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NASA NTRS2003

Broadband Noise Predictions for an Airfoil in a Turbulent Stream

Loading noise is predicted from unsteady surface pressure measurements on a NACA 0015 airfoil immersed in grid-generated turbulence. The time-dependent pressure is obtained from an array of synchronized transducers on the airfoil surface. Far field noise is predicted by using the time-dependent surface pressure as input to Formulation 1A of Farassat, a solution of the Ffowcs Williams - Hawkings equation. Acoustic predictions are performed with and without the effects of airfoil surface curvature. Scaling rules are developed to compare the present far field predictions with acoustic measurements that are available in the literature.

Casper, J.↗

NASA NTRS2003

Effect of Sub-Boundary Layer Vortex Generations on Incident Turbulence

Sub-boundary layer vortex generators were tested in a wind tunnel to assess their effect on the velocity field within the wake region of a turbulent boundary layer. Both mean flow quantities and turbulence statistics were measured. Although very small relative to the boundary layer thickness, these so-called micro vortex generators were found to have a measurable effect on the power spectra and integral length scales of the turbulence at a distance many times the height of the devices themselves. In addition, the potential acoustic impact of these devices is also discussed. Measured turbulence spectra are used as input to an acoustic formulation in a manner that compares predicted sound pressure levels that result from the incident boundary-layer turbulence, with and without the vortex generators in the flow.

Casper, J.↗

NASA NTRS2003

Some Analytic Results for the Study of Broadband Noise Radiation from Wings, Propellers and Jets in Uniform Motion

Alan Powell has made significant contributions to the understanding of many aeroacoustic problems, in particular, the problems of broadband noise from jets and boundary layers. In this paper, some analytic results are presented for the calculation of the correlation function of the broadband noise radiated from a wing, a propeller, and a jet in uniform forward motion. It is shown that, when the observer (or microphone) motion is suitably chosen, the geometric terms of the radiation formula become time independent. The time independence of these terms leads to a significant simplification of the statistical analysis of the radiated noise, even when the near field terms are included. For a wing in forward motion, if the observer is in the moving reference frame, then the correlation function of the near and far field noise can be related to a space-time cross-correlation function of the pressure on the wing surface. A similar result holds for a propeller in forward flight if the observer is in a reference frame that is attached to the propeller and rotates at the shaft speed. For a jet in motion, it is shown that the correlation function of the radiated noise can be related to the space-time crosscorrelation of the Lighthill stress tensor in the jet. Exact analytical results are derived for all three cases. For the cases under present consideration, the inclusion of the near field terms does not introduce additional complexity, as compared to existing formulations that are limited to the far field.

Farassat, F.↗

NASA NTRS2003

Some Analytic Results for the Study of Broadband Noise Radiation from Wings, Propellers and Jets in Uniform Motion

Alan Powell has made significant contributions to the understanding of many aeroacoustic problems, in particular, the problems of broadband noise from jets and boundary layers. In this paper, some analytic results are presented for the calculation of the correlation function of the broadband noise radiated from a wing, a propeller, and a jet in uniform forward motion. It is shown that, when the observer (or microphone) motion is suitably chosen, the geometric terms of the radiation formula become time independent. The time independence of these terms leads to a significant simplification of the statistical analysis of the radiated noise, even when the near field terms are included. For a wing in forward motion, if the observer is in the moving reference frame, then the correlation function of the near and far field noise can be related to a space-time cross-correlation function of the pressure on the wing surface. A similar result holds for a propeller in forward flight if the observer is in a reference frame that is attached to the propeller and rotates at the shaft speed. For a jet in motion, it is shown that the correlation function of the radiated noise can be related to the space-time crosscorrelation of the Lighthill stress tensor in the jet. Exact analytical results are derived for all three cases. For the cases under present consideration, the inclusion of the near field terms does not introduce additional complexity, as compared to existing formulations that are limited to the far field.

