[PPT] - Abdu dullra llrahman hman Al Al-Muqb Muqbal ali Supervisor Dr. PowerPoint Presentation

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Abdu dullra llrahman hman Al Al-Muqb Muqbal ali

Supervisor Dr. Anton Purnama

Presentation on: Sultan Qaboos University College of Science Department Of Mathematics and =============================

Model studies of sea outfall effluent discharge

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Sea outfall discharge

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Contents of the Presentation

1) Far field model ( Mathematical Model)

Single point source discharge
Two point sources discharges
Multiple point sources discharges

2) Near field model (3-D)

CORMIX
VISJET

Model studies of sea outfall effluent discharge 4

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Desalination brine discharged plumes

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Far field model (Mathematical model)

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 

my y h 

Uniformly sloping beach U Shoreline Diagram of multiple point sources

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Far field model (Mathematical model)

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In far field model we use a two – dimensional advection diffusion equation on sloping beach for a point source where , Where : C : Concentration (vertically well-mixed) h : water depth Q : rate of discharge δ: Dirac delta function (point source)

 

k k

y x , h k xk   

  0

h k yk    

     

n k k k k k k

c hUc hD Q x x y y x y y  



                 With boundary conditions , and

) 0,

k y

c i hD y y    

 

) , 0 ,

k

ii c x y y  

D : Coefficient of dispersivity (proportional to )

3 2

h

U : drift current (proportional to )

1 2

h

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Far field model (Mathematical model)

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   

) lim , lim ,

k k

k k y y y y

i c x y c x y

 

 



)

k k

ii hUc dy Q







There are two matching conditions :

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 

                y c hD y hUc x

k k

k

y y  

Outfall Point source

k

y y   

Region A Region B

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Far field model (Mathematical model)

In terms of dimensionless quantities Equation is reduced to

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2 * * * 0 * *

, , ( , ) ( , )

h k k

y y x x h c x y c x y Q h U   

2 * * * * 2 * * *

5 2 c c c y y x y          

where h U D  

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Far field model (Mathematical model)

By using Laplace transform Equation is reduced a second –ordinary differential equation Which can be simplified further to the modified Bessel’s equation By writing

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 

___ * * * * * * *

, ( , )

px k k xk

c p y e c x y dx

 

 

2 * * * * 2 * *

5 2

k k k

d c dc y p c dy dy    

 

3 4 * * * *

, ( ) 2

k

c p y y u z with z py 



 

2 2 2 2

9 ( ) 4 d u du z z z u dz dz    

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Far field model (Mathematical model)

To obtain the particular solution, the functions and can be determined from the matching conditions

and

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 

3 4 * * 3 2 * * 3 4 * * 3 2 * *

, ( ) 2 , , ( ) 2 ,

k k k k

c p y A p y I py for y y c p y B p y K py for y y  

 

                 

( ) 3 2 3 2 * * * * * * * * ( )

, ,

k k k k k

q y c p y dy y c p y dy pm

      

 

 

the general solution in the two regions is given by

 

* * * * * *

lim , lim ,

k k y k y k

c p y c p y

       



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Far field model (Mathematical model)

It is found that and the inversion of the Laplace transform

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 

3 2 3 4

2 ( ) 2 ( ) ( )

k

q A p K p k m k       

 

3 2 3 4

2 ( ) 2 ( ) ( )

k

q B p I p k m k       

we obtain the exact analytical solution in the form

3 4 * * * * * 3 2 * * * *

2 ( ) ( ) 1 ( , ) exp ( ) [ ]

k k

k y y k c x y q I m x k k y x k x k                                   

After summing for all concentration from the n+1 multiport sources, the analytical solution of Equation is given by

* * *

( , )

k

c x y

3 4 * * * * * 3 2 * * * *

2 ( ) ( ) 1 ( , ) exp ( ) [ ]

n n k k

k y y k c x y q I m x k k y x k x k      



                            



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Far field model (Mathematical model)

Contours of concentration for single point source when and

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3   4   One point source

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Far field model (Mathematical model) Value of shoreline’s concentration

In the limit as We obtain

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*

y 

 

5 2 * * * *

4 ( ,0 exp 3

k n

q k c x x k x k m                           

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By differentiation Equation the maximum value of concentration is which occurs at the position at This maximum value inversely proportional to the point source

