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Аэродинамические характеристики системы «Винт в кольце» в условиях обтекания горизонтальным потоком под нулевым углом атаки..pdf

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Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
ɍȾɄ 629.735
ȺɗɊɈȾɂɇȺɆɂɑȿɋɄɂȿ ɏȺɊȺɄɌȿɊɂɋɌɂɄɂ ɋɂɋɌȿɆɕ
«ȼɂɇɌ ȼ ɄɈɅɖɐȿ» ȼ ɍɋɅɈȼɂəɏ ɈȻɌȿɄȺɇɂə
ȽɈɊɂɁɈɇɌȺɅɖɇɕɆ ɉɈɌɈɄɈɆ ɉɈȾ ɇɍɅȿȼɕɆ ɍȽɅɈɆ ȺɌȺɄɂ
ȼ.ɂ. ɒȺɃȾȺɄɈȼ
ȼɢɧɬ ɜ ɤɨɥɶɰɟ ɦɨɠɟɬ ɩɪɢɦɟɧɹɬɶɫɹ ɜ ɤɚɱɟɫɬɜɟ ɮɟɧɟɫɬɪɨɧɨɜ ɨɞɧɨɜɢɧɬɨɜɵɯ ɜɟɪɬɨɥɟɬɨɜ, ɞɜɢɠɢɬɟɥɟɣ ɦɚɥɨɫɤɨɪɨɫɬɧɵɯ ɫɚɦɨɥɟɬɨɜ, ɞɢɪɢɠɚɛɥɟɣ, ɚ ɬɚɤɠɟ ɜ ɜɢɞɟ ɚɜɬɨɧɨɦɧɵɯ ɫɢɫɬɟɦ ɞɢɫɬɚɧɰɢɨɧɧɨ ɩɢɥɨɬɢɪɭɟɦɵɯ ɥɟɬɚɬɟɥɶɧɵɯ ɚɩɩɚɪɚɬɨɜ (ȾɉɅȺ). Ⱦɚɧɧɚɹ ɪɚɛɨɬɚ ɹɜɥɹɟɬɫɹ ɩɪɨɞɨɥɠɟɧɢɟɦ ɢɫɫɥɟɞɨɜɚɧɢɣ ɚɜɬɨɪɚ ɜ ɨɛɥɚɫɬɢ ɚɷɪɨɞɢɧɚɦɢɤɢ ɜɢɧɬɚ ɜ ɤɨɥɶɰɟ.
ɉɪɟɞɥɚɝɚɟɬɫɹ ɦɟɬɨɞ ɪɚɫɱɟɬɚ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɫɢɫɬɟɦɵ «ɜɢɧɬ ɜ ɤɨɥɶɰɟ» ɫ ɰɢɥɢɧɞɪɢɱɟɫɤɢɦ
ɞɢɮɮɭɡɨɪɨɦ ɨɝɪɚɧɢɱɟɧɧɨɣ ɞɥɢɧɵ ɜ ɪɟɠɢɦɚɯ ɨɛɬɟɤɚɧɢɹ ɩɨɞ ɧɭɥɟɜɵɦ ɭɝɥɨɦ ɚɬɚɤɢ. ɂɫɫɥɟɞɭɟɬɫɹ ɯɚɪɚɤɬɟɪ ɨɛɬɟɤɚɧɢɹ
ɫɢɫɬɟɦɵ ɜɧɟɲɧɢɦ ɩɨɬɨɤɨɦ. Ⱦɚɸɬɫɹ ɮɨɪɦɭɥɵ ɞɥɹ ɪɚɫɱɟɬɚ ɫɤɨɪɨɫɬɟɣ ɩɪɨɬɟɤɚɧɢɹ ɩɨɬɨɤɚ ɱɟɪɟɡ ɞɢɫɤ ɜɢɧɬɚ, ɤɨɬɨɪɵɟ
ɭɦɟɧɶɲɚɸɬɫɹ ɫ ɪɨɫɬɨɦ ɞɥɢɧɵ ɞɢɮɮɭɡɨɪɚ ɢ ɫɤɨɪɨɫɬɢ ɩɨɥɟɬɚ.
Ɉɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟ ɩɨɞɴɟɦɧɵɯ ɫɢɥ ɜɢɧɬɚ ɢ ɤɨɥɶɰɚ ɧɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɪɟɠɢɦɚɯ, ɚ ɬɚɤɠɟ
ɢɦɩɭɥɶɫɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɢɫɬɟɦɵ, ɜɨɡɧɢɤɚɸɳɟɟ ɜɫɥɟɞɫɬɜɢɟ ɤɪɭɬɨɝɨ ɩɨɜɨɪɨɬɚ ɩɨɬɨɤɚ ɜ ɤɚɧɚɥɟ. ȼɟɥɢɱɢɧɚ
ɢɦɩɭɥɶɫɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɚ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɨɬɤɥɨɧɟɧɢɸ ɧɚɡɚɞ ɩɨɥɧɨɣ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɢɥɵ ɫɢɫɬɟɦɵ. ɗɬɨɬ ɭɝɨɥ ɪɚɫɬɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɞɥɢɧɵ ɞɢɮɮɭɡɨɪɚ ɢ ɧɚ ɫɪɟɞɧɢɯ ɫɤɨɪɨɫɬɹɯ ɦɨɠɟɬ ɞɨɫɬɢɝɚɬɶ 30°.
Ⱦɨɫɬɨɜɟɪɧɨɫɬɶ ɩɪɟɞɥɚɝɚɟɦɵɯ ɚɥɝɨɪɢɬɦɨɜ ɩɨɞɬɜɟɪɠɞɟɧɚ ɫɪɚɜɧɟɧɢɟɦ ɪɟɡɭɥɶɬɚɬɨɜ ɪɚɫɱɟɬɨɜ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ ɞɥɹ ɮɟɧɟɫɬɪɨɧɚ ɜɟɪɬɨɥɟɬɚ, ɚ ɬɚɤɠɟ ɤɨɪɩɭɫɚ ȾɉɅȺ, ɢɫɩɵɬɚɧɧɨɝɨ ɜ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɥɚɛɨɪɚɬɨɪɢɢ ɆȺɂ.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɫɢɫɬɟɦɚ «ɜɢɧɬ ɜ ɤɨɥɶɰɟ», ɮɟɧɟɫɬɪɨɧ, ɝɨɪɢɡɨɧɬɚɥɶɧɵɣ ɩɨɥɟɬ, ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ.
