Influence of inlet and outlet placement on the hydrodynamics of culture tanks for Atlantic salmon

The salmon farming industry has recently shifted to larger culture tanks with greater water flows to optimize the land-based production, but tanks approaching 1000 m 3 in volume create challenging hydrodynamics. This paper presents a computational study of four combinations of inlet and outlet designs of a commercial landbased aquaculture tank. Windows-based OpenFOAM solvers are used to solve the conservation equations for tank hydrodynamics with an implicit unsteady second-order Eulerian (finite volume) technique on unstructured hybrid meshes. The model is validated by the velocity measurements at discrete locations in the tank using acoustic doppler velocimetry. To understand the dispersion of biosolids in the tank, 500 particles with a uniform size of 200 μm are tracked in the Lagrangian frame. While the tank’s Reynolds number varies between 2E6 3.5E6 depending on the flow exchange rate, the local Reynolds number at the inlet pipe is about 2E5 which discovers the drag-crisis phenomenon. The effect of inlet and outlet placement on the velocity, vorticity and turbulence is addressed. The existing tank design could be improved using the bottom-drain and corner-inlet options, which strengthens rotational flow with better uniformity. Such design change is also proved to provide better particle removal and thus ensure the improved self-cleaning ability of the tank.


Nomenclature
A area (m 2 ) C 1 , C 1 , C 2 , C 3 , C model constants of Realizable k -model C d drag coefficient C f skin-friction coefficient d particle diameter (m) D mean diameter of the tank (m)  stretching tensor f p force exerted on particle (N) g acceleration due to gravity (m/s 2 ) h water column height in the tank (m) I identity matrix T i turbulence intensity k turbulent kinetic energy (m 2 /s 2 ) m particle mass (kg) p pressure (pa) G k , G b production terms of TKE R tank radius (m) Re reynolds number R h hydraulic radius of the tank (m) S ij deformation tensor S k , S user-defined source terms of k and St stokes number t time (s) t e eddy life time (s) t int particle-eddy interaction time (s) t p particle relaxation time (s) t tr transit time of the particle through the eddy (s) v velocity (m/s) ̄ and v ′ mean and fluctuating velocity components ϑ particle volume (m 3 ) v 0 inlet nozzle velocity (m/s) v p particle velocity (m/s) x p particle displacement (m) y + non-dimensional wall distance Greek symbols flow uniformity index Γ vortex strength (J) kronecker Delta dissipation rate of turbulent kinetic energy (m 2 /s 3  In practice, each plug of flow injected into a large culture tank has its own residence time, which depends on inflow and outflow momentum, flow turbulence, and internal design of the tank including the placement of inlet and outlet structures. The result is a non-uniform flow domain including low-momentum zones in the tank. Considerable effect of inlet and outlet characteristics on the global flowfield has been found in many bioresource systems such as bioreactors [35] , biofilters [8] , and flow columns [1] . However, the existing literature in aquaculture research fails to address the effect of such design parameters on the tank hydrodynamics, let alone improve them.
The rotational velocity in a culture tank, which implicitly depends on inlet flowrate and hence the impulse force plays an important role in creating a healthy rearing environment [14,26,42,44] . Flow pattern and turbulence in the tank are primarily influenced by the inlet and outlet characteristics [25,27,28,34,39] . Other than these authors, different inlet and outlet configurations in RAS tanks have been used in past studies but most of it has been ad-hoc research. In the development of an integrated recirculating aquaculture and olericulture plant, McMurtry et al. [36] used a free-fall inflow model, and the water was drawn by means of a pump from the bottom of the tank using a pipe. In a recirculation system for oyster larval culture, Qiu et al. [45] used a suspended inlet and central elevated outlet. However, a tangential inlet flow and central bottom drain have been the most common flow boundaries in several studies [46,49,50] . The physiological studies of Davidson et al. [16] and Good et al. [22] deployed circular RAS tanks with tangential inlet and Cornell type dual-drain system. Indeed, the combination of a central bottom outlet and an elevated wall drain is often used in circular RAS tanks to achieve a controlled flow pattern. However, the location of the inlet and outlet structures affect the hydrodynamics of large culture tanks.
An empirical investigation on the water velocities in large circular and octagonal RAS tanks with tangential inlet nozzles was performed by Gorle et al. [26] . The authors found that circular tanks, which had a central bottom outlet, experienced approximately 50% lesser variation in water velocity at the centre, compared to octagonal tanks that had a central top outlet. Also, both tanks appeared to have different velocity profiles across the tank. The octagonal tanks used in the fish performance studies of Espmark et al. [19] had the inlet pipe near the corner wall. Such design aspects of flow boundaries considerably influence the overall hydrodynamics of the tank, which cannot be ignored when trying to improve the environmental conditions for the fish.
The usual placement of the inlet pipes in land-based RAS facilities is near the tank's periphery to ensure that a stronger rotational flow occurs, but this will, in turn, cause a flow resistance due to the structural obstruction in the highest velocity region. The net drag force on the inlet pipe is the sum of friction drag and form drag. Form drag, characterised by vortex shedding and flow separation, is a dominant component in such bluff bodies like a circular cylinder at high Reynold numbers. In RAS culture tanks, the mean hydraulic retention time of 30 -55 min. is the preferred water exchange rate for sufficient water quality for the fish. The rotational flow past the inlet pipes at these operating conditions results in a Reynolds number of approximately 2E5. At this critical Reynolds number, the drag force on a smooth cylinder abruptly drops. The present explanatory analysis of the inlet pipe location excludes the physics of the 'drag-crisis phenomenon', as named by Schlichting [47] . Out of numerous flow control techniques, 'blowing' is an active method where the flow separation zone on the leeward side of the cylinder is reenergized by streaming a jet through an orifice. The bluff body hydrodynamics associated with the flow past an inlet pipe is characterized by a low-pressure wake region on the rear side of the cylinder. The pressure drag is a dominant component, which can be reduced up to 65% by modifying the geometry of base flow [3,7] . 'Jet blowing' has been widely studied in different applications to energize the recirculation zone [31,56] , and thus reduce the drag force of the body. Representation of these dynamic features around the inlet pipe and the effect of its location was not made by previous studies in the case of culture tanks.
A circular flow pattern with dominant tangential velocity in circular or octagonal culture tanks translates the linear water inflow into a rotating vortex flow [39,40] . One of the most critical features of a central outlet in a confined flow domain is the evolution of locally organized coherent structures at a wide range of length scales [27,28] , which dominate the turbulence transport mechanisms like skin friction, mixing, etc. The experimental observations of such phenomena involve huge costs and efforts and often deliver uncertain outcomes [37] . On the other hand, a simulation-driven development provides a less-costly vir- tual environment to understand physics and improve the design, thanks to high-performance computing. In this study, an octagonal shaped commercial RAS tank of 788 m 3 size was investigated using turbulence modelling. In addition to the Base design, three design variants in terms of inlet and outlet locations are considered in this study to examine the qualitative and quantitative parameters of Atlantic post-smolt tank hydrodynamics. The novelty of the study is that the flow physics behind the rotating turbulent flow associated with the culture tanks is explored. The combined vortical-streamlined-vectorial representation explains the flowfield structure near different outlets. Better inlet placement in the tank is studied based on the force estimates. This research also quantifies the effect of inlet/outlet locations on the field variables including flow velocity, uniformity, circulation, and the motion of the biosolids in the tank. In the long-term, such studies can improve RAS energy, bioresource use, and fish performance, health, and welfare in aquaculture.

