Simulation Of Open Channel Flow Research Articles

On the role of the Froude number on flow, turbulence, and hyporheic exchange in open-channel flow through boulder arrays

In this paper, the results of numerical simulations of open-channel flow through boulder arrays at varying Froude numbers are reported. The simulations aim at clarifying the role of the Froude number on flow, turbulence, and hyporheic exchange. At low and intermediate Fr, the boulder top is above the water surface, and time-averaged streamwise flow velocity, Reynolds shear stresses, and the turbulent kinetic energy (TKE) are relatively low in the wake of boulders. Conversely, at high Fr values, the boulders are submerged, hence the flow separates at the boulder crest, creates vertical recirculation, and reattaches on the bed downstream, resulting in an area of elevated Reynolds shear stresses and TKE downstream of the boulders. Two dominant turbulence structures are observed: (i) flapping of boulder wakes with a characteristic length of 2.1 times the boulder diameter (D) at low and intermediate Fr and (ii) an upstream oriented hairpin vortex with a length scale of 1.0D at high Fr. These turbulence structures influence hyporheic exchange downstream of boulders within a limited region of x/D<2.0. In other locations, hyporheic flow is driven by downwelling flow immediately upstream of boulders with a wavelength larger than 2.9D. Finally, the normalized time-averaged hyporheic flux increases with increasing Fr, but it decreases at higher Fr values once the overtopping flow disrupts the formation of the boulder wake.

Direct numerical simulation of open-channel flow over a heterogeneous particle bed at low relative submergence

This study investigates turbulent open-channel flows over beds of irregularly arranged particles, using direct numerical simulations at a friction Reynolds number of Reτ=300. Two distinct cases are examined: a polydisperse bed (P800) composed of multiple layers of randomly distributed spheres of varying sizes, and a monodisperse bed (M1015) formed by a random distribution of uniform sized spheres, with a bottommost single layer of varied-sized particles to introduce realistic randomness. Our investigation unveils a rich network of low- and high-speed streaks within the flow field, exhibiting distinctive behaviors in different bed configurations. The P800 case presents a poorly organized flow pattern induced by the varied particle sizes and arrangements, while the M1015 case shows a more regular flow pattern, marked by larger streaks. We also observe that total wall shear stress is substantially influenced by surface roughness-induced drag, extending beyond the effects documented in existing studies of open-channel flows. The present study reveals intricate secondary flow patterns over irregular particle beds. Large-scale circulations are discerned around particle crests in the P800 case and localized circulations with increased turbulence in the M1015 case. Furthermore, analysis of Reynolds stress tensor components indicates that roughness disrupts coherent turbulent eddies, consequently mitigating peak stress. We quantify correlations between drag force and local fluid velocity fluctuations. Notably, a larger deviation in drag is observed in the P800 case compared to M1015, accentuating the influence of particle size and distribution on fluid–particle interactions.

Hydrodynamics and turbulence of free-surface flow over a backward-facing step

Three large-eddy simulations of open channel flow over a backward-facing step are performed to investigate the effect of submergence on the turbulence, hydrodynamics, and water surface deformation downstream of the step. The deformation of the water surface, the extent of the recirculation zone as well as the strength of the shear layer are a function of relative submergence. All flows downstream of the step exhibit elevated levels of turbulent shear stress and contain significant amounts of turbulent kinetic energy. The instantaneous flow features rollers immediately behind the step and horseshoe-shaped vortices shed from the shear layer, the latter being advected towards the water surface where they cause deformations. It is shown that these vortices can originate from any location along the dividing streamline; however, they contain more energy the closer to the mean attachment location they originate.

