Computational fluid dynamics modelling of boundary roughness in gravel‐bed rivers: an investigation of the effects of random variability in bed elevation

Results from a series of numerical simulations of two‐dimensional open‐channel flow, conducted using the computational fluid dynamics (CFD) code FLUENT, are compared with data quantifying the mean and turbulent characteristics of open‐channel flow over two contrasting gravel beds. Boundary roughness effects are represented using both the conventional wall function approach and a random elevation model that simulates the effects of supra‐grid‐scale roughness elements (e.g. particle clusters and small bedforms). Results obtained using the random elevation model are characterized by a peak in turbulent kinetic energy located well above the bed (typically at y/h = 0·1–0·3). This is consistent with the field data and in contrast to the results obtained using the wall function approach for which maximum turbulent kinetic energy levels occur at the bed. Use of the random elevation model to represent supra‐grid‐scale roughness also allows a reduction in the height of the near‐bed mesh cell and therefore offers some potential to overcome problems experienced by the wall function approach in flows characterized by high relative roughness. Despite these benefits, the results of simulations conducted using the random elevation model are sensitive to the horizontal and vertical mesh resolution. Increasing the horizontal mesh resolution results in an increase in the near‐bed velocity gradient and turbulent kinetic energy, effectively roughening the bed. Varying the vertical resolution of the mesh has little effect on simulated mean velocity profiles, but results in substantial changes to the shape of the turbulent kinetic energy profile. These findings have significant implications for the application of CFD within natural gravel‐bed channels, particularly with regard to issues of topographic data collection, roughness parameterization and the derivation of mesh‐independent solutions. Copyright © 2001 John Wiley & Sons, Ltd.     

Turbulence in mobile-bed streams

This study is devoted to quantify the near-bed turbulence parameters in mobile-bed flows with bed-load transport. A reduction in near-bed velocity fluctuations due to the decrease of flow velocity relative to particle velocity of the transporting particles results in an excessive near-bed damping in Reynolds shear stress (RSS) distributions. The bed particles are associated with the momentum provided from the flow to maintain their motion overcoming the bed resistance. It leads to a reduction in RSS magnitude over the entire flow depth. In the logarithmic law, the von Kármán coefficient decreases in presence of bed-load transport. The turbulent kinetic energy budget reveals that for the bed-load transport, the pressure energy diffusion rate near the bed changes sharply to a negative magnitude, implying a gain in turbulence production. According to the quadrant analysis, sweep events in mobile-bed flows are the principal mechanism of bed-load transport. The universal probability density functions for turbulence parameters given by Bose and Dey have been successfully applied in mobile-bed flows.     

High-resolution numerical simulation of turbulence in natural waterways

We develop an efficient and versatile numerical model for carrying out high-resolution simulations of turbulent flows in natural meandering streams with arbitrarily complex bathymetry. The numerical model solves the 3D, unsteady, incompressible Navier-Stokes and continuity equations in generalized curvilinear coordinates. The method can handle the arbitrary geometrical complexity of natural streams using the sharp-interface curvilinear immersed boundary (CURVIB) method of Ge and Sotiropoulos (2007) [1]. The governing equations are discretized with three-point, central, second-order accurate finite-difference formulas and integrated in time using an efficient, second-order accurate fractional step method. To enable efficient simulations on grids with tens of millions of grid nodes in long and shallow domains typical of natural streams, the algebraic multigrid (AMG) method is used to solve the Poisson equation for the pressure coupled with a matrix-free Krylov solver for the momentum equations. Depending on the desired level of resolution and available computational resources, the numerical model can either simulate, via direct numerical simulation (DNS), large-eddy simulation (LES), or unsteady Reynolds-averaged Navier-Stokes (URANS) modeling. The potential of the model as a powerful tool for simulating energetic coherent structures in turbulent flows in natural river reaches is demonstrated by applying it to carry out LES and URANS in a 50-m long natural meandering stream at resolution sufficiently fine to capture vortex shedding from centimeter-scale roughness elements on the bed. The accuracy of the simulations is demonstrated by comparisons with experimental data and the relative performance of the LES and URANS models is also discussed.     