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Far field model (Mathematical model)

The concentration at the beach for a single point source

5 2 5 2

4 5 5 exp 2 2 3

m

c m               

*

2 5

m

x  



𝛽

Maximum value

f concentration

3 1.96 4 0.95

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Two point sources discharges

Diagram of two sea outfalls

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Far field model (Mathematical model)

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Contours of concentration for two point sources when α=3 and ħ=2 : left, ℓ = 3 and right, ℓ = 8 Two point sources

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Far field model (Mathematical model)

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Compounded concentration at the beach for two point sources

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Far field model (Mathematical model)

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Merging of contours of concentration for five points sources when

6  

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Near field model (Computational model)

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VISJET CORMIX Scenario I Scenario II Positively buoyant plume (heated brine discharges) for single port and multiport discharges. Negatively buoyant plume (dense brine discharges) for single port and multiport discharges.

Plume Plume

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Near field model (Computational model)

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Thanks for person Dr. Doneker for given me a permission to use CORMIX in this study.

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Near field model (CORMIX)

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Table3.1: Input data for CORMIX simulations of single port discharges

Parameter Heated brine discharge Dense brine discharge Outfall type Single Ambient (unbounded coastal environmental) Velocity of the currents (m/s) 0.3 Depth at discharge (m) 8.73 Wind speed (m/s) 2.5 Temperature (degree C ) 27 Salinity (ppt) 35 Manning or Darcy –Weisbach f 0.025 (Uniform) Density (kg/m3) 1022.72 Brine effluent Flow rate (m3/s) 0.7 Temperature (degree C ) 40 30 Salinity (ppt) 37 50 (Uniform) density(kg/m3) 1019.45 1032.64 Distance to shoreline ( m) 500 Number of ports 1 Port height (m) 1 Port diameter (m) 0.7 Shoreline location Right Vertical angle (degrees) 30 Horizontal angle (degrees) 90 Mixing zone Water Quality Standard (degree C ) 1

Water Quality Standard (ppt)
2

Regulatory Mixing Zone (m) 150 Region of Interest (m) 1000 Output steps per module 50

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Near field model (CORMIX)

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3.1.1 Scenario I: Heated brine discharges

The positively buoyant plume from single port discharges

500m  

Density (kg/m3) Ambient

1022.72

Effluent

1019.45

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Near field model (CORMIX)

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Side view of the positively plume in Figure 3.2

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Near field model (CORMIX)

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3.1.2 Scenario I I: Dense brine discharges The negatively buoyant plume from single port discharges

500m  

Density (kg/m3) Ambient

1022.72

Effluent

1032.64

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Near field model (CORMIX)

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Side view of the negatively buoyant plume in Figure 3.6

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Near field model (CORMIX)

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Table 3.4: Input data for CORMIX simulations of multiport discharges

Parameter Heated brine discharge Dense brine discharge Outfall type Multiport Ambient (unbounded coastal environment) Velocity of the currents (m/s) 0.3 Depth at discharge (m) 8.73 Wind speed (m/s) 2.5 Temperature (degree C) 27 Salinity (ppt) 35 Manning or Darcy –Weisbach f 0.025 (Uniform) Density (kg/m3) 1022.72 Brine effluent Flow rate (m3/s) 0.7 Temperature (degree C) 40 30 Salinity (ppt) 37 50 (Uniform) density (kg/m3) 1019.45 1032.64 Distance to shoreline (m) 500 Number of ports 7 Port height ( m) 1 Port diameter (m) 0.7 Shoreline location Right Contraction ratio (m) 1 Alignment angle (degrees) 90 Undirectional Vertical angle (degrees) 30 Horizontal angle (degrees) 90 Relative orientation angle BETA (degrees) Nozzle Direction Same direction Mixing Zone Water quality standard (degree C) 1

Water quality standard (ppt)
2

Regulatory mixing zone (m) 150 Region of interest (m) 1000 Output steps per module 50

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Near field model (CORMIX)

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The positive buoyant plume from multiport discharge

7 ports

Scenario I: Heated brine discharges Multiport diffuser

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Near field model (CORMIX)

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Figure 3.11: Side view of the positively buoyant plume in Figure 3.10

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Near field model (CORMIX)

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Figure 3.14: The negative buoyant plume from multiport discharges Scenario I I: Dense brine discharges

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Near field model (CORMIX)

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Figure 3.15: Side view of the negative buoyant plume in Figure 3.14

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Near field model (VISJET)

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Why we do VISJET?

