MATEMÁTICA APLICADA I

Transcrição

1 1 MATEMÁTICA APLICADA I

2 Coupling case study Cartagena outfall (Colombia) 2 Cartagena Source: World Bank

3 3 Cartagena - water quality problems inhabitants: 1 mio. sewer connection: 60 % ww-treatment: preliminary / none ww-discharge: bay or nearshore high bacterial pollution at open sewers and nearshore waters strong health impacts (i.e.high child mortality) Masterplan (240 mio. US$) improving: sewer system (80 km) treatment (primary) discharge: long outfall (25 mio. US$) N 10 km Boca Grande Bahía de Cartagena Outfall Manzanillo del Mar La Boquilla Punta Canoa Cienega de Tesca Cartagena Planta de Tratamiento Arroyo de Piedra Tierra Baja Puerto Bay Estación de Bombeo Paraíso Source: World Bank Santos Bay, Brazil

4 4 Available field data Three year hourly data: Water levels (3 locations) weak tides (approx. +/- 0.5 m) Density profiles (planned outfall location) mostly uniform, weak temperature stratification in upper layer ( 5 m) Wind measurements (Cartagena Airport) mainly north-northeast, average 5 m/s Current profiles (planned outfall location) mainly north-northeast, parallel to coast, average 0.4 m/s mostly fully mixed logarithmic profile with strong surface velocities correlation with large-scale circulation (ELCOM model)

5 5 BC - measured currents Punta Canoas for February 1998

6 6 BC - Measured currents at Punta Canoas February 1998 Santos Bay, Brazil

7 Delft 3D - Hydrodynamic modeling B.C.: unsteady currents (logarithmic) (merged ELCOM and measurements) density profile B.C.: unsteady water levels (tidal measurments) density profile B.C. (surface): free surface (sigma layer) unsteady, uniform wind shear B.C.: closed boundary 10,000 cells in horizontal 13 layers in vertical 10 h calculation time for 1 month simulation B.C. (bottom): bed stress (quadratic formulation) 25 km 7

8 Delft3D - Hydrodynamic model results 8

9 Delft3D - Hydrodynamic model results 9

10 Delft3D - Hydrodynamic model results 10

11 Delft3D - Hydrodynamic model results 11

12 12 Results: bacteria concentration distributions Depth averaged total coliform concentration (C o = MPN/m³) [MPN / m³] km Bathing water standard 10 6 How to decide regarding discharge permit? 0

13 Results Bathing water standard: 10 7 counts / m³ = 10 3 counts / 100 ml How to decide regarding discharge permit? Modeled depth averaged concentration [MPN / m³] of total coliforms for February 98 13

14 14 Delft3D - WAQ results Exceedance frequency of water quality standard at coast: 4 % for worst case month e.g. WHO, or California: total coliforms at bathing waters should not exceed 1000 MPN / 100ml at 95 or 80 % of the time Exceedance frequency of total coliforms exceeding 1000 MPN / 100 ml for the surface layer (0.4 m thickness) for the month February 1998

15 15 Risk analysis Exceedance of standard at 5 % of time Mean concentration exceeds standard

16 16 Laboratorio: jato denso em escoamento (vista lateral)

17 17 Laboratory visualization: Dense jet with crossflow (top view)

18 18 Laboratorio: jato denso em escoamento Vista lateral angulo vertical da descarga Vista planta

19 19 JET REGION: CorJet: Buoyant Jet Integral Model, part of CORMIX system See reviews for validation: Jirka (2004), Env. Fluid Mech., 4,1-56 single jet Jirka (2006), Env. Fluid Mech., 6, multiport jets Definition sketch for three-dimensional buoyant jet discharge into ambient flow with global and local coordinate system, respectively ambient stratification a (z) non-linear density / temp. / salinity ambient current u a (z) with skew angle a (z) Ekman profile Gaussian profiles jet width b (e -1 width) dispersion ratio

20 20 CorJet: Buoyant Jet Integral Model Conservation equations dq E ds d M 2 2 cos cos Eu a F D 1 cos cos ds d M cos sin FD ds 2 cos sin cos cos cos d M 2 2 sin b g c F ds D sin cos cos cos cos dj ds g d a Q sin dz ref dq c ds 0 dx cos cos, dy cos sin, dz sin ds ds ds

21 21 Região do jato: CorJet: Buoyant Jet Integral Model, part of CORMIX system 10 See reviews for validation: Jirka (2004), Env. Fluid Mech., 4,1-56 single jet Jirka (2006), Env. Fluid Mech., 6, multiport jets

22 22 Rotacao da Terra