tobiasbleninger mecÂnica dos fluidos …bleninger/arquivos/mecflui/8-experimentos.pdf · 1 tobias...

1

Tobias Bleninger

Universidade Federal do Paraná (UFPR)

Departamento de Engenharia Ambiental(DEA)

www.tobias.bleninger.info

MECÂNICA DOS FLUIDOS

AMBIENTAL I

Tobias Bleninger

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Tobias Bleninger




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Tobias Bleninger




Todos métodos requerem

1. Entendimento dos processos e fenômenos

(descrição qualitativa)

2. Descrição quantitativa (física / modelagem)

3. Solução (matemática)

4. Interpretação

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Tobias Bleninger




Laboratorio didático de mecânica dos fluidos

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Tobias Bleninger




Medições de velocidades com ADV

(Acoustic Doppler Velocimeter)

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Fonte: www.sontek.com

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Tobias Bleninger




Fonte: www.sontek.com



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Tobias Bleninger






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R = 0,67

R = 0,99

Perguntas a fazer

Source: http://www.tylervigen.com/

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Tobias Bleninger




Caso 1


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Tobias Bleninger





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0 20 40 60 80 100 120 140-10

-5

0

5

10

15

20

time [s]

velo

city [

cm

/s]

u

v

w

Series temporais

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Tobias Bleninger




0 20 40 60 80 100 120 140-10

-5

0

5

10

15

20

time

velo

city [

cm

/s]

u

v

w

-10 -5 0 5 10 15 200

200

400

600

velocity [cm/s]

frequencia

u-velocity

-10 -5 0 5 10 15 200

200

400

600

velocity [cm/s]

frequencia

v-velocity

-10 -5 0 5 10 15 200

200

400

600

velocity [cm/s]

frequencia

w-velocityDirection Mean [cm/s] std median varianca

u 9.6614 2.3859 9.5500 5.6925

v 0.7440 2.0750 0.7300 4.3058

w -0.5636 1.0668 -0.5000 1.1381

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Tobias Bleninger




0 20 40 60 80 100 120 1400

2

4

6

8

10

12

14

16

18

20

time

velo

city [

cm

/s]

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Tobias Bleninger




0 20 40 60 80 100 120 140-10

-5

0

5

10

15

20

time

velo

city [

cm

/s]

u

v

w

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Tobias Bleninger




Source:

Wernher Brevis, University of Sheffield

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0 20 40 60 80 100 120 1400

5

10

15

20

time

velo

city

[cm

/s]

cumulative mean

0 20 40 60 80 100 120 1408

10

12

14

16

cumulative mean

totalmean

0 20 40 60 80 100 120 140-2

0

2

4

6

cumulative mean-totalmean

-5.2620e-4-0.0030-0.0178

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Tobias Bleninger




0 20 40 60 80 100 120 140-10

-5

0

5

10

15

20

time

velo

city [

cm

/s]

u

v

w

-10 -5 0 5 10 15 200

200

400

600

velocity [cm/s]

frequencia

u-velocity

-10 -5 0 5 10 15 200

200

400

600

velocity [cm/s]

frequencia

v-velocity

-10 -5 0 5 10 15 200

200

400

600

velocity [cm/s]

frequencia

w-velocity

Direction Mean [cm/s] std median varianca

u 9.6614 2.3859 9.5500 5.6925

u-mean 0 2.3859 -0.1114 5.6925

v 0.7440 2.0750 0.7300 4.3058

v-mean 0 2.0750 -0.0140 4.3058

w -0.5636 1.0668 -0.5000 1.1381

w-mean 0 1.0668 0.0636 1.1381

-10 -5 0 5 10 15 200

200

400

600

velocity [cm/s]

frequencia

u-velocity

-10 -5 0 5 10 15 200

200

400

600

velocity [cm/s]

frequencia

v-velocity

-10 -5 0 5 10 15 200

200

400

600

velocity [cm/s]

frequencia

w-velocity

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Direction Mean [cm/s] std median varianca

u 9.6614 2.3859 9.5500 5.6925

u-mean 0 2.3859 -0.1114 5.6925

v 0.7440 2.0750 0.7300 4.3058

v-mean 0 2.0750 -0.0140 4.3058

w -0.5636 1.0668 -0.5000 1.1381

w-mean 0 1.0668 0.0636 1.1381

0 20 40 60 80 100 120 140-10

-5

0

5

10

15

time

velo

city f

luctu

ations [

m/s

]

u´

v́

w´

Flutuacoes

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Tobias Bleninger




Flutuações

-10 -5 0 5 10

-8

-6

-4

-2

0

2

4

6

8

10

v́

w´

-10 -5 0 5 10

-8

-6

-4

-2

0

2

4

6

8

10

x´

w´

-10 -5 0 5 10

-8

-6

-4

-2

0

2

4

6

8

10

u´v´

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Tobias Bleninger




Causa

Vórtices• no escoamento com estruturas dominantes/coerentes

Flutuações• = Oscilações?

