Shu-Qing Yang

Reply to comment by M. Bayani Cardenas and John L. Wilson on “Flow resistance and bed form geometry in a wide alluvial channel”

[1] The authors would like to thank Cardenas and Wilson [2006] for their valuable comments and interesting discussions. The main points raised by the commenters are summarized as follows. [2] 1. Cardenas and Wilson’s main interest lies in the estimation of the characteristic length (L00) of the separation zone behind the bed form. [3] 2. Equation (28a) of Yang et al. [2005] suggests that a may vary from 12 to 45, while Engel [1981] and Karahan and Peterson [1980] suggested that a has a value in the range of 4–6; thus it appears that equation (28a) overestimates the value of a by as much as 300% or more. The commenters concluded that the errors in a propagates into the analysis for the energy slope. [4] 3. The commenters were not clear on the values of a used for the calculation of Sc, and how Figure 4 of the Yang et al. was derived. The commenters assumed that the authors had used a value of a = 16 in the computation of energy slope S and found that the value of a was not constant. [5] The authors would like to stress that the objective of the paper is to develop a method to estimate the energy slope using easily obtainable data from the field or laboratory, such as the discharge, channel width, flow depth and sediment size. We will show that the different conclusions drawn by the commenters and the writers are attributable to the different research objectives. [6] First, the authors’ purpose is to evaluate the energy slope S which is expressed as follows (equation (6) of Yang et al.)

Strategy of water pollution prevention in Taihu Lake and its effects analysis

ABSTRACT Taihu Lake, the third largest freshwater lake in China, is located in the Chanjiang Delta of the Yangtze River. Its waters are used by agriculture, industry and as major drinking water for several cities including Shanghai and Wuxi. The lake also is important for tourism, aquaculture and flood control. Taihu Lake and its surrounding areas are facing three major water-related threats: deteriorating water quality with inflow and runoff from its watershed; flooding during the rainy seasons; and water shortages during drier months. Noxious algae blooms are occurring with increasing frequency and water quality continues to decline. Remedial actions implemented to date have been ineffective. This paper proposes that the problems could be remedied by constructing a by-pass channel (BPC), which would divert low-quality water from the lake during low precipitation periods and allow better quality water to flow into the lake during high flow periods. This remedial action would simultaneously deal with the deteriorating water quality of Lake Taihu and maintain its water level at a desired level. A preliminary assessment of this strategy shows that, if the BPC were implemented, the water quality of Taihu Lake would be improved significantly in few years, the flood disaster would be greatly mitigated, and the water shortage problem in the basin would be alleviated.

Turbulent drag reduction with polymer additive in rough pipes

Friction factor of drag-reducing flow with presence of polymers in a rough pipe has been investigated based on the eddy diffusivity model, which shows that the ratio of effective viscosity caused by polymers to kinematic viscosity of fluid should be proportional to the Reynolds number, i.e. u ∗ R /ν and the proportionality factor depends on polymers type and concentration. A formula of flow resistance covering all regions from laminar, transitional and fully turbulent flows has been derived, and it is valid in hydraulically smooth, transitional and fully rough regimes. This new formula has been tested against Nikuradse and Virks experimental data in both Newtonian and non-Newtonian fluid flows. The agreement between the measured and predicted friction factors is satisfactory, indicating that the addition of polymer into Newtonian fluid flow leads to the non-zero effective viscosity and it also thickens the viscous sublayer, subsequently the drag is reduced. The investigation shows that the effect of polymer also changes the velocity at the top of roughness elements. Both experimental data and theoretical predictions indicate that, if same polymer solution is used, the drag reduction (DR) in roughened pipes becomes smaller relative to smooth pipe flows at the same Reynolds number.

Investigation of near wall velocity in 3-D smooth channel flows

This paper presents an investigation of velocity distribution in steady, uniform flows in smooth rectangular channels. Theoretical study and experimental data show that the near wall velocity distribution in 3-D channels cannot be represented well by the classical log-law where the shear velocities are identical on both sides of the equation (Tracy and Lester, US Department of Interior,Washington, DC, 1961, pp. A1-A18). This paper examines the appropriate expressions of two shear velocities that may be different. In the light of Tracy and Lesters work, this study found that when the measured near wall velocity and wall normal distance are normalized by the global shear velocity and the local shear velocity, then the near wall velocity can be described by the well-known wall function without an empirical coefficient. The basic mechanism is attributed to the concept proposed by Yang and Lim [J. Hydraul. Engng. ASCE 123 (1997) 684] that surplus mechanical energy is transported towards boundary along shortest path. The derived equations are in good agreement with experimental data in the literature.

