FlowduetoMultipleJetsDownstreamofaBarrage:Experimentsand3‐DCFDModellingusingSTAR‐CCM+

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2012 The  flow through and downstream of a row of seven open draft 

tubes  in  a  barrage  has  been  investigated  through  laboratory experiment  in a wide flume and 3‐D CFD simulation using StarCCM+. Agreement between  the experiments and 3‐D modelling  is shown  to be good, including the prediction of an asymmetric Coandă effect. One aim  is  to determine  the distance downstream where depth‐averaged modelling gives  reasonable prediction and  this  is shown  to be about 20 tube diameters (20D) downstream of the barrage.   

PennyJeffcoatePeterStansbyDavidApsley

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FLOW DUE TO MULTIPLE JETS DOWNSTREAM OF A BARRAGE:

EXPERIMENTS AND 3-D CFD MODELLING USING STARCCM+

Penelope Jeffcoate, Peter Stansby, David Apsley University of Manchester, UK

ABSTRACT

The flow through and downstream of a row of seven open draft tubes in a barrage has been

investigated through laboratory experiment in a wide flume and 3-D CFD simulation using

StarCCM+. Agreement between the experiments and 3-D modelling is shown to be good,

including the prediction of an asymmetric Coandă effect. One aim is to determine the distance

downstream where depth-averaged modelling gives reasonable prediction and this is shown to be

about 20 tube diameters (20D) downstream of the barrage.

INTRODUCTION

Tidal barrage schemes are being considered for energy generation where the resulting

electricity is renewable, predictable and reliable, using established technology; for example, the

220MW tidal power plant in La Rance, France has been operational since 1966 (EDF 2011).

There are, however, environmental impacts due to barrages associated with reduced tidal ranges

upstream, enhanced scour and sediment transport, and modified mixing downstream and

upstream.

Coastal flow models that cover large domains have been developed to include barrage

schemes, to determine their impact on the far-field environment, and are generally based on

depth-averaged shallow-water equations for computational efficiency. For example, Burrows et

al (2009) used two-dimensional modelling to model the entire Irish Sea and estuary approaches

in order to determine the far-field effects of five proposed barrages on the West Coast of the UK.

Depth-averaged modelling has also been used by Xia et al (2010) to predict large-scale barrage-

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induced hydrodynamics and by Ahmadian et al (2010) to predict the associated hydro-

environmental parameters of water quality, and sediment and bacterial concentrations. Three-

dimensional flows, however, appear not to have been investigated with regard to barrage

implementation and thus the near-field limits of applicability of depth-averaged modelling are

unknown.

Three-dimensional jets have been the subject of research for many years; circular jets and

wall jets are most relevant here and have been reviewed in Law and Herlina (2002) and Pani

(2012). The effect of boundaries on jet flow tends to be significant, producing less dilution than

free jets (Johnston and Halliwell 1986 and Raiford and Khan 2009). The effect of jets on the bed

shear stress is also substantial (Wu and Rajaratnam 1990). Whilst flows through barrages may

have similarities to previous jet experiments, the flows will differ due to the larger exit area

compared to the channel cross section, proximity to the bed and the downstream flow eventually

becoming almost uniform channel flow.

In this paper we consider the flow resulting from multiple equi-spaced jets emerging from a

barrage in a wide flume, with the following aims in mind: to understand the behaviour and

interaction of multiple jets in a confined flow; to establish, through full 3-D calculation, the

downstream distance at which depth-averaged modelling might be justified; to examine the bed

stress distribution for potential erosion implications.

In this study, laboratory experiments have been undertaken for steady flow through a barrage

containing seven equi-spaced parallel draft tubes. This flow is modelled using STAR-CCM+

code; this gives more flow information than is generally possible from experiments and, once

verified, provides a valuable analysis tool. In particular, bed shear stress may be determined

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which is difficult to measure experimentally and is a vital parameter for sediment transport and

mixing processes.

EXPERIMENTS AND MODELLING

A 1:143 scale model was constructed based upon the proposed Severn barrage geometry

given in DEP Energy Paper (1981). The draft tubes were simplified to be of constant radius,

R=0.055m. The model was fitted into an experimental flume, giving barrage dimensions of

0.539m long × 1.22m wide × 0.28m high. The flume extended 1.1m upstream and 2.8m

downstream of the barrage. Seven tubes with a centreline spacing of 0.145m were built into the

barrage, with the central pipe at mid-width, thus creating a symmetric geometry. A two-

component Vectrino ADV (Acoustic Doppler Velocimeter) was set up downstream of the barrage

on a gantry. The downstream depth was set by a 0.15m high weir at 2.8m downstream from the

barrage. The experimental set up is shown in Fig.1. The discharge was set so that the tubes were

fully submerged; the inlet discharge, Q, was 0.0291m3/s, the average upstream height close to the

barrage, h1, was 0.233m, giving an average upstream inlet velocity, Uin, of 0.102m/s. The

average height immediately downstream, h2, was 0.216m, giving a head difference across the

barrage, H, of 0.017m. This corresponds to a head difference of 2.43m at full scale, which was

found by Xia et al (2010) to be optimal for energy generation.

