# Applied Computational Fluid Dynamics by Hyoung Woo Oh - HTML preview

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VALIDATION

CODE

SIMULATED

VERIFICATION

REALITY

Fig. 4. Process of developing CFD code.

Fig. 5. Layout of AL-DEWANYIA WTP

6. Model development, applications and results

6.1 Introduction

The full-scale horizontal settling tanks at the drinking treatment plant of AL-DEWANYIA

were opted for. Most settling tanks of Iraq Water exhibit a horizontal settling tank. This

research was focused on this type of settling tanks.

Figure 5 represents treatment of water obtained from a deep well in AL-DEWANYIA WTP a

The AL-DEWANYIA WTP were built to remove turbidity and organic material.

A Computational Fluid Dynamics Model of Flow and Settling in Sedimentation Tanks

25

6.2 Simulation

To limit computational power requirements, the rectangular settling tank was modeled in

2D. The major assumption in the development of the model is that the flow field is the same

for all positions; therefore, a 2D geometry can be used to properly simulate the general

features of the hydrodynamic processes in the tank. As a first step, a mesh was generated

across the sedimentation tank. As a result, the solutions from the grid of 137,814

quadrilateral elements were considered to be grid independent.

For simulation purposes, the range of the suspended solids was divided into thirteen

distinct classes of particles based on the discretization of the measured size distribution.

The number of classes was selected in order to combine the solution accuracy with short

computing time. Two other numbers, 6 and 15, were tested. While the predictions

obtained using 6 classes of particles were found to be different from those resulting from

the 13 classes, the difference between the predictions made by the 13 and the 15 classes

were insignificant. Therefore, a number of 13 classes were selected as a suitable one.

Within each class the particle diameter is assumed to be constant (Table 1). As it can be

seen in Table 1, the range of particle size is narrower for classes that are expected to have lower settling rates.

Range of particle

Mean particle size

Class

Mass fraction

size (μm)

(μm)

1 10-30

20

0.025

2 30-70

50

0.027

3 70-90

80

0.039

4 90-150

120

0.066

5 150-190

170

0.095

6 190-210

200

0.115

7 210-290

250

0.126

8 290-410

350

0.124

9 410-490

450

0.113

10 490-610

550

0.101

11 610-690

650

0.077

12 690-810

750

0.057

13 810-890

850

0.040

Table 1. Classes of particles used to account for the total suspended solids in the STs in AL-DEWANYIA STs.

6.3 The influence of particle structure

The settling velocity of an impermeable spherical particle can be predicted from Stokes’ law.

However, the aggregates in the water not only are porous but it is well known that they

have quite irregular shapes with spatial varying porosity. The flow chart of this

computations sequence is presented in Figure 6.

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Applied Computational Fluid Dynamics

Fig. 6. Flow chart of computation sequence.

6.4 Simulation of existing sedimentation tanks

The AL-DEWANYIA water treatment plant uses lime, and (NH4)2SO4 and Fe2(SO4)3 to

flocculate the and solid concentrations, respectively before entering the sedimentation tanks.

There are 4 rectangular tanks at the AL-DEWANYIA WTP .

The Physical and hydraulic data during study periods, and settling tank data for two WTPs

are shown in Table 2 .

Geometry Value

Tank length

30.0 m

Tank width

4.50 m

Hopper depth

2.50 m

Bottom slop

0.00

Weir length

4.50 m

Weir width

0.70 m

Weir depth

0.50 m

SOR

2.7 m/h

Inlet concentration

30-80 mg/l

Density of water

1000 kg/m3

Density of particulate

1066 kg/m3

Tank parameter

Value

Average flow rate

60-80 l/s

Sludge pumping rate

5-15 l/s

Inflow temperature average

4oC -11oC , and 20oC -27oC

Inflow suspended solids

25-80 mg/l

Detention time

2.5-3.6 hr

Cmin 0.17

mg/l

μ 0.002

N.s/m2

Table 2. Physical and hydraulic data during study periods, and settling tank data.

