9th International Conference on Urban Drainage Modelling Belgrade 2012

1

Surface roughness effect on near bed Turbulent

Kinetic Energy in a large stormwater detention basin

Hexiang Yan, Gislain Lipeme Kouyi*, Jean-Luc Bertrand-Krajewski

University of Lyon, INSA Lyon, LGCIE (Laboratory of Civil and Environmental Engineering) F-69621, Villeurbanne, France *Corresponding author, e-mail: gislain.lipeme-kouyi@insa-lyon.fr

ABSTRACT

The effect of surface roughness on near bed turbulence is of great importance for sediments deposition and entrainment in stormwater detention basin. In this paper, effects of surface roughness in sedimentation processes have been investigated by means of RANS approach (CFD technique based on Reynolds Averaged Navier Stokes equations). Previous work has showed the ability of CFD modelling to allow the identification of the preferential deposition zones in a large detention basin. The new boundary condition on the bottom was based on the interaction between near bed turbulence and particle settling characteristics such as V80 settling velocity. In order to further clearly understand the effects of surface roughness on sedimentation, simulations with different surface roughness have been carried out and measurements of sediment thickness and distribution have been performed in the Django Reinhardt large stormwater detention basin in Chassieu (close to Lyon, France). Analysis of simulated results compared to measurement data reveals that the contour of preferential deposition zones linked to near-bed turbulent kinetic energy distribution is sensitive to surface roughness. The maximum value of the near-bed turbulent kinetic energy distribution in deposition zones is sensitive to

surface roughness and is lower than 280V .

KEYWORDS

Detention basin, surface roughness, turbulent kinetic energy, sediment distribution

1 INTRODUCTION

Turbulent boundary layer over roughness elements is of great interest in hydraulic engineering. Effects of surface roughness on sediments distribution are of great importance as reminded by Papanicolaou et al. (2001). Turbulent boundary layer over a rough surface contains a roughness sublayer within which the flow is directly influenced by the individual roughness elements and is not spatially homogenous. The height of this sub-layer presumably depends on the height of the roughness elements. Experimental and numerical studies have been performed to investigate the effects of surface

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roughness on wall bounded turbulence to get a clearer picture of the impact of roughness in turbulent boundary layer. Perry et al. (1987) performed experiments using both three dimensional diamond-shaped mesh roughness and streamwise wave length. They observed that smooth and rough wall boundary layer have quite different structures. Papanicolaou et al. (2001) provided experimental evidence that various packing density configuration encountered in natural gravel bed streams affect the turbulence characteristics of the flow. Shafi and Antonia (1997) measured the root mean square (rms) vorticity fluctuations normalized by the friction velocity and boundary layer thickness. They found that the effects of roughness on the vorticity is less pronounced than on the Reynolds stress, which conflicts with the traditional picture of wall similarity.

Recently computational fluid dynamics (CFD) is of increasing interest for many engineering fields. In urban drainage systems, CFD technique could be used to evaluate actual water treatment facilities and to improve the design procedure (Wood et al., 1998; Krishnappan and Marsalek, 2002; Hribersek et al., 2011). In traditional hydraulics the influence of roughness has been cataloged in the form of a roughness coefficient based on data obtained from a wide range of field and laboratory observations (Souders and Hirt, 2002). Typically roughness coefficients are defined in one of the three ways: (1) Chzy resistance coefficient C, (2) Mannings coefficient n, or (3) equivalent sand grain roughness (ks). When a turbulence transport model (e.g., k - model) is used in CFD simulations, there must be a suitable boundary condition for the turbulence quantities (e.g., turbulent kinetic energy k and turbulent dissipation ) only at the inlet and outlet boundary of the computational domain. Regarding the influence of the wall roughness, the so-called wall functions are widely used for that purpose. It is assumed that a logarithmic velocity profile (called log-law of wall) exists near a wall, and a modified law of wall is often used to account for the roughness effect on the wall.

A detailed modelling of fluid flow and pollutants transport in a full scale stormwater detention tank is a difficult task due to the complex geometry and variable time-dependent processes (deposition, near-bed transport, resuspension, etc) as well as limitation in computational resources in the case of a large structure (due to a lot of computational mesh elements). Preliminary work on modelling of hydrodynamic and solid transport in a large stormwater detention basin was undertaken in order to reproduce the preferential sediment zone and efficiency (Yan et al., 2011). A new boundary condition was proposed to determine particle state (deposited or suspended) near the bottom using Lagrangian particle tracking approach to simulate solid transport in fluid flow. This boundary condition was based on the interaction between the near bed turbulent kinetic energy and near bed particles energy thanks to settling velocity. In fact, Bagnold (1966) proposed one of the first criteria to estimate the threshold condition for particle suspension. This was based on the assumption that particles sustain in suspension by the fraction of turbulent energy. From this point of view, the near bed turbulent kinetic energy plays an important role in the settling processes. Unfortunately, few studies have been carried out in order to further highlight effects of roughness on sedimentation processes which are strongly impacted by near bed turbulence characteristics. Therefore the present paper aims to study the sensitivity of the near bed turbulence quantities (particularly Turbulent Kinetic Energy TKE) to the bed surface roughness in the Django Reinhardt large stormwater basin in Chassieu (Rhne, France), which is a part of OTHU programme site (Field Observatory in Urban Hydrology www.othu.org).

