This document describes a CFD model developed to simulate circulation patterns and temperature distribution in Lake Binaba, a small and shallow reservoir in Ghana. The model aims to predict heat storage and evaporation. It uses OpenFOAM to solve equations of motion and heat transfer over the lake's complex bathymetry under wind and atmospheric conditions. Results show velocities, heat fluxes at the surface, temperature profiles, and total heat storage over time. The CFD model provides a valuable tool for understanding small and shallow lakes.

1. Introuduction
Lake Binaba
CFD Model
Conclusion
CFD Modeling of Shallow and Small Lakes
Ali Abbasi
Nick van de Giesen
Delft University of Technology
Water Resources Management
February 13, 2014
1 / 24

2. Introuduction
Lake Binaba
CFD Model
Conclusion
Aims of the study
Outline
1
Introuduction
Aims of the study
2
Lake Binaba
Description
Why 3D-CFD Model?
3
CFD Model
CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
4
Conclusion
Conclusion
2 / 24

3. Introuduction
Lake Binaba
CFD Model
Conclusion
Aims of the study
Aims of the study
The following goals are considered:
To develop a three-dimensional time-dependent hydrodynamic
and heat transfer model(CFD model)
Simulating the effects of wind and atmosphere conditions over a
complex bathymetry.
To predict the circulation patterns as well as the temperature
distribution in the water body.
To estimate total heat storage of small and shallow
lakes(reservoirs) in order to estimate evaporation from water
surface.
3 / 24

4. Introuduction
Lake Binaba
CFD Model
Conclusion
Description
Why 3D-CFD Model?
Outline
1
Introuduction
Aims of the study
2
Lake Binaba
Description
Why 3D-CFD Model?
3
CFD Model
CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
4
Conclusion
Conclusion
4 / 24

5. Introuduction
Lake Binaba
CFD Model
Conclusion
Description
Why 3D-CFD Model?
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 the
provision 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
5 / 24

6. Introuduction
Lake Binaba
CFD Model
Conclusion
Description
Why 3D-CFD Model?
Location
Lake Binaba:
Figure: Location of lake Binaba
6 / 24

7. Introuduction
Lake Binaba
CFD Model
Conclusion
Description
Why 3D-CFD Model?
Location
Lake Binaba:
Figure: Location of lake Binaba(Google earth)
7 / 24

8. Introuduction
Lake Binaba
CFD Model
Conclusion
Description
Why 3D-CFD Model?
Why 3D-CFD Model?
Using 3D-CFD Model for shallow lakes:
Inalnd water bodies such as lakes and reservoirs are very
important parts of the continental land surface.
Understanding the heat storage in lakes and reservoirs is essential
to estimate evaporation in energy budget methods.
Small and shallow lakes response to atmospheric conditions very
fast.
Accurate estimation of the heat transfer between the atmosphere
and water is extremely important to model the temperature
dynamics and stratification in the lakes.
1-D & 2-D models are not able to consider horizontal advection
term in morphometrically complex lakes and reservoirs
8 / 24

9. Introuduction
Lake Binaba
CFD Model
Conclusion
CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
Outline
1
Introuduction
Aims of the study
2
Lake Binaba
Description
Why 3D-CFD Model?
3
CFD Model
CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
4
Conclusion
Conclusion
9 / 24

10. CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
Introuduction
Lake Binaba
CFD Model
Conclusion
CFD Work Flow
��� ���������� ��������
��������
�������
���� �����
�����������
������
�����
�����������
������
���������
��������
��������
�������������
������������ ������
��������
��������
������
��������
������
�����
������ ���������
������
�����
������
�������
����
������
������
������
��������
������
� �������������
����������
��������� �������� ��������� ��� ��� ���� ������ ����������������������� �� �����
����������� ����������������� � ���� �� ��� ���� ���� ����������� �����
10 / 24

11. Introuduction
Lake Binaba
CFD Model
Conclusion
CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
Geometry
The starting point for all problems is a “geometry”.
Figure: Geometry of lake using in CFD model(V.S:100)
11 / 24

