ISSN 2542–0380 
Труды Института механики им. Р.Р. Мавлютова
Электронный научный журнал  Electronic Scientific Journal
Proceedings of the Mavlyutov Institute of Mechanics

In this paper the fluid flow in a flat channel with a hydraulic resistance is studied for two cases of a dynamic change in the channel geometry: transverse compression of the opening of the hydraulic resistance (the flow is caused by a pressure drop applied to the layer) and longitudinal movement of the hydraulic resistance along the channel (the flow is caused by this movement). It is obtained that in a geometry with transverse compression the flow is laminar without the formation of vortices. In a geometry with longitudinal movement of the hydraulic resistance the flow rate of the liquid remains constant with the formation of stable vortices that move along the channel at the rate of motion of the hydraulic resistance. On the base of the modeling results an analytical model that takes into account the flow rate of the fluid from the width of the through hole of the resistance is constructed. This model contains four interpolation parameters and it can be used as an element of a computational stand for determining the generalized flow of liquid in the system under consideration.
hydrodynamics,
movable geometry,
finite element method,
a computer stand
Purpose: Construction of an element of a computational stand for a flat channel with a hydraulic resistance of a changing geometry, which allows one to find the flow of a liquid by means of simple interpolation formulas.
Methodology: numerical calculation of the NavierStokes equations was carried out using the finite element method at irregular computational grid in FreeFem++ package. In the development of a computer model the interpolation methods for different sets of input parameters to approximate the response of the system have been used.
The findings of research:
1. in a geometry with transverse compression the flow is laminar without the formation of vortices;
2. in a geometry with longitudinal movement of the hydraulic resistance the flow rate of the liquid remains constant with the formation of stable vortices that move along the channel at the rate of motion of the hydraulic resistance;
3. an analytical model that takes into account the flow rate of the fluid from the width of the through hole of the resistance is constructed. This model contains four interpolation parameters, calculated on four points from one simulation of the full model.
Originality/value: The analytical model can be used as an element of a computational stand for determining the generalized flow of liquid in the system under consideration. Simulation of dynamic change in geometry opens up great opportunities for the development of new technical devices. For example, the longitudinal motion of hydraulic resistance can be used to create a flow channel with a constant pressure, and transverse compression — for regulating fluid flow in a channel with nonzero differential pressure.