2 METHODOLOGY

2.1 Experimental field site

The Django Reinhardt detention-infiltration facility was built in 1975 in order to store stormwater from a 185 ha industrial catchments during wet weather time. The facility consists of two sub-basins

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connected by a 60 cm diameter pipe. The first one is a detention and settling basin (Figure. 1a) where the stormwater is stored before being discharged downstream to the infiltration sub-basin. The bottom of the detention basin is sealed with bitumen and is equipped with a low flow trapezoidal channel collecting and guiding the dry weather flow towards outlets. The sides of the detention basin are covered with the plastic liner. Stormwater enters the detention basin via two 1.6 m diameter circular concrete pipes (labelled as inlet 1 and inlet 2 in Figure.1a). In order to improve the settling process, a 1 m high detention wall was built in 2004. There are three 19 cm diameter outlet orifices (labelled o1, o2 and o3 in Figure. 1a) and an overflow weir in the detention wall. The stormwater outflow towards the infiltration sub-basin is limited to 350 L/s by a regulator (Hydroslide gate).

52JLBK, INSA de Lyon, 24 Nov. 2006

SEDIMENT SAMPLING

inletoutlet

(a) (b) Figure 1. (a) Sketch of the Django Reinhardt basin (Bardin and Barraud, 2004) and (b) Sediment trap locations in the basin (Torres, 2008)

The inlet and outlet discharges are calculated from simultaneous measurements of water depth and velocity in the pipes. Three water depth sensors are located on the bottom of the basin (labelled h1, h2 and h3 in Figure 1a). All variables are recorded with a 2 minute time step to a S50 Sofrel data logger. Twelve sediment traps installed on the bottom of the basin collect settled sediments during storm events (Figure. 1b). The sediment traps are numbered according to their altitude, from 1 (lowest) to 12 (highest). After a storm event, samples made up of a mixture of water and sediments are transported as quickly as possible to the laboratory, where the particles settling velocity and particle size distributions are measured respectively according to the VICAS protocol and Laser Particle Sizer (LPS) technique (Torres, 2008).

2.2 Sediments measurement

Lot of sediments has been accumulated in the detention basin since the rehabilitation in 2004. In order to analyze the spatial distribution of the cumulate sediment in the basin, the profile of preferential sediments zone and discrete point sediment thickness were measured. The layout of spatial interval of measurement point is 5 m for the preferential sediment zone (left part of basin, Figure 2). Refined spacing of measurement points has been used in the centre of the basin and measurement points have been distributeded more sparsely close to the inlet of the basin (shown in Figure 2).

Figure 2. Layout of the sediments thickness measurement points

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2.3 Numerical model

The purpose of this part is to highlight the used numerical models integrated into the CFD software package Ansys Fluent (version 14.0). The key models employed are based on the Reynolds Averaged Navier-Stokes (RANS) equations. The k- renormalization group (RNG) model was employed to involve the turbulent phenomena. It is better than standard k- model since more features are included in this model. While the standard k- model is a high-Reynolds number model, the k- RNG model provides an analytically derived differential formula for effective viscosity that accounts for low-Reynolds number effects as well. These features make the k- RNG model more accurate and reliable for a wider class of flows than the standard k- model. Compared to the standard k- model and the k- RNG model, RSM (Reynolds Stress Model) is more time consuming as it needs to solve more equations. Dufresne et al. (2009) and Mignot et al. (2011) tested the standard k- model, the k- RNG model and the RSM in various urban drainage structures (three combined sewer overflow chambers for solid separation and open channel junctions). They found that the RSM model did not give significant improvement compared to the results deriving from the k- RNG model.

The surface roughness effects on turbulence quantities and bed shear stress is considered through the modified law-of-the-wall for roughness. The standard wall functions in Ansys Fluent are based on the Launder and Spalding (1974) work and have been most widely used in industrial flows (ANSYS, 2011; Souders and Hirt , 2002). Experiments in rough pipes and channels indicate that the mean velocity distribution is influenced by the near rough walls and in the usual semi-logarithmic scale, has the same slope (1/) but a different intercept (Tachie et al., 2004; Akinlade et al., 2004). Thus, the law-of-the-wall for mean velocity impacted by rough wall has the form (ANSYS, 2011):

Byu

Euu p

w

p )ln(

1 **

(1)

where 2141

* kCu

= Von Krmn constant (= 0.4187) E= empirical constant (= 9.793) up= mean velocity of the fluid at the near-wall node P k= turbulent kinetic energy at the near-wall node P yp= distance from point to the wall = dynamic viscosity of the fluid

B is a roughness function that quantifies the shift of the intercept due to roughness effects. B depends on the type (uniform sand, rivets, threads, ribs, mesh-wire, etc.) and size of the roughness. There is no universal roughness function valid for all types of roughness. However, for a sand-grain roughness and similar types of uniform roughness elements B has been found to be well-correlated with the non-dimensional roughness height, /*uKK ss

, where Ks is the physical

roughness height.

The turbulent flow regime is subdivided into three regimes, and the formulas proposed by Cebeci and Bradshaw (1977) based on Nikuradse's data are adopted to compute the roughness function, B , for each regime (ANSYS, 2011).

For the smooth regime (Ks+ < 2.25): 0B (2)

For the transitional regime (2.25 < Ks+ < 90):

811.0ln4258.0sin75.87

25.2ln

1

ssss KKC

KB

(3)

where Cs is a roughness constant, and depends on the type of the roughness.

