Strangely the various higher resolution linear mesh schemes vary more from the quadratic case than the nominal case. That may be because each test case
only provided mesh refinement in one direction at a time, while the quadratic simulation provided second-order element shape functions in all directions.
The most consistently predictable zones were the extremes: where sand would be eroded and where sludge flocs settle. Almost as consistent was the prediction
of the area where silt would be scoured. The extent of the regions of silt scouring was slightly over-predicted with respect to the quadratic simulation. Fortunately
such error would provide conservative pond engineering if erosion control were to be provided in response to these simulations.
It was found that nominal mesh parameters produced reasonably indicative results when applied to form linear non-quadratic finite elements. Given a finite
capacity of random access memory on our computer, coarser mesh rules were accepted for the ‘real-world’ simulation of multiple-aerators.
5. Results
Simulation results of individual aerators are presented in Figs. 8 – 11, where the plotted zones of benthic shear stress provide a measure of pond condition as
hypothesized by Peterson 1999b. The plot axes have units of metres in the north and west directions, respectively, while contours represent the magnitude of
benthic shear stress in Nm
2
, tangential to bottom and bank surfaces. Wall functions were disrupted within those finite elements which adjoin both the
bottom and a bank, and so these conflicts resulted in the appearance of certain zigzag contours.
Table 8 Bottom stress predictions for NW paddlewheel in Pond X
a
Clay Feed
Cells Dead
Mesh Sand
Silt Over 0.1
0.003–0.01 0.01–0.03
0.001–0.003 0.03–0.1
Under 0.001 Nm
2
Nm
2
Nm
2
Nm
2
Nm
2
Nm
2
37.4 17.8
20.7 15.9
5.3 2.9
Nominal 44.4
8.7 13.2
22.0 8.3
3.3 a22l16
3.0 8.8
23.6 13.0
alays32 8.5
43.0 13.5
22.4 7.9
3.3 llays32
44.3 8.7
42.6 8.6
12.2 slays8
24.2 9.3
3.1 9.1
45.9 meshsp1
3.6 8.1
20.1 13.1
2.7 7.0
21.7 13.5
10.8 44.4
Plays16 48.9
10.4 12.5
Plays8 –Q 20.4
3.2 4.6
a
Values in percentages. Refer to Table 3 for description of alternative simulations.
Fig. 8. Single paddlewheel deployed in SW corner of Pond X.
5
.
1
. Paddlewheel Alternative simulations of a paddlewheel deployed in the southwest SW and
northwest NW corner of the pond are illustrated in Figs. 8 and 9, respectively. A smaller zone of sand scour greater than 0.1 Nm
2
was found in the SW corner deployment than resulted from the NW corner deployment. The SW deployment
caused the aerator jet to travel somewhat inclined offshore towards the middle of the next bank, with only 1.7 of the pond bottom experiencing enough stress to
mobilize sand, whereas the NW deployment would cause sand to be scoured from 2.9 of the bottom area.
The additional scouring of sand caused by the NW deployment may have been due to shallower water and a slightly inshore inclination. Conversely, the area of silt
scour was about half for the NW deployment as it was for the SW arrangement. The total area of sand and silt scour was similar in both cases, measuring 8.2 for
the NW and 10.8 for the SW. It would seem that the high stress area of sand erosion resulting from the NW deployment did not cascade into silt erosion, but
resulted in a more diffused downstream effect, causing nearly 60 of the pond bottom to experience stress within the zones of cells, feed, and clay.
Both cases demonstrate that a paddlewheel effectively transmits momentum into the water column, causing a swath of excessive stress across the pond, followed by
reasonably good circulation around the pond periphery. Between 55 and 60 of the pond bottom would experience shear stress in the cells-feed-clay range of 0.001 –
0.03 Nm
2
, which is thought to be preferable to higher and lower stress conditions.
5
.
2
. Propeller-aspirator Fig. 10 illustrates the shear stress distribution resulting from a propeller-aspira-
tor. Stress is very intense within the impingement crater, and much weaker in the surrounding region. A close-up of the region around the impingement crater is
detailed in Fig. 11, while the pond wide picture illustrates how minimal this disturbance is. The patch of sand t \ 0.1 Nm
2
corresponds to the conditions observed in the real pond, where there is a localized scour-hole. A single propeller-
aspirator appears to be unable to cause sufficient circulation in a 1-ha pond, as the simulation predicts that most of the bottom would be dead less than 0.001 Nm
2
, without the benefit of forced convection.
It is presumed that high accelerations and gradients in this region were responsi- ble for numerical noise which prevented force-equilibrium. Benthic shear stress in
Fig. 9. Single paddlewheel deployed in NW corner of Pond X.