ȼɢɧɬ ɜ ɤɨɥɶɰɟ ɦɨɠɟɬ ɩɪɢɦɟɧɹɬɶɫɹ ɜ ɤɚɱɟɫɬɜɟ ɮɟɧɟɫɬɪɨɧɨɜ ɨɞɧɨɜɢɧɬɨɜɵɯ ɜɟɪɬɨɥɟɬɨɜ,
ɞɜɢɠɢɬɟɥɟɣ ɦɚɥɨɫɤɨɪɨɫɬɧɵɯ ɫɚɦɨɥɟɬɨɜ, ɞɢɪɢɠɚɛɥɟɣ, ɚ ɬɚɤɠɟ ɜ ɜɢɞɟ ɚɜɬɨɧɨɦɧɵɯ ɫɢɫɬɟɦ ɞɢɫɬɚɧɰɢɨɧɧɨ ɩɢɥɨɬɢɪɭɟɦɵɯ ɥɟɬɚɬɟɥɶɧɵɯ ɚɩɩɚɪɚɬɨɜ (ȾɉɅȺ). Ⱦɚɧɧɚɹ ɪɚɛɨɬɚ ɹɜɥɹɟɬɫɹ ɩɪɨɞɨɥɠɟɧɢɟɦ ɢɫɫɥɟɞɨɜɚɧɢɣ ɚɜɬɨɪɚ ɜ ɨɛɥɚɫɬɢ ɚɷɪɨɞɢɧɚɦɢɤɢ ɜɢɧɬɚ ɜ ɤɨɥɶɰɟ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɜ ɪɹɞɟ ɪɚɛɨɬ [1, 2, 3]. ȼ ɱɚɫɬɧɨɫɬɢ, ɜ ɫɬɚɬɶɟ [1] ɪɚɫɫɦɚɬɪɢɜɚɥɫɹ ɪɟɠɢɦ ɪɚɛɨɬɵ ɧɚ ɦɟɫɬɟ ɜɢɧɬɚ ɜ ɤɨɥɶɰɟ ɫ
ɤɨɪɨɬɤɢɦ ɰɢɥɢɧɞɪɢɱɟɫɤɢɦ ɞɢɮɮɭɡɨɪɨɦ. Ɂɞɟɫɶ ɠɟ ɢɫɫɥɟɞɭɟɬɫɹ ɪɟɠɢɦ ɨɛɞɭɜɤɢ ɜɨɡɞɭɲɧɵɦ ɩɨɬɨɤɨɦ ɩɨɞ ɧɭɥɟɜɵɦ ɭɝɥɨɦ ɚɬɚɤɢ (ɩɨ ɧɨɪɦɚɥɢ ɤ ɨɫɢ ɜɢɧɬɚ). ɉɪɢ ɪɚɡɪɚɛɨɬɤɟ ɪɚɫɱɟɬɧɨɣ ɦɨɞɟɥɢ
ɬɟɱɟɧɢɹ ɩɪɢɦɟɧɹɟɬɫɹ ɬɨɬ ɠɟ ɩɨɞɯɨɞ, ɱɬɨ ɢ ɜ ɪɚɛɨɬɚɯ [1, 2, 3]. ȼɫɹ ɫɢɫɬɟɦɚ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ
ɜɨɡɞɭɲɧɚɹ ɫɟɬɶ, ɫɨɫɬɨɹɳɚɹ ɢɡ ɤɨɥɥɟɤɬɨɪɚ, ɜɢɧɬɚ, ɞɢɮɮɭɡɨɪɚ ɢ ɜɧɭɬɪɟɧɧɢɯ ɭɫɬɪɨɣɫɬɜ ɜ ɤɚɧɚɥɟ,
ɞɚɸɳɢɯ ɫɨɩɪɨɬɢɜɥɟɧɢɟ. ɋɭɦɦɚɪɧɵɟ ɩɨɬɟɪɢ ɞɚɜɥɟɧɢɣ ɜ ɤɚɧɚɥɟ ɨɩɪɟɞɟɥɹɥɢɫɶ ɤɚɤ ɫɭɩɟɪɩɨɡɢɰɢɹ
ɦɟɫɬɧɵɯ ɩɨɬɟɪɶ. ɋɚɦ ɜɢɧɬ, ɪɚɛɨɬɚɸɳɢɣ ɜ ɤɚɧɚɥɟ, ɦɨɞɟɥɢɪɨɜɚɥɫɹ ɩɨ ɫɯɟɦɟ ɞɢɫɤɨɜɨɣ ɜɢɯɪɟɜɨɣ
ɬɟɨɪɢɢ [4] ɫ ɭɱɟɬɨɦ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɢɧɞɭɤɬɢɜɧɨɝɨ ɩɨɬɨɤɚ, ɧɚɜɟɞɟɧɧɨɝɨ ɤɨɥɶɰɨɦ. Ʉɨɥɥɟɤɬɨɪ ɢ
ɞɢɮɮɭɡɨɪ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɜ ɪɚɛɨɬɟ [1], ɦɨɞɟɥɢɪɭɸɬɫɹ ɷɤɜɢɜɚɥɟɧɬɧɵɦ ɜɢɯɪɟɜɵɦ ɰɢɥɢɧɞɪɨɦ ɜɵɫɨɬɵ ɇ. Ɋɚɡɜɢɬɢɟɦ ɦɟɬɨɞɚ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ [2] ɹɜɥɹɟɬɫɹ ɭɱɟɬ ɨɝɪɚɧɢɱɟɧɧɨɣ ɞɥɢɧɵ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ
ɱɚɫɬɢ ɞɢɮɮɭɡɨɪɚ, ɧɟ ɫɩɨɫɨɛɧɨɣ ɨɛɟɫɩɟɱɢɬɶ ɩɨɥɧɨɟ ɪɚɫɲɢɪɟɧɢɟ ɩɨɬɨɤɚ ɧɚ ɜɵɯɨɞɟ ɢɡ ɤɚɧɚɥɚ.
ɉɪɢɧɹɬɵɟ ɭɫɥɨɜɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɬɟ ɠɟ, ɱɬɨ ɢ ɜ ɪɚɛɨɬɟ [1].
ɋɂɋɌȿɆȺ «ȼɂɇɌ ȼ ɄɈɅɖɐȿ»
ȼ ɍɋɅɈȼɂəɏ ɈȻȾɍȼɄɂ ɉɈȾ ɇɍɅȿȼɕɆ ɍȽɅɈɆ ȺɌȺɄɂ
ȼ ɞɚɧɧɨɦ ɪɚɡɞɟɥɟ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɫɥɭɱɚɣ ɨɛɬɟɤɚɧɢɹ ɫɢɫɬɟɦɵ «ɜɢɧɬ ɜ ɤɨɥɶɰɟ» ɜɨɡɞɭɲɧɵɦ ɩɨɬɨɤɨɦ ɩɨɞ ɧɭɥɟɜɵɦ ɭɝɥɨɦ ɚɬɚɤɢ (ɜɟɤɬɨɪ ɫɤɨɪɨɫɬɢ ɧɚɛɟɝɚɸɳɟɝɨ ɩɨɬɨɤɚ V ɩɟɪɩɟɧɞɢɤɭɥɹɪɟɧ ɨɫɢ ɜɢɧɬɚ). ɉɪɢ ɩɨɫɬɪɨɟɧɢɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɩɪɢɦɟɧɹɟɬɫɹ ɬɨɬ ɠɟ ɩɨɞɯɨɞ,
ɱɬɨ ɢ ɜ ɪɟɠɢɦɟ ɪɚɛɨɬɵ ɧɚ ɦɟɫɬɟ. Ɉɬɥɢɱɢɟ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɢɫɬɟɤɚɸɳɚɹ ɢɡ ɤɚɧɚɥɚ ɫɬɪɭɹ ɨɬɤɥɨɧɹɟɬɫɹ ɧɚɛɟɝɚɸɳɢɦ ɩɨɬɨɤɨɦ ɧɚɡɚɞ, ɜɟɤɬɨɪ ɩɨɥɧɨɣ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɢɥɵ Ra ɬɚɤɠɟ ɨɬɤɥɨ165
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɧɹɟɬɫɹ ɧɚɡɚɞ ɧɚ ɭɝɨɥ ϑ ɢ ɞɚɟɬ ɫɨɫɬɚɜɥɹɸɳɭɸ Qɢ ɜ ɜɢɞɟ ɢɦɩɭɥɶɫɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɩɪɢɥɨɠɟɧɧɭɸ ɤ ɡɚɞɧɟɣ ɫɬɟɧɤɟ ɤɚɧɚɥɚ. ȼ ɩɪɨɟɤɰɢɢ ɧɚ ɨɫɶ ɜɢɧɬɚ ɫɢɥɚ Ra ɞɚɟɬ ɫɨɫɬɚɜɥɹɸɳɭɸ ɬɹɝɢ
T = Tɤ + Tɜ . Ɂɞɟɫɶ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɜ ɪɟɠɢɦɟ ɨɫɟɜɨɣ ɨɛɞɭɜɤɢ, ɩɨɞ ɬɹɝɨɣ ɤɨɥɶɰɚ Tɤ ɩɨɧɢɦɚɟɬɫɹ ɬɨɥɶɤɨ ɬɚ ɟɟ ɫɨɫɬɚɜɥɹɸɳɚɹ, ɤɨɬɨɪɚɹ ɫɨɡɞɚɟɬɫɹ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɤɨɥɥɟɤɬɨɪɚ, ɩɨɩɚɞɚɸɳɟɣ
ɜɧɭɬɪɶ ɫɬɪɭɢ.
ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɟɨɪɟɦɨɣ ɢɦɩɭɥɶɫɨɜ [5] ɩɥɨɫɤɨɫɬɶ ɜɢɯɪɟɜɵɯ ɤɨɥɟɰ, ɦɨɞɟɥɢɪɭɸɳɢɯ
ɜɢɯɪɟɜɨɣ ɫɥɟɞ, ɞɨɥɠɧɚ ɛɵɬɶ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚ ɜɟɤɬɨɪɭ Ra . ɉɨɝɨɧɧɚɹ ɰɢɪɤɭɥɹɰɢɹ ɫɜɨɛɨɞɧɵɯ
dȽ
ɜɢɯɪɟɣ ɩɨ ɨɛɪɚɡɭɸɳɟɣ ɫɤɨɲɟɧɧɨɝɨ ɜɢɯɪɟɜɨɝɨ ɰɢɥɢɧɞɪɚ ɛɭɞɟɬ γ =
(ɪɢɫ. 1). Ɋɚɡɥɨɠɟɧɢɟ
dl
ɜɢɯɪɟɜɨɣ ɫɢɫɬɟɦɵ ɧɚ ɤɨɥɶɰɟɜɵɟ ɢ ɩɪɨɞɨɥɶɧɵɟ ɜɢɯɪɢ ɨɛɭɫɥɚɜɥɢɜɚɟɬ: ɤɨɥɶɰɟɜɵɟ ɜɢɯɪɢ – ɬɹɝɭ Ɍ
ɢ ɤɨɦɩɨɧɟɧɬ v2 y ɢɧɞɭɤɬɢɜɧɨɣ ɫɤɨɪɨɫɬɢ v 2 , ɩɪɨɞɨɥɶɧɵɟ ɜɢɯɪɢ – ɢɦɩɭɥɶɫɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ Qɢ
ɢ ɤɨɦɩɨɧɟɧɬɵ v n ɢ v2 x .