Farassat, F.↗

NASA NTRS2002

Broadband Noise Predictions Based on a New Aeroacoustic Formulation

A new analytic result in acoustics called 'Formulation 1B,' proposed by Farassat, is used to compute the loading noise from an unsteady surface pressure distribution on a thin airfoil in the time domain. This formulation is a new solution of the Ffowcs Williams-Hawkings equation with the loading source term. The formulation contains a far-field surface integral that depends on the time derivative and the surface gradient of the pressure on the airfoil, as well as a contour integral on the boundary of the airfoil surface. As a first test case, the new formulation is used to compute the noise radiated from a flat plate, moving through a sinusoidal gust of constant frequency. The unsteady surface pressure for this test case is specified analytically from a result that is based on linear airfoil theory. This test case is used to examine the velocity scaling properties of Formulation 1B, and to demonstrate its equivalence to Formulation 1A, of Farassat. The new acoustic formulation, again with an analytic surface pressure, is then used to predict broadband noise radiated from an airfoil immersed in homogeneous turbulence. The results are compared with experimental data previously reported by Paterson and Amiet. Good agreement between predictions and measurements is obtained. The predicted results also agree very well with those of Paterson and Amiet, who used a frequency-domain approach. Finally, an alternative form of Formulation 1B is described for statistical analysis of broadband noise.

Casper, J.↗

NASA NTRS2002

Trailing Edge Noise Prediction Based on a New Acoustic Formulation

A new analytic result in acoustics called 'Formulation 1B,' proposed by Farassat, is used to compute broadband trailing edge noise from an unsteady surface pressure distribution on a thin airfoil in the time domain. This formulation is a new solution of the Ffowcs Williams-Hawkings equation with the loading source term, and has been shown in previous research to provide time domain predictions of broadband noise that are in excellent agreement with experiment. Furthermore, this formulation lends itself readily to rotating reference frames and statistical analysis of broadband trailing edge noise. Formulation 1B is used to calculate the far field noise radiated from the trailing edge of a NACA 0012 airfoil in low Mach number flows, using both analytical and experimental data on the airfoil surface. The results are compared to analytical results and experimental measurements that are available in the literature. Good agreement between predictions and measurements is obtained.

Casper, J.↗

NASA NTRS2002

A New Time Domain Formulation for Broadband Noise Predictions

A new analytic result in acoustics called "Formulation 1B," proposed by Farassat, is used to compute the loading noise from an unsteady surface pressure distribution on a thin airfoil in the time domain. This formulation is a new solution of the Ffowcs Williams-Hawkings equation with the loading source term. The formulation contains a far field surface integral that depends on the time derivative and the surface gradient of the pressure on the airfoil, as well as a contour integral on the boundary of the airfoil surface. As a first test case, the new formulation is used to compute the noise radiated from a flat plate, moving through a sinusoidal gust of constant frequency. The unsteady surface pressure for this test case is analytically specified from a result based on linear airfoil theory. This test case is used to examine the velocity scaling properties of Formulation 1B and to demonstrate its equivalence to Formulation 1A of Farassat. The new acoustic formulation, again with an analytic surface pressure, is then used to predict broadband noise radiated from an airfoil immersed in homogeneous, isotropic turbulence. The results are compared with experimental data previously reported by Paterson and Amiet. Good agreement between predictions and measurements is obtained. Finally, an alternative form of Formulation 1B is described for statistical analysis of broadband noise.

Casper, J.↗

NASA NTRS1993

A comparison of two formulations for high-order accurate essentially non-oscillatory schemes

The finite-volume and finite-difference implementations of high-order accurate essentially nonoscillatory shock-capturing schemes are discussed and compared. Results obtained with fourth-order accurate algorithms based on both formulations are examined for accuracy, sensitivity to grid irregularities, resolution of waves that are oblique to the mesh, and computational efficiency. Some algorithm modifications that may be required for a given application are suggested. Conclusions that pertain to the relative merits of both formulations are drawn, and some circumstances for which each might be useful are noted.

Casper, J.↗

NASA NTRS1981

A remote sensing evaluation of potential for sinkhole occurrence

The relationship between lowering of the water table and sinkhole development in Pierson and in Hillsborough County, Florida was investigated. The locations of recently developed (1973) collapses were examined with respect to lineaments or fracture traces that are expressed in the terrain and visible in aerial photography and satellite imagery. It was anticipated that these relationships would provide the basis for establishment of criteria for mapping those land areas that have the greatest potential for sinkhole development. A very good correlation was found between mapped lineament intersections and known location of sinkhole occurrences for both study areas. This indicates that lineament and fracture trace mapping may be very useful in locating zones with the greatest potential for sinkhole development. It is further shown that this information is quite beneficial in land use planning applications.

Casper, J.↗