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In the fully rough regime (Ks+ > 90):

ssKCB 1ln1

(4)

2.4 CFD model setup

The flow regime in a detention basin can be described as transient due to the complex geometry of basin, rough surface conditions (concrete and vegetated sediments at the bottom), variable inflow and outflow rate, etc. Preliminary tests have been carried out and they proved that a steady state simulation was able to predict the preferential sediment zone and evaluate the basin efficiency (Yan et al., 2011). Figure 3 shows a curve of water depth h1 against inflow rate in the basin for the reference storm event on 31/5/2007 (Torres, 2008). The measured water depth was approximately kept in a same level for a period of time during the rainfall event (Figure 3). Hence the corresponding water level was chosen as free surface level. Meanwhile, the inflow rate of 350L/s was chosen since the outflow rate is limited by a regulator which enables fixing the outflow rate to 350 L/s. A quasi-steady state condition can be accepted under this situation. As shown in Figure 1(a),it was observed that there was no sediments in the second compartment close to the outlet. Thus, in order to reduce the number of computational meshes and then to save computation time, this second part of the basin is cut in order to simplify geometry and boundary conditions as shown in Figure 4.

Figure 3. water depths h1 versus inflow rates Figure 4. Sketch of the simplified geometry of the

Django Reinhardt basin

The mesh-independent tests have been carried out. Three different mesh resolutions have been established and tested: one coarse mesh size with 650 000 cells, a medium mesh size of 850 000 cells and a refined mesh size of 1000 000 cells. Fairly similar results were obtained with the medium and refined resolution mesh. Thus the medium resolution mesh with 850 000 cells was used for all simulations.

The following boundary Conditions have been used. Uniform velocity distribution was set at the inlet cross-section, corresponding to the inflow rate of 0.35m3/s (corresponding to the outflow rate limited by a regulator valve). Three orifices and overflow weir were set as pressure-outlet. A specific pressure was set at orifice 2 as it was completely submerged under free water surface. For the free water surface, a symmetry condition was set instead of Volume-of-Fluid (VOF) model for air-water interface capturing in order to reduce the computational time. The symmetry condition means that zero normal velocity and zero normal gradients of all variables at the symmetry plane. It can be used to model zero-shear slip walls in viscous flows (Dufresne, 2008; Stovin et al., 2008). The surrounding wall sides were considered as smooth since they were covered with a plastic liner and were set as no slip condition with zero roughness height. Lastly, the bottom of basin was considered as rough surface and was set as no slip wall condition with non-zero roughness height. Initially the bottom was covered by concrete and later a part of it was covered by accumulated sediments with or without vegetation.

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However, it was difficult to determine equivalent roughness height for vegetated sediment surface. Therefore, the bottom was considered to be covered by the concrete and the equivalent sand grain roughness height was estimated by means of equation (5) proposed by Hager (2010). Table 1 shows a series of Strickler coefficients K and equivalent sand grain roughness heights ks for concrete (Graf and Altinakar, 2000).

gkK s 5.661

(5)

where g is the gravity acceleration.

Table 1. Strickler roughness coefficient K and equivalent sand grain roughness height ks. Cases ks1 ks2 ks3 ks4 K(m1/3/s) 75 65 55 50 ks (m) 0.00040 0.00094 0.0026 0.0045

3 RESULTS AND DISCUSSION

3.1 Spatial sediments distribution

A lot of sediment settled during the storm event and accumulated in the basin since the rehabilitation of basin in 2004. Figure 5 shows evidently the top view of sediments in the bottom of detention basin in 2007. Figure 6 shows colour contours of sediment thickness according to the measurement data in 2011, which was processed using Matlab software. The blank part means almost no sediment in the basin or very thin. As shown in Figure 6, the important amount of sediments was located in the centre zone of the basin. Initially, the bottom of the basin was covered by bare concrete. Later, part of the bottom of basin was covered by the settled sediment. Vegetation was also observed on the thick sediment layer. It is expected that the effect of surface roughness existed due to a rough bare concrete and cumulate sediment layer with or without vegetation.

Figure 5. Photo of detention basin (2007) from Google Earth

Figure 6. Contour of observed sediment thickness(m) measurement in 2011

Concrete area

vegetation

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3.2 Effect of surface roughness on near bed turbulence

Four simulation cases have been carried out with the same configuration except for varying the parameter of bottom surface roughness height. Different concrete resistance coefficients were tested.

ks1

ks2

ks3

ks4

Top view of sediment in 2007

Figure 7. Similarity between observed deposition zones and simulated Bed TKE distribution according to ksi (i=1, 2, 3, 4) values related to different surface roughness. The simulated deposition zones correspond to bottom area where TKE is lower than kc=Vs

2 .Vs is the settling velocity and represents a coefficient which enables to account for uncertainties on settling velocity assessment and the cohesion of particles, etc.

