| HYDRAULIC ENGINEERING |
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Diffusion convection model for conduit multiregime transient-mixed flow |
| ZHANG Dong, WANG Enzhi, LIU Xiaoli, WU Chunlu |
| Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China |
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Abstract The evolution of free-surface and pressurized flows and their simultaneous occurrence (mixed flow) often appear in pipe drainage systems (e.g., urban sewerage systems, water conveyance pipelines and karst conduits) due to variable inflow and outflow conditions. Accurately simulating the transition between free-surface and pressurized flows is of particular significance for infrastructural damage and operational control in engineering. However, the transition process between free surface-pressurized mixed flows in the channel and conduit leads to difficulties in numerical simulation and poor stability, especially in long-term hydrodynamic forecasting. Thus, an accurate, numerically stable, and low computational cost physical-mathematical model is urgently needed. Based on the diffusion wave approximation of the Saint-Venant equations, the water hammer equations are extended, and the fluid compressibility is considered to establish a linear relationship between fluid density and pressure head. The transition of flow regimes (free surface, pressurized, and mixed flow) during the flow process is also analyzed, and the Swamee-Swamee formula is adopted. A multiregime mixed flow diffusion convection model is then proposed in the paper. The model not only describes the evolution of flow types but also considers the transition of multiregime flows. Furthmore, the comparison between the proposed and previous models is conducted to demonstrate improvements and developments in the new proposed model. Numerical simulations for some benchmark questions are carried out and compared with previous models. The following results are presented. 1) Regardless of free-surface or pressurized flow, an evolution and transition of laminar, transition, and turbulent flows are observed in the pipeline flow with the change in water depth or flow rate, and laminar and transition flow states cannot be ignored. 2) The simulation results of the proposed model are close to those of the SWMM(storm water management model), which reach the requirements of engineering. The proposed model has high numerical stability and minimal limitations on the time step and is suitable for long-term hydrodynamic process prediction. The proposed model can accurately describe the mixed flow process in the pipe when the momentum simplification condition is satisfied. 3) The accuracy of the proposed model is higher than that of the Rob model. The multiregime model corrects the mass balance error caused by density variation, ensures mass conservation in the process of pressure flow, and eliminates the local singular values in the results of the Rob model. 4) Compared with the Rob model, the proposed model also has superior convergence and numerical stability. The proposed model assumes that fluid density changes continuously during the free surface-pressurized flow to avoid the numerical discontinuity of the water storage coefficient. Furthermore, the concept of water storage capacity per unit length of the pipeline is defined, and the L scheme is adopted to guarantee the unconditional convergence of the algorithm when Ln ≥ d. The proposed model is highly consistent with the theoretical solution, SWMM simulations, and experimental data. The model successfully and accurately simulates the hydrodynamic process of transient-mixed flow in pipes. Compared with the SWMM simulations, the proposed model is stable at the free surface-pressurized flow interface with minimal restriction in spatiotemporal discreteness. The proposed model can provide theoretical and methodological support for the simulation and prediction of long-term hydrodynamic processes in conduits, such as conduit flow in karst areas.
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| Keywords
conduit flow
free surface-pressurized mixed flow
diffusion wave
diffusion convection
multiregime
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Issue Date: 23 April 2023
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2023,
Vol. 63
