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Sveučilište u Zagrebu Vizualni identitet Priručnik grafičkih standarda za oblikovanje vizualnih identiteta sastavnica Znak Sveučilišta Verzija 2 c/b pozitiv 2.2. Crno – bijeli pozitiv znaka Sveučilišta u Zagrebu (verzija 2) standardno je reproduciran u crnoj boji Pantone Black, odnosno njenom cmyk ekvivalentu. Detaljne specifikacije nalaze se u poglavlju Program boja Priručnika grafičkih standarda za oblikovanje vizualnih identiteta sastavnica. Validation of the model is carried out on a 140◦ channel test cases with movable sand bed. -0.05 -0.05 -0.1 -0.1 -0.15 -0.2 -0.25 -0.25 -0.5 0 x [m] 0.5 -0.3 -1 1 y [m] D x / B = 7.65 0 -0.05 -0.05 -0.1 -0.1 -0.15 -0.2 -0.25 -0.25 0 x [m] 0.5 -0.3 -1 1 0 -0.05 -0.05 -0.1 -0.1 -0.15 -0.2 -0.25 -0.25 0.5 -0.3 -1 1 Bed-load transport vector is directly coupled with the Exner equation. Flow and Sediment Transport in a 140◦ Channel With a Mobile Bed -0.05 -0.05 -0.1 -0.1 -0.15 -0.2 -0.2 -0.25 -0.25 0 x [m] 0.5 -0.3 -1 1 0 -0.05 -0.05 -0.1 -0.1 -0.15 -0.2 -0.25 -0.25 0 x [m] 0.5 -0.3 -1 1 0 -0.05 -0.05 -0.1 -0.1 -0.15 1 0.5 1 0.5 1 -0.15 -0.2 -0.2 -0.25 -0.25 0 x [m] 0.5 D x / B = 21.53 0 -0.5 0 x [m] -0.5 D x / B = 19.63 -0.3 -1 0 x [m] -0.5 -0.15 -0.2 -0.5 1 D x / B = 18.08 0 -0.3 -1 0.5 -0.15 D x / B = 16.55 Bed elevation η is evaluated using the Exner equation (FAM): (2) 0 -0.5 0 x [m] -0.5 D x / B = 14.93 0 -0.3 -1 1 -0.15 -0.2 y [m] (1) 0.5 D x / B = 11.17 0 0 x [m] 0 x [m] -0.5 D x / B = 10.07 -0.5 1 -0.15 -0.2 -0.5 0.5 D x / B = 8.90 0 -0.3 -1 0 x [m] -0.5 D x / B = 13.15 where τb is the bed shear stress vector, C is a constant (1.5 - 2.3), ∇s is a surface gradient and η is bed elevation. 1 ∂η [∇•qb + D − E] = ∂t 1 − n -0.15 -0.2 -0.3 -1 τb − C|q0| · ∇sη , qb = q0 |τb| y [m] 0 -0.3 -1 where c is the sediment concentration, vs is the sediment fall velocity and νt is sediment diffusivity. Bed-load transport is modelled by an explicit expression and discretised using the Finite Area Method (FAM): 0 y [m] The sediment module incorporates suspended load and bed-load transport, with sand bed elevation evaluated using the Exner equation. Deformation of sand bed due to sediment deposition and scour is performed by the automatic mesh motion solver. Suspended load transport of sediment is modelled by the convection-diffusion equation: g ∂c + ∇• U − vs c = ∇•(νt∇c) , ∂t |g| D x / B = 6.32 y [m] The flow solver is based on the Ghost Fluid Method finite volume solver gfmFoam, which will be incorporated in the next release of foam-extend package. Mathematical Model y [m] A 3D numerical model for simulation of free surface flow and sediment transport with sand bed deformation is presented in this study. D x / B = 3.50 y [m] ABSTRACT Figure 2: Comparison of water depth levels y [m] Simulation of flow and sediment transport in channels, rivers and shallow seas is a challenging, but important problem due to the impact of sediment erosion and deposition on river beds, sea beds and marine objects. Coupling between the fluid flow and sediment transport is required in order to achieve satisfying results. This includes accurate predictions of the flow and free surface waves, realistic shear stress values, correct suspended and bed-load sediment transport calculations with stable bed motion capabilities. y [m] Introduction Vanja ŠKURIĆ Flow and sediment transport in a 140◦ channel is simulated. The channel is covered with a 30 cm sand layer, where suspended transport, bed-load transport and bed deformation occur simultaneously. Bed depth measurements performed by Olesen (1985) are used for validation. The case is considered steady-state, since the experiment reaches equilibrium conditions. Comparison between the simulated and measured water depth levels at various sections of the curved channel are shown. y [m] 9 y [m] University of Zagreb Faculty of Mechanical Engineering and Naval Architecture Department of Energy, Power Engineering and Environment korekcija znaka za smanjenje od 14 mm Numerical Model of Sediment Transport in Free Surface Flow y [m] FSB Radi kvalitete i preciznosti reprodukcije, znak Sveučilišta nije dozvoljeno rekonstruirati (precrtavati, skenirati...) Vektorizirani znak nalazi se na elektroničkom mediju koji je sastavni dio Priručnika grafičkih standarda za oblikovanje vizualnih identiteta sastavnica. 0.5 1 -0.3 -1 -0.5 0 x [m] Conclusion Figure 1: Experimental set-up of a 140◦ channel 8th Floor CFD@FSB Zagreb, 2017 Numerical model for simulation of free surface flow and sediment transport was presented here. Results from a curved channel simulation show very good agreement with the experimental data in most sections, which can be further improved with a better definition of inlet and outlet flow boundary conditions. Further validation is required. Supervisor: Prof. Hrvoje Jasak www.fsb.hr/cfd Feel free to contact us at [email protected] or take a look at our YouTube channel: 8th Floor CFD@FSB.