2016. № 90

Mechanics

Theoretical mechanics

Zaitsev V. V.

Consider a dynamic system under limited uncontrolled factors impact is under consideration. A problem of aircraft movement study in many cases narrows down to such systems research. Uncontrolled factors of no little significance can be aircraft aerodynamic characteristics approximation errors, forces and moments allowing for wind impact, atmosphere characteristics deviation from normal (and corresponding disturbance in aerodynamic characteristics).

It is common knowledge that solutions for non-linear systems can be obtained in special cases. Thus, the problem of a system phase flow evaluation arises (in a corresponding definition — evaluation of system integral funnel).

This work considers the system with the same critical points nonoccurrence for all parameters, or system critical points nonoccurrence in the region under consideration.

The main problem of the known method of comparison is lack of comparison systems building algorithms for common non-linear systems.

The paper considers corresponding comparison systems building for systems with «drift» and estimation improvement issues. Comparison systems are developed using various generalizations of Lyapunov special functions (the system of functions with equiscalar surfaces distorted by hyperplanes in particular). The temporal separation of the integral funnel under study is evaluated (in particular) as an intersection of sets, bounded by Lyapunov special functions surfaces. The possibility of obtaining high-accuracy evaluations is demonstrated in some suppositions.

The paper gives examples of system solutions evaluation for planar motion in a vertical plane for the problem of estimation of errors impact while aerodynamic performance characterization on the system phase flow.

Methods and corresponding algorithms for a dynamic system integral funnel estimation suggested in this work can be effectively implemented in theory of differential equations (solutions evaluation), control theory (attainability domains estimation), aircraft and spacecraft dynamics applications (allowance for aerodynamic coefficients errors, wind impact, etc.), as well as for motion ballistics and dynamics of submersible craft in games theory dynamic problems.

The indisputable advantage of the suggested techniques consists in obtaining analytical functions describing estimations and high efficiency of algorithms. The result of the suggested technique presents warranted estimations contrary to direct integration (which allow integrate finite number of trajectories, and using additionally methods of integrating results processing obtain some heuristic evaluations).

Keywords: dynamic system flow estimation, comparison systems, uncontrolled factors impact, aircraft dynamics

Aslanov V. S., Alekseev A. V., Ledkov A. S.

This paper studies a process of space debris removal by space tether system. The stages of space debris capture by a tethered harpoon and commencing of towing are considered. The system consists of a tug, equipped with low thrust engine; a passive object, i. e. space debris, modeled by a spread rigid body, heavier than the tug, and an elastic tether. The aim of this paper consists in defining the space tethered system parameters, which provide safe space debris towing after its capture by the harpoon. The mathematical model of described system was developed. The model accounts for of the towed object rotation around its center of mass and the possibility of the tether slack. The disturbances occurring from the harpoon impact on debris were identified for the worst case, when the harpoon enters the most distant point from the space debris center of mass. Border values of towing system parameters, ensuring safe capture and following space debris removal, were obtained by numerical simulations series. It was shown that in case of a low thrust of the tug, the system rotation could result in its transition into a chaotic mode. In case of a high-thrust, the towed object may start rotating due to the harpoon impact and a periodic disturbance of the elastic tether. The results of this work can be used for new space systems for space debris de-orbit design.

Keywords: space debris, space tether system, equations of motion, dock, harpoon, chaos

Fluid, gas and plasma mechanics

Gidaspov V. Y., Moskalenko O. A.

The paper studies the process of detonation initiation of a of gas-droplet kerosene-air mixture incidental shock wave in a shock tube. A simplified physical-mathematical model of the process was developed. Drops of hydrocarbon fuel are considered as a single component of fuel droplets evaporation and gas-phase chemical transformations. The paper focuses on mass fraction droplets in the processes of detonation wave formation and propagation in the channel.

The authors propose consistent methods of recovery according to the reference data on the thermal part of the Gibbs potential of gasoline, kerosene and diesel fuel in liquid and gaseous states.

The results, obtained by numerical simulation time scanning process, encompass the following:

  • Interaction of the incident shock wave with kerosene-air gas-droplet mixture; heating of the combustible mixture; evaporation of kerosene droplets with the subsequent exothermic gas-phase chemical transformations;

  • Formation of compression waves;

  • Formation and distribution of the detonation wave;

  • Output of the detonation wave in the mode close to the stationary one.

By computation, we found and observed experimentally two fire-ignition modes of the combustible mixture.

Keywords: numerical simulation, metallic fuel, chemical reactions, phase transitions, combustion, detonation

Dynamics, strength of machines, instruments and equipment

Larionova A. A., Dudchenko A. A., Sergeev V. N.

In this article considered method of analytical solution by determine parameters the transition zone of the wing joint for transmission of load from the composite to the metal. The developed method allows determine efficient length of transition seam zone, which depends on the value of loads, the diameter of the bolts, and material of composite and metal. First of all, it is determined by the length of the inclusion zone. Then, it is determined by the required number of rows for fasteners, depending on the diameter of the bolt or rivets. Mechanical connections have a significant disadvantage associated with the drilling of holes for bolts or rivets, which leads to cutting fibers, stress concentration at the site of setting bolts and weakening of the strength and rigidity of the construction at this location. However, thanks to good strength and stiffness characteristics with low weight, the composite material (CM) are used in load-bearing structural elements of aviation and space technology.

