Applicability of hydraulic performance graph for unsteady flow routing.

摘要

The applicability of the hydraulic performance graph (HPG ) for unsteady-flow routing is investigated herein. The HPG is a summary of backwater profiles in a channel reach in terms of discharge and water stages at its downstream and upstream ends. Traditionally, in hydraulic flow routing the Saint-Venant equations, or their approximations, are solved numerically. It is unclear from the solution how much of the wave damping and phase shifting is physical and how much is numerical. Moreover, because numerical solutions depend on the computational grid size, numerical robustness is often a problem. In the flow-routing approach proposed here, the momentum equation is replaced by the HPG and coupled numerically with the equation of continuity. This approach results in a new hydraulic flow-routing method, the varied flow method ( VFM). In the VFM, routing is simulated in a stepwise-steady fashion, which is suitable for unsteady-flow simulation when the flow acceleration with time is not large. The method is validated with seven available unsteady-flow experiments from three different sources for flow through single prismatic channels. It is shown that, in general, VFM simulations compare as well as or better than noninertia simulations with the experimental data. In addition, a set of nine scenarios of unsteady-flow through single channels representing a variety of initial and boundary conditions that, according to the criterion in Ponce et al. (1978), are best represented by the full dynamic wave, are also simulated with the VFM, and compared with dynamic-wave (DW) and noninertia (NI) simulations. The simulation results of these nine scenarios demonstrate that, although slightly less accurate than the DW model, the VFM is more accurate than the NI model. Furthermore, the numerical robustness of the VFM is evaluated based on its relative accuracy with respect to the DW model as a function of the grid size for six scenarios of flood routing through a single rectangular channel, and compared with that of the NI model. This evaluation shows that the VFM is numerically more robust than the NI model. Finally, the applicability of the VFM for flood routing through natural channels is demonstrated with an application example.