A Hydraulic Friction Model for One-Dimensional Unsteady Channel Flows with Experimental Demonstration

Abstract

Abstract:As a critical parameter of the steady uniform friction model, the roughness coefficient changes with flow unsteadiness in flood events; i.e., the flow conditions of the stream segment significantly affect the flow resistance. In this study, a modified formula was established to improve the unsteady friction simulation; ten terms relating to the first-and second-order time and space partial derivatives of hydraulic parameters were selected as additional terms. The results of a hydraulic experiment show that the hysteresis between flow depth and mean cross-sectional velocity cannot be neglected in unsteady flows that disturb the performance of a steady uniform friction model. Six terms have a strong correlation with objective friction. Further, three of them have a small variance in correlation coefficient. Then, the composition of the proposed formula was determined. The results show that adding too many additional terms provides better performance in the calibration phase, yet reduces the accuracy of the validation phase because of an overfitting phenomenon. The optimal number of additional terms is three, and the established formula can improve the unsteady friction simulation.

The Modified One-Dimensional Hydrodynamic Model Based on the Extended Chezy Formula

“…where f is the Fanning friction factor, F 1 is a function of the factors which affect both steady uniform and unsteady frictions, and F 2 contains the factors which only affect unsteady friction, which depends on time and space derivatives of hydraulic parameters, such as ∂D/∂x, ∂D/∂t, ∂V/∂x, and ∂V/∂t. Based on dimensional analysis, a modified friction model for unsteady flow has been proposed by Bao et al [24]. The modified model states the following:…”

“…As a result, these coefficients are very unstable and unpredictable in an unsteady flow regime [21]. Many studies in the literature are devoted to developing new models for calculating 1D unsteady channel friction, like Tu and Graf [21], Rowiński et al [22], Mrokowska et al [23], and Bao et al [24]. The proposed unsteady friction models contain the terms of time and space derivatives of hydraulic parameters, which better demonstrate the dependence of unsteady friction on flow unsteadiness and flow non-uniformity.…”

“…On the other hand, although some of the proposed formulas can be used to compute the friction slope in the 1D hydrodynamic model, these formulas are more complex than the Chezy and Manning formulas. For example, Bao et al proposed a 1D unsteady friction formula based on dimensional analysis instead of the inverse analysis of momentum equation [24]. However, in their proposal, more empirical parameters were introduced to describe the dependence of unsteady friction on spatio-temporal derivatives of hydraulic parameters.…”

“…To uncover the potential advantages of unsteady friction formulas, a modified 1D hydrodynamic model is proposed in this paper, referred to as the modified SVN model, based on the unsteady friction formula presented by Bao et al [24]. Since the steady uniform component of the unsteady friction model is the same as the Chezy formula, a classic 1D hydrodynamic model with the friction calculator of the Chezy formula is used for comparison, referred to as the original SVN model.…”

A bivariable coupling model for river channel routing developed from the flow continuity equation and its application

“…The hydraulic methods have no forecasting function, and even if they have forecasting function, the lead time will be lost. However, hydrological methods only require the cross-section survey data of flood control section, and can forecast the future water level process well (Bao et al, 2018;Zhang and Bao, 2012).…”