Designs under study
Optimization of large flow domains, such as culture tanks of close to 1000 m 3 in volume, is not straight forward because the optimal solutions, as functions of design and operating conditions, cannot be found by simple numerical programming. An exhaustive search for a perfectly optimized tank design over a full set of continuous variables involves rigorous computational effort and thus offers an impractical method. A comparative study between a few selected solutions is instead a more effective and time-saving method. Our earlier research on an octagonal RAS tank of 788 m 3 size investigated the effect of the inlet nozzle angle on the tank's performance [28] . While the same design was taken as reference i.e base design , this study considered three additional combinations of inlet-outlet locations as presented in Fig. 1 .
• Base design ( Fig. 1 a), which is currently in operation at a Norwegian smolt producer, has two inlet pipes near the sidewalls. Each inlet pipe has 11 nozzles that discharge the water into the tank parallel to the sidewalls so that a clockwise flow pattern develops when viewed from the top. The tank has an elevated outlet at the centre, which collects the water near the floor of the tank through four vertical pipes around it. The effective inlet and outlet surface areas are 0.0226 m 2 and 2.95 m 2 , respectively. • Redesign 1 ( Fig. 1 b) has the same outlet as the Base design but the inlet pipes were moved close to the near the corner walls. The distance from the corner wall to the pipe's centre is 1.49 m and that to the tank's centre is 8.2 m. Thus, the redesign follows the inlet pipe location at 1/5th of radial distance from the corner wall in NCRA's RAS tank in Norway [19,55] . The nozzle configuration on the pipes and inflow direction are the same as the Base design. • Redesign 2 ( Fig. 1 c) has the inlet pipes near the sidewalls, as in Base design, but here the complex central elevated outlet was replaced by a simple bottom drain, as used by Summerfelt et al. [52] and Davidson and Summerfelt [14] . The outlet consists of 47 exit nozzles of 15 mm diameter each, surrounded by two radially patterned rectangular slots. The effective outlet surface area was reduced from 2.95 m 2 in the elevated drain to one-fourth in the bottom drain. • Redesign 3 ( Fig. 1 d) has the inlet pipes near the corner walls and a central bottom drain.
The aforementioned tank designs were tested for practical flow conditions, as obtained from the commercial salmon site, using the computational fluid dynamics. This research considered the tanks with no biomass and hence the analysis of biosolids was not in the scope of the study. Through flow blockage, the fish response to velocity and vorticity increases the overall turbulence. However, the relative comparison between the tank designs can be equally valid for the tanks with biomass.

