| Compared with smooth spillway,stepped spillway is convenient for mechanized construction,with high energy dissipation rate and remarkable aeration effect.It has been widely used in water conservancy and hydropower projects at home and abroad in recent30 years.The water flow in stepped spillways is a complex water-gas two-phase flow.At present,most scholars use direct method to study its hydraulic parameters,and the hydraulic calculation theory of smooth spillway is used for reference in calculation of water surface profile of stepped spillway.However,the obtained laws of hydraulic parameters are complex and the mature and reliable calculation method of water surface profile has not yet been obtained.In order to summarize the relatively simple laws and put forward relatively reliable calculation methods of water surface profile,this paper compared the hydraulic parameters at the same section between the stepped spillway and the corresponding smooth spillway,and introduced a series of relative hydraulic parameters to carry out systematic research,in order to reveal laws of relative hydraulic parameters of skimming flow in stepped spillways and put forward some new calculation methods of water surface profile,which provides theoretical reference and technical support for the design of stepped spillways.In this paper,the energy dissipation rate,the law of relative hydraulic parameters,the law of dimensionless relative hydraulic parameters and their application in water surface profile calculation of stepped spillway are systematically and deeply studied by means of physical model test.The main innovation of this paper is that by introducing relative hydraulic parameters,the complex curve variation law of hydraulic parameters along the way is transformed into a good linear correlation relationship of relative hydraulic parameters along the way.Based on dimensional analysis and quantitative research,the empirical formula for dimensionless relative hydraulic parameters and water surface profile calculation is given,which provides a new way for the calculation of complex hydraulic parameters and water surface line in the uneven flow section of stepped spillway.The main conclusions are as follows:(1)The law of total energy dissipation rate and relative energy dissipation rate of skimming flow in stepped spillways is revealed.The total energy dissipation rate has a linear correlation in the whole flow length and the mean value of the determination coefficient is 0.9975,while the relative energy dissipation rate has a linear correlation in the non-uniform flow region and the mean value of the determination coefficient is 0.9968,increases along the curve in the quasi-uniform flow region,and the increasing gradient decreases gradually.At the same flow length in the non-uniform flow region,the total energy dissipation rate and relative energy dissipation rate are negatively correlated with the discharge per unit width,and positively correlated with the step height and spillway slope.At the same position in the non-uniform flow region,the relative energy dissipation rate is positively correlated with the spillway slope,while the total energy dissipation rate is less affected by the spillway slope.(2)The law of relative hydraulic parameters of skimming flow in the non-uniform flow region of stepped spillways is revealed.In the non-uniform flow region,the water depth,velocity,Froude number and cross-section specific energy all have complex curve relationships along the way,and the influence of various factors on them is also complex.After introducing the relative hydraulic parameters,the law of relative hydraulic parameters obtained by the relative and indirect method is obviously better than those obtained by the direct method.In the non-uniform flow region,the relative velocity,relative Froude number and relative cross-section specific energy are all linearly correlated,the mean values of determination coefficients are 0.9945,0.9957 and 0.9973,respectively,and all of them are negatively correlated with the discharge per unit width,and positively correlated with the step height and spillway slope.(3)The law of dimensionless relative hydraulic parameters of skimming flow in the non-uniform flow region of stepped spillways is revealed,and the empirical formulas for calculating dimensionless relative hydraulic parameters are put forward.In the non-uniform flow region,the dimensionless relative velocity,relative Froude number and dimensionless relative cross-section specific energy are linearly correlated along the way,the mean values of determination coefficients are 0.9946,0.9966 and 0.9976,respectively,.The slopes of the dimensionless relative velocity and relative Froude number are negatively correlated with the relative critical water depth in power function.The slopes of the dimensionless relative velocity,relative Froude number and dimensionless relative cross-section specific energy are negatively correlated with the spillway slope.On the basis of quantitative study on the slopes of linear relation of dimensionless relative hydraulic parameters,empirical formulas for calculating dimensionless relative hydraulic parameters are put forward,which provide a new way for calculating complex hydraulic parameters of stepped spillways.(4)A new method—dimensionless relative hydraulic parameter method,is proposed to calculate the water surface profile of skimming flow in the non-uniform flow region of stepped spillways.Based on empirical formulas for calculating dimensionless relative hydraulic parameters and definitions of relative hydraulic parameters,dimensionless relative velocity method,relative Froude number method and dimensionless relative cross-section specific energy method for calculating water surface profile of skimming flow in the non-uniform flow region of stepped spillways are put forward.Compared with the existing calculation methods of water surface profile,and considering the calculation accuracy,calculation simplicity,application scope and engineering practice,it is recommended that the relative Froude number method should be used first to calculate the water surface profile in the non-uniform flow region of the stepped spillway,followed by the dimensionless relative velocity method and the dimensionless relative cross-section specific energy method. |
PDF Full Text Request