10 research outputs found
How Ordinary Elimination Became Gaussian Elimination
Get PDFNewton, in notes that he would rather not have seen published, described a
process for solving simultaneous equations that later authors applied
specifically to linear equations. This method that Euler did not recommend,
that Legendre called "ordinary," and that Gauss called "common" - is now named
after Gauss: "Gaussian" elimination. Gauss's name became associated with
elimination through the adoption, by professional computers, of a specialized
notation that Gauss devised for his own least squares calculations. The
notation allowed elimination to be viewed as a sequence of arithmetic
operations that were repeatedly optimized for hand computing and eventually
were described by matrices.Comment: 56 pages, 21 figures, 1 tabl
The Application of a Linear Microphone Array in the Quantitative Evaluation of the Blade Trailing-Edge Noise Reduction
No full textThis paper concerns the application of a linear microphone array in the quantitative evaluation of blade trailing-edge (TE) noise reduction. The noise radiation from the blades with straight and serrated TEs is measured in an indoor open-jet wind tunnel. The array data are processed using the inverse method based on the Clean algorithm based on spatial source coherence (Clean-SC). In order to obtain correct application and achieve the best effect for the microphone array test, the computing software for array data reduction is firstly developed and assessed by Sarradj’s benchmark case. The assessment results show that the present array data processing method has a good accuracy with an error less than 0.5 dB in a wide frequency range. Then, a linear array with 32 microphones is designed to identify the noise source of a NACA65(12)-10 blade. The performance of the Clean-SC algorithm is compared with the Clean algorithm based on point spread functions (Clean-PSF) method for experimentally identifying the noise sources of the blade. The results show that there is about a 2 dB error when using the Clean-PSF algorithm due to the interference of different aerodynamic noise sources. Experimental studies are conducted to study the blade TE noise reduction using serrated TEs. The TE noise for the blade with and without sawtooth configurations is measured with the flow speeds from 20 m/s to 70 m/s, and the corresponding Reynolds numbers based on the chord are from 200,000 to 700,000. Parametric studies of the sawtooth amplitude and wavelength are conducted to understand the noise reduction law. It is observed that the TE noise reduction is sensitive to both the amplitude and wavelength. The flow speed also affects the noise reduction in the serrated TEs. To obtain the best noise suppression effect, the sawtooth configuration should be carefully designed according to the actual working conditions and airflow parameters
The Application of a Linear Microphone Array in the Quantitative Evaluation of the Blade Trailing-Edge Noise Reduction
No full textThis paper concerns the application of a linear microphone array in the quantitative evaluation of blade trailing-edge (TE) noise reduction. The noise radiation from the blades with straight and serrated TEs is measured in an indoor open-jet wind tunnel. The array data are processed using the inverse method based on the Clean algorithm based on spatial source coherence (Clean-SC). In order to obtain correct application and achieve the best effect for the microphone array test, the computing software for array data reduction is firstly developed and assessed by Sarradj’s benchmark case. The assessment results show that the present array data processing method has a good accuracy with an error less than 0.5 dB in a wide frequency range. Then, a linear array with 32 microphones is designed to identify the noise source of a NACA65(12)-10 blade. The performance of the Clean-SC algorithm is compared with the Clean algorithm based on point spread functions (Clean-PSF) method for experimentally identifying the noise sources of the blade. The results show that there is about a 2 dB error when using the Clean-PSF algorithm due to the interference of different aerodynamic noise sources. Experimental studies are conducted to study the blade TE noise reduction using serrated TEs. The TE noise for the blade with and without sawtooth configurations is measured with the flow speeds from 20 m/s to 70 m/s, and the corresponding Reynolds numbers based on the chord are from 200,000 to 700,000. Parametric studies of the sawtooth amplitude and wavelength are conducted to understand the noise reduction law. It is observed that the TE noise reduction is sensitive to both the amplitude and wavelength. The flow speed also affects the noise reduction in the serrated TEs. To obtain the best noise suppression effect, the sawtooth configuration should be carefully designed according to the actual working conditions and airflow parameters
