1
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
HYDRODYNAMICS OF
ENVIRONMENTAL AQUATIC SYSTEMS
Tobias Bleninger, Michael Mannich
3
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
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
4
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
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)
5
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
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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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
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
7
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
DEFINITION AND EXAMPLES
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Definition
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
9
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Definition
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
10
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Definition
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
11
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Mixing
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
12
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
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)
13
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
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
14
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Source: seafriends.org.nz
Examples: Wind induced mixing
15
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Source: waterontheweb.org
Examples: Environmental consequences
16
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.infoExamples: Environmental consequences,
nutrient cycles
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.infoExamples: Environmental consequences,
carbon cycles
18
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
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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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Instability needs triggers and/or external forcings
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
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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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Source: seafriends.org.nz
Examples: Coastal waters
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Source: seafriends.org.nz
Examples: Density driven circulation!
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Source: seafriends.org.nz
Examples:
Coastal currents are density driven flows
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.infoDensity currents: Flow induced ONLY by
density diferences, no other forcings
36
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.infoExamples
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Density currents
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.infoActive mixing: Jets and plumes
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.infoActive mixing: Jets and plumes
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.infoPapermill discharge in Rhine River:
heated discharge with substances
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
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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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
17 km
Related Environmental modeling
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
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
80
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80
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Guarujá 432.586 55 55
Fonte: Brambilla, SABESP
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.infoDrinking water storage tanks
Roberts, 2005
Stadtwerke Karlsruhe
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
▪ 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
48
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
➢ Colder water stratifies
➢ Changes residence times → influences desinfection calculations and operation
Drinking water storage tanks:
Lab studies, filling process
49
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
intake
outfall
Wastewater Treatment settling tank (source: www.HydroGrav.de)
Waste water treatment and reuse:
Settling tanks, separation processes
50
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
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
51
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
GOVERNING EQUATIONS
- EQUATION OF STATE
- HYDROSTATICS
- HYDRODYNAMICS
52
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Mixing, equation of state
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
53
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Mixing, equation of state
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
54
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Hydrostatics
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
55
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Hydrostatics
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
56
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Stratified flow parameters
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
57
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Stratified flow parameters: disturbance vs. damping
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
59
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Example: Lake mixing regimes
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
Characteristic velocity: Wind induced mixing
Characteristic density variation: hypolimnion - epilimnion
Characteristic length: depth of mean density
Lake Richardson number:
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Example: Lake mixing regimes
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
61
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Hydrodynamics
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
→ Mass conservation equation does not change when considering density variations
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Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Hydrodynamics
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
63
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Hydrodynamics: Approximations and simplifications
Boussinesq Approximation• From Euler equation (previous slide)
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
64
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Hydrodynamics: Approximations and simplifications
Source: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
Used for internal wave solutions and models• Not covered further here
• Check: Socolofsky, S. A. and Jirka, G. H. (2005) “Environmental Fluid Mechanics”
65
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
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
66
Tobias Bleninger
Universidade Federal do Paraná (UFPR)
Departamento de Engenharia Ambiental (DEA)
www.bleninger.info
Thank you
www.bleninger.info
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