DEPTH-AVERAGE ANALYSIS OF HYSTERESIS BETWEEN FLOW AND SEDIMENT TRANSPORT UNDER UNSTEADY CONDITIONS

1 INTRODUCTION Flow and sediment transport in natural rivers are generally unsteady, and exhibit temporal and spatial lags. Traditionally, in most hydraulic engineering problems the unsteady flow and sediment transport are approximately treated as steady …     

Fully coupled free‐surface flow and sediment transport modelling of flash floods in a desert stream in the Mojave Desert,California

For most of the year, a dry‐bed desert wash is void of water flow. Intensive rain events, however, could trigger significant flash floods that bring about highly complicated hydrodynamics and morphodynamics processes within a desert stream. We present a fully coupled three‐phase flow model of air, water, and sediment to simulate numerically the propagation of a flash flood in a field‐scale fluvial desert stream, the so‐called Tex Wash located in the Mojave Desert, California, United States. The turbulent flow of the flash flood is computed using the three‐dimensional unsteady Reynolds‐averaged Navier–Stokes equations closed with the shear stress transport k ? ω model. The free surface of the flash flood at the interface of air and water phases is computed with the level‐set method, which enables instantaneous tracking of the water surface as the flash flood propagates over the dry bed of the desert stream. The evolution of the desert fluvial stream's morphology, due to the action of the propagating flash flood on the mobile bed, is calculated using a Eulerian morphodynamics model based on the curvilinear immersed boundary method. The capabilities of the proposed numerical framework are demonstrated by applying it to simulate a flash flood event in a 0.65‐km ‐long reach of the Tex Wash, the intricate channel morphology of which is obtained using light imaging detection and ranging technology. The simulated region of the stream includes a number of bridge foundations. The simulation results of the model for the flash flood event revealed the formation of a highly complex flow field and scour patterns within the stream. Moreover, our simulation results showed that most scour processes take place during the steady phase of the flash flood, that is, after the flash flood fills the stream. The transient phase of the flash flood is rather short and contributes to a very limited amount of erosion within the desert stream.     

A Bed-load function based on kinetic theory

Bed-load transport plays a fundamental role in morphological processes of natural rivers and human-made channels.This paper presents bed-load function derived on the basis of kinetic theory. The bed-load function is obtained by integrating the pick-up rate of bed sediment with respect to its longitudinal travel distance,following the basic concept on bed-load put forward by Einstein.The pick-up rate is expressed as an upwards flux of bed sediment and determined by invoking the particle velocity distribution function derived by solving the Boltzmann equation of kinetic theory. Comparisons of the present formula with six other bed-load formulas and the experimental data are also made in this paper.The results show that the present bed-load formula agrees well with the experimental data.In addition,the influences due to collision between particles on bed-load is discussed which shows that an appreciable damping of the intensities of bed-load is observed only when the shear acting on particles is large enough to increase the concentration and intensity of random motion of bed load particles so that the collisions between sediment particles can occur.     

Well-balanced high-order centered schemes on unstructured meshes for shallow water equations with fixed and mobile bed

In this paper, we study the numerical approximation of the two-dimensional morphodynamic model governed by the shallow water equations and bed-load transport following a coupled solution strategy. The resulting system of governing equations contains non-conservative products and it is solved simultaneously within each time step. The numerical solution is obtained using a new high-order accurate centered scheme of the finite volume type on unstructured meshes, which is an extension of the one-dimensional PRICE-C scheme recently proposed in Canestrelli et al. (2009) [5]. The resulting first-order accurate centered method is then extended to high order of accuracy in space via a high order WENO reconstruction technique and in time via a local continuous space–time Galerkin predictor method. The scheme is applied to the shallow water equations and the well-balanced properties of the method are investigated. Finally, we apply the new scheme to different test cases with both fixed and movable bed. An attractive future of the proposed method is that it is particularly suitable for engineering applications since it allows practitioners to adopt the most suitable sediment transport formula which better fits the field data.     

Modification of the Engelund bed-load formula

The classic Engelund bed-load formula involves four oversimplified assumptions concerning the quantity of particles per unit bed area that can be potentially entrained into motion, the probability of sediment being entrained into motion at a given instant, the mean velocity of bed-load motion, and the dimen-sionless incipient shear stress. These four aspects are reexamined in the light of new findings in hydrodynamics, and a modified bed-load formula is then proposed. The modified formula shows promise as being reliable in predicting bed-load transport rates in a wide range of flow intensities.     

