Abstract
Context. The problem of mass transfer of a cylindrical body with a uniform translational flow of a viscous incompressible fluid is examined in the paper. Objective. The purpose of this work is to develop a new method for numerical analysis of the problem of mass transfer of a cylindrical body with a uniform translational flow, which based on the joint application of the R-functions structural method and the Galerkin projection method. Method. In general case, the problem of stationary mass transfer of a cylindrical body with a viscous incompressible fluid flow is reduced to the solution of the equation of hydrodynamic flow passing a surface and an equation for concentration with corresponding boundary conditions on the surface of the body and far away from it. The geometry of the area, and also the boundary conditions (including the condition at infinity) may be taken into account precisely by using the constructive apparatus of the R-functions theory by V. L. Rvachev, the Academician of Ukrainian National Academy of Sciences. In this study, a complete structure of the solution of a linear boundary value problem for the concentration that exactly satisfies the boundary conditions on the boundary and condition at infinity is constructed on the basis of the R-functions theory methods, and this made it possible to lead the tasks in the infinite domain to tasks in the finite domain. To solve the linear problem for concentration the numerical algorithm on the basis of Galerkin method is developed. Results. The computational experiment for the problem of the flow past circular and elliptical cylinders at various Reynolds and Peclet numbers was carried out. Conclusions. The conducted experiments have confirmed the efficiency of the proposed method of numerical analysis of the problem of mass transfer of a cylindrical body with a uniform translational flow, based on the joint application of the R-functions structural method and Galerkin projection method. The prospects for the further research may be to use the developed method for the implementation of iterative methods for solving the task of nonlinear mass transfer, semi-discrete and projection methods for solving the non-stationary tasks, as well as in solving the tasks of optimal management of relevant technological processes.
Highlights
The problems of calculating viscous flows, which are complicated by mass transfer, are widely used in heat power engineering, chemical and food technologies, geo- and astrophysical studies, and environmental protection
The conducted experiments have confirmed the efficiency of the proposed method of numerical analysis of the problem of mass transfer of a cylindrical body with a uniform translational flow, based on the joint application of the R-functions structural method and Galerkin projection method
The development of new, as well as the improvement of existing methods of mathematical modeling and numerical analysis of external stationary problems of hydrodynamics of a viscous incompressible fluid, which take into consideration the mass transfer, is an actual scientific issue
Summary
The problems of calculating viscous flows, which are complicated by mass transfer, are widely used in heat power engineering, chemical and food technologies, geo- and astrophysical studies, and environmental protection. The laws of hydrodynamics, heat and mass transfer are essential for the entire technological process. Processes of heat and mass transfer are ones of the most important in the energy sector, as well as in a number of the technological processes in the metallurgical and other industries. The problems of mass transfer of bodies with a uniform viscous flow underlie the calculation of many technological processes, which are associated with dissolution, extraction, evaporation, precipitation of colloids, etc. The development of new, as well as the improvement of existing methods of mathematical modeling and numerical analysis of external stationary problems of hydrodynamics of a viscous incompressible fluid, which take into consideration the mass transfer, is an actual scientific issue
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