A Computational Fluid Dynamics Model of Flow and Settling in Sedimentation Tanks

27

6.4.1 AL-DEWANYIA WTP

Figure 7 shows the velocity profiles of the existing tanks for a flow rate of 80 l/s and an inlet concentration of 50 mg/l (~75 NTU). High velocities are present at the inlet (0.065 m/s). The flow is further accelerated towards the bottom of the hopper due to the density differences

as well as the wedge shape of the hopper. The strong bottom current is balanced by a

surface return current inside the hopper. The velocities near the effluent weir are very low.

The solids concentration profile is shown in Figure 8. Note the high concentration

downstream of the sludge hopper. The sludge that is supposed to settle in the hopper is

washed out of the hopper into the flat section of the tank. Over time a significant amount of sludge accumulates. According to both the field observations and the modeling of the

existing process, each of the following reasons (or combination of them) may cause the ST

problems, i.e. the flocculant solids blowing out:

1. The location of the existing weir (distributed in a range of 1 meter at the very

downstream end of the ST) cause very strong upward currents, which could be one of

the major reasons that the flocculant solids were blowing out around the effluent area.

2. The strong upward flow is not only related to the small area the effluent flow passes

through but also to the rebound effect between the ST bottom density current and the

downstream wall. The “rebound” phenomenon has been observed and reported by

many operators as well as field investigators, especially in ST with small amounts of

sludge inventory. A reasonable amount of sludge inventory can help dissipate the

kinetic energy of the bottom density current.

3. In the existing operation, the bottom density current must be fairly strong due to the lack of proper baffling and the shortage of sludge inventory in the tank.

Fig. 7. Velocity contours of existing tank (m/s)

Fig. 8. Solids concentration profile for existing tank

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Applied Computational Fluid Dynamics

7. Simple improvements to the existing sedimentation tank in WTP

Field data collected from the laboratories during the last 3 years was used to analyze the

tank behavior and to enhance the performance of the settling tanks at the AL-DEWANYIA

WT Plant. Several tank modifications including flocculation baffle, energy dissipation

baffles, perforated baffles and inboard effluent launders, were recommend based on their

field investigation

The relationship between the effluent SS and the hydraulic loading is summarised in Table 3

for the existing STs and with different modification combinations. The predicted Effluent SS

(ESS) in Table 3 and Figure 9 indicates that the average ESS can be significantly reduced by improving the tank hydraulic efficiency. The comparison of model predictions with the

subsequent field data indicates that the significantly improvement of STs performance was

obtained by using the minor modifications based on the 2-D computer modeling.

Q=

50

l/s

Q= 70 l/s

Q= 80 l/s

Q= 80 l/s

Influent

Influent

Influent conc.= 50 Influent conc.=

conc.= 40

conc.= 40

mg/l

75 mg/l

mg/l

mg/l

Predicted average effluent concentration

Existing tank

20

30

40

50

Modification 1

12

11

30

22

Modification 2

6

8

12

13

Modification 1 and 2

4

6

7

9

(1) Perforated baffle distance from inlet = 16m; gap above bed = 0.5 m; height above bed =

1.8 m; porosity = 55%

(2) Length of launder = 12 m.

Table 3. Performance data for modelled settling tank

Fig. 9. Comparison of solids distributions on surface layer between existing and modified

tanks

8. Modelling the scraper mechanism

The gravitational (and laminar) flow along the bottom, which may go up to 8-15 mm/s near

the sump, is blocked for 40 minutes of scraper passage. This is clearly seen in Figure 10. The scraper blade thus constrains the bottom flow discharge by counteracting the gravitational

force. Near the floor the velocity increases with height in the shear flow region, but is

obviously limited by the scraper’s velocity.

A Computational Fluid Dynamics Model of Flow and Settling in Sedimentation Tanks

29

Fig. 10. Effect of scraper on solids concentration profiles

9. Design procedures and guidelines

The design procedures are necessarily based on many assumptions, not normally stated as

shortcomings and limitations during the design process. To demonstrate the implications of

these assumptions and the way in which these assumption deviate from real tanks. (Ghawi,

2008) tried to improve design procedure as show in Table 4.

