MATHEMATICAL MODELING OF FLUID FLOW IN A RECTANGULAR CAVITY WITH MOVING BOUNDARIES
Authors:
1.
KNITU
2.
Kazan National Research Technological University
Type:
Article
Pages:
from 151
to 154
Status:
Published
Received:
23.12.2025
Accepted:
23.12.2025
Published:
23.12.2025
Language:
Russian
Keywords:
NUMERICAL MODELING, PLANE FLOW, DISTRIBUTION OF PRINCIPAL STRESSES
Abstract (English):
This article is devoted to the study of viscous Newtonian fluid in a rectangular cavity with moving boundaries in a plane setting. The treatment of the fluid causes the movement of three moving walls of the oral cavity. The fourth wall remains stationary. This formulation of the problem models the mixing process in the channel of a planetary extruder. Such simplification nevertheless preserves a qualitative picture of the liquid flow and allows us to explain the effects associated with the growth of stresses at the corner points of the cavity. It is assumed that possible solid inclusions included in the mixed liquids are small enough and do not affect the flow pattern of the liquid in this cavity. It is also assumed that the liquid is already a homogeneous medium and does not have non-Newtonian properties. The problem is solved by the method of control volumes (MCV), characterized by the property of conservatism, the implementation of integral balance relations. The purpose of this work is to study the fluid flows in the cavity under study, as well as in the vicinity of corner zones. To achieve the set goal, the flow lines in the studied area were investigated, as well as the stress distributions in different sections of the cavity. The obtained modeling results allow us to obtain the distributions of the first difference of principal stresses (PSD) in different sections of the cavity, which allows us to evaluate the influence of stagnant zones in the vicinity of corner points on the overall flow pattern. The paper presents flow line patterns that allow the flow structure to be analyzed. In addition, isolines of the difference in principal stresses in the flow region are presented. The influence of stress changes in the vicinity of corner points on the structure of fluid flow is discussed. It is shown that stagnant zones are characterized by an abnormal increase in stresses, which is associated, among other things, with the singularity of stress behavior in stagnant zones.
This article is devoted to the study of viscous Newtonian fluid in a rectangular cavity with moving boundaries in a plane setting. The treatment of the fluid causes the movement of three moving walls of the oral cavity. The fourth wall remains stationary. This formulation of the problem models the mixing process in the channel of a planetary extruder. Such simplification nevertheless preserves a qualitative picture of the liquid flow and allows us to explain the effects associated with the growth of stresses at the corner points of the cavity. It is assumed that possible solid inclusions included in the mixed liquids are small enough and do not affect the flow pattern of the liquid in this cavity. It is also assumed that the liquid is already a homogeneous medium and does not have non-Newtonian properties. The problem is solved by the method of control volumes (MCV), characterized by the property of conservatism, the implementation of integral balance relations. The purpose of this work is to study the fluid flows in the cavity under study, as well as in the vicinity of corner zones. To achieve the set goal, the flow lines in the studied area were investigated, as well as the stress distributions in different sections of the cavity. The obtained modeling results allow us to obtain the distributions of the first difference of principal stresses (PSD) in different sections of the cavity, which allows us to evaluate the influence of stagnant zones in the vicinity of corner points on the overall flow pattern. The paper presents flow line patterns that allow the flow structure to be analyzed. In addition, isolines of the difference in principal stresses in the flow region are presented. The influence of stress changes in the vicinity of corner points on the structure of fluid flow is discussed. It is shown that stagnant zones are characterized by an abnormal increase in stresses, which is associated, among other things, with the singularity of stress behavior in stagnant zones.
Keywords:
NUMERICAL MODELING, PLANE FLOW, DISTRIBUTION OF PRINCIPAL STRESSES
NUMERICAL MODELING, PLANE FLOW, DISTRIBUTION OF PRINCIPAL STRESSES
