Date of Award
Doctor of Philosophy
Wind farms are subjected to significant aerodynamic interference due to the unsteady wakes of the individual turbines as well as the complex terrains on which they are erected. Numerical modeling of complex geometries necessitates the use of curvilinear body-fitted coordinates. In the present research, conservation equations efficient for convection-dominated flows over complex terrain, are developed. The Navier-Stokes equations written in the novel mixed basis form allows discretization of the convective flux to be compactly represented, while also preserving the diagonal dominance in the discrete pressure equation. The resulting generalized conservation equations closely resemble the orthogonal equations. Hence they lend themselves suitable to algorithms for orthogonal systems with the addition of a source term. Additionally, the efficiency of the mixed basis formulation is illustrated by simplifying the equations to various geometries of practical applications like tubular, rotated, extruded, and orthogonal. By developing a single solver using the mixed formulation that retains the majority of the terms to be invariant and implementing geometry-based simplifications in the source term, a general, efficient solution procedure can be obtained for all geometries ranging from the complex body-fitted coordinates to the Cartesian coordinates. A momentum source method is used to model the wind turbines. The newly formed conservation equations are solved on a structured grid using the SIMPLER algorithm. Three different RANS closure models, including the standard, RNG, and realizable K − ε, are implemented. Results validating the ability of the numerical procedure to simulate flow over complex terrains and wind turbines are presented. Applications providing insights into the performance and loading of the turbines as well as the turbine-wake and turbine-terrain interactions are analyzed.
Murali, Avinaash, "A new mixed basis Navier-Stokes formulation for simulating wind turbines on complex terrain" (2016). Graduate Theses and Dissertations. 15980.