DEPTH-INTEGRATED MODELING FOR AGGRADING/DEGRADING MOBILE CHANNELS I： MODEL DEVELOPMENT

1 INTRODUCTION The study of sediment transport in alluvial river is one of the most important fields in hydraulic engineering. Sediment transport has direct influence on the evolution of riverbeds, estuaries and coastlines, and, in turn, affects decision-making of flood control, operating rule of reservoir, design of hydraulic structure and many other aspects. Models with different orders of dimensions were presented in the literature, and most of them had common basis that they were formu…     

TWO DIMENSIONAL NUMERICAL SIMULATION OF FLOW AND GEO-MORPHOLOGICAL PROCESSES NEAR HEADLANDS BY USING UNSTRUCTURED GRID

1 INTRODUCTION In recent years, due to the increase in population and industrial developments, mankind has faced manyproblems associated with rivers, coastal waters and reservoirs. Some of these problems are flood control,water supply, power generation, and irrigation. In addition, making new hydraulic structures changesnatural conditions. Prediction of these changes is necessary for designing such constructions. For solutionof these problems usually an assessment of flow pattern, sedim…     

Formation process of meandering channel by a 2D numerical simulation

A 2D depth-averaged model for hydrodynamic,sediment transport and river morphological adjustment is presented.The sediment transport submodel considers non-uniform sediment,bed surface armoring,impact of secondary flow on the direction of bed-load transport,and transverse slope of river bed.The bank erosion submodel incorporates a simple simulation method for updating bank geometry during either degradational or aggradational bed evolution.The model is applied to a 180°bend with a constant radius under unsteady flow conditions,and to Friedkin’s laboratory meander channels.The results are in acceptable agreement with measurements,confirming the two dimensional model’s potential in predicting the formation of river meandering and improving understanding of patterning processes.Future researches are needed to clarify some simplifications and limitations of the model.     

Numerical investigation of fluid mud motion using a three-dimensional hydrodynamic and two-dimensional fluid mud coupling model

A water-fluid mud coupling model is developed based on the unstructured grid finite volume coastal ocean model (FVCOM) to investigate the fluid mud motion. The hydrodynamics and sediment transport of the overlying water column are solved using the original three-dimensional ocean model. A horizontal two-dimensional fluid mud model is integrated into the FVCOM model to simulate the underlying fluid mud flow. The fluid mud interacts with the water column through the sediment flux, current, and shear stress. The friction factor between the fluid mud and the bed, which is traditionally determined empirically, is derived with the assumption that the vertical distribution of shear stress below the yield surface of fluid mud is identical to that of uniform laminar flow of Newtonian fluid in the open channel. The model is validated by experimental data and reasonable agreement is found. Compared with numerical cases with fixed friction factors, the results simulated with the derived friction factor exhibit the best agreement with the experiment, which demonstrates the necessity of the derivation of the friction factor.     

Coherent structure dynamics and sediment particle motion around a cylindrical pier in developing scour holes

Recent investigations on the dynamics of the turbulent horseshoe vortex system (THV) around cylindrical piers have shown that the rich coherent dynamics of the vortical structures is dominated by low-frequency bimodal fluctuations of the velocity field. In spite of these advances, many questions remain regarding the changes of the flow and sediment transport dynamics as scour progresses. In this investigation we carry out laboratory experiments to register the development of the scour hole around a cylindrical pier in a fine-sand bed (d ₅₀ = 0.36 mm). We use the bathymetry measured in the experiment to simulate the flow field employing the detached-eddy simulation approach (DES), which has shown to resolve most of the turbulent stresses around surface-mounted obstacles. From these simulations we compare the dynamics of the THV to the flat-bed case, and analyze the effects on particle transport and sediment flux using the Lagrangian particle model of Escauriaza and Sotiropoulos (2011b) to study the impact of the changes of the flow on the sediment dynamics.     

Experimental study on flow pattern and sediment transportation at a 90°open-channel confluence

In this paper,the evolutions of flow pattern and sediment transportation at a 90° open-channel confluence with different discharge ratios (q*) of the tributary flow to the total flow were studied.The e...     

