Russian Federation
Moskva, Moscow, Russian Federation
The computational error analysis for coefficient of reflection of plane sound waves at the end of opening channel without flange performed by means of formulas commonly used in practice has demonstrated their unacceptability for accurate acoustic calculations, and limitations of the Helmholtz numbers’ range, where these formulas are applicable. In this work have been proposed calculated dependences, convenient for practical usage and enabling more accurately calculate by computer approach the considered quantity’s values in a whole range of existence of the plane waves in the channel.
plane wave, reflection coefficient, acoustic impedance, reflection coefficient module, hole’s cut-in length, end correction, calculation result error, Bessel function.
1. Введение
Коэффициент отражения плоских звуковых волн, распространяющихся по каналу, от его концевого отверстия без фланца в показательной форме может быть представлен в виде:
R = − R e j2kl , (1)
1. Gutin L. Ya. O zvukovom pole porshnevykh izluchateley [On the sound field of piston radiators]. ZhTF [ZhTF]. 1937, V. VII, I. 10, pp. 1096-1106. (in Russian).
2. Levine H., Schwinger J. On the Radiation of Sound from an Unflanged Circular Pipe. J. Phys. Rev., 1948. V.73. I. 4. Pp. 383-406.
3. Davies P. O.A.L., Bento Coelho J. L., Bhattacharya M. J. Reflection coefficients for an unflanged pipe with flow. J. Sound Vibr. 1980. V.72. I. 4.R. 543-546.
4. Norris A. N., Sheng I. C. Acoustic radiation from a circular pipe with an infinite flange. J. Sound Vibr. 1989. V.135. I. 1. Pp. 85-93.
5. Silva F., Guillemain Ph., Kergomard J., Mallaroni B., Norris A. N. Approximation formulae for the acoustic radiation impedance of a cylindrical pipe. J. Sound Vibr. Elsevier. 2009. V. 332. I. 1-2. Pp. 255-263.
6. Andrey R. Da Silva, Paulo Henrique Mareze, ArcanjoLenzi Approximate expressions for the reflection coefficient of ducts terminated by circular flanges. J. Braz. Soc. Mech. Sci. & Eng. Rio de Janeiro. 2012. V.34. I. 2.R.1-13.
7. Mathcad 15/Mathcad Prime 1.0. - St. Petersburg, BKhVPeterburg Publ., 2012. - 432 p. (in Russian).
8. MATLAB. Samouchitel’. Prakticheskiy podkhod [MATLAB. Self-teacher. Practical approach]. St. Petersburg, Nauka i Tekhnika Publ., 2012. 448 p. (in Russian).
9. Tupov V. V. Raschet prisoedinennoy dliny kontsevogo otverstiya kanala bez flantsa pri vypolnenii proektnykh akusticheskikh razrabotok [Calculation of the connected length of the end hole Channel without a flange during design acoustic development]. Bezopasnost’ v tekhnosfere [Safety in the technosphere]. 2016, I. 2, pp. 69-76. DOI:https://doi.org/10.12737/21037. (in Russian).