Experimental–analytical investigation of super- to subcritical flow transition without a hydraulic jump

Abstract

AbstractAn experimental–analytical investigation was performed to explore whether a hydraulic jump in a transition from super- to subcritical flow regime can be avoided. As the free-surface profile passes the critical depth, the transitional point is a singular point. A transition structure was designed based on the energy principle and the singular point theory to gradually increase the flow depth, thereby eliminating the hydraulic jump. This profile was designed for approach flow Froude numbers between 1.5 and 7. To validate the analytical model, a comprehensive experimental study was conducted. Six hydraulic models of transition structures were experimentally investigated on the basis of the theoretical approach. The analytical results agreed well with the experimental results and those of former investigations. Observations indicated that the hydraulic jump is absent for a certain range of the Froude numbers.Keywords: Analytical–experimental modelsingular pointsubcritical flowsupercritical flowtransition AcknowledgementsThe authors wish to express their gratitude to Professor Willi H. Hager, VAW, ETH Zürich, Switzerland, for his interest and constructive comments on this paper.FundingWe are grateful for the financial support from IWRM (Iran Water Resources Management Company).NotationB = =channel widthe = =objective function = =upstream Froude numberg = =acceleration due to gravityHt = =total energy headHmax = =total energy at maximum structural heightLc = =horizontal length corresponding to location of ycLj = =length of the classic hydraulic jumpLmax = =horizontal length corresponding to ZmaxLopt = =optimal transition lengthLs = =specific length of transitionPo = =bottom pressureQ = =dischargeR = =radius of the curvatureSo = =channel bottom slopeT = =transitional profileV = =flow velocityVo = =bottom velocityV1 = =upstream supercritical flow velocityy = =flow depthy1 = =supercritical flow depth at toe of jumpy2opt = =optimal downstream water depthyc = =critical depthZ = =water surface profilez, zmax = =height and maximum height of the transitionρ = =water density