1. Introduction
This paper presents the results of computational fluid dynamics CFD simula- tions of the aerator driven circulation and sediment shear stress in an intensively
aerated shrimp growout pond. Such physical processes strongly affect the biological productivity of a pond. Understanding and controlling these processes may help to
mitigate some of the problems which plague the aquaculture industry: electrical power load; bank erosion; anoxic pond sediment conditions; wasteful feed-conver-
sion; and high water exchange rates.
CFD is the generic term for numerical schemes which account for the flow of mass and momentum throughout a fluid continuum. CFD has the advantage that
it does not generally require calibration, because it is derived from universal equations which govern fluid flow. To the authors’ knowledge, CFD has not been
applied in research on aquaculture ponds. The method has only recently been applied to wastewater treatment ponds.
Wood et al. 1995 simulated water exchange through wastewater oxidation ponds using a commercially available CFD code. They first attempted to model the
problem in two-dimensions for laminar flow, neglecting the effects of bottom friction. Wood et al. 1997 published results of simulations of three-dimensional
water exchange through an effluent retention pond, using the standard k – o turbu- lence model. This simulation was validated with observations of hydraulic retention
time in a real pond, using a tracer dye.
The present paper introduces a methodology to build CFD simulations of aerator driven aquaculture ponds and interprets the effect of these machines on the
banks and sediments. Methods and computer source code are detailed in the thesis by Peterson 1999a, which are referred to collectively as the automatic pond
simulation methodology, AUTOPOND. The methodology works with the fluid dynamics analysis package, FIDAP, to build computer simulations of aerated
ponds. The methodology is capable of simulating a wide variety of pond geometries and aerator specifications, given access to a high performance computer running
FIDAP. Details of FIDAP were published by FDI 1993, 1995.
Simulation results presented herein are interpreted in the context of the theory of Peterson 1999b, whereby water currents are assessed with regard to the underlying
shear stress exerted in the particular pond of interest. The magnitude of the bottom shear stress is related to the sediment condition, and the pond bottom is classified
into six zones on that basis. Results of simulations have been compared with the experimental data obtained by Peterson 2000 from an intensive shrimp aquacul-
ture pond.
2. Mathematical model
The pond model is based on a solution of the equations governing conservation of mass and momentum for a Newtonian, incompressible fluid. For laminar flows
these equations are exact. However, aerator driven flow is turbulent and it is not
feasible to resolve all the scales of motion operating in such an aerated pond. The practical approach is to consider only the time-averaged flow field. The product of
fluid density and the six time-averaged correlations of mutually orthogonal velocity- fluctuations
r · u
i
u
j
is viewed as a stress tensor, termed the Reynolds Stress. Eq. 1 is the incompressible continuity equation for the mean flow, written in vector notation, and simply states
that fluid mass is neither created nor destroyed.
9 · u = 0
1 Eq. 2 is a statement of momentum conservation for each component of the
time-averaged flow, and is commonly called the Reynolds averaged Navier – Stokes RANS equation. The term on the far right represents the driving force field, f
b
.
u · 9u = − 9pr + 9 · [n + n
t
9u] + f
b
2 Eqs. 1 and 2 give a total of four equations for four flow variables velocity
components and pressure, p. Solution of the RANS equation is not possible unless the magnitude of eddy viscosity, n
t
, can be quantified throughout the domain of the problem. The eddy viscosity is a variable relating the Reynolds stress to the
gradient of the time-averaged flow. Eddy viscosity is not a constant fluid property, but varies throughout the flow field. Our pond model makes use of the standard
k-epsilon turbulence model, whereby n
t
= 0.09k
2
o .
Ferziger and Peric 1996 as well as the ASCE’s Task Committee on Turbulence Models in Hydraulic Computations ASCE, 1989 reviewed the standard k – o model
of eddy viscosity. Isotropic turbulent kinetic energy, k, represents the energy of turbulence Jkg or m
2
s
2
, and o represents the dissipation rate of turbulent kinetic energy m
2
s
3
. The k – o model accounts for the generation, advection, diffusion, and destruction of k and o.
Solution of the conservation equations depends on the specification of boundary conditions. No-slip conditions were applied at solid boundaries of the pond, and
wall elements parameterized the effect of boundary layers Ferziger and Peric review the law of the wall. Our pond model invokes the special case of hydrauli-
cally rough walls, as implemented by FIDAP. Nikuradse roughness of 1 cm was applied at the banks of the pond, and the bottom roughness was taken to be 1 mm
and 100 mm in the peripheral and central portions of the pond, respectively. The surface was free to flow horizontally, but with a fixed elevation.
As an important digression, we explain how we may neglect the effect of waves. According to Wetzel 1983 the maximum wave height in a lake is estimated from
the fetch, Y, with wave height = 0.0105 m
12
× Y. Wetzel also indicated that
wavelength is typically 20 times wave height. Consequently, wavelengths on the order of 2 m are possible in a 1-ha pond experiencing high winds. Waves do not
affect the bottom if depth is greater than half the wavelength 1 m. It is conceded that waves are an important factor at the banks.
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
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