Dimensionless Shear Stress Research Articles

SEDIMENT DYNAMICS AND STABILITY STATUS OF THE KARRA KHOLA, HETAUDA DUN VALLEY, CENTRAL NEPAL SUB-HIMALAYA

The Karra Khola in Hetauda, Siwalik region, originates within the Dun Valley, and contributes the Rapati Nadi in Hetauda Metropolitan city. The stability status of the river is of main concern because of rapid growing of the river corridor and peripheral land areas into suburban city. The river was surveyed for hydraulic parameters, sediment characteristics, and sediment loads. Rate of sediment transport and sediment yields were computed, and competency of the river was evaluated using Shield’s parameters and Reynolds numbers. The results show that the river sediments are sandy gravel to gravelly sands, and are moderately to very poorly sorted. The total sediment yield of the whole basin near the outlet is around 2% of the maximum total sediment yield. The specific stream power (SSP) ranges from 20.98 to 2866.34 Wm-2. The dimensionless boundary shear stress to dimensionless critical shear stress ratio exceeds unity, revealing that the river is competent enough to transport its bed material loads, except in downstream stretch before the river confluences with the Rapati Nadi. The Karra Khola clearly exhibits status of degradation in the upstream stretch, high rates of transportation due to lateral erosion in the midstream stretch, and aggradation in the downstream stretch.

Analytical Solutions for a General Mixed Boundary Value Problem Associated with Motions of Fluids with Linear Dependence of Viscosity on the Pressure

An unsteady flow of incompressible Newtonian fluids with linear dependence of viscosity on the pressure between two infinite horizontal parallel plates is analytically studied. The fluid motion is induced by the upper plate that applies an arbitrary time-dependent shear stress to the fluid. General expressions for the dimensionless velocity and shear stress fields are established using a suitable change of independent variable and the finite Hankel transform. These expressions, that satisfy all imposed initial and boundary conditions, can generate exact solutions for any motion of this type of the respective fluids. For illustration, three special cases with technical relevance are considered and some important observations and graphical representations are provided. An interesting relationship is found between the solutions corresponding to motions induced by constant or ramptype shear stresses on the boundary. Furthermore, for validation of the results, the steady-state solutions corresponding to oscillatory motions are presented in different forms whose equivalence is graphically proved.

Heat transfer of a radial, nanofluid water-graphene oxide hydromagnetic flow between coaxial pipes with a variable radius ratio

The main objective of the present study is to analyze the heat transfer of a water-graphene oxide nanofluid flow between coaxial pipes, analytically. The radius ratio of pipes is variable, and a radial constant magnetic field applies to the pipes. Moreover, the Robin boundary condition is considered on the pipe’s walls. As a novelty, the exact solution is utilized to obtain the velocity distribution; further, the energy equation is solved employing the semi-analytical collocation method. The results reveal that the enhancement of nanoparticle volume fraction and radius ratio increases the dimensionless shear stress on pipes walls by 2% and 100%, respectively; consequently, the friction on walls grows. Though, the magnetic parameter has the contrary effect. Furthermore, it is observed the Eckert number augmentation decuples the bulk temperature and the heat transfer. Moreover, when the outer pipe Biot number and radius ratio increase, the bulk temperature and the heat transfer augment more than 90%. However, the magnetic parameter and nanoparticle volume fraction have a contrary effect. Also, as the inner pipe Biot number rises, we do not observe a constant pattern for the dimensionless temperature and heat transfer rate variation.