Improved design procedure

Step description

Step 1

Measurement of settling velocity and sludge density

Step 2

Set up of computational grid

Step 3

Simulate tank

Step 4

Evaluate results and check for evidence of the following:

- short circuiting

- high velocities zones

- high overflow concentration

- poor sludge removal

Step 5

If none of the above is present, tank size can be reduced to reduce capital cost.

- inlet

- position of sludge withdrawal

- position of overflow launders

Also consider using perforated, porous and deflecting baffles

Step 6

Repeat until a satisfactory tank geometry is obtained and check final geometry

for various process changes such as density, concentration and inflow rate.

Step 7

Asses the influence of the settling velocity and sludge density input

parameters and repeat steps 3 – 6 if necessary.

Table 4. Proposed CFD enhanced design procedure.

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Applied Computational Fluid Dynamics

10. Temperature effect

Settling velocity correction factor

In order to define a correction factor for the settling velocities based on temperature

difference, the temperature effect on the zone settling velocity has to be determined.

Figure 11 displays graphically the value of the relationship VsT2 / VsT1 and μT2 /μT1 for the data presented in Table 5 at temperatures Ts (summer temperature) and Tw (winter

temperature).

CFD Calculated at summer temperature

SS

Settling velocity V

Inlet

Outlet

Dynamic viscosity μ

mg/l

m/h

temperature

temperature

kg/m.s

oC

oC

60 1.5

27.5 27.5 8.5e-04

50 1.7

27.5 27.5 8.6e-04

25 1.83

26

26

8.7e-04

15 2.52

25.4 25.4

8.8e-04

CFD Calculated at cooled temperature

60 0.95

8

9.2

1.3e-03

50 1.05

6.6

6.8

1.35e-03

25 1.9

7.8 8.8 1.29e-03

15 2.7

7

8.9 1.30e-03

Table 5. Settling velocity and dynamic viscosities for summer and winter temperature.

From Figure 11 can be observed that the numerical values of the ratios VsT2 / VsT1 and μT2

/μT1 are very close, suggesting that an easy correction in the zone settling velocity for

different temperatures can be made with a correction factor based on the dynamic viscosity

of the water at the two temperatures. Figure 12 shows an extended data set indicating the

relationships between the ratios VsT2 / VsT1 and μT2 /μT1.

Fitting a straight line to the data point presented in Figure 13 can find a correction factor for the settling velocities based on temperature

247.8

T 1 133.15

 10

 

ST

V

S

V T

 (1)

247.8

2

1

T 2 133.15

 10

 

Equation 1 can be applied to correct the settling velocities for difference in temperatures in whichever of the four types of sedimentation, i.e., unflocculated discrete settling, and

flocculated discrete settling. Even though equation 1 can be used for a sensitivity analysis on the performance of the model for different seasons, e.g. summer and winter, there is no

evidence that the settling properties can be accurately extrapolated from one season to

another.

A Computational Fluid Dynamics Model of Flow and Settling in Sedimentation Tanks

31

Fig. 11. Ratios of VsT2 / VsT1 and μT2 /μT1 for Different suspended solid (SS) concentrations.

Fig. 12. Effect of Temperature on Settling Velocity.

11. Validation of the model

The validation process involves comparing the model response to actual measured data. The

model was validated using measured data from the AL-DEWANYIA WTPs.

After the development of the hydrodynamic model, and turbulence model, the ST model

was tested. The ESS predicted by the model was tested during seven days (from a 10 day

period) showing a very good agreement with the field data. Figure 13 presents a comparison

between the experimentally measured and the simulated values of the floc concentration in

the effluent of the existing tanks in AL-DEWANYIA. Apparently, there is a good agreement

between measured and predicted values.

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Applied Computational Fluid Dynamics

Fig. 13. Validation of the ESS Simulated by the Model

The average values of effluent concentration of improvement are presented in Table 6. The

tank operation conditions in the data collection periods (February-April, 2007, (June-August, 2006)) and the CFD model predictions are very close as shown in Table 6. The comparison of

model predictions with the subsequent field data indicates that the significantly

improvement of tank performance was obtained by using the minor modifications based on

the 2-D computer modeling.

