Elastic fields generated by inhomogeneities: Far-field asymptotics, its shape dependence and relation to the effective elastic properties
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Igor Sevostianov↗
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On the relationship between acoustic energy density flux near the jet and far field acoustic intensity
The relationship between the distribution of the outflow of acoustic energy over the jet boundary and the far-field directivity and intensity distribution is established by measurement and analysis. The numerical and experimental procedures involved have been checked out by using a known source. The results indicate that the acoustic power output per unit length of the jet, in the region from which the sound emanates, peaks at approximately 9 diameters downstream. The acoustic emission for a jet Strouhal number of about 0.3 exceeds the emission for all other Strouhal numbers nearly everywhere along the measurement plane. However, the far-field peak intensity distribution obtained from the contribution of each station was found to depend on the spatial extent of the region where sound emanates from the jet, which, in turn, depends more on the far-field angle than on the Strouhal number. The implications of these results for sound suppression techniques are discussed.
Maestrello, L.↗
Supersonic far-field boundary conditions for transonic small-disturbance theory
Characteristic far-field boundary conditions for supersonic freestream flow have been developed and implemented within a transonic small-disturbance code. The boundary conditions have been implemented within the CAP-TSD code which has been developed recently for aeroelastic analysis of complete aircraft configurations. These boundary conditions improve the accuracy of the solutions for supersonic freestream applications. They also allow the extent of the grid to be much smaller, thus providing savings in the computational time required to obtain solutions. Comparisons are shown between surface pressures computed using large and small grid extents for the NACA 0012 airfoil and the F-5 wing at various Mach numbers and angles of attack. Both steady and unsteady results are presented and comparisons are made with Euler results and with experimental data to assess the accuracy of the new far-field boundary conditions. Comparisons of these results show that the supersonic boundary conditions allow a much smaller grid to be used without losing accuracy.
Gibbons, Michael D.↗
An Acoustical Comparison of Sub-Scale and Full-Scale Far-Field Measurements for the Reusable Solid Rocket Motor
Recently, members of the Marshall Space Flight Center (MSFC) Fluid Dynamics Branch and Wyle Labs measured far-field acoustic data during a series of three Reusable Solid Rocket Motor (RSRM) horizontal static tests conducted in Promontory, Utah. The test motors included the Technical Evaluation Motor 13 (TEM-13), Flight Verification Motor 2 (FVM-2), and the Flight Simulation Motor 15 (FSM-15). Similar far-field data were collected during horizontal static tests of sub-scale solid rocket motors at MSFC. Far-field acoustical measurements were taken at multiple angles within a circular array centered about the nozzle exit plane, each positioned at a radial distance of 80 nozzle-exit-diameters from the nozzle. This type of measurement configuration is useful for calculating rocket noise characteristics such as those outlined in the NASA SP-8072 "Acoustic Loads Generated by the Propulsion System." Acoustical scaling comparisons are made between the test motors, with particular interest in the Overall Sound Power, Acoustic Efficiency, Non-dimensional Relative Sound Power Spectrum, and Directivity. Since most empirical data in the NASA SP-8072 methodology is derived from small rockets, this investigation provides an opportunity to check the data collapse between a sub-scale and full-scale rocket motor.
Haynes, Jared↗
Far-field boundary conditions for transonic lifting solutions to the Euler equations
Far-field boundary conditions for the Euler equations are formulated and applied to transonic lifting flow over an airfoil in an unbounded domain. An expansion of the linearized small-disturbance equation in the far field is developed and the leading-order term, corresponding to a point vortex representation for the airfoil, is retained. A comprehensive evaluation across the Mach number range of the procedure's effectiveness in eliminating dependence of the numerical results on the boundary extent is presented. Extension of the method to three dimensions is also outlined.