Ɋɢɫ. 1. ɋɯɟɦɚ ɪɚɡɥɨɠɟɧɢɹ ɫɜɨɛɨɞɧɨɝɨ ɜɢɯɪɟɜɨɝɨ ɫɥɟɞɚ ɧɚ ɩɨɩɟɪɟɱɧɵɟ ɢ ɩɪɨɞɨɥɶɧɵɟ ɜɢɯɪɢ
ȼɜɟɞɟɦ ɪɚɫɱɟɬɧɵɟ ɫɟɱɟɧɢɹ ɫɬɪɭɢ: 1-1 ɜ ɩɥɨɫɤɨɫɬɢ ɜɢɧɬɚ, 2-2 ɜ ɭɞɚɥɟɧɧɨɦ ɜɢɯɪɟɜɨɦ ɫɥɟɞɟ. ɉɨɥɚɝɚɟɦ, ɱɬɨ ɫɤɨɪɨɫɬɢ ɩɨ ɫɟɱɟɧɢɹɦ ɩɨɫɬɨɹɧɧɵ.
ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɦɨɞɟɥɶɸ ɨɛɨɛɳɟɧɧɨɣ ɞɢɫɤɨɜɨɣ ɜɢɯɪɟɜɨɣ ɬɟɨɪɢɢ [4] ɩɨɥɚɝɚɟɦ,
ɱɬɨ ɜ ɜɢɯɪɟɜɨɣ ɫɥɟɞ ɡɚ ɤɚɠɞɵɣ ɦɚɥɵɣ ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ ¨t ɩɨɫɬɭɩɚɟɬ ɧɚɤɥɨɧɟɧɧɨɟ
ɩɨɞ ɭɝɥɨɦ 5 ɜɢɯɪɟɜɨɟ ɤɨɥɶɰɨ ɫ ɰɢɪɤɭɥɹɰɢɟɣ dȽ ɢ ɩɥɨɳɚɞɶɸ F (ɪɢɫ. 2). ɂɫɩɨɥɶɡɭɟɦ ɬɟɨɪɟɦɭ
ɀɭɤɨɜɫɤɨɝɨ – Ⱦɭɛɚɫɨɜɚ (ɫɦ. [5]) ɨ ɤɨɥɢɱɟɫɬɜɟ ɞɜɢɠɟɧɢɹ, ɜɵɡɵɜɚɟɦɨɦ ɡɚɦɤɧɭɬɵɦ ɜɢɯɪɟɜɵɦ
JJG
ɤɨɥɶɰɨɦ ɜ ɫɩɥɨɲɧɨɣ ɫɪɟɞɟ dM = ȡdȽ F. ɂɦɩɭɥɶɫ ɫɢɥɵ Ra ɡɚ ɜɪɟɦɹ dt ɫɨɫɬɚɜɥɹɟɬ Radt = dM. ȿɫɥɢ ɫɤɨɪɨɫɬɶ ɩɟɪɟɦɟɳɟɧɢɹ ɜɢɯɪɟɜɵɯ ɤɨɥɟɰ ɜ ɜɢɯɪɟɜɨɦ ɫɥɟɞɟ ɛɭɞɟɬ Vɜɫ , ɬɨ dt = dl / Vɜɫ . Ɉɬɫɸɞɚ
dM
dȽ
R=
=ρ
FVɜɫ = ργ FVɜɫ . ɂɡ [1] ɫɥɟɞɭɟɬ, ɱɬɨ γ = K H v1 y . ɋɤɨɪɨɫɬɶ ɜɵɯɨɞɚ ɜɢɯɪɟɜɵɯ ɤɨɥɟɰ
dt
dl
ɢɡ ɞɢɮɮɭɡɨɪɚ ɜ ɫɜɨɛɨɞɧɵɣ ɩɨɬɨɤ ɦɨɠɧɨ ɩɪɢɧɹɬɶ ɪɚɜɧɨɣ
Vɜɫ = V1 = V 2 + v1y2 .
(1)
ɂ ɬɨɝɞɚ ɩɨɥɧɚɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɚɹ ɫɢɥɚ ɛɭɞɟɬ
Ra = ργ FV1 = K H ρ Fv1 yV1 .
ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ ɫɭɦɦɚɪɧɚɹ ɬɹɝɚ ɫɢɫɬɟɦɵ
166
(2)
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T = Ra cos ϑ = K H ρ Fv 1 yV1 cos ϑ .
(3)
ɂɦɩɭɥɶɫɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɩɨɬɟɪɹɧɧɨɦɭ ɤɨɥɢɱɟɫɬɜɭ ɞɜɢɠɟɧɢɹ,
ɩɪɨɬɟɤɚɸɳɟɝɨ ɱɟɪɟɡ ɤɚɧɚɥ ɩɨɬɨɤɚ ɧɚ ɫɪɟɡɟ ɞɢɮɮɭɡɨɪɚ:
Qɢ = ρ F1v1 y v1x = K Hx ρ F1v1 y v1x ,
(4)
ɝɞɟ v1x = K HxV , K Hx – ɤɨɷɮɮɢɰɢɟɧɬ ɬɨɪɦɨɠɟɧɢɹ ɩɨɬɨɤɚ ɧɚ ɡɚɞɧɟɣ ɫɬɟɧɤɟ ɤɚɧɚɥɚ. ȼɜɟɞɟɦ ɤɨɷɮɮɢɰɢɟɧɬɵ
ɋH =
K Hx
F
ɩɥɨɳɚɞɶ ɞɢɫɤɚ ɜɢɧɬɚ
;f = 1 =
.
KH
F ɩɥɨɳɚɞɶ ɜɢɯɪɟɜɨɝɨ ɤɨɥɶɰɚ ɜ ɫɥɟɞɟ
(5)
ɍɝɨɥ ɡɚɜɚɥɚ ɧɚɡɚɞ ɜɟɤɬɨɪɚ Ra (ɢɥɢ ɭɝɨɥ ɧɚɤɥɨɧɚ ɜɢɯɪɟɜɨɝɨ ɤɨɥɶɰɚ ɜ ɫɥɟɞɟ ϑ ) ɧɚɣɞɟɦ ɢɡ
ɫɨɨɬɧɨɲɟɧɢɹ
sin ϑ =
Qɢ ( 4 ) K Hx F1 V
V
=
=
= CH f .
Ra ( 2 ) K H F V1
V1
(6)
ȼɯɨɞɹɳɟɟ ɜ (6) ɨɬɧɨɲɟɧɢɟ V V1 ɧɚɣɞɟɦ ɢɡ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ ɫɤɨɪɨɫɬɟɣ ɜ ɫɥɟɞɟ (ɪɢɫ. 2):
V
V
1
,
= cos θ =
=
2
2
V1
V + v1 y
1 + Cv2
ɝɞɟ Cv =
v1y
V
(7)
.
θ = arccos
1
1 + Cv2
(8)
Ɍɟɩɟɪɶ ɢɡ (6) ɢ (7) ɫɥɟɞɭɟɬ:
sin ϑ = CH f cos θ , cos ϑ = 1 − C H2 f 2 cos 2 θ .
(9)
ɋɨɨɬɧɨɲɟɧɢɟ ɩɥɨɳɚɞɟɣ F1 ɢ F ɧɚɣɞɟɦ ɢɡ ɪɢɫ. 2 ɩɨ ɬɟɨɪɟɦɟ ɫɢɧɭɫɨɜ.
F
sin(π − δ )
=
F1
sin θ
; sin(π − δ ) = sin(δ ) = sin(θ + ϑ ) ; sin(δ − ϑ ) = sin(θ ) ; f =
.
sin(θ + ϑ )
sin(δ − ϑ )
ɉɨɫɥɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɢ ɩɨɞɫɬɚɧɨɜɤɢ ɮɨɪɦɭɥ (9) ɩɨɥɭɱɢɦ ɛɢɤɜɚɞɪɚɬɧɨɟ ɭɪɚɜɧɟɧɢɟ
ɋɇ2 cos 2 θ f 4 − (2CH cos 2 θ + sin θ ) f 2 + sin 2 (θ ) = 0 .
