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Energies 2019, 12, 2791 5 of 22 Design Variables GV Angle (degree) LE Radius (mm) Chord Length (mm) PS Radius (mm) LE Angle (degree) Stagger Angle (degree) TE Angle (degree) 3. Numerical Modelling Lower Bound 15 1 40 0.35 30 −30 30 Upper Bound 50 3 70 0.6 80 −20 70 Initial Geometry 27 1.96 62 0.45 57.5 −25 45 Table 2. Design variables with upper and lower limits. Numerical simulation tools were employed to optimise the design of the initial outflow turbine in steady-state. The computational simulations were conducted using ANSYS CFX. The turbine performance was described by a set of parameters [35]: torque coefficient CT, input power coefficient CA, turbine efficiency η and flow coefficient φ as given by CT = T0/ρVR2 + U2ARrR/2 (1) CA = ∆P0Q/ρVR2 + U2ARVR/2 (2) η= T0ω = CT (3) ∆P0Q CAφ φ = VR/U (4) The detailed definitions of the variables contributing to these coefficients are given in the nomenclature section. The quasi-steady assumption of the flow was assumed because the rotating frequency is much higher than the frequency of the wave cycle in the OWC chamber [21,39]. As an external modelling software was used for the creation of the parametric geometry, the turbo-mode tool in ANSYS-CFX was used to set up the problem to ease the iterative process of the optimisation study. The Moving Reference Frame (MRF) approach was used to set up the steady model by assuming that the rotor rotates at a constant speed of 120 rad/s and considering a frozen rotor interface between the rotor and the stationary domains. In this approach, both stationary and rotating domains are solved at steady-state with a frame change model to connect them. It is clear that the actual condition is unsteady, and an unsteady analysis delivers more accuracy, however, it could lead to increased solution time. Thus, the MRF model was chosen to provide an acceptable computational overhead for the large number of design simulations required in an optimisation study. However, to evaluate the errors due to ignoring the unsteady interaction between the rotating and the stationary domains, the optimum design of the optimisation study was later analysed in a transient model (as will be described in Section 6.3). The simulations were performed at a Reynolds number of 2.64 × 105. The flow was assumed incompressible and the realizable k-ε turbulence model was selected due to being economical in terms of computational time. This turbulence model has been utilized in many similar studies in the field and accurate results were obtained [40,41]. Other turbulence models such as k-ω and the hybrid SST could obtain more accurate results in this study as a strong effect of the wall, adverse pressure gradients, and flow separation phenomena are present in the simulations. However, these turbulence models were more computationally expensive than the k-ε turbulence model and were not economical considering the simulation time of the optimization study. This choice of turbulence model can reduce the accuracy of results at higher flowrates, however, according to the typical operation of turbines in an OWC, the peak efficiency falls in smaller flow coefficients, and the results of this analysis are still reliable. Periodic boundaries were set on the sides of each domain, and the interfaces between the rotating and stationary domains were set to the frozen rotor. A pitch angle ratio close to 1 was set at the interface,PDF Image | Unidirectional Radial-Air-Turbine OWC Wave Energy Converters
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