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Expressions to describe the correlation length scales of turbulent inflow to an aerodynamic body are derived as functions of the classic integral length scale and anisotropy correction factors. These one-point parameters are significantly easier to determine experimentally than traditional correlation-scale measurement techniques, which involve multiple probes at multiple locations. As such correlation scales are necessary to properly estimate the aeroacoustic response of the body, such a technique could have substantial benefit in a wide variety of applications. The approach is applied to a recent experimental study examining the response of a stator downstream of a propeller that is itself ingesting broadband turbulence. Results suggest that the derived expressions not only accurately represent correlation length scales, but also enable the accurate prediction of the acoustic output of the stator. Nomenclaturevector of quantity i i 1 = quantity i in the freestream direction i 2 = quantity i in the direction normal to airfoil (stator) surface i 3 = quantity i in the spanwise direction of airfoil (stator) surface i ∞ = freestream quantity i * = complex conjugate of quantity i k = wave number L i = geometric length scale M = Mach number q = dynamic pressure R i j = correlation function between turbulent velocity components u i and u j r = separation distance between two points Se = aerodynamic response function (Sears function) U = mean velocity component u = turbulent velocity component x = flow location (position) α c , β c = anisotropy scaling factors β = angle between acoustic source and receiver, measured with respect to dipole axis γ 2 = coherence function δ = Dirac delta function , 1 = classic turbulence integral length scale i | j = turbulence correlation scale of jth component of velocity in ith direction ρ 0 = density of fluid ii = autopower spectrum in the ith direction ii (r) = cross-power spectrum in the ith direction (separated by distance r)p rad = radiated far-field acoustic pressure φ ii (r) = nondimensional cross-spectral density function of turbulence in the ith direction (separated by distance r) ω = gust or event frequency (=2π f )

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To examine the aeroacoustic response of the downstream blade row of a rotor/stator pair, the turbulent flowfield between the two components must be accurately represented. To that end, a recent experimental study sought to examine this complex flowfield, establishing a causal relationship between the flowfield influences and their relative contributions to the total turbulence. Although these influences and their relative impact might depend on specific geometry, two will play a dominant role in almost every rotor/stator application: wake turbulence from the upstream blade row (the topic of Part 1) and turbulence ingested by the system and modified by the upstream blade row (the topic of Part 2). The extensive scope of decomposing these influences necessitates their discussion in seperate publications. Part 1 begins with an overview as to the relevence and utility of separating these influences, providing motivation for the study. The paper then examines the contribution of the broadband and tonal contributions associated with wake turbulence. A model is proposed that infers broadband turbulence levels from a single, appropriately chosen length scale. This length scale is determined through reconstruction of the temporal mean wake profile shape utilizing the tonal component of the ensemble-averaged, measured wake spectra. Results show that simple models can be used effectively to isolate the wake turbulence contribution, forwarding the concept of a globally applicable theory for use in modeling efforts involving similar flowfields. Part 2 examines turbulence ingested by the system and modified by the upstream upstream blade row. A theoretical model is adapted to predict the level of ingested turbulence suppression using easily quantified geometric arguments. With an appropriate choice of coordinate system, this model accurately predicts broadband suppression of ingested turbulence, showing that simple models can be used to isolate contributions and forwarding the concept of a globally applicable theory for extracting such information from other similar flowfields. Nomenclature B= number of propeller blades D = propeller diameter f = temporal frequency i wake = quantity specifically dealing with propeller wake i 1 = i x = quantity i in the freestream direction i 2 = quantity i in the direction normal to airfoil (stator) surface i 3 = quantity i in the spanwise direction of airfoil (stator) surface i ∞ = freestream quantity J = propeller advance ratio k = wave number n = propeller rotation rate, rev/s p = wake exponential shape factor R = radial distance from propeller centerline R tip = radial distance of propeller tip from propeller centerline U = mean velocity component U def = mean velocity defect associated with upstream component wake V 0 = wake magnitude coefficientx/M = distance downstream from turbulence generation grid nondimensionalized by grid mesh spacing δ, δ v = propeller wake half-width θ = circumferential position = classic turbulence integral length scale ii = turbulence spectrum in ith direction ...