cfd modeling of shallow and small lakes

IntrouductionLake BinabaCFD ModelConclusion

CFD Modeling of Shallow and Small Lakes

Ali AbbasiNick van de Giesen

Delft University of TechnologyWater Resources Management

February 13, 2014

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Aims of the study

Outline

1 IntrouductionAims of the study

2 Lake BinabaDescriptionWhy 3D-CFD Model?

3 CFD ModelCFD Work FlowGeometrySolvingUsing OpenFOAMResults and Post-processing

4 ConclusionConclusion

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Aims of the study

Aims of the study

The following goals are considered:

To develop a three-dimensional time-dependent hydrodynamicand heat transfer model(CFD model)

Simulating the effects of wind and atmosphere conditions over acomplex bathymetry.

To predict the circulation patterns as well as the temperaturedistribution in the water body.

To estimate total heat storage of small and shallowlakes(reservoirs) in order to estimate evaporation from watersurface.

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DescriptionWhy 3D-CFD Model?

Outline





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Description

Lake Binaba:

Location: an artificial lake located in northern Ghana

Surface: the average area of the lake surface is 4.5 km2

Average depth: only 3 m

Maximum depth: 7 m

Usage: a small reservoir, used as a form of infrastructure for theprovision of water

Air temperature: fluctuates between 24 C and 35 C

Water surface temperature: varies from 28 C to 33 C

Climate: (semi-)arid region

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Location

Lake Binaba:

Figure: Location of lake Binaba

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Location

Lake Binaba:

Figure: Location of lake Binaba(Google earth)

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Why 3D-CFD Model?

Using 3D-CFD Model for shallow lakes:

Inalnd water bodies such as lakes and reservoirs are veryimportant parts of the continental land surface.

Understanding the heat storage in lakes and reservoirs is essentialto estimate evaporation in energy budget methods.

Small and shallow lakes response to atmospheric conditions veryfast.

Accurate estimation of the heat transfer between the atmosphereand water is extremely important to model the temperaturedynamics and stratification in the lakes.

1-D & 2-D models are not able to consider horizontal advectionterm in morphometrically complex lakes and reservoirs

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CFD Work FlowGeometrySolvingUsing OpenFOAMResults and Post-processing

Outline





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CFD Work Flow

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Geometry

The starting point for all problems is a “geometry”.

Figure: Geometry of lake using in CFD model(V.S:100)

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Equations

Continuity equation(mass is conserved):

∂uj∂xj

= 0 (1)

Momentum equations using Boussinesq approach

∂ui∂t

+∂

∂xj(ujui)−

∂

∂xj

{νeff

[(∂ui∂xj

+∂uj∂xi

)− 2

3

(∂uk∂xk

)δij

]}= − ∂p

∂xi+ gi [1 − β(T − Tref )]

(2)

Temperature(energy is conserved) in the water body

∂T

∂t+

∂

∂xj(Tuj) − κeff

∂

∂xk(∂T

∂xk) = ST (3)

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Equations

In the model, for incompressible flows the density is calculated asa linear function of temperature as:

ρk = 1 − β (T − Tref ) (4)

Incoming shortwave radiation is included in the source term(ST ).

ST (z∗, t) =1

ρ0CpηI0 exp(−ηz∗) (5)

This function allows the radiation to be absorbed through a finitedistance in the upper layers of the model water column ratherthan only at the air-water interface.

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Boundary Conditions

Wind over water surface affects lake currents, sensible and latentheat fluxes.

Shear Stress BC(U):

τsurf,u = ρ0

((νt + ν)

∂u

∂z

)(6)

τsurf,v = ρ0

((νt + ν)

∂v

∂z

)(7)

For Temperature, the water surface temperature is not needed.

Using a mixed(implicit) BC (T):

ρ0Cp

(κeff

∂T

∂z

)surf

= Hnet (8)

Hnet = HLA +HLW +HS +HE (9)

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OpenFOAM

OpenFOAM: Open Source Field Operation andManipulation

Open-Source Library

Free of Charge

Running in LINUX OS

C++ Library

Linking with PYTHON

New solvers and BCs can be implemented by the user

Running in parallel on distributed processors(tested for up to1000 cores)

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Results

Figure: Bathymetry of Lake Binaba

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Results

Figure: Simulated velocity in the lake(t=3930 sec)

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Results

0

50

100

150

200

250

300

350

0 20000 40000 60000 80000 100000 120000 140000 160000 180000

Late

nt H

eat F

lux[W

m-2

]

Time(s)

minHlat

maxHlat

aveHlat

Figure: Calculated latent heat flux over water surface(simple case)

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Results

-20

-15

-10

-5

0

5

10

15

20

25

30

0 20000 40000 60000 80000 100000 120000 140000 160000 180000

Sensib

le H

eat F

lux[W

m-2

]

Time(s)

minHS

maxHS

aveHS

Figure: Calculated sensible heat flux over water surface(simple case)

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Results

-350

-300

-250

-200

-150

-100

-50

0

0 20000 40000 60000 80000 100000 120000 140000 160000 180000

Net H

eat F

lux[W

m-2

]

Time(s)

minHnet

maxHnet

aveHnet

Figure: Calculated net heat flux over water surface(simple case)

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Results

9.35e+15

9.4e+15

9.45e+15

9.5e+15

9.55e+15

9.6e+15

9.65e+15

9.7e+15

9.75e+15

0 20000 40000 60000 80000 100000 120000 140000 160000 180000

Heat S

tora

ge[J

]

Time(s)

SumHStorage

Figure: Calculated heat storage of water body (simple case)

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Conclusion

Outline





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Conclusion

Conclusion

Computational fluid dynamics (CFD) analysis has proven to be avaluable design tool in the water resources

Modelling is one of the best means to gain understanding ofcomplex flow fields

Wind over water surface affects lake currents, sensible and latentheat fluxes

Buoyancy effect due to density gradiant in water body should beconsidered in temperature profile

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Conclusion

Questions?

Thanks for your attention

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cfd modeling of shallow and small lakes

Design

dcfd model

geometry of lake

cfd modelv

location lake binaba

description lake binaba

lake surface

model water column

lake currents