Laminar Open Channel Flow Research Articles

Vertical concentration distribution of fine settling particles in a pulsatile laminar open channel flow

Vertical concentration distribution of fine settling particles in a pulsatile laminar open channel flow

Overland flow hydrodynamic characteristics in rough beds at low Reynolds numbers

This paper considers overland flow resistance at low Reynolds numbers through analysis of experimental runs carried out using water only and water/glycerol mixtures. We first examined the power relationship between the Darcy–Weisbach friction factor f and the Reynolds number Re to obtain the values of the K coefficient and b exponent. These results confirmed the applicability of the values of b suggested in literature, while K required a specific calibration for laminar open-channel flows. The analysis revealed that transition from a laminar to turbulent flow regime for water only flows occurred at a threshold value of Re equal to 500 as described historically. The estimate of f by the power relationship and the calibrated b and K values were reliable for water only runs when Re ≥ 500. The measurements were also used to test a theoretical flow resistance law based on a power-velocity distribution. The calibrated theoretical relationship between the velocity profile parameter Γv, bed slope, flow Froude number and Re enabled a good estimate of f for water flows. For mixed fluid flows, the effect of the velocity profile shape was considered calibrating this relationship by two datasets obtained setting a threshold Reynolds number equal to 7. For flows with Re < 7, the shape of the velocity profile can be linear or convex while for flows at Re ≥ 7 the shape of the velocity distribution is always concave. The theoretical flow resistance allowed an accurate estimate also for mixed fluid flows, even at Re < 7. The different shape of the power-velocity distribution highlighted that mixed flows behave differently as compared to water only flows.

Migration of buoyancy-controlled active particles in a laminar open-channel flow

The migration of active particles in a laminar open-channel flow is significant for many ecological and biological processes associated with ambient water, for example, the harmful algae blooms in the long-distance water conveyance project. This paper presents an analytical analysis of the migration of the buoyancy-controlled active particles in a laminar open-channel flow. The analytical solution of concentration distribution has also been derived for the active particle cloud in the laminar open-channel flow under the combined action of ambient flow and self-migration of active particles, by combing Chatwin’s long-time asymptotic expansion and central concentration moments. The analytical solution shows that the active particle cloud accumulates near the surface rather than uniform distribution in the cross-section even for the long-time evolution. The analytical solutions are also been rigorously derived to reflect the holistic characteristics of the active-particle cloud, including the total quantity over each streamline, moving velocity of mass center, longitudinal dispersivity, skewness, and kurtosis have been rigorously derived for an instantaneous point source in a laminar open-channel flow. It is found that the distribution of total active particles over each streamline, centroid motion, and longitudinal dispersion eventually reach a stable status with a necessary time dependent on the relative strength of the vertical migration velocity and the total vertical diffusion. However, the self-migration of active particles results in the deviation of the moving velocity of mass center from the depth-averaged flow velocity. The longitudinal dispersivity of the active particle cloud gradually increases to the peak and then decreases to a constant value, in contrast to the monotonous increase for the passive particle cloud. It is also found that the strong vertical self-migration can result in changes of skewness and kurtosis of concentration distribution: negative skewness and positive kurtosis during the initial stage. However, both of them gradually tend to zero for the long-time evolution of the active particle cloud.

Continuous hydraulic jumps in laminar channel flow

Abstract

Drag force and torque of a stationary sphere in a uniform laminar open channel flow

Drag force and torque of a stationary sphere in a uniform laminar open channel flow

On the effect of solute release position on plume dispersion

Associated with Taylor dispersion, in this paper we analyze how the vertical position of a point-source solute release will affect the transport process in laminar open channel flow, through obtaining and applying analytical solution by the two-scale perturbation analysis (Wu and Chen, 2014, J. Fluid Mech., 740, 196–213), which is verified and supported by results from numerical simulations. Based on multi-dimensional spatial concentration distribution of the solute plume, we resort to the previously proposed criterion for identifying the stage of solute transport characterized by the dispersion-dominated (Taylor dispersion) regime, focusing on the relative uniformity of concentration distribution across a given family of curved surfaces (Wu et al., 2016, Sci. Rep., 6, 20556). The most important finding is that for the solute transport transition into the dispersion-dominated regime, the necessary time is about 50% more for the case of solute release at free water surface compared with that at the channel bed, which is substantial under typical physical parameters. Other effects of release position include affecting the displacement of the solute plume centroid, the value of the maximum mean concentration, and non-Gaussian properties regarding the form of the streamwise distribution of the mean concentration.

Solute dispersion in open channel flow with bed absorption

Reactive solute dispersion is of essential significance in various ecological and environmental applications. It is only qualitatively known that boundary absorption depletes pollutant around the boundary and reduces the concentration nearby. All the existing studies on this topic have been focused on the longitudinally distributed mean concentration, far from enough to fully characterize the transport process with tremendous cross-sectional concentration nonuniformity. This work presents an analytical study of the evolution of two-dimensional concentration distribution for solute dispersion in a laminar open channel flow with bed absorption. The fourth order Aris-Gill expansion proposed in our previous study (Wang and Chen, 2016b) is further extended for the case with bed absorption to cover the transitional effects of skewness and kurtosis. Results reveal the extremely nonuniform cross-sectional concentration distribution, and demonstrate that concentration at the bed instead of the mean should be used for reliable quantification of the absorption flux. The accurate two-dimensional concentration distribution presented in this study brings important environmental implications such as risk assessment associated with peak concentration position and duration of toxic pollutant cloud in open channel waters.

