The flow in an aquaculture pond may be forced by aerators, wind, water exchange, and natural convection solar. Of these, only aerators were considered,
as the whole purpose of the present research has been to evaluate the effect of these machines. Aerators are intended to supply dissolved oxygen and strip carbon
dioxide, but they also impart momentum as required to circulate and turning over the water column. The present research has focussed on understanding the thrust
effect of paddlewheel and propeller-aspirator aerators. Our approach was to impose the propulsive thrust of each machine as a body force, uniform within the small
parcel of water swept by blades. The body force is applied in Eq. 2 with the f
b
term. Stern et al. 1991 used a similar approach to model the propeller of a ship. Airborne droplets, waves and submerged bubbles produced by aerators are not
detailed in our model, since the total momentum of these effects is lumped in the specification of propulsive thrust ascribed to each individual aeration machine.
The discretised forms of the governing equations were solved using the finite element method as implemented in FIDAP FDI, 1993, 1995. RANS and k – ep-
silon equations must be linearized each iteration, based upon successive estimates of field variables u, 6, w, p, k, o. Gaussian elimination would simply invert the global
equation system at each step, but this was not possible due to the enormous size of our problem. We adopted the segregated-iterative solver reviewed by Haroutunian
et al. 1993 because it was the only feasible approach to handling large CFD problems. In this approach, the equations for each field variable are solved
sequentially in an outer iteration, and an iterative method is used to solve the set of linearized equations as they appear at each sub-step. The process could be
repeated endlessly, but should be programmed to conclude when certain conver- gence criteria are satisfied, or stopped if the exercise is found to be futile.
3. Methods
The simulation of pond hydrodynamics involves a number of steps. First the geometry of the pond and layout of aerators must be specified and represented by
a mesh of finite elements. Then governing equations and boundary conditions must be specified. Finally the system of equations must be numerically solved and then
results processed to yield useful information.
Peterson 1999a developed AUTOPOND as an application shell which drives FIDAP to simulate pond dynamic processes. The objective was to simulate the
turbulent flow field caused by aerators and post-process the results to calculate zones of erosion and sedimentation. Given particle size and density, the simulation
system is then capable of using the computed flow field in an advection – diffusion analysis of suspended sediment transport. The AUTOPOND program works by
creating a sequence of command scripts which cause the constituent modules of FIDAP to simulate pond dynamic processes. Separate command scripts are pro-
duced to control the mesh generation, pre-processing, solving, and post-processing of each pond model.
The AUTOPOND methodology provides a concentration of computational mesh around jets emanating from different types of aerators, and three-dimensionally
transitions these into a sparse mesh filling the vast majority of the pond bathyme- try. This is a crucial innovation. The high accelerations and steep gradients in the
near-field around an aerator necessitate a fine-scaled mesh as small as 1 cm
3
. One-hectare of pond averaging 1 m deep has a volume of 10
10
cm
3
. Since computation cost increases faster than the square of the number of elements,
non-transitional meshing would create unmanageable matrices. Transitional mesh- ing brings the number of computational elements in the pond problem down to a
fraction of 10
6
. By exploiting the segregated solver provided with FIDAP the pond problem may be simulated in 64 bit precision within one gigabyte of random access
memory RAM.
3
.
1
. Pond modelling data structure Given bathymetric survey data and the aerator deployment specification for a
particular pond, AUTOPOND will generate a governing command script and a series of FIDAP command files which contain all of the instructions necessary to
sequentially build a CFD model of an aerated pond. Table 1 outlines the default values of AUTOPOND parameters. Results also depend upon the specification of
pond geometry and aerator deployment.
3
.
1
.