VISJET capable to explicitly display group of effluent jets discharged from a multiport

diffuser. CORMIX does not have this feature

Therefore VISJET be useful as a tool to effectively design a multiport diffuser effluent discharges.

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Near field model (VISJET)

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Thanks to SQU for buying this software to use in this study

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Near field model (VISJET)

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Parameter Scenario I Scenario II Ambient water Depth below surface (m) 8.73 Salinity (ppt) 35 Temperature (oC) 27 Horizontal current speed (m/s) 0.3 Depth at discharge (m) 7.73 Outfall with riser Depth below surface (m) 8.73 Effluent salinity (ppt) 37 50 Effluent temperature (oC) 40 30 Length of the outfall (m) 500 Width/diameter of the outfall (m) 0.7 Riser Sum of the effluent flow of all risers (m3/s) 0.7 Distance for each riser (m) from the offshore end of the outfall Radius at the bottom of the riser (m) 0.35 Radius at the top of the riser (m) 0.35 Height of the riser (m) 1 Jet for each riser Effluent flow from the port (m3/s) 0.7 Port diameter (m) 0.7 Port height (m) 1 Vertical angle (90o for a vertical port) 30 Horizontal angle (90o for crossflow) 90 Effluent salinity (ppt) 37 50 Effluent temperature (oC) 40 30

Input parameters for VISJET simulations of single outfall discharges

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Near field model (VISJET)

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Single port

4.1.1 Scenario I: Heated brine discharges The heated brine discharge rises to the surface from a submerged single port

Density (kg/m3) Ambient

1022.72

Effluent

1019.45

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Near field model (VISJET)

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The horizontal plane view of Figure 4.1

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Near field model (VISJET)

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Single port

Scenario I I: Dense brine discharges The dense brine discharge sinks to the seabed from a submerged single port

Density (kg/m3) Ambient

1022.72

Effluent

1032.64

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Near field model (VISJET)

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The horizontal plan view of Figure 4.4

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Near field model (VISJET)

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Parameter Scenario I Ambient water Depth below surface (m) 8.73 Salinity (ppt) 35 Temperature (oC) 27 Horizontal current speed (m/s) 0.3 Depth at discharge (m) 7.73 Outfall with riser Depth below surface (m) 8.73 Effluent salinity (ppt) 30 Effluent temperature (oC) 40 Length of the outfall (m) 515 Width/diameter of the outfall (m) 0.7 Riser R1 R2 R3 R4 R5 R6 R7 Sum of the effluent flow of all risers (m3/s) 0.1 0.1 0.1 0.1 0.1 0.1 0.1 Distance for each riser (m) from the offshore end of the outfall 5 10 15 20 25 30 Radius at the bottom of the riser (m) 0.35 0.35 0.35 0.35 0.35 0.35 0.35 Radius at the top of the riser (m) 0.35 0.35 0.35 0.35 0.35 0.35 0.35 Height of the riser (m) 1 1 1 1 1 1 1 Jet for each riser Jet1 Jet2 Jet3 Jet4 Jet5 Jet6 Jet7 Effluent flow from the port (m3/s) 0.1 0.1 0.1 0.1 0.1 0.1 0.1 Port diameter (m) 0.7 0.7 0.7 0.7 0.7 0.7 0.7 Port height (m) 1 1 1 1 1 1 1 Vertical angle (90o for a vertical port) 30 30 30 30 30 30 30 Horizontal angle (90o for crossflow) 90 90 90 90 90 90 90 Effluent salinity (ppt) 37 37 37 37 37 37 30 Effluent temperature (oC) 40 40 40 40 40 40 40

Table 4.3: VISJET input parameters for a multiport diffuser for Scenario I

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Near field model (VISJET)

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Multiport Diffuser

4.2.1 Scenario I: Heated brine discharges The group of jets rises to the surface from a multiport diffuser discharge

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Near field model (VISJET)

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4.2.2 Scenario I I: Dense brine discharges The group of jets sinks to the seabed from a multiport diffuser discharge

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Near field model (VISJET)

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The horizontal plane view of Figure 4.10 Not overlapping plumes

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Comments or questions

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