This is a repository copy of Feasibility of the porous zone approach to modelling vegetation in CFD.

White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/97784/

Version: Accepted Version

Proceedings Paper:Sonnenwald, F., Stovin, V. orcid.org/0000-0001-9444-5251 and Guymer, I. (2016) Feasibility of the porous zone approach to modelling vegetation in CFD. In: Rowiński, P.M. and Marion, A., (eds.) Hydrodynamic and Mass Transport at Freshwater Aquatic Interfaces. 34th International School of Hydraulics, 11-14 May 2015, Żelechów, Poland. GeoPlanet: Earth and Planetary Sciences . Springer , pp. 63-75. ISBN 978-3-319-27749-3

https://doi.org/10.1007/978-3-319-27750-9_6

eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/

Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website.

Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.

Feasibility of the porous zone approachto modelling vegetation in CFD

Fred Sonnenwald, Virginia Stovin, and Ian Guymer

Abstract Vegetation within stormwater ponds varies seasonly and its pres-ence affects the flow field, which in turn affects the pond’s Residence TimeDistribution and its effectiveness at pollutant removal. Vegetated flows arecomplex and, as a result, no suitable tools exist for evaluating realistic storm-water pond designs. Recent research has suggested using a porous zone torepresent vegetation within a CFD model, and this paper investigates thefeasibility of this approach using ANSYS Fluent. One of the main benefits ofusing a porous zone is the ability to derive the relevant parameters from theknown physical characteristics of stem diameter and porosity using the Ergunequation. A sensitivity analysis on the viscous resistance factor 1/α and theinertial resistance factor C2 has been undertaken by comparing model res-ults to data collected from an experimental vegetated channel. Best fit valuesof C2 were obtained for a range of flow conditions including emergent andsubmerged vegetation. Results show the CFD model to be insensitive to 1/αbut very sensitive to values of C2. For submerged vegetation, values of C2

derived from the Ergun equation are under-predictions of best-fit C2 valuesas only the turbulence due to the shear layer is represented. The porous zoneapproach does not take into account turbulence generated from stem wakessuch that no meaningful predictions for emergent vegetation were obtained.C2 values calculated using a force balance show better agreement with best-fit C2 values than those derived from the Ergun equation. Manually fixingvalues of k and ε within the porous zone of the model shows initial promiseas a means of taking stem wakes into account.

F. Sonnenwald · V. StovinDepartment of Civil and Structural Engineering, The University of Sheffield, Mappin St.,Sheffield, S1 3JD, UK.e-mail: f.sonnenwald@sheffield.ac.uk, e-mail: v.stovin@sheffield.ac.uk

I. GuymerSchool of Engineering, University of Warwick, Coventry CV4 7AL, UKe-mail: i.guymer@warwick.ac.uk

1

2 Fred Sonnenwald, Virginia Stovin, and Ian Guymer

1 Introduction

Stormwater, the run-off from rainfall events, typically carries pollutants thatnegatively affect the environment. Engineered devices, commonly referred toas SuDS, or Sustainable Drainage Systems, are introduced to detain flowsand help remove pollutants, protecting receiving waters. As they are engin-eered devices, they are designed and implemented with specific goals in mind.However, as semi-natural systems they are complex and in many cases robusttools to assess both their design and performance do not exist.

Stormwater treatment ponds, for example, contain both open water andvegetation in highly asymmetric configurations. Pond performance is typic-ally assumed to depend on the nominal residence time, V/Q, where V is pondvolume and Q is discharge (Persson, 2000). A Residence Time Distribution(RTD) (Levenspiel, 1972), describing the range of times water takes to travelthrough the pond, can be experimentally determined after construction andbetter reflects pond performance. An RTD closer to “plug flow”, where all wa-ter remains in the pond for a similar time (i.e. the nominal residence time),is considered ideal for treatment (Holland et al, 2004).

