1      Hydro-morphological model

1.1    Model background

To simulate the dam operation, the Funagira reservoir and the Tenryuu River downstream of the dam, two software packages are used: 

-       Delft3D4: an open-source software package which allows 2D and 3D modelling of hydrodynamics, transport of water-borne constituents (e.g. heat and salinity), and sediment transport and morphological change (Deltares, 2017). 

-       RTC: The Real-Time Control (abbreviated to RTC) module allows you to vary the bottom level of the gates during the simulation. The RTC module can be used to prescribe a time function for a quantity (e.g. overrule a constant gate height by a time-varying height following a user-defined              time function) or to change a quantity by means control rules based on simulation results. The tool, normally, used to control hydraulic structures like weirs, pumps, hydropower structures and water intakes. In this assignment, the PID (Proportional Integrating Differentiating) controller in              the RTC tool is used to simulate the dam operation. The PID allows the model to automatically operate the gates to maintain the user-defined reservoir water level (Omer et al, 2018).

 The grid (fine grid) of the Funagira reservoir of the previous study (Omer et al, 2018) was used in this project. The grid was coarsened (coarse grid) to have shorter computation time.

Delft3D software and real-time control (RTC) toolbox are used to mimic the correct hydrodynamic condition of the reservoir. The following section describes the grids used, the bed topography, the boundaries and the gates.

1.2      Computational Grids

The coarse grid is generated because the computation time for the fine grid is quite long. The grid is coarsened in the longitudinal direction (approximately one cell in the coarse grid represent 3 cells in the fine grid).

The schematization of the dam in the coarse model is represented by three gates, which means one gate simulates three gates.

Figure 1.1   The computational grids and the modelling domain of the study. The blue grid is the fine grid and the pink grid is the coarse gird.

1.3      Boundary conditions

The figure below shows the discharge used at the upstream condition (inflow), the turbine outflow discharge and the reservoir water level. The three-input data has been imposed on the model to simulate the correct hydrodynamic conditions. The reservoir water level is used by the PID controller in the RTC to mimic the reservoir water level.

Figure 1.2 The upstream discharge inflow, the turbine discharge and the reservoir water level.

 The operation function has been used to represent the discharge passing through the power plant. So, basically, the discharge is abstracted at the upstream area of the dam and release again at the downstream area of the dam at the outlet location of the powerhouse.

 The downstream boundary of the model is the rating curve of Tenryuu river cross-section at the bridge located 4.85 km downstream of the dam (see Figure 1.3). 

Figure 1.3   Discharge and water level data at the bridge downstream of the dam. These data are used as a downstream boundary condition of the model (source: Omer et al, 2016)

The figure below shows part of the model calibration process to achieve the water level in the reservoir. The figure shows two model results with different time step to the data.

                                                                             time

Figure 1.4   Comparison between the measured and simulated reservoir water level for 2015 using PID controller. The simulations have reservoir flushing level of 50.6,48.5 and 47.

1.4      Morphodynamic modelling

The hydrodynamic model is extended to include morphology. The eight sediment fractions are used to setup the morphological model.

Initially, the grain sizes are evenly spread over the reservoir and river bottom. Sorting takes place. To arrive at a proper initial sediment distribution, an initialization run has been carried out. The initial sediment layer thickness is 5 m (8000 kg/m²) upstream the dam and 2 m (3200 kg/m²) downstream the dam, see Figure 1.5. The banks and the dam area are considered fixed (non-erodible) and therefore modelled with 0 m layer thickness (Omer et al, 2016). In the spin-up runs, Ashida-Michue (1974) and Partheniades-Krone (1965 are used to calculate the sediment transport of the sand and mud respectively).

For the non-cohesive sediment, the upstream boundary is set to the equilibrium condition for the bed load. This means that the sediment load entering through the boundaries is adapted to the local flow conditions to keep the bed level at the boundary constant. Six fractions have been used for these simulations. In these scenarios, Ashida-Michue (1974) is used to calculate sediment transport.

Figure 1.5   Initial sediment-08-layer thickness after the spin-up.

The formula calculates the bed load transport rate due to the current. The formula is used before the transported sediment in the previous studies of Funagira Reservoir (Omer et al, 2016 and 2017). The Ashida-Michiue formula has been tuned in the previous studies. As a result of the default values of m,p and n are used and suitable values for and  are selected to be 0.6 and 0.035, respectively.