• Analise estatística usando series e transformadas de Fourier

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Tobias Bleninger






Fonte: http://www.usbr.gov/pmts/hydraulics_lab/twahl/winadv/wadv-ex.html

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Perfil de velocidade

Fonte: Jirka e Lang, 2009

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Tobias Bleninger




Flutuações turbulentas

Jirka and Lang, 2009

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Tobias Bleninger




Visualização do escoamento e processos de mistura

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U = average velocitylarge river B/h > (5 - 10)

0 u ghIρ

h

B

l, u*

lgroße

Wirbel

B) Turbulent Diffusion in river

u* = , Friction velocity,

typical u* = (0,05 – 0,1)U

ghI

▪ Eddy generation due to roughness:

0 = ghsin ghI

I = slope sin

h

B

l, u*

llarge

eddy

Turbulent▪ eddy spectrum:u´ = eddy velocity

l h = eddy size

▪ Duffusion analogy (Dm ~ mum):E h u* turbulent Diffusivity [m²/s]

E = 0,1(+/-50%) u* h for rivers

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Tobias Bleninger




▪ Vertical passive mixing (method-of-images)

Mixing if z h, then x = xMV

independent of velocity

morphology dominates!

Bsp. 1: Rhein near Karlsruhe

B = 250m, h = 3m, U = 3m/s

xMV = 70x3 = 210m ~fast!

U

xt = = „flowtime“ (Advection)

MV*

h²U h²Ux 70h

2E 2(0,07u h)

0,10U

Bsp. 2: Small river in Schwarzwald (Murg)

B = 5m, h = 0,5m

xMV = 70x0,5 = 35m ~fast!

Vertical mixing (Advection + Diffusion)

▪ vertical Diffusivity: Ez = zu*h z = 0,07 +/- 50%

▪ vertical distribution:U

x2Et2Eσ zzz

vertical mixing is fast process!

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Tobias Bleninger




▪ Horizontal mixing (river bank)Lateral mixing if y B, x = xML

independent of velocity

morphology dominates!

h

B²10

h)2(0,5u

B²U

2E

B²Ux

*ML

0,10U

Bsp. 1: Rhein near Karlsruhe

xML 10x250²/3

= 208.000m 200km slow!

lateral mixing is slow process!

Lateral mixing (Advection + Diffusion)

Horizontal▪ Diffusivity: Ey = yu*h z = 0,5 +/- 50%

moderate heterogeneities

Horizontal▪ distribution:U

x2Eσ yy

Bsp. 2: small river in Schwarzwald (Murg)

xML 10x5²/0,5

= 500m = 0,5km

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Tobias Bleninger




University Karlsruhe

Germany

Uruguay

Rio Uruguay

Argentina

Rio de la Plata

estuary

Av. annual discharge: 23,000 m³/s

50 km

4-7 m deep

Buenos Aires:

about 15 mio. people

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Tobias Bleninger



www.tobias.bleninger.infoADCP e vento

Courtesy: Phil Roberts, Georgia Tech

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Tobias Bleninger



www.tobias.bleninger.infoPolar Scatter Diagrams of

Currents

No. 6

No. 5

No. 4

No. 3

No. 2

No. 1

N

5 km

100 cm/s


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Tobias Bleninger



www.tobias.bleninger.infoGPS

Drifters

10 Experiments each with ten drifters at surface and near bottom

GPS recorders and transmittersCourtesy: Phil Roberts, Georgia Tech

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Tobias Bleninger



www.tobias.bleninger.infoDrifter Experiment

Riachuelo2 December 2009


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Tobias Bleninger



www.tobias.bleninger.infoMathematical Model

Domains


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Tobias Bleninger



www.tobias.bleninger.infoModel Comparisons with

ADCP5August 11-18

8/11 8/16

-0.8

-0.4

0

0.4

0.8

Sp

ee

d(m

/s)

SimulatedMeasured

Second Principal Component

8/11 8/16

-0.8

-0.4

0

0.4

0.8

Sp

ee

d(m

/s)

First Principal Component


First PC

Second PC

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Tobias Bleninger



www.tobias.bleninger.infoSimulation Results – Particle Tracking Model

Nested Grid

R2B3


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tobiasbleninger mecÂnica dos fluidos …bleninger/arquivos/mecflui/8-experimentos.pdf · 1 tobias...

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