and Computational Methods

Rubric: "05.07.00 Aviation and Rocket-Space Engineering"

doi: 10.18698/2309-3684-2014-1-6881

The authors developed the analytical formula for fast and accurate calculation of pressure on the surface of rotation bodies with arbitrary shape, which were flown by supersonic gas. The paper provides examples of applying the method for three-dimensional flows of gas.

Kotenev V., Sysenko V. Analytical formula with improved accuracy for calculating pressure distribution on the surface of convex, blunt rotation bodies of arbitrary shape. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 68-81

doi: 10.18698/2309-3684-2016-1-1737

The article examines the problem of mathematical modeling tests of massive tire bench run with the chassis dynamometer. Conducted tests enable to define the characteristics of resistance to the tire rolling. The article contains the main stages of model building. We give a formulation for the contact problem of tire stationary free rolling on the test drum considering the energy dissipation in the rubber during cyclic deformation. We also describe a rubber viscoelastic behavior by the model Bergstrom – Boyce and ascertain its numerical parameters according to the samples tests results. The contact conditions for normal and tangential directions are formulated on basis of the penetration function. For the contact restrictions implementation we use the penalty method and obtain the numerical solution of the three-dimensional viscoelasticity problem by the finite element method. To estimate the adequacy of the built model, we compare the calculation results with the test data received for massive tire on Hasbach test equipment. For this purpose rolling resistance forces under different loads were collated. The pressure distribution in the contact area obtained from calculations and experiments by using XSENSOR Technology Corporation equipment are also juxtaposed.

Belkin A., Semenov V. Mathematical modeling of massive tire stationary rolling on the chassis dynamometer with regard to energy dissipation in rubber. Маthematical Modeling and Coтputational Methods, 2016, №1 (9), pp. 17-37

doi: 10.18698/2309-3684-2015-1-8393

We have analysed and presented observations of artificial celestial body 43096. We obtained the observations in 2006–2012 within the project “Scientific Network of Optic Instruments for Astrometric and Photometric Observations” (ISON). We have determined the Kepler orbit elements and state vector as of 1 hour 55 minutes 50,76 seconds, November 24, 2006 UTC (1:55:50,76 November 24,2006 UTC). We have performed numerical integration of the motion equations, taking into account the perturbations from the polar compression of the Earth, the Moon, the Sun and the solar radiation pressure. We propose a method for deorbiting artificial celestial bodies in high altitude orbits. The method is based on a numerical model of motion in circumterrestrial space, which takes into account only the largest perturbations. For the first time ever we have obtained such a great amount of data on objects with a large area of surface to mass ratio over long time spans. The data allowed us to study the objects and reveal their peculiar properties.

Bazey A., Bazey N., Borovin G., Zolotov V., Kashuba V., Kashuba S., Kupriyanov V., Molotov I. Evolution of the orbit of a passive fragment with a large area of surface in high Earth orbit. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 83-93

doi: 10.18698/2309-3684-2014-3-5573

The article presents a method of accounting for secondary combustion effects when solid propellant power device is used for the gas-dynamic ejection of lifting vehicles. The method is based on thermo chemistry calculations. The suggested method can be easily applied to engineering calculations of aircraft gas-dynamic ejection systems as well as to the analysis of experimental data involving secondary combustion effects.

Plyusnin A. Calculation of aircraft gas-dynamic ejection systems with due consideration of the secondary combustion effects. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 55-73

doi: 10.18698/2309-3684-2017-1-5577

The article introduces and provides a rationale for the mathematical theory which defines the mass-consuming characteristics of the power devices designed for providing the gas-dynamic ejection of the flying vehicle from the launcher-container with the set-up restrictions on parameters. We present a visual geometrical interpretation of the offered method. The calculations of the gas-dynamic emission parameters and the intraballistic computation of the power device with the propellant grain operation confirm the correctness of the theoretical constructions and their practical feasibility.

Plyusnin A. Simulating mass-consuming characteristics of power devices providing gas-dynamic ejection of the flying vehicle with setup parameters. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 55-77

doi: 10.18698/2309-3684-2014-4-8894

The article presents estimated accuracy of the engineering design procedure of the mass flow rate of gas through the laminar boundary layer on a hemisphere of [1]. A similar engineering method of extra accuracy is proposed.

Gorskiy V., Sysenko V. Simulation of gas flow through the laminar boundary layer on the hemisphere surface in a supersonic air flow. Маthematical Modeling and Coтputational Methods, 2014, №4 (4), pp. 88-94

doi: 10.18698/2309-3684-2017-2-3964

The study deals with a one-dimensional analytical model for computing the loads on the body of an aircraft caused by water entering the annular space of a launch canister. We used potential theory to solve the "external" hydrodynamic problem. Solving Lamé equations for the static case accounts for the strain in the walls of the aircraft and the launch canister.

Plyusnin A.V. Mathematical simulation of the process of water entering the annular space of a canister during submarine gas-driven aircraft ejection. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 39-64

doi: 10.18698/2309-3684-2015-1-1730

The article discusses a method for constructing an aircraft geometric shape for computing the parameters of aerogasdynamic flow as well as a method of meshing near the model to simulate the flow within the Navier–Stokes equations in the thin layer approximation. The results of the flow simulation are given. The calculations were performed on a multiprocessor computer system.

Bratchev A., Dubrovina A., Kotenev V., Maksimov F., Shevelev Y. Problem solution of aerodynamic design using multiprocessor computers. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 17-30

doi: 10.18698/2309-3684-2014-3-7488

We examined effects of typical for different climatic zones atmospheric conditions on flight program optimization for a subsonic long-haul passenger aircraft. Simulation of flight and power plant performance was based on current traditional approaches used in solving problems of this kind. The acceleration-climb flight segment has been optimized by minimizing fuel consumption at this flight segment. The cruising flight segment has been optimized considering operating limitations accepted for civil aviation. The in-built model of bypass turbojet engine was used for simulating the flight. This model allows calculating power plant performances under any flight conditions. The flight of subsonic aircraft has been examined in one vertical plane. Calculations have been performed for 6 standard air temperature variations with altitude (depending on climatic zone). Atmospheric pressure variation near Earth surface was considered and effects of atmospheric conditions on flight program optimization were estimated.

Mozzhorina T., Gubareva E. Simulating atmospheric conditions influence on flight program optimization for a subsonic passenger aircraft. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 74-88