Fred Sonnenwald

Transverse and longitudinal mixing in real emergent vegetation at low velocities

Understanding solute mixing within real vegetation is critical to predicting and evaluating the performance of engineered natural systems such as storm water ponds. For the first time, mixing has been quantified through simultaneous laboratory measurements of transverse and longitudinal dispersion within artificial and real emergent vegetation. Dispersion coefficients derived from a routing solution to the 2-D Advection Dispersion Equation (ADE) are presented that compare the effects of vegetation type (artificial, Typha latifolia or Carex acutiformis) and growth season (winter or summer). The new experimental dispersion coefficients are plotted with the experimental values from other studies and used to review existing mixing models for emergent vegetation. The existing mixing models fail to predict the observed mixing within natural vegetation, particularly for transverse dispersion, reflecting the complexity of processes associated with the heterogeneous nature of real vegetation. Observed stem diameter distributions are utilized to highlight the sensitivity of existing models to this key length-scale descriptor, leading to a recommendation that future models intended for application to real vegetation should be based on probabilistic descriptions of both stem diameters and stem spacings.

Feasibility of the Porous Zone Approach to Modelling Vegetation in CFD

Vegetation within stormwater ponds varies seasonly and its presence affects the flow field, which in turn affects the pond’s Residence Time Distribution and its effectiveness at pollutant removal. Vegetated flows are complex and, as a result, few suitable tools exist for evaluating realistic stormwater pond designs. Recent research has suggested using a porous zone to represent vegetation within a CFD model, and this paper investigates the feasibility of this approach using ANSYS Fluent. One of the main benefits of using a porous zone is the ability to derive the relevant parameters from the known physical characteristics of stem diameter and porosity using the Ergun equation. A sensitivity analysis on the viscous resistance factor \(1/\alpha\) and the inertial resistance factor \(C_{2}\) has been undertaken by comparing model results to data collected from an experimental vegetated channel. Best fit values of \(C_{2}\) were obtained for a range of flow conditions including emergent and submerged vegetation. Results show the CFD model to be insensitive to \(1/\alpha\) but very sensitive to values of \(C_{2}\). For submerged vegetation, values of \(C_{2}\) derived from the Ergun equation are under-predictions of best-fit \(C_{2}\) values as only the turbulence due to the shear layer is represented. The porous zone approach does not take into account turbulence generated from stem wakes such that no meaningful predictions for emergent vegetation were obtained. \(C_{2}\) values calculated using a force balance show better agreement with best-fit \(C_{2}\) values than those derived from the Ergun equation. Manually fixing values of \(k\) and \(\varepsilon\) within the porous zone of the model shows initial promise as a means of taking stem wakes into account.

Configuring Maximum Entropy Deconvolution for the Identification of Residence Time Distributions in Solute Transport Applications

The advection-dispersion equation (ADE) or aggregated dead zone (ADZ) models and their derivatives are frequently used to describe mixing processes within rivers, channels, pipes, and urban drainage structures. The residence time distribution (RTD) provides a nonparametric model that may describe mixing effects in complex mixing contexts more completely. Identifying an RTD from laboratory data requires deconvolution. Previous studies have successfully applied maximum entropy deconvolution to solute transport data, with RTD subsampling used for computational simplification. However, this requires a number of configuration settings which have to date not been rigorously investigated. Four settings are investigated here: the number and distribution of sample points, the constraint function, and the maximum number of iterations. Configuration options for each setting have been systematically assessed with reference to representative solute transport data by comparing the goodness-of-fit of recorded and predicted downstream profiles using the Nash-Sutcliffe efficiency index, evaluating RTD smoothness with a measure of entropy, and through consideration of the mass-balance of the RTD. New methods for defining sample point distribution are proposed. The results indicate that goodness-of-fit is most sensitive to constraint function and that smoothness is most sensitive to the number and distribution of sample points. A set of configuration options that includes a new sample point distribution is shown to perform robustly for a representative range of laboratory solute transport data.

Residence time distributions for turbulent, critical and laminar pipe flow

AbstractLongitudinal 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 downstream 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 the Reynolds number, R, between 3,000 and 20,000 is presented. For laminar flow, here identified as R<3,000, the RTDs do not conform to the Gaussian assumption because of insufficient available time for the...