The water depths were measured at 1D, 2D, 5D, 10D and 20D downstream, where the tube

diameter (D) is 0.11m. The velocity profiles across the tank were recorded at depths of 0.04m,

0.08m, 0.12m, 0.16m and 0.195m from the bed and at 0.185m from the bed at 20D, due to

decreasing water depth; the probe locations are shown in Fig.2.

The experimental set-up was simulated using the CFD package StarCCM+. This solves the

Reynolds-averaged Navier-Stokes (RANS) equations with a standard k-ε turbulence model

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(Launder and Spalding 1974), with a high Reynolds number (log law) wall treatment. Other

turbulence models such as a nonlinear k-ε, a realizable k-ε (Shih et al 1994), k-ω SST and

Spalart-Allmaras model were also tested, but the results were almost identical, so results for the

standard k-ε model are shown.

The computational domain extended 1.1 m upstream and 2.8 m downstream of the barrage.

The water depths were set to the experimental values; the upstream depth, h1, and downstream

depth sloping at a constant gradient from the depth on the downstream side of the barrage, h2, to

that at 2.8m downstream extrapolated from the experimental value at 2.2m (to avoid the local

influence of the weir in the computation).

The geometry was meshed with an unstructured polyhedral mesh with a base size of 0.02m

(Fig.3); the mesh in the tube, close to the downstream barrage wall and close to the bed used

refinement down to 0.005m, approximately 5% of the pipe diameter, to resolve internal pipe flow

and the jet exit. The longitudinal cell size was increased with downstream distance to the base

size; the model had a total of 333,540 cells. Mesh sensitivity studies with varying base and

refinement sizes were conducted and the coarsest mesh which did not affect the finer-mesh

results was selected; this was analysed by comparing the velocity profiles at the duct mid-height

at 1D, 2D and 5D downstream.

The inlet velocity was set equal to that in the experiment. The walls and floor were modelled

as rough, no-slip walls to represent the experimental tank, with a roughness height of 0.001m

(appropriate for painted wood). The free surface was treated as a rigid plane lid with a slip (zero

stress), symmetry plane, boundary condition and the downstream boundary was set as a constant

pressure/head outlet.

In order to assess the bed friction, the ratio of the local bed shear stress to a reference stress was

determined. The local bed stress, which varies with local flow velocity, was output from the model. The

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reference bed stress was calculated using a bed friction coefficient and the channel-averaged velocity at

20D downstream; the bed friction coefficient formula was derived by integrating the rough-wall

logarithmic velocity profile:

. (1)

where h0 is the depth and ks was the wall roughness height, 0.001m, at model scale. The Shields parameter

and critical bed stress (Soulsby 1997) for silt were also calculated to determine the threshold of motion.

RESULTS

The experimental water depths immediately upstream and downstream of the barrage and at

1D, 2D, 3D, 5D, 10D, 15D and 20D from the barrage were recorded on one side (right side

looking downstream) of the flume. The 3-D surface variation from the rigid lid was derived from

the surface pressure difference from zero, assuming hydrostatic pressure (Fig.4); the surface

elevations used these values added to the lid level. Fig.5 shows the water depth recorded in the

experiments and predicted by the 3-D StarCCM+, both on the right side of the flume and at the

centreline.

The experimental water depth decreased with distance downstream; the water levels at the

barrage and at 2.2m were 0.216m and 0.206m respectively, a drop of 0.01m. The 3-D model also

shows decreasing water depth with distance from the barrage, though the water depths predicted

are slightly less than those shown in the experiments; close to the barrage there is a 2.66mm

discrepancy, with depths set to be equal at 2.2m downstream. The StarCCM+ model also

predicts a slight variation across the tank, between values at the centreline and near the flume

sides, but at greater distances from the barrage this difference becomes negligible. Close to the

barrage the water depth at the centreline is lower than at the sides, where there is stagnant water.

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The measured experimental velocities and computed velocities from StarCCM+ are shown to

be in close agreement and the velocity vectors in the downstream region are shown in Fig.6-8.