Results were obtained in carrying out the work:

  1. Conducted calculations by the formula shown effective accuracy of calculation of mechanical coupling components. These formulas enable us to determine the inclusion in the work zone for bolted, riveted joints and needle.

  2. The work area depends on the thickness of connection and properties of the material.

  3. These ratios allow us to determine the number of rows of coupling elements, the diameter of the bolt and the pitch between the bolts.

  4. Analytical calculation is checked by finite element method (FEM).

It shows good agreement between the calculation results.

Keywords: mechanical connections, analytical calculation, metal materials, composite materials, bolts, rivets, needles, finite element technique

Aeronautical and Space-Rocket Engineering

Aerodynamics and heat-exchange processes in flying vehicles

Golovkin M. A., Golovkina E. V.

Results have been given of a flow structure visualization in the neighborhood of a number of models of aircraft, such as MiG-23, MiG-29, Su-27, «Buran» orbital vehicle, delta-winged and forward swept wing aircraft models, and the models with intakes mounted on the upper surface of lifting body. The investigations were intended for revealing specific features of flows and vortex structures generated during flow over aircraft elements.

Model tests have been performed in TsAGI HT-150 and HT-400 very low-speed water tunnels (flow velocity of ) wherein the velocity is formed by the gravity of water flowing out from the large container disposed above into the working section. Flow visualization was accomplished by the method of colored jets. Colored liquid in the form of aqueous solution of aniline colors was fed to the model inner cavities through the sting «by gravity» due to altitude difference from containers disposed by ~3 meters higher the model level. The liquid flowed out through the drainage pinholes on the model outer surface and drifted by approach flow tangentially to the surface of the aircraft model. When required, the visualization of external flow was carried out using streamlets flowing out from the «comb», the thin tubes positioned upstream in front of the model. HT-150 water tunnel was equipped with the mirrors located on the right and on the left of its working section, which made it possible to take views or carry out video filming of three model projections simultaneously.

As a result of the conducted investigations some specific features were revealed of flows and vortex structures generated during flow over a number of aircraft models.

Visualization of flow over the MiG-23 aircraft model at a sweep angle χ=47°of wing outer panels at the leading edge showed that in the presence of sliding at the angles of attack α above 17° the windward vortex core generated by confluence of forebody and wing extension vortex cores, approaches the vertical tail and passes above it. Due to the strong downwash induced by the united vortex core in the vertical tail region, the rolling and yawing instability of the aircraft model develops. The leeward united vortex core shedding from the forebody and wing extension propagates along the right wing outer panel, which causes the still greater development of rolling instability at these angles of attack. As a consequence of the investigations on visualization a mechanism of yawing and rolling stability loss of the MiG-23 aircraft model confirmed in wind tunnels was revealed and the original ways of improving these aerodynamic characteristics were found.

Visualization of flow structure on the MiG-23 aircraft model with a sweep angle χ=74° at the leading edge of wing outer panels showed that the above-mentioned united vortex cores (windward and leeward ones) descend in the tip wing sections and pass at a considerable distance from the vertical tail. Therefore, the noted above degradation of lateral static stability characteristics for the model with χ=74° did not occur, that is confirmed by wind tunnel tests.

Investigations of flow structure in the neighborhood of the delta-winged model showed that the vortex cores generated nearby the wing leading edges slightly rise from the tip chord of vertical tail. In the presence of sliding the vortex structure is not as much skewed as in case of the MiG-23 model with χ=74°; as a result, one might expect that the lateral characteristics of such model must be satisfactory.

Visualization of flow over the forward swept wing model has revealed the following flow features. Tip vortex cores of the wing can be plainly seen. Due to the flow in the boundary layer of such wing directed from tip sections to the plane of symmetry up to the very large angles of attack, a greatly considerable (spanwise) part of the tip sections is flowed round without flow separation. Nearby the trailing edges of wing the vortex cores are generated which move to the plane of model symmetry. The vortex cores of wing extension can also be plainly seen, which unite with the said trailing edge vortex cores. Such vortex structure and the absence of flow-separation phenomena in the tip wing sections define good lateral characteristics of such model up to the very large angles of attack, which is confirmed by the model wind tunnel tests.

For the model with air intakes on the lifting body it is shown that the vortex cores generated on its upper surface, including if there is sliding, do not ingest into the engine intake.

Detailed investigations into visualization of flow over the «Buran» orbital vehicle model conducted over a wide range of angles of attack α and sideslip β have revealed the following main features. At α=15°, β=0 the sufficiently powerful vortex cores are visualized which are generated on the forebody and wing extension and passing at some distance from the fuselage. On the backside of cockpit canopy, an extensive separated flow is developed and two more other vortex cores are generated which move along the fuselage upper surface. In this case, the flow over the wing extension is the one without separation. As the angle of attack increases, the wing extension vortex cores lose the stability and their «burst» takes place (at α=25° it occurs about in the middle of the wing root chord and at α=30° it does immediately behind the wing extension) so that practically all wing outer panels are surrounded by separated flow. If there is sliding, the vortex structure is markedly warped so that the windward vortex core generated above the cockpit canopy and passing over the fuselage approaches the vertical tail and the leeward vortex core moves away from it.

