1 Applied Mathematics and Mechanics in Aerospace Industry
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different initial data are presented. When studying the flow of viscous gas between
the cylinders of different temperatures, the flow modes with the flat vortex structures
and with the Taylor vortices as well as the three-dimensional flow corresponding to
the combination of these two flow types were found.
Part II introduces a numerical simulation of plasma and multiphase flows and
involves six chapters.
Chapter 6 is devoted to mathematical modeling of gas-dynamic flows with the
phase transformations (condensation and evaporation) [7, 8]. The system of the
Navier–Stokes equations is used to describe the flow parameters, and the system
of moment equations is used to describe the parameters of a two-phase medium. A
numerical algorithm for solving the general system of equations is constructed on
the basis of the Godunov scheme with the approximation AUSM + for solving the
Riemann problem. The developed numerical model was optimized and adapted for
the case of pure argon condensation in a nozzle based on Hagena’s semi-empirical
theory. In numerical experiments, certain values of the parameters of the condensation model are determined, such as accommodation coefficient and the nucleation
correction factor multiplier.
Chapter 7 conducts a physical and comprehensive numerical study of the generation of plasma bunches with high specific energy with the use of a plasma gun [9, 10].
The parameters of the plasma bunch upon exit from the plasma accelerator and during
propagation in the ionosphere (h > 200 km) to considerable distances (≈100 km)
have been calculated. A special numerical algorithm is presented to study the impact
of a rarefied high-velocity gas flow (~5 × 10 7 cm/s) on the surface of crystalline
and amorphous solid bodies. Based on the results, the electron concentration and the
scale of the ionized region that formed during the passage of a high-speed toroidal
plasma bunch through the rarefied air were estimated.
Chapter 8 is dedicated to the numerical study of pulsating gaseous detonation
wave propagation. The mathematical model is based on the Euler equations written
for the multicomponent gas and supplemented by the detailed chemical reactions
model to describe the combustion of the hydrogen-air mixture [11, 12]. The Petersen
and Hanson kinetics is applied as the detailed chemical model. The numerical algorithm is based on the finite volume approach, essentially non-oscillatory scheme,
AUSM numerical flux, and the Runge–Kutta method. The numerical investigation
of pulsating detonation wave propagation with direct detonation initiation near the
closed end of the channel is carried out. The peculiarities of high-frequency and
high-amplitude pulsations modes are discussed.
Chapter 9 considers a multi-temperature code for a multicomponent gas-dynamic
[13, 14]. The gas-dynamic part is the Godunov-type method based on the efficient
approximate solution of the Riemann problem operating with all components of the
homogeneous gas mixture. The method assumes the table equation of state, but the
system of the hydrodynamic equations should be hyperbolic. This work contains
the test of the method on a strong shock wave in hydrogen plasma, so-called the
Shafranov’s solution. By taking into account the radiation component, the chapter
discusses the applicability of the two temperature model for the strong shock wave in
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different initial data are presented. When studying the flow of viscous gas between
the cylinders of different temperatures, the flow modes with the flat vortex structures
and with the Taylor vortices as well as the three-dimensional flow corresponding to
the combination of these two flow types were found.
Part II introduces a numerical simulation of plasma and multiphase flows and
involves six chapters.
Chapter 6 is devoted to mathematical modeling of gas-dynamic flows with the
phase transformations (condensation and evaporation) [7, 8]. The system of the
Navier–Stokes equations is used to describe the flow parameters, and the system
of moment equations is used to describe the parameters of a two-phase medium. A
numerical algorithm for solving the general system of equations is constructed on
the basis of the Godunov scheme with the approximation AUSM + for solving the
Riemann problem. The developed numerical model was optimized and adapted for
the case of pure argon condensation in a nozzle based on Hagena’s semi-empirical
theory. In numerical experiments, certain values of the parameters of the condensation model are determined, such as accommodation coefficient and the nucleation
correction factor multiplier.
Chapter 7 conducts a physical and comprehensive numerical study of the generation of plasma bunches with high specific energy with the use of a plasma gun [9, 10].
The parameters of the plasma bunch upon exit from the plasma accelerator and during
propagation in the ionosphere (h > 200 km) to considerable distances (≈100 km)
have been calculated. A special numerical algorithm is presented to study the impact
of a rarefied high-velocity gas flow (~5 × 10 7 cm/s) on the surface of crystalline
and amorphous solid bodies. Based on the results, the electron concentration and the
scale of the ionized region that formed during the passage of a high-speed toroidal
plasma bunch through the rarefied air were estimated.
Chapter 8 is dedicated to the numerical study of pulsating gaseous detonation
wave propagation. The mathematical model is based on the Euler equations written
for the multicomponent gas and supplemented by the detailed chemical reactions
model to describe the combustion of the hydrogen-air mixture [11, 12]. The Petersen
and Hanson kinetics is applied as the detailed chemical model. The numerical algorithm is based on the finite volume approach, essentially non-oscillatory scheme,
AUSM numerical flux, and the Runge–Kutta method. The numerical investigation
of pulsating detonation wave propagation with direct detonation initiation near the
closed end of the channel is carried out. The peculiarities of high-frequency and
high-amplitude pulsations modes are discussed.
Chapter 9 considers a multi-temperature code for a multicomponent gas-dynamic
[13, 14]. The gas-dynamic part is the Godunov-type method based on the efficient
approximate solution of the Riemann problem operating with all components of the
homogeneous gas mixture. The method assumes the table equation of state, but the
system of the hydrodynamic equations should be hyperbolic. This work contains
the test of the method on a strong shock wave in hydrogen plasma, so-called the
Shafranov’s solution. By taking into account the radiation component, the chapter
discusses the applicability of the two temperature model for the strong shock wave in