Natural vegetation, which may vary by season and year, affects the flowfield and makes assessing pond performance complex. The nominal residencetime does not take vegetation into account and it is impractical to exper-imentally determine the RTD of every pond repeatedly as the vegetationgrows or dies off. A more robust modelling approach capable of assessingpond performance that includes vegetation would therefore be of benefit.

1.1 Modelling vegetation

Modelling the impacts of vegetation on flow (and thereby mixing) is necessaryto robustly estimate residence times. This is a problem not only in stormwaterponds, but also in channels (Souliotis and Prinos, 2011; Patil and Singh,2011), wetlands (Kjellin et al, 2007; Huang et al, 2008), and coastal areas(Lightbody and Nepf, 2006). There are several parallel tracks of investigationbeing undertaken to understand and quantify the impacts of vegetation onflow, from the very theoretical (Nepf, 1999) to more practical engineeringapproaches (Kadlec, 1990).

Most approaches to modelling vegetation consist of estimating a co-efficient of drag, CD, obtained through experimental and/or theoreticalmeans, e.g. Jadhav and Buchberger (1995); Nepf (1999); Tanino and Nepf(2008). More empirical approaches use Manning’s n, e.g. Hoffmann (2004);Wu and He (2009). King et al (2012) propose a new k − ε turbulence modelfor inclusion in a Computational Fluid Dynamics (CFD) model that takes theeffects of vegetation into account. Alternatively, Stoesser et al (2010) directlysimulated flow through vegetation stems using Large Eddy Simulation.

Feasibility of the porous zone approach to modelling vegetation in CFD 3

1.2 CFD Modelling of ponds

CFD has become established as a common tool for pond design and evalu-ation, e.g. Shilton (2000); Peterson et al (2000); Persson (2005); Shilton et al(2008); Khan et al (2012); Alvarado et al (2013). These studies have typicallyfocused on pond shape or configuration, but have not taken into account thepresence of vegetation.

Saggiori (2010), Tsavdaris et al (2013), Tsavdaris et al (2014), and Li(2014) have modelled vegetated ponds using the commercial CFD code AN-SYS Fluent (ANSYS, Inc., 2012) by treating vegetated areas as a “PorousZone”. A CFD model solves a discretised form of the Navier-Stokes equa-tions, which balance forces acting on a volume of water. Equation 1 showsthe balance of forces acting in the x-direction, assuming a 2-D problem andexcluding turbulence (Fluent Inc., 1998), where ρ is density, u is velocity inthe x-direction, v is velocity in the y-direction, p is pressure, and τ is shearstress in the subscripted directions.

∂ρuu

∂x+

∂ρvu

∂y= −

∂p

∂x+

∂τxx∂x

+∂τxy∂y

+ Fx (1)

Fx = −

(

µ

αu+ C2

(

1

2ρu|u|

))

(2)

The effects of the porous zone are included as part of the additional sourceterm Fx, shown in Equation 2, where µ is the fluid viscosity, 1/α is a viscousresistance coefficient (based on Darcy’s law), and C2 is an inertial resistancecoefficient. ANSYS suggests that the 1/α and C2 parameters may be calcu-lated using Equations 3 and 4 respectively, which are derived from the Ergunequation (Ergun, 1952), where d is stem diameter and φ is porosity. Thispaper further investigates the porous zone approach to modelling vegetationin CFD.

α =d2

150

φ3

(1− φ)2(3) C2 =

3.5

d

(1− φ)

φ3(4)

2 Methodology

A preliminary 2D investigation of the porous zone approach to modellingvegetation in CFD has been carried out in 2 stages using ANSYS Fluent14.5 (the double precision solver). The first stage consists of evaluating thesensitivity of the porous zone parameters (1/α and C2). The second stageconsists of fitting these parameters to different experimental conditions.

