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Numerical modeling on inlet aperture effects on flow patternin primary settling tanks

Fatemeh Rostami, Mahdi Shahrokhi, Md Azlin Md Said ⇑, Rozi Abdullah, SyafalniSchool of Civil Engineering, Universiti Sains Malaysia, 14300 Nibong Tebal, Seberang Perai Selatan, P. Penang, Malaysia

a r t i c l e i n f o

Article history:Received 25 April 2010Received in revised form 2 December 2010Accepted 9 December 2010Available online 21 December 2010

Keywords:Settling tanksInlet structureKinetic energyNumerical simulations

a b s t r a c t

Inlets should be designed to dissipate the kinetic energy or velocity head of the mixedliquor and to prevent short-circuiting, mitigate the effects of density currents, andminimize blanket disturbances. Flow in primary settling tank is simulated by means ofcomputational fluid dynamics. The fluid is assumed incompressible and non-buoyant. Atwo-dimensional computational and one phase fluid dynamics model was built to simulatethe flow properties in the settling tank including the velocity profiles, the flow separationarea and kinetic energy. In this study, the RNG turbulent model was solved with theNavier–Stokes equations. In order to evaluate hydraulic influences on the velocity profile,separation length and kinetic energy, three different of opening positions and two andthree aperture in inlets were simulated. The flow model uses to apply a fixed-grid of cellsthat are all rectangular faces; the fluid moves through the grid and free surfaces are trackedwith the volume-of-fluid (VOF) technique. Effects of numbers and locations of inlet aper-tures on the flow field are presented and the results show the positions of inlet aperturesare affected on the flow pattern in the settling basin and increasing the numbers of slotscan reduce kinetic energy in the inlet zone and produce uniform flow.

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1. Introduction

The process of removing suspended particles from water by gravity is known as sedimentation. This method, which hasbeen used for over 1000 years, is an integral part of any water and wastewater treatment plant. Settling tanks are among themain parts of a treatment plant, especially those involved in the purification of turbid flows. In these tanks, turbid waterflows through the length of the tanks at a low speed, giving enough time for suspended particles to settle. As such, findingnew and useful methods to increase hydraulic efficiency is the objective of many theoretical, experimental, and numericalstudies.

Settling tanks can be rectangular with horizontal flow or circular with radial flow patterns. Energy dissipation is the mainobjective of designing a primary clarifier inlet. In rectangular tanks, the influent enters the basin at the inlet, the energy ofwhich must be dissipated at the inlet zone by selecting the best position and configuring the inlet or by using the baffles inthe inlet zone [1].

Because the rate and extent of the flocculation reaction is dependent on the concentration of the particles to be floccu-lated, among others, the design engineer must ensure optimum conditions for flocculation at the inlet where the concentra-tion of solids is highest. While much has been done to improve inlet designs in secondary clarifiers to promote flocculation,there has been little improvement on primary clarifiers [1].

0307-904X/$ - see front matter � 2010 Elsevier Inc. All rights reserved.doi:10.1016/j.apm.2010.12.007

⇑ Corresponding author. Tel.: +60 45995834x6202; fax: +60 45941009.E-mail addresses: fa.rostami@gmail.com (F. Rostami), mhd.shahrokhi@gmail.com (M. Shahrokhi), azlin@eng.usm.my (M.A. Md Said), cesrozi@eng.usm.

my (R. Abdullah), cesyafalni@eng.usm.my (Syafalni).

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Enlarging the size of the inlet zone and using inlet energy for flocculation can improve the removal of suspended solids.Impinging flow streams against one another is an effective way of promoting flocculation [2]. Imam et al. [3], simulated pri-mary settling tanks and found a relation between inlet wall submergence and inlet eddy length. Larger eddies comprisesmaller inlet apertures, thus decreasing removal efficiency.

Density effects and potential energy may decrease due to the low position of the inlet, as proposed by some studies [1].Bretscher et al. [4] confirmed these theoretical considerations through prototype measurements in rectangular tanks. In theirstudy, the inlet aperture was not quantified and flocculation or energy dissipation was not taken into account. Tamayol et al.[5] suggested that the best position for the inlet is somewhere in the middle depth of the tank, and inlets at the bottom of thetank are believed to be better than inlets at its surface. Flocculation and avoiding floc breakup were the main objectives ofLarsen’s [6] inlet design, which was developed in pure-water model tests by evaluating velocity profiles in place of flowthrough curves (FTCs).

