Hydrokinetic Assessment of the Kvichak River near Igiugig, Alaska, Using a Two-Dimensional Hydrodynamic Model ()
1. Introduction
The growth of worldwide energy demand and the need to reduce dependence on fossil resources to avoid undesirable environmental consequences have led to new investigations of renewable energy sources. Extensive research efforts have been carried out in recent years on tidal and in-stream energy resources. Studies have involved many direct and indirect topics related to these sources of renewable energy, such as resource assessments, technology reviews, energy extraction, and fish/ turbine interactions. Resource assessments have been done at different spatial scales, including national [1-3], regional [4,5], state [6,7], and site-specific scales [8-10]. Technology reviews [11,12] and energy extraction mechanisms [13-15] have been also published. Literature on fish and its interactions with hydrokinetic devices is somewhat limited [16,17].
Numerical models with different levels of complexity were used in resource characterization efforts. For instance, one-dimensional models were used to estimate water depths and velocities [18,19]; two-dimensional hydrodynamic models were used to estimate vertically averaged velocity distributions on river cross sections [10]. Finally, three-dimensional models were used to study the effects of turbines on the entire flow field [14,20,21].
In Alaska, initial work on hydrokinetic resource assessment was done considering cross-sectionally averaged velocity [18]. A probable consequence of this approach, which considered a single velocity along the river cross section, was that existing resources could be considerably underestimated.
This paper presents the first resource assessment, on a monthly basis, of the Kvichak River near Igiugig using an existing two-dimensional hydrodynamic model. Instantaneous power density, reduced by an energy extraction coefficient, along the computational domain is also calculated. In addition, suitable sites for deploying turbines are presented, and the importance of adequate bathymetric surveys and methodology used in resource assessment is discussed. The effect of turbine(s) blockage on flow conditions and detailed analysis of macroturbulence (i.e., to estimate off-directional stresses along river cross sections) are beyond the scope of this paper. Analyses of these topics constitute, without a doubt, stand-alone articles.
2. Study Site and Available Data
The study reach is located in southwest Alaska along the Kvichak River near Igiugig, a small village situated at 59˚19′ N, 155˚54′ W. This rural community has no access road [22]. Figure 1 shows the study area.
The mouth of the Kvichak River is at Iliamna Lake, which constitutes the primary source of water for the river [22]. The stream in the area is ice-free during winter months, but has some moving ice, that originates at Iliamna Lake, during spring breakup [18]. In general, the water in the stream is clear, which indicates low or negligible sediment transport [22]. Bed sediment along the reach consists of cobbles, coarse and medium gravel, with insignificant amounts of finer sediment [22].
The United States Geological Survey (USGS) installed and operated a gauging station (ID 15300500) from 1967 to 1987. Historical data can be found at: http://waterdata.usgs.gov/nwis/nwisman/?site_no=15300500&agency_cd=USGS. Table 1 provides the average monthly discharge for the period of record.
Figure 1. Aerial view of the study reach. Main (surveyed) and secondary (not surveyed) river channels are indicated in the image. Flow direction is from right to left.
Table 1. Historical monthly averaged discharge.
The study reach was intensively investigated by Terrasond (http://www.terrasond.com/) during 2011 as part of a resource reconnaissance and physical-characterization study. Fieldwork activities involved velocity measurements using an Acoustic Doppler Current Profiler (ADCP), water slope measurements, and river reach bathymetry [22].
3. Methods
The approach followed to estimate annual power density along the Kvichak River comprised three main tasks: 1) two-dimensional hydrodynamic model setup; 2) model calibration; and 3) power density calculation. Specific details for each task are described in the following paragraphs.
3.1. Hydrodynamic Model Setup
An existing numerical model, the CCHE2D developed at the National Center for Computational Hydroscience and Engineering (NCCHE), University of Mississippi (http://www.ncche.olemiss.edu/), was used in this work. The model is free but is not an open source. The CCHE2D Model Package is composed of two different applications: CCHE_GUI, the two-dimensional flow and sediment transport model, and CCHE_MESH, the mesh generator [23].
The CCHE2D is a depth-integrated two-dimensional model, which was successfully validated in different river settings [24,25]. The model was also used on the Tanana River at Nenana, Alaska, to assess the in-stream hydrokinetic resource [10].
