was beneficial to solid suspension by enhancing the turbulent intensity at the bottom.Compared with the anchor,the inner Rushton turbine played a dominant role in solid suspension due to its high rotational speed,whereas an extremely high inner impeller speed would make the uniformity of solid distributions become worse.Additionally,the effects of solid phase properties were also investigated,the results revealed that the higher the overall solid volume fraction and the smaller the Shields number,the worse the performance of solid suspension,meanwhile the solid suspension was more susceptible to solid density compared with particle diameter within the same Shields number gradient.

Differential Transform Method for Some Delay Differential Equations

This paper concentrates on the differential transform method (DTM) to solve some delay differential equations (DDEs). Based on the method of steps for DDEs and using the computer algebra system Mathematica, we successfully apply DTM to find the analytic solution to some DDEs, including a neural delay differential equation. The results confirm the feasibility and efficiency of DTM.

THE COUPLING OF NBEM AND FEM FOR QUASILINEAR PROBLEMS IN A BOUNDED OR UNBOUNDED DOMAIN WITH A CONCAVE ANGLE

Based on the Kirchhoff transformation and the natural boundary element method, we investigate a coupled natural boundary element method and finite element method for quasi-linear problems in a bounded or unbounded domain with a concave angle. By the principle of the natural boundary reduction, we obtain natural integral equation on circular arc artificial boundaries, and get the coupled variational problem and its numerical method. Moreover, the convergence of approximate solutions and error estimates are obtained. Finally, some numerical examples are presented to show the feasibility of our method. Our work can be viewed as an extension of the existing work of H.D. Han et al..