Goula et al. [7] studied the effect of inlet baffle heights on flow patterns and particle trajectories throughout or at the out-let of tanks and found that the baffle affects the inlet section and the area near the bottom of the tank. It seems that theextended baffle provides better influent mixing and isolation between the tank influent and effluent than the short bafflein the original tank design, thus significantly enhancing sedimentation. The extended baffle increases the kinetic energyand the dissipation rate in the inlet baffle in the region and, consequently, weakens the current in the area.

2. Governing equation

2.1. Time averaged flow equations

The governing equations that determine flow are the general mass continuity and momentum expressions. The turbu-lence model is also used to calculate the Reynolds stresses. The mass continuity equation for fluid is simple: as the flow pat-tern is assumed to be two dimensional (2D), two momentum equations in the x and z directions respectively represent thelength and height of the tank to be solved. The general mass continuity equation is as follows [8,9]:

Vf@q@tþ @

@xðquAxÞ þ

@

@zðqwAzÞ ¼ 0; ð1Þ

where Vf is the fractional volume of the flow in the calculation cell and q is the fluid density. The variables (u, w) are thevelocity components in the length and height (x, z) directions. The momentum equations for the fluid velocity componentsin the (x, z) directions are described by the Navier–Stokes equations [10]:

@u@tþ 1

VfuAx

@u@xþwAz

@u@z

� �¼ � 1

q@P@xþ Gx þ fx

@w@tþ 1

VfuAx

@w@xþwAz

@w@z

� �¼ � 1

q@P@zþ Gz þ fz:

ð2Þ

where Gx, Gz are the body accelerations and fx, fz are the viscous accelerations for a variable dynamic viscosity l:

qVf f x ¼ wsx� @

@xðAxsxxÞ þ

@

@zðAzsxzÞ

� �; qVf f z ¼ wsz� @

@xðAxsxzÞ þ

@

@zðAzszzÞ

� �

where:

sxx ¼ �2l @u@x; szz ¼ �2l @w

@z; sxz ¼ �l @u

@zþ @w@x

� �

In the above expressions, the terms wsx and wsz are wall shear stresses. If these terms are omitted, there is no wall shearstress because the remaining terms contain the fractional flow areas (Ax, Az) which vanish at walls. The wall stresses aremodeled by assuming a zero tangential velocity on the portion of any area closed to flow. Mesh boundaries are an exceptionbecause they can be assigned non-zero tangential velocities. For turbulent flows, a law-of-the-wall velocity profile is as-sumed near the wall, which modifies the wall shear stress magnitude [10].

When a free surface flows simulated in Flow-3D, the volume of fluid (VOF) method is active automatically to calculate thefree surface configuration in surface cells. Therefore, it is impossible to consider the free surface as a rigid boundary. In VOFmethod, grid cells are classified as empty, full, or partially filled with fluid. Cells are allocated with fluid fractions varyingfrom zero to one, depending on the quantity of fluid. Thus, fluid exists in F = 1, and F = 0 corresponds to void regions. Thisfunction illustrates the VOF per unit volume and satisfies the following equation [8]:

@F@tþ 1

VF

@

@xðFAxuÞ þ @

@zðFAzwÞ

� �¼ 0: ð3Þ

The free surface slope of a partially filled cell is calculated by the free surface angle and the location of the neighborhoodcells. It is determined by a series of connected lines in 2D or by connected surfaces in 3D simulations. These fractions arederived into all terms of the Reynolds-averaged Navier–Stokes (RANS) equations.

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2.2. RNG turbulent model

To model turbulence, the RNG model was used and turbulent viscosity was computed using a differential equation. TheRNG model is useful for cases with curved streamlines, as in circulation regions, and applies statistical methods to derive theaveraged equations for turbulence quantities, such as turbulent kinetic energy and its dissipation rate. RNG-based modelsrely little on empirical constants while setting a framework for the derivation of a range of models at different scales [11,12].

