and Computational Methods

#### 539.3 Finite-element modeling of thermal stresses in composite structures with thermal decomposition under aerodynamic heating

**Dimitrienko Y. I. (Bauman Moscow State Technical University), Koryakov M. N. (Bauman Moscow State Technical University), Yurin Y. V. (Bauman Moscow State Technical University), Zakharov A. A. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2019-2-1534

The coupled task of aero-thermo-mechanics of heat-loaded structures from thermally destructive polymer composite materials under the influence of an intense aerodynamic flow is considered. The mathematical formulation of the conjugate problem is formulated and algorithms for the numerical solution of this problem are proposed. The algorithms are based on an iterative solution of three types of problems: aerodynamics, internal heat and mass transfer, and thermomechanics of the modeling aircraft structure. An example of a numerical solution to the problem for an aircraft structural element in the form of a blunt cone is presented. It is shown that the effect of high temperatures of aerodynamic heating of the structure leads to thermal degradation of the polymer composite material, which results in the generation of a large amount of gases in the pores and thermo-chemical shrinkage, which under certain conditions can lead to premature destruction of the heat-loaded composite structure.

Димитриенко Ю.И., Коряков М.Н., Юрин Ю.В., Захаров А.А. Конечно-элементное моделирование термонапряжений в композитных термодеструктирующих конструкциях при аэродинамическом нагреве. Математическое моделирование и численные методы, 2019, № 2, с. 15–34.

#### 696.11 Numerical simulation of flow in a centrifugal separator based on SA and SARC models

**Madaliev M. E. (Institute of Mechanics and Seismic Stability of Structures named after M.T.Urazbaev of the Academy of Sciences of the Republic of Uzbekistan)**

doi: 10.18698/2309-3684-2019-2-3550

The results of mathematical modeling of two-phase swirling turbulent flow in the separation zone of a centrifugal apparatus are presented. The motion of the carrier gas flow was modeled using the averaged Navier – Stokes equations, for closure of which the well-known Spalart Allmares SA turbulence model was used and Schur and Spalart proposed an amendment to the Spalart-Allmaras SARC model. Based on the field obtained, the averaged velocities of the carrier medium, taking into account turbulent diffusion.

Мадалиев М.Э. Численное моделирование течения в центробежном сепараторе на основе моделей SA и SARC. Математическое моделирование и численные методы, 2019, № 2, с. 35–50.

#### 533.6.011.6 Heat exchange and friction in a thin air laminar-turbulent boundary layer over a hemisphere surface

**Gorskiy V. V. (Bauman Moscow State Technical University/JSC MIC NPO Mashinostroyenia), Loktionova A. G. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2019-2-5167

Spherical aircraft elements are related to a number of their fragments influ-enced by the maximum heat fluxes. As a result calculating thermal and force loading of a hemisphere is of particular interest. This problem is one of the most acute within the extremely high Reynolds numbers that correspond to laminar-turbulent gas flow in a boundary layer over a hemisphere. At the same time, the fundamental monograph [1] on the aircraft convective heat exchange, which summarizes the results of many years of research on this problem, doesn’t pay proper attention to this issue. At the same time, the work [2] shows that using the approaches for a hemisphere outlined in the monograph [1] is associated with a number of significant errors within the range of extremely high Reynolds numbers. Calculating heat transfer and friction on the porous wall which correct solution has been missing by now is one of the least studied problems of laminar-turbulent heat exchange. The purpose of this article is to develop a highly accurate engineering method for calculating heat transfer and friction in a laminar-turbulent boundary layer on a hemisphere.

Горский В.В., Локтионова А.Г. Моделирование теплообмена и трения в тонком воздушном ламинарно-турбулентном пограничном слое над поверхностью полусферы. Математическое моделирование и численные методы, 2019, № 2, с. 51–67.

#### 551.513 Сlimatic effects modeling of the large asteroid impact 66 million years ago

**Parkhomenko V. P. (Bauman Moscow State Technical University/Computing Centre of RAS)**

doi: 10.18698/2309-3684-2019-2-6883

Studies indicate the mass death on Earth of a significant number of biological groups, in particular - dinosaurs, at the end of the Cretaceous, 66 million years ago. The final cause of this phenomenon remains the subject of discussion. Currently, there are two main theories: large-scale volcanic eruptions and the impact of an asteroid that formed the Chicxulub crater (Mexico). The production of sulfur-containing gases from the evaporation of the surface layers of the Earth during collisions is now considered the main source of climatic effects, since they form stratospheric sulfate aerosols that block sunlight and thus cool the atmosphere of the Earth and prevent photosynthesis. This paper presents the use of a joint climate model to study the effects of this asteroid on the Earth’s climate. It was established that, depending on the time spent in the stratosphere of the aerosol, the global annual average temperature of the surface air decreased by 18 ° C–26 ° C, remained below zero for 4-30 years and a recovery time of more than 30 years was observed.

Пархоменко В.П. Моделирование климатических последствий падения крупного астероида 66 млн лет назад. Математическое моделирование и численные методы, 2019, № 2, с. 68–83.

#### 519.8 Probabilistic models of bilateral combat operations with linear dependencies of effective rates of fire of combat units of the parties on the time of the battle with a preemptive strike of one of them

**Chuev V. U. (Bauman Moscow State Technical University), Dubogray I. V. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2019-2-8498

On the basis of the theory of continuous Markov processes the models of bilateral military operations with linear dependences of effective rates of fire of combat units of the parties on the time of battle with a preemptive strike of one of them are developed. The algorithm allowing to calculate the main indicators of fight is developed. A comparison with the simulation results obtained on the basis of probabilistic models of combat with constant effective rates of fire and the model of the dynamics of the average with linear dependencies of effective rates of fire on the time of battle. The influence of a preemptive strike of one of the warring parties on the outcome and the main indicators of the battle is studed.

Чуев В.Ю., Дубограй И.В. Вероятностные модели двухсторонних боевых действий с линейными зависимостями эффективных скорострельностей боевых единиц сторон от времени боя при упреждающем ударе одной из них. Математическое моделирование и численные методы, 2019, № 2, с. 84–98.

#### 629.7.015.4 Modeling of stressed-deformed state of rotation shells under conditions of material creep

**Butina T. A. (Bauman Moscow State Technical University), Dubrovin V. M. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2019-2-314

One of the main properties of structural materials is creep. The prob-lem of determining the stress-strain state of axisymmetrically loaded shells of rotation at creep is considered

Бутина Т.А., Дубровин В.М. Моделирование напряженно-деформированного состояния оболочек вращения в условиях ползучести материала. Математическое моделирование и численные методы, 2019, № 2, с. 3–14.