Computational Aerodynamics

calculation of aerodynamic characteristics of various bodies for sub-, trans-, super- and hypersonic regimes, laminar, transient and turbulent, inner and outer flows
taking into account various physical-chemical processes: excitation of inner molecular and atomic freedom degrees, chemical nonequilibrium, ionization, radiation and others for hypersonic flows
calculation conjugated heat transfer problem with and without ablation and heating of inner part of bodies overflowed
simulation sub- and supersonic combustion processes
calculation unsteady turbulence flows
calculation various atmosphere phenomena: typhoon, tornado and so on
determination temperature distribution for various practical applications:
for envelope of blast furnace, nuclear reactor and others
simulation blood flow through large blood vessels for investigation of cardiovascular sickness
calculation flow of natural gas and oil through channels, compressors and others
visualization of complex aerodynamic phenomena, present numerical results as a video

programs may be used for solution of sufficiently complex arbitrary systems of part-differential equations describing various areas of men vital functions.

Diverse methods of computational aerodynamics are developed at TsAGI to investigate the structure of hypersonic flow fields and the behavior of aerodynamic characteristics of bodies in flow as applied to various problems of external and internal aerodynamics. Simulation of hypersonic flows is based on numerical analysis of nonstationary Euler equations for inviscid medium in motion, nonstationary Navier-Stokes equations for laminar conditions or nonstationary Reynolds equations for laminar, transitional, and turbulent conditions of viscous medium motion. In the last case, the set of equations of gas dynamics is closed with either algebraic or differential model of turbulence. The numerical simulation of hypersonic flows suggests the application of different models of medium in motion: model of perfect gas with constant specific heat capacities, constant Prandtl number and dynamic viscosity which depends only on temperature; model of equilibrium gas when medium in motion is in thermodynamic equilibrium; model of nonequilibrium gas when nonequilibrium thermochemical processes proceed in medium in motion, and other models. High effectiveness of the developed methods of numerical analysis makes it possible to apply the methods of computational aerodynamics in the following lines:

Fundamental investigations involving systematic calculations to study the flow field structure, the basic laws of heat transfer and the influence of governing problem parameters on them.
For example:

Fig.1 (Temperature field and streamline patterns (separation zone) for a circular cylinder at Re=1 106 and M=2 (a) and 5 (b).) shows the calculated supersonic perfect gas flow pattern about a circular cylinder. Support of the aerodynamic experiment when the calculations are carried out as applied to the experiment conditions with the purpose of evaluating the experiment potentialities and analyzing the experimental data. As an example, Fig.2 presents calculated supersonic gas flows in the channel with air injection and suction through the side vertical surfaces.

Fig.2 Temperature field in the variable-section plane channel at entry Mach number M=4 and Re=5?106 in the absence (a) and in the presence (b) of mass transfer through vertical walls. Applied activity related to calculations on request of industry.

Fig.3 presents an example of calculated flows over axisymmetric bodies with circular flaps.