4 Fred Sonnenwald, Virginia Stovin, and Ian Guymer

Experimental data collected by Shucksmith et al (2010) has been used forvalidation of the CFD model. They investigated longitudinal dispersion ina vegetated channel, emergent or submerged depending on flow rate. Carex,a common aquatic plant, was grown for a period of 26 weeks in a channel14.48×0.6 m. 8 measurement sets (outlined in Table 1) were collected overthis period as the vegetation grew, each consisting of vertical velocity profiles(at 5.6 m into the vegetation) and 5 repeat solute transport traces at 5 flowrates ranging between 9.19 and 29.42 ls-1. These flow rates correspond tomean velocities of 0.099–0.264 ms-1 and stem Reynolds numbers of 1490–7083. The solute was injected onto the surface at the start of the vegetationand the traces were recorded at 3 locations within and above the vegetationat 7.36, 9.80, and 12.24 m downstream using fluorometers.

The CFD model geometry used is a simplified 2D representation of thechannel centreline. 15 m of open water was added before the vegetation forflow establishment, the vegetation was changed to a 14.5 m length, and 0.5 mfree water was added after the vegetation. The vegetation itself was modelledas a porous zone, with the 1/α and C2 parameters applied in the x-directiononly. Boundary conditions were specified as a velocity-inlet, a pressure-outlet,symmetry boundary (fixed-lid approximation) at the surface, and a channelbed roughness height of 7e-4 m (representative of gravel).

A mesh independence study showed that a rectangular mesh with a cellsize of 14.625 mm was a good balance of mesh independence, number of cells,and the log-law boundary layer treatment requirement of 30 < y+ < 300.According to the results of a discretisation settings and turbulence modelsensitivity study, second order spatial discretisation, the PRESTO! pressurediscretisation formulation (an interpolation scheme to calculate pressure oncell faces), the Standard Wall Functions (a log-law viscous sub-layer approx-imation), and the Realisable k−ε turbulence model have been used. The inletand outlet turbulence boundary conditions have been specified as a turbulentintensity of 5% and a turbulent length scale equivalent to the water depth.All models were run for sufficient iterations for their residuals to stabilise,indicating model convergence. The SIMPLE pressure-velocity coupling wasused (an uncoupled solver).

Particle tracking was used to generate solute trace data comparable tothe experimental dye injections. This approach has previously compared fa-vourably with experimental results, e.g. Stovin et al (2008). 40,000 neutrallybuoyant particles were injected just below the surface at the start of the ve-getation and tracked using the Discrete Random Walk Model until leavingthe outlet. As the particles crossed the three monitoring planes, the times atwhich they crossed and whether they crossed in the vegetation or water wasrecorded.

Feasibility of the porous zone approach to modelling vegetation in CFD 5

2.1 Sensitivity of 1/α and C2

A sensitivity analysis was carried out to explore the impact of the porous zoneparameters 1/α and C2 on the modelled solute transport in the vegetatedchannel. Logarithmically spaced values were used: 1/α = 0.60, 3.11, 16.10,83.40, 431.80, 2236.60, 11584.20, and 60000 m-2; and C2 = 0.20, 0.54, 1.44,3.86, 10.34, 27.79, 74.55, and 200 m-1. The 64 combinations of these valuesare representative of d from 1 to 50 mm and φ from 0.900 to 0.999. The CFDmodel was configured to represent measurement set 3 with a 28.66 ls-1 flowrate, for a flow depth of 0.234 m, a vegetation depth of 0.160 m, and a meanvelocity of 0.204 ms-1. Measured values of d = 0.02 m and φ = 0.992, giving1/α = 24.6 m-2 and C2 = 1.41 m-1.

To compare the CFD solute traces with the experimental data, the latterhas been pre-processed to subtract background concentration using a linearapproximation based on the first and last 5 seconds of data. As the laborat-ory calibration data could not be found, the experimental traces were scaledaccording to the mass-balance of their CFD counterparts, assuming 100%conservation of mass. The start times of the experimental data were unavail-able and so were approximated based on the CFD results.