The RNG model uses equations that are similar to those for the k–e model. However, the equation constants found empir-ically in the standard k–e model are derived explicitly in the RNG model. The turbulence kinetic energy, k, and its rate ofdissipation, e, are obtained from the following transport equations:

@k@tþ 1

VFuAx

@k@xþwAz

@k@z

� �¼ P þ Gþ Diff � e; ð4Þ

@e@tþ 1

VFuAx

@e@xþwAz

@e@z

� �¼ C1e � e

kðP þ C3eÞ þ DDif � C2e �

e2

k: ð5Þ

where P represents the shear production, G is the buoyancy production, Diff and DDif represent diffusion, and C1e, C2e, C3e areconstants. In the RNG model, C1e = 1.42, C2e = 1.68, and C3e = 0.2 [11,12]. Generally, the RNG model has wider applicabilitythan the standard k–e model. In particular, the RNG model is known to describe low-intensity turbulence flows and flowshaving strong shear regions more accurately.

In this paper, a Flow-3D� flow solver module, which utilized finite difference schemes for structured meshes, was used tosimulate the free surface flow. The flow field is divided into fixed rectangular cells. The local average values of all dependentvariables calculated for each cell. Pressures and velocities are associated implicitly using time-advanced pressures in themomentum equations and time-advanced velocities in the mass (continuity) equations. These semi-implicit formulationsof the finite-difference equations provide for the efficient solution of low speed and incompressible flow problems. However,these results in coupled sets of equations must be solved by an iterative technique [10].

3. Numerical model

Steady-state incompressible flow conditions with viscose effects are generally considered in hydraulic numerical model-ing, and the Navier–Stokes equation has been well modified to solve the governing equation. The Navier–Stokes equation isan incompressible form of the conservation of mass and momentum equations, and is comprised of non-linear advection,rate of change, diffusion, and source terms in the partial differential equation. The mass and momentum equations joinedthrough velocity can be used to obtain an equation for the pressure term. When the flow field is turbulent, the computationbecomes more complex. Hence, the RANS equations, which are modified forms of the Navier–Stokes equation including theReynolds stress term, which approximates the random turbulent fluctuations by statistics, are prevalently used.

In this study, the available computational fluid dynamics (CFD) program Flow-3D, developed by Flow Sciences, was usedfor the numerical simulation. Flow-3D solves the RANS equations by the finite volume formulation obtained from a rectan-gular finite difference grid. The fractional area/volume obstacle representation (FAVOR) method, which was developed byHirt and Sicilian [9], was used to investigate the geometry in finite-volume meshes. The FAVOR technique determines theobstacles in calculation cells with a fractional value between zero to one as an obstacle fills the cell. The geometry of theobstacle is inserted into the mesh by setting the area fractions on the cell faces along with the volume fraction open to flow[13]. This enables the independent geometry formation on the grid, causing a complex obstacle to be generated.

For each cell, the average values of the flow parameters, such as pressure and velocity, are computed at discrete times.The new velocity in each cell is calculated from the coupled momentum and continuity equations using previous time stepvalues in each center of the face of cells. The pressure term is obtained and adjusted using the estimated velocity to satisfythe continuity equation. With the computed velocity and pressure for later time, the remaining variables, including turbu-lent transport, density advection and diffusion, and wall function evaluation, are estimated.

3.1. Validation test

To validate the software simulation of settling tanks, the experimental conditions used by Imam et al. [3] were consid-ered. The test was carried out in a settling tank with length of 73 cm, depth of 11.9 cm, an opening inlet of 6.9 cm, and a flowrate of 109 cm3/s/cm. Some sediment particles were imported in the sedimentation basin to measure the efficiency of thetank [3]. In this study, the numerical model was applied to simulate this basin using a uniform rectangular mesh. The cellsize in each direction is about 8 mm. The RNG turbulence model was selected to calculate turbulence effects on the flowfield. In this study, the flow is clear and has no particles. In order to find the effect of the free surface in sedimentation tanks,two models were considered, i.e. using VOF method (free surface) and confined surface.

Fig. 1 shows a comparison between the results of the numerical models and experiments by Imam et al. [3]. From Fig. 1,the two sets of numerically results show a good prediction to the experimental data. However, the results of VOF (free sur-face) show more precise results in comparison with confined surface. As obvious in the Fig. 1, the results of confined surfaceare over estimated in the upper zone of the tank. These results differ from using VOF method especially in the first section.

