Mesh and load distribution requirements for actuator line CFD simulations

Fundamental numerical testing has been carried out to determine mesh density and force distribution guidelines for an actuator line-based computational fluid dynamics method for simulating kinetic turbines. The method computes forces from lifting surfaces (i.e. wings or blades) by using the evolving flowfield and tabulated airfoil data. The forces are applied to the flow as momentum source terms distributed with a Gaussian smoothing function about the physical locations of the blade/wing quarter-chord line. The chosen length scale of the Gaussian distribution affects the magnitude and distribution of the resulting induction and necessitates a minimum grid resolution for accurate results. Tests have been conducted to determine appropriate distribution length scales and mesh spacing by using an infinite span wing and finite span wings with constant and elliptical spanwise circulation distributions. These test cases were chosen because they have simple analytical solutions derived from lifting line theory. The eventual goal is to simulate turbine rotors; however, these fundamental test cases provide a means to evaluate the required mesh spacing and the appropriate distribution length scale without the complexity of modeling a turbine rotor wake. It was found that the source distribution length scale E should be proportional to the local airfoil chord length c with a ratio E/c of approximately 1/4 and that the mesh spacing at the actuator line should satisfy E/(grid)4. This limit is likely somewhat code specific and should be evaluated for all solvers used for actuator line simulations. Copyright (c) 2012 John Wiley & Sons, Ltd.