Reservoir Design Improvement Using CFD
D R Glynn* and A Shilton+
*
+
Flowsolve Limited, 130 Arthur Road, London SW19 8AA. cfd@flowsolve.com
Institute of Technology and Engineering, Massey University, Private Bag 11222,
Palmerston North, New Zealand. A.N.Shilton@massey.ac.nz
Abstract
This paper describes how CFD has been used to analyse the hydraulics of two potable water
storage reservoirs currently under construction. The study highlights how stagnant zones and
short-circuiting pathways, which are undesirable features of reservoir flow, can be minimised
using modelling techniques. For both reservoirs studied, the numerical predictions have led
to design revisions, yielding benefits to reservoir performance. The paper includes a
discussion of several numerical aspects of the simulations which have proved to be of
importance: attainment of convergence, choice of turbulence model, and use of a higher-order
differencing scheme.
1.
Introduction
Water distribution systems include reservoirs which provide security of supply and even out
supply and demand. Quality of the water supply is a prime requirement. Water quality can
be adversely affected by a poor flow pattern in a reservoir, for instance if there are any
significant stagnant zones or short-circuiting pathways. CFD has the potential to provide
valuable design insight into the hydraulics of reservoirs, which is difficult to acquire from
experimental techniques. Applications of CFD in this field are, however, still relatively rare.
The first application of PHOENICS to the analysis of reservoir flows (Glynn, Creasey and
Oakes, 1998) compared numerical predictions with experimental data for three reservoir
configurations, with features typical of current designs.
The present paper describes two practical cases where CFD has been used to analyse the
hydraulics of potable water storage reservoirs currently under construction. In both cases the
numerical predictions have led to design revisions yielding benefits to reservoir performance.
The reservoirs studied were (i) Hartshead Moor Service Reservoir, Yorkshire, England, under
construction by North Midland Construction plc for Yorkshire Water, one of the major water
companies in the UK; and (ii) Inglewood Reservoir, Taranaki, New Zealand, under
construction by New Plymouth District Council. In both cases the reservoirs are circular. For
Hartshead Moor, the objective was to assess the performance of the reservoir both with and
without baffles. For Inglewood, attention was concentrated upon the possibility of improving
performance by repositioning the outlet.
2.
Description of the Model
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Equations solved
The partial differential equations solved represent conservation for steady flow of mass, three
components of momentum, and residence time. The momentum equations are the familiar
Navier-Stokes equations which govern fluid flow. Turbulence was represented using the kepsilon model. Use of the Chen-Kim extension to the k-epsilon model is discussed below. A
cylindrical-polar grid was used.
Wall friction
Wall friction was imposed on the reservoir walls and floor, using wall functions which are
based on the logarithmic law of the wall. All walls were assumed to be smooth. The water
surface was modelled as a frictionless boundary.
Columns
Glynn, Creasey and Oakes (1998) found that inclusion of a suitable flow resistance to
represent the presence of columns had little effect on the predicted flow field. Columns were
therefore not considered in the analyses described here.
Representation of the inlet
For both reservoirs, inlet is by means of a bellmouth just above the water surface, located
close to the periphery. Water emerges from the bellmouth and falls back to the surface. A
simple analysis showed that the water impinges on the surface in an annulus with a
substantial vertical velocity component, and a small horizontal component. It would not be
practical to represent this annular inlet region exactly in the CFD model. Instead, the
inflowing water was assumed to have joined together as a compact downwards-oriented jet,
located at the surface. Justification for this assumption was provided by a separate simple
CFD analysis of the inlet region (based on a polar grid centred on the inlet). This
demonstrated that a vertically oriented annular flow of water impinging on the surface does
indeed come together as a vertical jet a short distance below the surface, as shown in figure
15.
Residence time
An equation was solved for “residence time”, this being the mean age in the water in each cell
since its entry to the reservoir. Contour plots of this variable give a good indication of how
well mixed the water is, and whether there are any stagnant zones.
