Li Xiang Zhang

SPH simulation of free overfall in open channels with even and uneven bottom

The free overfall can be used as a simple and accurate device for flow measurement in open channels. In the past, the solution to this problem was found mainly through simplified theoretical expressions or on the basis of experimental data. In this paper, using the meshless smoothed particle hydrodynamics (SPH) method, the free overfall in open channels with even and uneven bottom is investigated. For the even bottom case, subcritical, critical and supercritical flows are simulated. For the uneven bottom case, supercritical flows with different Froude numbers are considered. The free surface profiles are predicted and compared with theoretical and experimental solutions in literature and good agreements are obtained.

Numerical Simulation of Blade Channel Vortex in a Low Head Francis Turbine

The paper presents numerical simulation of blade channel vortex in a low head Francis turbine using OpenFoam code. A mixture assumption and a finite rate mass transfer model were introduced to analyze blade channel vortex. The finite volume method is used to solve the governing equations of the mixture model and the pressure-velocity coupling is handled via a Pressure Implicit with Splitting of Operators (PISO) procedure. Simulation results have shown that using cavitation model to analyze blade channel vortex is very effective.

Numerical Prediction of Sediment Erosion on Francis Turbine Blades

The paper presents the numerical prediction of sediment erosion on Francis turbine blades using CFD code. The 3-D turbulent particulate-liquid two-phase flow equations are employed in this study. The computing domain is discretized with a full three-dimensional mesh system of unstructured tetrahedral shapes. The finite volume method is used to solve the governing equations and the pressure-velocity coupling is handled via a Pressure Implicit with Splitting of Operators (PISO) procedure. Simulation results have shown that the sand erosion rate on pressure side is more than on the suction side of the blade. The numerical simulation results are consistent with the real situation.

Numerical Analysis of Erosive Wear on the Guide Vanes of a Francis Turbine

The paper presents the numerical analysis of erosive wear on the guide vanes of a Francis turbine using CFD code. The 3-D turbulent particulate-liquid two-phase flow equations are employed in this study. The computing domain is discretized with a full three-dimensional mesh system of unstructured tetrahedral shapes. The finite volume method is used to solve the governing equations and the pressure-velocity coupling is handled via a Pressure Implicit with Splitting of Operators (PISO) procedure. Simulation results have shown that the volume fraction of sand at the top of the guide vanes is higher than others and the maximum of volume fraction of sand is at same location with the maximum of sand erosion rate density. The erosive wear is more serious at the top of the guide vanes.

An Investigation of the Vortex in a Submersible Axial Flow Pump Impeller

The paper presents numerical simulation of the vortex in a submersible axial flow pump impeller using OpenFoam code. A mixture assumption and a finite rate mass transfer model were introduced to analyze vortex. The finite volume method is used to solve the governing equations of the mixture model and the pressure-velocity coupling is handled via a Pressure Implicit with Splitting of Operators (PISO) procedure. Simulation results have shown that the cavitation may occur on the lower portion of impeller suction side. And the blade channel vortex will be formed in the impeller. It can induce the pressure pulsation in the impeller and can result in reduced efficiency of the submersible axial flow pump.

A Posterior Model Reduction Method Based on Weighted Residue for Linear Partial Differential Equations

This paper is concerned with a new model reduced method based on optimal large truncated low-dimensional dynamical system, by which the solution of linear partial differential equation (PDE) is able to be approximate with highly accuracy. The method proposed is based on the weighted residue of PDE under consideration, and the weighted residue is used as an alternative optimal control condition (POT-WR) while solving the PDE. A set of bases is constructed to describe a dynamical system required in case. The Lagrangian multiplier is introduced to eliminate the constraints of the Galerkin projection equation, and the penalty function is used to remove the orthogonal constraint. According to the extreme principle, a set of the ordinary differential equations is obtained by taking the variational operation on generalized optimal function. A conjugate gradients algorithm on FORTRAN code is developed to solve these ordinary differential equations with Fourier polynomials as the initial bases for iterations. The heat transfer equation under a potential initial condition is used to verify the method proposed. Good agreement between the simulations and the analytical solutions of example was obtained, indicating that the POT-WR method presented in this paper provides the most effective posterior way of capturing the dominant characteristics of an infinite-dimensional dynamical system with only finitely few bases.

Effects of Reynolds Number on Vortex Structure Evolution in a Square Cavity with Two Opposite Moving Lids

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.

Study on Vortex Evolution Processes of Transient Driven Flow in a Square Cavity

The transient vortex structure evolution process of two-dimensional flow in a driven square cavity with one moving end was studied. The time curves of flow field variables, the flow patterns of different specific moments and the required times of flow field from static to statistical steady state were comparatively analyzed for different Reynolds numbers. Transient simulating results show that the nascent vortices always appear near the boundaries in the initial driving stage, then gradually move away from the boundaries to form a large vortex almost occupying entire cavity and two secondary vortices in left and right corners of the cavity bottom. The greater the Reynolds numbers, the longer the required times of the flow field reaching by the statistical steady state, also, the more complex of the vortex structure evolution.

Simulation of 3-D Unsteady Flows in a Tubular Hydro-Turbine on DES

Taking a hydropower station as the research object, the establishment of a numerical model that contains the full passage Tubular Turbine is given. Based on the transient incompressible N-S equations, a three-dimensional unsteady flow research is conducted. Numerical simulation of steady turbulent flow channel is calculated as the initial condition, the detached eddy simulation (DES) and slip grid technology are adopted to simulate the static-dynamic interference in the unsteady turbulent flow, The instantaneous pressure distribution in full channel and vorticity distribution of the representive section are obtained, so the three-dimensional transient vortex structures in full flow channel of the hydraulic turbine are captured. These studies aiming to explore the mechanism for the formation of vortex-induced vibration of hydro-turbine are valuable for the engineering reference.

Effects of Weakly Compressibility on Propagating Properties of Water Hammer in a Long Pipe

This paper is concerned with propagating features of pressure waves induced by water hammer in a long liquid-conveyed pipe subjected to hyper high water head. Effects of dynamically weak compressibility of the water in pipe and pipe wall elasticity on the propagating physics were investigated by comparing in-site measurements and theoretical analyses. The pressure wave form and propagating speed were significantly effected due to weak compressibility of the water and the interactions of the waves. The wave performs a strong unsteadiness while it propagates along the pipe. This study tries to explain an event with consideration of both the dynamically weak compressibility of the water in pipe and the closing features of the valves controlled actively.