Simulation-based optimization of in-stream structures design: rock vanes

Abstract

We employ a three-dimensional coupled hydro-morphodynamic model, the Virtual Flow Simulator (VFS-Geophysics) in its Unsteady Reynolds Averaged Navier–Stokes mode closed with \(k-\omega\) model, to simulate the turbulent flow and sediment transport in large-scale sand and gravel bed waterways under prototype and live-bed conditions. The simulation results are used to carry out systematic numerical experiments to develop design guidelines for rock vane structures. The numerical model is based on the Curvilinear Immersed Boundary approach to simulate flow and sediment transport processes in arbitrarily complex rivers with embedded rock structures. Three validation test cases are conducted to examine the capability of the model in capturing turbulent flow and sediment transport in channels with mobile-bed. Transport of sediment materials is handled using the Exner equation coupled with a transport equation for suspended load. Two representative meandering rivers, with gravel and sand beds, respectively, are selected to serve as the virtual test-bed for developing design guidelines for rock vane structures. The characteristics of these rivers are selected based on available field data. Initially guided by existing design guidelines, we consider numerous arrangements of rock vane structures computationally to identify optimal structure design and placement characteristics for a given river system.

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Acknowledgements

This work was supported by National Cooperative Highway Research Program Grants NCHRP-HR 2433 and 2436. The computational resources were partly provided by the Center for Excellence in Wireless and Information Technology (CEWIT) of the College of Engineering and Applied Science at the Stony Brook University.

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Correspondence to F. Sotiropoulos.

Appendices

Appendix 1: Investigating the effect of initial river-bed morphology on the calculated bed bathymetry at equilibrium

For all cases in this paper the rock vane structures were installed at the start of the simulation on an initially flatbed geometry. This situation cannot be realized in the field, however, where structures are typically installed on an already scoured river-bed and in the presence of bed forms. In this appendix we report a series of computational experiments, which seek to investigate the effect of the initial river-bed geometry on the equilibrium scour patterns following the installation of in-stream structures. We simulate one \(30^{\circ }\) rock vane placed in a gravel bed river but for two different initial river-bed conditions: flat bed, and equilibrium scoured bed for the river without structures. In what follows we present the results of these simulations.

The initial bed geometry and the corresponding results of the bed morphodynamic simulations for the one \(30^{\circ }\) rock vane structure in the gravel bed river are shown in Fig. 34. The main characteristics of sediment transport processes for this case are; (a) formation of a scour hole downstream of the tip of rock vane; (b) deposition of sediment material at the upstream corner of structure; and (c) scour pattern at the outer bank of the meander due to the extended shear layer originating from the tip of rock vane (see Fig. 34).

Fig. 34
figure34

a Initial and b its corresponding computed bed morphology (time averaged at equilibrium) for the gravel bed river with a \(30^{\circ }\) rock vane structure. The results are only shown for the middle meander bend. Flow is from left to right

We now use the equilibrium bed geometry of the empty gravel bed river (as shown in Fig. 15a) and mount in it the same rock structures to address the effect of starting from fully deformed bed geometry (as shown in Fig. D-2(a)). Starting from the bed geometry of Fig. 35a as our initial bed geometry, after almost the same period of physical time the bed geometry reaches equilibrium and Fig. 35b shows the time averaged bed elevation of this simulation. Again, it is worth to mention that once the bed morphology reaches quasi-equilibrium we start time averaging the bed geometry to create such quasi-equilibrium time averaged bed morphologies.

Fig. 35
figure35

a Initial and b its corresponding computed bed morphology (time averaged at equilibrium) for the gravel bed river with a \(30^{\circ }\) rock vane structure. The results are only shown for the middle meander bend. Flow is from left to right

In Fig. 36 we show the percentage of difference between the results of the two cases (Figs. 35b vs. 34b) which is scaled by the flow depth as the characteristic length of river flow. The comparisons show that both have the same main characteristics of sediment transport in such environment with the presence of one rock vane structure. As shown in Fig. 36 for most of the river the difference is less than five percent.

These results support the simulation procedure followed in the present work. Furthermore, they provide more confidence in the proposed guidelines as the initial channel topography will vary from one river to another.