Simulation of open channel flows by an explicit incompressible mesh-free method

Simulation of open channel flows by an explicit incompressible mesh-free method

Numerical investigation of the wave interaction with flexible vegetation: model setup and validation for a single stem study case

Aquatic flexible vegetation plays a very important role in ecosystem, and has been widely used in river or coastal bank revetment. Flexible vegetation contributes to wave attenuation and soil retention. In this study, a fluid-structure bidirectional coupled numerical model (FSC model) was developed based on the codes in-house software HydroFlow@ to study the interaction between water flow and flexible vegetation. The water wave was simulated using the non-hydrostatic numerical model. Based on the nonlinear theory of elastic thin rod, a dynamic numerical model of flexible vegetation (FV model) was developed using the Finite Element Method (FEM) to simulate the large bending deformation and finite extension of a thin rod. A domain extension method was used to transfer the contact force between waves and the vegetation stem in the coupling process. The FSC model was validated using available experimental results focusing on a single stem dynamic simulation coupling with the free surface open channel flow simulation. The numerical results were in good agreements with the experiments. Relative errors of maximum deflection were less than 10%. Asymmetrical bending during a wave period were captured well compared with the measurements.

On the role of turbulent large-scale streaks in generating sediment ridges

The role of turbulent large-scale streaks or large-scale motions in forming subaqueous sediment ridges on an initially flat sediment bed is investigated with the aid of particle resolved direct numerical simulations of open channel flow at bulk Reynolds numbers up to 9500. The regular arrangement of quasi-streamwise ridges and troughs at a characteristic spanwise spacing between 1 and 1.5 times the mean fluid height is found to be a consequence of the spanwise organisation of turbulence in large-scale streamwise velocity streaks. Ridges predominantly appear in regions of weaker erosion below large-scale low-speed streaks and vice versa for troughs. The interaction between the dynamics of the large-scale streaks in the bulk flow and the evolution of sediment ridges on the sediment bed is best described as ‘top-down’ process, as the arrangement of the sediment bedforms is seen to adapt to changes in the outer flow with a time delay of several bulk time units. The observed ‘top-down’ interaction between the outer flow and the bed agrees fairly well with the conceptual model on causality in canonical channel flows proposed by Jiménez (J. Fluid Mech., vol. 842, 2018, P1, § 5.6). Mean secondary currents of Prandtl's second kind of comparable intensity and lateral spacing are found over developed sediment ridges and in single-phase smooth-wall channels alike in averages over ${O}(10)$ bulk time units. This indicates that the secondary flow commonly observed together with sediment ridges is the statistical footprint of the regularly organised large-scale streaks.

Significance of generating synthetic turbulence for zonal detached eddy simulation of shallow water flows

A zonal detached eddy simulation (ZDES) is suitable for large-scale open-channel flows with a free surface, e.g. river flow. In ZDES, only a local region is required to be investigated using large eddy simulation (LES) to obtain a high resolution of vortical structures in hydraulic engineering. In this study, a fully non-hydrostatic free-surface flow model is developed for a ZDES-type model. The focus is to analyse the critical strategy of the turbulent forcing method, which is very important for the ZDES-type model. A well-validated synthetic eddy method was established using a numerical framework and applied to generate velocity fluctuations. Based on the synthetic turbulent velocity, a new formulation of the body force term was fed into the momentum equations. A test case of a fully developed open-channel flow with a free surface was used to verify the numerical strategy. Then, another common flow problem of a free-surface flow over a fixed dune was adopted to further validate the numerical approach. The results show that the proposed numerical strategy can promote the application of the hybrid Reynolds-averaged Navier–Stokes/LES method in natural large-scale open-channel flow simulation.

On the suitability of second-order accurate finite-volume solvers for the simulation of atmospheric boundary layer flow