Dufresne (2008) reveals that the distribution of bed turbulent kinetic energy (BTKE) under a critical value (0.00010-0.00030m2/s2) is very similar to the deposition zone in a pilot tank. Previous work in the same investigation (Yan et al., 2011) suggested that particle settling velocity (Vs measured with VICAS protocol, Torres, 2008) could be used to estimate the critical value to determine the particle state (e.g., deposited or re-suspended) based on the assumption that near bed turbulent kinetic energy has a significant influence on the motion of particle close to the bed. According to the previous study, the V80(=23.5m/h) settling velocity was used to estimate the critical value. Then kc=V80

2 is the critical

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turbulent kinetic energy. The bed turbulent kinetic energy (BTKE) distributions of simulations with different bed surface roughness height were shown in Figure 7 (ks1, ks2, ks3 and ks4). Regarding the observed spatial sediment distribution in 2011 and the top view of sediment observation in 2007, all the simulated BTKE distributions showed similar outer contour of preferential sediment zone except at the downstream corner near the overflow weir (Figure 7). It suggests that the outer contour was affected slightly by the surface roughness. It also reveals that the BTKE with an appropriate critical value could enable to identify the preferential sediment outer contour in the full scale detention basin. Among all cases, contour simulated with ks1 is similar to the observed one if one just focuses on upstream blank part (shown in Figure 7 with black trapezoid). The simulation with ks4 shows the best accordance if one just focuses on central thickness of sediments (shown in Figure 7 with red polygon). With the assumption that the low BTKE corresponds to the thicker sediment layer, this might suggest that the sand grain roughness height for sediment layer should be higher than that for bare concrete. Difference of the zone of outer contour indeed existed but the global shape was similar. For example, all the cases represent almost the same low value BTKE zone in front of orifice 1 (see Figure 4 labelled with o1) which corresponded to the observation.

Checked points

p1

p2

p3

p4

Figure 8. Layout of the checked points and vertical TKE distribution according to different roughness

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In order to further understand the effects of surface roughness on the near bed turbulence, local vertical TKE distribution analysis were carried out at several specific locations. The position of these local points is shown in Figure 8 (the upper). As shown in Figure 8 (p1, p2, p3 and p4) the near bed turbulent kinetic energy is affected by the surface roughness and hence is sensitive to the surface roughness. Basically, the vertical turbulent kinetic energy distribution shows similar profile at almost all points and for all rough surfaces the maximum bed turbulent kinetic energy is obtained close to the bed due to the influence of the rough element on the bed (see p1, p3 and p4 in Figure 8). The similar vertical profile was also obtained with experimental investigation carried out by Dey et al. (2011). But this is not always the same (see p2 in Figure 8). At p2, simulated secondary currents were observed. This might be the reason for the difference of vertical TKE profile between p2 and the others. In fact more vertical secondary currents above the gutter were observed looking into the vertical plane regarding the gutter stream. They were sensitive to the surface roughness.

(a)

(b)

Figure 9. (a) Global max BTKE at the inlet point versus different rough bed surface and (b) peak values of TKE according to different rough surface

Figure 9a shows evidently that the global maximum BTKE increases with the increase of the sand grain roughness height. The global maximum BTKE is often observed near the inlet zone. Figure 9b reveals that the peak near-bed TKE values show a slight downward trend with the increasing of the non-dimensional roughness Ks

+. The BTKE values remain lower than the threshold kc for points p2, p3 and p4 where sediment depositions are always observed. However, no clear relation has been found in our case between BTKE values and surface roughness height.

4 CONCLUSIONS

With the attempt to clearly understand the effect of surface roughness on the near bed turbulence quantities in a large detention basin, simulations with different surface roughness have been carried out. Measurement of sediment thickness and distribution were conducted in field site. Comparison between simulated and observed contours of sediments zones was performed. Analysis of simulated results compared to observed data reveals that the near bed turbulent kinetic energy distribution could be used in order to estimate the outer contour of preferential sediment zone. The outer contour is slightly sensitive to the surface roughness. The maximum value of the near-bed turbulent kinetic energy distribution in deposition zones is sensitive to surface roughness and is lower than kc. However, no clear relation has been found between BTKE values and surface roughness height. Different

kc

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surface roughness should be set for bare concrete surface and sediment layer as well as other inlet flow rates.

5 ACKNOWLEDGEMENTS

The authors thank the OTHU (Field Observatory in Urban Hydrology) at Lyon France and IMU for scientific support and for financing, ANR (CABRRES Project CESA programme) for financing this project and the Chinese Scholarship Council for PhD funding for CFD modelling of hydrodynamics and sedimentation in stormwater detention basin.

6 REFERENCES

ANSYS Inc. (2011). ANSYS FLUENT Theory guide release 14.0. Canonsburg. U.S.

Akinlade O.G.,Bergstrom D.J., Tachie M.F. and Castillo L.(2004). Outer flow scaling of smooth and rough wall turbulent boundary layers. Experiments in Fluids, 37, 604-612.

Bagnold R.A.(1966). An approach to the sediment transport problem for general. GEOLOGICAL SURVEY PROFESSIONAL PAPER 422-I, U.S., Geological Surgey, Washington, D.C.

Bardin J.P. and Barraud S. (2004). Aide au diagnostic et la restructurqtion du bassin de rtention de Chassieu(Diagnostic and restructuration aid of the retention basin in Chassieu). Rapports pour le compte de la Direction de lEau du Grand Lyon. INSA de Lyon. Villeurbanne, France.

Cebeci T. And Bradshaw M.G.(1977). Momentum Transfer in Boundary layers. Hemisphere Publishing Corporation, New York.

Dey S., Sarkar S. and Solari L.(2011). Near-bed turbulence characteristics at the entrainment threshold of sediment beds. Journal of Hydraulic Engineering, 137(9), 945-958.

Dufresne M., Vazquez J., Terfous A., Ghenaim A., and Poulet J.-B. (2009). CFD modelling of solid separation in three combined sewer overflow chamber. Journal of Environmental Engineering, 135(9), 776-787.

Dufresne M.(2008). La modlisation 3D du transport solide dans les bassins en assainissement : du pilote exprimental la louvrage rel (Three-dimensional modeling of sediment transport in sewer detention tanks : physical model and real-life applicaiton). PhD thesis, INSA de Strasbourg, Strasbourg, France.

