Estimation of the longitudinal dispersion coefficient using a two-zone model in a channel partially covered with artific
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Estimation of the longitudinal dispersion coefficient using a two‑zone model in a channel partially covered with artificial emergent vegetation Jiao Zhang1 · Wen‑Xin Huai1 · Hao‑Ran Shi1 · Wei‑Jie Wang2,3 Received: 24 July 2019 / Accepted: 1 September 2020 © Springer Nature B.V. 2020
Abstract Understanding scalar transport in solvents is important in chemical engineering, pollution control, and water remediation, where the longitudinal dispersion coefficient (LDC) is a key parameter for describing solute transport in fluids. For flow in classic conditions such as in a pipe or a regular open channel, formulas for LDC are derived from adopting the ideas of the advection–diffusion equation. However, when the flow encounters largescale roughness, such as an open channel with vegetation, longitudinal dispersion becomes complicated. This paper aims to estimate LDC in an open channel that is partially covered with artificial vegetation. This kind of artificial vegetation is emergent, which comprises eight floats. A two-zone model is proposed to determine LDC in this channel condition. In validating our model, experiments are conducted with Rhodamine as a tracer, whose timeconcentration curves are measured at two locations. The routing procedure is applied to obtain LDC from these curves. Results show that the measured LDCs are consistent with the predicted ones, thereby validating the accuracy and reliability of our proposed twozone model. Keywords Open-channel flow · Scalar transport · Artificial vegetation · Longitudinal dispersion coefficient · Routing procedure · Two-zone model
* Wei‑Jie Wang [email protected] 1
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, Hubei, China
2
State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
3
Department of Water Ecology and Environment, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
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Environmental Fluid Mechanics
1 Introduction 1.1 Analysis of LDC Understanding the transport of contaminants in solvents is important in chemical engineering, pollution control, and water remediation [10, 11, 14, 21, 24, 30, 37, 42, 48, 52, 72]. Contaminant transport in rivers depends on several mechanisms (e.g., molecular diffusion, advection, turbulent diffusion, dispersion, and convection), with longitudinal dispersion being important in unidimensional flows [1, 5, 15, 29, 45, 60]. Longitudinal dispersion coefficient (LDC) was first proposed by Taylor [61], who described the unidimensional dispersion mechanism in a laminar tube flow:
𝜕2 C 𝜕C 𝜕C +u = Kx 2 , 𝜕t 𝜕x 𝜕x
(1)
where C is the cross-sectional average concentration of contaminants; t is the time; u is the time-averaged longitudinal velocity; x is the streamwise direction, and Kx is LDC. The methods for estimating LDC in various laminar flows are proposed by many researchers [5, 13, 22]. However, the f
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