Hydraulic residence time distribution curves
Where younger and older water mix, the residence time represents the mean of the ages. For
the Inglewood reservoir an important requirement was to ensure a minimum dwell time for
the water. For this purpose a transient simulation was required, to track the motion of a burst
of simulated tracer around the reservoir, so that the variation of tracer outflow rate with time
could be plotted. From this curve the minimum dwell time could be deduced. The transient
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was restarted from the steady solution, with only the tracer concentration being solved, the
pressure and velocities being stored.
3.
Hartshead Moor
Hartshead Moor Service Reservoir consists of two circular tanks of internal diameter 35m.
Inlet is by means of a bellmouth just above the water surface, located close to the periphery.
The outlet is in the floor, diametrically opposite the inlet. For the purpose of the model, the
water depth was taken to be 4.1 m, and the flow rate 60 l/s. The principal objective was to
discover whether any improvements would be gained by the introduction of baffles.
Simulations were therefore performed both with and without the presence of baffles.
The flow pattern for the case without baffles is shown by means of velocity vectors in figures
1 and 2, which correspond to flow at the surface and the floor respectively. After impinging
on the reservoir floor, the flow fans out radially. It moves outwards and upwards to the
perimeter of the reservoir, is guided around by the perimeter, and then turns back along the
main diameter towards the inlet. A significant feature of the flow pattern at the floor is a
separation line where the incoming flow lifts off the floor, when it meets water returning in
the opposite direction. It should be remarked that in figure 2 and other figures showing
velocities on the floor, the vector arrows which lie outside the reservoir circle indicate large
velocities close to the inlet position. They do not imply that any flow penetrates the reservoir
wall.
The flow field is further illustrated in figure 3, which shows how the outward flow at the floor
rises when it meets the perimeter. (For clarity, vectors are not shown in the region close to
the inlet.)
Figure 4 shows residence time of water at the surface. The residence time shows little
variation (between 17 and 19 hours), showing that the water is well mixed.
For the case with baffles, velocity vectors and residence time for the water surface are shown
in figures 5 and 6. There are two parallel baffles, oriented at approximately 40o to the
diameter joining inlet and outlet, and arranged so as to form an S-shaped path for the water.
The velocity vectors show that the momentum of the inlet drives a relatively energetic
recirculatory flow upstream of the first baffle. Outward flow past this baffle lies close to the
perimeter wall, and continues along it to the second baffle. Between the baffles, and
downstream of the second baffle, lie recirculation regions of relatively quiescent water, with
residence times up to 42.5 hours.
This maximum residence time is much greater than for the case without baffles. The reason
for this is that the baffles tend to suppress the mixing driven by the inlet momentum. The
energetic flow near the inlet is largely screened from the remainder of the reservoir by the
first baffle. The flow separates off the end of each baffle, giving rise to regions of
recirculation within which the residence time remains high.
The introduction of baffles is therefore seen to be counterproductive. As a result of the
modelling exercise, the water company that commissioned the study has decided not to
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include baffles in the second reservoir of the installation. Baffles had already been
constructed in the first, and these will be retained. There will therefore be an opportunity for
the effect of the baffles to be demonstrated during operational experience.
4.
Inglewood Reservoir
Inglewood Reservoir, Taranaki, New Zealand, is at present under construction by New
Plymouth District Council. The reservoir is circular in plan, with internal diameter 30.6 m.
The inlet arrangement is similar to that for Hartshead Moor, i.e. a bellmouth just above the
water surface, close to the periphery. The reservoir was assumed to be operating at 75%
capacity, giving a water depth of 4.65 m. A flow rate of 120 m3/hour (i.e. 33.3 l/s) was used
for the analysis.
The initial design located the outlet close to the perimeter, and 0.85 m above the reservoir
floor. (This ensures that if the outlet pipe should fracture in the event of earthquake, there
would be an emergency supply of water retained in the reservoir.) The inlet and outlet
locations subtended an angle of 116o at the reservoir centre.