Potential dynamics of non-tidal sea bed in remote foreshore under waves and currents

The paper presents results of considerations on possibility of bottom sandy sediment transport in the south Baltic remote foreshore under waves and currents. The analysis is based on theoretical modelling of nearbed motion of water and sand in conditions defined by the long-term wave-wind climate. The wave and wind data were collected near Lubiatowo (Poland). The study site represents the area of hydrodynamics and lithodynamics typical of the south Baltic coast built of fine sands. The wind velocities and directions were measured at the Coastal Research Station (CRS) in Lubiatowo while the wave data were collected near CRS Lubiatowo, 1–2 Nm from the shoreline, at the depth of 15–20 m. Theoretical studies comprise nearbed wave-induced oscillatory velocities, wind-induced currents and wave-current interactions. The flow velocities constitute the input for determination of the bed shear stresses. The computational results, expressed in terms of the dimensionless shear stresses (values of Shields parameter), imply a potential (possibility) of intensive nearbed sand transport under extreme wave-wind conditions. The analysis shows that the sea bed lithodynamics under respective rare conditions can yield significant short-term bottom level changes in the long-term scale.

Extension and validation of aerosol wash-down model on inclined wall

During severe accidents, fission products as aerosols are released into the containment and consequently deposited on walls. The condensate flow on walls could wash the deposited aerosols downwards to the sump. The aerosol wash-down process on walls is significant to evaluate radiative source term distribution in nuclear containment. In this paper, the aerosol wash-down model AULA is extended to be valid for inclined walls and cohesive aerosols. Moreover, the condensate coverage is coupled to calculate the aerosol mass washed down by the condensate flow. A correlation of condensate coverage is proposed and validated against experimental data. In order to improve the dimensionless critical shear stress model, a correction factor, which considers wall inclination and aerosol cohesion, is deduced by the force analysis. The extended aerosol wash-down model is validated against the THAI-AW3-LAB experiment. The results comparison show generally good agreements. Furthermore, the model characteristics under severe accident conditions and the analyses on parameters, such as aerosol density, diameter, and inclination are presented and discussed.

Modeling the initiation of sediment motion under a wide range of flow conditions using a Geno-Mamdani Fuzzy Inference System method

The current study introduces a novel approach to estimate the incipient motion of sediments under a wide range of flow regimes by developing a fuzzy model with a fuzzy-band that refers to a transition from weak motion to general motion of sediment. The partial sediment entrainment is defined by fuzzy sets considering the uncertainty related to the individual ratio of inertia to viscous forces which is the definition of shear Reynolds number. In the current study, the Mamdani Fuzzy Inference System (Mamdani FIS) is used to develop a comprehensive fuzzy model of the incipient motion of sediment. The Mamdani FIS has a shortcoming regarding the training of the fuzzy model. To estimate the dimensionless shear stress, a new method is developed by combining a genetic algorithm with the fuzzy approach which is named the Geno-Mamdani Fuzzy Inference System (GMFIS) method. The performance of the GMFIS model is evaluated using experimental data by considering root mean square error (RMSE), Nash-Sutcliffe coefficient of efficiency (CE), degree of robustness (Dr), and concordance coefficient (CC) as evaluation criteria. The GMFIS model performed very well based on the RMSE, CE, Dr, and CC values and satisfactorily represented the three types of incipient motion. Finally, a new range of fuzzy, dimensionless, critical shear stress values is established in all flow conditions from weak to general sediment entrainment.

Exact solutions for unsteady motion between parallel plates of some fluids with power-law dependence of viscosity on the pressure

Unsteady motion between two infinite horizontal parallel plates of incompressible viscous fluids with a power-law dependence of viscosity on the pressure is studied analytically. The fluid motion is generated by the lower plate that is moving in its plane with a time dependent velocity. General solutions for dimensionless velocity and shear stress fields are established using suitable changes of independent variable and unknown function. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any motion of this kind of respective fluids. Consequently, the problem in discussion is completely solved. For illustration, three particular cases with engineering applications are considered and graphical representations are presented and discussed. The solutions corresponding to some motions due to an accelerated plate are connected to those of the simple Couette flow by means of Riemann-Liouville fractional integral operator. The solutions corresponding to oscillating motions are presented as sums of steady-state and transient components and, for the validation of results that have been obtained, the steady-state solutions are presented in different forms whose equivalence is graphically proved. The required time to reach the steady-state is graphically determined both for oscillating motions and the simple Couette flow.