Fig. 10. Single propeller-aspirator deployed at north end of Pond X.
the pond would need to average 0.008 Nm
2
higher than the simulation predicts to balance the applied aerator thrust. It is not known if the unaccounted force actually
presents itself near the aerator or over a wide region of the pond benthos. Three-dimensional curvature of the scour crater has been neglected, exaggerating
the deceleration at impact. Numerical instabilities might not be so severe if the jet were modelled within the curvature imposed by the real crater.
5
.
3
. Real-world simulation The practical validity of the modelling methodology may be assessed if the results
of simulations are taken at face value and challenged with measurements from a real pond. This task is made possible with the observations of Pond X described in
Peterson 2000. In this case, the pond was aerated by a mixed deployment of two paddlewheels and four propeller-aspirators. Only the nominal set of meshing
parameters was used to simulate the real-world test case. This limitation was imposed by the enormous computational cost of the multiple aerator deployment,
as detailed in Table 5.
5
.
3
.
1
. Circulation Figs. 12 and 13 compare the simulated speed contours with observation vectors
at a depth of 150 mm below the surface and 200 mm above the bottom, respectively. The simulation predicted velocities at over 500 000 computational
nodes on an irregular grid, while there were only 68 observation points. The nodes and measurements points were not coincident, and so the two data sets have been
interpolated onto the same rectangular grid. Note that the ragged contours along the shorelines are artifacts of this interpolation. Vectors from the simulation were
sampled every 10 m marked as thin gray lines to enable comparison with observation vectors bolded black.
The layout of survey stakes in Pond X is shown in Table 9 and the pond surface circulation observations and simulation are compared in Table 10. Speed dis-
crepancy and directional differences indicate a conglomeration of many factors, including simulation and experimental errors, and possibly some transient events.
The discrepancy between surface speed observations and simulation results cer- tainly include turbulence and wind effects. The simulation is not necessarily invalid,
as the theoretical basis is the long time Reynolds-averaged flow field. A linear regression analysis of all surface data gives a correlation coefficient of 0.1049, as
Fig. 11. Close-up of shear stress contours near the impingement of the jet spear-like symbol denotes the centerline alignment of the propeller.
Fig. 12. Near surface speed simulation contours and observation vectors.
plotted on Fig. 14. The poor correlation indicates a very weak signal to noise ratio. Partitioning of the zero-wind data gives a correlation coefficient of 0.5228 with a
slope of 0.7949, which suggests that the simulation slightly underpredicts actual surface speed.
Comparisons of simulation direction and all observation data are plotted in Fig. 15. Flotsam was visually observed and subjectively averaged over a period longer
than wind events. The simulation results provide a reasonable comparison with the observations.
The lower water column circulation speed and direction are given in Table 11, comparing the results of the simulation with speed measurements. Data have not
been partitioned according to the nil-wind instances noted in Table 10. Near bottom speed correlation of simulations and observations is shown in Fig. 16. The
speed observation data presented here are generally accepted with greater confi- dence than was the case with the near surface data. This is due to the fact that the
bottom of the pond is protected by inertia from the transient breezes which first impact upon the surface.
Fig. 17 indicates that bottom flow direction was predicted with a correlation coefficient of 0.7983, which further validates the simulation. Bottom flow direction
was not visible, but derived from a series of samples taken repeatedly in the eight octant directions N, NE, E, SE, S, SW, W, NW by the methodology described in
Peterson 2000.
5
.
3
.
2
. Sediment condition Fig. 18 shows the benthic shear stress predicted by the simulation of a ‘real-
world’ deployment of two paddlewheel and four propeller-aspirator aerators in Pond X. The simulation results were interpolated onto the 20 × 20 m grid described
in Peterson 2000, so that sediment and shear stress magnitude are sampled at the same resolution. The interpolation was the result of kriging from the thousands of
simulation nodes surrounding each stake. The interpolation of simulated shear stress was then paired with observations of sediment conditions at the correspond-
ing sampling locations. Foremost of interest is the mean size of sediment deter- mined by laser diffraction. Assuming all samples were principally silica allows
plotting on the Shields curve given in Fig. 19. This clearly illustrates that most locations were below the Shields curve, and therefore subjected to the process of
sedimentation.
Calculated shear stress provides an important measure of the sediment condition. Particle size and stress together form a complete picture which illustrates the
suspended sediment transport in the pond microcosm. In each case, the conjugate of particle size and shear stress plotted on or below the Shields curve of incipient
motion. Note that conditions plotting above the curve would be expected for water column suspended solids, not core samples.
