A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations on locally refined fully unstructured Cartesian grids in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggered/non-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. Auxiliary/hanging nodes are used to facilitate the discretization of the governing equations. The second-order accuracy of the solver is ensured by using multi-dimension Lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries. The discrete momentum equation is solved with the matrix free Newton-Krylov method and the Krylov-subspace method is employed to solve the Poisson equation. The second-order accuracy of the proposed method on unstructured Cartesian grids is demonstrated by solving the Poisson equation with a known analytical solution. A number of three-dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of Reynolds numbers and flow regimes. Laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy, the efficiency and the smooth transition of scales and coherent structures across refinement levels. Large-eddy simulation (LES) past a miniature wind turbine rotor, parameterized using the actuator line approach, indicates the ability of the fully unstructured solver to simulate complex turbulent flows. Finally, a geometry resolving LES of turbulent flow past a complete hydrokinetic turbine illustrates the potential of the method to simulate turbulent flows past geometrically complex bodies on locally refined meshes. In all the cases, the results are found to be in very good agreement with published data and savings in computational resources are achieved.

An effective way to develop arrays of hydrokinetic turbines in river and tidal channels is to arrange them in TriFrame T M 1 configurations where three turbines are mounted together at the apexes of a triangular frame. This TriFrame can serve as the building block for rapidly deploying multi-turbine arrays. The wake structure of a TriFrame of three model turbines is investigated using both numerical simulations and experiments. In the numerical part, we employ large-eddy simulation (LES) with the curvilinear immersed boundary method (CURVIB) for fully resolving the turbine geometry details to simulate intra-turbine wake interactions in the TriFrame configuration. First, the computed results are compared with experiments in terms of mean flow and turbulence characteristics with overall good agreement. The flow-fields are then analyzed to elucidate the mechanisms of turbine interactions and wake evolution in the TriFrame configuration. We found that the wake of the upstream TriFrame turbine exhibits unique characteristics indicating presence of the Venturi effect as the wake encounters the two downstream turbines. We finally compare the wakes of the TriFrame turbines with that of an isolated single turbine wake to further illustrate how the TriFrame configuration affects the wake characteristics and power production in an array of TriFrames.

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