#### 531.6.011.32:532.582.4:517.958 Construction of a semi-infinite equivalent body in mathematical modeling of subsonic separated axisymmetric flow

##### Timofeev V. N. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2016-4-6783

The purpose of the work was to do mathematical modeling of axisymmetric body separation flow at subsonic velocities of incident flow. In our research we used the concept of viscous-inviscid interaction. We found velocities and pressures on the surface of the body under study according to the results of calculating of some equivalent body inviscid flow. The wake turbulence effect was simulated by the tailed section of the equivalent body. We examined the semi-infinite tailed sections of the equivalent body instead of the tailed sections of finite length. Moreover, we studied flow separation conditions in the base region. For the numerical simulation we used the discrete vortex method. The base pressure was found by Horner formula. We carried out mathematical modeling of the flow around cylindrical bodies with the head part of the ogival form.

Timofeev V. Construction of a semi-infinite equivalent body in mathematical modeling of subsonic separated axisymmetric flow. Маthematical Modeling and Coтputational Methods, 2016, №4 (12), pp. 67-83

#### 531.6.011.32:532.582.4 Method for organizing an iterative process in modeling subsonic separated flow around elongated bodies using an equivalent surface and cubic splines

##### Timofeev V. N. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2021-4-80102

In the aspect of improving the methodology of mathematical modeling of subsonic detachable flow around elongated bodies with partial implementation of the concept of viscosity-inviolable interaction, the issues of organizing the iterative process of constructing the surface of an equivalent body are considered. A flow diagram with a semi-infinite equivalent surface was used. Numerical modeling was carried out according to the algorithms of the technique using the method of discrete vortices. For greater versatility, when constructing a calculated grid on the surface of an equivalent body, approximation with smoothing cubic splines was used. Data on the influence of the shape of the tail section of the equivalent surface on the distribution of speed and pressure during axisymmetric flow around bodies with a bottom section are presented.

Тимофеев В.Н. Методика организации итерационного процесса при моделировании дозвукового отрывного обтекания удлиненных тел с применением эквивалентной поверхности и кубических сплайнов. Математическое моделирование и численные методы, 2021, № 4, с. 80–102.

#### 531.6.011.32:532.582.4 Modeling of subsonic separation flow around bodies by the method of discrete vortices based on the concept of an equivalent surface with cubic splines

##### Timofeev V. N. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2020-4-2743

For mathematical modeling of subsonic separation flow around axisymmetric bodies with a bottom section, a technique with a partial implementation of the concept of visco–inviscid interaction was used. A flow scheme with an equivalence semi-infinite surface was used. Numerical simulations were carried out according to the algorithms of the method using the method of discrete vortices and approximation by smoothing cubic splines. Data on the influence of the shape of the tail section of an equivalent surface on the velocity and pressure distribution during axisymmetric flow around bodies with a bottom section are presented. The proposed recommendations make it possible to apply this technique more universally.

Тимофеев В.Н. Моделирование дозвукового отрывного обтекания тел методом дискретных вихрей на основе концепции эквивалентной поверхности с кубическими сплайнами. Математическое моделирование и численные методы, 2020, № 4, с. 27–43.

#### 532.582.4:517.958 Simulation of subsonic detachable flow of axisymmetric bodies with bottom slice at non-zero angles of attack

##### Timofeev V. N. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2020-3-99116

According to the current scheme with the equivalent half-bottom surface, the subsonic streamlining of the axisymmetric bodies with the separation line located in the bottom cut area is examined. Recommendations have been made to improve the calculation method in the case of non-zero angles of attack. The estimated ratios of the technique are adapted to use the method of discrete vortexes. Detailed data on the distribution of speed and pressure on the surface of the cylindrical body with a bottom cut and the head part of the liveable shape at non-zero angles of attack are presented.

Тимофеев В.Н. Моделирование дозвукового отрывного обтекания осесимметричных тел с донным срезом при ненулевых углах атаки. Математическое моделирование и численные методы, 2020, № 3, с. 99–116.

#### 531.6.011.32:532.582.4 Simulation of the subsonic detachable body with a bottom cut on the current pattern with an equivalent half-infinite surface at small angles of attack

##### Timofeev V. N. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2019-4-3149

The subsonic flow of cylindrical bodies with a detachment located in the vicinity of the bottom cut is considered. The current scheme with an equivalent surface, which is accompanied by a half-infinite section is used. Recommendations have been given on the formation of a configuration of such an equivalent semi-infinite surface at non-zero attack angles. The laboriousness of the calculations is reduced by taking into account the specifics of the applied flow pattern and the use of P-shaped vortex threads in the method of discrete vortexes. The results of mathematical modeling of the flow of cylindrical bodies with a revitalized head and a bottom slice at small angles of attack are presented.

Тимофеев В.Н. Моделирование дозвукового отрывного обтекания тел с донным срезом по схеме течения с эквивалентной полубесконечной поверхностью при малых углах атаки. Математическое моделирование и численные методы, 2019, № 4, с. 31–49.

#### 531.6.011.32:532.582.4:517.958 Special features of vortex diagram in simulation of subsonic detached flow around the semi-infinite equivalent body

##### Timofeev V. N. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2017-4-7391

The paper introduces some special features of mathematical simulation of subsonic detached flow around the bodies, the flow being localized in the vicinity of the ground shear. The formation of vortex diagram for the semi-infinite equivalent body is examined. The formulae for determining the vector functions of the vortex segments velocity are reduced to a form allowing one to easily pass to the limit as the points of the origin or ends of these segments are moved off to infinity. Furthermore, the study shows the relationships for finding the velocity function vectors of semi-infinite vortex segments and U-shaped vortex lines, the relationships being adapted for computer calculations. Findings of mathematical simulation of the flow around cylindrical bodies with the head part of the ogival form are given.

Timofeev V.N. Special features of vortex diagram in simulation of subsonic detached flow around the semi-infinite equivalent body. Mathematical Modeling and Computational Methods, 2017, №4 (16), pp. 73-91.