Fig. 36
figure36

The difference between computed bed topographies (Figs. 35b and 34b) at equilibrium scaled by flow depth. Flow is from left to right

Appendix 2: Investigating the effect of free-surface on the calculated bed bathymetry at equilibrium

As it is mentioned, thus far for all cases in this paper we employed the rigid-lid boundary condition for the free-surface. In order to study the effect of water surface elevation on the bed morphodynamics calculations we carried out a series of simulations for the gravel bed river to investigate the sensitivity of computed bed morphology to the location of water surface. In this sensitivity study, we employed the level-set free-surface module of the model along with the flow and sediment transport models (for details of level-set method see [24]). We used a quasi-coupled approach to couple together the hydrodynamic, bed morphodynamics and free-surface simulation modules of the numerical model, which is described as follows.

First, using the coupled flow and sediment transport model we simulated the bed morphodynamics of gravel bed river by treating the free-surface as a rigid-lid (i.e. the free surface is prescribed on the top boundary of flow domain with a slope of \(32\times 10^{-4}\) which is the bed slope of the gravel bed river). Figure 37 shows the so-computed three-dimensional bed morphology (time averaged) of the gravel bed river at equilibrium (note that this figure is identical to Fig. 15a in which we only show the middle meander).

Fig. 37
figure37

Computed bed morphology of the gravel bed river at equilibrium when the free-surface is treated as a rigid-lid boundary. Flow is from left to right

Second, the hydrodynamic and level-set free-surface modules of the model were coupled together to calculate the free-surface elevation over the bed bathymetry simulated in the first step. Figure 38 demonstrates the calculated free-surface elevation at the steady state condition.

Fig. 38
figure38

Computed free surface elevation at steady state condition. The bottom boundary is prescribed using the pre-calculated bed morphology (as shown in Fig. 37) and held fixed. The free-surface elevation is normalized by the mean flow depth (\(=0.9~\hbox {m}\)). The initial flat bed elevation is located at \(z_{b}=0.0\). Flow is from left to right

As shown in Fig. 38, the difference between water surface elevation at the entrance and outlet is about 20 cm. Considering the total length of gravel bed meander (755.5 m), the calculated water surface slope is equal to \(2.8\times 10^{-4}\) which is one order of magnitude smaller that the bed slope of \(32\times 10^{-4}\) (for the gravel bed river).

Third, the free-surface elevation calculated in step 2 above was prescribed and held fixed (instead of rigid-lid assumption used in step 1) as the top (free-surface) boundary of flow domain and the hydrodynamic and morphodynamic modules are employed to calculate the new bed elevation. Figure 39 shows the calculated bed morphology with the calculated free surface.

Fig. 39
figure39

Computed bed morphology of the gravel bed river at equilibrium when the free-surface is calculated using level-set module. Flow is from left to right

In order to evaluate the importance of free-surface calculations on the calculated bed morphology in Fig. 40 we show the absolute deviation between the results of the two cases (Figs. 37 vs. 39) which is scales by the flow depth as the characteristic length of river flow. The comparisons show that with the rigid-lid assumption the main characteristics of sediment transport in such environment has been captured (e.g. the locations of deep scour holes and the point bar). As shown in Fig. 40 for the most of the middle meander the difference is less than five percent. The main difference in the computed bed morphology can be seen in the first meander at which the free surface is 0.135 m underestimated by the rigid-lid assumption. The High flow depth at the first meander (captured by level-set method) has led to more pronounced scour depth and deposition height of sediment material. However, for the rest of the meander length including the middle meander, which was the main focus of this paper, the deviation is less than five percent. The results of this sensitivity study support the simulation procedure followed in the present work in which the rigid-lid boundary condition is employed for free-surface.

Fig. 40
figure40

The absolute deviation between computed bed topographies (Figs. 37 and 39) at equilibrium scaled by flow depth. Flow is from left to right

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Khosronejad, A., Kozarek, J.L., Diplas, P. et al. Simulation-based optimization of in-stream structures design: rock vanes. Environ Fluid Mech 18, 695–738 (2018). https://doi.org/10.1007/s10652-018-9579-7

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Keywords

  • Bed-morphodynamics
  • Computational fluid dynamics
  • Rock vane
  • URANS