Applications of the concept of river tracer data similarity

The response of a river to a pollution incident is heavily influenced by the river's flow rate. To capture the full range of this response, tracer experiments are often used. The paper discusses how the concept of similarity of temporal concentration profiles can be used to better exploit the information content of such experiments. Examples are given showing that poor quality tracer data that might be thought to be of little use may yet contain valuable information. Extracting this information has the potential of improving predictions of pollutant travel times, in particular, as well as offering the prospect of improving estimates of flow rates (via dilution gauging) and dispersion coefficients (via several methods)

Residence Time Distributions for Turbulent, Critical and Laminar Pipe Flow

Longitudinal dispersion processes are often described by the Advection Dispersion Equation (ADE), which is analogous to Fick’s law of diffusion, where the impulse response function of the spatial concentration distribution is assumed to be Gaussian. This paper assesses the validity of the assumption of a Gaussian impulse response function, using Residence Time Distributions (RTDs) obtained from new laboratory data. Measured up- and down-stream temporal concentration profiles have been deconvolved to numerically infer RTDs for a range of turbulent, critical and laminar pipe flows. It is shown that the Gaussian impulse response function provides a good estimate of the system’s mixing characteristics for turbulent and critical flows, and an empirical equation to estimate the dispersion coefficient for Reynolds Number, Re, between 3,000 and 20,000 is presented. For laminar flow, here identified as Re < 3000, the RTDs do not conform to the Gaussian assumption due to insufficient time being available for the solute to become cross-sectionally well mixed. For this situation, which occurs commonly in water distribution networks, a theoretical RTD for laminar flow that assumes no radial mixing is shown to provide a good approximation of the system’s mixing characteristics at short times after injection

Vertical variation of mixing within porous sediment beds below turbulent flows

River ecosystems are influenced by contaminants in the water column, in the pore water and adsorbed to sediment particles. When exchange across the sediment-water interface (hyporheic exchange) is included in modelling, the mixing coefficient is often assumed to be constant with depth below the interface. Novel fibre-optic fluorometers have been developed and combined with a modified EROSIMESS system to quantify the vertical variation in mixing coefficient with depth below the sediment-water interface. The study considered a range of particle diameters and bed shear velocities, with the permeability Péclet number, image between 1,000 and 77,000 and the shear Reynolds number, image between 5 and 600. Different parameterisation of both an interface exchange coefficient and a spatially variable in-sediment mixing coefficient are explored. The variation of in-sediment mixing is described by an exponential function applicable over the full range of parameter combinations tested. The empirical relationship enables estimates of the depth to which concentrations of pollutants will penetrate into the bed sediment, allowing the region where exchange will occur faster than molecular diffusion to be determined

Longitudinal dispersion in unsteady pipe flows

Temporal concentration profiles resulting from an injected pulse of fluorescent tracer were recorded at multiple locations along a pipe during controlled unsteady flow conditions. A linear temporal change in discharge over durations of 5, 10, or 60 s for both accelerating and decelerating flow conditions was studied. Tests were performed for flows that changed within the turbulent range, between Reynolds numbers of 6,500 and 47,000, and for laminar to turbulent flows, between Reynolds numbers of 2,700 and 47,000. Analysis of the data shows the limitations of employing steady-state routing of temporal concentration profiles in unsteady flows. Employing a ‘flow weighted time’ routing approach, using tracer mean velocity and dispersion coefficients, provides accurate predictions of mixing in unsteady flow. For decelerating flows, longitudinal dispersion coefficients were lower than for the equivalent mean steady discharge. Previously unreported disaggregation of the tracer cloud was observed during all experiments accelerating from laminar to turbulent conditions

The impact of cylinder diameter distribution on longitudinal and transverse dispersion within random cylinder arrays

