Extended Scaling Method for Nonsimilarity in Reynolds Number, Stagger Angle and Blade Number

3.1 Development of Analytical and Computational Methods

The similarity of Reynolds and Mach number, relative roughness and relative gap for fan model and prototype cannot be retained for the dimensioning of large industrial fans. Thus the efficiency of model and prototype changes. Scaling methods are supposed to compensate these differences in efficiency from model to prototype.
The efficiency η=η(σ,Re,Ma,k_+,s_+,φ) depends on the type (specific speed σ), the dimensionless size (Reynolds- and Mach number Re,Ma), the quality (relative roughness and relative gap k_+,s_+) and the operating point (flow coefficient φ). The change of stagger angle results in a change of specific speed or fan type. The loss distribution changes and the scaling method shall include that change. Common scaling laws like Ackeret’s formula are easy to use, but they show a large deviation between prediction and measurement. This paper focuses on incidence losses for axial fans. The loss model and the limits are an important part of the paper, which is an expansion of the scaling method Pelz & Saul (2017). The predicted efficiencies are validated by experimental investigations of a fan model with a specific speed σ=1…1.4 with a stagger angle range of Δβ_s=-18°:6°:+12°. Additionally, measurements are done for full- and half-bladed rotor, which is a common method of the industry to match a fan to a specific task. Measurements show, that the incidence angle and the number of rotor blades have an impact on the efficiency and the efficiency scaling potential, which is Δη=3…5.5 % in the Reynolds number range of Re=2.2…6.5 E6. The presented scaling method considers the incidence angle with the help of design and flow parameters, which are all known parameters.
The result is an extended scaling method, taking incidence loss into account.