Graf W.H. and Altinakar M.S.(2000).Hydraulique Fluviale: coulement et phnomnes de transport dans les canaux gomtrie simple(Fluvial Hydraulics: Flow and transport processes in channels with simple geometry). Trait de Gnie Civil, Volume 16, Lcole polytechnique fdrale de Lausanne, Publi sous la direction de Ren Walther, Presses polytechniques Romandes.

Hribersek M., Zajdela B., Hribernik A. and Zadravec M. (2011). Experimental and numerical investigations of sedimentation of porous wastewater sludge flocs. Water Research, 45, 1729-1735.

Hager W.H.(2010). Wastewater Hydraulics: theory and practice. 2nd edn, Springer, Switzerland.

Krishnappan B.G.and Marsalek J.(2002). Modelling of flocculation and transport of cohesive seiment from an on-stream stormwater detention pond. Water Research, 36, 3849-3859.

Launder B.E. and Spalding D.B. (1974). The numerical computation of turbulent flows. Comp. Methods Appl. Mech. Eng., 3, 269-289.

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Mignot E., Bonakdari H., Knothe P., Lipeme Kouyi G., Bessette A., Rivire N., Bertrand-Krajewski J.-L. (2011). Experiments and 3D simulations of flow structures in junctions and of their influence on location of flowmeters. 12th International Conference on Urban Drainage, Porto Alegre, Brazil, 11-16 September 2011.

Papanicolaou A.N., Diplas P., Dancey C.L., and Blakarishnan M. (2001). Surface roughness effects in near-bed turbulence: implication to sediment entrainment. Journal of Engineering Mechanics, 127(3), 211-218.

Perry A.E., Lim K.L. and Henbest S.M.(1987). An experimental study of turbulence structure in smooth- and rough-wall boundary layers. Journal of fluid Mechanics, 177, 437-466.

Shafi H. S. and Antonia R. A. (1997). Small-scale characteristics of a turbulent boundary layer over a rough wall. Journal of Fluid Mechanics, 342, 263-293.

Souders D.T. and Hirt C.W. (2002). Modeling Roughness Effects in Open Channel Flows Flow. Science Report FSI-02-TN60, Flow Science Inc., Santa Fe, N.M.

Stovin V.R, Grimm J.P. and Lau S-T.D.(2008). Solute Transport Modeling for Urban Drainage Structures. Journal of Environmental Engineering, 134(8),640-650.

Tachie M.F., Dergstrom D.J. and Balachandar R.(2004). Roughness effects on the mixing properties in open channel turbulent boundary layers. Journal of Fluids Engineering, 126, 1025-1032.

Torres A. (2008). Dcantation des eaux pluviales dans un ouvrage rel de grande taille : lments de rflexion pour le suivi et la modlisation (Stormwater settling process within a full-scale sedimentation system: elements of reflection for monitoring and modeling). PhD thesis, INSA de Lyon, Villeurbanne, France.

Wood M.G., Howes T., Keller J., Johns M.R.(1998).Two dimensional computational fluid dynamic models for waste stabilization ponds. Water Research, 33, 958-963.

Yan H., Lipeme Kouyi G., Bertrand-Krajewski J.-L. (2011). 3D modelling of flow, solid transport and settling processes in a large stormwater detention basin. Proceedings of the 12th International Conference on Urban Drainage, 11-16 September 2011, Porto Alegre, Brazil.

9th International Conference on Urban Drainage Modelling Belgrade 2012

1

Effects of computational meshes on hydrodynamics of

an open channel junction flow using CFD technique

Adrien Momplot1, Hossein Bonakdari1,2*, Emmanuel Mignot3, Gislain Lipeme Kouyi1, Nicolas Rivire3, Jean-Luc Bertrand-Krajewski1

1Universit de Lyon, INSA Lyon, LGCIE - Laboratory of Civil & Environmental Engineering, F-69621 Villeurbanne cedex, France 2Department of Civil Engineering, Razi University, Kermanshah, Iran 3LMFA, CNRS-Universit de Lyon, INSA de Lyon, Bat. Joseph Jacquard, 20 avenue A. Einstein, F-69621 Villeurbanne cedex, France *Corresponding author, e-mail: bonakdari@yahoo.com

ABSTRACT

This paper deals with numerical calculation of flow structures in open-channel junction flows which are typical singularities encountered in urban drainage systems. The objective is to evaluate the impact of the mesh shape, mesh refinement, and free-surface modelling approach on the simulation. The ability of CFD strategy (appropriate numerical options, particularly: computational meshes, discretization schemes, turbulence models linked to wall treatment functions and air-water interface capturing approach) is determined by comparing simulated results against experimental one obtained on laboratory scaled open-channel junction where PIV measurement technic was set-up. Comparisons emphasis on simulated and measured horizontal velocity field, mixing interface between both inflows and recirculation zone at two elevations, near the free-surface and close to the bottom of the channel.

The mesh was refined until no significant changes are observed on the main flow structures. Nevertheless, whatever the mesh refinement, CFD modelling has some trouble to simulate accurately the recirculation zone extension near the bottom. The mesh shape has no influence on the velocity field even if hexahedral meshes give better representation of the mixing interface in the junction than tetrahedral meshes. Nonetheless, both mesh types do not enable to represent properly the recirculation in the near-bottom region. Finally, the use of the VOF model leads to a similar velocity field, but seems to give less ability to represent the mixing interface in the junction and the extension of recirculation zone.

