Inverse Design of Single- and Multi-Rotor Horizontal Axis Wind Turbine Blades using Computational Fluid Dynamics

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.Comment: 19 pages, 12 figure

Tunnel splittings for one dimensional potential wells revisited

The WKB and instanton answers for the tunnel splitting of the ground state in a symmetric double well potential are both reduced to an expression involving only the functionals of the potential, without the need for solving any auxilliary problems. This formula is applied to simple model problems. The prefactor for the splitting in the text book by Landau and Lifshitz is amended so as to apply to the ground and low lying excited states.Comment: Revtex; 1 ps figur