During flow structure visualization nearby the MiG-29 and Su-27 aircraft models the following features are revealed. On the wing extensions of the models sufficiently powerful vortex cores are generated which uniting with the forebody vortex cores, pass nearby (inside) the tail panels. At α=25°the vortex cores «burst» in the vicinity of a quarter of wing chord. If there is sliding at α=15° the windward vortex core passes inside the right panel of vertical tail; the leeward forebody and wing extension vortex cores do not unite so that the wing extension vortex core passes inside the left panel of vertical tail and the forebody one does nearby the trailing edge of left wing panel. At α=20° and in the presence of sliding the vortex cores «burst» before reaching the vertical tail, with the leeward vortex core «bursting» up-stream of the windward one. At α=20°, β=4° the vortex cores «burst» in the vicinity of the quarter of root chord of wing. Drooped leading edges on all said conditions are flowed round without flow separation.

The results on visualization found use in improving aerodynamics of the said aircraft, in analysis of force tests in wind tunnels, and may be useful in developing other aircraft.

In addition to wind tunnel tests, investigations into the flow visualization nearby the aircraft models in the low-speed water tunnel are the high-performance and low-cost method for revealing features of flow over aircraft models.

Keywords: water tunnel, method of colored jets, vortex structures, wing extension

Design, construction and manufacturing of flying vehicles

Makarov L. K.

While aircraft developing and upgrading, the research on its balancing capability during various flight phases and with various types and versions of air-launched weapons (ALW) allocation including asymmetric configuration [1, 2] is carried out. This process consists in definition of required corners of controls displacement and the bank angle value. Flight tests provide the most reliable estimation of balance characteristics. However, carrying out such tests is accompanied by huge material and time expenses. Moreover, such process sometimes presents considerable risk.

In references [3, 7] at calculation of balance characteristics of an aircraft with ALW allocated asymmetrically underneath the wing, the interference between them is not considered. Nevertheless, during some flight phases there is a significant interference between the aircraft wing and ALW. This interaction is characterized by occurrence of horizontal, vertical and lateral interference forces [4–6]. Significant values of interference forces alter aircraft aerodynamic characteristics, so that trim angles of controls displacement and bank angle value changes. Besides, significant in magnitude interference forces lead to occurrence additional wing bending and torques which deform an aicraft wing. Thus, design out and application of the techniques, allowing consider influence of interference interaction between an elastic wing and asymmetrically disposed ALW on aircraft trim, is a topical problem.

Keywords: supersonic flight, balancing, aerodynamic interference, elastic wing, reliability

Arutyunov A. G., Dydyshko D. V., Endogur A. I., Kuznetsov K. V., Tolmachev V. I.

At present, three extensive areas of the transport airplanes, encompassing various types of cargo exist:

— Standardized aircraft containers and pallets transported by freighter aircraft, such as Boeing B-747-400F or Airbus A310-200F;

— Unique cargoes transported by special cargo planes (e. g. Boeing B-747 LCF or Airbus A300-600ST);

— Non-convential industrial cargoes, mechanisms and vehicles transported using airlifters with cargo ramp such as Antonov An-124-100 or Lockheed C-5M.

Specifics of ramp cargo aircraft are as follows:

  1. Special cargo hatches facilitating access to the cargo compartment, but having complicated and weighty structure;

  2. Large fuselage midsection area — about 25 ... 30% greater than that of a passenger aircraft;

  3. Necessity of cargo floor and other airplane parts reinforcement to carry concentrated load;

  4. Necessity of loading height minimization for mobile machinery transportation. Thus, the majority of ramp airlifters are of high-wing monoplane type;

  5. Degradation of the aerodynamic cruise performance as well as the desire to improve takeoff and landing characteristics lead to cruise speed reduction;

  6. Turboprop engines are implemented more often on airlifters than passenger aircrafts to improve their takeoff and landing characteristics;

  7. Transportation of cargoes of various size and functions entails the presence of cargo-handling equipment on board (e. g. cranes, hoists) increasing an airplane weight.

  8. It is advisable to consider development of airlifters in the intermediate-range (6-15 years) and long-range (16-30 years) perspectives.

Specifics of an intermediate-range airplane will be as follows:

— Classic aerodynamic scheme with fuselage, wing and empennage;

— Supercritical wing with a thick airfoil (with average relative thickness of 12 to 13%);

— High aspect ratio (λ ≈ 8.5 ... 9) and moderate sweep angle ( χ ≈ 23 ... 250);

— Relatively simple high-lift devices (e. g. single-slotted or fowler flaps with slats).

For heavy lifters maximum L/D ratio will be about 18...19. Cruise speed of such aircraft will be about 800 km/h. Turbofan engines with high bypass ratio m ≈ 10 and low specific consumption Cp = 0.5 kg/kgf∙h will be used as the power plant of intermediate-range heavy lifters. Airframe weight can be reduced through wide using of composite materials. For intermediate-range aircraft, designers can consider implementation of the unconventional empennage (for example V-tail).

The follwing features probably will be typical for long-range transport aircraft:

— Hybrid wing-body aerodynamic scheme with maximum L/D ratio about 23...24;

— Distributed power plant with low specific consumption about 0.4 kg/kgf∙h;

— Implementation of boundary layer ingestion systems increasing L/D ratio by about 3...5 units.

