title: Ð Ð°ÑÑÐµÑ ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ Ð² Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÐºÑÐ¾Ð²ÐµÐ½Ð¾ÑÐ½Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ´Ð° Ñ Ð°ÑÐ¸Ð¼Ð¼ÐµÑÑÐ¸ÑÐ½ÑÐ¼ ÑÑÐµÐ½Ð¾Ð·Ð¾Ð¼
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 Steady Flow in a Model of a Blood Vessel with Asymmetric Stenosis
Creators: name: ÐÐ°Ð¹Ð¾ÑÐ¾Ð², ÐÐ¸Ð¼Ð¸ÑÑÐ¸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: 2024
Subjects: Ð°ÑÑÐµÑÐ¸Ð°Ð»ÑÐ½ÑÐ¹ ÑÑÐµÐ½Ð¾Ð·
Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÐºÑÐ¾Ð²Ð¾ÑÐ¾ÐºÐ°
ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ansys cfx
Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ
ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ
arterial stenosis
blood flow modeling
numerical modeling
laminar flow
turbulent flow

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð¼Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ Ð¸ ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ Ð² Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÐºÑÐ¾Ð²ÐµÐ½Ð¾ÑÐ½Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ´Ð° Ñ Ð°ÑÐ¸Ð¼Ð¼ÐµÑÑÐ¸ÑÐ½ÑÐ¼ ÑÑÐµÐ½Ð¾Ð·Ð¾Ð¼. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¾ Ð´Ð»Ñ ÑÐ¸ÑÐµÐ» Ð ÐµÐ¹Ð½Ð¾Ð»ÑÐ´ÑÐ° Ð¾Ñ 100 Ð´Ð¾ 1800. ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¾ÑÑÑÐµÑÑÐ²Ð»ÑÐµÑÑÑ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐµÑÐµÐ½Ð¸Ñ ÑÐ¸ÑÑÐµÐ¼Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ ÐÐ°Ð²ÑÐµ-Ð¡ÑÐ¾ÐºÑÐ° Ð¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½Ð¾ÑÑÐ¸ (k-Ï, BSL, BSL-R, SST). Ð ÑÐ°Ð±Ð¾ÑÐµ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ñ ÑÐ»ÐµÐ´ÑÑÑÐ¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸: 1. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ Ð»Ð¸ÑÐµÑÐ°ÑÑÑÐ½Ð¾Ð³Ð¾ Ð¾Ð±Ð·Ð¾ÑÐ° Ð¿Ð¾ ÑÐµÐ¾ÑÐ¸Ð¸ Ð¸ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½Ð¾Ð¼Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐµÑÐµÐ½Ð¸Ð¹ Ð² ÑÐ¾ÑÑÐ´Ð°Ñ ÑÐ¾ ÑÑÐµÐ½Ð¾Ð·Ð¾Ð¼. 2. Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ Ð¸ ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ð¹ Ð² Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÐ¾ÑÑÐ´Ð° ÑÐ¾ ÑÑÐµÐ½Ð¾Ð·Ð¾Ð¼ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð³Ð¾ ÐºÐ¾Ð¼Ð¿Ð»ÐµÐºÑÐ° ANSYS CFX. 3. Ð¡ÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ñ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐ¼Ð¸ Ð´Ð°Ð½Ð½ÑÐ¼Ð¸ Ð¸ Ð»Ð¸ÑÐµÑÐ°ÑÑÑÐ½ÑÐ¼Ð¸ Ð¸ÑÑÐ¾ÑÐ½Ð¸ÐºÐ°Ð¼Ð¸. