Analytical and Numerical Assessment of Force Prediction in Actuator Line Model with Spanwise Varying Kernel Size

The objectives of this study are (i) to establish practical guidelines for selecting the kernel width in a modified actuator line model (ALM) for isolated rotor simulations and (ii) to evaluate its ability to predict aerodynamic interference between a rotor and nearby bodies. The ALM represents a rotor by distributing body forces from the blades onto a line of control points. In this work, we investigate a modified version of ALM, which combines the actuator curve embedding (ACE) to smooth the aerodynamic forces two-dimensionally within the airfoil cross-sectional plane —without applying a Gaussian distribution in the spanwise direction— with an elliptically varying Gaussian kernel width. First, the results of single-rotor simulation for a small fixed-pitch rotor used on multicopters are compared with those of conventional ALM and blade-resolved simulations. The results show that the modified distribution function mitigates the over-prediction of the aerodynamic load near the blade tip. A sensitivity study is performed for the same rotor. The results indicate that, among kernel widths resolvable by the computational grid, selecting the smallest kernel width is preferable to minimize induced velocity decay. Next, a rotor paired with a downstream disk to emulate ground-effect interference is analyzed. The modified ALM reproduces the disk-induced thrust increase over the mid-span region. These findings demonstrate that an ALM equipped with ACE and a span-adaptive Gaussian kernel provides a mesh-consistent, computationally efficient approcach to high-fidelity prediction of rotor performance and aerodynamic interference, making it suitable for early-stage multicopter design.