HYDRODYNAMICS OF ENVIRONMENTAL AQUATIC SYSTEMS · 1 Tobias Bleninger Universidade Federal do Paraná (UFPR) Departamento de Engenharia Ambiental (DEA) HYDRODYNAMICS OF ENVIRONMENTAL

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Tobias Bleninger

Universidade Federal do Paraná (UFPR)

Departamento de Engenharia Ambiental (DEA)

www.bleninger.info

HYDRODYNAMICS OF

ENVIRONMENTAL AQUATIC SYSTEMS

Tobias Bleninger, Michael Mannich

http://www.ufpr.br/

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Tobias Bleninger



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References

Course script:

• Gerhard Jirka: “Stratified Flows”

Further reading:

• Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”,

Additional articles on experiments and modeling

Suggested reference books:

• Fernando, H. J. S. (2013) Handbook of Environmental Fluid Dynamics. Volumes 1 and 2. Boca

Raton, FL: CRC Press, Taylor & Francis.

• Fischer, H.B., List, E.G., Koh, R.C.Y., Imberger, J. & Brooks, N.H. (1979), Mixing in Inland and

Coastal Waters, Academic Press, New York, NY.

• Hemond, H. F. & Fechner-Levy, E. J. (2000), Chemical Fate and Transport in the Environment,

Academic Press, San Diego, CA.

• Kundu, P.K. & Cohen, I.M. (2002), Fluid Mechanics, 2nd Edition, Academic Press, San Diego,

CA.

• Rutherford, J.C. (1994), River Mixing, John Wiley & Sons, Chichester, England./li>

Suggested Conference series: ISSF - International Symposium on Stratified Flows (IAHR)

http://www.ufpr.br/

https://docs.ufpr.br/~bleninger/arquivos/hidrodinamica/script_stratified_flow.pdf

https://ceprofs.civil.tamu.edu/ssocolofsky/CVEN489/Downloads/Book/Socolofsky_Jirka.pdf

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Content

• Definition of Stratified Flows

• Revision of equations for 1, 2 and 3D considerations

• Governing equations including density effects

• Hydrostatics

• Hydrodynamics

• Approximations and simplifications

• Solutions and applications for stratified flows

• Example of lock-exchange: theory, laboratory

• Modelling applications

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Summary of definition and examples

• Density changes may drive flows

• Density gradients damp or drive flows

• Density variations are all around environmental

systems and technical installations

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Tobias Bleninger



www.bleninger.infoSummary of governing equations

• Density variations in the environment are small (~ 2%)

• Equation of state defines density as function of Temperature and Salinity

• Important non-dimensional numbers: Richardson and Froude, using g´

• Momentum equation becomes more complicated

• Flow (disturbances) can change density distribution → changing flow and conc.

• Density changes may drive flows

• Momentum equ. needs to be coupled to transport equation for heat and salinity

• Full solution of equations only possibly numerically (next course) or for

simplified conditions (as follows) or by physical modelling (as follows):

• No friction or simplified considerations of friction

• Boussinesq appr. (small density variations, only considered in gravity term)

• Small amplitude motions

• Usually for 2 layer systems

• → Screening anlysis, Benchmark for models, Process understanding

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Examples

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MODELLING APPLICATIONS

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www.bleninger.infoProjeto de Modelagem Computacional em uma

Empresa de Consultoria

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U(t)

A(z)

Qin (t) Qout (t)

q(t)

Ta(t)

z(m)

g

T(°C)

z(m

)

ρ (kgm-3)

ρ (kgm-3)

T(°C)

a

Meterological conditions (forcings)

In and outflow (forcings)

Figura 1.a) Principais parâmetros do transporte de calor, com vazões pequenas de entrada e saída

Thermal stratification in lakes

Source: Bruna Polli, Ph.D. thesis, PPGERHA

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Tobias Bleninger



www.bleninger.infoModelagem de transporte de calor


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Heat transport modeling

Is a complex modelnecessary to representthe system and periodsof interest?

Is it possible to simplifymodel representation?

Sector Model

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Graduate Program in Water Resources and Environmental Engineering– PPGERHAFederal University of Paraná


Methods: numerical modeling

• 1D: MTCR-1

• 1D in different points

• 3D: Delft3D

• Sector model

– MTCR-1 with connection

– Delft3D with sectors

12Graduate Program in Water Resources and Environmental Engineering– PPGERHAFederal University of Paraná

z(m)

Sector 1

Sector 2

U(t)Ta(t)

g

s(m)

nzp qz

TEc −=

nzp q

z

TEc −=

0=

z

T

0=

z

T

Qin

Tin

Qout

T

Sectors exchange

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Input data

• Meteorological data

• In/Outflow and temperature

• Reservoir information

• IC

MTCR-1 Model

• Implicit finite volume

• Fortran 95

• Vossoroca: Δz = 0.20 m e Δt = 120 s

• Vossoroca model – error: 0.26±1.42°C (Polli, 2014)

BC

Modeling: MTCR-1 Model

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Sector Model

And if temperature profiles in more than one point are

needed?


