| Autor: |
Yadav, Mannu, Sadasivan, Anil Lal |
| Zdroj: |
International Journal of Advances in Engineering Sciences & Applied Mathematics; Sep2023, Vol. 15 Issue 2/3, p110-114, 5p |
| Abstrakt: |
The area ratio-Mach number (Stodola) and Prandtl–Meyer (PM) functions are explicit functions of Mach number for the area ratio and the Prandtl–Meyer angle. These functions are related to isentropic expansion in the flow of gases. The inverses of these functions express the Mach number as a function of area ratio or Prandtl–Meyer angle have no explicit mathematical form. Currently used methods either estimate the values of Mach number by interpolation of values taken from gas dynamics tables or generate approximate numerical solutions. In this paper, explicit Taylor series solutions are developed using differential transform method (DTM), to determine the nearly exact values of the Mach number. Since the radius of expansion of Taylor's series is limited by its radius of convergence, a finite number of series expansions with different centers are used for computing the inverses. The recursive relations derived for Taylor's series coefficients are computer coded in FORTRAN. The subroutine that returns series coefficients corresponding to a set of center of expansions is included in a main program provided in GitHub. Other materials given in GitHub include: data files consisting of coordinates of different centers of expansions of each series, coefficients of Taylor's series expansions, computer programs for generating inverse gas dynamics tables for subsonic and supersonic expansions in terms of area ratio, and computer program for the table of supersonic Mach number in terms of PM angle. The error in the computed values given in these tables is negligible. The computer programs and data can be easily incorporated into any computer code. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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