1
. Pond geometry Pond geometry is specified with the Cartesian coordinates x, y, z of the bottom
and banks. At least six survey data files are required to describe pond boundaries for example surface, bottom, north, east, south, and west. Additional bank-seg-
ments may be used to describe a convoluted shoreline in piece-wise fashion. We then apply a linear regression analysis to the bottom and each bank. The result is
an array of best fit equations in the form of expression 3.
z = C
1
+ xC
2
+ yC
3
3 The standard estimate of error is used to report the goodness of fit m height
with Eq. 4. SEE =
z−fx,yn−2 4
AUTOPOND reports on the bathymetric analysis, and then determines lines of intersection between adjoining bank-segments and the bottom. These lines defini-
tively bound the model.
3
.
1
.
2
. Aerator deployment Any number of aerators may be simulated in a pond. The aerator deployment file
specifies macro names. Suitable choices are the macros ‘aero2’ and ‘paddle4’. The performance parameters of aero
2
and paddle
4
are detailed in Table 2. Macros are functionalized on the basis of specification variables for each aerator in the pond.
The coordinate variables x and y m specify the point where the aero2 shaft enters the water, while they represent the central gearbox of the four-rotor paddlewheel.
The variable orientation is the horizontal angle of aerator jet. The variable plunge specifies the downward angle degrees of an aero2 and the depth m of scooping
of a paddlewheel.
3
.
2
. Discretisation of the problem The problem must be properly meshed to obtain a meaningful solution. This was
achieved by investing most computational resources within the jets produced by an aerator. A scheme was developed to gradually transition the mesh into the
Table 1 Default values of parameters defined in meshrule and property files
Value Description
Parameter meshrule
MESHSPACING 2.0
m per element Elements per corner
8 CORNEREDGE
MINMESHSPACING 0.5
m per element 18
THRESHOLD m aerator’s radius of influence
Fraction of bank end length to remain unsplit 0.15
MARGINS 8
PLAYERS Pond layers water column
24 ALAYERS
Aerator layers orbiting macro 6
SLAYERS Streamwise layers at outlet of propeller
Lengthwise layers alongside of jets LLAYERS
18 Bank layers paver guidance at boundary
2 BANKLAYERS
BANKFIRSTLENGTH m first layer out from bank
0.125 BANKSECONDLENGTH
m thickness of next layer 0.250
1.5 m further layers
BANKGROWTH 0.1
HYPOLIMLENGTH m lower water column thickness
property °C
WATERTEMP 30.0
ppt 35.0
SALINITY DENSITY
kgm
3
1024.0 DYNAVISC
0.0014 N sm
2
m
2
s MOLECDIFF
1.0E−09 BANKROUGH
m 0.01
SEDROUGH 0.001
m SEDIMENT –SIZE
m 0.0001
SEDDENSITY kgm
3
1075.0 30.0
°C DRYBULB
WETBULB 25.0
°C 2.0
WINDSPEED ms
° 135.0
DIRECTION 0.1013E+06
BAROMETRIC Pa
Table 2 Default values for aero
2
and paddle
4
parameter file Parameter
Nominal value Description
paddle
4
aero
2
Number of propellers or wheels ROTORS
1 4
m, shaft length from water to propeller or spacing between 1.667
1.0 SHAFTL
paddle wheels m, outside diameter of propeller or paddlewheel blades
0.650 DIAMETER
0.140 m, inside diameter of propeller or paddlewheel blades
ANNULAR 0.040
0.350 m, axial length of propeller or width of paddlewheel blades
0.21 AXIAL
0.025 2.042
0.440 m, downstream displacement per revolution
PITCH Motor-to-propeller gear ratio
14.0 1.0
GEARING 4
4 Number of motor poles
MPOLES 50.0
50.0 Revolutions per second Hz
HZ –NOMINAL 1.9
kW, electrical power requirement
a
1.9 KWE –
NOMINAL 2.0
BHP – 2.0
hp, mechanical power requirement
a
NOMINAL 200.0
THRUST – Newtons of force
200.0 NOMINAL
rms velocitymean velocity 0.2
INTENSITY 0.2
0.0 EDDY –
0.0 m
SPECIFIED 1.58
SAE – 2.13
kg O
2
kW h oxygen transfer effect
a
NOMINAL
a
Variable not used by the present version of AUTOPOND.
surrounding water column. It was also necessary to control the element thickness along the banks and bottom to meet the requirements of the wall functions.
