title: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð¿Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ ÑÐ»Ð¾Ñ Ð½Ð° ÐºÑÑÐ»Ð¾Ð²Ð¾Ð¼ Ð¿ÑÐ¾ÑÐ¸Ð»Ðµ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ ÑÐµÐ¾ÑÐ¸Ð¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: The study of the stability of the boundary layer on the wing profile based on linear theory
Creators: name: ÐÐ»Ð°Ð´Ð¸Ð¼Ð¸ÑÐ¾Ð², ÐÐ²Ð³ÐµÐ½Ð¸Ð¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸
Ð²Ð¾Ð»Ð½Ñ Ð¢Ð¾Ð»Ð»Ð¼Ð¸Ð½Ð°-Ð¨Ð»Ð¸Ñ ÑÐ¸Ð½Ð³Ð°
ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÐÑÑÐ°-ÐÐ¾Ð¼Ð¼ÐµÑÑÐµÐ»ÑÐ´Ð°
ÑÐ¿ÐµÐºÑÑÐ°Ð»ÑÐ½ÑÐ¹ Ð¼ÐµÑÐ¾Ð´
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Ð³Ð»Ð¾Ð±Ð°Ð»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸
one-dimensional stability analysis
Tollmien-Schlichting waves
Orr-Sommerfeld equation
spectral method
Chebyshev polynomials
global stability analysis

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¾ÑÐµÐ½ÐºÐµ ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ Ð¿Ð°ÑÐ°Ð»Ð»ÐµÐ»ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð´ÑÐ¾Ð´Ð° Ð¿ÑÐ¸ ÑÐ°ÑÑÐµÑÐµ ÑÐ°Ð·Ð²Ð¸ÑÐ¸Ñ Ð²Ð¾Ð»Ð½ Ð¢Ð¾Ð»Ð»Ð¼Ð¸Ð½Ð°-Ð¨Ð»Ð¸ÑÑÐ¸Ð½Ð³Ð° Ð² Ð¿Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐ½Ð¾Ð¼ ÑÐ»Ð¾Ðµ Ð½Ð° Ð¿Ð¾Ð²ÐµÑÑÐ½Ð¾ÑÑÐ¸ ÐºÑÑÐ»Ð¾Ð²Ð¾Ð³Ð¾ Ð¿ÑÐ¾ÑÐ¸Ð»Ñ, Ð¿ÑÑÐµÐ¼ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÐµÐ³Ð¾ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ñ Ð³Ð»Ð¾Ð±Ð°Ð»ÑÐ½ÑÐ¼ Ð°Ð½Ð°Ð»Ð¸Ð·Ð¾Ð¼ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸. ÐÐ»Ñ ÑÐµÑÐµÐ½Ð¸Ñ ÑÑÐ¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð² ÑÑÐµÐ´Ðµ Matlab R2022 Ð±ÑÐ» ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½ÑÐ¹ ÐºÐ¾Ð´ Ð´Ð»Ñ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð¿Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ ÑÐ»Ð¾Ñ. Ð­ÑÐ¾Ñ ÐºÐ¾Ð´ Ð±ÑÐ» Ð²ÐµÑÐ¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°Ð½ Ð½Ð° Ð·Ð°Ð´Ð°ÑÐµ ÑÐ°ÑÑÐµÑÐ° Ð¿Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ ÑÐ»Ð¾Ñ Ð½Ð° Ð¿Ð»Ð¾ÑÐºÐ¾Ð¹ Ð¿Ð»Ð°ÑÑÐ¸Ð½Ðµ Ð±ÐµÐ· Ð³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ° Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ. ÐÐµÐ»Ð¸ÑÐ¸Ð½Ð° N-ÑÐ°ÐºÑÐ¾ÑÐ° Ð´Ð»Ñ Ð¿Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ ÑÐ»Ð¾Ñ Ñ Ð½ÐµÐ±Ð¾Ð»ÑÑÐ¸Ð¼ Ð³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ¾Ð¼ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð½Ð° ÐºÑÑÐ»Ð¾Ð²Ð¾Ð¼ Ð¿ÑÐ¾ÑÐ¸Ð»Ðµ, ÑÐ°ÑÑÑÐ¸ÑÐ°Ð½Ð½Ð°Ñ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¿Ð°ÑÐ°Ð»Ð»ÐµÐ»ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð´ÑÐ¾Ð´Ð°, Ð¾ÑÐ»Ð¸ÑÐ°ÐµÑÑÑ Ð¾Ñ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð³Ð»Ð¾Ð±Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð½Ðµ Ð±Ð¾Ð»ÐµÐµ ÑÐµÐ¼ Ð½Ð° 5%, ÑÑÐ¾ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÐµÑ ÐµÐ³Ð¾ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°ÑÑ Ð´Ð»Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð¿Ð¾Ð´Ð¾Ð±Ð½ÑÑ Ð·Ð°Ð´Ð°Ñ. ÐÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼Ð¾ÑÑÑ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð´ÑÐ¾Ð´Ð° Ð´Ð»Ñ ÑÐµÑÐµÐ½Ð¸Ð¹ Ñ ÑÑÑÐµÑÑÐ²ÐµÐ½Ð½ÑÐ¼Ð¸ Ð¿ÑÐ¾Ð´Ð¾Ð»ÑÐ½ÑÐ¼Ð¸ Ð³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ°Ð¼Ð¸ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ ÑÑÐµÐ±ÑÐµÑ Ð´Ð°Ð»ÑÐ½ÐµÐ¹ÑÐµÐ¹ Ð¿ÑÐ¾Ð²ÐµÑÐºÐ¸.
description: This work is devoted to assessing the accuracy of the parallel approach in the calculation of the development of Tollmien-Schlichting waves in the boundary layer on the surface of the wing profile, by comparing its results with a global stability analysis. To solve this problem, a computer program for boundary layer stability analysis was developed in the Matlab R2022 environment. The program was verified on the problem of calculating the boundary layer on a flat plate without a pressure gradient. The value of the N-factor for the boundary layer with a small pressure gradient on the wing profile calculated using the parallel approach differs from the results of the global stability analysis by no more than 5%, which allows it to be used to solve similar problems. The applicability of the one-dimensional approach for flows with significant longitudinal pressure gradients requires further verification.