Abstract. The present work analyzes the quality and reliability of an important class of general-purpose, second-order accurate finite-volume (FV) solvers for the large-eddy simulation of a neutrally stratified atmospheric boundary layer (ABL) flow. The analysis is carried out within the OpenFOAM® framework, which is based on a colocated grid arrangement. A series of open-channel flow simulations are carried out using a static Smagorinsky model for subgrid scale momentum fluxes in combination with an algebraic equilibrium wall-layer model. The sensitivity of the solution to variations in numerical parameters such as grid resolution (up to 1603 control volumes), numerical solvers, and interpolation schemes for the discretization of nonlinear terms is evaluated and results are contrasted against those from a well-established mixed pseudospectral–finite-difference code. Considered flow statistics include mean streamwise velocity, resolved Reynolds stresses, velocity skewness and kurtosis, velocity spectra, and two-point autocorrelations. A quadrant analysis along with the examination of the conditionally averaged flow field are performed to investigate the mechanisms responsible for momentum transfer in the flow. It is found that at the selected grid resolutions, the considered class of FV-based solvers yields a poorly correlated flow field and is not able to accurately capture the dominant mechanisms responsible for momentum transport in the ABL. Specifically, the predicted flow field lacks the well-known sweep and ejection pairs organized side by side along the cross-stream direction, which are representative of a streamwise roll mode. This is especially true when using linear interpolation schemes for the discretization of nonlinear terms. This shortcoming leads to a misprediction of flow statistics that are relevant for ABL flow applications and to an enhanced sensitivity of the solution to variations in grid resolution, thus calling for future research aimed at reducing the impact of modeling and discretization errors.

Large-eddy simulation of an open-channel flow bounded by a semi-dense rigid filamentous canopy: Scaling and flow structure

We have carried out a large-eddy simulation of a turbulent open-channel flow over a marginally dense, fully submerged, rigid canopy. The canopy is made of a set of rigid, slender cylinders normally mounted on a solid wall. The flow in the canopy is resolved stem-by-stem by means of an immersed boundary method. It is found that the flow behavior can be categorized according to the velocity distribution into two separate spatial regions: the canopy itself and the outer region above it. Within the region occupied by the canopy elements, the velocity magnitude is found to be related to the local shear stress. Outside the canopy, a logarithmic velocity profile matching the canonical turbulent open-channel flow over rough walls is recovered albeit the strong manipulation exerted by the canopy on the buffer layer. In the innermost layer, the presence of the stems is responsible for redistributing the local momentum fluctuations from a streamwise to a spanwise leading component, inhibiting the survival of the wall streamwise velocity streaks. On the other hand, the outer region presents a structure very similar to the well-known logarithmic boundary layer with the presence of large and energetic streamwise velocity streaks generated by a system of quasistreamwise vortices. These vortices strongly contribute to the intracanopy fluctuations through vigorous sweep and ejection events that affect all the region occupied by the stems. Consistent with the results of previous investigations [H. Nepf, “Flow and transport in regions with aquatic vegetation,” Annu. Rev. Fluid Mech. 44, 123–142 (2012)], it is found that the inflection point in the mean velocity profile, produced by the drag discontinuity at the canopy tip, promotes the appearance of another system of spanwise oriented vorticity structures. However, different from previous results reported in the literature [J. Finnigan, “Turbulence in plant canopies,” Annu. Rev. Fluid Mech. 32, 519–571 (2000)], in our simulations, the presence of alternating head up–head down hairpin vortices generated by a mutual induction of the counter-rotating spanwise vortices is not observed. Instead, we advocate that the modulation of the spanwise coherent vorticity is due to the action of the external logarithmic layer structures (i.e., the outer streamwise vortices that penetrate the canopy) rather than by upwash and downwash motions induced by the mutual interaction of the spanwise rollers.

Design of experiments and goodness-of-fit in comparison of velocity fields in curved open channel flow simulation

Abstract In this paper, a methodology is suggested to evaluate the goodness-of-fit between observed and numerically predicted variables in curved open channel flows. The mathematical model uses the continuity and the Reynolds averaged Navier–Stokes (RANS) equations with the RNG κ-ɛ turbulence model, numerically solved with the commercial software Ansys Inc. The concept of design of experiments (DOE) together with some criteria of goodness-of-fit was used in a new coherent suggested methodology for the calibration and validation of the numerical model. The goodness-of-fit criterion was applied to secondary flow variables like helicity, intensity of the secondary current and the vortex index instead of the primary variables like the velocity field and the free surface. This methodology guarantees that the numerical model reproduces values of the response variables very near to the observed values and it is valid for the mesh independence analysis and the setup of other numerical parameters, including those related to the boundary conditions.

