Numerical Simulation of Pressure Fluctuations in a Large Francis Turbine Runner

The pressure fluctuation caused by unsteady flow in runner is one of the main reasons of vibration for a large Francis hydraulic turbine. It directly affects the steady operation of the hydraulic turbine unit. The existing research of the pressure fluctuation in hydraulic turbine mainly focuses on the unsteady flow in draft tube. Accurate distribution of pressure fluctuations inside a runner is not very clear. In this paper, the numerical method for predicting the pressure fluctuations in runner is investigated and the numerical simulation is performed for a large Francis hydraulic turbine. It is proved that the combination of shear-stress transport（SST） k-o） turbulence model and pressure-implicit with splitting of operators（PISO） algorithm could give more reliable prediction of pressure fluctuations in runner. The frequencies of pressure fluctuations in runner are affected by the flow in guide vane and the flow in draft tube The first dominant frequency is significantly determined by the flow in draft tube, especially at part load condition. This frequency is approximately equal to one-third of the runner rotating frequency. The evident second dominant frequency is exactly equal to the guide vane passing frequency. The peak-to-peak amplitudes of pressure fluctuations in runner at small guide vane open angle are larger than that at large open angle at the same operating head. The amplitudes at points on blade pressure surface are generally greater than that on suction surface. The research results could be used to direct the hydraulic design and operation stability improvement of a large Francis hydraulic turbine.

Carbon and nitrogen isotopes analysis and sources of organic matter in the upper reaches of the Chaobai River near Beijing,China

The carbon and nitrogen isotopes in the surface sediments,plants,and soil in the upper reaches of the Chaobai River have been researched.The results showed 27.75‰-21.58‰ and 1.32‰-6.74‰ for carbon and nitrogen isotopic ratios in the surface sediments,respectively.The sources of sedimentary organic matter in this area are soil organic matter,aquatic vascular plants,and riverine plankton,respectively,and a significant contributor to sediment in the Chaohe River,the Baihe River,and the Miyun Reservoir areas is soil organic matter.Furthermore,part of sedimentary organic matter in the Miyun Reservoir is attributed to the input from the Chaohe River and the Baihe River,the other is from C4 vegetation growing around individual point stations at the Miyun Reservoir.Compared with the situation in Hebei Province,the contribution of soil organic matter decreased significantly and river plankton and aquatic vascular plants increased significantly in Beijing municipal areas.This study reveals that the source of organic matter has a close relationship with the soil erosion.

Shape-free finite element method:The plane hybrid stress-function (HS-F) element method for anisotropic materials

The sensitivity problem to mesh distortion and the low accuracy problem of the stress solutions are two inherent difficulties in the finite element method.By applying the fundamental analytical solutions (in global Cartesian coordinates) to the Airy stress function of the anisotropic materials,8-and 12-node plane quadrilateral hybrid stress-function (HS-F) elements are successfully developed based on the principle of the minimum complementary energy.Numerical results show that the present new elements exhibit much better and more robust performance in both displacement and stress solutions than those obtained from other models.They can still perform very well even when the element shapes degenerate into a triangle and a concave quadrangle.It is also demonstrated that the proposed construction procedure is an effective way for developing shape-free finite element models which can completely overcome the sensitivity problem to mesh distortion and can produce highly accurate stress solutions.