The predicted flow pattern was similar in its general characteristics to that described above
for Hartshead Moor. The inlet flow falls as a jet, impinges on the reservoir floor, and fans out
radially. It moves outwards towards the perimeter, tends to rise, and after approaching the
point diametrically opposite the inlet, moves back towards the inlet. On the floor, this
backward flow meets the outward flow at a separation line, seen clearly in a plot of velocity
vectors (figure 7).
Tracer analysis
It is clear from figure 7 that part of the outward flow at the reservoir floor is directed into
close proximity to the outlet. This means that water may tend to short-circuit out of the
reservoir, without the benefit of mixing and retention in the full volume of the reservoir. This
would mean that chlorination might have insufficient time to be fully effective. The extent of
this short-circuiting cannot be determined from the predicted mean residence time for steady
flow, since it is the minimum rather than the mean residence time that is required. To predict
this a transient analysis is necessary. This simulates the motion through the reservoir of a
short burst of tracer (with an initial concentration of 1), so that the variation of tracer flow
rate at the outlet can be monitored.
The transient tracer analysis is illustrated in figures 8, 9 and 10, which show the movement of
the pulse of tracer immediately following impingement on the floor. The separation line
impedes the progress of the tracer, pushing it towards the circumference, and into the vicinity
of the outlet.
To observe the effect of short-circuiting quantitatively, the variation of tracer outflow with
time was plotted; this can be seen as the curve labelled “original” in figure 11. (These curves
are similar to the classic “hydraulic residence time distribution curves” generated in
experimental tracer studies.) The tracer first reaches the outlet after 3 minutes, and the curve
is seen to rise to a sharp peak. As the main body of tracer passes the outlet, the peak is passed
and the concentration decreases. As some of the tracer gets caught in local eddies and as the
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main body of tracer circulates back to the inlet and is swept around again, a series of smaller
peaks follow. As the tracer is progressively mixed into the main body of the reservoir it
becomes diluted, and the concentration (and so the peaks) tail off.
The specification for adequate chlorination is that the minimum retention time for water
should be 30 minutes. The tracer study shows that for the specified outlet position, 3% of the
tracer has exited the reservoir before this time. There is therefore scope for improvement.
Changes to outlet position
Figure 7 clearly indicates that the minimum retention time might be improved if the outlet
position were to be moved further away from the inlet. Three further simulations were
performed with the outlet placed diametrically opposite to the inlet, and sited respectively
0.8m, 2m and 5m from the far wall.
By comparing the new tracer curves with the original (figure 11), it can be seen that the time
taken for the first fractions of tracer to escape from the reservoir has been approximately
doubled. Positioning the outlet further from the wall shows progressive improvement in this
regard. Also, the concentration of the first tracer peak decreases as the outlet is located
further from the wall. This is due to the additional time available for mixing and therefore
dilution of the tracer before it reaches the outlet. The secondary peak has been largely
eliminated from the curves for the new outlet positions, further improving the hydraulic
efficiency of the system.
Flow pattern and residence times for revised outlet position
Moving the outlet to a location directly opposite the inlet creates a symmetric flow pattern.
This is shown in figure 13, for the case where the outlet is 5m from the wall. This may be
compared with the asymmetric flow field shown in figure 7.
The corresponding mean residence times for flow near the floor are shown in figure 14. The
older water behind the separation line is clearly visible. Study of similar plots for higher
levels in the reservoir shows that the region with the longest retention time is the zone where
the flow has circulated right around the reservoir, and is re-approaching the inlet. This is
more desirable than the situation for the original outlet location, where the oldest water was to
be found at the centres of stagnant zones around which the flow recirculates.
The theoretical mean residence time for the reservoir under the given operating conditions is
1.03 x 105 s, or 28.5 hours. The predicted maximum time with the outlet 5m from the wall is
1.12 x 105 s, or 31.1 hours, only 2.6 hours longer than the theoretical mean. This figure
highlights the absence of any significant stagnant zones. The 2.6 hours may be compared
with a corresponding figure of 5.9 hours for the original outlet position; this provides a
quantitative measure of the improvement gained.
5.