(10)
Ɋɟɲɢɦ ɭɪɚɜɧɟɧɢɟ, ɜɵɛɪɚɜ ɤɨɪɟɧɶ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɣ ɮɢɡɢɱɟɫɤɨɣ ɤɚɪɬɢɧɟ ɦɨɞɟɥɢ ɬɟɱɟɧɢɹ (ɪɢɫ. 2). ɉɪɨɞɟɥɚɜ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ, ɩɨɥɭɱɢɦ
167
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f =
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Vol. 19, ʋ 04, 2016
2sin θ
( 2C
2CH cos θ + sin θ +
2
cos θ + sin θ ) − 4C cos θ
2
2
H
2
H
.
(11)
2
ɋɨɫɬɚɜɢɦ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɤɨɪɨɫɬɟɣ v1 y ɜ ɩɥɨɫɤɨɫɬɢ ɞɢɫɤɚ ɜɢɧɬɚ, ɢɫɩɨɥɶɡɨɜɚɜ ɮɨɪɦɭɥɵ (3) ɢ (1):
T
f
= v1 y V 2 + v12y
K H ρ F1 cos ϑ
(12)
ȼɜɟɞɟɦ ɤɨɷɮɮɢɰɢɟɧɬ
Cf =
f
(11)
=
cos ϑ (9)
(13)
ɉɟɪɟɣɞɟɦ ɤ ɨɬɧɨɫɢɬɟɥɶɧɵɦ ɫɤɨɪɨɫɬɹɦ v1 y = v1 y v1ɭɜ ; V = V v1ɭɜ , ɝɞɟ v1ɭɜ ɛɟɪɟɬɫɹ ɞɥɹ v1ɭ
ɩɪɢ V = 0. Ɍɨɝɞɚ ɢɡ (12) ɩɨɫɥɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɩɨɥɭɱɢɦ ɛɢɤɜɚɞɪɚɬɧɨɟ ɭɪɚɜɧɟɧɢɟ. ȼɵɛɪɚɜ ɤɨɪɟɧɶ ɭɪɚɜɧɟɧɢɹ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɣ ɭɫɥɨɜɢɸ v1 y > 0 , ɩɨɥɭɱɢɦ
v1 y =
)
(
1 2
−V + V 4 + 4C 2f .
2
(14)
Ʉɚɤ ɜɢɞɢɦ, ɮɨɪɦɭɥɵ (8), (11), (13), (14) ɜ ɧɟɹɜɧɨɦ ɜɢɞɟ ɜɵɪɚɠɚɸɬ ɮɭɧɤɰɢɨɧɚɥɶɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ v1 y (V ) . ɉɨɷɬɨɦɭ ɪɟɲɟɧɢɟ ɞɨɥɠɧɨ ɩɪɨɜɨɞɢɬɶɫɹ ɦɟɬɨɞɨɦ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɯ ɩɪɢɛɥɢɠɟɧɢɣ. Ɋɚɫɱɟɬ ɜɟɞɟɬɫɹ ɩɨ ɫɥɟɞɭɸɳɟɦɭ ɚɥɝɨɪɢɬɦɭ. Ⱦɥɹ ɡɚɞɚɧɧɵɯ ɡɧɚɱɟɧɢɣ C ɢ V ɩɨɫɥɟɞɨɜɚH
ɬɟɥɶɧɨ ɜɵɱɢɫɥɹɸɬɫɹ (ɜ ɫɤɨɛɤɚɯ ɭɤɚɡɚɧɵ ɧɨɦɟɪɚ ɮɨɪɦɭɥ):
1) C ′f = 1 → v1 y (14),
2) Cv (7), ϑ (8), f (11), cos ϑ (9), C ′′f (13).
ɐɢɤɥ ɩɨɜɬɨɪɹɟɬɫɹ ɞɨ ɫɨɜɩɚɞɟɧɢɹ ɫɨɫɟɞɧɢɯ ɪɟɡɭɥɶɬɚɬɨɜ ɫ ɡɚɞɚɧɧɨɣ ɬɨɱɧɨɫɬɶɸ.
ɉɪɢ ɪɟɲɟɧɢɢ ɞɚɧɧɨɣ ɡɚɞɚɱɢ ɜɨɡɧɢɤɚɟɬ ɜɨɩɪɨɫ ɨ ɜɵɛɨɪɟ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ
K
CH = Hx
ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɤɚɧɚɥɚ ( rɤ ɢ H ɞ ). Ɍɚɤ ɤɚɤ ɤɨɷɮɮɢɰɢKH
ɟɧɬ K H ɨɞɧɨɡɧɚɱɧɨ ɨɩɪɟɞɟɥɟɧ (ɫɦ. [1]), ɨɫɬɚɟɬɫɹ ɨɩɪɟɞɟɥɢɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɬɨɪɦɨɠɟɧɢɹ ɩɨɬɨɤɚ
K Hx . ɋɬɪɨɝɨ ɝɨɜɨɪɹ, ɷɬɨɬ ɤɨɷɮɮɢɰɢɟɧɬ ɞɨɥɠɟɧ ɧɚɯɨɞɢɬɶɫɹ ɢɡ ɭɫɥɨɜɢɹ ɧɟɩɪɨɬɟɤɚɧɢɹ ɩɨɬɨɤɚ ɧɚ
ɡɚɞɧɟɣ ɫɬɟɧɤɟ ɤɚɧɚɥɚ. Ɉɞɧɚɤɨ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɟɝɨ ɜɟɥɢɱɢɧɚ ɦɨɠɟɬ ɛɵɬɶ ɧɚɣɞɟɧɚ ɢɡ ɝɪɚɧɢɱɧɵɯ ɭɫɥɨɜɢɣ. ɉɪɢ H ɞ = 0 , rɤ = 0 (ɢɡɨɥɢɪɨɜɚɧɧɵɣ ɜɢɧɬ), K H = 2, K Hx = 0 ; ɩɪɢ H ɞ = ∞ ,
K H = 1, K Hx = 1 (ɩɨɥɧɨɟ ɬɨɪɦɨɠɟɧɢɟ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɫɤɨɪɨɫɬɢ ɢɥɢ ɩɨɜɨɪɨɬ ɩɨɬɨɤɚ ɧɚ 90°). ȼ ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɫɥɭɱɚɹɯ ɞɥɹ K Hx ɩɪɢɛɥɢɠɟɧɧɨ ɦɨɠɧɨ ɜɡɹɬɶ ɥɢɧɟɣɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬɧɨɫɢɬɟɥɶɧɨ K H :
K Hx = 2 − K H , ɢ ɬɨɝɞɚ CH =
168
KHx
KH
=
2
−1 .
KH
(15)
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ȼɨ ɜɫɟɯ ɩɨɫɥɟɞɭɸɳɢɯ ɪɚɫɱɟɬɚɯ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ CH ɩɪɢɦɟɧɹɟɬɫɹ ɮɨɪɦɭɥɚ (15).
Ɋɢɫ. 2. ȼɟɤɬɨɪɧɵɟ ɦɧɨɝɨɭɝɨɥɶɧɢɤɢ ɫɤɨɪɨɫɬɟɣ
ɜ ɭɞɚɥɟɧɧɨɦ ɫɟɱɟɧɢɢ ɜɢɯɪɟɜɨɝɨ ɫɥɟɞɚ
( )
Ɋɢɫ. 3. Ƚɪɚɮɢɤ v1 y = f V .