KEYWORDS

Computational Fluid Dynamics, Hydrodynamics, Junction, Mesh size

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1 INTRODUCTION

Computational Fluid Dynamics (CFD) offers a suitable understanding of open channel flow pattern and enables to study flow characteristics in different hydraulic and physical situations, including urban drainage systems. It is known that CFD solution is strongly impacted by the selected modelling parameters such as grid, boundary conditions, turbulence model, under-relaxation factors, interface capturing model, spatial and time discretization schemes, etc. One of the main steps in CFD approach is the spatial discretization of the fluid body into cells or elements forming a computational grid. Then, CFD codes compute the solution of mass continuity, energy and momentum equations in each cell of the defined grid.

The grid quality (shape, size and distribution, density of meshes, number of nodes per length of edge, etc) is among the most important parameters affecting the accuracy and convergence of a finite volume calculation. Decreasing the mesh size leads to increase the number of cells and the number of equations and unknowns. This causes longer iterations of the calculation before reaching convergence or increases the round-off error and sometimes causes problem of divergence (due to numerical diffusion). This is especially important in three dimensional modeling of two-phase turbulent flow in open channel (Bonakdari and Lipeme Kouyi, 2010).

The paper aims to investigate the impact of the mesh characteristics on CFD solution when open channel junction flows encountered in urban drainage systems are simulated. Indeed, such geometrical singularities exhibit a complex flow pattern sketched in figure 1 (see Weber et al., 2001) with i) an interface plane (shear plane) between both inflows where mixing occurs if one inflow contains a given concentration of passive or solid material, ii) a recirculation region in the downstream branch with lower velocities where solid material should deposit and passive material should be trapped and iii) an acceleration region facing the recirculation region where high velocities are encountered and thus where erosion of previously deposited material should occur. The present paper is thus focused on the impact of the computational meshes on the CFD prediction of the extension and velocity magnitude of the mixing interface and recirculation region.

Figure 1. Scheme of the main flow structures (from Weber et al., 2001).

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2 METHODS

2.1 Experimental data

The experiments are performed in the channel intersection facility at the Laboratoire de Mcanique des Fluides et dAcoustique (LMFA) at the University of Lyon (INSA-Lyon, France), sketched in Fig. 2 (see Rivire et al., 2011). The facility consists of three horizontal glass channels of L=2m length and b=0.3m width each. The channels intersect at 90 with two inlet branches, labeled the main branch along x axis with the flow rate Qxi and the lateral branch along y axis with the flow rate Qyi and one downstream branch along x axis aligned with the main branch. Each inlet branch is connected to a large storage tank. The water passes through a honeycomb to stabilize and straighten each inflow, collides in the junction, flows through the downstream branch and is collected by the downstream tank. A sharp crest weir ends the downstream branch which total length is finally 2.6m. The water circulation is maintained by pumping from the downstream tank to the inlet tanks. Both inlet flow-rates are measured in the pumping loops using electromagnetic flow-meters. The three parameters which govern the flow configuration are: the inlet flow-rates Qxi= Qyi=2L/s and the water depth at the downstream end of the downstream branch hd=12 cm which is controlled by the weir. Due to negligible wall friction, the water depth is almost the same in the whole flow and only a slight water depth decrease appears (maximum of 3% of hd from the upstream to the downstream tank).

UpstreamTank

DownstreamTank

LateralTank

Qxi=2L/s

Qyi=2L/s

hd

b=30cm

Qyi

L=2m

PumpL=2m

xQxi

y

PIV area

Figure 2. Scheme of the experimental set up.

Velocity fields are measured using a horizontal PIV technique at two elevations (z = 3 cm and 9 cm). Polyamid particles (50 m diameter) are added to the water. A white light generator along with a simple slot of less than 1 mm opening layer is used to create a 5 mm thick light sheet at the desired elevation in the channel junction. A 1280x1920 pixel CCD-camera connected to a PC computer is located above the free surface at an elevation of about 1.5 m. Inserting the whole set-up in the dark finally permits to record the particle motion at the lightened elevation at a fixed frame-rate of 30Hz during 133s with a horizontal resolution of about 0.5 mm. The commercial software Davis (from Lavision) permits to correct the optical distortions, to subtract the background and to compute the mean velocity field. Repeatability, time convergence and spatial coherency were verified and the resulting measured velocity accuracy is estimated to about 5mm/s.

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2.2 Numerical study

The 3D numerical modelling is carried out by means of the commercial Ansys - CFX and FLUENT (version 14) CFD software packages using a steady-state formulation which solves the three-dimensional fundamental flow equations. As for most sewer flows, the experimental junction flow shows an appropriate Reynolds number (Re ~ 15000 in the upstream branches and 30000 in the downstream branches). A relevant turbulence model is thus of great importance in order to obtain accurate numerical results. The key equations for fluid motion in the whole domain are: (1) the continuity equation for the incompressible fluid in Eulerian approach:

0i

i

u

x

(1)

and (2) the Reynolds time-averaged Navier-Stokes (RANS) equations for an incompressible turbulent fluid flow for steady flow condition:

''1ji

j

i

jiij

ij uu

x

u

xx

P

x

zg

x

uu

(2)

with i and j = 1, 2 and 3, where xi represents the three coordinate axes, iu the time-averaged velocity

along axis i, z the vertical free-surface elevation, P the pressure, the fluid density and i ju ' u ' the

Reynolds stresses with the prime sign referring to time fluctuations. Solving Eqs. 1 and 2 requires a turbulence model to set the Reynolds stresses. Among the proposed turbulence models, Bradbrook et al. (1998), Shakibainia et al. (2010) and Mignot et al. (2011) have shown that the RNG (Re-Normalization Group) form of the k- model (initially introduced by Yakhot et al., 1992) accurately computes the 3D behaviour of a junction flow. This turbulence model is then used for the present work.

