Numerical and experimental studies of flows in open-channels with gravel and vegetation roughnesses

Abstract

Open-channels made up of simple geometry and free of obstructions are desirable for efficient water conveyance. Nowadays, large and flexible roughness elements, such as gravels and vegetation, are commonly deployed into artificial open-channels to stabilize the channel sectional shapes and to maintain the ecological balance there. Consequently, the hydrodynamic behaviour of flows in these channels will be significantly affected. The determination of the velocity and turbulence intensity profiles, as well as the hydraulic resistance, is of practical importance in the engineering design of these channels. This study aims to quantify the gravel and vegetation induced roughness effects on flows and mixings in open-channels using experimental and numerical methods. The whole study can be subdivided into the following four parts. Firstly, a three-dimensional (3D) Reynolds Averaged Navier-Stokes (RANS) model with the Spalart-Allmaras (S-A) turbulence closure has been developed to simulate the fully developed open-channel flows with smooth surface and submerged vegetation canopy. By comparing to the well-documented laboratory measurements and direct numerical simulation (DNS) results, the S-A model was valid for simulating open-channel flows with low Reynolds number (Reτ = 439) and higher Reynolds number (Reτ = 2143) over smooth bed. Furthermore, as the turbulence kinetic energy (TKE) cannot be calculated explicitly in the S-A model, an empirical equation were proposed and used to estimate the TKE. The resulting profiles of mean velocity, shear stress and TKE agree well with the well-documented experimental data. The drag force method (DFM) was used to simulate the resistance effect induced by submerged vegetation. This method is found to be able to faithfully reproduce the mean flow and turbulence structure in open-channel flows with rigid or flexible vegetation canopy. Secondly, a Double Averaged Navier-Stokes equation (DANS) model has been developed for depth-limited open-channel flows over gravels. Within the gravels the flow is highly obstructed and the porosity is low, the use of the RANS equations may not be accurate enough. Three test cases are used to validate the model: (1) an open-channel flow over a densely packed gravel bed with small-scale uniform roughness (D/d₅ ₀ ~ 13, d₅₀ = median diameter of roughness elements, D = water depth); (2) open-channel flows over large-scale sparely distributed roughness elements (D/Δ = 2.3 and 8.7, Δ = roughness height) and (3) steep slope gravel-bed river flows with D/d₅₀ = 7 ~ 25. Various methods of treatment of the gravel-induced resistance effect have been investigated. The results show that the wall function approach (WFA) is successful in simulating flows over small gravels but is not appropriate for large gravels since the vertical profile of the longitudinal velocity does not follow the logarithmic-linear relationship. The drag force method (DFM) performs better but the non-logarithmic velocity distribution generated by sparely distributed gravels cannot be simulated accurately. Noting that the turbulence length scale within the gravel layer is governed by the gravel size, the DANS model incorporating the DFM and a modified S-A turbulence closure is proposed. The turbulence length scale parameter in the S-A model is modified to address the change in the turbulence structure within the gravel layer. The computed velocity profiles agree well with the corresponding measured profiles in all cases. Particularly, the model reproduces the S-shape velocity profile for sparsely distributed large size roughness elements. The DFM is robust and can be easily integrated into the existing numerical models. Thirdly, laboratory measurements of the velocity profiles and flow resistances of open-channel flows over fixed gravel patches (GPs) under different bed slopes and flow rates were carried out. Two GPs with identical individual element size and different lengths (3.81m and 7.5m) were tested. The depth-limited uniform flow regime with relative submergence Sr (= D/ks) ranging from 2.68 to 5.94 was produced by adjusting the tailgate weir. The velocity profiles were carefully measured by using both an ultra-sound velocity profiler (UVP) and an acoustic Doppler velocimeter (ADV). The two sets of profiles measured were found to be consistent and have high correlation. The conventional methods used to determine the zero-plane displacement and estimate the bed shear velocity were then reviewed and compared. The uncertainty of the shear velocities estimated with different methods appears to be greater for the case with shorter patch length than that with longer patch length. The measured double-averaged (DA) velocity profiles were found to fit well with the log law and defect law with a non-universal Karman constant κ. Under relatively small submergence, the κ-value decreases to 0.22 for the fitting the velocity profiles by the logarithmic flow resistance law. The values of the constant Br in the logarithmic law fall within the normal range between 3.25 and 6.25. The streamwise turbulence intensity distributions were found to agree well with the available experimental data in the intermediate region and wall region. Finally, the hydrodynamics of flows over a finite length flexible vegetation patch (VP) was investigated in the laboratory. Plastic strips were attached vertically onto the flume bed section (3.4 m long × 0.3 m wide) to simulate the flexible VP. Uniform real gravels were paved before and behind the VP to represent the natural river bed. The ADV technique is used for monitoring the 3D velocity above and within the VP at high-frequency sample rates. The density effect of VP was analyzed by comparing the measured results for the high density (HD) patch (α = vegetative coefficient = 0.056 m⁻¹) and those for the low density (LD) patch (α = 0.028 m⁻¹). The VP, which retarded the flow within the canopy and accelerated the overlying flow, appeared to be swaying under different flow rates. As the elevation of occurrence of the maximum velocity gradient increases with the distance downstream from the leading edge, the position of the maximum shear stress rises with distance from the channel bottom to the time-averaged deflected height of the VP. Correspondingly, the turbulence structure changes from the boundary-layer type to the mixing-layer type and the peak TKE occurs at the top of the trailing edge, similar to those observed in the flows with rigid VP. However, comparing to the case with rigid VP, the high-level turbulence region within the adjustment region occurred at a farther downstream distance from the leading edge for the case with flexible VP, as the high frequency vibration of the strips dissipates part of the TKE. In the fully-developed region the increasing canopy density leads to the increasing degree of inflection in the mean velocity profile. The existence of the Kelvin-Helmholtz (K-H) vortices within the shear layer is confirmed by both the flow visualization and the quadrant analysis. The flow evolution within the VP was successfully replicated by a 3D RANS model incorporating the DFM and the S-A turbulence closure. In summary, the present research contributes to the knowledge and understanding of open-channel flows with gravel and vegetation roughnesses. It reveals the mean flow and turbulence structure in the fully developed flows with gravels or submerged flexible vegetation as well as the flow evolution across the finite vegetation patch. The findings are supported by both laboratory measurements and numerical modelling results, and can be useful for engineering applications.