Construction Of Finite Volume Scheme For Pressurized Flow In Pipeline And Establishment Of Full Narrow Slot Model For Open And Full Flow

In the long-distance water conveyance system,the water conveyance pipeline can reach tens or even hundreds of kilometers.It is very important to establish a high-precision early warning model of alternating transient flow.At present,the MOC(Method of Characteristics)is mainly used to solve the water hammer pressure wave,and the six-point implicit scheme is used to solve the free-surface pressure flow.However,the MOC is constrained by the Courant number,resulting in limited calculation speed.The six-point implicit scheme cannot simulate the free-surface-pressure alternating flow including the negative pressure flow.In view of the above problems,this study improves the finite volume numerical algorithm of pipeline transient flow and introduces high-order formats to realize the rapid capture of pipeline pressure wave.In addition,based on the existing Preissmann slit method model,this paper improves and proposes a numerical model of alternating bright and full transient flow that can simulate unsteady open flow and negative pressure flow.The main conclusions of this paper are as follows:(1)By constructing the TVD framework,selecting the optimal limit function,and using the virtual grid at the upstream and downstream interfaces,a water hammer solution algorithm based on the finite volume method Godunov numerical format is proposed,and the calculation speed and dissipation performance of the algorithm is compared through the pipe network example.The results show that the two-order finite volume method can obtain the best calculation results at a lower Courant number.Compared with the MOC and Sweby TVD difference methods,the calculation time is saved by 28.6 % and 85.3 % respectively.The model selects the Van Leer limiter,and the Courant value range is 0.2 ≤ Cr ≤ 0.5.The model is more flexible in meshing,and any grid spacing that meets the range of Courant number can be selected according to the actual needs,which can realize the rapid calculation of transient flow in variable space step pipe network system.(2)The third-order ENO and fifth-order WENO finite volume schemes are used to solve the one-dimensional pipeline unsteady flow equations.Based on the Lax-Friedrichs flux splitting method,the interface flux is reconstructed.Combined with the boundary conditions of the cross-pipe network,a set of efficient and high-precision numerical models for solving transient water hammer waves in pipelines is established.GPU acceleration technology is introduced to achieve efficient calculation of large water conveyance systems.The model is verified by MOC,first-order,and second-order Godunov finite volume schemes.The results show that the high-order scheme can maintain good discontinuous capture performance and no non-physical oscillation at very low Courant numbers.At the same time,the high insensitivity to the Courant number makes the model highly flexible when meshing and can significantly improve the calculation speed.The application of GPU acceleration technology shows that the model has an obvious acceleration effect when there are more grids,and the acceleration effect is significant with the increase of grid number.The model can provide theoretical support for the efficient,accurate,and rapid simulation and prediction of the unsteady transient process of longdistance water conveyance system.(3)Coupled with the dichotomous pressure method and Preissmann ’s negative slit idea,a set of numerical models for simulating unsteady open flow,negative pressure flow,and alternating flow with open and full flow are established.Based on the CFL constraint conditions,the discrimination method of negative pressure flow and open flow is proposed.Through the complex examples of open channel water filling,water hammer in pressure pipeline,alternating open and full flow formed by valve closing during water filling,and simultaneous action of water hammer,it is shown that the model established in this paper breaks through the limitation that the traditional Preissmann slit method cannot simulate negative pressure and the difficulty of distinguishing open flow and full negative pressure flow by dichotomy pressure method,and realizes the accurate simulation of alternating open and full transient flow without considering gas-liquid two-phase interaction.