Performance of the analytical solutions for Taylor dispersion process in open channel flow

Summary The present paper provides a systematical analysis for concentration distribution of Taylor dispersion in laminar open channel flow, seeking fundamental understandings for the physical process of solute transport that generally applies to natural rivers. As a continuation and a direct numerical verification of the previous theoretical work (Wu, Z., Chen, G.Q., 2014. Journal of Hydrology, 519: 1974–1984.), in this paper we attempt to understand that to what extent the obtained analytical solutions are valid for the multi-dimensional concentration distribution, which is vital for the key conclusion of the so-called slow-decaying transient effect. It is shown that as a first estimation, even asymptotically, the longitudinal skewness of the concentration distribution should be incorporated to predict the vertical concentration correctly. Thus the traditional truncation of the concentration expansion is considered to be insufficient for the first estimation. The analytical solution by the two-scale perturbation analysis with modifications up to the second order is shown to be a most economical solution to give a reasonably good prediction.

Experimental setup for measuring roll waves on laminar open channel flows

Experimental studies on open channel flows are explored mostly because of their importance in validating analytical and numerical models. Although steady flows are usually measured and explored, difficulties arise in the precise execution of this task when the free surface becomes oscillatory. This paper presents a methodology for measuring a particular non-stationary phenomenon that occurs under specific conditions, namely, roll waves. Limited data exists in literature on roll waves. The objective of this work is to contribute to this database and to describe a useful experimental method for measuring roll waves. Based on some well-known literature experiments, an experimental setup was designed to achieve the free surface flow of a viscous fluid in a steady and uniform configuration. The flow was set to generate roll waves and controlled disturbances were applied at the inlet to develop roll waves. These waves were then measured using a photometric device based on a light absorption technique. The wave profiles for different flow configurations are presented. Experimental results were compared with numerical simulations to assess the validity of the measurements taken.

Analytical solution for scalar transport in open channel flow: Slow-decaying transient effect

Summary It is well known that the extensively applied Taylor dispersion model only predicts the longitudinally distributed mean concentration. While at the same time, applications as the risk assessment for toxic pollutant transport in environmental fluid flows require detailed information on the cross-sectional concentration distribution. As shown by some recent progress (Wu, Z., Chen, G.Q., 2014, J. Fluid Mech., 740, 196–213.), the deviation of transverse concentration from the mean can be remarkable for a very long time, which is termed as the slow-decaying transient effect. Thus it is important to examine the process of concentration evolution for scalar transport in laminar open channel flow. In this paper, the idealized case of a uniform and instantaneous scalar release across the channel is analytically explored by a two-scale perturbation analysis. The validity of the Taylor dispersion model for the mean concentration is discussed by the obtained analytical solution. For the first time, the two-dimensional concentration distribution for the open channel flow is explored analytically. Corresponding time scales for the concentration evolution are determined, indicating that the process for the vertical concentration difference to diminish will be much slower than that for the mean concentration to become Gaussian. Dominated by the so-called slow-decaying transient effect, the uniform vertical distribution needs to be modified to predict the vertical concentration distribution correctly.

Open channel flows of magnetic fluid induced by traveling magnetic field

A theoretical analysis is made on laminar open channel flows of magnetic fluid induced by a non uniform traveling magnetic field which is applied with a stator of a single-sided linear induction motor. The induced flows are mainly in the direction opposite to the traveling direction of the magnetic field and in proportion to the phase velocity of the magnetic field. The velocity profiles are greatly affected by dimensionless wave number of the magnetic field. Near the bottom of the channel, the theoretical velocity distributions agree well with experimental ones which are measured with a laser optical fiber velocity sensor. However, the experimental velocity distributions become larger near the free surface.

A study on the stability of laminar open-channel flow over a sandy rippled bed

The bed of a river often features some kinds of bedform, such as sand ripples, dunes, and so on. Even if the bed is smooth initially, disturbances arising from the bed or other external sources will cause the laminar flow in an open channel to become unstable as soon as the flow develops, thereby leading to the formation of sand ripples on the bed. In return, the formation of the sand ripples will modify the instability path of the laminar flow passing over them. The wavy character of the bed will induce further instability of the flow, which is essentially different from that on a smooth bed: the neutral curve will move forward and the critical Reynolds number will decrease. The flow is unstable in response to a wider range of the disturbance wave number, or the laminar flow instability can happen more easily. The propagation speed of the sand ripples also affects the flow instability, since the stability of open channel flow over a movable bed is fundamentally different from that on a rigid bed. These instability effects are discussed in detail in this paper.

Sand wavelets in laminar open-channel flows

The results of experimental investigations indicate that sand wavelets can be generated from plane-bed conditions in open-channel laminar flow, the lengths, shapes and patterns of generation for these wavelets being consistent with observations for alluvial flows. Wavelets are of a preferred wavelength which is relatively insensitive to the characteristics of the applied flow and primarily a function of the size of the sediment, these wavelengths λ for alluvial and laminar open-channel flows over beds of quartz and lightweight sediments of size d = 0.2 mm to d = 1.6 mm being simply described by λ = 175d 0.75, where λ and d are expressed in millimetres. The laminar-flow sand-wavelet data present significant implications to contemporary understanding of bed-form mechanics, with both ripples and dunes being postulated to subsequently develop from these wavelets for alluvial flows. The data also raise significant questions as to whether the generation of ripples and dunes in alluvial flows can be attributed to an organised structure of turbulence within the flow.

Hydraulics of laminar open-channel flow

The concepts of onedimensional flow and quasi-uniform flow are employed to derive the fundamental differential equation of gradually varied laminar flow in open channels. The equation is solved for...