Statement of the problem calculation of the velocity field of the air environment between two equidistant planes committed by simultaneous harmonic

Abstract

This article presents the problem formulation for calculating the characteristics of air movement under the action of moving the working surfaces in the form of a boundary value problem. Formalized boundary conditions allowing further used differential equations lead to a system of algebraic equations solved by known numerical methods. As a mathematical model used model of an ideal gas. The impact of the oscillating surfaces of the air mass that lies between the parallel planes is described using Euler's equation and the continuity equation. In coordinate form the data vector equations allow to make the differential equation system of four equations. The number of unknowns that must be determined for each point of the air volume between the working surfaces is also equal to four. This projection of the velocity vector of the air element of the continuum on the axis of the coordinate system associated with surfaces, and the amount of air pressure in the considered point. Field parameters air velocities are calculated for a limited area, Ξ, having a parallelepiped shape. Suggested in the article boundary conditions allow to calculate the values of the projections of the velocity vector and pressure points of the air mass, located on the border of the air box between working surfaces.