Debasish Pal

Grain-size distribution in suspension over a sand-gravel bed in open channel flow

Abstract Grain-size distributions of suspended load over a sand-gravel bed at two different flow velocities were studied in a laboratory flume. The experiments had been performed to study the influence of flow velocity and suspension height on grain-size distribution in suspension over a sand-gravel bed. The experimental findings show that with an increase of flow velocity, the grain-size distribution of suspended load changed from a skewed form to a bimodal one at higher suspension heights. This study focuses on the determination of the parameter β n which is the ratio of the sediment diffusion coefficient to the momentum diffusion coefficient of n th grain-size. A new relationship has been proposed involving β n , the normalizing settling velocity of sediment particles and suspension height, which is applicable for widest range of normalizing settling velocity available in literature so far. A similar parameter β for calculating total suspension concentration is also developed. The classical Rouse equation is modified with β n and β and used to compute grain-size distribution and total concentration in suspension, respectively. The computed values have shown good agreement with the measured values of experimental data.

Vertical distribution of fluid velocity and suspended sediment in open channel turbulent flow

To predict the vertical distribution of streamwise fluid velocity and suspended sediment concentration profiles in an open channel turbulent flow, we derive a theoretical model here based on the Reynolds averaged Navier–Stokes equation and the mass conservation equations of solid and fluid phases. The model includes the effects of secondary current in terms of the vertical velocity of fluid, additional vertical velocity of fluid due to the suspended particles, mixing length of sediment-laden flow and settlement of the suspended particles due to gravitational force. We numerically solve our model as coupled differential equations and the obtained solution agrees well with a wide spectrum of experimental data. A detailed error analysis asserts the superior determination accuracy of our model in comparison to the traditional log-law and Rouse equation and other existing theoretical models. The significance of the turbulent features included in the model and the importance of their co-existence to compute velocity and concentration profiles are explained. In sharp contrast to the previous researchers, the present model has significant contribution in unveiling several latent phenomena of particle-turbulence interaction throughout the flow region. The model can also address various crucial phenomena of velocity and concentration profiles that occur during flow in real situation.

Effect of particle concentration on sediment and turbulent diffusion coefficients in open-channel turbulent flow

To achieve a complete knowledge about the effect of particle concentration on sediment and turbulent diffusion coefficients in open-channel turbulent flow is a long-standing problem for the community of researchers. The effect of particle concentration is investigated on the sediment and turbulent diffusion coefficients through the inverse of turbulent Schmidt number or β which is defined by the ratio of sediment diffusion coefficient to turbulent diffusion coefficient. It is observed that with increasing particle concentration, the sediment diffusion coefficient decreases more in comparison with the turbulent diffusion coefficient for both dilute and non-dilute sediment-laden flows. The physical characteristics of β observed are expressed mathematically in terms of normalized settling velocity, reference level and reference concentration. The applicability of the mathematical formulae is confirmed by the agreement analysis between experimental data and particle concentration profile computed from the Rouse equations modified through the newly proposed expression of β. Apart from the better agreement between dilute particle concentration data and the developed Rouse equation, the striking observation is that the modified Rouse equation shows reasonable computational accuracy for non-dilute particle concentration data also. Minimum error is obtained from the present model when it is compared with the models proposed by the previous researchers.

Comparison of Turbulent Hydrodynamics with and without Emergent and Sparse Vegetation Patch in Free Surface Flow

In the present study, we have compared the turbulent hydrodynamics in open turbulent flow with and without an emergent and sparse vegetation patch. The rigid patch, located at the middle cross-sectional region, was made by acrylic cylindrical rods with regular spacing between them along streamwise and transverse directions. The measurements of flow velocity components were taken by a Nortek Vectrino Plus acoustic Doppler velocimeter, and experimental data were collected along cross section for vegetation-free fully developed flow and along the cross section which is located at the middle of the streamwise length of the vegetation patch. Inside the vegetation patch, we have observed decreased value of time-averaged streamwise velocity in comparison with those of the vegetation-free fully developed flow. The time-averaged values of transverse and vertical velocities show increased magnitude with respect to the corresponding values in the vegetation-free fully developed flow. Inside the vegetation patch, with increasing transverse length from right-hand sidewall to left-hand sidewall, the magnitudes of normal stresses gradually increase and exceed the corresponding magnitudes of normal stresses in the vegetation-free fully developed flow. Along the cross section inside the patch, the magnitudes of governing Reynolds shear stress are smaller than the corresponding values of Reynolds shear stress without the vegetation. Along the cross section inside the patch, the vectors of secondary current follow are directed towards the left-hand sidewall together with zigzag pattern in vertical direction. In the interior of the vegetation, the strength of anticlockwise vortex in terms of the magnitude of moment of momentum is greater than that of the vegetation-free fully developed flow.

