Journal of Hydraulic Engineering

Bottom racks are a standard hydraulic structure used as intakes in mountainous regions, to divert water to turbines, and to retain sediment and other solid matter larger than rack spacing. These racks are also used for fish ways, and to retain floating matter. The present project was directed to explore the hydraulics of bottom rack intakes, without considering any solids in the fluid. Based on extended laboratory observations, the effect of various parameters were explored, such as the bottom slope, the rack geometry, and the rack porosity. In addition, a novel approach to determine the discharge coefficient of a rack structure was developed. Finally, the intake channel below the bottom rack was investigated and several interesting features were found, including a significant flow instability that may have a strongly adverse effect on the rack performance. Guidelines for successful rack designs are given, and the results of the present study may be readily applied.

Dam-break problems involve the formation of shocks and rarefaction fans. The performance of 20 explicit numerical schemes used to solve the shallow water wave equations for simulating the dam-break problem is examined. Results from these schemes have been compared with analytical solutions to the dam-break problem with finite water depth and dry bed downstream of the dam. Most of the numerical schemes produce reasonable results for subcritical flows. Their performance for problems where there is a transition between subcritical and supercritical flows is mixed. Although many numerical schemes satisfy the Rankine-Hugoniot condition, some produce solutions which do not satisfy the entropy condition, producing nonphysical solutions. This was the case for the majority of first-order schemes examined. Numerical schemes which consider critical flow in the solution are guaranteed to produce entropy satisfying solutions. Second-order schemes avoid the generation of expansive shocks; however, some form of flux or slope limiter must be used to eliminate oscillations that are associated with these schemes. These limiters increase the complexity and the computational effort required, but they are generally more accurate than their first-order counterparts. The limiters employed by these second-order schemes will produce monotone or total variation diminishing solutions for scalar equations. Some limiters do not exhibit these properties when they are applied to the nonlinear shallow water wave equations. This comparative study shows that there are a variety of shock-capturing numerical schemes that are efficient, accurate, robust, and are suitable for solving the shallow water wave equations when discontinuities are encountered in the problem.

The experimental study shows how an open-channel flow would respond to a sudden change (from smooth to rough) in bed roughness. Using a two-dimensional acoustic Doppler velocimeter and a laser Doppler velocimeter, the velocity, turbulent intensities, and Reynolds stress profiles at different locations along a laboratory flume were measured. Additionally, the water surface profile was also measured using a capacitance-type wave height meter. The experimental data show the formation of an internal boundary layer as a result of the step change in bed roughness. The data show that this boundary layer grows much more rapidly than that formed in close-conduit flows. The results also show that the equivalent bed roughness, bed-shear stress, turbulent intensities, and Reynolds stress change gradually over a transitional region, although the bed roughness changes abruptly. The behavior is different from that observed in close-conduit flows, where an overshooting property—which describes the ability of the bed-shear stress to attain a high-peak value over the section with the larger roughness, was reported. A possible reason for the difference is the variation of the water surface profile when an open-channel flow is subjected to a sudden change in bed roughness.

The results of an experimental investigation of the time variation of scour hole and the flow characteristics of the quasi-equilibrium state of scour of a cohesive bed downstream of an apron due to a submerged horizontal jet issuing from a sluice opening are presented. Experiments were carried out with natural cohesive sediment for various sluice openings, jet velocities, and lengths of apron. Attempts are made to explain the similarity existing either in the process of scour or in the scour profiles that the scour holes follow downstream of an apron. The scour profiles at different times follow a particular geometrical similarity and can be expressed by a polynomial using relevant parameters. The characteristic parameters affecting the time variation of scour depth are identified based on the physical reasoning and dimensional analysis. An equation for time variation of maximum scour depth is obtained empirically. The diffusion characteristics of the submerged jet, growth of boundary layer thickness, velocity distribution within the boundary layer, and shear stress at the quasi-equilibrium state of scour are also investigated. The expression of shear stress is obtained from the solution of the von Kármán momentum integral equation.

The results of a series of laboratory modeling experiments are presented for the case of a vertical, turbulent, plane, negatively buoyant jet impinging on a horizontal solid surface placed a distance H below the jet source. The results show that the impingement results in the generation of a complex two-dimensional disturbance field at the site of the impact and the generation of a buoyancy-driven boundary current carrying away fluid from the impingement zone. The disturbance field is seen to extend vertically along the time-averaged axis of the incident buoyant jet, thereby distorting the vertical velocity and concentration fields over a vertical distance that depends upon the value of the parameter $F{d}_0^{-4/3}\text{,}$ where $F{d}_0$ is the source Froude number of the buoyant jet. Transverse velocity and concentration profiles taken at different axial distances from the source reveal systematic departures from the far-field Gaussian similarity profiles as the solid boundary is approached. Such departures are utilized to quantify and parameterize the vertical distance $z*$ from the boundary at $z=0$ beyond which the impingement of the buoyant jet does not affect significantly the incident flow. Measurements indicate that $z*/b\sim 0.4F{d}_0^{4/3}\text{.}$ For distances $z<z*\text{,}$ the degree of distortion of the vertical velocity profile within the jet (1) increases strongly with decreasing values of $(z/b)F{d}_0^{-4/3}$ and (2) shows a weak dependence upon the Froude number $F{d}_0\text{.}$ Measurements of (1) the rebound height of the disturbance field in the impingement zone and (2) the maximum horizontal velocity in the spreading gravity current confirm the ubiquity of the $F{d}_0^{-4/3}$ scaling for other aspects of the impingement flow. Data indicate also that the thickness of the current reaches a constant value $h_b$ outside the immediate impact zone, with $h_b/H$ depending linearly upon $F{d}_0\text{.}$

The design of a straight benthic flow-through flume for in situ studies of cohesive sediment dynamics is described including the flume structure and probes installed for routine measurements of suspended sediments and flow velocity. The flume was calibrated for two roughness types covering the range of possible cohesive bed roughnesses. The calibration included a set of three-dimensional velocity measurements using acoustic Doppler velocimeter. These measurements were used to develop calibration relationships between the bed shear stress (which is difficult to measure directly in routine deployments) and the flume centerline flow velocity, which is routinely measured. An example of a successful deployment of the flume is presented. The limitations and potential for further improvements are also briefly discussed.

A user-friendly total bed-material load transport formula for flow in alluvial channels under equilibrium transport conditions has been developed based on dimensional analysis. The main advantages of this formula are its ease of computation, accuracy in prediction, and the wide range of application. The total sediment discharge $g_t$ is computed directly and is linearly related to the new total load transport parameter, $T_T\text{.}$ The latter involves variables that can be easily measured in field conditions, i.e., flow depth, mean flow velocity, energy slope, median sediment size and density, and water temperature. The factor of proportionality k in the formula has been checked for a wide range of hydraulic conditions and it remains a constant equal to 12.5. Comparisons between the computed and measured total sediment discharge indicate that the predictions are good.

In pipeline transport of slurries, it is desirable that the solid particles should be suspended by the fluid phase. Within the body of the flow, turbulent diffusion promotes suspension, but this mechanism is not effective near the lower boundary. Under certain conditions, near-wall fluid lift can provide the necessary support for the particles. The Kutta-Zhukovski equation is used to relate the lift force to the shape of the fluid velocity profile. Comparison with experimental findings shows that this lift may be associated with profiles of solid concentration that show a decreased concentration as the bottom of the pipe is approached. Observed reductions of pressure gradients result from this “off-the-wall” lift force. In certain instances, the slurry pressure gradient is found to be less than that for the “equivalent fluid,” with favorable implications for pipeline economics.