The influence of magnetized couple stress heat, and mass transfer flow in a stretching cylinder with convective boundary condition, cross-diffusion, and chemical reaction

This paper addresses an analysis for axisymmetric boundary layer couple stress fluid flow by stretching cylinder under the influence of the magnetic field, chemical reaction, Soret, and Dufour. The leading partial differential equations of boundary layer flow are transformed into nonlinear differential equations by applying similarity transformations then solved by the Bvph2.0 based on Homotopy analysis method (HAM). The effect of pertinent parameters shown graphically and observed that velocity decreases when Reynold number and magnetic parameters are increased. The velocity, temperature, and concentrations are enhanced with curvature parameter rise. The dimensionless skin shear stress (skin friction coefficient), heat and mass transfer rates are computed and its convergence analysis also studied. It is assumed that the axial velocity decelerates for the couple stress parameter while the thermal and solutal profile reverse situation is observed.

Modeling Bed Shear Stress Distribution in Rectangular Channels Using the Entropic Parameter.

The evaluation of bed shear stress distribution is fundamental to predicting the transport of sediments and pollutants in rivers and to designing successful stable open channels. Such distribution cannot be determined easily as it depends on the velocity field, the shape of the cross section, and the bed roughness conditions. In recent years, information theory has been proven to be reliable for estimating shear stress along the wetted perimeter of open channels. The entropy models require the knowledge of the shear stress maximum and mean values to calculate the Lagrange multipliers, which are necessary to the resolution of the shear stress probability distribution function. This paper proposes a new formulation which stems from the maximization of the Tsallis entropy and simplifies the calculation of the Lagrange coefficients in order to estimate the bed shear stress distribution in open-channel flows. This formulation introduces a relationship between the dimensionless mean shear stress and the entropic parameter which is based on the ratio between the observed mean and maximum velocity of an open-channel cross section. The validity of the derived expression was tested on a large set of literature laboratory measurements in rectangular cross sections having different bed and sidewall roughness conditions as well as various water discharges and flow depths. A detailed error analysis showed good agreement with the experimental data, which allowed linking the small-scale dynamic processes to the large-scale kinematic ones.

EXACT SOLUTIONS FOR OSCILLATING MOTIONS OF SOME FLUIDS WITH POWER-LAW DEPENDENCE OF VISCOSITY ON THE PRESSURE

Analytical expressions for the steady-state components of the dimensionless starting solutions corresponding to some oscillatory motions through a horizontal rectangular channel of two classes of incompressible Newtonian fluids with power-law dependence of viscosity on the pressure are established in the simplest forms. The fluid motion is generated by the lower plate that oscillates in its plane. For validation, three limiting cases are considered and interesting graphical representations are provided. It is worth pointing out the fact that such solutions are important in practice for those who want to eliminate the transients from their experiments. In addition, the dimensionless steady shear stresses corresponding to the simple Couette flow of such fluids are constants on the whole flow domain although the adequate velocity fields are functions of y

Scouring by submerged steady water jet vertically impinging on a cohesive bed

In this study, an experimental apparatus was designed and set up a in laboratory to observe the vertical submerged jet scouring of cohesive beds. The critical conditions for the onset of scouring, as well as the scour hole dimensions were investigated. The test cohesive beds had different water contents and contained 12.5% clay, 73.5% silt, and 14% fine sand. Based on the experimental and dimensional analysis results, the scour hole dimensions are predicted as functions of the jet velocity, scouring duration, impingement height, jet nozzle diameter, water content, and critical shear stress of the bed sediments. In addition, a scour rate formula for the initial stage is proposed in terms of the dimensionless water content and the dimensionless excess shear stress. As these parameters are defined and already known, the developed functional relationships have immense potential and application in engineering works such as dredging or extraction of objects such as anchors from sediment bed.