CFD modelling
A cost-effective computational framework was developed for the high-fidelity CFD simulations. The tank geometries were developed using CATIA V5 R21 (Dassault Systèmes, Vélizy-Villacoublay, France). The fluid domain was extracted in the STEP format to effectively transfer the CAD metadata structures for robust interoperability between different software platforms. 3D-Tool V12 (3D-Tool GmbH & Co. KG, Weinheim, Germany) was used to translate the STEP file into a Parasolid format to make it compatible with the meshing tool. An automated meshing tool, Castnet (DHCAE Tools GmbH, Krefeld, Germany), was employed for finite volume-based domain discretization. After a thorough checked for different quality parameters, the mesh was imported into the CFD tool, BlueCFD (BlueCAPE, Casais da Serra, Portugal), which offers Windows version of OpenFOAM solvers along with a graphical interface, called RunGui. The results of coupled Eulerian-Lagrangian simulations for the hydrodynamics and particle dispersion in the culture tank were then post-processed in Paraview 5 (Kitware, New York, USA) and Matlab R17 (MathWorks, Natick, Massachusetts, USA). The details of model equations and problem setup are presented in this section.

Continuous phase
The modelling of the flow domain in the RAS tank was performed in a three-dimensional unsteady incompressible framework with the RANSbased turbulence model. The mass and momentum conservation equations are where v is the velocity field, , p and represent the density, pressure and kinetic viscosity of the fluid, respectively. Using the Reynolds decomposition of instantaneous velocity v into average ( ̄ ) and fluctuating ( v ′ ) components, the Eq. (2) becomes where ( = ) is the Reynolds stress term. The closure approximation in RANS modelling to eliminate fluctuating velocity v ′ yields is the turbulent kinetic energy, I is the identity matrix, t is the eddy viscosity and  is the averaged stretching tensor, defined by 1 2 ( grad ̄ + grad ̄ ) . Using the hypotheses of gradient diffusion and eddy viscosity, the momentum equation becomes Although numerous models exist to solve the transport equations for k and relevant scalar variables, each has some advantages and limitations depending on the application. For industrial cases, the twoequation models that solve the equations for k and its dissipation rate are more popular due to their robustness, computational feasibility, and reasonable accuracy. In this study, the realizable k − model is used which enforces the realizability on the formulation of by relating the model constant to the strain tensor. The model respects the binding constraints of Reynolds stresses and realizes the physics of turbulent flows. This is more significant in accurately modelling the flow features such as rotations and vortices; the critical aspects of culture tank hydrodynamics. The conservation equations for k and its dissipation rate therefore become is computed same as in other k − models, the difference arises from the calculation of C . While the Standard and RNG models assume C to be constant, the realizable model defines it as where Ω = Ω − 3 . The inclusion of mean rate-of-rotation tensor Ω along with strain rates, angular velocity and the turbulence parameters k and ,in the definition of C and hence in the computation of t makes the realizable k − model more superior than the standard and RNG models in predicting the spreading of round jets from the inlet nozzles of a culture tank. In addition, the transport equation for considers the transport of the mean-square vorticity fluctuation, which made the model the means of turbulence modelling in the current study.