2.2 Porous zone parameter fitting

Best fit porous zone model parameters for the experimental results have beengenerated. CFD models for all 8 vegetation measurement sets at all 5 flowrates (covering emergent and submerged vegetation) have been created. Res-ults to be discussed show that the porous zone model in the scenarios ex-amined is primarily sensitive to values of C2 and so 1/α has been fixed at avalue of 1. Based on those same results, the range of values of C2 was mod-ified so that 10 values of C2 = 0.20, 0.36, 0.65, 1.17, 2.11, 3.79, 6.84, 12.32,22.20, 40.00 m-1 have been used. For each configuration, the solute tracesgenerated using particle tracking have been compared to their correspond-ing experimental solute traces. This comparison was carried out using theR2 correlation measure [Equation 5 (Nash and Sutcliffe, 1970)] after aligningthe centroids of the traces. The value of C2 with the highest R2 is assumedto best represent the experimental data as R2 values close to 1.0 indicate abetter fit, while values below 0 indicate no fit.

R2 = 1−

∑N

i=1(Ci − Ci)

2

∑N

i=1(Ci − Ci)2

(5)

6 Fred Sonnenwald, Virginia Stovin, and Ian Guymer

Concen

trati

on [

-] 1/α=16.10 m-2

C2=1.44 m

-1

0.00

0.02

0.041/α=16.10 m

-2

C2=3.86 m

-11/α=16.10 m

-2

C2=10.36 m

-1

Time (seconds)

Concen

trati

on [

-] 1/α=83.37 m-2

C2=1.44 m

-1

0 50 1000.00

0.02

0.04

Time (seconds)

1/α=83.37 m-2

C2=3.86 m

-1

0 50 100

Time (seconds)

1/α=83.37 m-2

C2=10.36 m

-1

0 50 100

Experi

men

tal

CFD

Mid

CFD

DS

CFD

US

Fig. 1 Particle tracking solute traces recorded at 7.36 (US), 9.80 (Mid) and 12.24 m(DS) within the open water above the vegetation compared to experimental solute traces,showing variation in the CFD model with 1/α and C2 (measurement set 3 at 28.66 ls-1)

3 Results and discussion

8 values of 1/α and 8 values of C2 were used in 64 combinations to evaluateCFD model sensitivity to the porous zone parameters. A subset of these ispresented in Fig. 1, which shows CFD model particle tracking solute traces re-corded in the open water above the vegetation compared to the experimentalresults. The traces are significantly less sensitive to the 1/α parameter thanto C2. Considering Equation 2, the viscous (1/α) term is several orders ofmagnitude lower than the inertial (C2) term for most combinations of 1/αand C2. However, as velocity approaches zero, the viscous term becomes moresignificant. Therefore, the insensitivity of the model to 1/α may need to berevisited at lower velocities.

The model predictions are very sensitive to the C2 parameter. Visual in-spection suggests that C2 = 3.86 m-1 produces a much better fit to experi-mental data than C2 =1.44 m-1 (comparable to the value of 1.41 m-1 derivedfrom the Ergun equation for this experimental configuration). Even small er-rors in estimating d or φ can therefore significantly influence the model. Giventhe inherent variability in measuring vegetation, this suggests that using theErgun equation to estimate 1/α and C2 may not be robust.

Equation 6 is the standard stem drag formula, where a is frontal area. Itis similar to the inertial loss term of Equation 2. This, combined with thesensitivity analysis presented above, suggests that the viscous loss term canbe ignored, while maintaining the relevant model physics. This assumptionallows the second stage of investigation to focus solely on C2.