Boundary shear stress distributions in trapezoidal channels

This paper deals with the boundary shear stress distributions in trapezoidal open channels. The direction of the transport of surplus energy is discussed, which leads to the assumption that the surplus energy within any unit volume of fluid in 3-D flow will be transferred towards the nearest boundary to be dissipated. Based on this concept, the flow cross-sectional area in trapezoidal open channels is divided into various elements according to the shape of cross-section, aspect ratio and roughness distribution. Analytical equations for the local and mean boundary shear stress along the wetted perimeter are presented. The formulae and the experimental data available in literature are in good agreement.

Drag Reduction in Turbulent Flow With Polymer Additives

The mean velocity profile and friction factor in turbulent flows with polymer additives are investigated using Prandtls mixing-length theorem. This study reveals that the mixing-length theorem is valid to express the drag-reducing phenomenon and that the presence of polymer additives increases the damping factor B in van Driests model; subsequently reducing the mixing-length, this interprets that the polymer hampers the transfer of turbulent momentum flux, the velocity is increased, and flow drag is reduced. This study also discusses the onset Reynolds number for drag reduction to occur. The predicted velocity, friction factor, and onset Reynolds number are in good agreement with the measured data in the literature.

Drag reduction in a flat-plate boundary layer flow by polymer additives

This paper presents a theoretical study on the velocity distribution and the friction factor of boundary layer flows with polymer additives starting from the concept of “stress deficit.” A novel method of order of magnitude analysis is developed, which converts the governing equations of boundary layer flow into a solvable ordinary differential equation, thus the total shear stress distribution is obtained, then the formulas for the mean velocity profiles and the friction factor for a boundary layer flow are derived after introducing appropriate expressions for the “effective viscosity” and the thickness of viscous sublayer. The derived velocity equation is able to depict the velocity from a solid wall to the outer edge of boundary layer with or without polymer additives using only one fitted parameter D* that is a function of polymer species, its concentration, and Reynolds number. By integrating the velocity profiles, the friction factor and the thickness of boundary layer development are obtained. Expe...

Prediction of total bed material discharge

A new and user-friendly formula for the computation of total bed material load in alluvial channels under equilibrium transport conditions has been developed based on the stream power concept and diffusion theory. The advantages of this formula include: high accuracy in prediction, the ease of computation and the wide range of application. The total sediment concentration is computed directly using the variables of flow depth, mean flow velocity, energy slope, median sediment size and sand density, and water temperature. The verification for the new equation uses over 3500 published total-load data from flume studies, and the over-all results show that 84% of the data are predicted within 0.5 and 2 times the measured values. This is an encouraging score considering the large database and the range of variables covered.

Depth-Averaged Shear Stress and Velocity in Open-Channel Flows

Turbulent momentum and velocity always have the greatest gradient along wall-normal direction in straight channel flows; this has led to the hypothesis that surplus energy within any control volume in a three-dimensional flow will be transferred toward its nearest boundary to dissipate. Starting from this, the boundary shear stress, the Reynolds shear stress, and the velocity profiles along normal lines of smooth boundary may be determined. This paper is a continuous effort to investigate depth-average shear stress and velocity in rough channels. Equations of the depth-averaged shear stress in typical open channels have been derived based on a theoretical relation between the depth-averaged shear stress and boundary shear stress. Equation of depth mean velocity in a rough channel is also obtained and the effects of water surface (or dip phenomenon) and roughness are included. Experimental data available in the literature have been used for verification that shows that the model reasonably agrees with the measured data.

Modeling of viscoelastic turbulent flow in channel and pipe

This paper investigates turbulent flows with or without polymer additives in open channels and pipes. Equations of mean velocity, root mean square of velocity fluctuations, and energy spectrum are derived, in which the shear stress deficit model is used and the non-Newtonian properties are represented by the viscoelasticity α*. The obtained results show that, with α* increment, (1) the streamwise velocity fluctuations is increased, (2) the wall-normal velocity fluctuation is attenuated, (3) the Reynolds stress is reduced, and (4) there is a redistribution of energy from high frequencies to the low frequencies for the streamwise component, but dimensionless distribution over all frequencies almost remains the same as that in Newtonian fluid flows. Good agreement between the derived equations and experimental data in small drag-reduction regime is achieved, which indicates that the present model is workable for Newtonian/non-Newtonian fluid turbulent flows.