Furthermore, the strategy was developed to accommodate an arbitrary number and arrangement of aerators within a single pond of any geometric shape.
Hexahedron brick elements were used, each having front, back, left, right, top, and bottom faces. Fig. 1 illustrates a sectional profile through the depth of a pond,
schematically discretised with four layers of finite elements. The elements adjoining banks and bottom must be structured so that the first node within the fluid
continuum is situated within the logarithmic portion of the turbulent boundary layer. The height of these special wall elements must be adapted so that their
dimensionless thickness, y
+
= u · L
n
n is between 30 and 1000. Ferziger and Peric,
as well as FDI, warn that serious errors will result if the first computational node above the wall has a dimensionless thickness less than 30. The height of the finite
element measured normal to the wall surface is L
n
= y
+
· nu. The height of finite elements adjoining the pond bottom and levee banks were adapted at various
points within the pond system to meet these requirements. The dimensionless thickness needs to be greatest at the centre of a pond.
Fig. 2 shows the schematic approach to three-dimensional transitioning with brick elements in the vicinity of an aerator. The aerator’s rotor is represented by the
small zone of dense mesh in the centre of the illustration. Some number players of mesh layers surrounds the aerator, and then transitions in the local region of the
aerator. The small packet of fluid swept by the blades of the aerator is assumed to have a force of acceleration equal to the propulsive thrust divided by volume and
divided by density, represented by body force vectors. The aerator is orbited by a succession of finite elements enveloping the aerator alayers, like the layers of an
onion. The aerator is also dissected by slayers and llayers layers of finite elements in the streamwise and lateral directions.
Meshing variables are controlled in each run of AUTOPOND with the meshrule file detailed in Table 1. Parametric mesh generation ensures that the network of
Fig. 1. Diagrammatic section through pond mesh.
Fig. 2. Transition around aerator.
Fig. 3. Long section of meshing scheme for a paddlewheel aerator.
Fig. 4. Cross section of meshing scheme for a paddlewheel aerator.
mesh is coordinated so that the entire pond volume is filled with finite elements, without gaps or discontinuities.
Fig. 3 presents a long-section through the paddlewheel mesh. This is an applica- tion of the conceptual scheme of Fig. 2. Both illustrations indicate a concentration
of force in the region of water swept by rotors, but the latter provides for the gradual expansion of the jet at a ratio of 1:7 diagram not to scale, while the
transition at the inlet is abrupt. The arrows on Fig. 3 were drawn along mesh elements, but they are also thought to be similar to streamlines in the vicinity of the
paddlewheels. The paddles are repeated four times as illustrated in Fig. 4. The paddle
4
macro is detailed in Peterson 1999a. The standard propeller-aspirator design used in the wastewater and aquaculture
industries has a motor located above the water surface. A hollow shaft is directed at a plunge angle, f, into the water column to drive a cavitating propeller. The jet
impinges into the pond bottom, to diverge outwards with a wide spreading pattern. Figs. 5 and 6 illustrate the meshing scheme applied to propeller-aspirator aerators.
The macro aero
2
may be found in Peterson 1999a, having a name reminiscent of the Aire-O2™ by Aeration Industries.
Pa6ing provides a transitional layer of brick elements adjoining a surface of any shape, with any number of voids. Paving is evoked on the bottom of our pond
model, by going around each aerator macro block as illustrated in Fig. 7. Brick elements were then mapped upwards through the water column players times,
transitioning in conformance with banks.
Fig. 5. Long section of meshing scheme for a propeller-aspirator aerator.
Fig. 6. Plan of meshing scheme for a propeller-aspirator aerator.
Fig. 7. Paving around SW paddlewheel in Pond X.
4. Solution quality