Operation

Effluent concentration (mg/l) and improvement

conditions

Ave.

Baffle and

No

baffle

concentration

launder

Modifications

Modifications

mg/l

Modifications

Field Data

June-August

50 28 - -

2006

Model

47

27

6 (+78%)

5 (+82%)

Predictions

Table 6. Comparison of model predictions with field data

12. Conclusions

The introduction of this study made clear that many factors influence the performance of

settling tanks. They may be categorised as physico-chemical and hydraulic influences. To

account for them in terms of process operation and design, mathematical models may be

utilised. In this respect, Computational Fluid Dynamics (CFD) enables the investigation of

internal processes, such as local velocities and solids concentrations, to identify process in efficiencies and resolve them. Although these complex models demand for considerable

computational power, they may become an option for the study of process operation and

control as computer speed increases. Nowadays, they mostly find applications in the world

of settling tank design.

A Computational Fluid Dynamics Model of Flow and Settling in Sedimentation Tanks

33

The main purpose of this investigation was to develop a CFD ST model capable of

simulating the major processes that control the performance of settling tanks, this goal

was achieved. The accomplished objectives of this research include: the development of a

compound settling model that includes the representation of the settling velocity for the

suspended solids usually encountered in this type of tank (horizontal sedimentation

tanks) the inclusion of iron removal effects, a flocculation sub-model, and a temperature

sub-model.

These types of sub-models have not been previously incorporated in CFD ST models. The

model was rigorously tested and validated. The validation process confirms the utilities and accuracy of the model. An important benefit of this research is that it has contributed to a better understanding of the processes in STs. The results presented in this research clarify important points that have been debated by previous researchers.

This research may also open the discussion for future research and different ways for

improving the performance of existing and new STs. In summary, this research has led to

more complete understanding of the processes affecting the performance of settling tanks,

and provides a useful tool for the optimization of these corn stone units in water treatment.

The major conclusions, general and specifics, obtained from this research are:

1. CFD modeling was successfully used to evaluate the performance of settling tank.

2. The usually unknown and difficult to be measured particle density is found by

matching the theoretical to the easily measured experimental total settling efficiency.

The proposed strategy is computationally much more efficient than the corresponding

strategies used for the simulation of wastewater treatment.

3. Solid removal efficiency can be estimated by calculating solids concentration at effluent.

4. High solid removal efficiency was achieved for all cases tested.

5. Baffling inlet arrangement succeeded in controlling kinetic energy decay.

6. Improved energy dissipation due to an improved inlet configuration.

7. Reduced density currents due to an improved inlet configuration.

8. Improved sludge removal due to the inlet configuration.

9. Troubleshoot existing STs and related process operations.

10. The effluent quality can be improved by more than 60% for any cases.

11. Evaluated ST design under the specified process conditions.

12. Develop reliable retrofit alternatives with the best cost-effectiveness.

13. The changes in temperature on STs play an important role on the performance of STs.

14. Scrape is important in the settling process and play a big role in changing the flow field.

15. In this work we improved the STs guidelines design procedure.

16. The fairly good agreement between model predictions and field data.

In general the study demonstrated that CFD could be used in reviewing settling tank design

or performance and that the results give valuable insight into how the tanks are working. It can be inferred that CFD could be use to evaluate settling tank designs where the tanks are

not functioning properly.

13. Acknowledgement

This chapter is supported by the Scientfic Grant Agency of Ministry of Education-VEGA

Projekt No. 1/1143/11 with at the Department of Sanitary and Environmental Engineering,

Faculty of Civil Engineering, Slovak University of Technology in Bratislava.

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Applied Computational Fluid Dynamics

14. References

[1] Huggins D.L., Piedrahita R.H., & Rumsey T., (2005). Use of computational fluid

dynamics (CFD) for aquaculture raceway design to increase settling effectiveness,

Aquacult. Eng. 33, 167–180.

