Research Of Numerical Simulation On The Process Of Water Hammer With Surge Chamber Based On TVD Schemes

The pressure pipe is commonly used in the hydropower station and long distance watertransfer project, due to the valve operation error, unexpected power outages, water pumpmutations, pump unit startup and shutdown and other reasons can cause pipe flow changedrastically, resulting in surge wave. Only in-depth study transmission and attenuationcharacteristics of water hammer, in order to select a reasonable transition flow control process,to reduce the water hammer wave oscillation, and protect the water turbine machinery andhydraulic structures.At present, the water hammer calculation methods varied, each have advantages anddisadvantages. TVD schemes, a class of high resolution shock capturing schemes which risein recent years, have been widely used in Aerodynamics, dam break hydraulics, Thermalphysics and so on. In terms of the fundamental equation properties, water hammer equation isa quasilinear hyperbolic partial differential equations the same as the unsteady Eulerequations and the shallow water equation. Now, High-resolution TVD scheme has beensuccessfully applied to the water hammer equation. Through the validation of the physicalmodel test, the scholars obtained the practical engineering solution.This paper introduced the TVD difference scheme and the structure of high-order TVDdifference scheme. On the basis of previous research, it is regard the downstream pressurepipe, upstream diversion tunnel and surge chamber as a whole for unsteady flow calculation,and combine the TVD difference scheme for solving the equations of water hammer withsurge chamber calculation, which not only can get the water hammer pressure, but also findthe surge chamber water level variation.Based on the analysis and summary of previous research that the process and calculationmethods of the water hammer, this paper further studied the water hammer phenomenon ofhydropower station with the surge chamber. The conclusions are as follows:1. Expounded the feasibility of the TVD scheme to solve water hammer equation as wellas a variety of second-order TVD scheme structure, deduced water hammer equations ofsecond-order TVD difference scheme. 2. Applied the methods of TVD scheme solve the water hammer equations to theupstream surge chamber system hydraulic transition process, combined with certain boundaryconditions. There was good consistency between the calculation results and measured results,and the error is in the allowable range. The results show that the method can better simulatethe upper surge chamber of hydropower station water hammer pressure changes.3. Calculated the upstream surge hydraulic transient process of the system with thefirst-order Lax-Friedrichs scheme and second-order McCormack scheme and compared theboth results with the TVD scheme calculation results, showed that the latter results do notoccur larger dissipation nor spurious numerical oscillations. This suggests that the TVDscheme has the merits of high resolution, high precision, low dissipation, no spuriousnumerical oscillations and strong shock wave capture capabilities.Previous research slave the water hammer equation is on the basis of the pressure pipeconnected to the reservoir directly. Besides, this paper joined the surge chamber building; it isin the form of a reservoir-surge chamber-pressure pipe. In the hydropower station with surgechamber, use the TVD scheme numerical simulation to study the hydraulic transient processof water hammer has received the good effect in the practical engineering. Thus the TVDscheme in the application of water hammer equations can promote to the hydraulic transitionprocess of hydropower station with surge chamber.