Tidal stream energy assessment with and without a shock capture scheme - Incorporating a non-constant thrust force coefficient

Abstract

Tidal currents provide a significant energy source in many locations worldwide, particularly at coastal areas where bathymetric conditions intensify their magnitudes. Potential sites for tidal-stream energy resource harvesting require realistic assessments and reliable simulations of effects of turbine arrays on tidal dynamics. Accuracy of the analysis has direct implications on economic and technical aspects of tidal energy project developments. An alternative approach for simulating turbine array energy capture, momentum sink-TOC, was developed to improve conventional methodologies for assessing tidal-stream energy resource. The method uses a non-constant thrust force coefficient calculated based on turbines operating-conditions, and relates turbine near-field changes produced by power extraction to turbine thrust forces. Sink-TOC combines linear momentum actuator disc in open channel flows theory with the momentum sink method. Momentum sink-TOC was implemented in two depth-average complex hydrodynamic models to simulate different marine turbine configurations and to perform tidal-stream energy resource assessments. The first model solves smooth and slow flows (SSF) with an alternating direction implicit scheme. The second model solves rapidly varying flows (RVF) combining MacCormack and total variation diminishing schemes. The RVF solver incorporates a computational less expensive approach for simulating sharp gradients produced by power extraction than existing techniques. Benchmarking of numerical results against analytical solutions indicates that both models correctly compute momentum extracted by turbines. Calculation of turbine velocity coefficients and head drops across turbine arrays enabled the calculation of turbine efficiency, total power extracted, power dissipated by turbine wake-mixing, and power available for electricity generation. These metrics represent an advantage over traditional methodologies used to assess resources. Assessment of bounded flow scenarios through a full fence configuration performed better using the SSF solver, because head drop was more accurately simulated. However, this scheme underestimates velocity reductions due to power extraction. Evaluation of un-bounded flow scenarios through a partial-fence was better performed by the RVF solver as the head drop was more correctly approximated by this scheme. The free-surface flow simulations led to identification of non-uniform upstream conditions for the partial-fence configuration. Computational performance comparisons indicated that the RVF solver requires higher computational cost independently of domain-size, and whether energy extraction procedure is incorporated or not. Tidal-stream energy resource evaluations with fence and partial-fence configurations indicate that a computationally economical pre-assessment can be adequately performed using an SSF solver. However, more accurate evaluation requires the solution of the discontinuities produced in the tidal-stream by power extraction. The methodology and numerical models obtained in this research could be use to determine realistic upper limits of available power with turbine arrays in farm format in real-world coastal environments.