Keywords: transport aircraft, cargo ramp, cargo airdrop, cargo compartment, unique oversized cargo, general cargo, ramp cargo plane, special transport aircraft

Kolykhalov D. G., Sysoev O. E., Ivanov I. N.

“Manufacturability”, as a concept for complex technical products or systems is a complex of characteristics that determine the ease of manufacture, the unification, standardization and interoperability, as well as the economic costs of production and operation.

Manufacturability can be considered a product that requires no special difficulties in the manufacture, does not require large economic costs, consists of a minimum number of parts, uniformly and maintainable.

In the early stages of the design, you can pre-determine the technological operations of aircraft’s pipeline systems production, from the shape of pipelines can be concluded about the complexity of the product as a whole.

Designers solve the problem of pipelines, their modification and analysis of the design decisions in the early stages of aircraft’s hydraulic systems design. For this purpose, use specialized CAD-system. The degree of complexity of e-pipe model increases with the transition to the next stages of design. For example, in the early stages of design (preliminary design) designer carries out the basic units in the compartments, pipe lines appear simplistic. Connecting fittings and fasteners are not being worked. Later model detail, broken down into its assembly units, standard products.

As a result, at the final stage of the electronic layout design is a high degree of approximation of the real piping system as an integral and inseparable part of the electronic product layout.

Analyzing the possibility of splitting pipelines in some areas can offer an estimation of pipelines manufacturability for two incoming assembly zones: pipes and piping sections made entirely of tube billets with an additional study of the process.

Evaluation manufacturability pipes and pipe sections are based on a comparison of the resulting configuration, taking into account the complexity of manufacturing, and configuration, taking into account the direct unprocessed portions of the pipeline.

Factors that were taken into account when calculating the manufacturability:

— total number of straight sections;

— total number of bevel angles in the plane;

— total number of bevel angles in two planes;

— total amount of bending angle;

— total number of rotation angles;

— total number of processed ends;

— total number of steeply curved horn-shaped areas;

— total number of flanged holes in the pipe wall.

To evaluate the manufacturability can set the threshold value of the coefficient manufacturability (eg — 0.5) below which assume that the estimated element has a low manufacturability, higher — high manufacturability. However, the productions often use the concept of “level of manufacturability”, We know about the four levels. In this regard, we can establish the following ranges of values ​​of the coefficients for the comparative assessment of manufacturability:

— first (0.70 ... 1.0) — a high level of manufacturability;

— second (0.40 ... 0.69) — the average level of manufacturability;

— third (0.20 ... 0.39) — Low level of manufacturability;

— fourth (0.05 ... 0.19) — very low level of manufacturability.

Pipeline with low manufacturability may have very high durability, reliability and survivability performance. However, the cost of producing this kind of products is very high and can be justified in some cases, in the production of rocket, space and military equipment. An improvement in manufacturability for mass production of civil aircraft becomes very relevant, since it increases the efficiency of production by reducing the complexity and the use of the most efficient processes.

Keywords: manufacturability, manufacturability coefficient, pipeline systems, aircraft

Thermal engines, electric propulsion and power plants for flying vehicles

Kuroedov A. A., Laptev I. V., Borisov D. M.

The purpose of this work consists in numerical study of the condensed phase effect on the finite amplitude disturbances in the solid propellant power plant (SPPP) combustion chamber. The goal of the study is determining the decay factor for the first two combustion chamber longitudinal oscillations eigen modes, and condensed phase particles optimal size, leading to maximum decay of the disturbances under study.

Two-phase ambience motion is considered as a multiphase flow of the gas phase and dummy gas particles. The condensed phase represents solid rigid spherical particles of the same size and weight. Density, temperature and heat capacity of the particle are considered constant over its volume. Force and thermal interactions between carrier ambience and the particles are accounted for.

The problem is solved in the quasi-unidimensional set up. Computational domain corresponding to the SPPP duct is split into two subdomains: the combustion chamber and the nozzle. The problem is solved numerically by Godunov method, based on arbitrary interruption decomposing problem solution.

Time dependencies of relative deviation of pressure in model set chamber for various frequencies and condensed phase solid particles radiuses were obtained in the course of numerical experiment. Based on the obtained distributions decay factor values were determined for the first two gas phase carrier longitudinal oscillations. The particles size range corresponds to the particles size in solid propellant, used in actual power plants.

Solid particles optimal sizes leading to maximum decay of finite amplitude disturbances were determined as a result of numerical simulation. The obtained data conforms the results obtained while solving the equation of motion of a solitary solid particle in a continuous medium.

Further analysis shows that there is optimum particle size for each mode, which causes the greatest attenuation of finite amplitude perturbations. These results correspond to the results obtained by solving the motion equation of a solitary solid particle in a continuous medium.

The developed mathematical model is suitable for predicting the evolution of finite amplitude disturbances in the SPPP ducts.

Keywords: acoustic instability, two-phase, decay factor, dissipation

Borisov A. D.

The advantage of the combined air-jet engine structure, with gas generator placed in its loop, consists in work process better stability due to relative independence of the processes in gas generator and main combustion chamber. Gasification and partial fuel decomposition (with a small quantity of oxidizer) occur in the gas generator due to pyrolysis and/or burning reaction. The derived gas is mixed with the air and reheated in the main combustion chamber. Gas generator jet high temperature must ensure self-ignition and flame stabilization. The important problem consists in providing efficient mixing of the two-phase gas generator gas flow with the main flow. It is necessary to calculate the injected get propagation in cross-flow to determine optimal injection angle, since the fuel and oxidizer pattern and mixing behavior over chamber cross-sections affects significantly the combustion chamber work process.

