Blade Count Versus Chord at Fixed Solidity in a Small Ducted Fan

RANS Performance Trends and the Reynolds-Number Effect They Miss

Abstract

A small ducted fan can reach a given rotor solidity with more blades or with wider ones, and at chord Reynolds numbers near 10⁵ the two routes need not be equivalent. Seven rotors for a 150 mm ducted fan in hover at 6000 rpm, with four or six untwisted S1223 blades of 20–45 mm chord (σ = 0.34–1.02), were simulated with steady RANS and the k–ω SST model on single periodic passages. In the simulations, figure of merit and thrust-to-power ratio fall monotonically with solidity for both blade counts (figure of merit from 0.32 to 0.17) because shaft power rises almost linearly with solidity while thrust levels off near 2.2 N. The simulations do not resolve an effect of blade count at fixed solidity, as two matched-solidity pairs differ by amounts comparable to numerical uncertainty, with one pair changing sign under a change of discretisation. Sectional validation shows that at a chord Reynolds number of about 10⁵ the fully turbulent closure over-predicts S1223 drag by 46% and captures less than half of its measured fall with Reynolds number, whereas XFOIL reproduces the drag trend for the blade section. A blade-element estimate built on XFOIL polars indicates that this missing Reynolds-number effect favours wider chords: it shifts the matched-pair figure-of-merit differences by 3 to 21 percentage points towards the four-blade rotors for turbulent inflow and removes the simulation advantage of the least solid, narrowest-chord rotor, leaving the optimum unresolved. In this regime efficiency depends on chord Reynolds number as well as solidity, and a fully turbulent model under-represents that effect.