The present paper introduces cyclostationary spectral analysis as a new approach to analyze the turbulence velocity measurements generated by a rotor. To apply this technique, a random signal should have periodic statistical characteristics and should be suitable for many rotating mechanical system as shown in recent studies. However, this method has never been applied on rotor velocity measurements. Via a Wigner-Ville representation, the instantaneous power spectra of the turbulence in the wakes and in between the wakes will be depicted and analyzed. The usefulness of the technique applied to rotor-generated turbulence is that it can separate the spectrum of the turbulence in between the wakes from that in the wake with a much greater frequency resolution than conventional spectral analysis.
NomenclatureF s = sampling frequency, Hz f = frequency, Hz K = number of cycle in the measurements time length L = number of samples of the measurement L w = wake width, m m w = coherent velocity average, m=s N = number of samples per cycle N s = number of overlapping samples between adjacent segments N v = window length R ww = instantaneous autocorrelation function, m 2 =s 2 R ww; j = cyclic autocorrelation function, m 2 =s 2 r = radius, m SC ww = spectral correlation, m 2 =s 2 Hz 2 S ww; j = cyclic power spectrum, m 2 =s 2 Hz T = cycle time, s T BPF = time duration between two successive blades passage, s t = time, s v = window WV ww = Wigner-Ville spectrum w = mean value, m=s wt = total measured velocity, m=s wt = fluctuating velocity component, m=s w 2 t = instantaneous variance, m 2 =s 2 j = cyclic frequency, Hz = turbulence length scale, m = circumferential position, deg = time lag, s ' = lag angle, deg = rotation speed, rad=s Subscripts exp = measurement rot = shaft rotation Superscript = conjugate of