Mesh generation: The mesh represents the computational domain where the governing equations are discretized and solved; it is generated by CCHE_MESH software [23]. The software does not allow the inclusion of structures to simulate turbines in the domain. Figure 2(a) shows the mesh built with the bathymetric data collected by Terrasond in August 2011 [22]. A comparison between Figures 1 and 2(a) reveals that bathymetric data for the secondary channel near the river bend located in the center of the figure were not collected. The lack of information on this channel poses a serious restriction to any modeling effort because water flow is divided into the main and the secondary channels in that area. To palliate this limitation, a rough rectilinear channel was added to the original bathymetry (Figure 2(b)). The bathymetry along this secondary channel was linearly interpolated from the upstream to the downstream end. This issue is further discussed in the results and discussions section. The final mesh consisted of 10,000 nodes, distributed along a domain defined by 50 by 200 lines.
Boundary conditions: The CCHE2D requires inlet and
(a)
(b)
Figure 2. (a) Computational bathymetry generated with the model using field data. (b) Secondary channel, using linear interpolation along the bed, added to the numerical domain. Flow direction is from right to left.
outlet boundary conditions [23]. The upstream boundary conditions were defined in terms of average monthly river discharge, Q, given in Table 1. The downstream boundary conditions during the monthly simulations were set in terms of water surface level. Specifically, some water surface levels were measured at different river conditions [22]; others (corresponding to any particular monthly simulation) were calculated using a linear function defined by measured discharge and water level values.
3.2. Model Calibration
Initial work was done to back-calculate the Manning’s roughness coefficient, n, using data gathered in the field by Terrasond during June 2011 [22]. Following the methodology described by Toniolo et al., [26], the ADCPgenerated measurements of channel area, width, and velocity along one river cross section were used, along with the water-surface slope measurement to calculate the roughness coefficient given by
(1)
where U denotes the cross-sectional average velocity, H denotes the average depth, and S denotes the water-surface slope. The average cross-sectional depth is obtained as
(2)
where A denotes the cross-sectional area, and B denotes the channel width.
Table 2 shows data gathered on 21 June 2011 on a cross section located approximately 750 m from the river mouth. Water slope at the river cross section was measured on 18 June 2011 [22]. The calculated n value was 0.026. Table 3 shows ADCP data collected on the same river cross section in subsequent field measurements. The n value previously calculated (Table 2) was used to estimate the water slope for different flow conditions. Results indicate a slight increment in S with increasing discharge.
The roughness coefficient was applied to the entire numerical domain, which included the secondary channel near the river bend, and used in preliminary model runs. The objective was to match the modeled water slope with the measured water slope (on 18 June 2011) along the entire reach, which was 0.0005. The agreement between measured and modeled slopes was reached using n = 0.032, which is in the range of reported values for sediments found in the study area. Thus, the calibration process was finished.
Additional model parameters, such as time step and total simulation time, were 10 seconds and 20,000 seconds, respectively. Steady-state solutions were reached with the selected simulation time. A parabolic eddy viscosity model was used to close the momentum equations.
3.3. Power Density Calculation
The HYDOKAL model [27] was used to estimate instantaneous power density along the entire river reach. Specifically, the instantaneous power density of a parcel of fluid [8,9] is defined as
(3)
where P denotes power, Ap denotes cross-sectional area
Table 2. Calculation of manning’s coefficient.
Table 3. Variation of slope as function of discharge.
of a parcel of fluid, r denotes water density, and V denotes velocity magnitude.
Equation (3) was applied to the velocity field produced by the numerical model. HYDROKAL includes a userdefined energy extraction coefficient, which is fundamental for estimating the energy that could be harvested from the river [27]. This value was set to 0.59, which corresponds to the maximum power limit for wind turbines [28]. The wind/channel analogy is valid if the ratio of the turbine cross section over the channel cross section is small [29]. However, recent research in tidal environments considering ideal turbine models [29] reported values slightly larger than 59%.
As a first approximation, it is assumed here that the wind/channel analogy is valid. Thus, the values reported in the following section constitute the maximum energy that could be extracted from the current. Note that turbine efficiency and blockage are not considered in the calculation.
4. Results and Discussions
Figure 3 shows velocity distributions generated by the model, with and without the secondary channel, and the