Theoretical prediction of counter-rotating propeller noise
A theoretical prediction scheme has been developed for the tone noise generated by a counter-rotation propeller. We start by deriving formulae for the harmonic components of the far acoustic field generated by the thickness and steady loading noise sources. Excellent agreement is shown between theory and measurements. Asymptotic approximation techniques are described which enable us to simplify considerably the complex radiation formulae, whilst retaining all of their important characteristics, and thus save, typically, 95% of computer processing time. Next we derive formulae for the radiated sound field generated by aerodynamic interactions between the blade rows. Here, however, the inputs to the formulae include a knowledge of the fluctuating blade pressure fields which cannot generally be assumed given and must therefore be calculated within the prediction scheme. In the case of viscous wake interactions we consider various models for the wake profile which is written as a series of harmonic gusts. The fluctuating pressure distribution on the downstream blades can then be calculated in the high frequency limit. Comparisons are made between measurements and predictions for a counter-rotation propeller and for rotor/stator interaction on a model fan rig. For potential field interactions we describe the flow fields due to blade circulation and blade thickness in terms of harmonic gusts with the flow assumed incompressible. The blade response is calculated for both finite and semi-infinite airfoils. Some important differences between these two cases are noted in both high and low frequency limits. Predicted noise levels are much improved over those obtained using only the viscous wake model. The inclusion of compressibility, in both flow field and airfoil response calculations, provides a further improvement in the predicted noise levels. The discrepancy between measurements and predictions at this stage is, typically, 2 or 3 dB.