For the cohesive sediment, Partheniades-Krone transport formulae are used for the mud fractions in combination with the bed load transport formula of Ashida-Michue (1974). Two fractions have been added to the model as cohesive sediment.

Mud is deposited when water is still. In fact, there is always an exchange of material between bed and water column, but if the water flow causes bed friction () higher than the critical shear stress) again all material is entrained, and the entrainment rate can be given by the following general formula (Partheniades, 1964). Regarding the deposition and entrainment of mud sediment fraction in Delft3D software, the sink and source terms are always located in the bottom computational cell; the term can be seen later in the contribution of erosion and deposition flux. The cohesive sediment fluxes between the water phase and the bed phase are calculated with Partheniades-Krone formulations (Partheniades, 1965). There are two shear parameters (), can be adjusted to satisfy the sedimentation and erosion behaviour of the model under the following condition:

To realize the values of the critical shear stress of erosion and the erosion rate, many simulations are executed. The results of the sediment transport sensitivity to those parameters are discussed later in this report.

The table below shows the eight sediment fractions used in the model the first two fractions are the cohesive sediment while the other fractions are simulated as non-cohesive sediment.

Table 1.1 The sediment fractions diameters and fall velocities

The Koch & Flokstra (1980) formula for the effect of bed slopes on transport capacity is used. The Ashield and Bshield parameters were tuned to obtain realistic bed topography between the inner and outer bends within the river corridor.

 We used 10 under layers and the thickness of the transport layer was selected to be 0.5 m.The hiding and exposure function was also turned off as this function is not working with cohesive sediment. The calibration factor of spiral flow was set to 0.5. The other morphological input used in the model is displayed in more detail previous projects (Omer et al, 2016). 

As the high flow velocity at the dam and just downstream of makes the numerical scheme unstable, which was reflected in the morphological calculation of sediment transport, a bed composition is introduced with a variable sediment grain size. Furthermore, a high value of roughness is used with some adaptation of the topography just downstream the dam. 

To decrease the computation time, variable morphological factor (Morfac) has been used. A Morfac of 1 is sued during the flood season to simulate properly the filling and emptying of the reservoir. For the dry season, as the fluctuation of the reservoir water level is not that much, a Morfac of 20 is used. This means the model simulates a time of 1 day and multiplies the bed changes by 20 to provide a result of 20 days bed changes. The model simulates the period from 2005 to 2007 with realistic discharges.

2      Water quality model

2.1      Model setup

The water quality model is built upon the hydrodynamic output of the Delft3D-FLOW simulations described above.

 To perform the water quality calculations, Delft3D-FLOW output has been aggregated in space and time. The temporal aggregation was set to 12 hours. The spatial aggregation consisted of a 3 by 3 lumping of the grid cells, i.e. a water quality grid cell contains nine hydrodynamic grid cells. The model considers six substances: dissolved oxygen (𝐷𝑂), biological oxygen demand (𝐵𝑂𝐷), ammonium (𝑁H4), nitrate (𝑁𝑂3), ortho-phosphate (𝑃𝑂4) and inorganic matter (𝐼𝑀), which represents suspended sediments. Oxygen is consumed by the decay of BOD and replenished by exchanges with the atmosphere at the water surface. The nitrification process converts ammonium to nitrate, which is consumed by the denitrification process. Inorganic matter settles on the bottom, or is re-suspended, depending on the shear stress calculated by the hydrodynamic model. Water temperature is not modelled but imposed as external forcing.

 The upstream boundary conditions of the model were imposed using concentration measurements from Akiba Dam Outflow, which is the station closest to the upstream boundary covering the simulated period (2005-2007). The initial conditions for each of the simulated years were chosen close to the concentrations measured at the beginning of each year. The water temperature forcing varies in time but not in space. This is justified by the relatively small temperature differences observed between the three stations located inside the model domain (Akiba Dam Outflow, Funagira Dam Outflow & Kashima Bridge). The actual values of the temperature forcing come from station Funagira Dam Outflow, as it is located at the centre of the modelled domain and therefore considered more representative of both upstream and downstream conditions.