Fx = −

(

1

2CDaρu2

)

(6)

Feasibility of the porous zone approach to modelling vegetation in CFD 7

3.1 The porous zone problem

A CFD model has been created with constant 1/α = 1 m-2 for each com-bination of 8 measurement sets, 5 flow rates, and 10 values of C2, giving 400models in total. Not all of these models ran as expected. Fig. 2 shows anexample of poor model prediction, where the CFD-generated solute tracesindicate plug flow. This is clearly not the case in the experimental results.The unexpected plug flow traces occur in all cases when the vegetation isemergent or only just submerged—only the fully submerged cases producereasonable results. In all cases the velocity profiles match the experimentaldata. However, it is evident that the turbulence, which influences the particletracking (i.e. mixing), is not being properly modelled.

Turbulence around vegetation can be thought of as being primarily gener-ated by two mechanisms. When vegetation is submerged, water travels slowerin the vegetation than the water above it due to resistance and as a resultof this differential in velocity a shear layer forms, expressed as an asymptotein a velocity profile. This shear layer generates turbulence. Within the veget-ation, the mean flow velocity is fairly uniform due to the drag of the stemsacting on the water passing them. Although there is no velocity differentialand no shear layer, turbulence is still generated as a result of the wake effectof water passing the stems.

When representing submerged vegetation via a porous zone, the flow isslowed in the porous zone and a shear layer forms at the porous zone/openwater interface as a result of the velocity differential. However, nothing withinthe CFD model generates the within-vegetation wake effect, i.e. there is nosource of turbulence within the porous zone. As such no mixing can take placewhen the vegetation is emergent, as observed. It is clear that the default por-ous media approach to vegetation modelling is inappropriate for reproducingmixing effects. Despite this, the CFD model appears to function well in thesubmerged vegetation cases when there is a sufficient depth of water abovethe vegetation for the shear layer to fully form, suggesting the mixing causedby a shear layer dominates.

Fig. 3 compares velocity and turbulent kinetic energy profiles for emer-gent and submerged vegetation, clearly showing the lack of turbulence within

Fig. 2 Emergent veget-ation particle trackingsolute traces recorded at7.36 (US), 9.80 (Mid) and12.24 m (DS) compared toexperimental solute tracesfor C2 = 1.71 (measure-

ment set 3 at 10.19 ls-1)Time (seconds)

Concen

trati

on [

-]

0 60 1200.00

0.02

0.04

0.06

0.08

0.10Experimental

CFD US

CFD Mid

CFD DS

8 Fred Sonnenwald, Virginia Stovin, and Ian Guymer

Velocity (ms-1

)

Depth

(m

)Surface

Emergent

0.150 0.1700.00

0.10

0.20

Velocity (ms-1

)

Vegetation

Submerged

0.0 0.1 0.2

Turbulent Kinetic Energy (m2s

-2)

0.000 0.005 0.010

Experi

men

tal

Em

erg

ent

Subm

erg

ed

Fig. 3 Velocity and turbulent kinetic energy for emergent vegetation and submerged ve-getation (measurement set 3 at 10.19 and 28.66 ls-1 respectively)

the emergent vegetation model. The experimental velocity profiles have beenscaled according to the ratio of their area-weighted average to the mean ve-locity (Saggiori, 2010) to account for an experimental mass-balance errorbelieved to be due to the existence of a preferential flow path around the ve-getation at the side of the channel. This preferential path is also may accountfor some of the differences between the CFD generated and the experimentalsolute traces.

3.2 Best fit values of C2 for submerged vegetation

As previously mentioned, the predicted solute traces for the submerged casesclosely match the experimental data. Fig. 4 shows a subset of the submergedvegetation particle tracking data within the vegetation for measurement set6 at 28.74 ls-1 flow. Visual inspection indicates that the best fit C2 value isin the range of 6.84 to 12.32 for this experimental trial. Fig. 5 shows therange of best fit C2 values determined by R2 value at the maximum flowrate (25.22–29.42 ls-1) for each dye injection trial at each measuring point.There is some variation within each measurement set, although for sets 3–8the median values are consistently 6.84. The higher values for measurementset 1 may correspond to stiffer vegetation, causing increased mixing.