The velocity vectors are shown close to the bed (Fig.6), at the duct centre plane (Fig.7) and close

to the surface (Fig.8). At the two lower levels, the vectors show that jets form directly

downstream from the tube exits. Minima in the velocity occur between each of the jets close to

the barrage, but as distance from the barrage increases the jets merge and the velocity magnitude

becomes more uniform across the flume. Close to the surface, however, the jets are no longer

evident, with marked cross-stream flow occurring.

Asymmetric eddies form on both sides of the flume, leading to reversed flow at the tank

sides; the largest eddy extends up to 10D downstream, with maximum strength and width at 5D.

The asymmetry is due to the Coandă effect causing the jets to incline towards one side of the

flume (described in Reba 1996); the Coandă effect occurs where the presence of the flume wall

does not allow entrainment of fluid from one side of a jet, thus pulling the jet towards the flume

wall. The eddy formation also forces the outer jets to incline towards the centre of the flume,

causing enhanced merging of the jets. The streamlines in Fig.9 show the jet merging and

recirculation in the flume; the streamlines originate from the duct centreline and the eddies are

seen to extend throughout the depth, causing vertical vortices.

The variation of streamwise velocity throughout the depth was compared at 0.04m, 0.08m,

0.12m, 0.16m and 0.185m/0.195m from the bed, at 1D, 2D, 5D, 10D and 20D downstream. At

1D (Fig.10) and 2D downstream from the barrage, jets are clearly apparent at 0.04m to 0.12m

from the bed, directly downstream of each draft tube. Both the experimental and 3-D

computational results predict a similar peak streamwise velocity of approximately 0.5m/s at 1D

at 0.08m, which is close to the duct centre level (0.075m). At 2D downstream the peak velocity

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has reduced and there is some merging of the outer jets, leading to less defined minima between

the jets. Close to the surface at both 1D and 2D downstream the jets are not discernible, with

marked vertical and cross-stream flow, as seen by the velocity vectors and streamlines. The jets

have merged further by 5D downstream (Fig.11) and are not evident even at the tube centre level.

The experimental and StarCCM+ results are very similar, both in terms of the jet locations, jet

merging and the velocity magnitudes. Note the asymmetry in StarCCM+ flow could be triggered

in either direction and only the direction matching experiments is shown here.

The eddy sizes at the flume sides predicted by the experiments and the CFD model are quite

similar. As distance from the barrage increases the difference between the experimental and

computed eddy sizes increases somewhat, because StarCCM+ under predicts the spreading of the

jets, although the maximum reverse velocity is still similar. At 5D the results are quite similar.

The eddy width also reaches a maximum at 5D downstream, with maximum reverse velocity of

0.2m/s. As the Coandă effect causes the central jets to incline towards one side of the tank, large-

scale asymmetry is produced in the flow. The asymmetry is also depth dependent.

Some asymmetry in the results across the flume is evident at 10D downstream from the

barrage and the location of the merged jet is depth dependent; close to the bed the peak velocities

occur on the right side of the flume, while further downstream the jet moves to the left side. At

20D downstream (Fig.12) the velocity profiles are fairly constant across the width and depth,

with slight residual asymmetry leading to a slight decrease in velocity on the right side of the

flume. At this distance downstream there is very little change in the velocity profile throughout

the depth, suggesting that depth-averaging at this distance will be a reasonable approximation.

The magnitude of local bed shear stress, τb, is shown in Fig.13 as a multiple of a reference stress, τ0, at

20D downstream. The reference bed stress was 0.0926 N/m2, calculated using the skin friction coefficient

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computed from Eq. (1) (0.0138) and the average velocity at 20D (0.116m/s). The contours show that

downstream of the barrage the local bed stress can be up to 5 times the reference stress where the jets

become attached to the bed. Low bed stress ratios occur along the tank walls and at 20D, where the

velocity is small. This shows that even if Uavg is known the friction coefficient is highly influenced by 3-D

effects, as jet attachment to the bed causes magnification of friction. 3-D effects remain significant at 10D

downstream and a reference stress calculated from Uavg can only be used at 20D.

The ratio of full scale Shields parameters to the critical bed stress (Fig.14) describes the regions

where the threshold of motion is exceeded, i.e. τ*>τ*crit. The full scale barrage would cause silt to move at

all regions within 20D of the barrage, though low ratios occur where the velocity is small, so movement

will be minimal. High ratios occur close to the barrage potentially indicating the presence of scour.