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ ÑÐ¸ÑÐ»Ð° Ð ÐµÐ¹Ð½Ð¾Ð»ÑÐ´ÑÐ° Ð½Ð° ÑÑÑÑÐºÑÑÑÑ ÑÐµÑÐµÐ½Ð¸Ñ Ð¸ Ð¿ÑÐ¾ÑÑÐ¶ÐµÐ½Ð½Ð¾ÑÑÑ Ð·Ð¾Ð½Ñ Ð²Ð¾Ð·Ð²ÑÐ°ÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ. Ð ÑÐ»ÑÑÐ°Ðµ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð° ÑÑÐµÐ½Ð¾Ð·Ð¾Ð¼ ÑÐ¾ÑÐ¼Ð¸ÑÑÐµÑÑÑ Ð¿ÑÐ¾ÑÑÐ¶ÐµÐ½Ð½Ð°Ñ ÑÑÑÑÑ Ð¸ Ð·Ð¾Ð½Ð° ÑÐµÑÐ¸ÑÐºÑÐ»ÑÑÐ¸Ð¸ (Ð²Ð¾Ð·Ð²ÑÐ°ÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ), Ð¿ÑÐ¸Ð±Ð»Ð¸Ð·Ð¸ÑÐµÐ»ÑÐ½Ð¾ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾ ÑÐ²ÐµÐ»Ð¸ÑÐ¸Ð²Ð°ÑÑÐ°ÑÑÑ Ñ ÑÐ¾ÑÑÐ¾Ð¼ ÑÐ¸ÑÐ»Ð° Ð ÐµÐ¹Ð½Ð¾Ð»ÑÐ´ÑÐ°. ÐÑÐ¸ Re &gt; 300 Ð¿ÑÐ¾Ð¸ÑÑÐ¾Ð´Ð¸Ñ ÑÑÑÐ±ÑÐ»Ð¸Ð·Ð°ÑÐ¸Ñ Ð¿Ð¾ÑÐ¾ÐºÐ° Ð·Ð° ÑÑÐµÐ½Ð¾Ð·Ð¾Ð¼, ÑÑÐ¾ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸Ð·ÑÐµÑÑÑ ÑÐµÐ·ÐºÐ¸Ð¼ ÑÐ¼ÐµÐ½ÑÑÐµÐ½Ð¸ÐµÐ¼ Ð´Ð»Ð¸Ð½Ñ Ð·Ð¾Ð½Ñ Ð²Ð¾Ð·Ð²ÑÐ°ÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ Ñ Ð¿Ð¾ÑÐ»ÐµÐ´ÑÑÑÐ¸Ð¼ Ð¿ÑÐ¸Ð±Ð»Ð¸Ð·Ð¸ÑÐµÐ»ÑÐ½ÑÐ¼ Ð¿Ð¾ÑÑÐ¾ÑÐ½ÑÑÐ²Ð¾Ð¼ ÐµÐµ Ð´Ð»Ð¸Ð½Ñ Ñ ÑÐ¾ÑÑÐ¾Ð¼ ÑÐ¸ÑÐ»Ð° Ð ÐµÐ¹Ð½Ð¾Ð»ÑÐ´ÑÐ° (Ð·Ð½Ð°ÑÐµÐ½Ð¸Ðµ Ð¾ÐºÐ¾Ð»Ð¾ 5-ÑÐ¸ ÐºÐ°Ð»Ð¸Ð±ÑÐ¾Ð²). ÐÐ¾Ð´ÐµÐ»Ñ ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½Ð¾ÑÑÐ¸ BSL-R Ð¿Ð¾ÐºÐ°Ð·Ð°Ð»Ð° Ð½Ð°Ð¸Ð±Ð¾Ð»ÑÑÐµÐµ ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²Ð¸Ðµ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐ¼ Ð´Ð°Ð½Ð½ÑÐ¼.
description: The given work is devoted to studying of steady laminar and turbulent flow in a model of a blood vessel with asymmetric stenosis. The investigation covers Reynolds numbers ranging from 100 to 1800. The modeling is based on solving the Navier-Stokes equations and various turbulence models (k-Ï, BSL, BSL-R, SST). The research set the following goals: 1. Conducting a literature review on the theory and experimental modeling of flows in vessels with stenosis. 2. Numerical modeling of laminar and turbulent flows in a vessel model with stenosis using the ANSYS CFX software package. 3. Comparing numerical modeling results with experimental data and literature sources. The effect of the Reynolds number on the flow structure and the length of the back flow zone has been studied. In the case of laminar flow, an extended jet and a recirculation zone (return flow) are formed behind the stenosis, which increases approximately linearly with an increase in the Reynolds number. At Re &gt; 300, turbulence of the flow behind the stenosis occurs, which is characterized by a sharp decrease in the length of the back flow zone, followed by an approximate constancy of its length with an increase in the Reynolds number (a value of about 5 calibers). The BSL-R turbulence model showed the good agreement with experimental data.