Table 1 shows the C2 values for each measurement set derived from Equa-tion 4. The calculated values consistently under-estimate the best-fit values.This may be in part due to the latter compensating for the lack of stem eddymixing by artificially increasing the shear layer mixing. In turn the flow fieldwill be affected, under-estimating flow in the vegetation and over-estimatingit in the canopy, as seen in Fig. 3. The under-estimate also potentially indic-ates the Ergun equation is unsuitable for this application.

Tsavdaris et al (2013) used the porous zone approach to model the hy-draulic effects of vegetation in a channel, but noted that it could not be usedto predict turbulence. Without taking into account the turbulent effects ofthe vegetation stems, no CFD model utilising a porous zone will produce an

Feasibility of the porous zone approach to modelling vegetation in CFD 9

accurate description of the treatment capability of a pond (e.g. an accurateRTD). Despite this, Tsavdaris et al (2014) used the porous zone approachto evaluate various pond designs, including those with emergent vegetation.They note increased turbulence around vegetation, which is the result of aporous zone interface, but their models do not account for turbulence withinthe vegetation. Their conclusions on large scale hydraulics do not appear tobe directly affected by this, but their results imply a level of functionality ofporous zone modelling that is not the case.

3.3 The porous zone solution?

Two problems have been identified with using porous zones. The first prob-lem is the potential unreliability in estimating C2. The second is the lack ofturbulence generation within the porous zone to represent stem wake effectswithin vegetation. It is possible that relationship between C2 and CD couldbe developed (Zinke, 2010; King et al, 2012). Equation 7 provides an estimateof C2 by balancing of gravity forces and drag forces, where g is the accelera-tion due to gravity, S is channel slope, and h is flow depth. Table 1 shows C2

values derived with this equation, which provide reasonable agreement withthe best fit values.

Time (seconds)

Concen

trati

on [

-] C2=6.84 m

-1

0 50 1000.00

0.02

0.04

Time (seconds)

C2=12.32 m

-1

0 50 100

Time (seconds)

C2=22.20 m

-1

0 50 100Experi

men

tal

CFD

US

CFD

DS

Fig. 4 Particle tracking solute traces recorded at 7.36 (US) and 12.24 m (DS) withinthe the vegetation compared to experimental solute traces, showing variation in the CFDmodel with C2 (measurement set 6 at 28.74 ls-1)

Table 1 Outline of measurement sets, Ergun equation derived C2 values, best fit C2 valuesat 29 ls-1 flow rate, and C2 values derived from a force balance

Measurement set 1 2 3 4 5 6 7 8

Age (weeks) 2 5 7 10 16 20 24 26d (m) 0.010 0.015 0.020 0.030 0.040 0.045 0.050 0.055φ 0.998 0.996 0.992 0.982 0.969 0.960 0.951 0.941

Ergun C2 (m-1) 0.69 1.04 1.41 2.17 3.03 3.49 4.00 4.54Best fit C2 (m-1) 40.00 3.79 6.84 6.84 6.84 6.84 6.84 6.84Force C2 (m-1) 5.01 6.10 6.23 6.49 6.27 5.58 7.50 9.18

10 Fred Sonnenwald, Virginia Stovin, and Ian Guymer

Fig. 5 A box plot com-paring best fit C2 valuesat the 29 ls-1 flow rateacross measurement setfor each possible R

2 com-parison between CFD andexperimental solute traces,where the thick line is themedian, the box showsthe 25th–75th percentile,

the whiskers ±2.7σ, andthe pluses values that falloutside the range of thewhiskers

C2

Measurement set

87654321

0

10

20

30

40

C2 =2gS

u2h(7)

