MECÂNICA DOS FLUIDOS AMBIENTAL I

Transcrição

1 1 MECÂNICA DOS FLUIDOS AMBIENTAL I

2 2

3 3 Todos métodos requerem 1. Entendimento dos processos e fenômenos (descrição qualitativa) 2. Descrição quantitativa (física / modelagem) 3. Solução (matemática) 4. Interpretação

4 4 Laboratorio didático de mecânica dos fluidos

5 5 Medições de velocidades com ADV (Acoustic Doppler Velocimeter)

6 Medições de velocidades com ADV (Acoustic Doppler Velocimeter) Fonte: 6

7 7 Medições de velocidades com ADV (Acoustic Doppler Velocimeter) Fonte:

8 8 Medições de velocidades com ADV (Acoustic Doppler Velocimeter)

9 9 Perguntas a fazer R =,67 R =,99 Source:

10 1 Caso 1 Source:

11 Source: 11

12 velocity [cm/s] 12 Series temporais 2 15 u v w time [s]

13 velocity [cm/s] frequencia frequencia frequencia u v w u-velocity time velocity [cm/s] v-velocity Direction Mean [cm/s] std median varianca u v w velocity [cm/s] w-velocity velocity [cm/s]

14 velocity [cm/s] time

15 velocity [cm/s] 2 15 u v w time 15

16 16 Source: Wernher Brevis, University of Sheffield

17 velocity [cm/s] 17 2 cumulative mean time cumulative mean totalmean cumulative mean-totalmean e

18 velocity [cm/s] frequencia frequencia frequencia frequencia frequencia frequencia u v w 6 4 u-velocity velocity [cm/s] v-velocity velocity [cm/s] w-velocity velocity [cm/s] time u-velocity Direction Mean [cm/s] std median varianca u u-mean v v-mean w w-mean velocity [cm/s] v-velocity velocity [cm/s] w-velocity 6 4 2

19 velocity fluctuations [m/s] 19 Flutuacoes 15 u v w time Direction Mean [cm/s] std median varianca u u-mean v v-mean w w-mean

20 w w v Flutuações u v x 2

21 21 Causa Vórtices no escoamento com estruturas dominantes/coerentes Flutuações = Oscilações? Analise estatística usando series e transformadas de Fourier

22 24 Medições de velocidades com ADV (Acoustic Doppler Velocimeter) Fonte:

23 25 Perfil de velocidade Fonte: Jirka e Lang, 29

24 Jirka and Lang, Flutuações turbulentas

25 Visualização do escoamento e processos de mistura 27

26 28 B) Turbulent Diffusion in river h große large Wirbel eddy l l, u * B U = average velocity Eddy generation due to roughness: = ghsin ghi I = slope sin ρ u ghi u * = ghi, Friction velocity, typical u * = (,5,1)U large river B/h > (5-1) Turbulent eddy spectrum: u = eddy velocity l h = eddy size Duffusion analogy (D m ~ m u m ): E h u * turbulent Diffusivity [m²/s] E =,1(+/-5%) u * h for rivers

27 29 Vertical mixing (Advection + Diffusion) vertical Diffusivity: E z = z u * h z =,7 +/- 5% vertical distribution: Vertical passive mixing (method-of-images) Mixing if z h, then x = x MV independent of velocity morphology dominates! σ z 2E z t x 2E MV z x U t = x = flowtime (Advection) U h²u h²u 7h 2E 2(,7u h) *,1U Bsp. 1: Rhein near Karlsruhe B = 25m, h = 3m, U = 3m/s x MV = 7x3 = 21m ~fast! Bsp. 2: Small river in Schwarzwald (Murg) B = 5m, h =,5m x MV = 7x,5 = 35m ~fast! vertical mixing is fast process!

28 Lateral mixing (Advection + Diffusion) Horizontal Diffusivity: E y = y u * h z =,5 +/- 5% Horizontal distribution: Horizontal mixing (river bank) Lateral mixing if y B, x = x ML independent of velocity morphology dominates! σ y 2E y x U moderate heterogeneities x ML B²U 2E B²U 2(,5u h) * B² 1 h,1u Bsp. 1: Rhein near Karlsruhe x ML 1x25²/3 = 28.m 2km slow! Bsp. 2: small river in Schwarzwald (Murg) x ML 1x5²/,5 = 5m =,5km lateral mixing is slow process! 3

29 Rio de la Plata estuary Rio Uruguay Av. annual discharge: 23, m³/s Uruguay Buenos Aires: about 15 mio. people 5 km 4-7 m deep Argentina University Karlsruhe Germany 31

30 32 ADCP e vento Courtesy: Phil Roberts, Georgia Tech

31 Polar Scatter Diagrams of Currents N 5 km 1 cm/s No. 1 No. 2 No. 5 No. 3 No. 6 No. 4 Courtesy: Phil Roberts, Georgia Tech 33

32 34 GPS Drifters 1 Experiments each with ten drifters at surface and near bottom GPS recorders and transmitters Courtesy: Phil Roberts, Georgia Tech

33 35 Drifter Experiment Riachuelo 2 December 29 Courtesy: Phil Roberts, Georgia Tech

34 36 Mathematical Model Domains Courtesy: Phil Roberts, Georgia Tech

35 Speed (m/s) Speed (m/s) 37 Model Comparisons with August ADCP5.8 First Principal Component Simulated Measured /11 8/16.8 Second Principal Component /11 Second PC 8/16 First PC Courtesy: Phil Roberts, Georgia Tech

36 Simulation Results Particle Tracking Model Nested Grid R2B3 Courtesy: Phil Roberts, Georgia Tech 38