This paper introduces the 3D numerical simulation of unsteady turbulent flow in the entire flow passage of a Francis turbine with computational fluid dynamics (CFD) technology. The boundary conditions have been implemented based on the 3D averaged Navier-Stokes equations. The governing equations are discreted on space by the finite volume method and on time step by the finite difference method. The 3D unsteady turbulent flow in an entire Francis turbine model is calculated successfully using the CFX-TASCflow software and RNG k-ε turbulence model. Transient flow fields are simulated in the spiral case, the distributor, the runner, and the draft tube for the optimum operating condition. Meanwhile, the velocity and pressure at any points in the flow fields can be obtained so as to provide the great value on the performance prediction. By means of the numerical simulation in a flow field, it is verified that every component in a Francis turbine model is designed reasonably. The basis for the further researches on hydraulic turbines is also built.

The vortex structure of two-dimensional flow in a cavity is calculated using the differential quadrature method. The numerical simulation focuses on investigating the effects of Reynolds number on vortex structure evolution of the flow in a square cavity with two opposite and equal speed moving lids. The streamline patterns and bifurcation diagrams are determined. The numerical results show that the flow in the cavity takes on the streamline pattern of completely symmetric vortex structure when the Reynolds number approaches zero. With the Reynolds number increasing, the sizes and center positions of the sub-vortexes appear to be affected, whereas the saddle point is still located at the cavity center, resulting in a skewed flow pattern in the cavity. It is observed that one large vortex occupies the entire cavity and the shape of the large vortex becomes more circular after a critical value of the Reynolds number is exceeded. If the Reynolds number is increased further, two secondary eddies emerge simultaneously on the upper left corner and the lower right corner near the sidewalls. The center of the large vortex is invariably located at the cavity centre. For different Reynolds numbers, the streamline patterns are symmetric about the cavity center which is always a stagnation point.

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According to indicators’ information repetition and subjectivity of the indicators’ weight set during the variable fuzzy comprehensive evaluation, Principal Component analysis can help solve the weight of the relative indicators and reduce comprehensive evaluation dimensions of the variable fussy comprehensive evaluation. This paper has made a comprehensive evaluation of the status quo of Yunnan’s low carbon economy development(2005-2009), which turns out to be more practical compared with the mere variable fussy theory analysis, thus, principal component-variable fuzzy evaluation is a kind of feasible way to analyze the regional low carbon development status.

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