It is possible to simulate additional turbulence within the vegetation. AN-SYS Fluent allows the k and ε values of a porous zone to be manually set.Assuming that the vegetation is uniform and that the velocity distributionover the depth of the vegetation is uniform (two assumptions made for theapplication of the porous zone), the mixing effects of the stem wakes couldbe reproduced by choosing the correct k and ε values. Fig. 6 shows CFD gen-erated solute traces corresponding to k = 0.005 and ε = 0.0003 for the sameexperimental configuration as Fig. 2, and shows more reasonable agreementwith the experimental solute traces. These initial results are promising, butthere are questions to be answered and potential limitations.

k and ε are complex parameters and suitable values should ideally bederived from the physical characteristics of the vegetation. The new k − εmodel proposed by King et al (2012) for vegetation may offer insight intohow k and ε values may be determined empirically. Their results suggest thismay be possible down to Reynolds number as low as 36. However, furtherwork is required to implement and evaluate this approach.

Fig. 6 Particle trackingsolute traces recorded at7.36 (US), 9.80 (Mid) and12.24 m (DS) within thevegetation compared toexperimental solute tracesfor C2 = 1.71 with fixedk = 0.005 and ε = 0.0003(measurement set 3 at10.19 ls-1, emergent vegeta-tion) Time (seconds)

Concen

trati

on [

-]

0 60 1200.00

0.02

0.04

0.06

0.08

0.10Experimental

CFD US

CFD Mid

CFD DS

Feasibility of the porous zone approach to modelling vegetation in CFD 11

4 Conclusions

This study showed CFD models of vegetation using a porous zone were in-sensitive to 1/α, but very sensitive to C2. The porous zone approach couldnot reproduce solute transport data with emergent vegetation. This is attrib-uted to the lack of a source of turbulence within the CFD model equivalentto that generated by stem wakes. As such, the default approach to modellingvegetation with a porous zone is inappropriate for reproducing mixing effects.

Best fit C2 values for submerged vegetation show that C2 values derivedfrom the Ergun equation are under-estimates, and therefore the Ergun equa-tion may not be an appropriate means of estimating porous zone parameters.The higher best fit values may be compensating for the missing mixing effectsof the vegetation stems. Better estimates of C2 may possibly be obtained bytreating it similarly to a drag coefficient, i.e. CD, and using a force balanceto estimate it from experimental data. Values obtained using this approachshow better agreement with the best fit values, although such an approachstill fails to represent the within-vegetation generation of turbulence.

To better represent vegetation, the porous zone can be configured withfixed k and ε values, simulating the additional turbulence caused by stemwakes. This shows promising initial results and it may be possible to estimatesuitable values based on vegetation characteristics. Therefore, although atpresent care must be taken when using the porous zone approach to modellingvegetation in CFD as it only reproduces the flow field, it may be feasible touse it to accurately represent the effects of vegetation on mixing in the future.

Acknowledgements This research was funded by EPSRC grants EP/K024442/1 andEP/K025589/1. The authors are grateful to Dr. James Shucksmith for access to the ex-perimental data used in this research.

References

Alvarado A, Vesvikar M, Cisneros JF, Maere T, Goethals P, Nopens I (2013) CFD study todetermine the optimal configuration of aerators in a full-scale waste stabilization pond.Water Res 47(13):4528–4537

ANSYS, Inc (2012) ANSYS Fluent 14.5. Cecil Township, PAErgun S (1952) Fluid flow through packed columns. Chem Eng Prog 48:89–94Fluent Inc (1998) FLUENT 5 User’s Guide Volume I. Lebanon, NHHoffmann MR (2004) Application of a simple space-time averaged porous media model to

flow in densely vegetated channels. J Porous Media 7(3)Holland JF, Martin JF, Granata T, Bouchard V, Quigley M, Brown L (2004) Effects of

wetland depth and flow rate on residence time distribution characteristics. EcologicalEngineering 23(3):189–203

Huang YH, Saiers JE, Harvey JW, Noe GB, Mylon S (2008) Advection, dispersion, andfiltration of fine particles within emergent vegetation of the florida everglades. WaterResour Res 44(4)