12. Introuduction
Lake Binaba
CFD Model
Conclusion
CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
Equations
Continuity equation(mass is conserved):
∂uj
=0
∂xj
(1)
Momentum equations using Boussinesq approach
∂ui
∂
∂
∂ui ∂uj
+
(uj ui ) −
νef f
+
∂t
∂xj
∂xj
∂xj ∂xi
∂p
=−
+ gi [1 − β(T − Tref )]
∂xi
−
2
3
∂uk
∂xk
δij
(2)
Temperature(energy is conserved) in the water body
∂T
∂
∂ ∂T
+
(T uj ) − κef f
(
) = ST
∂t
∂xj
∂xk ∂xk
(3)
12 / 24

13. Introuduction
Lake Binaba
CFD Model
Conclusion
CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
Equations
In the model, for incompressible flows the density is calculated as
a 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
ηI0 exp(−ηz ∗ )
ρ0 Cp
(5)
This function allows the radiation to be absorbed through a finite
distance in the upper layers of the model water column rather
than only at the air-water interface.
13 / 24

14. Introuduction
Lake Binaba
CFD Model
Conclusion
CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
Boundary Conditions
Wind over water surface affects lake currents, sensible and latent
heat 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):
ρ0 Cp κef f
∂T
∂z
= Hnet
(8)
surf
Hnet = HLA + HLW + HS + HE
(9)
14 / 24

15. Introuduction
Lake Binaba
CFD Model
Conclusion
CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
OpenFOAM
OpenFOAM: Open Source Field Operation and
Manipulation
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 to
1000 cores)
15 / 24

16. Introuduction
Lake Binaba
CFD Model
Conclusion
CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
Results
Figure: Bathymetry of Lake Binaba
16 / 24

17. Introuduction
Lake Binaba
CFD Model
Conclusion
CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
Results
Figure: Simulated velocity in the lake(t=3930 sec)
17 / 24

18. CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
Introuduction
Lake Binaba
CFD Model
Conclusion
Results
350
minHlat
maxHlat
aveHlat
300
-2
Latent Heat Flux[Wm ]
250
200
150
100
50
0
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
Time(s)
Figure: Calculated latent heat flux over water surface(simple case)
18 / 24

19. CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
Introuduction
Lake Binaba
CFD Model
Conclusion
Results
30
minHS
maxHS
aveHS
25
20
-2
Sensible Heat Flux[Wm ]
15
10
5
0
-5
-10
-15
-20
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
Time(s)
Figure: Calculated sensible heat flux over water surface(simple case)
19 / 24

20. CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
Introuduction
Lake Binaba
CFD Model
Conclusion
Results
0
minHnet
maxHnet
aveHnet
-50
-2
Net Heat Flux[Wm ]
-100
-150
-200
-250
-300
-350
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
Time(s)
Figure: Calculated net heat flux over water surface(simple case)
20 / 24

21. Introuduction
Lake Binaba
CFD Model
Conclusion
CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
Results
9.75e+15
SumHStorage
9.7e+15
9.65e+15
Heat Storage[J]
9.6e+15
9.55e+15
9.5e+15
9.45e+15
9.4e+15
9.35e+15
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
Time(s)
Figure: Calculated heat storage of water body (simple case)
21 / 24

22. Introuduction
Lake Binaba
CFD Model
Conclusion
Conclusion
Outline
1
Introuduction
Aims of the study
2
Lake Binaba
Description
Why 3D-CFD Model?
3
CFD Model
CFD Work Flow
Geometry
Solving
Using OpenFOAM
Results and Post-processing
4
Conclusion
Conclusion
22 / 24

23. Introuduction
Lake Binaba
CFD Model
Conclusion
Conclusion
Conclusion
Computational fluid dynamics (CFD) analysis has proven to be a
valuable design tool in the water resources
Modelling is one of the best means to gain understanding of
complex flow fields
Wind over water surface affects lake currents, sensible and latent
heat fluxes
Buoyancy effect due to density gradiant in water body should be
considered in temperature profile
23 / 24

24. Introuduction
Lake Binaba
CFD Model
Conclusion
Conclusion
Questions?
Thanks for your attention
24 / 24