MATHEMATICAL MODELS, NUMERICAL METHODS AND RESULTS OF STUDY OF TRANSSONIC FLOW AROUND PROFILES OF BLADE SYSTEMS

Abstract

The aerodynamic characteristics of blade profiles in a transonic flow of an ideal gas are considered, which are obtained on the basis of the numerical solution of the system of gas dynamics equations (laws of conservation) in integral form. The solution is found by stabilizing over time, which avoids complications in the numerical method for a stationary system of variable-type equations with unknown lines of change from elliptic to hyperbolic and vice versa. The peculiarities of the position of the shock wave (jump) depending on the algorithm for calculating the parameter values on the faces of the cells of the difference grid in the finite-volume algorithm are pointed out. The calculation of numerical flows on the faces of the volume is based on the solution of the problem of the decay of an arbitrary discontinuity of parameters on them in a one-dimensional direction along the normal to the face. The choice of the working difference scheme is based on the indicators of accuracy (order of approximation) and complexity (explicit and implicit) of transition to the next time layer. The development of difference schemes of a higher order of approximation allows to obtain more detailed information about gas-dynamic flows on real grids, which was unattainable when using schemes of the first order of accuracy with high scheme (approximation) viscosity and inconsistency of the propagation of disturbances on a heterogeneous background of parameter values (dispersion calculation effects). The results of calculations using S.K. Godunov's scheme of a higher order of approximation, aerodynamic characteristics of the rigid profile and their comparison with experimental data are given. The characteristics of a profile that performs incoherent angular and vertical oscillations according to a given law are studied.