Direct numerical simulation of open-channel flow over smooth-to-rough and rough-to-smooth step changes

Direct numerical simulations (DNS) are reported for open-channel flow over streamwise-alternating patches of smooth and fully rough walls. The rough patch is a three-dimensional sinusoidal surface. Owing to the streamwise periodicity, the flow configuration consists of a step change from smooth to rough, and a step change from rough to smooth. The friction Reynolds number varies from 437 over the smooth patch to 704 over the rough patch. Through the fully resolved DNS dataset it is possible to explore many detailed aspects of this flow. Two aspects motivate this work. The first one is the equilibrium assumption that has been widely used in both experiments and computations. However, it is not clear where this assumption is valid. The detailed DNS data reveal a significant departure from equilibrium, in particular over the smooth patch. Over this patch, the mean velocity is recovered up to the beginning of the log layer after a fetch of five times the channel height. However, over the rough patch, the same recovery level is reached after a fetch of two times the channel height. This conclusion is arrived at by assuming that an error of up to 5 % is acceptable and the log layer, classically, starts from 30 wall units above the wall. The second aspect is the reported internal boundary-layer (IBL) growth rates in the literature, which are inconsistent with each other. This is conjectured to be partly caused by the diverse IBL definitions. Five common definitions are applied for the same DNS dataset. The resulting IBL thicknesses are different by 100 %, and their apparent power-law exponents are different by 50 %. The IBL concept, as a layer within which the flow feels the surface underneath, is taken as the basis to search for the proper definition. The definition based on the logarithmic slope of the velocity profile, as proposed by Elliot (Trans. Am. Geophys. Union, vol. 39, 1958, pp. 1048–1054), yields better consistency with this concept based on turbulence characteristics.

Smoothed Particle Hydrodynamics Method for Three-Dimensional Open Channel Flow Simulations

To date, the Smoothed Particle Hydrodynamics (SPH) method has been successfully applied to reproduce the hydrodynamics behind three-dimensional flow-structure interactions. However, as soon as the effect of flow resistance becomes significant, the results obtained are not consistent with observations. This is the case for open channel flows (OCF), in which the water surface is largely influenced by the boundary friction. The roughness generated by the current boundary condition methodologies is solely numerical and cannot be associated to physical values of friction. In light of this challenge, the authors present a novel formulation for the friction boundary condition. The new implementation includes an additional shear stress at the boundaries to reproduce roughness effects, allowing for the adequate three-dimensional simulation of open channel flows using the SPH method. Finally, in order to reduce the high computational cost, typical of the Lagrangian models, without interfering in the representativeness of the SPH simulations, a criterion to define the adequate fluid particle size is proposed.

Identification of parametric models in the frequency-domain through the subspace framework under LMI constraints

In this paper, an algorithm to identify parametric systems with an affine (or polynomial) parameter dependence through the subspace framework is proposed. It stands as an extension of the standard subspace-based algorithm which is well established in the linear time invariant (LTI) case. The formulation is close to the LTI identification scheme and simply involves frequency-domain data obtained at different operating points (the parameters are frozen during each experiment). The proposed algorithm allows to identify directly a parameter-dependent model instead of interpolating multiple local models as in traditional local approaches. Another contribution is that it is possible to impose the poles location through linear matrix inequalities (LMI) constraints, extending what has been done in the LTI case. This technique is applied to a numerical example and to real industrial frequency-domain data originating from an open-channel flow simulation for hydroelectricity production.

A 1D–2D coupled SPH-SWE model applied to open channel flow simulations in complicated geometries

Abstract In this study, a one- and two-dimensional (1D–2D) coupled model is developed to solve the shallow water equations (SWEs). The solutions are obtained using a Lagrangian meshless method called smoothed particle hydrodynamics (SPH) to simulate shallow water flows in converging, diverging and curved channels. A buffer zone is introduced to exchange information between the 1D and 2D SPH-SWE models. Interpolated water discharge values and water surface levels at the internal boundaries are prescribed as the inflow/outflow boundary conditions in the two SPH-SWE models. In addition, instead of using the SPH summation operator, we directly solve the continuity equation by introducing a diffusive term to suppress oscillations in the predicted water depth. The performance of the two approaches in calculating the water depth is comprehensively compared through a case study of a straight channel. Additionally, three benchmark cases involving converging, diverging and curved channels are adopted to demonstrate the ability of the proposed 1D and 2D coupled SPH-SWE model through comparisons with measured data and predicted mesh-based numerical results. The proposed model provides satisfactory accuracy and guaranteed convergence.

