Junke Guo

Turbulent velocity profiles in sediment-laden flows

A theoretical analysis shows that velocity profiles in sediment-laden flows are similar to those in clear water. The modified log-wake law, which is developed for clear water by Guo, is also valid in sediment-laden flows. The analysis of the effects of sediment suspension on turbulent kinetic energy and turbulent diffusion shows that: (1) sediment suspension increases mean flow energy loss; (2) sediment suspension weakens turbulent diffusion in the vertical direction and then increases velocity gradient; and (3) sediment suspension affects velocity profile in two ways: average concentration and density gradient. The comparison with narrow-channel laboratory data confirms the theoretical analysis and shows that: (1) the modified log-wake law agrees well with experimental data for sediment-laden flows; (2) both average concentration and density gradient reduce the von Karman constant; and (3) for a given width-depth ratio, sediment concentration slightly increases the wake strength while density gradient has little effect on it. In addition, the modified log-wake law can reproduce experimental data where the maximum velocity occurs below the water surface.

Logarithmic matching and its applications in computational hydraulics and sediment transport

This study presents an asymptotic matching method, the logarithmic matching. It states that for a complicated nonlinear problem or an experimental curve, if one can find two asymptotes, in extreme cases, which can be expressed as logarithmic or power laws, then the logarithmic matching can merge the two asymptotes into a single composite solution. The applications of the logarithmic matching have been successfully tried in several cases in openchannel flows, coastal hydrodynamics and sediment transport such as: 1) the inverse problem of Manning equation in rectangular open-channels, 2) the connection of different laws in computational hydraulics. 3) the solution of linear wave dispersion equation, 4) criterion of wave breaking. 5) wavecurrent turbulence model. 6) sediment settling velocity, 7) velocity profiles of sediment-laden flows, and 8) sediment transport capacity. All these applications agree very well with numerical solutions or experimental data. Besides, it is pointed out that there are several other cases where the logarithmic matching has potential applications.

Application of the Modified Log-Wake Law in Open-Channels

The modified log-wake law, which was developed for turbulent boundary layers and pipe flows, is extended to turbulent flows in open-channels. Turbulent velocity profiles in open-channels can be approximated with three components: (1) the law of the wall that results from the constant bed shear stress; (2) the law of the wake that reflects the effects of gravity, secondary currents and bed roughness; and (3) the cubic correction near the maximum velocity. A procedure to determine the four model parameters from velocity measurements while keeping κ = 0.41 is presented. The modified log-wake law compares very well with experimental data from Coleman, Lyn, Kironoto and Graf and Sarma et al. It also replicates the measured velocity profiles of the Mississippi River. In particular, it can well fit the velocity dip phenomenon in openchannels where the conventional log-wake law fails.

Modified log-wake law for zero-pressure-gradient turbulent boundary layers

This paper shows that the turbulent velocity profile for zero-pressure-gradient boundary layers is affected by the wall shear stress and convective inertia. The effect of the wall shear stress is dominant in the so-called overlap region and can be described by a logarithmic law in which the von Karman constant is about 0.4 while the additive constant depends on a Reynolds number. The effect of the convective inertia can be described by the Coles wake law with a constant wake strength about 0.76. A cubic correction term is introduced to satisfy the zero velocity gradient requirement at the boundary layer edge. Combining the logarithmic law, the wake law and the cubic correction produces a modified log-wake law, which is in excellent agreement with experimental profiles. The proposed velocity profile law is independent of Reynolds number in terms of its defect form, while it is Reynolds number dependent in terms of the inner variables. The modified log-wake law can also provide an accurate equation for skin friction in terms of the momentum thickness. Finally, by replacing the logarithmic law with van Driests mixing-length model in which the damping factor varies with Reynolds number, the modified log-wake law can be extended to the entire boundary layer flow.

Motion of spheres falling through fluids

Motion of spheres falling through fluids is a classic problem in fluid mechanics. The problem is solved for steady motion and other special cases such as for small and large Reynolds numbers, but not yet for transitional flow motion because of the complicated drag law. Recently, a series approximation for the transitional motion at zero initial velocity was proposed by applying a nonlinear perturbation method and Rubeys universal drag law to the Boussinesq–Basset–Oseen equation. This research presents a simple closed-form solution to the problem for arbitrary Reynolds numbers at nonzero initial velocity. The proposed solution is confirmed with experimental literature data and reproduces all well-known asymptotic values. The results can be directly used for particle size analysis in hydraulics laboratories; they may also help understanding the fluid–particle interactions in environmental engineering, meteorology, and powder technology.

