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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General Information

• See handout

• See course-page:• http://www.ambiental.ufpr.br/portal/professores/tobias/teaching/hydrodynamics/

• Watch movie from Robert Long

• https://www.youtube.com/watch?v=9hmjcIfy8wE

http://www.ufpr.br/

http://www.ambiental.ufpr.br/portal/professores/tobias/teaching/hydrodynamics/

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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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Objectives

• Create the ability of critical revisions, and developing model

conceptions using existing equations for environmental systems,

related to transport phenomena including density effects.

• Be able to plan, execute and analyze physical and numerical

experiments.

• Apply measurement methods to scaled models for specific

applications (lock-exchange, internal waves, buoyant jets, ...).

Apply numerical methods for hydrodynamic models.

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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, modeling

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DEFINITION AND EXAMPLES

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Definition

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

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Definition


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Definition


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Mixing


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Source: IfH, KIT

Stratification and instability• Even miscible fluids (same fluid, but different concentrations --> different density)

can be stably stratified

• Grid-stirred turbulence in two-layer system

Z (depth or elevation)

ρ (density)

ρ(z)

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Source: IfH, KIT

Z (depth or elevation)

ρ (density)

ρ(z)

Stratification and instability• Even miscible fluids (same fluid, but different concentrations --> different density)

can be stably stratified

• Grid-stirred turbulence in two-layer system

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Source: seafriends.org.nz

Examples: Wind induced mixing

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Source: waterontheweb.org

Examples: Environmental consequences

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www.bleninger.infoExamples: Environmental consequences,

nutrient cycles

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www.bleninger.infoExamples: Environmental consequences,

carbon cycles

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www.bleninger.infoReservoir profile measurements:

Vossoroca Reservoir, Curitiba, Brazil

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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25d

ep

th [

m]

T [°C], DO [mg/l], Cond/10 [µS/cm]

T [°C] - 14.04.10

T [°C] - 08.06.10

DO [mg/l] - 14.04.10

DO [mg/l] - 08.06.10

Cond/10 [µS/cm] -14.04.10

Cond/10 [µS/cm] -08.06.10

CO2 (mg/L) - 08.06.10

CO2 [mg/l] - 14.04.10

bed

Multiparameter probe

(Horiba)

Dissolved gas probe

(Franatech)

CTD – Conductivity, Temperature, Depth

(SONTEK)

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Instability needs triggers and/or external forcings

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0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

Em

isão

Hid

ráu

lica/t

erm

elé

tric

a a

Gás

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Source: Cardoso, 2011

Relative emissions from Brazilian reservoirs

Measured gas emissions / equivalent emission from

gas fired thermal power plant over lifetime

Stratification is key issue

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Examples: Coastal waters

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Examples: Density driven circulation!

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Examples:

Coastal currents are density driven flows

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www.bleninger.infoDensity currents: Flow induced ONLY by

density diferences, no other forcings

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www.bleninger.infoExamples

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Density currents

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www.bleninger.infoActive mixing: Jets and plumes

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www.bleninger.infoActive mixing: Jets and plumes

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www.bleninger.infoPapermill discharge in Rhine River:

heated discharge with substances

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www.bleninger.infoBrine discharge from desalination plant:

Salty (dense) effluent spreading on seabed

Barka RO Plant, Oman

Lab study of submerged dense discharge

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17 km

Related Environmental modeling

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Enseada

Santos

Praia Grande 1

Praia Grande 2

Sewage Outfalls at São Paulo Coast

Municipality Population Collect Treatment

Santos/S.Vincete

Praia Grande

856.726

562.376

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Guarujá 432.586 55 55

Fonte: Brambilla, SABESP

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www.bleninger.infoDrinking water storage tanks

Roberts, 2005

Stadtwerke Karlsruhe

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▪ Behälter vollständig aus Glas, Maßstab 1:10 (Natur: 8,2 x 6,1 x 4 m³)

Zugabe

Entnahme

Zugabe

Entnahme

Drinking water storage tanks:

Lab studies

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➢ Colder water stratifies

➢ Changes residence times → influences desinfection calculations and operation

Drinking water storage tanks:

Lab studies, filling process

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intake

outfall

Wastewater Treatment settling tank (source: www.HydroGrav.de)

Waste water treatment and reuse:

Settling tanks, separation processes

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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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GOVERNING EQUATIONS

- EQUATION OF STATE

- HYDROSTATICS

- HYDRODYNAMICS

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Mixing, equation of state


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Mixing, equation of state


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Hydrostatics


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Hydrostatics


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Stratified flow parameters


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Stratified flow parameters: disturbance vs. damping


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Example: Lake mixing regimes


Characteristic velocity: Wind induced mixing

Characteristic density variation: hypolimnion - epilimnion

Characteristic length: depth of mean density

Lake Richardson number:

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Example: Lake mixing regimes


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Hydrodynamics


→ Mass conservation equation does not change when considering density variations

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Hydrodynamics


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Hydrodynamics: Approximations and simplifications

Boussinesq Approximation• From Euler equation (previous slide)


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Hydrodynamics: Approximations and simplifications


Used for internal wave solutions and models• Not covered further here

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

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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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Thank you

[email protected]

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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