Numerous studies focus on flow and mixing within cylinder arrays because of their similarity to vegetated flows. Randomly distributed cylinders are considered to be a closer representation of the natural distribution of vegetation stems compared with regularly distributed arrays. This study builds on previous work based on a single, fixed, cylinder diameter to consider non-uniform cylinder diameter distributions. The flow fields associated with arrays of randomly distributed cylinders are modeled in two dimensions using the ANSYS Fluent Computational Fluid Dynamics software with Reynolds Stress Model turbulence closure. A transient scalar transport model is used to characterize longitudinal and transverse mixing (Dx and Dy) within each geometry. The modeling approach is validated against independent laboratory data, and the dispersion coefficients are shown to be comparable with previous experimental studies. Eight different cylinder diameter configurations (six uniform and two non-uniform) are considered, each at 20 different solid volume fractions and with seven different transverse positions for the injection location. The new dispersion data cover a broad range of solid volume fractions, for which simultaneous estimates of Dx and Dy have not been available previously. There are no systematic differences in non-dimensional Dx and Dy between uniform and non-uniform cylinder diameter distributions. When non-dimensionalized by cylinder diameter, both dispersion coefficients are independent of solid volume fraction. When non-dimensionalized by cylinder spacing, both longitudinal and transverse dispersion can be described as linear functions of the ratio of cylinder diameter to cylinder spacing

Predicting manhole mixing using a compartmental model

Manholes in combined sewers may become surcharged during storm events, resulting in complex mixing conditions. Although manhole hydrodynamics are reasonably well understood, predicting mixing across a surcharged manhole remains a challenge. An analytical compartmental mixing model for manholes, based on jet theory, has been further developed and applied to generate cumulative residence time distributions (CRTDs), which describe mixing. The modeled CRTDs were compared with the experimentally derived CRTDs of over 850 manhole configurations to evaluate how well the new compartmental model represents physical processes. The model underpredicts short-circuiting in manholes with manhole diameter to pipe diameter ratios greater than 4.4 and consequently overestimates mixing. Otherwise, the modeled CRTDs show good agreement with the experimental CRTDs. The new compartmental model represents key manhole hydrodynamics that are not represented in current software modeling packages, which assume manholes are instantaneously well-mixed. The compartmental model provides good predictions of the experimental downstream concentration profiles, although with reduced peak concentrations in those manhole configurations where short-circuiting is not well-predicted. Despite this, the compartmental model still predicts concentrations downstream of a manhole in closer agreement with the recorded data than the complete instantaneously well-mixed assumption. As an analytical model requiring no inputs other than manhole geometry, the new compartmental model applies to a wide range of manhole configurations, is robust, and is useful for predicting manhole mixing in practical applications

A multi‐component method to determine pesticides in surface water by liquid‐chromatography tandem quadrupole mass spectrometry

Pesticide pollution of surface water is a major concern in many agricultural catchments The development of rapid and accurate methods for determining pesticide concentrations in water samples is, therefore, important. Here we describe a method for the simultaneous analysis of six pesticides (metaldehyde, quinmerac, carbetamide, metazachlor, propyzamide and pendimethalin) in natural waters by direct aqueous injection with liquid chromatography-tandem mass spectrometry. The method validation showed good linearity from 0.2 to 50.0 µg/L with correlation coefficients between 0.995 and 0.999. Method accuracy ranged from 84 to 100% and precision Relative standard deviation (RSD) from 4 to 15%. The limits of detection for the targeted pesticides ranged from 0.03 to 0.36 µg/L. No significant matrix effects on quantification were observed (t-test). The method was tested on water samples from a small arable catchment in eastern England. Peak concentrations for the determinands ranged from 1 to 10 µg/L

A CFD-based mixing model for vegetated flows

This paper provides a CFD‐based modelling framework for predicting flow field, turbulence and mixing characteristics within vegetated environments such as ponds and wetlands. The framework has been implemented within a commercial CFD code – ANSYS Fluent 19 – via a set of user‐defined‐functions. Following the approach outlined by King et al. (2012), the standard k‐ε turbulence closure model has been modified to capture the energy transfer at the vegetation/clear flow shear interface and within the vegetation. The implementation assumes that vegetation is vertical, but non‐orthogonal flow in the horizontal plane is accounted for. Values for the drag coefficient and the mixing coefficients are estimated based on the vegetation stem diameter and density. Following Tanino and Nepf (2008), a switch has been incorporated to account for the fact that the relevant length scale changes from stem diameter to stem spacing as stem density increases. A set of model parameters is proposed, based on a re‐evaluation of previously published laboratory data and theoretical analysis. Five different experimental data sets are used to demonstrate that the model is able to predict mixing within fully‐vegetated systems and due to both vertical and horizontal shear layers. The framework was developed to provide a practical prediction tool for engineering purposes, in particular for the estimation of residence time distributions in real partially‐vegetated stormwater management ponds. Its implementation here within a commercial CFD package potentially facilitates application to complex pond geometries, including patches of different types of vegetation with different bulk stem diameter and density characteristics