Burst-like sediment suspension events in a sand bed river

In a much quoted paper, Jackson (1976) hypothesized that turbulent [bursting] motions such as those documented in laboratory boundary layers play a major role in alluvial sediment suspension. To date, the hypothesis remained largely untested, due to difficulties in monitoring turbulent suspension in rivers. This study provides field data documenting burst-like turbulent motions over a sandy bed channel and quantifying the role of these motions in sand suspension. The data were collected in a 10 m deep channel of the Fraser River near Mission, British Columbia, Canada. Turbulent fluctuations of both flow components, downstream and normal to the bed, along with the output of an optical suspended sediment sensor, were monitored 1 m above the river bed. Typical flow velocities averaged 0·9 ms⁻¹ at the sensors, where mean suspended sediment concentrations were 500 mgl⁻¹; decimetre height small dunes on the backs of larger, half-metre amplitude dunes covered the channel bed in the area. Brief but intense, burst-like [ejection and inrush] events were identified in the flow records, where they are responsible for a high degree of [intermittency] in shear stress over the dunes: 80 per cent of the turbulent momentum exchange across the 1 m level can be ascribed to such brief (3-8 s duration) events, active under 12 per cent of the time. In addition, the record of fluctuating sediment concentrations reveals these burst-like motions to be highly effective in vertically mixing suspended sediment and thus, ultimately, in maintaining suspended sediment transport above the dune bed. The bulk (60 and 90 per cent in two deployments) of the vertical sediment mixing was accomplished by intense events active some 10 per cent of the time. No discrete recurrence timescale for these ‘burst-like’ mixing events is evident, however. Rather, a continuous variation of return periods was observed as a function of the magnitude of vertical mixing event considered. To that extent, conceptual models of sediment transport in terms of burst events with a predictable recurrence such as proposed by Jackson (1976) may be misleading.     

Shallow sediment transport flow computation using time-varying sediment adaptation length

Based on the common approach,the adaptation length in sediment transport is normally estimated astemporally independent.However,this approach might not be theoretically justified as the process of reaching the sediment transport equilibrium stage is affected by the flow conditions in time,especially for fast moving flows,such as scour-hole developing flows.In this study,the two-dimensional（2D） shallow water formulation together with a sediment continuity-concentration（SCC） model were applied to flow with mobile sediment boundary.A timevarying approach was proposed to determine the sediment transport adaptation length to simulate the sediment erosion-deposition rate.The proposed computational model was based on the Finite Volume（FV） method.The Monotone Upwind Scheme of Conservative Laws（MUSCL）-Hancock scheme was used with the Harten Lax van Leer-contact（HLLC） approximate Riemann solver to discretize the FV model.In the flow applications of this paper,a highly discontinuous dam-break,fast sediment transport flow was used to calibrate the proposed timevarying sediment adaptation length model.Then the calibrated model was further applied to two separate experimental sediment transport flow applications documented in the literature,i.e.a highly concentrated sediment transport flow in a wide alluvial channel and a sediment aggradation flow.Good agreement with the experimental data were obtained with the proposed model simulations.The tests prove that the proposed model,which was calibrated by the discontinuous dam-break bed scouring flow,also performed well to represent rapid bed change and steady sediment mobility conditions.     

Comparison of bed shear stress in plane and curvilinear bed channel using multiple criteria

Experimental investigation on fluvial hydraulics needs a correct and accurate estimation of bed shear stress, which governs the hydrodynamics of the sediment transport. Present work compares bed shear stress estimated from the reach-averaged bed shear stress, Log profile, Quadratic stress law, Prandtl’s seventh power law, Reynolds shear stress, turbulent kinetic energy and graphical method approaches by doing experimentation on plane bed and curvilinear bed channel. On plane bed condition, the bed shear estimated from Reynolds stresses and Graphical methods are comparable to the reach-averaged bed shear stress (the difference is within 10%). However, all approaches estimate approximately less than 10% from reach-averaged bed shear stress in curvilinear bed channel.     