Since Eq. 2 is elliptic, boundary conditions are required. Uniform velocity distributions are set at each inlet cross-section U = Q/A (A being the wet cross-section) with hydrostatic pressure distribution and outlet extremity water depth h = hd = 12 cm is specified with zero longitudinal gradient of all flow characteristics. A sufficient length (10 meters) is provided upstream each inlet branch in order to obtain a fully developed turbulent velocity profile close to the junction. At the outlet, a hydrostatic pressure distribution is maintained across the entire cross-section. The rigid walls are considered smooth with no slip condition and the standard wall function method (proposed by Launder and Spalding, 1974) (see Table 1). Due to limited water depth variations observed in the experiments, the free surface is modelled either as a single-phase by rigid lid ( the free surface is considered as a wall, with free-slip conditions i.e. zero shear stress at the free surface as expected in experiments) or as an interface using volume of fluid (VOF) method (see Table 1).

2.3 Computational strategy

The construction of a suitable mesh is an important task for the numerical simulations because the accuracy and the calculation speed depend on the mesh resolution. In this study, different structured meshes with various cell concentrations are tested. Nine quite uniform rectangular meshes with decreasing cell sizes (see Fig. 3) are considered. These meshes are organized in three groups: coarse (meshes 1 to 3), medium (meshes 4 to 6) and refined (meshes 7 to 9). For these meshes, the rigid lid approach is used to model the free surface. Simulations have been performed under CFX (meshes 1 to 9) and FLUENT (meshes 10 and 11).

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Besides, two additional calculations are performed with meshes 10 and 11(see Table 1) in order to investigate the influence of the mesh shape (mesh 10: tetrahedral mesh) and the possible influence of VOF model (mesh 11: Cartesian mesh with VOF approach) on CFD solutions. For meshes 10 and 11, the mesh type and size, the boundary conditions and computational strategy are summarized in Table 1.

Figure 3. Computational meshes 1 to 9. Cell sizes are indicated in millimetres for each mesh, using the following convention: x*y*z.

Table 1. Description of the computational conditions, the discretization scheme, meshes shape and density (cell size) for meshes 10 and 11. Hexahedral meshes are detailed as x*y*z.

Mesh shape Cell size Discretization scheme/wall function VOF model

Mesh 10 tetrahedral Distance between nodes around 10 mm

Power law/standard wall function No

Mesh 11 hexahedral cartesian

20*20*10 Power law/standard wall function Yes

3 RESULTS

3.1 Velocity fields

Five simulated runs (among the 11 available) are selected and for each selected case, the velocity fields at two elevations z = 3 cm and z = 9 cm are plotted. Then, comparison against measurements are done (see Fig. 4). No measurements are available for 1.1

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to influence significantly the velocity field even though flow recovery downstream the recirculation region (x/b 3) for z=9cm is computed with better accuracy with VOF model.

U (m/s)

Coarse mesh (Mesh 1)

Medium mesh (Mesh 5)

Refined mesh (Mesh 8)

Tetrahedral fine mesh (Mesh 10)

Refined mesh with VOF (Mesh 11)

Figure 4. Experimental velocity profiles (Exp., top line) and simulated one (Num., lines 2 to 6) at z = 3 cm (left column) and z = 9 cm (right column). Arrows are the velocity field; colours are the velocity magnitude. Numerical results are plotted at each node location.

Experiments

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Comparisons between simulated velocity field obtained with mesh 8 (cartesian) and mesh 10 (tetrahedral with similar mesh density) demonstrates the influence of mesh shape on the velocity profile in the junction (see Fig. 4). One can note that the comparison is more difficult in this case, due to the non-regular distribution of the nodes in the tetrahedral mesh. It seems that the mesh shape does not influence significantly the velocity field. Flow recovery downstream the recirculation region (x/b 3.5) for z=9cm is different regarding all calculations but it is not obvious which resemble the most to experimental data.

3.2 Mixing interface

For all simulated and measured velocity fields, the mixing interface at each elevation is defined as the streamline which originates near the upstream corner of the junction: x/b~y/b~0 (see Fig. 5).

Fig.5 reveals that the mesh 1 cells arrangement (coarsen group) is sufficient to represent the main tendency of the mixing interface even though this solution has more difficulties to represent this interface near the bottom (z=3cm). CFD solution obtained with mesh 6 (medium group) does not improve the precision and the shape of the interface at z = 3 cm compared to the ones obtained with mesh 1. Finally, for mesh 9 (refine group) this interface calculation is in fair agreement with measurements.

(a) (b) (c)

Figure 5. Measured (in black) and modeled (in red) mixing interface between the two inflows in the junction, at z = 3 cm (solid line) and z = 9 cm (dashes) for coarse meshes (mesh 1) (a), medium meshes (mesh 6) (b) and refined meshes (mesh 9) (c).

