Modeling

M. Sadeghi-Delooee; R. Alimardani; H. Mousazadeh

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**Abstract **

IntroductionThere are two types of hydropower harvesting methods: conventional and unconventional. In the conventional method, the potential energy of water is harvested using a dam or barrage. However, in the unconventional method, the kinetic energy of flowing water is extracted using hydrokinetic ...
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IntroductionThere are two types of hydropower harvesting methods: conventional and unconventional. In the conventional method, the potential energy of water is harvested using a dam or barrage. However, in the unconventional method, the kinetic energy of flowing water is extracted using hydrokinetic turbines. Resource assessment is a pivotal step in developing hydrokinetic energy sites. Power density (power per unit area) is used to estimate the theoretical hydrokinetic power of a site. Flow velocity and cross-sectional area are the two variables that constitute the power density. Researchers use various methods such as numerical simulation, direct velocity measurement, or indirect velocity calculation using discharge data to conduct resource assessment. In the latter method, the Manning equation is used to convert the discharge data into velocity values. While this method is straightforward for canals, given their fixed and known geometry, it is cumbersome to calculate the hydraulic radius in rivers. To overcome this challenge, numerous researchers have proposed the utilization of hydraulic geometry (HG) to estimate the width and depth of a river reach, and then calculate the hydraulic radius based on these estimated values. The main objective of this study is to present and implement a fast method for assessing theoretical hydrokinetic power using the HG and the Manning equation.Materials and MethodsIn the present study, two hydrometry stations (Gachsar and Siera-Karaj) were selected in the Karaj dam watershed in Iran to implement resource assessment based on HG. A computer code comprising the following four steps was developed in Python using the Google COLAB environment.Data Preparation: The monthly-averaged discharge, Manning roughness coefficient, and slope were collected and imported into the code. The roughness coefficient could be determined directly or indirectly. In the present study, it was considered to be 0.045 for the Karaj River according to the literature review. ArcGIS software and the Digital Elevation Model (DEM) were used to extract the local slope of each hydrometry station. For this purpose, the stream network of Alborz province was first extracted, and then the longitudinal elevation profile was measured using the 3D Analyst tools. Discharge Data Processing: The flow duration curve (FDC) is one of the computational tools used by engineers to describe the hydrological regime of watersheds. FDC is a graphical representation of the cumulative distribution of flows. In the present study, an all-time record FDC for each station was constructed, and fitted with five different probability distribution functions (PDF). The results of PDF fittings were evaluated by different goodness-of-fit indices, and the best PDF was selected. Calculations of HG and the Manning Equation: The HG formulas were used to calculate the width and depth of flow using the reconstructed FDC from the previous step. These values, along with the roughness coefficient and slope, were used to calculate flow velocity using the Manning equation. After obtaining the flow velocity values, the power density was easily computed. Generating Outputs: In the final step, two categories of outputs are generated: (1) duration curves for width, depth, flow velocity, and power density, and (2) theoretical and turbine-extracted energy diagrams.Results and DiscussionThe goodness-of-fit indices for PDF fitting indicated that the log-normal PDF is the most suitable distribution to describe the FDC with a coefficient of determination of 0.99. The calculated average discharge (Q50) for the Gachsar and Siera stations was 2.34 and 7.68 m3s-1, respectively. These values are consistent with findings from previous studies. The results of the Manning equation calculations revealed that the flow velocity does not differ significantly between these stations (8% higher at Siera). The base flow depth at the Gachsar and Siera stations is less than 1 m. Therefore, as indicated in the literature review, axial flow (propeller) turbines are not suitable for installation in these rivers because they need to be fully submerged and require at least 1 m of depth. Overall, the use of wide and short turbines, such as Savonius turbines, is suggested in the Karaj River. The energy analysis results show that the maximum monthly theoretical energy at Gachsar and Siera equals 38,500 and 125,500 kWh, respectively. However, considering a turbine with a 1 m2 swept area and a power coefficient of 0.2, the maximum monthly extracted energy is limited to 940 and 1,142 kWh at these two stations.ConclusionThis study presents a fast method for the theoretical assessment of hydrokinetic power, which was applied to two hydrometry stations in the Karaj dam watershed. The results of HG calculations revealed that the base velocity (V90) of 1.34 and 1.49 m/s is present at the Gachsar and Siera stations, respectively. According to the available depths at these stations, the use of wide and short turbines such as Savonius turbines is suggested. Each individual Savonius turbine with a unit swept area at Gachsar and Siera is estimated to extract a maximum monthly energy of 940 and 1,142 kWh, respectively.