Modelling dam-break flows over mobile beds using a 2D coupled approach

Dam-break flows usually propagate along rivers and floodplains, where the processes of fluid flow, sediment transport and bed evolution are closely linked. However, the majority of existing two-dimensional (2D) models used to simulate dam-break flows are only applicable to fixed beds. Details are given in this paper of the development of a 2D morphodynamic model for predicting dam-break flows over mobile beds. In this model, the common 2D shallow water equations are modified, so that the effects of sediment concentrations and bed evolution on the flood wave propagation can be considered. These equations are used together with the non-equilibrium transport equations for graded sediments and the equation of bed evolution. The governing equations are solved using a matrix method, thus the hydrodynamic, sediment transport and morphological processes can be jointly solved. The model employs an unstructured finite volume algorithm, with an approximate Riemann solver, based on the Roe-MUSCL scheme. A predictor–corrector scheme is used in time stepping, leading to a second-order accurate solution in both time and space. In addition, the model considers the adjustment process of bed material composition during the morphological evolution process. The model was first verified against results from existing numerical models and laboratory experiments. It was then used to simulate dam-break flows over a fixed bed and a mobile bed to examine the differences in the predicted flood wave speed and depth. The effects of bed material size distributions on the flood flow and bed evolution were also investigated. The results indicate that there is a great difference between the dam-break flow predictions made over a fixed bed and a mobile bed. At the initial stage of a dam-break flow, the rate of bed evolution could be comparable to that of water depth change. Therefore, it is often necessary to employ the turbid water governing equations using a coupled approach for simulating dam-break flows.     

Spatial variation of flow characteristics in a subarctic meandering river in ice-covered and open-channel conditions: A 2D hydrodynamic modelling approach

To be able to understand year-round river channel evolution both at present and in the future, the spatial variation of the flow characteristics and their sediment transport capabilities under ice cover need to be detected. As the measurements done through cross-sectional drill holes cover only a small portion of the river channel area, the numerical simulations give insight into the wider spatial horizontal variation of the flow characteristics. Therefore, we simulate the ice-covered flow with a hydrodynamic two-dimensional (2D) model in a meandering subarctic river (Pulmanki River, Finland) in mid-winter conditions and compare them to the pre-winter open-channel low flow situation. Based on the simulations, which are calibrated with reference measurements, we aim to detect (1) how ice-covered mid-winter flow characteristics vary spatially and (2) the erosion and sedimentation potential of the ice-covered flow compared to open-channel conditions. The 2D hydrodynamic model replicated the observed flow characteristics in both open-channel and ice-covered conditions. During both seasons, the greatest erosional forces locate in the shallow sections. The narrow, freely flowing channel area found in mid-winter cause the main differences in the spatial flow variation between seasons. Despite the causes of the horizontal recirculating flow structures being similar in both seasons, the structures formed in different locations depended on whether the river was open or ice covered. The critical thresholds for particle entrainment are exceeded more often in open-channel conditions than during ice-covered flow. The results indicate spatially extensive sediment transport in open-channel conditions, but that the spatial variability and differences in depositional and erosional locations increase in ice-covered conditions. Asymmetrical bends and straight reaches erode throughout the year, whereas symmetrical, smaller bends mainly erode in open-channel conditions and are prone to deposition in winter. The long ice-covered season can greatly affect the annual morphology of the submerged channel. © 2019 John Wiley & Sons, Ltd.     

A new portable in situ flume for measuring critical shear stress on river beds

A new portable in situ flume(PISF)for measuring critical bed shear stress(CBSS)was developed in this study.The PISF consists of an open bottom sediment erosion chamber and an electrically-driven pump.Unlike most existing in situ flumes with similar designs,the new PISF does not rely on monitoring the flow conditions or particle density in the sediment erosion chamber;instead,it is a pre-calibrated flume.The calibration was performed by first determining CBSS of various selected sediment samples of known particle size and density(using the law of the wall),based on flow velocity-depth profiles measured in a 6 m straight open-channel flume using a Particle Image Velocimetry(PIV)system.These same particles of known CBSS were then used in the new in-situ flume under controlled lab conditions to obtain a series of calibration curves of CBSS vs.pump electrical power.A wide variety of particle types and sizes(simulated sediments)were used in this two-step calibration procedure to widen CBSS measurement range and simulate cohesive force effects.The size of the PISF is much smaller and more practical than other similar devices as lamellar flow conditions are not required and it can be applied to a wide range of sediment types including cohesive sediments.