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This difference is related to considering the dissipation energy by VOF method so the predicted values by VOF are less thanresults of confined surface.

Due to low concentration in the upper zone of the flow, the simulation results converge with those from the experimentsof Imam et al. [3]; however, the particles affect the flow field in the lower portion of the flow because of sedimentation. Theresults of clear water simulation differ from the experimental data, indicating that the software can accurately simulate flowpatterns in the basin.

3.2. Modeling approach

A pilot-scale rectangular settling tank was investigated in this study. The settling tank, with a length of 2.5 m, width of0.5, and depth of 0.5 m, was modeled. Five configurations (a–e) were considered: three of them involve one slot in the inletwall at different depths, while the two others involve two and three apertures in the inlet wall (Fig. 2). A schematic view ofthe settling tanks is shown in Fig. 3.

To reduce computational power requirements, the rectangular settling tank was modeled in 2D. The major assumption inthe study is that the flow pattern is the same for all cross-sections of the basin; therefore, a 2D model can properly be appliedto simulate the general characteristics of the hydrodynamic processes in the tank. First, a mesh was generated across thesettling tank. A grid dependency study was executed to eliminate errors due to the roughness of the grid and to determinethe best agreement between simulation accuracy, numerical stability, convergence, and computational time. The mesh wasfinest where velocity gradients were expected to be larger. The selected grid was composed of 21,440 rectangular elements.The computational mesh is shown in Fig. 4.

As mentioned before, the VOF method predicts more accurately data in comparison with confined surface consequentlythe VOF method was selected for further simulations. The RNG turbulence model was used to account for turbulence since itcan better describe flows with curvature streamlines. The converged solution was defined as the solution for which the nor-malized residual for all variables was less than 10�5. The water flow rate was 1.75 L/s and the depth of water in the tank was0.34 m. The aperture height of the inlet slot was 0.1 m for one opening, 0.05 m for two openings, and 0.04 m, 0.06 m, and0.04 m for three openings.

u/U ave

z/H

-1 0 1 2 30

0.2

0.4

0.6

0.8

1

x/L=0.84

u/U ave-1 0 1 2 3

x/L=2.52

u/U ave-1 0 1 2 3

x/L=3.36

u/U ave-1 0 1 2 3

x/L=5.04

Numerical Simulation(Confined surface)Numerical Simulation(VOF Method)

Imam et. al [3]

Fig. 1. Comparison of predicted velocity fields with experimental results.

Fig. 2. Five configurations of inlet apertures.

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3.3. Boundary conditions

In this study, a no slip wall function was assumed for all cases of rigid boundary and uniform velocity profiles in the inlet.The water surface profile was calculated by the VOF method. In addition, the symmetry condition was applied for zero gra-dient perpendicular to the boundary. A law-of-the-wall velocity profile was assumed near the wall, which modifies the wallshear stress magnitude. The inlet was specified as a plug flow of water at 0.035 m/s, and the outlet was indicated as the out-flow boundary condition.

4. Results and discussion

4.1. Flow pattern

The performance of the settling tanks depends on the flow pattern and the mixing regime in the tank. The inlet structurein the settling tanks must supply a uniform flow pattern through a minimum circulation zone. Therefore, the determinationof the flow and mixing characteristics is essential to predict tank efficiency. Fig. 5 presents the predicted streamlines for thedifferent types of inlet slots in the settling tanks. Generally, the flow pattern is characterized by a large recirculation regionspanning a large part of the tank from top to bottom. Between cases (a), (b), and (c), case (c) has the minimum circulationzone. In this case, the circulation zone is divided in two smaller parts. The same behavior was observed by Tamayol et al. [5]in their flow velocity predictions in a settling tank.

In cases (e) and (f), the circulation zone is smaller compared to the previous configurations. The circulation zone is 6.85%and 4.89% for cases (e) and (f), respectively, while the minimum occupied area by the eddies in case (b) is 11.21% (for a mid-dle opening at the inlet). As shown in Fig. 5, the streamlines are parallel after 0.75 m in case (b), 0.5 m in case (d), and 0.4 min case (e).