DISCUSSION AND CONCLUSIONS

Four main issues are addressed in this paper: how velocity varies with depth and distance downstream

of the barrage; how well this is predicted by 3-D CFD; where 2-D depth-averaged modelling is justified;

and how the bed shear stress varies. The experiment shows that high velocity jets form downstream

of the tubes and recirculating eddies form at the flume sides. Close to the surface, however, jets

are not apparent. As distance from the barrage increases the velocity variation across the width

and depth is reduced. The transverse velocity profiles are asymmetric and dependent on vertical

level up to 10D downstream of the barrage and have become almost uniform by 20D

downstream. The 3-D computational modelling using StarCCM+ provides reasonable

comparison with experiment. Depth-averaged modelling was expected to be inadequate close to

the barrage and this work suggests that it only becomes valid at least 20D downstream. Bed shear

is largely instrumental in driving sediment transport and it can be seen that local scour and deposition will

be considerably underestimated using depth-averaged assumptions in the near field. At full scale the

critical bed stress would be exceeded and bed-load transport would occur.

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REFERENCES

Ahmadian, R., Falconer, R.A., and Lin, B. (2010). “Hydro-environmental modelling of the

proposed Severn barrage.” Proc. Inst. Civ. Eng., Energy, 163(3), 107-117.

Burrows, R., Walkington, I.A., Yates, N.C., Hedges, T.S., Wolf, J., and Holt, J. (2009)a. “The

Tidal Range Energy Potential of the West Coast of the United Kingdom.” Appl. Ocean Res.

31(4), 229-238.

Department of Energy (1981). “Tidal Power from the Severn Estuary.” DEP Energy Paper, 46,

198.

EDF (2011). “L’usine maremotrice de la Rance: 40 ans d’exploitation au service d’une

production d’electricite inepuisable sans CO2.”

Johnston, A.J. and Halliwell, A.R. (1986). “Jet behaviour in shallow receiving water.” Proc. Inst.

Civ. Eng., 81(2), 549-568.

Launder, B.E. and Spalding, D.B. (1974). “The numerical computation of turbulent flows.”

Comput. Meth. Appl. Mech. Eng., 3, 269-289.

Law, A.W-K. and Herlina. (2002). “An experimental study on turbulent circular wall jets.” J.

Hydraul. Eng., 128, 161-174.

Pani, B.S. (2012). “Turbulent jets: A point-source method for hydraulic engineering.” Cambridge

University Press India.

Raiford, J.P. and Khan, A.A. (2009). “Investigation of circular jets in shallow water.” J. Hydraul.

Res., 47(5), 611-618.

Reba, I. (1966). “Applications of the Coandă Effect.” Sci. Am., 214(6), 84-92.

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Shih, T.-H., Liou, W.W., Shabbir, A., Yang, Z. and Zhu, J. (1994). “A New k-ε Eddy Viscosity

Model for High Reynolds Number Turbulent Flows -- Model Development and Validation.”

NASA TM 106721.

Soulsby, R. (1997). “Dynamics of Marine Sands”. Thomas Telford.

Wu, S. and Rajaratnam, N. (1990). “Circular turbulent wall jets on rough boundaries.” J.

Hydraul. Res., 28(5), 581-589.

Xia, J. Falconer, R. A. Lin, B. (2010). “Hydrodynamic impact of a tidal barrage in the Severn

Estuary, UK.” Renewable Energy, 35(7), 1455-1468.

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NOMENCLATURE

D Tube diameter (m)

h1 Upstream water height (m)

h2 Downstream water height (m)

H Head difference (m)

Q Discharge (m3/s)

R Turbine radius (m)

Uin Inlet velocity (m/s)

U, V, W Velocities in X, Y, Z direction (m/s)

X, Y, Z Length, Breadth, Depth (m)

FIGURES

Figure 1: Experimental set-up

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Figure 2: Experimental velocimeter locations

Figure 3: StarCCM+ model mesh

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Figure 4: StarCCM+ predictions of surface height variation downstream

Figure 5: Water depth variation

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Figure 6: Velocity vectors at 0.04m from the bed: a) Experiment; b) StarCCM+

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Figure 7: Velocity vectors at 0.075m from the bed, duct centreline: a) Experiment; b) StarCCM+

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Figure 8: Velocity vectors at 0.195/0.185m from the bed (close to surface): a) Experiment;

b) StarCCM+

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Figure 9: Streamlines originating at duct midheight: a) Plan view; b) Elevation view

Figure 10: Streamwise velocities at 1D downstream at different vertical locations, z

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Figure 11: Streamwise velocity at 5D downstream at different vertical locations, z

Figure 12: Depth-averaged streamwise velocities at 1D, 2D, 5D, 10D and 20D

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Figure 13: Ratio of local bed stress magnitude from StarCCM+ to reference bed stress

Figure 14: Ratio of full scale Shields parameter to critical bed stress