title: Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ñ ÐºÐ²Ð°Ð´ÑÐ°ÑÐ½Ð¾Ð³Ð¾ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ°, ÑÐ¾Ð²ÐµÑÑÐ°ÑÑÐµÐ³Ð¾ Ð²ÑÐ°ÑÐ°ÑÐµÐ»ÑÐ½ÑÐµ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ñ
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: Numerical simulation of laminar flow over a rotationally oscillating square cylinder
Creators: name: ÐÐ°Ð±ÐµÐ»Ð»Ð¾, ÐÐ¾Ð½ÑÑÐ°Ð½ÑÐ¸Ð½
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: 2022
Subjects: Ð´ÐµÑÐ¾ÑÐ¼Ð¸ÑÑÐµÐ¼ÑÐµ ÑÐ°ÑÑÑÑÐ½ÑÐµ ÑÐµÑÐºÐ¸
ÐºÐ²Ð°Ð´ÑÐ°ÑÐ½ÑÐ¹ ÑÐ¸Ð»Ð¸Ð½Ð´Ñ
Ð²ÑÐ½ÑÐ¶Ð´ÐµÐ½Ð½ÑÐµ Ð²ÑÐ°ÑÐ°ÑÐµÐ»ÑÐ½ÑÐµ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ñ
deformable calculation grid
square cylinder
forced rotational oscillations
flag-s

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: Â«Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ñ ÐºÐ²Ð°Ð´ÑÐ°ÑÐ½Ð¾Ð³Ð¾ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ°, ÑÐ¾Ð²ÐµÑÑÐ°ÑÑÐµÐ³Ð¾ Ð²ÑÐ°ÑÐ°ÑÐµÐ»ÑÐ½ÑÐµ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸ÑÂ». ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ:â¢ Ð ÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð´ÐµÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ Ð´Ð»Ñ Ð½ÐµÑÑÑÑÐºÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ ÑÐµÑÐ¾Ðº Ð² Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð¼ ÐºÐ¾Ð¼Ð¿Ð»ÐµÐºÑÐµ Flag-s.â¢ ÐÐµÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ Ð¼ÐµÑÐ¾Ð´Ð¸ÐºÐ¸ ÑÐ°ÑÑÑÑÐ° Ð¿Ð°ÐºÐµÑÐ¾Ð¼ Flag-s Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð´ÐµÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ ÑÐ°ÑÑÐµÑÐ½Ð¾Ð¹ ÑÐµÑÐºÐ¸ Ð½Ð° Ð¿ÑÐ¸Ð¼ÐµÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾ Ð²ÑÐ½ÑÐ¶Ð´ÐµÐ½Ð½ÑÑ Ð²ÑÐ°ÑÐ°ÑÐµÐ»ÑÐ½ÑÑ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸ÑÑ ÐºÐ²Ð°Ð´ÑÐ°ÑÐ½Ð¾Ð³Ð¾ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ° Ð² Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð¼ Ð¿Ð¾ÑÐ¾ÐºÐµ.â¢ ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²ÑÐ½ÑÐ¶Ð´ÐµÐ½Ð½ÑÑ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ ÐºÐ²Ð°Ð´ÑÐ°ÑÐ½Ð¾Ð³Ð¾ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ° Ð² Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð¼ Ð¿Ð¾ÑÐ¾ÐºÐµ Ð¿ÑÐ¸ ÑÐ¸ÑÐ»Ðµ Ð ÐµÐ¹Ð½Ð¾Ð»ÑÐ´ÑÐ° 100.Ð Ð°Ð±Ð¾ÑÐ° Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð° c Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÐºÐ¾Ð´Ð° Flag-s, ÑÐ°Ð·ÑÐ°Ð±Ð°ÑÑÐ²Ð°ÐµÐ¼Ð¾Ð³Ð¾ Ð² ÑÐµÐºÑÐ¸Ð¸ Ð³Ð¸Ð´ÑÐ¾Ð°ÑÑÐ¾Ð´Ð¸Ð½Ð°Ð¼ÐºÐ¸ ÐÑÑÑÐµÐ¹ ÑÐºÐ¾Ð»Ñ Ð¿ÑÐ¸ÐºÐ»Ð°Ð´Ð½Ð¾Ð¹ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÐºÐ¸ Ð¸ Ð²ÑÑÐ¸ÑÐ»Ð¸ÑÐµÐ»ÑÐ½Ð¾Ð¹ ÑÐ¸Ð·Ð¸ÐºÐ¸ Ð¤Ð¸Ð·Ð¸ÐºÐ¾-Ð¼ÐµÑÐ°Ð½Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¸Ð½ÑÑÐ¸ÑÑÑÐ° Ð¡ÐÐ±ÐÐ£, Ð² ÐºÐ¾ÑÐ¾ÑÑÐ¹ Ð±ÑÐ»Ð¸ Ð²Ð½ÐµÐ´ÑÐµÐ½Ñ Ð¼Ð¾Ð´ÑÐ»Ð¸ Ð¾ÑÐ²ÐµÑÑÑÐ²ÐµÐ½Ð½ÑÐµ Ð·Ð° Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð´ÐµÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ ÑÐµÑÐºÐ¸. ÐÐ»Ñ Ð´ÐµÐ²ÑÑÐ¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð²Ð°ÑÐ¸Ð°Ð½ÑÐ¾Ð² ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ° Ð±ÑÐ»Ð¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ ÑÐ¸Ð»Ð¾Ð²ÑÐµ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ¸, Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ñ Ð¤ÑÑÑÐµ-ÑÐ¿ÐµÐºÑÑÑ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ Ð¿Ð¾Ð´ÑÑÐ¼Ð½Ð¾Ð¹ ÑÐ¸Ð»Ñ. Ð Ð°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ñ Ð¿Ð¾Ð»Ñ Ð·Ð°Ð²Ð¸ÑÑÐµÐ½Ð½Ð¾ÑÑÐ¸ Ð¸ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð²Ð±Ð»Ð¸Ð·Ð¸ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ°. ÐÑÑÑÐµÑÑÐ²Ð»ÐµÐ½Ð° ÐºÑÐ¾ÑÑÐ¿Ð»Ð°ÑÑÐ¾ÑÐ¼ÐµÐ½Ð½Ð°Ñ Ð²ÐµÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÐºÐ¾Ð¼Ð¼ÐµÑÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿Ð°ÐºÐµÑÐ° ANSYS Fluent. ÐÐ¾Ð»ÑÑÐµÐ½Ð¾ ÑÐ¾ÑÐ¾ÑÐµÐµ ÑÐ¾Ð²Ð¿Ð°Ð´ÐµÐ½Ð¸Ðµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Fluent Ð¸ Flag-s. ÐÐ¾ÑÐ¿ÑÐ¾Ð¸Ð·Ð²ÐµÐ´ÐµÐ½Ñ Ð²ÑÐµ ÑÑÑÐµÐºÑÑ, Ð½Ð°Ð±Ð»ÑÐ´Ð°ÐµÐ¼ÑÐµ Ð² Ð»Ð¸ÑÐµÑÐ°ÑÑÑÐµ. ÐÐ±Ð½Ð°ÑÑÐ¶ÐµÐ½ Ð½ÐµÐ¿Ð¾ÑÑÐ¾ÑÐ½Ð½ÑÐ¹ ÑÐ°Ð·Ð¾Ð²ÑÐ¹ ÑÐ´Ð²Ð¸Ð³ Ð¼ÐµÐ¶Ð´Ñ ÑÑÐ¾Ð´Ð¾Ð¼ Ð²Ð¸ÑÑÐµÐ¹ Ð¸ ÑÐ³Ð»Ð¾Ð¼ Ð¿Ð¾Ð²Ð¾ÑÐ¾ÑÐ° ÐºÐ²Ð°Ð´ÑÐ°ÑÐ° Ð´Ð»Ñ Ð¾Ð´Ð½Ð¾Ð³Ð¾ Ð¸Ð· Ð²Ð°ÑÐ¸Ð°Ð½ÑÐ° ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ°.
description: The subject of the graduate qualification work is Â«Numerical simulation of laminar flow over a rotationally oscillating square cylinderÂ». The research set the following goals:â¢ Implementation of the deformation algorithm for unstructured meshes in the Flag-s.â¢ Verification of the computational method by the Flag-s using the grid deformation algorithm on the example of the problem of forced rotational oscillations of a square cylinder in a laminar flow.â¢ Investigation of forced oscillations of a square cylinder in a laminar flow at a Reynolds number 100.The work was carried out using the Flag-s code, developed in the Hydroaerodynamics section of the Higher School of Applied Mathematics and Computational Physics of the Institute of Physics and Mechanics of St. Petersburg State University, in which a module with a mesh deformation algorithm was introduced. Force characteristics were obtained for nine different variations of cylinder vibrations, and Fourier spectra of lift vibrations were determined. Vorticity and pressure fields near the cylinder are considered. Cross-platform verification was carried out using the commercial package ANSYS FLUENT.A good match of the results of Fluent and Flag-s was obtained. All the effects observed in the literature are reproduced. A non-constant phase shift has been detected for one of the cylinder oscillation variants between the separation of vortices and the angle of rotation of the square.