Various versions of axial gas generator nozzle with co-current injection unit were studied, and an optimal (from the combustion efficiency viewpoint) was sel ected. With the use of a gas generator nozzle cluster with multiple jets, mixing intensifies. The supersonic flow is further decelerated by the oblique shocks, occurring due to jets injection at the angle of chamber axis. It all leads to combustion efficiency increase for the structure with four circular jets and a central one.

The injection angle dependence of the mixing efficiency was studied for the case of jet injection fr om the combustion chamber wall. The results were compared with empirical formulas for the jet trajectory in a cross flow. Most uniform distribution of the injected gas was obtained at an angle α = 135°.

The necessity of the accounting for the condensed particles spectrum was demonstrated for two-phase gas-generator gas.

Keywords: flame stabilization system by jets, gas generator, mixing efficiency, condensed particles

Dynamics, ballistics, movement control of flying vehicles

Rozin P. E.

The paper describes the Earth observation «Auriga» small spacecraft attitude control and stabilization (ACSS) system. «Auriga» spacecraft has been under development since 2014 at Dauria Aerospace, based in Skolkovo, Moscow region.

The first part of the article presents the key parameters of ACSS measurement devices and actuators complied with requirements of ACSS on accuracy in three-axis stabilization mode. It also presents primary characteristics of the on-board autonomous ballistic task (6 meters accuracy for on-orbit position determination).

The second part of the article presents operation logic of on-board ACSS task for the three-axis stabilization mode. It shows that all operations can be presented as four sub-modes with different types of orientation program. At the end of the second part, information on the selected type of interpolation of the orientation program in one of the sub-modes is presented. The results of modeling show that spherical linear interpolation of quaternion is suitable for all types of rotations (except orbital orientation, which is calculated using autonomous ballistic task information) for «Auriga» spacecraft mission.

The third part of the paper presents the results of software-in-the-loop test for orbital orientation sub-mode. It shows, that all accuracy requirements confirmed with high level of margin, provided that at least one star tracker is operable. Without an operable star tracker, the «Auriga» spacecraft keeps stabilization using MEMS-gyro information. Since the gyro generates high-level noise, it was shown that it was impossible to comply with accuracy requirements for more than 1000 sec. But in other orientation modes, where accuracy requirements are not so severe and star tracker is inoperable, gyro becomes very important measurement device.

Keywords: Earth observation small spacecraft “Auriga”, three-axis orientation, on-board control system task software operation logic

Huang Y.

This work deals with the problem of lunar lander flight optimal control for soft landing at the sel ected point of the Moon, using the «hovering» scheme after the main deceleration step. The method of thrust vector control program selection for landing phases between hoverings, providing zero velocity and vertical orientation at the beginning and the end of this step is given.

The aim of this work is to provide a method of traction control problem approximate solution at the stage of controlled landing, satisfying all the given boundary conditions. Essentially, the optimality criterion is considered as the amount of required fuel for the controlled landing, which should be minimized.

Formulation and solution of the problem, resulting in this work, differs fr om formulation and solution, obtained in traditional papers. It is the difference, which at the beginning and the end of controlled landing ensures vertical orientation, zero speed and coordinates of lunar lander.

To achieve this goal a flight movement model of lunar lander was developed, an optimal control problem was formulated, simplifying assumptions were introduced, the methods for solving the boundary value problem in conjunction with optimization, using computational algorithm and program solutions, were formed. The results of a numerical computation example are presented.

The main result is a method of selection the angle pitch and engine thrust control program for the lunar lander between hoverings, providing zero velocity and vertical orientation for the lunar lander at the beginning and the end of this controlled landing step.

Keywords: lunar lander, soft landing, hovering, optimal control

Instrument making, metrology, information and measuring equipment and systems

Navigation instruments

Antonov D. A., Zharkov M. V., Kuznetsov I. M., Tchernodoubov A. Y.

The main source of navigation information of most known intelligent transportation system (ITS) projects is an on-board satellite navigation system (SNS) GPS-GLONASS receiver. The key feature of SNS consists in positioning accuracy and noise immunity level decreasing in case of operation in compact urban planning due to multipath. The paper analyses the requirements for a vehicle navigation system application as a part of ITS, and estimates functional limitations caused by the features operation specifics in urban environment conditions. Techniques of multipath occurring in dense urban conditions mitigation are also presented.

Today lots of satellite navigation system (as a part of ITS) accuracy and noise immunity improvement techniques exist and being researched at various levels. One of the most prospective approach is an on-board vehicle navigation system design, functioning in ITS, as navigation complex using cooperative information processing techniques form SNS receiver, inertial sensors, odometer measurements and other sensors and vehicle systems. The advantage of this approach is not only the accuracy of vehicle movement parameters improvement but also the possibility to improve fault tolerance by timely detection and exclusion of abnormal measurements from navigation solution, which oftenly occurs in compact urban planning conditions.