ɇɚ ɪɢɫ. 3 ɩɪɟɞɫɬɚɜɥɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ v1 y (V ) ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɣ H = H R . Ɂɞɟɫɶ H – ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɷɤɜɢɜɚɥɟɧɬɧɚɹ
ɜɵɫɨɬɚ ɤɨɥɶɰɚ (ɤɨɥɥɟɤɬɨɪ ɩɥɸɫ ɞɢɮɮɭɡɨɪ, ɫɦ. [1]). Ʉɪɢɜɚɹ H = 0 ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɢɡɨɥɢɪɨɜɚɧɧɨɦɭ ɜɢɧɬɭ. Ʉɚɤ ɜɢɞɢɦ, ɭɜɟɥɢɱɟɧɢɟ rɤ ɢ
Hɞ
(ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ
ɭɜɟɥɢɱɟɧɢɸ
ɷɤɜɢɜɚɥɟɧɬɧɨɣ
ɜɵɫɨɬɵ H )
ɜɟɞɟɬ ɤ ɫɭɳɟɫɬɜɟɧɧɨɦɭ ɫɧɢɠɟɧɢɸ ɫɤɨɪɨɫɬɢ ɩɪɨɬɟɤɚɧɢɹ v1ɭ ɜ
ɤɚɧɚɥɟ ɤɨɥɶɰɚ. ɇɚ ɪɢɫ. 4 ɩɨɤɚɡɚɧɨ ɢɡɦɟɧɟɧɢɟ ɭɝɥɚ ɨɬɤɥɨɧɟɧɢɹ ϑ
Ɋɢɫ. 4. Ƚɪɚɮɢɤ ϑ = f (V )
ɪɚɜɧɨɞɟɣɫɬɜɭɸɳɟɣ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɢɥɵ Ra ɧɚɡɚɞ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɤɨɪɨɫɬɢ V . ɇɚɢɛɨɥɶɲɢɣ ɭɝɨɥ ϑ = 30° ɩɨɥɭɱɚɟɬɫɹ ɞɥɹ ɛɨɥɶɲɢɯ H = 2 ɩɪɢ
V § 0,8.
ȼɜɟɞɟɦ ɩɨɧɹɬɢɟ ɤɚɱɟɫɬɜɚ ɫɢɫɬɟɦɵ «ɜɢɧɬ ɜ ɤɨɥɶɰɟ» ɜ ɭɫɥɨɜɢɹɯ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ
ɨɛɞɭɜɤɢ
K=
T
= ctgϑ , ɨɬɤɭɞɚ sin ϑ = 1
, cos ϑ = K
.
2
Qɢ
1+ K
1+ K2
(16)
ɇɚ ɪɢɫ. 5 ɩɨɤɚɡɚɧɨ ɢɡɦɟɧɟɧɢɟ ɤɚɱɟɫɬɜɚ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɤɨɪɨɫɬɢ V . Ɇɢɧɢɦɚɥɶɧɨɟ ɤɚɱɟɫɬɜɨ ɫɢɫɬɟɦɵ ɪɚɜɧɨ ɞɜɭɦ ɩɪɢ H > 1 ɢ V § 0,8.
Ⱦɥɹ ɜɵɩɨɥɧɟɧɢɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɪɚɫɱɟɬɚ ɫɢɫɬɟɦɵ «ɜɢɧɬ ɜ ɤɨɥɶɰɟ» ɜ ɪɟɠɢɦɚɯ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɨɛɞɭɜɤɢ ɬɪɟɛɭɟɬɫɹ ɡɧɚɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɬɹɝ ɦɟɠɞɭ ɜɢɧɬɨɦ ɢ ɤɨɥɶɰɨɦ. ȼ ɨɬɧɨɫɢɬɟɥɶɧɨɦ ɜɢɞɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɬɹɝɢ ɜɵɪɚɠɚɸɬɫɹ ɨɬɧɨɲɟɧɢɹɦɢ
T = Tɜ + Tɤ ; Tɜ = Tɜ T ; Tɤ = Tɤ T ; Tɜ + Tɤ = 1.
(17)
Ⱦɥɹ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɧɚ ɦɟɫɬɟ (V = 0) ɨɬɧɨɫɢɬɟɥɶɧɵɟ ɬɹɝɢ ɜɢɧɬɚ ɢ ɤɨɥɶɰɚ ɩɨɦɟɱɚɸɬɫɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɦ ɢɧɞɟɤɫɨɦ Tɜ0 , Tɤ0 . Ɉɬɧɨɫɢɬɟɥɶɧɚɹ ɬɹɝɚ ɜɢɧɬɚ Tɜ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɜ ɪɟɠɢɦɟ ɪɚɛɨɬɵ ɧɚ
ɦɟɫɬɟ, ɦɨɠɟɬ ɛɵɬɶ ɧɚɣɞɟɧɚ ɢɡ ɭɪɚɜɧɟɧɢɹ ɷɧɟɪɝɢɣ. ȼ ɥɟɜɨɣ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ ɫɬɨɢɬ ɷɧɟɪɝɢɹ, ɩɨɞɜɨɞɢɦɚɹ ɤ ɜɢɧɬɭ ɡɚ ɜɵɱɟɬɨɦ ɷɧɟɪɝɢɢ, ɡɚɬɪɚɱɢɜɚɟɦɨɣ ɧɚ ɪɚɛɨɬɭ ɫɢɥɵ ɢɦɩɭɥɶɫɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɚ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ – ɩɪɢɪɨɫɬ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɜ ɭɞɚɥɟɧɧɨɦ ɫɟɱɟɧɢɢ ɫɬɪɭɢ ɩɥɸɫ ɩɨɬɟɪɢ
ɞɚɜɥɟɧɢɹ ɧɚ ɜɯɨɞɟ ɜ ɤɚɧɚɥ (ɜ ɤɨɥɥɟɤɬɨɪɟ) ɢ ɧɚ ɩɨɜɨɪɨɬ ɫɬɪɭɢ. ɉɪɢ ɜɵɱɢɫɥɟɧɢɢ ɫɢɥ ɢ ɷɧɟɪɝɢɣ
ɢɫɩɨɥɶɡɭɟɦ ɝɢɩɨɬɟɡɭ ɉɪɚɧɞɬɥɹ – Ƚɥɚɭɷɪɬɚ ɞɥɹ ɤɪɵɥɚ ɢ ɜɢɧɬɚ ɨ ɬɨɦ, ɱɬɨ ɜɢɯɪɟɜɨɣ ɫɥɟɞ ɨɤɚɡɵɜɚɟɬ ɢɧɞɭɤɬɢɜɧɨɟ ɜɨɡɞɟɣɫɬɜɢɟ ɧɟ ɧɚ ɜɫɟ ɜɨɡɞɭɲɧɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ, ɚ ɬɨɥɶɤɨ ɧɚ ɨɝɪɚɧɢɱɟɧɧɭɸ ɜɨɡ169
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɞɭɲɧɭɸ ɫɬɪɭɸ. ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ ɫɟɤɭɧɞɧɵɣ ɦɚɫɫɨɜɵɣ ɪɚɫɯɨɞ ɜɨɡɞɭɯɚ ɜ ɫɟɱɟɧɢɢ 2-2 ɫɬɪɭɢ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɷɬɨɣ ɝɢɩɨɬɟɡɨɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ (ɪɢɫ. 2):
m = ρ FV2 .
(18)
ɉɪɢɦɟɦ, ɱɬɨ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɨɬɧɨɲɟɧɢɟ ɫɟɤɭɧɞɧɨɣ ɦɚɫɫɵ ɜɨɡɞɭɯɚ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɤɚɧɚɥ m1, ɤ ɫɟɤɭɧɞɧɨɣ ɦɚɫɫɟ ɜ ɫɥɟɞɟ ɞɨɥɠɧɨ ɛɵɬɶ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɨɬɧɨɲɟɧɢɸ ɩɥɨɳɚɞɟɣ F1 / F
m1 F1
= = f.
m F
(19)
Ɍɨɝɞɚ ɢɡ ɭɪɚɜɧɟɧɢɹ ɢɦɩɭɥɶɫɨɜ ɩɨɥɭɱɢɦ (ɪɢɫ. 2)
Ra = mv2 ; T = mv2 y ; Qɢ = mv2 x .
(20)
ɍɱɢɬɵɜɚɹ, ɱɬɨ v2 = K H v1 y , ɩɨɥɭɱɚɟɦ
v2 y = v2 cos ϑ = K H v1 y cos ϑ ; v2 x = v2 sin ϑ = K H v1 y sin ϑ .
(21)
2
m1v1 y
mV22x
mV22 mV 2
−
+ ξɫɬɪ
+ ξ KH
Ɂɚɩɢɲɟɦ ɬɟɩɟɪɶ ɭɪɚɜɧɟɧɢɟ ɷɧɟɪɝɢɣ Tɜ v1 y − QɢV =
.
2
2
2
2
ȼɵɱɢɫɥɢɦ ɩɪɢɪɨɫɬ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɫɬɪɭɢ ¨ȿ, ɢɫɯɨɞɹ ɢɡ ɬɪɟɭɝɨɥɶɧɢɤɚ ɫɤɨɪɨɫɬɟɣ
(ɪɢɫ. 2) ɢ ɭɱɢɬɵɜɚɹ ɮɨɪɦɭɥɵ (20):
2
Tν
Qν
mV22 mV 2 mν 2 y m (V −ν 2 x ) mV 2 mν 22
ΔE =
−
=
+
−
=
− QɂV = ɜ 2 y + ɂ 2 ɯ − QɂV .