Experimental Investigation of Turbulent Hydrodynamics in Developing Narrow Open Channel Flow

In the present study, a detailed experimental investigation of turbulent hydrodynamics is carried out on developing flow along the centreline of a narrow open channel. The characteristics of flow velocity, normal stresses and Reynolds stresses have been investigated. At the beginning of the modelled region, the time-averaged streamwise velocity increases up to 20% of the flow depth from the channel bed and decreases with further increase in vertical height. With increasing streamwise length, vertical location of the maximum time-averaged streamwise velocity is shifting away from the bed. The time-averaged lateral velocities are positive along the midsection in the modelling region, whereas the time-averaged vertical velocities exhibit negative value. In the modelled region, the maximum value of time-averaged lateral velocity occurs either near the channel bed or in the vicinity of the free surface; however, the peak value of time-averaged vertical velocity appears in the neighbourhood of the channel bed. In the developing flow region, the values of normal stresses in streamwise and lateral directions are maximum near the bed and decrease with vertical distance up to 40% of the flow depth from the channel bed and after that normal stresses increase with further increase in vertical distance from the channel bed. Moreover, the observed magnitudes of streamwise normal stresses are greater than the corresponding values of lateral normal stress. The normal stress in vertical direction increases with increasing vertical height from the channel bed; however, the increasing trend decreases with increasing streamwise distance. Before attaining the fully developed profile, the Reynolds shear stress exhibits a decreasing trend with increasing vertical height up to 60% of the flow depth from the channel bed, and with further increase in vertical distance, the Reynolds shear stress trend starts increasing. An important finding is that in the modelled region, the developing flow zone, the transition zone from developing flow to fully developed flow and the fully developed flow zone are detected. The present study provides a good quality data for further investigations of developing flow in a narrow open channel.

Hydrodynamics and turbulence in emergent and sparsely vegetated open channel flow

This present study reports the results of an experimental study characterizing thorough variation of turbulent hydrodynamics and flow distribution in emergent and sparsely vegetated open channel flow. An emergent and rigid sparse vegetation patch with regular spacing between stems along the flow and transverse directions was fixed in the central region of the cross-section of open channel. Experiments were conducted in subcritical flow conditions and velocity measurements were obtained with an acoustic Doppler Velocimetry system. Large variations of the turbulence intensities, Reynolds shear stress, turbulent kinetic energy and vortical motions are found in and around the vegetation patch. At any cross-section through the interior of the vegetation patch, streamwise velocity decreases with increase in streamwise length and the velocity profiles converge from the log-law to a linear profile with increasing slope. Time-averaged lateral and vertical velocities inside the vegetation patch increase with increasing streamwise distance and converge from negative values to positive values. Turbulence intensities interior of the sparse vegetation patch are more than those of without the vegetation patch. Similar to the trend of streamwise velocity profiles inside the vegetation, turbulence intensities and longitudinal-normal Reynolds shear stress profile decreases with streamwise direction. In the interior of the vegetation patch and downstream of the trailing edge, turbulent kinetic energy profiles are exhibiting irregular fluctuations and the maximum values are occurring in the outer layer. Analysis of flow distribution confirms sparse vegetation patch is inducing a serpentine flow pattern in its vicinity. At the leading edge, flow is rushing towards the right hand sidewall, and at the trailing edge, flow is turning to the left hand sidewall. In between the leading and trailing edges, the streamlines are following a zig-zag fashion at varied degree along the streamwise and lateral directions. Immediate upstream of the leading edge and in the interior of the vegetation patch, vortex motion is clearly visible and the vortices are stretched along the width of the channel with streamwise direction.

Theoretical modeling of suspended grain-size distribution in fluvial environment by stratification and secondary current approaches

Here we propose a theoretical model to compute the suspended grain-size distribution in fluvial environment. We derive the model based on the Reynolds averaged Navier–Stokes equation and the continuity equation of sediment phase. The model includes the effects of secondary current and stratification which are the cause of complex interaction between turbulence and grain-size distribution in the sediment-laden flow. Due to an immense importance of particle–particle and particle-turbulence interactions near the channel bed, we include their impacts in the boundary condition of the model. The present model has noteworthy contribution to demonstrate the phenomena of suspended grain-size distribution in the real world. Reported experimental data in literature shows well agreement with the numerical solution computed from the suggested model. The better computational accuracy of the present model is ascertained when the upper bound of calculated error between observed experimental data and computed values is found to be lowest for our model in comparison to a large number of existing models developed from different mathematical viewpoints.