Dispersed phase
The motion of the biosolids in the rearing domain is explored by means of Lagrangian particle tracking method. Uneaten feed pellets and faecal matter are the usual contributors of suspended solids in the culture tanks. The particle dispersion in Lagrangian frame is computed from the Eulerian flow field, and the particle motion is governed by where f p is the force experienced by the particle of diameter d , mass m when it has a velocity v p at position x p and time t . The presence of the any particulate matter in the culture tanks is critical to water quality and hence the fish growth. However, the volume ratios of the biosolids in the tanks are very small. For instance, Davidson et al. [13] shows that the total suspended solids (TSS) in culture tanks can range from 2.8 ± 0.2 ppm to 18.2 ± 5.9 ppm depending on the water exchange rate and the use of flow-flow ozonation. Also, [26] reported the TSS accumulation in different Norwegian commercial smolt tanks, ranging from 2.1 ± 0.5 to 12.1 ± 4.0 ppm in various tanks at the time of sampling. In such dilute suspensions, the particle-particle interaction and the effect of particle motion on the flow and turbulence are negligible [18] . The influence of fluid motion on the particles can be characterised by the Stokes number according to where p and d are the density and diameter of the particles, v is the flow, is the dynamic viscosity of the fluid and L is the characteristic length, which is the mean diameter of the tank in the present case. While the size of particles in culture tanks ranges from nano to millimetres, this study considered 200 μm uniformly sized rigid spherical particles. These specifications correspond to St < < 1 which represents the interaction between the flow and particles is one-way, i.e., from the former to the latter [10,21] . Although the consideration of lift terms on the particles of different sizes in turbulent flows has long been a topic of debate [33,58] , numerous studies on Lagrangian particle tracking ignored the lift terms when the particle diameter is sufficiently small (for instance, [4,56] ). Ignoring the pressure and added mass forces along with the Basset history term for the sake of simplicity for a relative comparison between the tank designs, the dominant forces on the particle are drag f d , buoyancy and gravitational force f g i.e., . The particles were assumed to have the drag components due to sphere drag and gravity. Therefore, the particle drag becomes where ( = | − v | ) is the particle Reynolds number, p is the particle density, v is the flow velocity and g ( = 9.81 m/s 2 ) is the gravitational acceleration, respectively. Assuming the constant mechanical properties, the particle drag coefficient C d is defined by The particle trajectory is computed within the turbulent field using the random-walk algorithm [5] where the particle position is updated at every time-step using the eddy-interaction model. Denoting the particle variables which are derived from the interpolation of Eulerian field at adjacent cells by the subscript p + , the effect of eddies on the particle's velocity is considered by adding the local fluctuating velocity component v ′ + . Therefore, the effective particle velocity becomes ṽ + = v + + v ′ + . The fluctuating velocity component is calculated from where is a random number generated from Gaussian probability distribution with null mean and unit variance, and √ 2 3 is the local RMS flow velocity fluctuations. A DNS correction factor is used in the stochastic model to counter the presumed isotropic turbulence within the boundary layer region. The transit time of the particle to travel through the eddy ( t tr ) and the eddy life time ( t e ) are determined from Here, ( = 4 3 | − v | ) is the particle relaxation time to respond to the changes in the local flow. The particle-eddy interaction time is calculated from t int = min ( t tr , t e ). Then, the particle's position and velocity at the n th Lagrangian time step are computed from

Domain discretization
The undesired entities such as slivers, small faces and open edges were removed, and the geometry was simplified using the built-in utilities of the meshing tool. Several meshes were created by changing the global cell size to evaluate mesh dependency. Several mesh quality parameters were thoroughly checked for each mesh using the builtin mesh-check utility. The convergence criterion of 1E-5 was set for the relative error in the computation of velocity magnitude. A series of mesh convergence tests on the Base design of the tank was conducted by refining the global cell size. Fig. 2 shows the mesh dependency results of the Base design for the average planar velocity at three heights of the water column where the empirical measurements were taken. The final mesh on the Base design had 797,819 unstructured finite volumes and any further size refinement produced an error smaller than 0.2% relative to the last refined mesh. This hybrid mesh containing the tetrahedral cells on solid boundaries and hexahedral cells in the core, as shown in Fig. 3 (a) and 3 (b) respectively, offers the advantage of negotiating the complex geometrical features with high-quality cell distribution at the reasonable computational effort. Four inflation layers with a height ratio of 1.15 were used to capture the velocity gradients in the near-wall region. The resulting the non-dimensional wall distance y + was above 30, and standard wall functions were used to compute the near-wall effects [43] . Although highly skewed cells don't hamper to solution stability, these, however, reduce the order of face integration. The final mesh had the cell skewness below 0.5. Over 95% of the cells had the dihedral angle between 70°and 120°, and 98% of the domain had the cell aspect ratio below 5 which ensured adequate mesh quality. For more details on the mesh topology and grid dependency results, please refer to our previous publication [28] . Similar topological settings were used to produce the meshes for the redesigns 1, 2 and 3 which created the final grids with the cell-counts of 796,226, 779,812 and 779,991, respectively. These surface mesh visuals are presented in Fig. 3 (c-e).