2
2
2
2
2
2
2
2
ɉɨɬɟɪɢ ɧɚ ɩɨɜɨɪɨɬ ɫɬɪɭɢ ɩɪɢɦɟɦ ɪɚɜɧɵɦɢ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɫɤɨɪɨɫɬɢ
ɬɨɪɦɨɠɟɧɢɹ ɩɨɬɨɤɚ ( ξɫɬɪ = 1 ). ɉɨɫɥɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɭɪɚɜɧɟɧɢɟ ɷɧɟɪɝɢɢ ɩɪɢɦɟɬ ɜɢɞ
m1v12y
1
TTɜ v1 y = Tɜ v2 y + Qɢ v2 x + ξ KH
. ɂɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɵ (13), (16), (20) ɢ (21), ɧɚɯɨɞɢɦ
2
2
K §
2
· ξK C f
Tɜ = H ¨ cos ϑ + sin ϑ ¸ + H
. Ɂɞɟɫɶ Ʉ – ɤɚɱɟɫɬɜɨ ɫɢɫɬɟɦɵ. ɉɪɟɞɫɬɚɜɢɦ Tɜ ɱɟɪɟɡ
2 ©
K
¹ 2K H
Tɜ0 [1]:
Tɜ = Tɜ0 + ΔTɜ ,
(22)
ξ KH ·
KH § 2
1§
· ξ KH
sin
cos
1
1− Cf ,
T
ϑ
ϑ
Δ
=
+
−
,
+
K
¨ H
¸
ɜ
¨
¸−
2 ©K
2©
KH ¹
¹ 2K H
ɢɥɢ ɫ ɭɱɟɬɨɦ ɮɨɪɦɭɥ (16) ɞɥɹ ɤɚɱɟɫɬɜɚ ɢ ɞɥɹ ξ K H
(
ɝɞɟ Tɜ0 =
ΔTB =
)
· 2 − KH
KH § 2 + K 2
− 1¸ −
ξ ɤɨɥ (1 − C f ) .
¨
2 © K 1+ K 2
2
¹
170
(23)
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
ȼɯɨɞɹɳɢɟ ɜ (22) ɢ (23) ɜɟɥɢɱɢɧɵ ɨɩɪɟɞɟɥɹɸɬɫɹ ɮɨɪɦɭɥɚɦɢ
(ɭɤɚɡɚɧɵ ɜ ɫɤɨɛɤɚɯ) ξ ɤɨɥ (ɫɦ. [1]); C f (13); Ʉ (16).
Ɉɬɧɨɫɢɬɟɥɶɧɚɹ ɬɹɝɚ ɤɨɥɶɰɚ ɧɚɣɞɟɬɫɹ ɢɡ ɫɨɨɬɧɨɲɟɧɢɣ (17):
Tɤ = 1 − Tɜ = Tɤ0 − ΔT .
ɇɚ ɪɢɫ. 6 ɩɪɟɞɫɬɚɜɥɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ Tɤ (V ) ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɣ H . Ʉɚɤ ɜɢɞɧɨ, ɧɟɫɭɳɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɤɨɥɥɟɤɬɨɪɚ
ɩɨ ɫɤɨɪɨɫɬɢ V ɫɧɚɱɚɥɚ ɩɚɞɚɟɬ, ɚ ɡɚɬɟɦ ɪɚɫɬɟɬ, ɜɨɫɫɬɚɧɚɜɥɢɜɚɹɫɶ
ɞɨ ɡɧɚɱɟɧɢɣ Tɤ , ɛɥɢɡɤɢɯ ɤ ɪɟɠɢɦɭ ɪɚɛɨɬɵ ɜɢɧɬɚ ɧɚ ɦɟɫɬɟ. ɇɚɢɛɨɥɶɲɟɟ ɩɚɞɟɧɢɟ ɬɹɝɢ ɤɨɥɶɰɚ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɤɨɪɨɫɬɢ V § 0,8.
ȼ ɷɬɨɦ ɫɥɭɱɚɟ, ɤɚɤ ɫɥɟɞɭɟɬ ɢɡ ɝɪɚɮɢɤɚ v (V ) (ɪɢɫ. 3), ɜɟ-
( )
Ɋɢɫ. 5. Ƚɪɚɮɢɤ K = f V
1y
ɥɢɱɢɧɚ v1y ≈ V ɢ ɩɨɬɨɤ ɧɚɬɟɤɚɟɬ ɧɚ ɤɨɥɥɟɤɬɨɪ ɩɨɞ ɭɝɥɨɦ ~ 45°.
ɇɚ ɡɚɞɧɟɣ ɱɚɫɬɢ ɤɨɥɥɟɤɬɨɪɚ ɫɢɥɶɧɨ ɭɯɭɞɲɚɸɬɫɹ ɭɫɥɨɜɢɹ ɨɛɬɟɤɚɧɢɹ,
ɱɬɨ ɜɟɞɟɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɩɨɬɟɪɶ ɞɚɜɥɟɧɢɹ ɢ ɫɧɢɠɟɧɢɸ ɧɟɫɭɳɟɣ
ɫɩɨɫɨɛɧɨɫɬɢ ɤɨɥɶɰɚ. ɇɚ ɪɢɫ. 7 ɩɨɤɚɡɚɧɚ ɩɪɢɦɟɪɧɚɹ ɤɚɪɬɢɧɚ
Ɋɢɫ. 6. Ƚɪɚɮɢɤ TK = f (V )
ɨɛɬɟɤɚɧɢɹ ɜɯɨɞɧɨɣ ɱɚɫɬɢ ɤɚɧɚɥɚ, ɨɬɤɭɞɚ ɜɢɞɧɚ ɩɪɢɱɢɧɚ ɩɚɞɟɧɢɹ ɬɹɝɢ ɤɨɥɶɰɚ. ɇɚ ɛɨɥɶɲɢɯ ɫɤɨɪɨɫɬɹɯ ɩɨɥɟɬɚ ( V > 2) ɩɨɞɫɚɫɵɜɚɸɳɢɣ ɷɮɮɟɤɬ ɜɢɧɬɚ ɨɱɟɧɶ ɫɥɚɛ, ɚ ɢɧɟɪɰɢɹ ɩɨɬɨɤɚ ɜɟɥɢɤɚ. ɇɚ ɡɚɞɧɟɣ ɱɚɫɬɢ ɤɨɥɥɟɤɬɨɪɚ
ɩɨɹɜɥɹɟɬɫɹ ɪɚɡɪɟɠɟɧɢɟ ɢ ɧɟɫɭɳɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɤɨɥɶɰɚ ɜɨɫɫɬɚɧɚɜɥɢɜɚɟɬɫɹ.
Ɋɢɫ. 7. ɉɪɢɛɥɢɠɟɧɧɚɹ ɤɚɪɬɢɧɚ ɨɛɬɟɤɚɧɢɹ ɜɢɧɬɚ ɜ ɤɚɧɚɥɟ ɞɥɹ ɪɚɡɧɵɯ ɫɤɨɪɨɫɬɟɣ ɩɨɥɟɬɚ V
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɦɟɹ ɪɚɫɯɨɞɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɢɫɬɟɦɵ «ɜɢɧɬ ɜ ɤɨɥɶɰɟ» ɜ ɪɟɠɢɦɟ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɨɛɞɭɜɤɢ ɢ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɬɹɝ ɦɟɠɞɭ ɜɢɧɬɨɦ ɢ ɤɨɥɶɰɨɦ, ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɚɥɝɨɪɢɬɦɵ ɪɚɫɱɟɬɚ ɜɫɟɯ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɫɢɫɬɟɦɵ, ɢɫɩɨɥɶɡɭɹ ɦɟɬɨɞɵ ɪɚɫɱɟɬɚ, ɩɪɢɜɟɞɟɧɧɵɟ ɜ [2]. ɉɨɥɭɱɟɧɧɵɟ ɧɚ ɷɬɨɣ ɛɚɡɟ ɚɥɝɨɪɢɬɦɵ ɢɫɩɨɥɶɡɨɜɚɧɵ ɜ ɪɚɫɱɟɬɚɯ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢɜɟɞɟɧɧɵɯ ɧɢɠɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɦɨɞɟɥɟɣ.
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ɇɚ ɪɢɫ. 8 ɩɪɢɜɨɞɢɬɫɹ ɱɟɪɬɟɠ ɦɨɞɟɥɢ ɮɟɧɟɫɬɪɨɧɚ «Ⱦɨɮɟɧ» ɮɪɚɧɰɭɡɫɤɨɣ ɮɢɪɦɵ «Ⱥɷɪɨɫɩɚɫɶɹɥɶ». Ɂɞɟɫɶ ɠɟ ɞɚɧɵ ɪɚɡɦɟɪɧɵɟ ɢ ɛɟɡɪɚɡɦɟɪɧɵɟ ɩɚɪɚɦɟɬɪɵ ɦɨɞɟɥɢ, ɞɥɹ ɤɨɬɨɪɵɯ ɩɪɨɜɟɞɟɧɵ ɪɚɫɱɟɬɵ ɫɭɦɦɚɪɧɨɝɨ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɹɝɢ CT Σ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɩɨɥɟɬɚ V ɢ ɭɝɥɨɜ ɭɫɬɚɧɨɜɤɢ ɥɨɩɚɫɬɟɣ ɜɢɧɬɚ ij7 ɩɪɢ ɧɭɥɟɜɨɦ ɭɝɥɟ ɫɤɨɥɶɠɟɧɢɹ
(Į = 0). ȼɟɥɢɱɢɧɚ ɡɚɡɨɪɚ ɩɪɢɧɹɬɚ δ = 0, 005 .
ɇɚ ɪɢɫ. 9 ɩɪɨɜɨɞɢɬɫɹ ɫɪɚɜɧɟɧɢɟ ɪɚɫɱɟɬɧɵɯ ɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ, ɜɡɹɬɵɯ ɢɡ ɪɚɛɨɬɵ [6]. ɇɚ ɪɢɫ. 10 ɩɪɢɜɨɞɹɬɫɹ ɤɪɢɜɵɟ ɤɚɱɟɫɬɜɚ ɫɢɫɬɟɦɵ, ɧɚɣɞɟɧɧɵɟ ɫ ɭɱɟɬɨɦ ɬɨɥɶɤɨ ɢɦɩɭɥɶɫɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜɢɧɬɚ ɜ ɤɨɥɶɰɟ. ȼ ɞɢɚɩɚɡɨɧɟ ɫɤɨɪɨɫɬɟɣ V = 0, 25...0,5 ɟɝɨ ɜɟɥɢɱɢɧɚ ɫɨɫɬɚɜɥɹɟɬ 2...2,5, ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ, ɩɪɢɜɟɞɟɧɧɵɦ ɜ [6] (ɪɢɫ. 11). Ɂɚɦɟɬɢɦ, ɱɬɨ ɜɧɟɲɧɟɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɨɪɩɭɫɚ ɮɟɧɟɫɬɪɨɧɚ ɫɭɳɟɫɬɜɟɧɧɨ ɭɯɭɞɲɚɟɬ ɟɝɨ ɤɚɱɟɫɬɜɨ. Ʉɚɤ
ɜɢɞɢɦ, ɫɨɜɩɚɞɟɧɢɟ ɪɚɫɱɟɬɧɵɯ ɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɜɩɨɥɧɟ ɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɨɟ.
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Vol. 19, ʋ 04, 2016
Ɋɢɫ. 8. ɑɟɪɬɟɠ ɢ ɩɚɪɚɦɟɬɪɵ
ɢɫɩɵɬɚɬɟɥɶɧɨɣ ɦɨɞɟɥɢ ɮɟɧɟɫɬɪɨɧɚ ɜɟɪɬɨɥɟɬɚ «Ⱦɨɮɟɧ»
Ɋɢɫ. 10. Ʉɪɢɜɵɟ ɤɚɱɟɫɬɜɚ
ɦɨɞɟɥɢ «Ⱦɨɮɟɧ»
Ɋɢɫ. 9. ɋɪɚɜɧɟɧɢɟ ɪɚɫɱɟɬɧɵɯ
ɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ
Ɋɢɫ. 11. Ƚɪɚɮɢɤ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɫɭ ɢ ɫɯ
ɞɥɹ ɤɚɱɟɫɬɜɚ Ʉ = 2. ɋɪɚɜɧɟɧɢɟ ɫ ɷɤɫɩɟɪɢɦɟɧɬɨɦ
ɋɊȺȼɇȿɇɂȿ ɊȺɋɑȿɌɇɕɏ ɂ ɗɄɋɉȿɊɂɆȿɇɌȺɅɖɇɕɏ ɏȺɊȺɄɌȿɊɂɋɌɂɄ
ɆɈȾȿɅɂ ȾɉɅȺ, ȼɕɉɈɅɇȿɇɇɈȽɈ ɉɈ ɋɏȿɆȿ «ȼɂɇɌ ȼ ɄɈɅɖɐȿ»
ȼ ɪɚɛɨɬɟ [7] ɩɪɢɜɨɞɹɬɫɹ ɪɟɡɭɥɶɬɚɬɵ ɷɤɫɩɟɪɢɦɟɧɬɚ ɫ
ɦɨɞɟɥɶɸ ȾɉɅȺ ɜ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɬɪɭɛɟ Ɍ-1 ɆȺɂ. ɇɚ
ɪɢɫ. 12 ɩɪɟɞɫɬɚɜɥɟɧ ɱɟɪɬɟɠ ɦɨɞɟɥɢ, ɚ ɬɚɤɠɟ ɟɟ ɪɚɡɦɟɪɧɵɟ
ɢ ɛɟɡɪɚɡɦɟɪɧɵɟ ɩɚɪɚɦɟɬɪɵ. ɉɪɨɮɢɥɶ ɤɨɥɥɟɤɬɨɪɚ, ɜɵɩɨɥɧɟɧɵɣ ɩɨ ɥɟɦɧɢɫɤɚɬɟ, ɢ ɞɨɫɬɚɬɨɱɧɨ ɞɥɢɧɧɵɣ ɞɢɮɮɭɡɨɪ
ɨɛɟɫɩɟɱɢɜɚɸɬ ɩɪɚɤɬɢɱɟɫɤɢ ɩɨɥɧɨɟ ɪɚɫɲɢɪɟɧɢɟ ɢɫɬɟɤɚɸɳɟɣ ɫɬɪɭɢ. ɉɨɷɬɨɦɭ ɜ ɪɚɫɱɟɬɚɯ ɩɪɢɧɹɬɨ K H = 1 . ȼɟɥɢɱɢɧɚ
ɡɚɡɨɪɚ δ = 0, 005 . Ɉɛɪɚɛɨɬɤɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ
ɩɪɨɜɟɞɟɧɚ ȿ.ɂ. Ɇɨɣɡɵɯɨɦ, ɪɚɫɱɟɬɵ ɜɵɩɨɥɧɟɧɵ Ɉ.Ⱥ. Ɂɚɜɚɥɨɜɵɦ.
ɇɚ ɪɢɫ. 13 ɩɨɤɚɡɚɧɨ ɫɪɚɜɧɟɧɢɟ ɪɚɫɱɟɬɧɵɯ ɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɬɹɝɨɜɵɯ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ
ɦɨɞɟɥɢ CTɜ , CTɤ , CT Σ [7], ɚ ɬɚɤɠɟ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɬɹɝɢ ɜɢɧ-
Ɋɢɫ. 12. ɑɟɪɬɟɠ ɢ ɩɚɪɚɦɟɬɪɵ ȾɉɅȺ
ɬɚ ɢ ɤɨɥɶɰɚ Tɜ , Tɤ , ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɭɝɥɚ ɭɫɬɚɧɨɜɤɢ ɥɨɩɚɫɬɟɣ ij7 ɜ ɪɟɠɢɦɟ ɜɢɫɟɧɢɹ. ɂɞɟɚɥɶɧɵɣ ɩɪɨɮɢɥɶ ɤɨɥɥɟɤɬɨɪɚ (ɥɟɦɧɢɫɤɚɬɚ) ɢ ɩɪɹɦɨɭɝɨɥɶɧɵɟ ɧɟɤɪɭɱɟɧɵɟ ɥɨɩɚɫɬɢ
ɨɛɟɫɩɟɱɢɜɚɸɬ ɜɵɫɨɤɭɸ ɧɟɫɭɳɭɸ ɫɩɨɫɨɛɧɨɫɬɶ ɤɨɥɶɰɚ
( Tɤ = 0, 6 ).
