and Computational Methods

Rubric: "05.07.00 Aviation and Rocket-Space Engineering"

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

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

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

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

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

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

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