12 Fred Sonnenwald, Virginia Stovin, and Ian Guymer

Jadhav RS, Buchberger SG (1995) Effects of vegetation on flow through free water surfacewetlands. Ecological Engineering 5(4):481–496

Kadlec RH (1990) Overland flow in wetlands: vegetation resistance. J Hydraul Eng116(5):691–706

Khan S, Melville BW, Shamseldin AY, Fischer C (2012) Investigation of flow patterns instorm water retention ponds using CFD. J of Environ Eng 139(1):61–69

King A, Tinoco R, Cowen E (2012) A k–ε turbulence model based on the scales of vertical

shear and stem wakes valid for emergent and submerged vegetated flows. J Fluid Mech701:1–39

Kjellin J, Wörman A, Johansson H, Lindahl A (2007) Controlling factors for water resid-ence time and flow patterns in Ekeby treatment wetland, Sweden. Adv Water Resour

30(4):838–850Levenspiel O (1972) Chemical Reaction Engineering. John Wiley & Son, Inc.Li Q (2014) Effects of vegetation on pond residence time distributions using CFD model-

ling. Master’s thesis, University of SheffieldLightbody AF, Nepf HM (2006) Prediction of velocity profiles and longitudinal dispersion

in emergent salt marsh vegetation. Limnol Oceanogr 51(1):218–228Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models part I - A

discussion of principles. J Hydrol 10(3):282–290Nepf H (1999) Drag, turbulence, and diffusion in flow through emergent vegetation. Water

Resour Res 35(2):479–489Patil S, Singh V (2011) Dispersion model for varying vertical shear in vegetated channels.

J Hydraul Eng 137(10):1293–1297Persson J (2000) The hydraulic performance of ponds of various layouts. Urban Water

2(3):243–250Persson J (2005) The use of design elements in wetlands. Nordic Hydrology 36(2):113–120Peterson EL, Harris JA, Wadhwa LC (2000) CFD modelling pond dynamic processes.

Aquacultural Engineering 23(1):61–93Saggiori S (2010) CFD modelling of solute transport in vegetated flow. Master’s thesis,

University of SheffieldShilton A (2000) Potential application of computational fluid dynamics to pond design.

Water Sci Technol 42(10):327–334Shilton A, Kreegher S, Grigg N (2008) Comparison of computation fluid dynamics simu-

lation against tracer data from a scale model and full-sized waste stabilization pond. JEnviron Eng 134(10):845–850

Shucksmith J, Boxall J, Guymer I (2010) Effects of emergent and submerged naturalvegetation on longitudinal mixing in open channel flow. Water Resour Res 46(4)

Souliotis D, Prinos P (2011) Effect of a vegetation patch on turbulent channel flow. Journalof Hydraulic Research 49(2):157–167

Stoesser T, Kim S, Diplas P (2010) Turbulent flow through idealized emergent vegetation.J Hydraul Eng 136(12):1003–1017

Stovin VR, Grimm JP, Lau STD (2008) Solute transport modeling for urban drainagestructures. J Environ Eng 134(8):640–650

Tanino Y, Nepf HM (2008) Lateral dispersion in random cylinder arrays at high reynoldsnumber. J Fluid Mech 600:339–371

Tsavdaris A, Mitchell S, Williams B (2013) Use of CFD to model emergent vegetation in

detention ponds. ARPN J Eng Appl Sci 8(7):495–503Tsavdaris A, Mitchell S, Williams JB (2014) Computational fluid dynamics modelling of

different detention pond configurations in the interest of sustainable flow regimes andgravity sedimentation potential. Water Environ J

Wu W, He Z (2009) Effects of vegetation on flow conveyance and sediment transportcapacity. International Journal of Sediment Research 24(3):247–259

Zinke P (2010) Flow resistance parameters for natural emergent vegetation derived froma porous media model. Proc RiverFlow 2010