Труды Института механики им. Р.Р. Мавлютова
Электронный научный журнал | Electronic Scientific Journal
Proceedings of the Mavlyutov Institute of Mechanics
In this paper the steady flow of technical fluid induced pressure drop in the channel with a cylindrical jet for the entire working temperature range have been studied. The Navier–Stokes equations are solved numerically in axially symmetric geometry by the finite element method. The temperature dependence of the material parameters of a number of liquids, most commonly used in technical devices have been obtained. A model of a cylindrical jet was built in the form of a computing element of the stand, which takes into account the pressure drop, the radius of passage opening jet and the liquid temperature for the areas with low and high pressure drops. This model allows without significant loss of accuracy replace the complete numerical simulation, requires more computational resources, by simple analytical formulas admitting modeling in computational stand in real time. The model can be used in various technical applications of microelectromechanical systems (at low pressure drops) to the fuel metering elements (at high pressures drops).
a cylindrical jet,
the fluid physical properties,
the influence of temperature
Problem: checking the temperature dependence of the analytical flow rate of fluid by simulation of the complete system of hydrodynamic equations and constructing a model of a cylindrical jet as an approximation of results of numerical calculations.
Methods: numerical calculation of the Navier-Stokes equations was carried out using the finite element method (first-order elements for pressure and second-order elements for the velocity components) by discretization according to the scheme of reverse differentiation on time of a second-order. Preliminary calculation was based on the linear scheme Picard and then on a non-linear calculation according to Newton's scheme.
The study shown that:
1. region of low pressure drop depends on the fluid temperature value T. In this area, the flow rate is inversely proportional to the dynamic viscosity and is increased with increasing temperature;
2. at high pressure drops, which is substantially independent of the T, the flow rate is inversely proportional to the fluid density and temperature increases.
Moreover for the low and high pressure drops formula, allowing high accuracy to calculate the fluid flow across the entire operating temperature range for the flow rate measurement unit for the a fixed temperature is obtained. In the intermediate region provided a method of constructing the liquid flow depending on the temperature as an the piecewise linear interpolation.