Thomas, J. L.↗
On the relationship between acoustic energy density flux near the jet axis and far field acoustic intensity
By measurement and analysis, the relationship between the distribution of the outflow of acoustic energy over the jet boundary and the far-field intensity is considered. The physical quantity used is the gradient of the pressure evaluated on a geometrical plane at the smallest possible radial distance from the jet axis, but outside the vortical region, in the area where the homogeneous wave equation is reasonably well satisfied. The numerical and experimental procedures involved have been checked out by using a known source. Results indicate that the acoustic power output per unit length of the jet, in the region from which the sound emanates, peaks at approximately 9 diameters downstream. The acoustic emission for a jet Strouhal number of about 0.3 exceeds the emission for all other Strouhal numbers nearly everywhere along the measurement plane. However, the far-field peak intensity distribution obtained from the contribution of each station was found to depend on the spatial extent of the region where sound emanates from the jet, which, in turn, depends more on the far-field angle than on the Strouhal number.
Maestrello, L.↗
Far field boundary conditions for computation over long time
A new class of computational far field boundary conditions for hyperbolic partial differential equations is developed. These boundary conditions combine properties of absorbing boundary conditions for transient solutions and properties of far field boundary conditions for steady-state problems. The conditions can be used to limit the computational domain when both traveling waves and evanescent waves are present. Boundary conditions for scalar wave equations are derived and analyzed. Extensions to systems of equations are discussed and results from numerical experiments are presented.
Engquist, Bjorn↗
Computer program documentation for a subcritical wing design code using higher order far-field drag minimization
A subsonic, linearized aerodynamic theory, wing design program for one or two planforms was developed which uses a vortex lattice near field model and a higher order panel method in the far field. The theoretical development of the wake model and its implementation in the vortex lattice design code are summarized and sample results are given. Detailed program usage instructions, sample input and output data, and a program listing are presented in the Appendixes. The far field wake model assumes a wake vortex sheet whose strength varies piecewise linearly in the spanwise direction. From this model analytical expressions for lift coefficient, induced drag coefficient, pitching moment coefficient, and bending moment coefficient were developed. From these relationships a direct optimization scheme is used to determine the optimum wake vorticity distribution for minimum induced drag, subject to constraints on lift, and pitching or bending moment. Integration spanwise yields the bound circulation, which is interpolated in the near field vortex lattice to obtain the design camber surface(s).
Kuhlman, J. M.↗
Far-Field Antenna Pattern From a Near-Field Test
Plane/polar geometry simplifies measurement of near-field data for this antenna and allows a determination of far-field pattern by Jacobi-Bessel series expansion of data. Measuring probe is an undersized, dielectrically loaded and open-ended waveguide with a far-field pattern similar to that of a small magnetic dipole in its forward directions, making it unnecessary to rotate probe in direction similar to antenna rotation.
Rahmat-Samii, Y.↗
Helicopter far-field acoustic levels as a function of reduced rotor speeds
This paper will present far-field measured noise levels relative to tests conducted with a model S-76A helicopter. The project was designed to provide supplemental experimental flight data which may be used to further study reduced helicopter rotor speeds (and thus, advancing blade-tip Mach number) effects on far-field acoustic levels. The aircraft was flown in straight and level flight while operating with both the rotor speed and flight speed as test variables. The rotor speed was varied over the range of 107 percent of the main-rotor speed (NR) to 90 percent NR and with the forward flight speed varied over the range of 155 to 35 knots indicated air speed. These conditions produced a wide range of advancing blade-tip Mach numbers to which the noise data are related.
Mueller, Arnold W.↗
Far-field distributions of semiconductor phase-locked arrays with multiple contacts
Experimental results on far-field patterns of semiconductor laser arrays with multiple contacts are reported. It is found that, by tailoring the distribution of the currents through the array elements, narrow single-lobe patterns, which are more useful in most applications, can be obtained from arrays that usually operate in a double-lobe mode. A diffraction-limited 1.8 deg-wide far field pattern was obtained from a three-element array.
Katz, J.↗
The electrically long antenna current, admittance and far field
Approximate formula for current distribution, driving point admittance, and far field of thin dipole antennas
CURRENT DISTRIBUTION↗
Potential theoretic methods for far field sound radiation calculations
In the area of computational acoustics, procedures which accurately predict the far-field sound radiation are much sought after. A systematic development of such procedures are found in a sequence of papers by Atassi. The method presented here is an alternate approach to predicting far field sound based on simple layer potential theoretic methods. The main advantages of this method are: it requires only a simple free space Green's function, it can accommodate arbitrary shapes of Kirchoff surfaces, and is readily extendable to three-dimensional problems. Moreover, the procedure presented here, though tested for unsteady lifting airfoil problems, can easily be adapted to other areas of interest, such as jet noise radiation problems. Results are presented for lifting airfoil problems and comparisons are made with the results reported by Atassi. Direct comparisons are also made for the flat plate case.