The paper discusses accuracy and noise immunity of vehicle navigation system improvement techniques using algorithmic and hardware/software approaches, including complex information processing algorithms. Based on current and prospective requirements to vehicle navigation system accuracy and the existing accuracy and noise immunity improvement techniques analysis, the recommendations for complex fault-tolerant vehicle navigation system design are formulated.

The study was performed under the financial support of Russian Foundation for Basic Research and The government of Moscow as a part of the research project No 15-38-70055. The main part of the research consists in recommendations on complex fault-tolerant vehicle navigation system design formation which should allow system design with declared specification at the next stage of the project using world experience in this area of research.

Keywords: intelligent transportation system, inertial navigation system, MEMS inertial sensors, satellite navigation system, multipath, optimal information processing, integrated navigation system

Belousov E. O.

Gyroscopes or angular velocity sensors are considered main component part of inertial navigation systems which are used for determining coordinates in space in absence of external reference sources. In present microelectromechanical sensors are widely applied because of their advantages such as small size, low power and cost. These advantages allow MEMS gyroscopes to be implemented on board of robotic unmanned landed or aerial vehicles.

Operation principle of the MEMS gyroscope involves measuring Coriolis force that is applied to vibrating or oscillating body. In this work semiconductor vibrating ring is considered as such body. Readout circuit provides an excitation signal to the resonating body while sensing and demodulating input signal which is modulated by the resonance frequency. Errors and nonidealities of the gyroscope consist of nonidealities of the microelectromechanical structure as well as integrated readout circuit. Both of these noise sources provide thermal and flicker noise to the output signal.

This work proposes a noise suppression method for the readout circuit using additional adaptive feedback. This feedback circuit senses corner frequency of the input signal and adjusts readout bandwidth and output noise in accordance with this corner frequency. Model of sensor and readout circuit was developed in order to estimate dynamic and noise performance of the system. Adaptive system architecture that consists of frequency sensing loop and decision device was proposed. Analysis of the adaptive system was performed which resulted in addition of reconfigurable compensation circuits to the system. Proposed method increases average signal-to-noise ratio by 5 dB which leads to increased horizontal positioning accuracy by 3,4 m after one minute integration.

Keywords: MEMS sensors, inertial navigation systems, integrated circuits, servo systems

Kuporosova E. S.

To study the accuracy of inertial reckoning algorithm operation with pedestrian navigation system, a robot’s movement, imitating human gait, was modeled. The experiment with a human movement over closed rectangular rout with inertial measurement unit (IMU) mounted on the users’ waist was carried out to evaluate quantitative and qualitative characteristics of a robot’s movement. The study focused on the accuracy of the input data processing algorithm (without an external correction).

The human motion model with IMU was developed as a kinematic model of a robot, imitating a human gait. Sensors transfer functions are assumed equal to 1. The real experiment and data recordings were carried out with IMU ADIS16405. Sampling time  ≈ 0.025 s. Sensor readings arrays were processed by means of moving average with 15 samples window extent using MATLAB Curve Fitting Tool libraries. Fourier transform and Fourier spectrum modeling were applied to smoothed signals. Reference oscillations frequency of the pitching motion parameter is f1 ≈ 1.55 Hz, and Reference oscillations frequency of lateral motion parameter is f2 ≈ f1/2 ≈ 0.77 Hz. Evaluation of oscillation amplitudes for the roll (γm = 1.13°) and pitch (ϑm = 0.69°) were made. The obtained experimental results were used in the robot motion model.

Conclusions:

  1. Harmonic oscillations of IMU cause error in pedestrian navigation system without correction even during sensor ideal performance.

  2. The greatest impact on human localization error is caused by IMU oscillations with respect to the horizon plane. The error value is linearly dependent on pitch and roll IMU oscillations amplitude.

  3. With equal pitch and roll, IMU angular and pitch oscillations amplitudes can cause human localization error seven times greater than roll oscillations.

Keywords: accelerometer, angular velocity sensor, angular oscillations, trajectory, а frame of reference, kinematic movement model, apparent acceleration, Fourier transform

Instrument production technology

Vancov S. V., Zwe M. M.

It is well known, that approximately 30% of failures occur in PCBs interconnections. Drilling is still the most popular process for producing a hole. The main surface defects of the holes appeared during PCB dielectric base drilling are as follows:

—made shaggy,

—vitrification,

— ribs formation at the entry and outlet of the drilled hole.

The occurrence of these defects is associated primarily with the drill bit heating during drilling. The accuracy of drilling is highly affected by the quality of the PCB, which, in turn, depends on the quality of the alignment layers and the parameters of the material [1-3].

It should be noted that the defects caused by drilling, could lead not only to failures, but also increase the products cost due to the increased cost of subsequent phases [4], as they require additional operations introduction to PCB manufacturing process.

While drilling heat is generated in the hole by frictional force on the back surface of еру drill. Cooling of drill bit takes place during the tool transition from hole to hole. The drill will be considered as isotropic heat conducting rod.

Let us consider the following practical conditions of a drilling process, namely:

— length to drill diameter ratio is greater than 10;

— heat transfer is significantly complicated;

— heat transfer, caused by heat exchange between the drill and the material of the dielectric substrate is even more complicated.

The equation of heat dissipation in the drilling cycle of heating

Here, T — temperature of the element of the drill;  — time; µ — friction coefficient on the drill back face; N — cutting force; v— velocity of the application point of the force N; λ —thermal conductivity coefficient; s — drill perimeter; α — heat transfer coefficient.

