ISSN 0021-8944, Journal of Applied Mechanics and Technical Physics, 2018, Vol. 59, No. 1, pp. 14–21.
Pleiades Publishing, Ltd., 2018.
Original Russian Text
A.M. Lipanov, S.A. Karskanov, A.I. Karpov.
DIRECT NUMERICAL SIMULATION OF A SUPERSONIC BASE FLOW
BEHIND A CIRCULAR CYLINDER
A. M. Lipanov, S. A. Karskanov, and A. I. Karpov
Abstract: A supersonic ﬂow in the near wake behind a cylinder is considered. Base pressure
distributions behind a circular cylinder for various Mach numbers M
are obtained and analyzed by
means of direct numerical simulation based on high-order approximation algorithms. For M
the results obtained in the present study are compared with available experimental and numerical
data. Generation of turbulent kinetic energy is calculated for various Mach numbers.
Keywords: supersonic ﬂow, Navier–Stokes equations, high-order approximation, direct numerical
simulation, base drag.
Numerical simulation of ﬂight processes for various ﬂying vehicles and aerodynamic bodies, such as projec-
tiles, bullets, and missiles, is a complicated problem. The primary reason is ﬂow unsteadiness. Moreover, this form
of motion of a continuous medium occurs in most cases due to interaction of engineering devices with the ambient
medium. Methods of the mathematical description of high-velocity ﬂows suitable for applications in practice have
been sought for more than 100 years, beginning from the academic activities of Reynolds. According to the modern
concepts, viscous ﬂuid ﬂows are described by the Navier–Stokes equations. However, despite signiﬁcant progress of
computer engineering, its capabilities are insuﬃcient for solving these equations for high Reynolds numbers (which
are of major interest); apparently, this situation will not be changed until the end of the 21st century . Therefore,
procedures and algorithms of computational ﬂuid dynamics should be permanently improved and revised. Theories
and methods recently capable of providing acceptable results can become invalid at later stages of development of
new ﬂying vehicles. Therefore, it is always necessary to ﬁnd a compromise between the model adequacy and the
possibility of its application in practice, which is primarily determined by the computational engineering potential.
One of the popular methods used recently is direct numerical simulation (DNS) based on the ﬁrst principles
of aerodynamics. However, it does not seem possible to use DNS for solving diﬃcult CFD problems at the moment
because such computations are extremely expensive. This method can be applied either at low Reynolds numbers
or in problems with simple geometry; for this reason, the method is mainly used in basic research. Nevertheless,
DNS results that contain no empirical parameters are very important in aerodynamic research because they can
be used for testing numerous semi-empirical turbulence models, especially being combined with experimental data.
Moreover, DNS allows one to obtain a comprehensive pattern of the ﬂow without averaging, which can be used for
studying the ﬂow structure and unsteady distributions of parameters.
The main task of computational ﬂuid dynamics is to determine the aerodynamic characteristics of various
bodies in the ﬂow by means of mathematical modeling. An important part of the problem is precise calculation of
Institute of Mechanics, Ural Branch, Russian Academy of Sciences, Izhevsk, 426067 Russia;
firstname.lastname@example.org; email@example.com; firstname.lastname@example.org. Translated from Prikladnaya Mekhanika i Tekhnicheskaya
Fizika, Vol. 59, No. 1, pp. 19–27, January–February, 2018. Original article submitted August 22, 2016; revision
submitted February 20, 2017.
2018 by Pleiades Publishing, Ltd.