Hariharan, S. I.↗
Far-Field Pattern Measurement and Simulation of VHF Antenna at 60 MHz for Europa Clipper Mission
This paper presents measurements and simulations of a linearly polarized VHF folded dipole operating at 60 MHz for NASA’s upcoming Europa Clipper mission. The spacecraft contains a ground penetrating radar, consisting of an array of four VHF antennas, that will characterize the surface of Jupiter’s icy moon Europa. Measured far-field radiation patterns and reflection coefficients above a 50×80m perfect ground plane are compared to predicted results using commercial software. Normalized Far-Field radiation pattern cuts are measured utilizing a biconical antenna and receiver mounted on a flying drone. Simulations of the radiation pattern show that the number of lobes increases with the distance of the antenna from the ground due to the ground-bounce phenomenon. In addition, the measured and simulated reflection coefficients stay unchanged for height above 2 meters, which matches the predicted calculation of the reactive-near field region of this antenna. However, the antenna electrical parameters are optimized for use on the spacecraft and become detuned in the presence of a ground plane. Simulated and measured return loss discrepancy less than 0.5 dB is presented. Radiation pattern comparisons show similar agreement when taking into account the effect of far-field measurement uncertainties.
Decrossas, Emmanuel↗
An improved far field drag calculation method for nonlinear CFD codes
An improved method to calculate drag based on far field conditions is presented and demonstrated. The method is illustrated using two CFD codes, PARC and CFL3D, and examining their ability to preserve lift and drag coefficients along grid line defined integration paths. The flow fields were generated by solving the Euler equations for a NACA 0012 airfoil at a free stream Mach number of 0.8 and angle of attack of 1.25 degrees. In comparison to force coefficients obtained by surface pressure integration, neither code acceptably preserved both force coefficients throughout the near and far fields. An investigation into the relationship between numerical prediction error and calculated force coefficients revealed a direct connection between solution mass conservation error and force coefficients error. A method to correct the predicted force coefficients based on integrated mass conservation error is described and demonstrated. The corrected force coefficients for both codes are shown to be more accurate than the uncorrected values. The correction method is applicable to both two and three dimensions and is independent of the algorithm used to generate the flow field.
Sirbaugh, James R.↗
Effects of atmospheric refraction on far-field sound propagation
Refractivity model for calculating far field sound intensity levels of static fired rocket booster
Smith, O. E.↗
Far-Field Rock Size-Frequency Distribution at the Mars Pathfinder Landing Site and Comparison to the Near Field
Detailed measurements of rocks in the far field at the Mars Pathfinder landing site are consistent with the near field exponential drop off in the cumulative number or area covered by large diameter rocks (and with similar behavior at the Viking sites).
Haldemann, A. F. C.↗
Experimental and Analytical Determination of the Geometric Far Field for Round Jets
An investigation was conducted at the NASA Glenn Research Center using a set of three round jets operating under unheated subsonic conditions to address the question: "How close is too close?" Although sound sources are distributed at various distances throughout a jet plume downstream of the nozzle exit, at great distances from the nozzle the sound will appear to emanate from a point and the inverse-square law can be properly applied. Examination of normalized sound spectra at different distances from a jet, from experiments and from computational tools, established the required minimum distance for valid far-field measurements of the sound from subsonic round jets. Experimental data were acquired in the Aeroacoustic Propulsion Laboratory at the NASA Glenn Research Center. The WIND computer program solved the Reynolds-Averaged Navier-Stokes equations for aerodynamic computations; the MGBK jet-noise prediction computer code was used to predict the sound pressure levels. Results from both the experiments and the analytical exercises indicated that while the shortest measurement arc (with radius approximately 8 nozzle diameters) was already in the geometric far field for high-frequency sound (Strouhal number >5), low-frequency sound (Strouhal number <0.2) reached the geometric far field at a measurement radius of at least 50 nozzle diameters because of its extended source distribution.
Koch, L. Danielle↗