Fig. 13. Near bottom speed simulation contours and observation vectors linear regression fit of data suggests that the simulation provides a valid representation of pond circulation at points 200 mm above
the bottom.
Table 9 Layout of survey stakes in Pond X
a
a
Dimensions are schematic distances from the southwest corner upper left above, northward along the west bank to the right across the top above and easterly on the south bank down on the left.
Refer to Peterson 2000 for a detailed survey of Pond X.
It is believed that the principal source of suspended solids were the banks and patches of the bottom directly impinged upon by aerator jets, of which stake c 3
was the only representative sample. Stake c 2 did not exactly plot as a scour site because it had completely lost all material other than cohesive clay, and it was
slightly missed by the simulated jet streamlines. Stake c 18 is the best representa- tive of the central sedimentation dead-spot, where anaerobic flocs had accumulated
in a deep drift. Other sampling locations were distributed at varying distances below the Shields curve, while they experienced similarly varying rates of sedimen-
tation, as documented in Peterson 1999a.
Alternatively these same data sets may be plotted with simulated shear stress as the independent variable. Various indices of sediment condition may then be
plotted as the dependent variable. Regression analysis yields correlation with respect to shear stress, but there is a great deal of scatter which is attributed to the
transport of suspended sediment. This material fallout is hypothesized to cause anaerobic conditions by burying organic material under a mineral overburden, as
evidenced by organic carbon content generally less than 1 of sample mass.
In spite of suspended sediment fallout interactions, there was a positive trend between applied shear stress and sandiness. The converse is true for the content of
silt and organic carbon, which appear to be inversely related to shear stress. Only silt demonstrated a correlation coefficient better than 0.25 with respect to benthic
shear stress, as plotted in Fig. 20.
Table 10 Near surface observations compared with the simulation
a
Difference Stake
Simulation Observed
Direction Discrepancy
Simulation °
ms °
° ms
ms 201
87 −
0.050 −
114 0.028
0.078 South of 1
0.045 0.017
− 0.028
132 142
10 1
0.117 0.083
South of 2 49
− 44
− 93
− 0.034
0.103 −
0.084 −
93 0.187
b
− 51
2 42
0.062 −
0.058 South of 3
− 93
0.119 −
122 −
29 3
0.199
b
0.176 −
0.022 −
93 −
109 −
16 0.081
0.131 0.050
− 93
40 133
East of 4 4
0.049 −
97 −
190 −
93 0.082
0.132 0.064
− 0.055
− 5
0.119
b
− 23
West of 6 −
18 0.162
0.009 6
− 5
0.154
b
− 21
− 16
0.027 −
0.043 7
− 116
0.070
b
− 38
78 58
− 36
− 94
− 0.007
West of 7 0.088
0.095 0.013
− 0.261
North of 8 −
139 0.274
− 75
64 8
0.114 66
− 73
− 139
− 0.099
0.015 0.125
0.068 −
139 0.058
− 149
9 −
10 0.164
0.088 West of 9
− 139
0.076 −
143 −
4 0.212
West of 11 0.043
0.169 −
5 −
13 −
8 −
9 11
0.150 0.202
0.051 −
5 −
14 0.034
− 0.020
− 5
0.054
b
− 8
West of 12 −
3 0.040
0.045 12
− 5
− 0.004
b
− 19
− 14
0.010 0.008
13 175
0.002
b
240 −
65 −
139 −
139 0.003
East of 13 0.012
0.009
b
0.033 −
0.078 West of 14
175 0.111
184 −
9 14
0.120 4
179 175
− 0.055
0.065 0.093
− 0.021
− 5
0.114
b
− 3
16 2
0.234 0.058
West of 16 −
5 0.176
− 7
− 2
0.040 0.031
− 0.009
− 5
1 6
West of 17 7
2 17
0.045
b
0.022 −
0.023 −
5 0.070
− 0.041
− 139
0.111 −
188 19
− 49
0.029 −
0.115 West of 19
175 0.144
177 2
21 0.085
0.082 −
0.004 −
5 41
46 0.192
b
0.036 −
0.155 −
5 19
24 West of 21
− 0.177
41 0.216
0.038 West of 22
1 42
0.041 −
0.012 41
0.054
b
69 22
28
a
Many observations were taken about 5 m away from the fixed survey stakes. These are denoted with a prefix indicating the direction of offset, i.e. ‘South of 1’.
b
Field notes recorded the comment ‘nil’ when wind was not perceptible.
Fig. 14. Surface speeds correlation of simulation with observations.
Fig. 15. Surface flow direction correlation of simulation with observations.
6. Discussion