Equation for the top of the drill takes the form,

T* — temperature at which cooling starts while idling;

Tc ambient temperature;

b — coefficient of heat exchange with environment.

The above relations allow make preliminary calculations of the drill temperature during the process of g holes drillin in PCBs and, thus, to determine the number of drilling cycles that can be performed without the risk of defecting holes.

Keywords: drilling, heat dissipation, printed circuit boards

Sokolsky A. M., Sokolsky M. L.

Ensuring highly moisture protection is one of the main factors of avionics reliability improvement. However, since it is impossible to ensure absolute moisture protection, moisture is accumulated among connecting links. Notwithstanding that moisture is purified from admixtures, conducting electric current, while passing through moisture-proofing material, it reacts with salts, alkalis and acids, used for PCB production and left on its surface after clearing operations. A medium propitious for electro migration process develops. As a result, it leads to short circuit inception with subsequent failure of onboard equipment.

Electro migration mechanism consists in creation a potential difference between loaded conductors, which forces positively charged metal ions of a conductor with higher potential to precipitate on the conductor with lower potential. It causes the growth of parasitic interconnections, i. e. dendrites.

Electro migration results in short circuit, which may be followed by equipment overheating, and further lead to inflammation onboard a aircraft.

The main factors affecting electrochemical migration phenomenon intensity are as follows: potential difference between conductors, ambient temperature and relative humidity (as a condition for condensate formation).

Keywords: avionics, electrochemical processes, failures, physical reliability, electrical design

Image and sound conversion devices and principles

Popov L. N.

Graphic equalizer (EQ) main building block is a set of bandpass filters (BPF), allowing convert the original signal into a set of narrowband signals [1]. Controlling their gain with subsequent summing up we obtain the required type of equalizer Bode diagram.

The advantage of digital filters with finite impulse response (FIR filters) implementation consists in the possibility of designing and EQ, which does not introduce phase distortions into transmitted signal. However, the use of such filters operating in real time is impeded by the necessity of executing a great number of multiplication operators per one sample of digital signal. The purpose of this paper consists in demonstrating the way to decrease the number of necessary multiplications by a certain delay of signal passage through the equalizer.

The author suggests to form each BPF using two low-pass filters (LPF) by subtracting the output signal of the LPF with a low boundary frequency, Fgk, fr om the output signal of the LPF with a high boundary frequency, Fgk+1. The above said LPF boundary frequencies herewith remain the BPF boundary frequencies under condition that the filters gain at boundary frequencies is equal to the half of its maximum value. The problem of equalizer filters design herewith comes to realizing LPF with boundary frequencies of Fg0, Fg1 ... FgN — 1, where N is required number of BPFs. Each of these BPFs forms a signal with a delay increasing with boundary frequency decreasing. The need to align the delays requires implementation of first genus FIR filters, which delay is equal to integer number of sampling periods.

To compute the filters coefficients a weighting method, implementing Kaiser Window [2, 3]., was used. The necessity to obtain the line of LPFs with similar amplitude-frequency response, required Kaiser Window modification, defining it with the equation

Here parameter µ can take a fractional value, contrary to the classical definition. It is shown that obtaining an LPF filter with similar characteristics and boundary frequencies Fg1 and Fg2, requires fulfillment of the condition:


Thus, if the sel ected parameters β and µ for the most wideband LPF of a line with boundary frequency of Fg0, then the similar parameters of a filter with boundary frequency of Fgn will be βn = β and µ = µRn under similarity hypothesis, where R = Fgk/Fgk + 1. Design equations allowing compute coefficients for the nth filter of the line with specified parameters β, µ and R. The paper shows that direct equalizer realization based on signal processor within operating frequency band of 20 Hz—20 kHz is impossible due to the great number of multiplication operators (no less than 15348) per one sampling period.

A known method of required multiplication operators’ reduction consists in implementing interpolated FIR (IFIR) filters with embedded structure [5, 6]. The author proposes equalizer filter functional scheme, where shaping sub-filters with higher boundary frequency act as masking sub-filters within IFIR filters with lower boundary frequency. Such structure is formed by cascade coupling of the blocks shown in the Figure below.


The first stage with parameter L = 1, generates the signals: , corresponding to the LPF with boundary frequencies  (assuming that the ratio R is a multiple of 1/3 of octave, which corresponds to the most common 15 and 30 channel equalizers). The coefficients of the corresponding FIR filters are denoted by the vectors     The lengths of these vectors according to similarity conditions equal respectively to . The block of the subsequent stages differ fr om the first one by the L parameter value, necessary to form the sub-filter with the corresponding boundary frequency. For 15-channel equalizer, wh ere R corresponds to 2/3 of octave, the value of L for each of the subsequent stages should be 4 times greater than for the previous one.

The equations allowing compute the equalizer frequency response for the specified parameters β and µ are presented. Based on numerical experiments the paper shows, that with ±12 dB control range the acceptable quality of 15-channel equalizer characteristics can be obtained with β = 4.5, µ= 6.92. The required number of multiplication operators herein equals 162 per one sampling period, which is 1000 times less than in the case of a direct scheme.

To evaluate the software realization complexity for the proposed equalizer structure, the storage space required to store constants and variables that define its current state was calculated. In the case of using 32-bit numbers, the storage space requires about 300 KB.