4.2. Velocity profiles

The velocity in the settling tanks must be as low as possible and the velocity profile must be uniform to achieve high ratesof sediment settlement. The inlet structure should be designed to reduce the velocity and produce more uniform velocityprofiles in the tanks. Fig. 5 shows the x-velocity vector, while Fig. 7 displays the non-scale x-velocity and z-velocity for allcases. In cases (a) and (c), the area that was occupied by the negative x-velocity is too large and the non-uniform velocityis up to 1.7 m of the inlet. In case (c), the velocity profile is like a wall jet, with maximum velocity near the bed; this is apoor condition in settling tanks.

The x-velocity profile in cases (b), (d), and (e) is fully developed at short distances of 1.7 m, 0.8 m, and 1 m, respectively, incomparison to cases (a) and (c). In addition, the maximum velocity in these cases is not near the bed, which is advantageous

z

x

L=2.50 m

H=0.34 m

Fig. 3. Schematic shape of settling tank.

Fig. 4. Computational 2D rectangular mesh for settling basin.

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for settling tanks since this prevents resuspension. From Fig. 7, the x-velocity profiles in x/L = 0.6 and 0.8 are very similar inall cases except case (a). Fig. 6 shows the x-velocity contour in the case of (d) and (e).

In the inlet zone, the z-velocity profile fluctuates (x/L = 0.2 in Fig. 7). This fluctuation is wider in cases (a), (b), and (c) thanin cases (d) and (e); meanwhile, this oscillation is at a minimum in case (e). In cases (d) and (e), water enters the tank fromseveral openings in the z-direction, which may reduce z-velocity fluctuations. In the other sections away from the inlet (x/L = 0.4, 0.6, and 0.8), these oscillations are reduced.

4.3. Turbulence kinetic energy

The inlet structure minimizes the kinetic energy (k) within the tanks. As can be seen in Fig. 8, the turbulence kinetic en-ergy is reduced in the tank. In all the sections, case (b) has the lowest turbulence kinetic energy compared to cases (a) and(c); meanwhile, the turbulence kinetic energy of cases (d) and (e) in all sections is lower than in other cases. In the first sec-tion (x/L = 0.2), the turbulence kinetic energy of section (e) is at the minimum and most uniform in the z-direction. However,in the last section (x/L = 0.8), the turbulence kinetic energies of cases (d) and (e) are similar.

4.4. Flow through curves and hydraulic efficiency

The FTC method is used to determine the efficiency of settling tanks. In this method, a specific amount of dye is injected atthe inlet section and the concentration of the dye at the outlet is measured at different time intervals until no dye is left inthe tank. The duration of dye injection at the inlet section is about 10% of the theoretical detention time (tTH):

Fig. 5. Streamlines and x-velocity vectors for different inlet conditions.

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tTH ¼Q D

V: ð6Þ

where QD is the flow rate of the tank and V is its volume. Fig. 9 shows an FTC diagram of the different types of inlet slot. In thischart, the concentration is normalized by the mean concentration of dye in the tank (C0). C0 is calculated by the total mass ofthe injected dye (Min) by the volume of the tank (V), and the tTH of the simulated settling tank is 242.86 s.

The FTC method can determine the efficiency of the tank, short-circuiting problems, and mixing. Its parameters are asfollows [5]:

Fig. 6. x-Velocity contour for cases (d) and (e).

Fig. 7. Vertical distribution of dimensionless x- and z-velocity (uU

and wU

are the dimensionless x- and z-velocities).

Fig. 8. Vertical distribution of dimensionless turbulence kinetic energy ðk=U2Þ.

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1. Short-circuiting problems can be determined by t0 and t10 (the percentage of dye that passes the outlet). Higher values forthese parameters indicate lower possibility of short circuiting.2. The parameters for investigating the degree of mixing in the tank are t75–t25, t90–t10, and t90/t10. When the values of theseparameters are higher, the flow is highly mixed in the tank.3. The parameters for the prediction of efficiency of the tank are denoted by t50 and tmax. When these parameters are higher,

the tank has higher performance.

Table 1 shows the values of the important parameters used in the FTC method. These values are consistent with the sim-ulation results in the last sections. Higher values of t0 and t10 are found for cases (d) and (e); therefore, there is less proba-bility of short-circuiting in these cases. The values of t75–t25, t90–t10, and t90/t10 illustrate the degree of flow mixing and werethe lowest for case (d). Moreover, the higher values of t50 and tmax demonstrate higher hydraulic performance. Cases (d) and(e) have the best hydraulic efficiency and thus are considered to be the best cases for inlet slots in settling tanks.