Boundary conditions and problem setup
The nozzles on the inlet pipes were assigned 'mass flow' boundary conditions, and the tank's outlet acted as 'outflow' boundary. All solid surfaces of the tank were defined as 'no-slip' smooth static walls which take zero-gradient condition for k , and p . Free-surface deformation in the tank is negligible due to the continuous replenishment of water into the tank with the same flowrates through the inlet and outlet boundaries [28] . Assuming a turbulence intensity T i of 5%, the initial k and were calculated from = 1 . 5 ( ̄ ) 2 and = c k 2 /5 . Time-dependant segregated viscous solver with second-order Gaussian linear discretisation for both convective and diffusive terms was used in the simulations. The pressure-velocity equations were coupled using SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm. While the pressure equation was solved with GAMG (geometric agglomerated algebraic multigrid) formulation, all other field equations were solved using Gauss-Seidel based smoothSolver. A constant time-step of 0.01 s was used with 30 inner-iterations. Simulations were run in parallel mode on a 28-core Intel Xeon E5 -2683v3 2.00 GHz computer.

CFD model validation
The CFD model of the Base design for validation was developed for an inflow of 292 kg/s. The Reynolds number is calculated from where the hydraulic radius ℎ ( = ℎ +2 ℎ ) is a function of tank's equivalent radius R ( = 8.15 m) and h is the height of water column ( = 3.9 m). Therefore, a mean retention time of 45 min, in this case, corresponds to Re of 2.3E6. The velocity measurements were taken at predefined locations in the salmon culture tank when operated without fish. A Nortek high-resolution acoustic Doppler profiler, Vector , was used for the measurements at 45 discrete locations in the tank across three heights, i.e., 17% and 43% and 68% of the water column. The validation of the CFD model using the velocity measurements in Fig. 4 shows that the simulation results largely fall within the standard deviation bars of the ADV findings. The latest developments of transducers have reduced the  blanking distance of modern ADV instruments to as low as 5 cm. However, the effect of flow disturbances, both due to the domain turbulence and the instrument inducement, on the performance of these transducers challenge the measurement accuracy [17] . Also, the Doppler noise is likely to influence the peak velocities recorded by the ADV module. Despite that low-quality data was removed by the signal filtering process, the signal aliasing was expected to combine with the Doppler noise and velocity fluctuations, which possibly influence the ADV measurements in the turbulent flows in a RAS tank. A correlation coefficient above 90% and signal-to-noise ratio of more than 15 dB was achieved with a sampling frequency of 25 Hz. The resulting coefficient of variation is approximately 7% and the average difference between the ADV and CFD results is 9%. This, along with our previous research [25][26][27] , highlights that ADV and CFD methods complement each other more than validate one another. For more details on the measurement setup, and the validation of velocity trends and flow angles across the tank, please refer to Gorle et al. [28] .

