Analysis of Water-Surface Oscillations Upstream of a Double-Right-Angled Bend with Incoming Supercritical Flow

Abstract

This study deals with the free-surface supercritical flow through a double-right-angled bend (DRAB), which can be found in storm drainage networks in steep terrains. Laboratory experiments showed that strong backwater effects and water-surface oscillations are generated upstream of the DRAB, especially in supercritical flow conditions. This paper investigated the DRAB hydraulic behavior and water-surface heading up (backwater), and oscillations under supercritical flow conditions. Thirty-four lab experiments were conducted with Froude numbers ranging between 1.03 and 2.63. Dye injection and video analysis were used to visually capture the flow structure and to record water-surface oscillations. A tracker package was utilized to analyze the collected visual data. Time series and spectral analysis were used to identify the statistical characteristics of recorded water level time series and the dominant frequencies. It was found that the dominant frequencies of water-surface oscillations upstream of the DRAB range between 1.6 and 4.6 Hz with an average value of about 3 Hz. The Strouhal number of the water-surface oscillations is more sensitive to the Froude number than to the Reynolds number. The Strouhal number ranged between 0.03 and 0.3 for Froude numbers ranging from 2.63 to 1.03. The study confirms that near critical flow conditions exhibit the highest water oscillation, and that the maximum nondimensional water depth upstream of the DRAB is underestimated by both the Grashof formula and Knapp and Ippen (1939) model. A new formula is proposed to estimate the maximum water depth upstream of the DRAB.