Numerical schemes

Modeling: Sector Model

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Shallow

MTCR-1a MTCR-1bMTCR-1cMedium

Deep

deepshallow medium

Figure 33 – Scheme showing regions of Vossoroca reservoir with different depths

Figure 34 – Scheme showing the approach to the Vossoroca reservoir sector model. a) Side view of the sectors and b) flows and exchange in each sector


+ turbulence model+ heat flux model

Modelo 3D: Delft3D-FLOW

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Data entry

• Met. data

• Inflow and temperature

• bathymetry

• Initial condition

1D: MTCR-1

• Finite volume

• Fortran 95

• Vossoroca: Δz = 0.20 m e Δt = 120 s

BCModel 1D: MTCR-1


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+ turbulence model + heat transfer model

Model 3D: Delft3D-FLOW


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www.bleninger.infoStudy area: Vossoroca reservoir

• São João river (56%,

main inflow)

• São Joãozinho river

(28%)

• Vossoroca river (16%)

Area: 3.3 km2

Volume: 35.7 106

m3

Maximum depth: 17 m

Mean depth: 8 m

Residence time: 117

days

• Constructed in 1949;

• Monomictic reservoir;

• Function is to regulate the flow to Chaminé hydropower plant (18 MW);


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Graduate Program of Water Resources and Environmental Engineering

(PPGERHA) http://www.prppg.ufpr.br/ppgerha/

Federal University of Paraná

Measurements: floating platform

Between 2012-2016:

• 7 temperature sensors

• 1, 3, 5, 7, 9, 11 m and

bottom )

• Resolution: 15 min


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Tobias Bleninger



www.bleninger.infoMeasurements: floating platform

Model period with 3D

modeling

• Between July and October

2012

Mean surface temperature= 17.68°C

Mean bottom temperature=14°CSource: Bruna Polli, Ph.D. thesis, PPGERHA

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Measurements: meteorological weather

station

0

5

10

U (

ms-1

)

0

20

40

Ta (

ºC)

0

50

100

UR

(%

)

0

1000

2000

02/06/20

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22/06/20

12

13/07/20

12

03/08/20

12

24/08/20

12

14/09/20

12

05/10/20

12

25/10/20

12

15/11/20

12

06/12/20

12

27/12/20

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17/01/20

13

07/02/20

13

27/02/20

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qs

(Wm

-2)

a

b

d

c

• Resolution: 2 min

• Since 2012

Since 2015: water level and

temperature are measured in São

João river


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Tobias Bleninger



www.bleninger.infoResults: 1D model (Vossoroca)

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Graduate Program in Water Resources and Environmental Engineering–

PPGERHA


• Effects of including bathymetry (Stepanenko et al., 2014) and no inflows/outflows =>

temperature increases faster in deeper layers

• Effects of including bathymetry+inflows/outflow in this Thesis => temperature in deeper

layers decreases faster: a solution?

How the model distributes the inflow?

MTCR-1 modified

RE = 0.21±1.44°C

MAE=1.18±0.84°C


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Tobias Bleninger



www.bleninger.infoResults: Sector model

No exchange With exchange

RE = 0.54±1.53°C

MAE=1.22±1.07°C

RE = 0.17±1.46°C

MAE=1.16±0.90°C

Sector 3

Shallow Shallow

Medium Medium

Deep Deep

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PPGERHA



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Tobias Bleninger



www.bleninger.infoResults: Sector model modified (Vossoroca)

No exchange

ShallowShallow

MediumMedium

DeepDeep

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PPGERHA


With exchange

Temperature in deeper layers

decreases slower

=> Error

Using a system of reactors

for the exchange, MAE

increased:

1.10±0.99°C


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www.bleninger.infoComparison: Measurements x 1D x 3D

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PPGERHA



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www.bleninger.infoResults: Vossoroca 3D model as a sector model

z=4 m

z=8 m

z=14 m

z=14 m

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PPGERHA



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www.bleninger.infoResults: Sector model analysis

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Tobias Bleninger



www.bleninger.infoResults: tracer transport modeling

• Added conservative tracer

• continuous flow and concentration (river and side arm)

• Mass transport due to changes in temperature

• Quantification: cumulative advective

and dispersive transport

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PPGERHA



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Results: river tracer modeling

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PPGERHA



http://www.ufpr.br/

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www.bleninger.infoResults: side arm tracer modeling

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PPGERHA



http://www.ufpr.br/

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www.bleninger.infoConclusions

1. Measurements showed vertical and horizontal variations in the reservoirs measured

2. Simplified models (1D or 1D/3D sectors) can be used for classification and stratification analysis

(complements 3D modeling)

3. Significant horizontal mass transport due to differential cooling/heating (river and side arms), but

necessary a 3D model

4. 3D model captures and quantifies such features

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PPGERHA



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Graduate Program of Water Resources and Environmental Engineering

(PPGERHA) http://www.prppg.ufpr.br/ppgerha/


Velocity

15-Aug-2012

14:00:00


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Tobias Bleninger



www.bleninger.infoTemperature gradients comparison

ΔT= Tsurface – Tbottom

Measured

data=3.38°C

1D Model=2.09°C

3D Model=3.24°C

Days: Measurement

s

1D

Model

3D

Model

ΔT>1°C 79 49 79

ΔT>2°C 61 42 61

ΔT>3°C 53 25 51

*From 94 daysSource: Bruna Polli, Ph.D. thesis, PPGERHA

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Thank you

[email protected]

www.bleninger.info

http://www.ufpr.br/

Documents

HYDRODYNAMICS OF ENVIRONMENTAL AQUATIC SYSTEMS · 1 Tobias Bleninger Universidade Federal do Paraná (UFPR) Departamento de Engenharia Ambiental (DEA) HYDRODYNAMICS OF ENVIRONMENTAL