Flow field around the inlet pipe
Previous studies have determined that the rotational velocity at the perimeter of circular tanks is strongly dependant upon the impulse force of water flow injected tangentially into the circular-type tank. Thus, the rotational velocity depends upon the hydraulic exchange rate and inlet nozzle velocity and the direction produced at the flow inlet structures. Fundamentally, the inlet pipe in the culture tank conditions for the problem of flow around a circular cylinder, which is one of the standard cases of fluid mechanics. In octagonal tanks, the flow near the corner walls turns into itself to negotiate its path with the tank walls. Therefore, the inlet pipes in the tank redesigns 1 and 3 experience a manoeuvring flow, represented by curvilinear streamlines in Fig. 5 (b). This has a significant effect on the locations of stagnation points, pressure distribution and wake formation, compared to the case of straight flow over the inlet pipes, i.e., the pipes near the sidewalls as in the Base design and Redesign 2. As a result, the pressure distribution on the pipe (partially shown in Fig. 5 ) is significantly different in both cases of inlet pipe location.
The distance of the tank's centre from the corner wall is 13% more than that from the sidewall, which causes the streamlines to spread more along the diagonals of the tank than along the x-or y -axis in a circular patterned flow. This means that the inlet pipe near the corner wall is exposed to a lower flow velocity (~15% lesser velocity) than those at the sidewalls. Using the empirical relationship between the drag force and Reynolds number, formulated by Cheng [9] , the drag coefficient C d of the inlet pipe with no jet from nozzles was found to be 1.206, which is consistent with the classical drag curve of a smooth cylinder [57] . With the jet blown at much higher velocities than base flow, Fre- und and Mungal [20] achieved zero drag on the body of interest. In the present study, the inlet velocity for mean hydraulic retention time (HRT) in the tank of 40 min is 2.69 m/s, which is approximately 4 times larger than the mean rotational velocity when the inlet pipe is placed near the sidewall. As depicted in Fig. 5 (a), the low-pressure wake region was replaced by a pressure recovery region, represented by the accelerated flow on the rear side of the pipe. Thus, the nozzle injection has greatly cancelled the drag force of the pipe by more than 99%. The nozzle flow from the inlet pipe near the corner wall is however not aligned with the base streamlines, resulting in an offset between the wake zone and peak velocity stream, as shown in Fig. 5 (b). Hendrick and Degrez [30] highlighted the significant effect of jet location on the flow-induced forces. Consistent with this, a relatively weak suppression of the low-pressure region downstream of the pipe is observed. However, the low-velocity flow near the corner wall keeps the drag force of the pipe lesser than when placed near the sidewalls by 29% which makes it a better placement in terms of average velocity and hence energy use. Another advantage of corner wall positioning of the inlet pipe is that the low-velocity region gains additional momentum due to the structural obstruction as well as inlet flow, and hence increases the flow uniformity in the tank.
The effect of outlet location is associated with keeping or removing the complex central outlet system, which is present in the Base design and Redesign 2. With such a draining system, the flow has to travel more distance from inlet to outlet. In addition, the rotational flow around the central vertical pipes creates additional drag, compared to redesigns 1 and 3. The comparison between the designs for the skin-friction coefficient, which is defined as C f = τ 0 . 5 2 with w being wall-shear stress, is shown in Fig. 6 . With an elevated outlet, the inlet pipe near the corner wall (Redesign 1) experiences 10% lesser C f than that near the sidewall (Base design), whereas this difference between the redesigns 2 and 3 becomes 20%. The reason for lesser C f with Redesign 1 compared to the Base design is that the flow in the former has low energy loss to the walls from the base flow, which is also true for Redesign 3 compared to Redesign 2. Over 30% less C f is observed with the replacement of complex central-top outlet by conventional bottom outlet. The Reynolds effect on the overall drag force is demonstrated by a slight but steady increase in C f with HRT.

Flowfield near the outlet
Ideal axisymmetric vortices, governed by Burger's equation, are based on the assumption that the effects of axisymmetric straining and viscosity diffusion are balanced. This is not true in real flows, and therefore the cylindrical vortices are not perfectly axisymmetric. Detailed characterization of vorticity is imperative as it affects the global velocity field of the tank [27] . Fig. 7 shows the cut-away view of the vortex column prevailing at the centre in the selected tank designs. The resultant circular flow pattern is the combination of streamlines across the plane ?? = constant, a large-scale cylindrical vortex around the outlet, and the rotational flow, represented by vectors. Here, the isovortex surface was quantified by Q -criterion, which is defined by the positive second invariant of velocity curl ( ∇ x v ), Mathematically, Q = | Ω ij | 2 − | S ij | 2 , where Ω and S are the rotational and deformation components of velocity gradient respectively [24] . The size of the vortex column with conventional bottom outlet, as in redesigns 2 and 3, is approximately 22% lesser than the central top outlet due to the space occupied by the pipes in the tank's centre (Base design and Redesign 1).