Investigation of velocity distribution and turbulence characteristics in subcritical circular open channel flows using a modified Reynolds stress model

The velocity distribution and turbulence characteristics in circular open channel flows are investigated numerically using the commercial CFD software Fluent. The Reynolds stress model, which has been widely used in open channel flow simulation since a dissipation rate formula for the surface boundary condition was proposed by Naot and Rodi, is employed herein to model the turbulence anisotropy. To reflect the surface damping effect and the sidewall retardation effect, a reduction factor is introduced to the surface correction term in the Reynolds transport equation, and a new constant is taken in the dissipation rate formula for the surface boundary condition. The proposed model is demonstrated to be able to reproduce the secondary currents, predict the dip phenomenon well and give right level of turbulence quantities. It is found that the pattern of secondary currents is affected by both the cross-section shape and the filling ratio. The secondary motion contributes to the dip phenomenon, which occurs when the filling ratio is greater than 50%. Turbulence intensities behave differently from those in rectangular channels when the water depth is over the radius while the eddy viscosity shows a parabolic distribution approximately irrespective of the filling ratio.

Direct numerical simulation of open-channel flow over a fully rough wall at moderate relative submergence

Direct numerical simulation of open-channel flow over a bed of spheres arranged in a regular pattern has been carried out at bulk Reynolds number and roughness Reynolds number (based on sphere diameter) of approximately 6900 and 120, respectively, for which the flow regime is fully rough. The open-channel height was approximately 5.5 times the diameter of the spheres. Extending the results obtained by Chan-Braun et al. (J. Fluid Mech., vol. 684, 2011, pp. 441–474) for an open-channel flow in the transitionally rough regime, the present purpose is to show how the flow structure changes as the fully rough regime is attained and, for the first time, to enable a direct comparison with experimental observations. Different statistical tools were used to investigate the flow field in the roughness sublayer and in the logarithmic region. The results indicate that, in the vicinity of the roughness elements, the average flow field is affected both by Reynolds number effects and by the geometrical features of the roughness, while at larger wall distances this is not the case, and roughness concepts can be applied. Thus, the roughness function is computed which in the present set-up can be expected to depend on the relative submergence. The flow–roughness interaction occurs mostly in the region above the virtual origin of the velocity profile, and the effect of form-induced velocity fluctuations is maximum at the level of sphere crests. In particular, the root mean square of fluctuations about the streamwise component of the average velocity field reflects the geometry of the spheres in the roughness sublayer and attains a maximum value just above the roughness elements. The latter is significantly weakened and shifted towards larger wall distances as compared to the transitionally rough regime or the case of a smooth wall. The spanwise length scale of turbulent velocity fluctuations in the vicinity of the sphere crests shows the same dependence on the distance from the wall as that observed over a smooth wall, and both vary with Reynolds number in a similar fashion. Moreover, the hydrodynamic force and torque experienced by the roughness elements are investigated and the footprint left by vortex structures on the stress acting on the sphere surface is observed. Finally, the possibility either to adopt an analogy between the hydrodynamic forces associated with the interaction of turbulent structures with a flat smooth wall or with the surface of the spheres is also discussed, distinguishing the skin-friction from the form-drag contributions both in the transitionally rough and in the fully rough regimes.

水面変動を考慮した開水路乱流の二次流構造と気液界面のガス交換機構に関する数値解析

We carried out a direct numerical simulation of open-channel flow with the free-surface fluctuation to investigate the effect of the fluctuation on the secondary flow and the air-water gas transfer. The DNS reproduces turbulent characteristics of the secondary flow such as the velocity-dip phenomena and counter-rotating vortex pairs, and they are almost similar to numerical results without the free-surface fluctuation. However, the maximum secondary flow velocity and the depth at which the streamwise velocity becomes maximum are changed by the influence of the free-surface fluctuation. The numerical results show the free-surface fluctuation enforces the secondary flow. The turbulent field near the sidewall that controls the air-water gas transfer is investigated on the basis of a statistical treatment such as the VITA technique. We can visualize the surface renewal eddies due to the secondary flow through the VITA technique.