ɇɚ ɪɢɫ. 14 ɞɥɹ ɪɟɠɢɦɚ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɨɛɞɭɜɤɢ
ȾɉɅȺ ɞɚɟɬɫɹ ɫɨɩɨɫɬɚɜɥɟɧɢɟ ɪɚɫɱɟɬɧɵɯ ɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɞɥɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ
ɬɹɝɢ CTɜ , CTɤ , CT Σ , ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɬɹɝ Tɜ , Tɤ , ɤɨɷɮɮɢɰɢ-
Ɋɢɫ. 13. ɋɪɚɜɧɟɧɢɟ ɪɚɫɱɟɬɧɵɯ
ɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɡɧɚɱɟɧɢɣ
ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɋɬ
ɟɧɬɚ ɢɦɩɭɥɶɫɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ CH ɢɦɩ ɢ ɤɚɱɟɫɬɜɚ Ʉ ɜ
ɢ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɬɹɝɢ ɤɨɥɶɰɚ
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ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɤɨɪɨɫɬɢ V . ɋɨɩɨɫɬɚɜɥɟɧɢɟ ɪɚɫɱɟɬɧɵɯ ɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ
ɞɚɧɧɵɯ ɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɨɟ, ɱɬɨ ɩɨɞɬɜɟɪɠɞɚɟɬ ɞɨɫɬɨɜɟɪɧɨɫɬɶ ɩɪɟɞɥɚɝɚɟɦɵɯ ɚɥɝɨɪɢɬɦɨɜ.
Ɋɢɫ. 14. ɋɪɚɜɧɟɧɢɹ ɫ ɷɤɫɩɟɪɢɦɟɧɬɨɦ
ɋɉɂɋɈɄ ɅɂɌȿɊȺɌɍɊɕ
1. ɒɚɣɞɚɤɨɜ ȼ.ɂ. Ⱥɷɪɨɞɢɧɚɦɢɤɚ ɜɢɧɬɚ ɜ ɤɨɥɶɰɟ ɫ ɤɨɥɥɟɤɬɨɪɨɦ ɢ ɤɨɪɨɬɤɢɦ ɞɢɮɮɭɡɨɪɨɦ ɜ
ɪɟɠɢɦɟ ɪɚɛɨɬɵ ɧɚ ɦɟɫɬɟ // ȼɟɫɬɧɢɤ Ɇɨɫɤɨɜɫɤɨɝɨ ɚɜɢɚɰɢɨɧɧɨɝɨ ɢɧɫɬɢɬɭɬɚ. 2013. Ɍ. 20. ʋ 4. ɋ. 36–46.
2. ɒɚɣɞɚɤɨɜ ȼ.ɂ. Ⱥɷɪɨɞɢɧɚɦɢɤɚ ɜɢɧɬɚ ɜ ɤɨɥɶɰɟ. Ɇ.: ɂɡɞ-ɜɨ ɆȺɂ, 1996. 88 c.
3. ɒɚɣɞɚɤɨɜ ȼ.ɂ., Ɂɚɜɚɥɨɜ Ɉ.Ⱥ. Ⱥɷɪɨɞɢɧɚɦɢɱɟɫɤɨɟ ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ ɮɟɧɟɫɬɪɨɧɚ. Ɇ.:
ɂɡɞ-ɜɨ ɆȺɂ, 1980. 66 c.
4. ɒɚɣɞɚɤɨɜ ȼ.ɂ. Ɉɛɨɛɳɟɧɧɚɹ ɞɢɫɤɨɜɚɹ ɜɢɯɪɟɜɚɹ ɬɟɨɪɢɹ ɢ ɦɟɬɨɞɵ ɪɚɫɱɟɬɚ ɢɧɞɭɤɬɢɜɧɵɯ ɫɤɨɪɨɫɬɟɣ ɧɟɫɭɳɟɝɨ ɜɢɧɬɚ ɜɟɪɬɨɥɟɬɚ // ɉɪɨɟɤɬɢɪɨɜɚɧɢɟ ɜɟɪɬɨɥɟɬɨɜ. ȼɵɩ. 66, Ɇ.: ɂɡɞ-ɜɨ
ɆȺɂ, 1977. ɋ. 9–28.
5. Ⱦɭɛɚɫɨɜ ȼ.Ɍ. Ʉɨɥɢɱɟɫɬɜɨ ɞɜɢɠɟɧɢɹ ɢ ɦɨɦɟɧɬ ɤɨɥɢɱɟɫɬɜɚ ɞɜɢɠɟɧɢɹ, ɫɨɡɞɚɜɚɟɦɨɝɨ ɡɚɦɤɧɭɬɵɦ ɜɢɯɪɟɜɵɦ ɲɧɭɪɨɦ // Ⱥɷɪɨɞɢɧɚɦɢɤɚ ɜɟɪɬɨɥɟɬɚ. Ɇ.: ɂɡɞ-ɜɨ ɆȺɂ, 1972. ɋ. 50–63.
6. Russier Ɇ. The Fenestron Antitorque Concept. The Royal Aeronautical Society Conference
on Helicopter Yaw Control Concepts, London, March 1990.
7. Ɇɨɣɡɵɯ ȿ.ɂ., Ʉɭɡɧɟɰɨɜ Ⱥ.ȼ., Ɂɚɜɚɥɨɜ Ɉ.Ⱥ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɞɢɫɬɚɧɰɢɨɧɧɨ-ɩɢɥɨɬɢɪɭɟɦɨɝɨ ɥɟɬɚɬɟɥɶɧɨɝɨ ɚɩɩɚɪɚɬɚ ɫ ɧɟɫɭɳɟɣ
ɫɢɫɬɟɦɨɣ «ɜɢɧɬ ɜ ɤɨɥɶɰɟ». Ɍɪɭɞɵ ɆȺɂ. 2012. ʋ 50. ɋ. 11.
AERODYNAMIC CHARACTERISTICS OF “FAN-IN-FIN” SYSTEM
IN CONDITION OF FLOWING UNDER ZERO ATTACK ANGLE
Shaydakov V.I.
Fan-in-fin system can be used as single-rotor helicopter fenestrons propulsion system of low-speed airplanes and
dirigibles as well as vehicles with remote control.
The article suggests way to continue the author’s research in the field of fan-in-fin system aerodynamics.
It also offers a method of aerodynamic characteristics of “fan-in-fin” (fenestron) system with cylindrical diffuser
of limited length in flow regime under zero angle of attack calculation. The article gives some formula to calculate the flow
velocity through the disk area which decrease with the increase of the defusser and air speed.
Correlation between fan thrust power and ring thrust on these regimes and momentum drag are found. Momentum
drag is high enough, this fact leads to back deviation of total aerodynamic force system. This angle increases with increase
of the diffuser length and at medium speed it can reach 30°.
Certainty of suggested algorithms is proved by comparison with experiments for helicopter fenestron and unmanned air vehicle by tests in wind tunnel of MAI.
Key words: fan-in-fin system, fenestron, horizontal flight, aerodynamics characteristics.
REFERENCES
1. Shaydakov V.I. Aerodynamics of the “fan-in-fin” system with short collector and the diffuser in a hover. The MAI [Moscow Aviation Institute] Scientific Bulletin. Moscow, 2013. Vol. 20.
No. 4. P. 36–46.
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Vol. 19, ʋ 04, 2016
2. Shaydakov V.I. Aerodynamics of “fan-in-fin” system. Moscow, MAI [Moscow Aviation
Institute] publishing, 1996.
3. Shaydakov V.I., Zavalov O.A. Aerodynamic design of helicopter fenestron. Moscow, MAI
[Moscow Aviation Institute] publishing, 1980.
4. Shaydakov V.I. Generalized vortex theory and inductive methods of calculation speeds of
helicopter rotor. In the book “Helicopter design”. Vol. 66. Moscow, MAI [Moscow Aviation Institute]
publishing, 1977.
5. Dubasov V.T. The momentum and angular momentum created by the closed vortex cord.
In the book “Helicopter aerodynamics”. Moscow, MAI [Moscow Aviation Institute] publishing, 1972.
6. Russier Ɇ. The Fenestron Antitorque Concept. The Royal Aeronautical Society Conference
on Helicopter Yaw Control Concepts, London, March 1990.
7. Moizykh E.I., Kuznetcov A.V., Zavalov O.A. Experimental study of aerodynamic characteristics of the remotely-piloted aircraft from the carrier system "fan-in-fin". Elektronnyj zhurnal
«Trudy MAI». 2012. No. 50. available at: http://www.mai.ru/science/trudy.
ɋȼȿȾȿɇɂə ɈȻ ȺȼɌɈɊȿ
ɒɚɣɞɚɤɨɜ ȼɥɚɞɢɦɢɪ ɂɜɚɧɨɜɢɱ, ɩɪɨɮɟɫɫɨɪ ɤɚɮɟɞɪɵ «ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ ɜɟɪɬɨɥɟɬɨɜ»
ɆȺɂ, ɞɨɤɬɨɪ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ.
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