[2] Dick, R. I. (1982) Sedimentation Since Camp, J Society of Civil Engrs, 68, 199-235.

[3] Abdel-Gawad, S. M. & McCorquodale, J. A. (1984b). Hydrodynamics of Circular primary clarifiers. Canadian J. Civil Engr. ,11, 299-307.

[4] Adams, E.W. & Rodi, W. (1990). Modelling flow and mixing in sedimentation tanks,

Journal of Hydraulic Engineering, 116(7):895-913, Jul.

[5] Launder, M. & Spalding, D. (1974). The numerical computation of turbulent flows,

Computer methods in applied mechanics and engineering, (3), 269-289.

[6] Ghawi, A.H., (2008). A numerical model of flow and settling in sedimentation tanks in

potable water treatment plants, Edícia vedeckých prác (Science Works Edition) ,

Workbook no. 64, STU Bratislava, pp. 150, ISBN 978-80-227-2964-2

3

Applied to the Greenhouse Environment

Jorge Flores-Velázquez1, Guillermo De la Torre-Gea2,

Enrique Rico-García2, Irineo L. López-Cruz1 and Abraham Rojano-Aguilar1

1Department of Agricultural Engineering, University of Chapingo, Chapingo

2Department of Biosystems, School of Engineering

Queretaro State University Querétaro

México

1. Introduction

In order to perform an accurate study of the climate inside a greenhouse, it is necessary to use models based on heat and mass transfer (Rico-García et al., 2008). Mathematical models based on mass and energy balances assume a homogeneous greenhouse environment. These

models generate a set of nonlinear ordinary differential equations without an analytical

solution. However, a more detailed monitoring of the environment inside the greenhouses

reflects a two-dimensional and three-dimensional variability of climatic variables.

Recently, this problem has been tackled using the fundamental equations of fluid

dynamics. The set of numerical methods applied in order to solve those equations are called

Computational Fluid Dynamics (CFD). Computational Fluid Dynamics (CFD) provides a

numerical solution from an energy balance of a controlled volume, which in comparison

with other methods and expensive technologies allows an efficient study of the climate

inside the greenhouse. CFD techniques consider the values of the independent variables as

primary unknowns in a finite number of places inside the domain, and then a set of

algebraic equations are derived from the fundamental equations applied to the domain and

can be solved by pre-establish algorithms.

In spite of, the greenhouse is a very complex bio-system, in which there are several physical, chemical and biological interacting process and phenomena, during the last decade, due to

the development of computer simulation tools and the increase in computational processing

power, it is possible to develop numerical models for the greenhouse environment such as

more accurate models for transport phenomena and energy exchange inside the greenhouse.

As a consequence, these studies have led improvements in the design of greenhouses

(Norton et al., 2007).

According to Boulard et al. (2002), CFD is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems involving fluids flow. Therefore, it

is possible with the use of computers to perform millions of calculations to simulate the

interaction of liquids and gases with surfaces defined by the boundary conditions. In recent studies the modeling of air flow, CFD has deepened to test their effectiveness in

relationships of climatic factors (Bournet and Boulard, 2010). Computational parametric

36

Applied Computational Fluid Dynamics

studies on greenhouse structures can help to the identification of design factors that affect greenhouse ventilation under specific climatic conditions (Romero-Gómez et al, 2008; Romero-Gómez et al. , 2010).

In the last years, many studies have used CFD to investigate the climatic conditions inside

greenhouses. CFD has been able to increase the degree of realism by taking into account

insect-proof screens and simulation of the crop effect, considering it as a porous medium,

among others in 3D models. The results have been able to improve our understanding of the

phenomenon of greenhouse ventilation. Therefore, this chapter discusses significant recent

studies to understand how the use of CFD has evolved.

2. Fundamental CFD equations and methodology

2.1 Finite element models using CFD

Computational fluid dynamics is based on the governing fluid dynamics equations

(continuity, momentum and energy). The set of equations obtained directly from the volume

or fixed element in space is known as "conservative form" Euler type. The equations obtained directly from the volume or movement with the fluid element are called "non-conservative form” Lagrange type (Anderson, 1995).