Entropy Analysis on Unsteady MHD Flow of Casson Nanofluid over a Stretching Vertical Plate with Thermal Radiation Effect

This article proposes to study the entropy analysis on an unsteady magnetohydrodynamic flow of Casson nanofluid and convective heat transfer over a time dependent stretching vertical plate. We have treated Buongiorno’s model to characterize the thermophysical properties of nanofluid. The effect of thermal radiation and viscous dissipation of energy for non-Newtonian nanofluid and the external magnetic field are examined. The set of partial differential equations for time dependent flow of nanofluid are reduced to a system of coupled ODEs by a suitable similarity transformation. These reduced equations are solved by employing the fourth order Runge–Kutta-Fehlberg method along with shooting technique. The flow behavior of non-Newtonian Casson nanofluid, heat transfer characteristics, nanoparticle concentration profiles and entropy analysis have been made to understand the impact of different dimensionless parameters. Furthermore, the expression for dimensionless wall shear stress, heat and mass transfer rate over a heated vertical plate have been investigated. The study shows that entropy generation sharply increases with Casson parameter, whereas it increases near the plate with the thermal radiation. The entropy generation measuring through Bejan number has significant impact in aeronautics propulsion and power engineering to predict the efficient performance of the entire system.

Bankfull Transport Capacity and the Threshold of Motion in Coarse‐Grained Rivers

AbstractThe threshold stress for bed sediment transport exerts a primary control on the geometry and stability of coarse‐grained rivers (diameter ≥ 5 mm). Understanding how riverbed mobility couples to channel form is a key mechanistic link for predicting river response to external perturbations such as land use practices and changing climate. Unfortunately, determination of a representative threshold stress is notoriously difficult in the field. Empirical studies have observed that the critical dimensionless shear (Shields) stress (τ*c) is correlated with channel slope, a property that is substantially easier to estimate. Mechanistic models have been developed to explain the observed correlation; however, limited field data preclude the widespread application of these models. For practical reasons, the empirical regressions between slope and τ*c are utilized as predictive models. Through a large compilation of field data, we demonstrate that there are two significant problems with using the empirical regressions: (1) they are based on a partial sampling of the observed parameter space of coarse‐grained rivers, and (2) they do not capture the covariation between the bankfull Shields stress (τ*bf) and τ*c. These regressions provide spurious predictions for the bankfull transport capacity (τ*bf/τ*c) of gravel‐bed rivers. When site‐specific empirical measurements of τ*c are made, coarse‐grained rivers exhibit a remarkably constant transport capacity that is in close agreement with equilibrium channel theory (τ*bf = 1.2τ*c). From these data we advocate that, in the absence of measurements, τ*c can be reasonably estimated from the τ*bf using equilibrium channel theory.

Combining multi-physical measurements to quantify bedload transport and morphodynamics interactions in an Alpine braiding river reach

Understanding the interactions between bedload transport and morpholdynamics in braided streams has important applications in river management and restoration. Direct field measurements addressing this question are however scarce as they are often challenging to perform. Here, we report an extensive two-month field campaign in an Alpine braided reach (La Séveraisse river, French Alps) that experienced predictable daily peak discharge (48 events observed) generating significant bedload transport and morphological changes during the melting season. We monitored these processes using a wide range of direct and indirect techniques (bedload sampling, continuous seismic measurements, pebbles tracking, topographic surveys, remote sensing using ground control cameras and drone flights). Doing so, surrogate measurements allowed to extend temporally discrete manual bedload sampling, and to extend spatially local riverbed cross section measurements. These measurements provide unique complementary constraints on the targeted physics, at various spatial and temporal scales which enabled us to draw robust conclusions. Data showed a progressive decrease in bedload transport for a given flow rate along the two months period. Simultaneously, river morphology in the braided sections changed from an incised to a more distributed configuration which led to a decrease of local maxima in dimensionless shear stresses in the braided reach for similar flow conditions. This control of bedload transport by maximum local shear stresses was in line with tracked pebble surveys indicating that coarse bedload particles were mostly transported in the main active channel. At the reach scale, this transport was found to be more efficient in laterally confined sections than in braided ones which has important implications in terms of bedload estimation in alternative confined and braided (unconfined) rivers. Finally, this study highlight the interest to combine a large variety of traditional and innovative measurements techniques to better understand complex sediment transport processes in the field.