Numerical Aspects
Symmetry of the impinging jet
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A jet impinging on a plane will spread radially outwards on the plane, and this spread may be
expected to be axisymmetric. It proves, however, to be difficult to attain axisymmetry when
the model is based on a cartesian grid (or, as here, a polar grid where the polar axis is parallel
to, but not coincident with, the jet axis). For such grids, the velocity of the radial outflow is
generally predicted to be different for flow along the grid diagonals and for flow in the
cartesian directions. This phenomenon has sometimes been referred to as the “butterfly
effect”.
This effect is clearly in evidence when the standard PHOENICS solution options are adopted
for the reservoir models; following impingement on the floor, the flow spreads outwards
principally on the grid diagonals. The effect may be clearly seen in figure 8 of the paper by
Glynn, Creasey and Oakes, 1998. At the time of writing that paper, the authors were
persuaded that the prediction of diagonal flow was a real physical effect. The opinion of the
present authors is that this was in fact a manifestation of the “butterfly effect”.
Considerable effort was expended in addressing this problem, as a result of which the
following solution options were selected: (i) GCV solver, and (ii) the higher-order UMIST
scheme on the velocity and turbulence variables. With these settings, the flow velocities
following impingement on the floor were approximately equal on the diagonals and in the
grid directions.
Turbulence model
The transient tracer predictions have proved to be extremely sensitive to the choice of
turbulence model. This is demonstrated in figure 12, which shows a comparison of the
predicted tracer curves for the Inglewood reservoir obtained (i) using the unmodified kepsilon model, and (ii) using the Chen-Kim extension. The Chen-Kim model predicts a
lower initial peak, and an earlier outflow of tracer. The difference may be attributed to the
reduced dissipation inherent in the Chen-Kim model, resulting in the prediction of stronger
recirculation zones. Discussions with Dr Mike Malin of CHAM revealed that he had recently
had similar experience for a problem of this nature. The Chen-Kim model was therefore
selected for the definitive simulations.
Convergence
It proved to be not at all easy to attain convergence for the reservoir flow solutions. This may
at first seem surprising, since the geometry is simple, and there is just one inlet and one
outlet. The reasons for the difficulty in achieving convergence are likely to be (i) that there is
no internal geometry (for the case without baffles), and (ii) that in much of the domain the
velocities are very low.
Where use could be made of a plane of symmetry, this was very helpful to convergence.
(This was not, of course, possible with the initial outlet position in the Inglewood case.)
Following extensive experimentation with relaxation values, it was in general possible to
attain full convergence. The following observations may be made about the convergence of
the individual cases.
Hartshead Moor, no baffles
Half-domain solved, due to presence of plane of
symmetry. Full convergence achieved.
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Hartshead Moor, with baffles
Full domain required. Full convergence achievable,
probably on account of the internal geometry.
Inglewood, initial outlet position
Full domain required. No internal geometry. Adequate
convergence achieved, but with a residual
“wobble” that could not be eradicated. Without
Chen-Kim convergence was perfect; Chen-Kim
was necessary, however (as described above).
Inglewood, revised outlet positions Half-domain solved, due to presence of plane of
symmetry. Full convergence achieved. (See figure 16.)
Concluding Remarks
It is difficult to study the flows in reservoirs by direct observation, and CFD offers a practical
method by which potential design improvements may be evaluated.
This paper describes how CFD has been used to predict water flow patterns in two potable
water storage reservoirs currently under construction: Hartshead Moor in England, and
Inglewood in New Zealand. The authors are not aware of any previous commercial
application of CFD to water industry design in New Zealand. New Plymouth District Council
are to be congratulated for their pioneering approach.
For both cases, the CFD model has been used to evaluate different options for a fundamental
design parameter, so as to minimise the presence of stagnant zones and short-circuiting
pathways.
For each of the two reservoirs studied, the numerical predictions have led to revisions of the
design specifications, yielding benefits to reservoir performance. This demonstrates the
importance of CFD as a design tool for the water industry.
Reference
Glynn D R, Creasey J and Oakes A, “Simulation of Flow Patterns in Potable Water
Reservoirs”, The PHOENICS Journal, Vol 12 No 1, April 1999.
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