An experimental investigation of the sources of propeller noise due to the ingestion of turbulence at low speeds

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 )

show abstract

“…Using the same arguments as outlined in Eqs. (24)(25)(26)(27) of Sec. II.B.1, k 3 is set to zero, and, after substitution of Eq.…”

Section: Spanwise Correlation Length Of the Normal Velocity Componentmentioning

confidence: 98%

Turbulence Correlation Length-Scale Relationships for the Prediction of Aeroacoustic Response

2005

View full text Add to dashboard Cite

show abstract

“…The normal component in conjunction with Eq. (9) gives the theoretical pressure distribution along the airfoil obtained by Sears.…”

Section: Unsteady Flow Conditionsmentioning

confidence: 99%

“…(7) and the velocity data presented previously.The Grace estimate was obtainedusing the acoustic data as an input to an inversion technique applied to Eq. (9). For incompressible ow, the solution depended on only a single term of the collocation technique used to complete the inverse process.…”

Section: Unsteady Surface Pressure Measurementsmentioning

confidence: 99%

“…Therefore, it is necessary to invert Eq. (9) to solve for the pressure jump on the plate surface. The numerical solution of this inversion process is discussed in detail by Grace et al 2 and is solved using a collocationtechniqueand singular value decomposition.The set of basis functions,which expresses the pressure distribution,is chosen to match the Sears method in the limit of vanishingMach number.…”

Section: Theoretical Developmentmentioning

confidence: 99%

“…Probe calibration and conversion of raw data to velocity are covered in detail in Ref. 9. The uncertainty of the velocity data is given as §2% of the reported value with 95% con dence.…”

Section: Unsteady Flow Conditionsmentioning

confidence: 99%

See 2 more Smart Citations

Experimental Investigation of Unsteady Aerodynamics and Aeroacoustics of a Thin Airfoil

Minniti

Mueller

1998

AIAA Journal

Self Cite

View full text Add to dashboard Cite

An experimental investigation of the unsteady problem for a thin, symmetric airfoil exposed to periodic gusting was performed in a free-jet anechoic wind-tunnel facility. The gusting events were created upstream such that there was a small longitudinal, i.e., spanwise, wave number and the gust could be approximated as two dimensional. Measurements of the unsteady velocity eld, the unsteady pressure at the airfoil surface, and the acoustic eld were made for two values of axial and normal reduced frequency. The unsteady pressure distributionalong the airfoil was computed using the Sears method and unsteady velocity data. In addition, the pressure distribution was computed using acoustic data as input to a numerical inversion technique. The results of each technique were compared with the experimentally obtained unsteady pressure distribution. The inversion technique showed good agreement with the Sears method. However, comparison with experimental results illustrated that the theoretical estimates, although exhibitingtrends similar to the experimental data, consistently underestimated the experimental unsteady pressure distribution at the lower reduced frequency, indicating the presence of viscous effects. Better agreement between experimental and theoretical results was obtained at the higher reduced frequency where viscous effects were less prominent. Nomenclature a = gust velocity vector C p 0 = unsteady pressure coef cient, p 0 =½a 2 U 1 c = airfoil chord f k = single discrete value within the frequency range of spectral analysis f RPF = primary rod passage frequency H .2/ v = vth-order Hankel function of the second kind K = Helmholtz operator k = wave number vector M 1 = freestream Mach number m = harmonic (mode) number P. y/ = acoustic pressure measured at observation location S.k 1 / = Sears function U .t / = axial velocity component U.x; t / = total velocity eld U D = velocity de cit in stationary frame U G = gust velocity vector U m = velocity de cit in wake behind the rod U R = rotational velocity of rod U 0 = relative velocity seen by rotating rod U 1 = freestream velocity vector u.x; t / = unsteady portion of velocity eld u a .x; t / = acoustic portion of unsteady velocity u 1 .x; t / = rotational portion of unsteady velocity V .t / = normal velocity component x = source position vector y = acoustic eld observation position vector 1p 0 .x ¤ 1 ; k ¤ 1 / = unsteady pressure jump on airfoil ½ = density of air ! = gust frequency

show abstract

Turbulence Ingestion Noise from an Open Rotor with Different Inflows

Alexander

Devenport

Molinaro

et al. 2018

Flinovia—Flow Induced Noise and Vibration Issues and Aspects-Ii

View full text Add to dashboard Cite

An experimental investigation of the sources of propeller noise due to the ingestion of turbulence at low speeds

Cited by 33 publications

References 21 publications

Turbulence Correlation Length-Scale Relationships for the Prediction of Aeroacoustic Response

Turbulence Correlation Length-Scale Relationships for the Prediction of Aeroacoustic Response

Experimental Investigation of Unsteady Aerodynamics and Aeroacoustics of a Thin Airfoil

Turbulence Ingestion Noise from an Open Rotor with Different Inflows

Contact Info

Product

Resources

About