5. Conclusion

Energy dissipation is the main objective of designing a primary clarifier inlet. The effect of inlet configurations on the flowpattern is simulated numerically in this paper. For verifying the numerical simulations, the experiments of Imam et. al. [3]was considered. Comparing the results showed the VOF method could predict more accurately values for velocity profiles inthe sedimentation basin.

Different types of inlet apertures in rectangular primary clarifier designs were simulated numerically. These designs gen-erally aimed to reduce high-velocity currents and prevent flow jets from traveling toward the effluent withdrawal area.Where one slot in the inlet wall is considered, using a middle aperture is suggested; however, in general, having two or threeslots serving as inlets is better compared to having only one aperture. Uniform flow was generated in shorter distances, andthe turbulence kinetic energy was considerably low. Moreover, the area occupied by the circulation zone in cases (d) and (e)was about less than half of this amount in the other cases. The FTC method was used to find a case with maximum efficiency.The FTC method also suggested that cases (d) and (e) are the best types of inlet slots. As a result, the existence of two or threeapertures as inlets has a significant role in the uniformity of flow from the inlet to the sedimentation zones and decreasesboth the turbulence kinetic energy and the size of the circulation zone.

References

[1] P. Krebs, D.l. vischer, W. gujer, Inlet structure design for final settling tanks, J. Environ. Eng. 121 (8) (1995) 558–564.[2] D. Das et al, Floc breakup in activated sludge plants, Water Environ. Res. 65 (2) (1993) 138–145.[3] E. Imam, J.A. McCorquodale, J.K. Bewtra, Numerical modeling of sedimentation tanks, J. Hydraul. Eng. 109 (12) (1983) 1740–1754.

0.00

0.50

1.00

1.50

2.00

2.50

0.00 0.50 1.00 1.50 2.00 2.50

C/C

0

t/t TH

case (a)

case (b)

case (c)

case (d)

case (e)

Fig. 9. FTCs diagram for different types of inlet.

Table 1Value of parameters in the FTCs method.

Case t0 t10 t75–t25 t90–t10 t90/t10 t50 tmax

(a) 0.49 0.59 0.248 0.725 2.236 0.80 0.90(b) 0.68 0.82 0.278 0.521 1.632 1.06 1.11(c) 0.54 0.68 0.253 0.521 1.770 0.91 1.00(d) 0.79 0.92 0.240 0.513 1.555 1.14 1.23(e) 0.73 0.91 0.278 0.585 1.647 1.14 1.17

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[4] U. Bretscher, W. Hager, W.H. Hager, Investigations into flow and solids distributions in final clarifiers, gwf Wasser Abwasser 125 (2) (1984) 81–90 (inGerman).

[5] A. Tamayol, B. Firoozabadi, G. Ahmadi, Effects of inlet position and baffle configuration on hydraulic performance of primary settling tanks, J. Hydraul.Eng. 134 (7) (2008) 1004–1009.

[6] P. Larsen, On the Hydraulics of Rectangular Settling Basins: Experimental and Theoretical Studies, Report No. 1001, Lund, Sweden, 1977.[7] A.M. Goula et al, A CFD methodology for the design of sedimentation tanks in potable water treatment case study: the influence of a feed flow control

baffle, Chem. Eng. J. 140 (2008) 110–121.[8] C.W. Hirt, B.D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comp. Phys 39 (1981) 201–225.[9] C.W. Hirt, J.M. Sicilian, A porosity technique for the definition of obstacles in rectangular cell meshes, in: Proc. Fourth International Conf. Ship Hydro.,

National Academy of Science, Washington, DC, 1985.[10] Flow-3D user manual; excellence in flow modeling software, v 8.2, Santa Fe, NM, 2003.[11] V. Yakhot, S.A. Orszag, Renormalization group analysis of turbulence. I: basic theory, J. Scient. Comput. 1 (1986) 1–51.[12] V. Yakhot, L.M. Smith, The renormalization group, the e-expansion and derivation of turbulence models, J. Scient. Comput. 7 (1992) 35–61.[13] C.W. Hirt, Volume-Fraction Techniques: Powerful Tools for Flow Modeling, Flow Science, Inc., Santa Fe, NM, 1992.

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