Optimisation and analysis of efficiency for contra-rotating propellers for high-altitude airships

An improved variational optimization approach is established to optimize and analyse the propulsion efficiency of the high-altitude contra-rotating propellers for high-altitude airships based on the Vortex Lattice Lifting Line Method. The optimum radial circulation distribution, chord and pitch distribution are optimized under the maximum lift-to-drag ratio of aerofoils. To consider the effects of the actual Reynolds number and the Mach number of each aerofoil section, aerodynamics such as lift coefficient, drag coefficient and lift-to-ratio are obtained by interpolating a CFD database, which is established by numerical simulations under different Reynolds number, Mach number and angles-of-attack. The improved method is verified by validation cases on a high-altitude CRP using the three-dimensional steady Reynolds-averaged Navier-Stokes solver and moving reference frames technique. The optimization results of thrust, torque and efficiency for both the individual front/rear propeller and CRP are shown to agree reasonably well with the CFD results. Using the improved approach, the influence of blade numbers, diameter, rotation speeds, axial distance and torque ratio on the optimum efficiency of CRPs is illustrated in detail by conducting parametric studies.