Pore-network modelling of non-Darcy flow through heterogeneous porous media

A pore-network model (PNM) was developed to simulate non-Darcy flow through porous media. This paper investigates the impact of micro-scale heterogeneity of porous media on the inertial flow using pore-network modelling based on micro X-ray Computed Tomography (XCT) data. Laboratory experiments were carried out on a packed glass spheres sample at flow rates from 0.001 to 0.1 l/s. A pore-network was extracted from the 3D XCT scanned volume of the 50 mm diameter sample to verify the reliability of the model. The validated model was used to evaluate the role of micro-heterogeneity in natural rocks samples. The model was also used to investigate the effect of pore heterogeneity on the onset of the non-Darcy flow regime, and to estimate values of the Darcy permeability, Forchheimer coefficient and apparent permeability of the porous media. The numerical results show that the Reynold's number at which nonlinear flow occurs, is up to several orders of magnitude smaller for the heterogeneous porous domain in comparison with that for the homogeneous porous media. For the Estaillades carbonate rock sample, which has a high degree of heterogeneity, the resulting pressure distribution showed that the sample is composed of different zones, poorly connected to each other. The pressure values within each zone are nearly equal and this creates a number of stagnant zones within the sample and reduces the effective area for fluid flow. Consequently, the velocity distribution within the sample ranges from low, in stagnant zones, to high, at the connection between zones, where the inertial effects can be observed at a low pressure gradient

Unifying advective and diffusive descriptions of bedform pumping in the benthic biolayer of streams

Many water quality and ecosystem functions performed by streams occur in the benthic biolayer, the biologically active upper (~5 cm) layer of the streambed. Solute transport through the benthic biolayer is facilitated by bedform pumping, a physical process in which dynamic and static pressure variations over the surface of stationary bedforms (e.g., ripples and dunes) drive flow across the sediment‐water interface. In this paper we derive two predictive modeling frameworks, one advective and the other diffusive, for solute transport through the benthic biolayer by bedform pumping. Both frameworks closely reproduce patterns and rates of bedform pumping previously measured in the laboratory, provided that the diffusion model's dispersion coefficient declines exponentially with depth. They are also functionally equivalent, such that parameter sets inferred from the 2D advective model can be applied to the 1D diffusive model, and vice versa. The functional equivalence and complementary strengths of these two models expand the range of questions that can be answered, for example, by adopting the 2D advective model to study the effects of geomorphic processes (such as bedform adjustments to land use change) on flow‐dependent processes and the 1D diffusive model to study problems where multiple transport mechanisms combine (such as bedform pumping and turbulent diffusion). By unifying 2D advective and 1D diffusive descriptions of bedform pumping, our analytical results provide a straightforward and computationally efficient approach for predicting, and better understanding, solute transport in the benthic biolayer of streams and coastal sediments. Plain Language Summary How far and fast pollutants travel downstream is often conditioned on what happens in a thin veneer of biologically active bottom sediments called the benthic biolayer. However, before a pollutant can be removed in the benthic biolayer, it must first be transported across the sediment‐water interface and through the interstitial fluids of these surficial sediments. In this paper we demonstrate that one important mechanism for transporting solutes to, and through, the benthic biolayer—bedform pumping—can be interchangeably represented as either a two‐dimensional advective process or a one‐dimensional dispersion process. The complementary nature of these models expands the range of benthic biolayer processes that can be studied and predicted with the end goal of improving coastal and stream water quality