and Computational Methods

doi: 10.18698/2309-3684-2016-1-6888

The article examines methods of aircraft motion parameters recovery from the data of their low resolution recordings in the gas-dynamic ejection experimental test. Desired conditions were satisfied by the use of Hermitian piecewise polynomial interpolation. Implementation of Tikhonov regularization provides the most flexible approach to the problem under consideration.

Plyusnin A. Aircraft motion parameters recovery from the data of their discrete registration. Part 1. Methods without use of regularization. Маthematical Modeling and Coтputational Methods, 2016, №1 (9), pp. 68-88

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

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

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: 10.18698/2309-3684-2019-3-5785

The paper proposes the theory for optimized selection of linear increasing over time mass-flow rates of energy devices designed for craft gas dynamic ejection from a launch container under the specified restrictions on parameters. Theory is also proposed for optimized selection of geometrical parameters of multigrain tubular charge for implementing these mass-flow rates. A visual geometric interpretation of theoretical developments is presented, and their practical feasibility is confirmed by numerical simulations of parameters of gas-dynamic ejection and internal ballistics processes.

Плюснин А.В. Математические методы оптимального выбора линейно нарастающих по времени массорасходных характеристик энергоустройств, обеспечивающих газодинамический выброс летательных аппаратов с заданными параметрами. Математическое моделирование и численные методы, 2019, № 1, с. 57–85.

doi: 10.18698/2309-3684-2018-3-6794

The problem of longitudinal and transversal oscillations of elastic cylinder generated by high velocity impact of the forward end on the water surface is considered from the point of the identification of hydrodynamic forces by treating optical measuring data of the opposite end motions. The statements of the direct and reverse problems are derived, based on the one-dimensional theories of Saint-Venan and Timoshenko, which provides the hyperbolicity of the governing equations. The results of the direct problem calculations by the finite-difference method are compared with the available experimental traces and show rather accurate qualitative coincidence.

Ерошин В.А., Плюснин А.В. Математические методы идентификации гидродинамических нагрузок при ударе о воду, основанные на одномерных теориях распространения упругих волн в стержнях. Математическое моделирование и численные методы, 2018, № 3, с. 67–94.

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: 10.18698/2309-3684-2019-4-1530

It is demonstrated that all 36 added mass and inertia coefficients of a body located in an unbounded ideal incompressible liquid may be introduced for the momentary state of rest by using acceleration potentials instead of classical velocity potentials specifying generally not-existent irrotational unseparated flows. The meaning of this conception is investigated with respect to real liquids having the compressibility property, by means of a numerical experiment fulfilled in the framework of an acoustical approach.

Плюснин А.В. Численный расчет коэффициентов присоединенных масс тела, движущегося в слабо-сжимаемой жидкости. Математическое моделирование и численные методы. 2019. № 4. с. 15–30.

doi: 10.18698/2309-3684-2020-3-6884

It may be expedient to integrate the preliminary design of solid propellant motors (SPM), especially the motors aimed for launching, into the overall design, when lifting vehicles are created with SPM included in their structure. This implies that the internal ballistic calculations have to be provided by utilizing the engineering mathematical models, the only complex point of which is the evaluation of the burning surface of the charge under consideration. A method for the computation of this relation is presented in this work, which optimizes one of the previously proposed methods as in efficiency of calculations so in the precision of the results.

Плюснин А.В. Оптимизация метода расчета площади поверхности горения для твердотопливных зарядов сравнительно несложных пространственных форм. Математическое моделирование и численные методы, 2020, № 3, с. 68–84.

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: 10.18698/2309-3684-2020-4-4460

The problem of unsteady gas flow between two volumes has been considered for the spatial and for the engineering formulations. The comparison of the two solutions has been presented which allows to assess the accuracy of the engineering approach usually utilized in practical calculations. The problem has been also considered of the determination of the unsteady force acting on the bottom of the canister at the stage of the lifting vehicle exit in the process of the gas dynamical ejection. The numerical simulation of the spatial problems has been completed in accordance with the classical Godunov’s method including the moving grid technique.

Плюснин А.В. Некоторые примеры численного моделирования нестационар-ных газодинамических явлений в обеспечение проектирования летательных аппа-ратов. Математическое моделирование и численные методы, 2020, № 4, с. 44–60.