Incompressible SPH simulation of open channel flow over smooth bed

The Smoothed Particle Hydrodynamics (SPH) modelling techniques are used in a variety of coastal hydrodynamic applications, but only limited works have been documented in the open channel flows. In this paper, we use the incompressible SPH model combined with an improved inflow boundary scheme to investigate the open channel flows in a laboratory scale. The inflow and outflow boundary conditions are treated by generating and removing the fluid particles at the channel end. The proposed ISPH model has been applied to the open channel laminar and turbulent flows of different flow depths and the computational results have been verified against the analytical solutions. Model convergence has been investigated through the numerical tests using different particle spacings and time steps. The artificial boundary drag force of numerical nature has been found under certain flow conditions. As further application of the model, two additional tests are also carried out, involving alternative solid boundary treatment and more complex channel topography. The present study could provide useful information on further exploitation of the SPH modelling technique in river hydrodynamics.

Large-eddy simulation of open channel flow with surface cooling

Results are presented from large-eddy simulations of an unstably stratified open channel flow, driven by a uniform pressure gradient and with zero surface shear stress and a no-slip lower boundary. The unstable stratification is applied by a constant cooling flux at the surface and an adiabatic bottom wall, with a constant source term present to ensure the temperature reaches a statistically steady state. The structure of the turbulence and the turbulence statistics are analyzed with respect to the Rayleigh number (Raτ) representative of the surface buoyancy relative to shear. The impact of the surface cooling-induced buoyancy on mean and root mean square of velocity and temperature, budgets of turbulent kinetic energy (and components), Reynolds shear stress and vertical turbulent heat flux will be investigated. Additionally, colormaps of velocity fluctuations will aid the visualization of turbulent structures on both vertical and horizontal planes in the flow. Under neutrally stratified conditions the flow is characterized by weak, full-depth, streamwise cells similar to but less coherent than Couette cells in plane Couette flow. Increased Raτ and thus increased buoyancy effects due to surface cooling lead to full-depth convection cells of significantly greater spanwise size and coherence, thus termed convective supercells. Full-depth convective cell structures of this magnitude are seen for the first time in this open channel domain, and may have important implications for turbulence analysis in a comparable tidally-driven ocean boundary layer. As such, these results motivate further study of the effect of surface cooling on tidal boundary layers simulated via an oscillating pressure gradient. Such large-scale structures may also have an important impact on RANS-based (Reynolds-averaged Navier–Stokes equations-based) modeling of turbulence within tidal, convective flows.

3D Simulation of Velocity Profile of Turbulent Flow in Open Channel with Complex Geometry

Abstract Simulation of open channel flow or river flow presents unique challenge to numerical simulators, which is widely used in the applications of computational fluid dynamics. The prediction is extremely difficult because the flow in open channel is usually transient and turbulent, the geometry is irregular and curved, and the free-surface elevation is varying with time. The results from a 3D non-linear k– ɛ turbulence model are presented to investigate the flow structure, the velocity distribution and mass transport process in a meandering compound open channel and a straight open channel. The 3D numerical model for calculating flow is set up in cylinder coordinates in order to calculate the complex boundary channel. The finite volume method is used to disperse the governing equations and the SIMPLE algorithm is applied to acquire the coupling of velocity and pressure. The non-linear k– ɛ turbulent model has good useful value because of taking into account the anisotropy and not increasing the computational time. The main contributions of this study are developing a numerical method that can be applied to predict the flow in river bends with various bend curvatures and different width-depth ratios. This study demonstrates that the 3D non-linear k– ɛ turbulence model can be used for analyzing flow structures, the velocity distribution and pollutant transport in the complex boundary open channel, this model is applicable for real river and wetland problem.