and Computational Methods

Rubric: "05.07.00 Aviation and Rocket-Space Engineering"

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

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

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: 10.18698/2309-3684-2014-3-324

In the article we propose an algorithm for the numerical simulation of conjugate gasdynamic and thermomechanical processes in composite structures of high-speed aircraft. The algorithm allows calculating all parameters of the three-dimensional gasdynamic flow near the surface of the aircraft, heat exchange on the surface, heat and mass transfer processes in the internal structure of thermodestructive polymer composite, as well as processes of composite construction thermodeformation, including the effects of changes in the elastic characteristics of the composite, variable thermal deformation, shrinkage caused by thermal degradation, building up interstitial gas pressure in the composite. An example of numerical simulation of conjugated processes in a model composite construction of high-speed aircraft illustrates the possibilities of the proposed algorithm.

Dimitrienko Y., Koryakov M., Zakharov A., Stroganov A. Computational modeling of conjugated gasdynamic and thermomechanical processes in composite structures of high speed aircraft. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 3-24

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

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

doi: 10.18698/2309-3684-2016-3-5378

The article considers the pressurization process of a container empty space with the help of a high-pressure cylinder, which antecedes the gas dynamic ejection of an aircraft. Comparative calculations of this process were done in the quasi-stationary approximation using equations of state for both ideal and real gases. The article shows the necessity of accounting deviations in thermodynamic properties of the operating medium from the ideal-gas behavior in order to estimate correctly both gas reserves in the cylinder and temperature variations in the pressurized volumes.

Plyusnin A. Pressurization parameters simulation of container empty space during aircraft gas dynamic ejection considering real gas properties. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 53-78

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

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