and Computational Methods

Rubric: "05.07.00 Aviation and Rocket-Space Engineering"

doi: 10.18698/2309-3684-2015-1-3149

We studied the dynamics of motion and energy transfer in supersonic flow in the base region. It is shown in the article that the current in the base region largely depends on the boundary layer structure in the area between the trailing edge and the sticking point on the centerline, where the boundary layer cut out from the rear edge converges. The study of the effect of gas mass injection into the base region from the body surface and the bottom as well as heat transfer in the bottom region is included. The resulting solution of the problem of the middle wake for axisymmetric body without considering recirculation at a limited distance from the stern has been obtained.

Sidnyaev N., Gordeeva N. Investigation of the energy and mass transfer influence on the wake flow of supersonic conical models. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 31-49

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

doi: 10.18698/2309-3684-2014-2-101114

We have built a mathematical model for deployment of multibody solar array with a cable system of deployment. On the basis of analysis of the kinematic scheme of deployment system we have chosen the dimensions of the radii of the rollers and gear ratio of the two types of gear mechanisms which provide the preset sequence of fixation of sections. We used Lagrange equation of the second kind for studying deployment of the solar battery array. A distinctive feature of this approach is application of iterative method for taking into account deformation of the cables of synchronizing system. The mathematical model can be used to choose optimal design factors and deployment system performance requirements. It is also valuable for dealing with worst-case situations and verifying the reliability of deployment procedure.

Bushuev A., Farafanov B. Mathematical modelling of deployment of large-area solar array. Маthematical Modeling and Coтputational Methods, 2014, №2 (2), pp. 101-114

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: 10.18698/2309-3684-2014-1-99114

The article presents the theoretical analysis of the long-period (phugoid) aircraft oscillations, which has a lifting force and performs a flight at hypersonic speeds in any atmosphere. Oscillations are caused by mutual transition of kinetic energy into potential energy during the flight along the path having an oscillatory character and being determined primarily by controlled longitudinal zero momentum in steady flight. The study shows that with the speed approximating to the first cosmic speed, the decrease in gravity at height dominates the decrease in density of the atmosphere, so that with increasing speed the period of phugoid oscillations tends asymptotically to the corresponding period of the satellite. During the research there were obtained analytical expressions for the short-period oscillations or vibrations at the angle of attack. The study demonstrates that these expressions, as well as the expressions for the long-period oscillations are in good agreement with numerical solutions.

Sidnyaev N., Glushkov P. Long-period oscillations of aircraft at hypersonic speeds. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 99-114

doi: 10.18698/2309-3684-2014-2-77100

The article considers inner and outer problems of non-stationary interaction between aircraft body and incompressible ideal fluid and statement of the problems in the form of boundary integral equations. By inner problems we mean vibration of fuel in tanks and by outer problems we mean determination of additional masses and moments of inertia. We provide formula of efficient solutions for these problems by the boundary element method as applied to bodies of revolution and examples of calculations.

Plyusnin A. Boundary-element-method modelling of inside and outside non-stationary interaction of aircraft body and liquid. Маthematical Modeling and Coтputational Methods, 2014, №2 (2), pp. 77-100

doi: 10.18698/2309-3684-2015-3-5867

The article considers the problem of determining the pressure on the body surface streamlined by a gas flow with a small supersonic speed (M < 1,5).The economic algorithm for calculating the pressure on the part of the surface of blunt bodies of revolution is developed. Examples of flow calculations over spheres and ellipsoids with different semi-axes ratios are presented. Comparison with accurate numerical calculations shows the effectiveness of the proposed approach.

Kotenev V., Sysenko V. Calculation of the pressure when streamlining blunt bodies with small supersonic speeds. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 58-67

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: 10.18698/2309-3684-2016-2-3954

The article examines methods of aircraft motion parameters recovery from the data of their low resolution recordings in the gas-dynamic ejection experimental test.

Plyusnin A. Aircraft motion parameters recovery from the data of their discrete registration. Part 2. Methods using regularization. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 39-54