Analysis of a Sector Crack in a Three-Dimensional Voronoi Polycrystal With Microstructural Stresses

The Mode I stress intensity factor of a sector crack in a three-dimensional Voronoi polycrystal is computed by the body force technique. Microstructural stresses arising from the elastic anisotropy of grains (cubic and hexagonal) and the random grain orientations are estimated using the Eshelby procedure and incorporated in the stress intensity factor calculations. For metallic polycrystals, it is shown that the stress intensity factor depends significantly on the elastic anisotropy ratio, the grain orientations, the remote stress state, and the microstructural stresses.

Semi-analytical model for temporal clear-water scour at prototype piers

The temporal pier scour process was studied extensively for laboratory scale but remains poorly understood for prototype piers. This research presents a novel semi-analytical solution for temporal clear-water scour at prototype piers with arbitrary initial scour conditions, by integrating the fundamental mass conservation law and the empiricism from previous studies. The proposed solution includes the conventional power-, log- and exponential laws for the initial, growth and decay phases, respectively, in a single model agreeing with recent high-quality data for long durations and prototype scour with a determination coefficient higher than 0.98. The results show that (i) temporal pier scour process is described by two basic parameters: characteristic time tc and equilibrium scour depth η∞; and (ii) the proposed solution may be useful for data correction in relation to η∞ and for real-time bridge scour monitoring during floods. Yet, its predictive power depends on the predictability of tc and η∞, indicating a future research need.

Turbulent velocity distribution with dip phenomenon in conic open channels

ABSTRACT Conic open-channel flow as occurs in sub-drains, sewers, and culverts is computed by Mannings or Darcys resistance equations for the cross-sectional average velocity only. Yet, fish passage culvert design requires the cross-sectional velocity distribution, which is proposed in this paper based on two hypotheses: (i) centreline velocity distribution follows the conventional log-law with a cubic deduction near the water surface; (ii) cross-sectional velocity distribution is described by Guo and Juliens modified log-wake-law but neglecting the squared sine function. These hypotheses result in a novel and simple velocity distribution model without any fitting parameter. Its graphical interpretation for the elliptic, parabolic, and hyperbolic channels indicates reasonable velocity contours with dip phenomenon. Further, it agrees well with circular pipe data related to the average shear velocity, velocity-dip position, centreline and cross-sectional velocity distributions. A potential application includes fish passage culvert design by specifying a low velocity zone near the wall.

Theoretical solution for laminar flow in partially-filled pipes

Partially-filled pipe flow as occurs in subsurface drains and sewers is computed by Mannings resistance equation or using the cross-sectional velocity distribution. Yet, Mannings equation is valid only for turbulent flow and no theoretical solutions and experiments are available for laminar, partially-filled pipe flow, although fully-filled pipe flow is well understood. This research solves the Navier–Stokes equations, using bipolar coordinates and the Fourier transform, for partially-filled pipe flow under steady uniform conditions, resulting in theoretical solutions for the cross-sectional velocity distribution, discharge, boundary shear stress and friction coefficient. Although the solutions are not tested with laminar flow data (a research need), they satisfy all boundary conditions and special cases. Particularly, their graphical interpretations agree qualitatively with related turbulent flow data, providing a benchmark for formulating analytical or empirical solutions for turbulent flow in the future. The proposed stage–discharge relationship is also useful for discharge measurements in drainage and sewerage systems.

Pier scour in clear water for sediment mixtures

The current pier scour design in the USA is mainly based on the CSU equation, yet a recent incisive evaluation indicates a need to change it because substantial advances were made in the last two decades for understanding the pier scour processes. The objective of this research is then to propose a simplified scour mechanism and a physically-based scour depth equation for practical design purposes. A critical review on selected previous studies is first made to form the basis of this research. A simplified scour mechanism is next proposed in terms of the pressure gradient through flow–structure, flow–sediment and sediment–structure interactions. A hypothesis on the equilibrium scour depth equation is then proposed based on the understanding of the scour mechanism and tested by flume data. Finally, the proposed scour depth equation provides a criterion and a rule of thumb for scour design and evaluation.