Application of Richardson's extrapolation to numerical evaluation of sonic-boom integrals
Richardson extrapolation applied to numerical evaluation of sonic boom integrals
SEARCH · Engineering Papers
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Richardson extrapolation applied to numerical evaluation of sonic boom integrals
Luminosity function of sporadic meteors and data extrapolation of influx rate to micrometeorite region
Vapor pressure data extrapolated to very high pressures for carbon and refractory metals with thermal absorption cross sections below five barns
Computerized Arrhenius equation component reliability extrapolation techniques
Ore deposits in volcanic rocks on earth with lunar extrapolation
Partially conserved axial vector currents and current algebra to obtain vertex functions at point having zero mass by extrapolations
Technique of extrapolating measured near-field overpressure data to larger altitude applied to wind tunnel overpressure data
Waveform parameters for extrapolating wind tunnel sonic boom signatures to far field
Extrapolation of measured overpressure data for predicting sonic boom characteristics of different aerodynamic configurations
Accelerated life test models, criteria for model selection, and extrapolation in overstress models
Hypersonic cruise aircraft configuration reliable Reynolds numbers extrapolation from laminar boundary to turbulent layer
The waveform parameter method of sonic boom extrapolation is derived and shown to be equivalent to the F-function method. A computer program based on the waveform parameter method is presented and discussed, with a sample case demonstrating program input and output.
Wind tunnel pressure signatures measured at Mach 10.1 for model of the Apollo Command Module and at Mach numbers from 3.01 to 7.91 for two models of the Saturn launch configuration are presented. The signatures for the command module were obtained at roll angles ranging from 0 deg to 180 deg. A brief discussion of the extrapolation of strong pressure signatures is included in the report.
Thermophysical properties data for oxygen at pressures below 5000 psia have been extrapolated to higher pressures (5,000-10,000 psia) in the temperature range 100-600 R. The tables include density, entropy, enthalpy, internal energy, speed of sound, specific heat, thermal conductivity, viscosity, thermal diffusivity, Prandtl number, and dielectric constant.
Results are described of an analytical study of the accuracy and limitations of a technique that permits the mathematical extrapolation of near-field noise data to far-field conditions. The effects of the following variables on predictive accuracy of the far-field pressure were examined: (1) number of near-field microphones; (2) length of source distribution; (3) complexity of near-field and far-field distributions; (4) source-to-microphone distance; and (5) uncertainties in microphone data and imprecision in the location of the near-field microphones. It is shown that the most important parameters describing predictive accuracy are the number of microphones, the ratio of source length to acoustic wavelength, (L/wavelength), and the error in location of near-field microphones. If microphone measurement and location errors are not included, then far-field pressures can be accurately predicted up to L/wavelength values of 15 using approximately 50 microphones. For maximum microphone location errors of + or - 1 cm, only an accuracy of + or - 2-1/2 db can be attained with approximately 40 microphones for the highest L/wavelength of 10.
A test was conducted in the Boeing Large Anechoic Chamber to determine static jet noise source locations of six baseline and suppressor nozzle models, and establish a technique for extrapolating near field data into the far field. The test covered nozzle pressure ratios from 1.44 to 2.25 and jet velocities from 412 to 594 m/s at a total temperature of 844 K.
Results are presented for an analytical study of the accuracy and limitations of a technique that permits the mathematical extrapolation of near-field noise data to far-field conditions. The effects of the following variables on predictive accuracy of the far-field pressure were examined: (1) number of near-field microphones; (2) length of source distribution; (3) complexity of near-field and far-field distributions; (4) source-to-microphone distance; and (5) uncertainties in microphone data and imprecision in the location of the near-field microphones. It is shown that the most important parameters describing predictive accuracy are the number of microphones, the ratio of source length to acoustic wavelength (L/lambda), and the error in location of near-field microphones. For maximum microphone location errors of plus or minus 1 cm, only an accuracy of plus or minus 2.5 dB can be attained with approximately 40 microphones for the highest L/lambda of 10.
Several extrapolation procedures are presented for increasing the order of accuracy in time for evolutionary partial differential equations. These formulas are based on finite difference schemes in both the spatial and temporal directions. On practical grounds the methods are restricted to schemes that are fourth order in time and either second, fourth or sixth order in space. For hyperbolic problems the second order in space methods are not useful while the fourth order methods offer no advantage over the Kreiss-Oliger method unless very fine meshes are used. Advantages are first achieved using sixth order methods in space coupled with fourth order accuracy in time. Computational results are presented confirming the analytic discussions.