Large-scale and small-scale turbulent structures
The evolution of turbulent structures at different length scales influences the global flowfield through vortex-vortex interaction, for example. The fine-scale coherent structures likely affect the dynamics of large-scale turbulence [11,48] , which in turn affect the dispersion of particles in the wall-bounded flows [6] . Therefore, it is necessary to characterize the turbulent structures in the different designs of the culture tank. In this study, the small-scale turbulence was identified by coherent vortical structures, using Q -criterion while the turbulent kinetic energy defined by = 0 . 5 ′ ′ with ′ being the fluctuating velocity component, was used to define the large-scale turbulent structures. As seen from Fig. 8 , the intensity of the time-averaged vorticity increases with the hydraulic exchange rate. The vortex ring in mid-radius location, by receiving the turbulent energy from the base flow, seems to be moving faster and contributes to the motion of the vortex core. The size of the vortex ring is approximately 12% lesser in the designs with inlet pipe near the corner walls, compared to that near the sidewalls.   9 shows the time-averaged distribution of turbulent kinetic energy (TKE) in the tank designs. On a general note, the TKE is not uniformly distributed throughout the domain. Mixing of inflow with the rotating flow in the tank creates the most intense turbulence, but further from this mixing region, the turbulence decays as the water spreads in the tank. Turbulence levels near the outlet are reasonably high due to the locally strained flow. Denser turbulent kinetic energy contours in the Base design, and redesigns 1 and 2, particularly at higher flow exchange rates, reveal the higher flow viscidity in the core of the tank. In particular, the higher TKE distribution in Base design explains that the flow pattern is more disorder and random, which is relatively negligible in redesigns 2 and 3. It can be concluded that the inlet pipes near the sidewalls and central top outlet configurations are more detrimental in terms of the flow uniformity and energy loss. The viscous effects in the conservation equations become dominant when the length scale of an eddy is adequately small. The turbulent kinetic energy is then quickly dissipated and therefore the nonuniformity of the flow vanishes. Thus, the dissipation rate of turbulent kinetic energy is a crucial parameter, which is governed by the dynamics of small-scale eddies. Fig. 10 compares the designs in terms of the time-averaged planar distribution of near the floor and water surface. Concentrated profiles of at the water surface in Base design and Redesign 1 explains higher turbulent diffusivity and hence better micromixing of the flow. On the other hand, the height-wise variation of in Redesign 2 is relatively negligible. The lowest amounts of TKE in Redesign 3 lead to low turbulent mixing and therefore low diffusion rate.

