Adaptive grid method for calculation of water hammer in hydropower station pipeline
In the numerical simulation of the actual flow, in some areas where the velocity field, the concentration field or the pressure field changes abruptly, in order to accurately simulate the information at the location, the grid in the flow field is partially encrypted during calculation, such as a pressure discontinuity zone, Near the object surface, the wake area, the pollutant discharge port and other nearby areas. Therefore, it is necessary to achieve an estimation of some areas where the physical quantity changes drastically, but this estimation is based on a large amount of practical experience, and sometimes these estimates are correct, and sometimes these estimates are incorrect. Especially for non-constant flow, the flow process itself changes, so it is necessary to constantly adjust the position of the mesh or the density of the mesh according to the change of the flow parameters. In this paper, by combining the adaptive grid method with the corresponding numerical discrete format, the water hammer of the hydropower station is improved, and the calculation accuracy of the local area is improved under the condition that the calculation amount does not change much. 2 Adaptive Grid In the study of numerical solution of the boundary value problem of ordinary differential equations, it is found that if the weight function w! ),Make! w! )da%const, the error of the numerical solution can be reduced. The form of discretization of this type is an adaptive grid, which is a very effective tool for solving the numerical solution of partial differential equations. It improves the existing method of uniform mesh and automatically generates sparseness according to the characteristics of the solution in the research problem. A grid of varying degrees. For areas where the physical quantity space changes drastically or the scale changes little, the grid points are automatically encrypted to increase the resolution of the grid, so that the distribution of the grid coincides with the characteristics of the solution. In the actual numerical calculation, the grid spacing is flexibly adjusted according to the characteristics of the research problem and the actual needs, so that not only the advantages of the non-uniform grid in improving the calculation efficiency, but also the uniform grid difference method can be effectively overcome. Limitations of problems such as shock capture, and can improve the accuracy of calculation results and more realistically simulate physical phenomena. In the one-dimensional calculation of the hydraulic transition process of the hydropower station's diversion system, the characteristic line method is mostly used. This method is relatively mature, but the direct water hammer of the simulated water hammer often cannot capture the front edge of the water hammer pressure wave very accurately. In this paper, according to the propagation speed of the water hammer wave, the position of the front edge of the water hammer wave is determined, and the grid is encrypted according to the sudden change of the water hammer pressure near the position, thereby more accurately capturing the change of the water hammer pressure. Intermittent initial value Others In order to facilitate the explanation of the problem, this paper first takes a simple hyperbolic equation as an example. When the above equation has a discontinuous initial value, numerical calculation will find that the low-order format will smooth the discontinuity, while the high-order format is Oscillation occurs again at the discontinuity. 1 The hybrid anti-diffusion format is used to combine the low-order and high-order formats, and the ideal results are obtained. In the /EN0 method, the microwave is captured and better results are obtained. The occurrence of oscillation, although able to overcome the shortcomings of oscillation in the discontinuous region, can not solve the accuracy of the discontinuous region, and the range of the discontinuous region is enlarged, and the accuracy is lowered, which is not a good method. In this paper, the adaptive grid method is applied to improve it effectively. The specific results can be seen in the numerical calculation results below. For the equation "), use the first-order upwind style, LW format, mixed inverse diffusion format to take =1, A" = 0.1s, = 0.2) and the hybrid inverse diffusion method combined with the adaptive grid method to solve the problem. with. The specific method of the hybrid anti-diffusion format is: the first-order format is obtained by inverse style, and the second-order format is obtained by adding an additional item after the first-order format, and the specific form is /; *1, that is, large; LW format has high precision, and the calculation result is It is also close to the analytical solution, but the oscillation phenomenon appears upstream of the discontinuity; the mixed anti-diffusion format in the discontinuous region is far from the actual, so this paper introduces a hybrid anti-diffusion format combined with adaptive mesh. Each calculation calculates the velocity on the current layer. When the velocity gradient between the two points is larger in the example of A'>0.1), the mesh is encrypted and then recalculated from the previous layer, in order not to affect the format. Stability, the spatial distance between two points is controlled by stability conditions. The calculation results of the two formats are as shown. It can be seen that the hybrid anti-diffusion format solves the phenomenon that the LW format oscillates in the discontinuous region, but the discontinuous region results are not ideal. The adaptive hybrid diffusion format can better capture the discontinuity region with less computational complexity and improve the low precision caused by adopting the first-order upwind style. The water hammer calculation is performed below. The characteristic line equation of the water hammer is that, in order to make the above format have second-order precision, the calculation results show that the inverse style calculation results do not fluctuate, but the accuracy is low, although there is no oscillation, the calculation result error is too given: Pipe diameter! It is 0.914m, the pipe length is 1296m, the length of the pipe is 10, the initial head of the valve is 91.44m, the initial flow rate in the pipe is 1.067m/s, the friction coefficient is 0.019, and the propagation speed c is 1 200m / s, the valve opening index (for 1, the valve is completely closed, gravity acceleration) is 9.81m / s2. See the specific calculation results. It can be seen that, by the feature line method combined with the adaptive mesh, the front edge of the water hammer wave can be better simulated with a small increase in the amount of calculation. 4 Conclusions In numerical calculations, meshing that fits the characteristics of the solution will help to obtain an accurate solution and more realistically simulate physical phenomena. This paper discusses the application of adaptive mesh in computational fluid dynamics, especially simulates the calculation of pipeline water hammer with pressure discontinuity, aiming to explore new methods in fluid mechanics calculation to better simulate the flow phenomena in nature. The adaptive method has good adaptability to the rapid flow simulation of fluid movement speed, pressure and pollutant concentration. Further research is to popularize and apply it to establish an adaptive method for simulating the discharge of pollutants on the shore. 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