Nian-Sheng Cheng

Incipient sediment motion with upward seepage

This study investigates the effect of upward bed seepage on the critical condition of incipient sediment motion in open channel flow both analytically and experimentally. The critical condition was derived by analyzing the forces acting on a sediment particle lying on a permeable horizontal bed subject to seepage. The ratio of the critical shear velocity with seepage to that without seepage depends on the ratio of theJiydraulic gradient of seepage to its critical value under the quick condition. Experimental results concerning incipient motion of cohesionless uniform sediments in open channel flow show that for a particular size of sediment, the critical shear velocity decreases with increasing seepage velocity. All measurements generally support the theoretically derived expression of the critical shear velocity in the presence of an upward seepage.

Exponential formula for computing effective viscosity.

Abstract An exponential model is proposed for evaluating the effective viscosity of a particle–fluid mixture. First, theoretical consideration is restricted to the dilute condition without effects of dynamic particle interactions and fluid turbulence. This leads to a power series expressed in terms of particle concentration, which can be viewed as an extension of the Einsteins formula. The derivation is then extended using an exponential model for the condition of high particle concentrations. The exponential formula obtained, which is not subjected to the maximum particle concentration, is found comparable to various empirical formulas available in the literature.

Hydraulic Radius for Evaluating Resistance Induced by Simulated Emergent Vegetation in Open-Channel Flows

The resistance induced by simulated emergent vegetation in open-channel flows has been interpreted differently in the literature, largely attributable to inconsistent uses of velocity and length scales in the definition of friction factor or drag coefficient and Reynolds number. By drawing analogies between pipe flows and vegetated channel flows, this study proposes a new friction function with the Reynolds number that is redefined by using a vegetation-related hydraulic radius. The new relationship is useful for consolidating various experimental data across a wide range of vegetation density. The results clearly show a monotonic decrease of the drag coefficient with the new Reynolds number, which is qualitatively comparable to other drag coefficient relationships for nonvegetated flows. This study also proposes a procedure for correcting sidewall and bed effects in the evaluation of vegetation drag.

Turbulent open-channel flow with upward seepage

Measurements of turbulent open-channel flow subjected to an upward bed seepage were performed in a laboratory flume using a two-dimensional Acoustic Doppler Velocimeter and a minipropeller. The experimental results show that the boundary seepage affects the time-mean streamwise velocity, the rnis values of the velocity fluctuations, the Reynolds shear stress and the bed shear stress in open-channel flow. Along the seepage zone, the mean streamwise velocity increases much more in the surface layer than that in the near-bed region, whereas the turbulent intensities and Reynolds shear stress increase significantly in the near-bed region. The bed shear stress that was computed using the momentum integral equation shows a steady reduction with increasing upward seepage velocity.

Review of seepage effects on turbulent open-channel flow and sediment entrainment

This paper presents a review on the state-of-the-art knowledge of how seepage affects the turbulence characteristics in open-channel flow and its implication on sediment entrainment. Published literature shows that some effects have been intensively examined and the results are well known, such as seepage effects on mean flow velocity distributions. Understanding of the other effects remains rudimentary, such as variations of turbulence intensity and bed shear stresses. In fact, many of these issues remain ambiguous with contradicting inferences and conclusions. For example, the published literature is still not unanimous as to how turbulence intensities, bed shear stresses and bed particle stability change in the presence of seepage. By reviewing literature in this area published over the past 35 years, this paper highlights the main conflicting results and attempts to explain these deviations with certain recommendations.

Two-phase modeling of suspended sediment distribution in open channel flows

Abstract The transport of suspended sediment in open channel flows is of key interest to the area of fluvial hydraulics. Traditionally, the phenomenon is analyzed as a one-phase composite system for simplification. In reality, two separate phases of liquid and solid are present. In this study, the two-phase approach of particle group model is adopted to quantify the behavior of suspended sediment transport in open channel flows. The analysis reveals a drift current due to the gradient of turbulence fluctuation, in additional to the Fickian-type dispersion due to the concentration gradient. In the vertical direction, the resulting equation from the analysis is similar to the classical convection-diffusion equation such as the Rouse model. However, the incoiporation of the additional dispersion terms predicts more accurately the sediment concentration distribution along the water depth. In the horizontal direction, the analysis shows that the mean fluid velocity is always larger than that of the sediments. The interaction between the sediment and fluid and the effects of sediment inertia are also addressed. Experiment data from the literature are used to verify the results.

Source term treatment of SWEs using surface gradient upwind method

Owing to unpredictable bed topography conditions in natural shallow flows, various numerical methods have been developed to improve the treatment of source terms in the shallow water equations. The surface gradient method is an attractive approach as it includes a numerically simple approach to model flows over topographically-varied channels. To further improve the performance of this method, this study deals with the numerical improvement of the shallow-flow source terms. The so-called surface gradient upwind method (SGUM) integrates the source term treatment in the inviscid discretization scheme. A finite volume model (FVM) with the monotonic upwind scheme for conservative laws is used. The Harten–Lax–van Leer-contact approximate Riemann solver is used to reconstruct the Riemann problem in the FVM. The proposed method is validated against published analytical, numerical, and experimental data, indicating that the SGUM is robust and treats the source terms in different flow conditions well.

Probability distribution of bed particle instability.

The probability distribution of the instability of bed particles is essential for application of statistical approaches to describe bedload transport. The instability generally depends on the near-bed flow conditions and characteristics of the particle packing on the bed surface. In this study, only irregularity of the bed particles is considered. The instability of each individual bed particle is characterised using an effective shear stress, beyond which the particle starts to move. The effective shear stresses vary randomly over the bed because of the randomness of the bed particles. For a flat bed comprised of uniform particles, the variation is demonstrated to be a narrow-banded random process with amplitudes equal to the magnitudes of the effective shear stress. A theoretical derivation shows that the probability density distribution of the effective shear stress follows the Rayleigh distribution. Subsequent analysis also indicates that the probability of the instability is proportional to the square of the bed shear stress for low rates of bedload transport.

Influence of shear stress fluctuation on bed particle mobility

Whether or not a sediment particle is entrained from a channel bed is associated with both average bed shear stress and shear stress fluctuation, the latter being flow-dependent and also related to bed irregularities. In the first part of this study, a preliminary analysis of possible fluctuations induced by bed roughness is presented for the case of an immobile plane bed comprised of unisized sediments. The result shows that the roughness-induced variation is generally comparable to that associated with near-bed turbulence, and both variations can be approximated as log-normal in terms of probability density distribution. The bed particle mobility is then analyzed by considering the effects of shear stress fluctuations. The relevant computations demonstrate that with increasing shear stress fluctuations, the probability of the mobility of a bed particle may be enhanced or weakened. For the case of low sediment entrainment, the probability is increased by turbulence. However, the probability may be reduce...

A diffusive model for evaluating thickness of bedload layer

Abstract The thickness of the bedload layer is a crucial parameter for evaluating sediment transport rates in open channel flow, but it is often determined empirically. Based on the concept of the hydrodynamic diffusion related to particle–particle interactions, an analytical model is proposed in this study for computing the thickness of the bedload layer. The coefficient of diffusion is assumed to be associated with the momentum transfer induced by the random particle motion and thus can be derived from the shear-induced particle stress. The analytical result shows that the ratio of the bedload thickness to the particle diameter depends on the dimensionless particle diameter and dimensionless bed shear stress. Differences are also examined between the present study and a few empirical formulas that are derived from experimental results for limited bed conditions.