Development of a vector‐based 3D grain entrainment model with application to X‐ray computed tomography scanned riverbed sediment

AbstractSediment transport equations typically produce transport rates that are biased by orders of magnitude. A causal component of this inaccuracy is the inability to represent complex grain‐scale interactions controlling entrainment. Grain‐scale incipient motion has long been modelled using geometric relationships based on simplified particle geometry and two‐dimensional (2D) force or moment balances. However, this approach neglects many complexities of real grains, including grain shape, cohesion and the angle of entrainment relative to flow direction. To better represent this complexity, we develop the first vector‐based, fully three‐dimensional (3D) grain rotation entrainment model that can be used to resolve any entrainment formulation in 3D, and which also includes the effect of matrix cohesion. To apply this model we use X‐ray computed tomography to quantify the 3D structure of water‐worked river grains. We compare our 3D model results with those derived from application of a 2D entrainment model. We find that the 2D approach produces estimates of dimensionless critical shear stress ( ) that are an order of magnitude lower than our 3D model. We demonstrate that it is more appropriate to use the c‐axis when calculating 2D projections, which increases values of to more closely match our 3D estimates. The 3D model reveals that the main controls on critical shear stress in our samples are projection of grains, cohesive effects from a fine‐grained matrix, and bearing angle for the plane of rotation (the lateral angle of departure from downstream flow that, in part, defines the grain's direction of pivot about an axis formed by two contact points in 3D). The structural precision of our 3D model demonstrates sources of geometric error inherent in 2D models. By improving flow properties to better replicate local hydraulics in our 3D model, entrainment modelling of scanned riverbed grains has the potential for benchmarking 2D model enhancements. © 2019 The Authors. Earth Surface Processes and Landforms Published by John Wiley & Sons Ltd.

Effect of seepage flow on incipient motion of sand particles in a bed subjected to surface flow

Understanding the interaction of the groundwater seepage flow and sediment transport along permeable boundaries is essential for managing soil beds and bank erosion. A significant bank failure may occur due to sediment transport under the boiling condition. In the present study, an experiment is conducted to investigate the effects of injection or upward seepage on the critical shear stress of a cohesionless soil bed subjected to surface flow. The upward seepage force acting on the soil bed particles may reduce the virtual weight of the particles. In turn, it may also reduce the critical shear stress acting on the particles. A theoretical analysis examines how the upward seepage force acts to modify the critical shear stress for the sediment entrainment due to the increase in the hydraulic gradient of the seepage flow. A force analysis reveals that the ratio of the critical shear stress with seepage to that without seepage is dependent on the ratio of the hydraulic gradient of seepage to its value at the quicksand condition. A test apparatus was built, and the effects of injection on the critical shear stress of cohesionless soil bed particles were measured. An acrylic channel with a rectangular cross section was prepared, and a section of a cohesionless soil bed subjected to an upward seepage flow was installed at the bottom of the channel. The experiment demonstrates that the induced seepage affects the dynamics of the channel flow, even though the magnitude of the seepage flow velocity is significantly smaller than that of the free surface water flow. The test results show that the dimensionless critical shear stress of the cohesionless soil bed particles decreases slightly as the hydraulic gradient of the seepage flow is increased when critical shear stress is determined at the upstream edge of the seepage zone. Furthermore, the dimensionless critical shear stress decreases sharply with the increment of the hydraulic gradient of the seepage flow when critical shear stress is determined in the seepage zone. However, it does not decrease in either case, as was theoretically assumed, even when the hydraulic gradient approaches to the critical hydraulic gradient or the quicksand condition.