Fig. 6 shows the influence of mesh shape and VOF model. Comparison between mesh 9 and mesh 10 (see figure 6 (a) and (b) respectively) shows the impact of the mesh shape. The tetrahedral shape has a strong impact on the position of the mixing zone in the near bottom region. Comparison between mesh 9 and mesh 11 (see figure 6 (a) and (c) respectively) shows the impact of the VOF model. We can observe that the mixing interface is not well captured in the near bottom region when using VOF model.

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(b) (a) (c)

(b) (c) (a)

Figure 6. Measured (in black) and modelled (in red) mixing interface between the two inflows in the junction, at z = 3 cm (solid line) and z = 9 cm (dashes) for mesh 9 (cartesian without VOF model) (a), mesh 10 (tetrahedral without VOF model) (b) and mesh 11 (cartesian with VOF model) (c).

Differences between the VOF solutions and others can be explained by the impact of the recirculation zone. This zone induces centrifugal effects which influence the pressure field and water depths, even if this impact is low (for example, the water depths gradient equals about 2 mm along the length, and 0.2 mm along the width in the recirculation zone). Indeed VOF model allows the free surface to be disturbed by these effects, whereas the rigid lid boundary condition doesnt. Additionally, even if the rigid lid condition seems to give better results, it needs to know a priori the heights field to have a good representation of the velocity field.

3.3 Extensions of the recirculation region

For both elevations, the length of the recirculation region L is defined as the location where the mean streamwise velocity (along x axis) of the measurement or CFD solution point closest to the side wall (y~0) changes sign from negative (towards the junction) to positive (towards downstream). Moreover, the width of the recirculation region is defined as the domain in which the net flow discharge (along x axis) computed from the side wall (y=0) to the recirculation width equals 0. The maximum width, noted B herein, is simply the maximum measured or simulated recirculation width, occurring between x/b=0 and x/b=1+L/b.

L and B are evaluated for each CFD solution and are compared to the measured one and data available in the literature (Gurram et al., 1997, Borghei et al., 2003, Best and Reid, 1984). Results of comparison are presented in Table 2 for L and Table 3 for B. It should be noted that B could not be evaluated from CFD solution obtained with meshes 1 to 4.

Table 2. Normalized length L/b of the recirculation zone for each mesh at two elevations: z = 3 cm and z = 9 cm.

Measured Mesh 1 Mesh 6 Mesh 8 Mesh 9 Mesh 10 Mesh 11 Gurram Borghei Best

z = 3 cm 1.25 1.33 2.33 2.00 2.05 2.37 1.66 - - -

z = 9 cm 1.97 2.13 2.67 2.77 2.37 2.50 1.88 2.53 1.70 1.87

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Table 3. Normalized maximum width B/b of the recirculation zone for each mesh at two elevations: z = 3 cm and z = 9 cm.

Measured Mesh 1 Mesh 6 Mesh 8 Mesh 9 Mesh 10 Mesh 11 Gurram Borghei Best

z = 3 cm 0.19 NaN 0.20 0.27 0.28 0.38 0.2 - - -

z = 9 cm 0.33 NaN 0.20 0.33 0.35 0.30 0.13 0.37 0.47 0.37

Tables 2 and 3 reveal that CFD approach mostly overestimates the length of the recirculation zone L compared to measurements except for mesh 11 case. The tetrahedral shape and the VOF model do not improve the estimation of the recirculation length at z=3cm and z = 9cm. Concerning the maximum recirculation width B, neither VOF model nor tetrahedral shape achieve an accurate estimation at all elevations while a clear tendency is observed from measurement data.

4 CONCLUSIONS

The aim of the present paper was to investigate the ability of CFD codes to simulate subcritical open channel junction flows - with a specific attention on the impact of the mesh characteristics using prismatic and tetrahedral cells and of the free-surface modelling approach on the CFD solution. The ability of CFD strategy is assessed through comparisons against laboratory experimental data for which velocity fields in the junction are measured using a horizontal PIV technique.

This comparison is focused on three criteria: the simulation at two elevations of i) the general flow pattern, ii) the mixing interface between both inflows in the junction and iii) the length and width of the recirculation zone in the downstream branch. Among all simulated runs, meshes 8 and 9 (using refined quite uniform rectangular cells aligned with the main flow and a rigid-lid approach for the free-surface representation) appeared to be the most efficient solution based on these criteria. Nevertheless, these two simulations do not reproduce with enough accuracy all criteria: the location of the mixing interface in the near-bottom region differs between measurements and simulations and the length of the recirculation zone is severely overestimated by the numerical models. In addition, the refinement of the mesh 9 compared to mesh 8 appears not to improve significantly CFD solution. Among all simulations, CFD solution performed with mesh 8 seems to have further capability to simulate hydrodynamics across subcritical open-channel junction.

Finally, when simple and widely used CFD approaches (RANS, k- model) are selected, the mixing-interface near the free-surface is accurately computed by very coarse meshes (mesh 1 for instance) - however the mixing-interface curve near the bottom and the recirculation extension in the downstream branch are simulated with poor accuracy even for the most elaborated CFD strategy (for example solution with mesh 9). Due to the importance of these flow structures for pollutants mixing or sediment transport, additional work is obviously required before reaching a satisfactory CFD strategy which enables to better simulate passive and solid transport and dispersion in such structures.

5 ACKNOWLEDGEMENTS

The research was prepared in the frame of OTHU and IMU, Lyon. It was funded by the INSA-Lyon-BQR program, the French INSU-EC2CO-Cytrix-2011 project No 231 and ANR-11-ECOTECH-007-MENTOR projects.

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