Performance metrics
The selected designs were further contrasted for three performance metrics; normalized rotational velocity ( v / v 0 ), flow uniformity index ( ) and vorticity strength ( Γ/ Dv 0 ), where v 0 is the inlet nozzle velocity. These hydrodynamic indicators were evaluated at four inflow conditions of 328, 292, 263 and 239 kg/s, representing the mean hydraulic   Fig. 11 , this classification was reflected in the velocity distribution in the tanks, and the placement of inlet pipes seems relatively inconsequential in this regard. The flow passages at the bottom and top of the outlet structure (i.e. 60% and 40%, respectively) in the Base case and Redesign 1 causes local accelerated regions, which leads to the peaks in the velocity profiles in Fig. 11 (a) and 11 (b). The confined flow geometry causes to spread the lower peak, i.e., at the bottom of the vertical outlet structure and negotiate with the adjacent velocity distributions, which resulted in a smooth velocity profile. The anomalous behaviour of the free-surface, however, limits this scenario for the flow through the casing channels, resulting in a near comparatively sharper velocity peaks. Replacing the complex centraltop outlet system simply by holes on the floor at the tank's centre have  drastically changed the velocity trends, as depicted in Fig. 11 (c) and 11 (d). Except near the floor and water surface where stronger flow gradients exist, the velocity is more uniform across the tank height with the central bottom outlet. The increase in the velocity magnitude with decreasing HRT is linear with the bottom-outlet, which is not true with top-outlet. The trend of velocity change with the water exchange rate is hard to quantify due to the nonlinear nature of the velocity distribution in the case of the central-top outlet.
One of the objectives in the culture tank development is to achieve the maximum possible flow uniformity across the tank, which would result in more consistent water velocities for the fish. Because of nonuniformity associated with the vortices in the form of velocity gradients, the overall flow uniformity is affected by the increasing vortex intensity and turbulence, which is common in most fluidic systems (for example, [38,41] ). The index was used in this study to quantify the flow uniformity in the tank. Mathematically, it is defined by where n is the number of computational cells in the section of area A, v i is the velocity in the cell, whose area is A i and v is the area-weighted mean planar velocity. The index is computed across the horizontal plane at every 10% height and interpolated to construct the flow uniformity profile for the entire height of the water column. The comparison between the Base design and the redesigns in Fig. 12 where is the vorticity magnitude and D is the characteristic length. The convective and viscous terms in the momentum transport equation depend on the Reynolds number. Therefore, the vortex strength that dominates the mean flow varied with the inflow rate of the tank. As observed from Fig. 13 , a gradual decrease in the vortex strength with increasing hydraulic retention time is observed with Base design and Redesign 1, whereas this drop is fairly constant in redesigns 2 and 3. This implies that the central bottom drain gives a more predictive performance than the central elevated drain, as vorticity distribution is concerned. Looking at the height-wise variation in the vortex strength, the central elevated drain yet again displays a highly non-linear distribution. The two peaks of the profiles in Fig. 13 (a) and 13 (b) represent increased vortex strength because of flow through four vertical pipes at 5 cm from tank's floor and 40% of the total flow through the openings of outlet casing near the water surface. In contrast, the vortex strength is more linearly distributed across the tank height in redesigns 2 and 3 ( Figs. 13 c and 13 d). The location of the outlet surface grossly determines the vortex strength of the water surface; the closer the outlet to water surface, the higher the vortex strength would be. The biosolids generated in the culture tank from the fish and biofilms need to be flushed rapidly as their hydrolysis leads to decomposition which decreases the dissolved oxygen levels and releases organic molecules, fine suspended solids and ammonia. Another danger that can occur in RAS using sea water is that toxic H2S can also accumulate in the tank, and it is likely that such a scenario is more probable if solids are not rapidly washed out [32] . To get rid of particle accumulation, the tank design needs to be self-cleaning so that the fish growth and welfare would not be negatively impacted. Hence, the practical implications of an incorrect tank design have profound effects on aquaculture operations. A common practice in the industry is to employ a particle trap near the outlet that receives approximately 1% or more of the total outflow. When a parcel of 500 particles with a specific gravity of 1.02 is released at the free-surface with an initial downward velocity of 1 cm/s, the distance between the despatch location to the domain exit in the case of elevated outlet is approximately double of that in the bottom outlet. To make a valid comparison for particle dynamics, only redesigns 2 and 3 with the same retention time of 55 min were examined where the outlet was on the tank's floor, but the inlets were near the sidewalls and corner walls, respectively. Particle breakup and surface roughness  effects were ignored which did not affect the model accuracy as particles' motion is concerned. Fig. 14 presents the integrated information about the particle dispersion in the tank designs over a time of 30 min. With the early particle flushing within 7 min, Redesign 2 dominates its counterpart for about 10 min until 10% of particles are flushed. Around this time, with a sudden fall in the particle count, Redesign 3 has a sudden fall in the particle count and continues to exhibit a superior flushing activity to Redesign 2. A salmon culture tank with Redesign 3 is therefore safer for the fish and gives better welfare and performance, because there is less time for particles to disintegrate and produce water quality problems from the breakdown products of these particles. From the particle visuals, it can be seen that Redesign 2 has more static particles (in blue colour) on the floor than Redesign 3. As viewed from the timehistory of linear kinetic energy, Redesign 2 creates a more fluctuating trend with a mean 18% more than Redesign 3. By the end of the considered duration, 18% more particles were left in Redesign 2, accounting for 14% higher kinetic energy than those in Redesign 3. Thus, mov-ing the inlet pipes from the sidewall location to the corner walls would considerably improve the flushing action of biosolids in the existing tank.

Conclusions
Rapid solids flushing out of salmon culture tanks is a prerequisite for adequate fish welfare and fish performance. In this study, we show that inlet and outlet placements have a considerable impact on both solids' removal from the tank as well as the energy used to sustain the flow in the tank. Confined rotating flow in a large domain with a central outlet as in this case results in a complex combination of a large vortex column at the centre and a range of turbulent filaments around it. By moving the inlet pipes to the corner wall this provides advantages, such as the reduction in the drag force and local re-energization of the flow, when compared to the practice of inlet pipes placed near the sidewall. Regarding tank outlet design, the study showed that the flow uniformity and circulation characteristics were better when using a flat bottom outlet than when using an elevated drain at the tank's centre. Also, it is concluded that, without changing the rearing volume and internal surface area, the mere shifting of inlet pipes close to the corner walls enhances the self-cleaning ability of the existing tank. By means of CFD-assisted design verification, the present study thus concluded that the hydrodynamic positioning of flow boundaries has a significant impact on the overall performance of the culture tank, which could potentially replace the existing practices of trial-and-error learning and experiencebased approaches. In the long term, (re)designing culture tanks like this can provide a better environment for the fish, and thus result in improved fish welfare and health, and ultimately to more efficient salmon production.

Declaration of Competing Interest
On behalf of the coauthors, listed immediately below, I certify that they have NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers' bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript.