Numerical Simulation Of Water Hammer With TVD Scheme Considered Windward

It is crucial to simulate the process of water hammer because of its serious harm on the normal operation of running hydro. Numerical method to simulate water hammer phenomenon is a hot research currently.At present, there are kinds of water hammer calculation methods, they have merits and demerits respectively. International scholars have carried out extensive and in-depth research to it and the numerical simulation is one of the key research direction. more successful in these formats is TVD scheme is a more successful method in these formats.TVD is still in its beginning in numerical simulation of water hammer. No one has considered windward of water in the previous studies. Due to the change of flow direction in the process of water hammer, the windward will influence the process of water hammer.In this paper a TVD scheme considered the windward applying in numerically the water hammer couple is used to solve the water hammer.Based on predecessors’ results of numerical simulation of water hammer with TVD scheme,this paper analysis the effect of the windward on the numerical simulation method further, demonstrate the necessity and feasibility of the windward TVD scheme for water hammer problems simulation and its main content includes the following several aspects:1.Expound the influence of the windward effect on the calculation process of the water hammer and the windward TVD scheme program is written to bring the windward TVD scheme into the calculation of the water hammer problem for the first time.2. A Roe TVD scheme considered the windward applying in numerically the water hammer couple is used to solve the water hammer equations to simulate water hammer pressure in a simple pipeline.A comparison with Lax-Friedrichs, MacCormark the TVD scheme not considered windward and analytical solutions shows that the TVD scheme considered the windward has the advantages of high resolution, high accuracy, and low dissipation etc and. And the TVD scheme considered the windward is more repressive and less dissipative than the TVD scheme.3. Explore the influence of flow velocity on the simulation of water hammer in TVD scheme. The simple pipeline water hammer in four different flow velocities are simulated by the upwind TVD scheme and the non upwind TVD scheme. Calculation results showthat with the increase of velocity, the resolution of upwind TVD scheme for water hammer in the numerical simulation has been very high and its stability is excellent.The capture ability of the non upwind scheme in the discontinuous position is decreased with the increasing of the velocity, and is negatively correlated. It shows that the upwind TVD scheme is more applicable to the simulation of the water hammer, especially for the water hammer of the high speed water flow.4. Preferred windward TVD scheme. The windward scheme is applied to 4 typical TVD schemes. The four schemes are modified Roe’s TVD scheme, Harten’s TVD,TVD-MacCormark scheme and full TVD-LF scheme. Calculation results show that Roe’s TVD scheme for water hammer simulation is the best one as it has good stability and high precision.5. The preferred Roe’s windward TVD scheme is applied to numerical simulation of water hammer in a hydropower station project in Gansu. Good results have been achieved by comparing the calculated results with the first order Lax-Friedrichs(LF) scheme, the two order MacCormark(MC) scheme, the TVD scheme without considering the upwind and the results of the physical model tests.