scholarly journals STOCHASTIC VORTEX BLOBS METHOD TO STUDY AXISYMMETRIC FLOWS OF INCOMPRESSIBLE VISCOUS FLUID

2016 ◽  
Vol 12 (10) ◽  
pp. 6739-6750
Author(s):  
M. R Hedar ◽  
R. S Kamel
Keyword(s):  
Viscous Fluid ◽  
Legendre Polynomials ◽  
Vortex Method ◽  
Stochastic Equations ◽  
Velocity Fields ◽  
Boundary Integral ◽  
Incompressible Viscous Fluid ◽  
Two Dimensional ◽  
Complete Elliptic Integrals ◽  
Total Velocity

This paper presents the mathematical and computational formulations of the stochastic Vortex Blobs Method (VBM). It isshow that how the method can be used to cover axisymmetric flows of incompressible viscous fluid. Also, the initialboundary problem is solved by using the Lagrangian vortex method. This method seems to be an extension of the well known two dimensional vortex blob method. When applying and extending this method two steps are required. First, wehave to design an axisymmetric vorticity carrier by using the standard functions as complete elliptic integrals and Legendre polynomials. Second, it is necessary to formulate the appropriate Neumann problem and boundary integral equation to find the potential velocity fields. Both steps are used to describe and compute the total velocity field and formulate the Ito stochastic equations which describing the motion of vorticity carriers.

scholarly journals Two-dimensional convection of an incompressible viscous fluid with the heat exchange on the free border

2016 ◽  
Vol 20 (3) ◽  
pp. 567-577 ◽  
Author(s):  
Svetlana Sergeevna Vlasova ◽  
Eugenii Yurevich Prosviryakov
Keyword(s):  
Heat Exchange ◽  
Viscous Fluid ◽  
Incompressible Viscous Fluid ◽  
Two Dimensional

Найдено точное стационарное решение краевой задачи, описывающее конвективное движение вязкой несжимаемой жидкости в плоском слое при квадратичном нагреве свободной поверхности в приближение Стокса. Линеаризация уравнений Обербека-Буссинеска позволяет описать движение жидкости в точках экстремумов давления и температуры. Выведено условие, при котором наблюдается противотечение (два встречных потока) в жидкости. При наличии застойной точки в жидкости наблюдается шесть незамкнутых вихрей.

scholarly journals A Fast Two-Dimensional Numerical Method for the Wake Simulation of a Vertical Axis Wind Turbine

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 49
Author(s):  
Zheng Yuan ◽  
Jin Jiang ◽  
Jun Zang ◽  
Qihu Sheng ◽  
Ke Sun ◽  
...  
Keyword(s):  
Velocity Distribution ◽  
Numerical Method ◽  
Three Dimensional ◽  
Particle Method ◽  
Vortex Method ◽  
Vertical Axis ◽  
Two Dimensional ◽  
Vertical Axis Wind Turbine ◽  
Wake Effect ◽  
Array Design

In the array design of the vertical axis wind turbines (VAWT), the wake effect of the upstream VAWT on the downstream VAWT needs to be considered. In order to simulate the velocity distribution of a VAWT wake rapidly, a new two-dimensional numerical method is proposed, which can make the array design easier and faster. In this new approach, the finite vortex method and vortex particle method are combined to simulate the generation and evolution of the vortex, respectively, the fast multipole method (FMM) is used to accelerate the calculation. Based on a characteristic of the VAWT wake, that is, the velocity distribution can be fitted into a power-law function, a new correction model is introduced to correct the three-dimensional effect of the VAWT wake. Finally, the simulation results can be approximated to the published experimental results in the first-order. As a new numerical method to simulate the complex VAWT wake, this paper proves the feasibility of the method and makes a preliminary validation. This method is not used to simulate the complex three-dimensional turbulent evolution but to simulate the velocity distribution quickly and relatively accurately, which meets the requirement for rapid simulation in the preliminary array design.

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