To suppress the adverse effect of the gear windage phenomenon in the high-speed aeronautic industry, a shroud as an effective alternative strategy is usually to enclose gears to reduce the windage behaviors of high-speed gears.To deeply understand these no-load power losses, this paper proposes a new simulation methodology based on the Lattice Boltzmann method to study the windage losses of puffy spa headband a shrouded spur gear and conducts a series of numerical studies.The models reproduce a shroud spur gear varying radial and axial clearances to evaluate the influence of casing walls on windage losses.The simulation results were then compared with experimental values, showing a satisfactory agreement.Furthermore, a torque containment factor integrating the air compressibility at high Mach numbers is introduced to represent the reduction in torque (windage power losses) for the shrouded gear compared to the free case, and the theoretical formulae for predicting click here windage power losses are further improved for better applicability as the tight shroud approaches the gear during the preliminary design stage.