  A method for inverse design of horizontal axis wind turbines (HAWTs) is
presented in this paper. The direct solver for aerodynamic analysis solves the
Reynolds Averaged Navier Stokes (RANS) equations, where the effect of the
turbine rotor is modeled as momentum sources using the actuator disk model
(ADM); this approach is referred to as RANS/ADM. The inverse problem is posed
as follows: for a given selection of airfoils, the objective is to find the
blade geometry (described as blade twist and chord distributions) which
realizes the desired turbine aerodynamic performance at the design point; the
desired performance is prescribed as angle of attack ($\alpha$) and axial
induction factor ($a$) distributions along the blade. An iterative approach is
used. An initial estimate of blade geometry is used with the direct solver
(RANS/ADM) to obtain $\alpha$ and $a$. The differences between the calculated
and desired values of $\alpha$ and $a$ are computed and a new estimate for the
blade geometry (chord and twist) is obtained via nonlinear least squares
regression using the Trust-Region-Reflective (TRF) method. This procedure is
continued until the difference between the calculated and the desired values is
within acceptable tolerance. The method is demonstrated for conventional,
single-rotor HAWTs and then extended to multi-rotor, specifically dual-rotor
wind turbines. The TRF method is also compared with the multi-dimensional
Newton iteration method and found to provide better convergence when
constraints are imposed in blade design, although faster convergence is
obtained with the Newton method for unconstrained optimization.
