Investigation of the finite element mesh local adaptation in the problem of supersonic flow near body

DOI: 10.34759/trd-2022-125-06

Аuthors

Snazin A. A., Shevchenko A. V.^*, Panfilov E. B.^**

Mlitary spaсe Aсademy named after A.F. Mozhaisky, Saint Petersburg, Russia

*e-mail: artnetru@yandex.ru
**e-mail: vka@mil.ru

Abstract

The traveling at supersonic speed generates a detached bow shock wave ahead of it. Downstream of that, the flow attains large increases of pressure and temperature, which are responsible for the high drag and aerodynamic heating. High drag values increase fuel usage and reduce the ratio of payload to total takeoff weight [1].

The paper considers supersonic flow at Mach number M=4.2. The condition of adhesion and isothermicity with a temperature T = 300 K is established on the streamlined surface of the object of study. The flow is considered axisymmetric with respect to the OX axis. The simulation was carried out in a two-dimensional formulation on a structured prismatic grid containing 506 thousand elements, 65 elements account for the boundary layer. The ratio of the diameter of the main cylinder to the length of the needle is L/D = 1.4.

During the calculation, the mesh cells are adapted in the zones of flow inhomogeneities. The number of adapted cells is 835 thousand, the number of unadapted cells of the original grid is 234 thousand. A homogeneous grid with the size of the cells corresponding to the adapted cells would contain about 2687 thousand cells. Thus, local adaptation allowed to reduce the amount of calculations by 2,5 times.

As a result of the calculations carried out, the difference in the distribution of the pressure coefficient on the surface of the model and in the position of the head shock wave between the adapted and non-adapted grid is clearly traced.

Comparison of the results of visualization of flow inhomogeneities in supersonic body flow obtained experimentally on a wind tunnel and numerical modeling. The results of numerical simulation are in good agreement with experimental data.

The calculations presented in the article showed that the use of local grid adaptation in the areas of gas-dynamic inhomogeneities allowed not only to reduce the cost of computing, but also to achieve a good agreement of numerical results with the results obtained experimentally on a supersonic wind tunnel.

Keywords:

supersonic flow, mesh adaptation

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