2.2 Substantial derivative

The substantial derivative physically is the exchange rate of any substance that moves with

a fluid element. It consists of two parts, where the first part is called the local derivative, which means the rate of change over time in a fixed point. The second part is called the

convective derivative, which physically is the exchange rate due to movement of the fluid

from one point to another in the field of fluid, where the fluid properties are spatially

different. The resulting material can be applied to any field variable fluid, for example:

velocity(u), pressure (p) or temperature (T) (Anderson, 1995).

  i

j

k

(1)

x

y

z

V  ( u, v, w)

dV

V

  dS  0





(2)

V

S

t

Du

p

t

t

t

yx

xx

zx

 

  fx

Dt

x

x

x

x

Dv

p

t

t

t

xy

yy

zy

 

  fy

Dt

x

x

x

x

Dw

p

t

t

t

yz

xz

zz

 

  fz

(3)

Dt

x

x

x

x

Advances in Computational Fluid Dynamics Applied to the Greenhouse Environment

37

2

Dw

V

 

T

   

T

 

 

T

  ( up) ( vp) ( wp)

e

   q

k

k

 

k

Dt

2

x

x

 

y

y

z

 

z

 

x

y

z

( ut ) ( ut ) 

yx

( ut )

( vt )

( vt )

( vt )

xy

yy

zy

xx

zx

x

y

z

x

y

z

( wt ) ( wt )

yz

( wt )

xz

zz

pf V (4)

x

y

z

1. Continuity equation

2. Momentum equation (a non-conservative)

3. Components in x, y and z

4. Energy equation (a non-conservative)

The fundamental CFD equations form a coupled system of nonlinear partial differential

equations. So far no analytical solution has been found. It is commonly assumed that the

fluid is an ideal gas where the intermolecular forces can be neglected. For an ideal gas, the state equation is:

p   RT (5)

Where R is the specific gas constant. For a calorically ideal gas we have:

e CvT , (6)

Where Cv is the specific heat at constant volume (Rodríguez, 2006, Norton et al, 2007).

2.3 CFD procedure applied to the greenhouse environment

Domain setting and grid generation are the first steps in the CFD modeling process. This

implies the choice of a computational domain that is large enough to correctly assess the

main mechanisms that occur in the system and to avoid interference with artificial

Boundaries (Bournet and Boulard, 2010). The CFD modeling process encompasses three

stages: preprocessing, solution and post-processing.

The preprocessing is the most time-consuming activity because of mesh generation that is

the basis for an accurate simulation, does require heavy calculations. Therefore, keeping an adequate strategy should allow reliability in the calculations and physically consistent

results. The meshing process is based on a serie of activities that can be summarized as

follows:

a. Geometry definition (Figure 1)

b. Geometry decomposition

c. Computational mesh generation (Figure 2), refining, giggling, quality

d. Functional and quality meshing

e. Definition of the boundary conditions and

f. Export mesh

One of the most important problems currently in CFD modeling of the greenhouse

environment is the time-consuming for a simulation to converge, due to the high number of

cells that come from the process of meshing. Thus, for many years was chosen to model only

38

Applied Computational Fluid Dynamics

in two dimensions (2D) (Flores-Velázquez, 2010). However, air distribution inner

greenhouse has a third-dimensional (3D) pattern, for that, nowadays 3D CFD models are

more commonly developed. According to Bournet and Boulard (2010) the calculation

process is an iterative procedure that requires the definition of convergence criteria, and the user of the CFD codes must to decide on an appropriate level of convergence, of the

solution. Generally, 10−4 of the value of a variable at all of the nodes is used. Faster

convergence may also be reached by optimizing the grid shape or by assuming the

Boussinesq model as density dependent rather than by setting up the problem on the basis

of the ideal gas theory. However, this choice may not be applicable in the case of large

thermal gradients and may also overlook the influence of temperature on air viscosity.

Fig. 1. Geometry generation for a greenhouse.