Time-domain analysis of contra-rotating propeller noise: wake interaction with a downstream propeller blade

Abstract

Abstract

Acoustic theory of the many-bladed contra-rotating propeller: the event line and the precession of the interaction source

“…That is not the case here.) For a swept blade, the Kingan & Parry (2020 b ) analysis showed, further, that the condition (4.4) – representing a trace Mach number of unity towards the observer – occurred when the reception times were stationary with respect to the radius and, as a consequence, it coincided with an enhanced accumulation of noise from across the blade span and to strong peaks in the resultant noise waveform received by the observer. In the time domain, therefore, (4.4) can be viewed as a condition, or requirement, for enhanced peaks in the radiated sound field.…”

“…In order to allow comparison with the results of Kingan & Parry (2019, 2020 a , b ) and Parry & Kingan (2019) we will use their notation where possible, though we will define the parameters here explicitly because of some differences between the frequency-domain and time-domain publications. The architecture involves two rotating frames, and one absolute frame, as well as important reference points such as the front rotor wake, the rear blade leading edge and the two propeller pitch change axes, and it will be necessary to use all of these frames and locations.…”

“…In order to demonstrate the effect of the source we show, in figure 4, a full numerical calculation for this contra-rotating propeller, in the time domain, with the pressure per unit span, , radiated from the mid-span () of the blade. Figure 4 has been recalculated and is plotted here in terms of (leading-edge) source time rather than reception time (as it was in figure 5( a ) of Kingan & Parry (2020 b )). The source period is normalised on so that pulses occur at multiples of , precisely as expected.…”

“…The analysis of Kingan & Parry (2020 b ) showed that the front and rear reference blades, on a contra-rotating propeller, interact at source times that vary across the blade span due to the effect of blade sweep. Their derivation (given as (2.11) in Kingan & Parry (2020 b )) is straightforward, as it is based solely on blade geometry and speed. With our normalised parameters and definition of , the expression simplifies and the reference blade interaction source times are , where both and are zero at the hub: .…”

“…Regarding analytical work on contra-rotating propeller noise in the time domain, the authors are aware only of the work of Kingan & Parry (2020 b ), who considered the interactions between convected wakes from the front propeller and a blade of the rear contra-rotating row. Kingan & Parry (2020 b ) hypothesised that the sharp peaks in the radiated acoustic waveform would be significantly enhanced when the reception time, for a particular wake–blade interaction, became stationary in terms of radius. They showed that, at such a radius, the local trace velocity was precisely sonic when resolved in the direction of the observer.…”