Correlation Measures for Solute Transport Model Identification and Evaluation

Correlation measures are used in a range of applications to quantify the similarity between time-series, often between model output and observed data. A software tool implemented by the authors uses optimisation to identify a system’s Residence Time Distribution (RTD) from noisy solute transport laboratory data. As part of the further development of the tool, an investigation has been undertaken to determine the most suitable correlation measures, both for solute transport model identification as an optimisation constraint and as an objective means of solute transport model evaluation. Correlation measures potentially suitable for use with solute transport data were selected for evaluation. The evaluation was carried out by manipulating synthetic dye traces in ways that reflect common solute transport model discrepancies. The conditions tested include change in number of sample points (discretisation/series length), transformation (scaling, etc.), transformation magnitude, and noise. BLC, \({\chi ^{2}}\), FFCBS, \(\mathrm R ^{2}\), RMSD, \(\text{ R}_\mathrm{t}^{2}\), ISE, and APE show favourable characteristics for use in model identification. Of these, \(\text{ R}^{2}\), \(\text{ R}{}_\mathrm{t}^{2}\) and APE are non-dimensional and so are also suitable for model evaluation.

A CFD Based Comparison of Mixing Due to Regular and Random Cylinder Arrays

Numerous studies have focused 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. In this study the flow fields associated with two arrays of regularly and randomly distributed cylinders are modelled in two dimensions, using ANSYS Fluent 16.1. The RSM turbulence model is used to model the turbulence closure, and all the variables are discretized using the second order upwind method. The resulting flow fields are used to run the solute transport model to characterize mixing within each geometry. For the same stem diameter and solid volume fraction, greater dispersion is evident in the random cylinder array compared with the regular array. Dispersion coefficient values are compared with those reported in the literature and a good agreement is shown. Turbulence length scales estimated from the velocity profiles and optimized dispersion coefficients are close to the cylinder diameter, which is in agreement with theories in the literature.

Estimating drag coefficient for arrays of rigid cylinders representing emergent vegetation

ABSTRACT Flow resistance due to vegetation is of interest for a wide variety of hydraulic engineering applications. This note evaluates several practical engineering functions for estimating bulk drag coefficient () for arrays of rigid cylinders, which are commonly used to represent emergent vegetation. Many of the evaluated functions are based on an Ergun-derived expression that relates to two coefficients, describing viscous and inertial effects. A re-parametrization of the Ergun coefficients based on cylinder diameter (d) and solid volume fraction (φ) is presented. Estimates of are compared to a range of experimental data from previous studies. All functions reasonably estimate at low φ and high cylinder Reynolds numbers (). At higher φ they typically underestimate . Estimates of utilizing the re-parametrization presented here match the experimental data better than estimates of made using the other functions evaluated, particularly at low φ and low .

Deconvolving smooth residence time distributions from raw solute transport data

A residence time distribution (RTD) provides a complete model of longitudinal mixing effects that can be robustly derived from experimental solute transport data. Maximum entropy deconvolution has been shown to recover RTDs from preprocessed laboratory data. However, data preprocessing is time consuming and may introduce errors. Assuming data were recorded using sensors with a linear response, it should be possible to deconvolve raw data without preprocessing. This paper uses synthetically generated raw data to demonstrate that the quality of the deconvolved RTD remains satisfactory when preprocessing steps involving data cropping or calibration are skipped. Provided noise levels are relatively low, filtering steps may also be omitted. However, a rough subtraction of background concentration is recommended as a minimal preprocessing step. Deconvolved RTDs often include small-scale fluctuations that are inconsistent with a well-mixed fully turbulent system. These are believed to be associated with oversampling and/or unsuitable interpolation functions used in the maximum entropy deconvolution process. This paper describes a new interpolation function—linear interpolation with an automatic moving average (LAMA)—and demonstrates that, in combination with fewer sample points (e.g., 20), it enables smoother RTDs to be generated. The two improvements, to deconvolve raw data and to generate smoother RTDs, have been validated with experimental data. Raw solute transport traces collected from a river were deconvolved after background subtraction. The deconvolved RTDs compare favorably with those generated from the more traditional advection-dispersion equation (ADE) and aggregated dead zone (ADZ) models, but provide more detail of mixing processes. A laboratory manhole solute transport data set was deconvolved with and without preprocessing using 40 sample points and linear interpolation. The raw data were also deconvolved using 20 sample points and LAMA interpolation. The two sets of RTDs deconvolved from the raw data show the same mixing trends as those deconvolved from preprocessed data. However, those deconvolved with LAMA interpolation and 20 sample points are significantly smoother.