Critical scaling for yield is independent of distance to isostaticity

Using discrete element simulations, we demonstrate that critical behavior for yielding in soft disk and sphere packings is independent of distance to isostaticity over a wide range of dimensionless pressures. Jammed states are explored via quasistatic shear at fixed pressure, and the statistics of the dimensionless shear stress $\mu$ of these states obey a scaling description with diverging length scale $\xi \propto |\mu-\mu_c|^{-\nu}$. The critical scaling functions and values of the scaling exponents are nearly independent of distance to isostaticity despite the large range of pressures studied. Our results demonstrate that yielding of jammed systems represents a distinct nonequilibrium critical transition from the isostatic critical transition which has been demonstrated by previous studies. Our results may also be useful in deriving nonlocal rheological descriptions of granular materials, foams, emulsions, and other soft particulate materials.

Effects of ice cover on the incipient motion of bed material and shear stress around side-by-side bridge piers

In the current study, a series of experiments were carried out to investigate the scouring process around side-by-side bridge piers under both open flow and ice-covered flow conditions. Three non-uniform natural sediments and four pairs of side-by-side bridge piers were used in this experimental study. The mechanism of incipient motion of the sediments under ice-covered conditions has been investigated. The role of the boundary shear Reynolds number, critical dimensionless shear stress, particle densimetric Froude number, grain size and roughness of ice cover on the incipient motion of bed material have been studied. Results show that the critical dimensionless shear stress increases with an increase in the particle densimetric Froude number. In addition, with an increase in the boundary shear Reynolds number, the critical dimensionless shear stress increases correspondingly. For the same critical dimensionless shear stress, the finer sediment needs a lower boundary shear Reynolds number for the incipient motion of sediment particles. For the same grain size of bed material, a lower critical dimensionless shear stress is needed for the incipient motion of sediment particles under rough ice-covered flow condition. Results of this study present valuable outcome to identify the feature of sediment motion near the scour hole under ice-covered flow conditions.

Experimental Investigation on the Erosion Threshold and Rate of Gravel and Silty Clay Mixtures

Abstract. The field of cohesive and noncohesive mixture erosion is not fully understood because of the numerous factors that influence soil erodibility. In this study, erosion experiments were conducted on mixtures of gravel and silty clay in proportions varying from 0% to 100% by weight. The critical shear stress of erosion and the erosion rate were quantified using an erosion function apparatus (EFA). Experimental data revealed that the mixture critical shear stress first decreased and then increased with an increasing cohesive fraction for mixtures with silty clay contents up to 50%. The critical shear stress of the mixture showed an increasing trend as the silty clay content varied from 60% to 100%. A transition from noncohesive to cohesive erosion behavior occurred at silty clay contents between 30% and 35%. The appropriateness of a dimensionless nonlinear excess shear stress model and the Wilson model was tested based on the EFA experimental data. The dimensionless excess shear stress model was shown to be appropriate for noncohesive mixtures, while the Wilson model performed better than the dimensionless excess shear stress model for cohesive mixtures. Keywords: Critical shear stress, Erosion rate, Dimensionless nonlinear excess shear stress, Soil mixture, Wilson model.

Critical runoff depth estimation for incipient motion of non-cohesive sediment on loose soil slope under heavy rainfall

Incipient motion of non-cohesive sediment, as a branch of water erosion, has been studied for decades, and criteria proposed in predicting incipient motion mainly focus on dimensionless shear stress and shear velocity. The two parameters could provide runoff erosive power, however, are invisible and not easy-measured in experiment. In this paper, critical runoff depth was recognized as another parameter, which is visible, measurable, and closely connected with shear velocity. To get it, a mathematical model coupling surface flow and subsurface flow was established, and they are governed by Navier‒Stokes equation and Brinkman‒extended Darcy equation, respectively. Velocity derived from the model could be indirectly applied in particle force analysis and finally a new criterion about critical runoff depth was obtained. Accuracy of the criterion was verified by comparison of experimental and theoretical values, e.g. theoretical critical runoff depth ranges from 2.71 ∼ 1.14 mm with a slope angle range of 20 ∼ 28° and mean particle diameter of 2.5 mm while the corresponding experiment values ranges from 3 ∼ 1 mm and the absolute errors are less than 0.3 mm. Compared with Yang’s formula, this criterion could also be applied in predicting incipient motion of non-cohesive sediment for its significant advantages of high accuracy and concise formulation.