Numerical Simulation On Water Hammer Process Applying ENO Scheme

Water hammer is a very typical and important process in the transition flow. In computational fluid dynamics, the ENO scheme is widely used in aerodynamics calculations, which has also been a good application effect in the field of dam break wave .The ENO scheme is first applied to the numerical simulation of water hammer process, which provides a new computing idea for the designing and operating of hydropower engineering.This paper discusses the following six aspects after analyzing the previous research results of water hammer process and calculation methods:1. In order to apply the ENO scheme, which is based on shock capturing method, this paper gets a conservative equation of water hammer by changing the equation form of basic differential equations of water hammer.2. The ENO scheme is determined to apply the numerical simulation of water hammer after discussing the research results of dam break waves and the development and application of ENO format. In order to demonstrate results, the TVD format and two classical formats in the computational fluid dynamics, MacCormark format and Lax-Friedrichs format are chosen to calculate the model at the same time.3. Different formats are used in the calculation of numerical model. Results show that the ENO format can be used in numerical simulation of the water hammer process, which maintain its high accuracy and almost no vibration characteristics, and the water hammer process of calculation is consistent with the analytical results.Compared with the classical MacCormark format, the ENO scheme has higher accuracy in smooth regions and can reflect the location of water hammer wave clearly in the break area .MacCormark format produces non-local physical oscillation, thus affecting the accuracy of the numerical solution.The Lax-Friedrichs compares with ENO scheme, which shows that the Lax-Friedrichs scheme has a large numerical dissipation at the smooth area and intermittent region.The TVD format used to calculate water hammer process can maintain a high numerical accuracy. There is tiny numerical dissipation compared with ENO format, but can quickly smoothing within 1-2 computational grid. TVD and ENO format have a strong ability to inhibit the oscillations.4. By reducing the compute nodes, contrast ENO and TVD formats. The calculation results show that the ENO format depends on the computing grid lower than the TVD, can get more accurate numerical solution at the same grid density. So ENO format has higher numerical stability than TVD format, and also can be more economical computation.5. The ENO scheme is applied to ALASHAN hydropower station. The calculation water hammer process are consistent with the physical model testing the water hammer pressure and the maximum error is less than 10%, which verifies the ENO scheme can solve practical problems.6. Computational results are compared and show that the pipeline resistance coefficient has a great influence for the water hammer decay process. The pipe resistance partition method used in this paper can simulate the attenuation process of water hammer wave.The results show that the ENO scheme has a good and strong ability to capture water hammer wave. It's successful application to the problem of water hammer will bring a new high precision calculation for water hammer, which can better solve the hydraulic transient flow problem.