The methods stated above can be implemented either in allied fields (frequency analysis, adaptive filtering [7], etc.).

Keywords: band pass filter, interpolated finite impulse response filters folded structure

Tikhomirov A. V., Ivanov M. S., Omel'yanchuk E. V.

In article the principle of operation of an acoustic direction finder is considered, the method of computation of temporal determination is defined, assessment of the required sampling time is made for hardware-software implementation of a digital part of an acoustic direction finder. It is shown that the level of development of the modern component basis for acoustic devices allows to reduce significantly their overall dimensions and to increase the accuracy of temporal determination. Thus, the possibility of effective combination of acoustic sensors with units of digital signal processing is available. It allows to increase number of at the same time analysable acoustic channels. The purpose of this article is determination of requirements to sampling time in case of hardware-software implementation of a digital part of an acoustic direction finder.

The specified principle of operation of a direction finder is based on computation of an azimuth of the purpose in delivered on distance of a basis two the direction finding of devices. Each of devices is defined a difference of the course of the sound wave coming to each of sensors and value of a lateral angle is calculated. On the basis of the direction finding method considered in article the distance to the purpose is calculated.

As a result of the taken laboratory measurements frequency rate of sampling in case of which the accuracy of determination of a lateral angle not worse 3 ° is reached was defined.

Search of the methods allowing to expand dynamic range of the researched loudspeaker system when saving the specified accuracy of determination of a lateral angle can be the direction of further researches.

Keywords: acoustic direction finder, basis of the direction finder device, temporal determination, lateral angle, sampling rate

Radio engineering and communication

Systems, networks and telecommunication devices

Kovalsky A. A.

Scientific work is devoted to the organization of statistical consolidation of a diverse traffic in channeling equipment of the terrestrial stations of satellite communication (TSSC) in the conditions of the changing interfering situation. Object of research is the terrestrial station of satellite communication. An object of research is the technology of consolidation of satellite radio lines by transfer of a multiservice traffic in terrestrial stations.

The purpose of researches consists in capacity growth of terrestrial stations of satellite communication due to statistical consolidation of a multiservice traffic in different conditions of an interfering situation.

Models of statistical consolidation and algorithms of scheduling of a diverse traffic taking into account priorities in service and not stationarity of the entering information flows on the basis of markovly the modulated poisson processes are developed. Research of dependences of increase in throughput of TSSC on application of technology of statistical consolidation and change of parameters of quality of service of a diverse traffic is conducted. Recommendations about upgrade of channeling equipment of TSSC are offered, and also the model of special program software of channeling equipment of TSSC is developed.

Keywords: statistical consolidation, scheduling of a traffic, terrestrial station of satellite communication

Radiolocation and radio navigation

Kartukov A. V., Merkishin G. V., Nazarov A. N., Nikitin D. A.

A number of engineering problems associated with the object movement in the air require the information on the air state right behind the moving object. For example, while large aircraft takeoff we need to know the period of turbulence existence to impose restrictions on the time interval between two airplanes takeoff. For airplanes and helicopters landing we need air-cushion size evaluation to work out requirements on minimum overflight height over buildings and constructions in the entry area. The turbulence presence is of great importance also during aerial refueling operations.

At the instant of beam breaking, one can observe strong pulses of positive and negative polarities, caused by recharging processes of capacitances in the circuit. After the end of breaking, the beam deflects to the areas with bigger pressure and oscillates in the region of red, blue and green zones. Approximately after 20 ms the beam returns to the yellow zone region, and oscillates with damped amplitude to the level, existing prior to beam breaking.

The existing research techniques do not allow registering the fast parameters variation and non-uniformity fluctuations in the air, and yield the averaged picture at a certain time interval.

The developed facilities allow registering the variations in medium density and disturbances behind a moving object in the form time function with resolution less than 0.1 ms. The paper presents the angle curves of the laser beam passing through disturbed environment fluctuations after four-channel square-shaped photoelectric detector.

The emitter (laser diode) is set at the side of an automobile road, and its beam is directed perpendicularly to automobile movement at the height of 1 m. And photodetector is set at the other side of the road. Its output signals were fed to the computer through ADC, where they were registered and processed. After an automobile crossed the beam, the occurring in the air turbulence and disturbances caused the beam refraction and its movement along the four-channel photodetector aperture. The current beam position was determined according to signal levels in the photodetector channels relationship.

The presented system allows performing analysis of pressure transmitted fluctuations in the air, occurring in response to the moving object, evaluate their amplitudes and frequencies, transient time. It can be useful for aerodynamic performance studies of the objects of various shapes.

Keywords: atmosphere analysis, laser, four-channel photoelectric receiver, analog-to-digital converter

Rastorguev V. V., Nuzhdin V. M., Konovaltsev A. V., Ananenkov A. E., Маrin D. V.

The article deals with the topical issue of onboard radar functional capabilities enhancement. The compact multi-mode airborne radar (CMMAR) is designed for mapping and radar monitoring of the Earth’s surface on board the aircraft, helicopters and unmanned aerial vehicles (UAVs). Onboard monitoring is especially important in the development of natural resources, fire-fighting and search and rescue operations in remote areas with severe climatic conditions, when difficult to observe in the optical range.

The placement of aerial vehicles (AV) and UAVs in such areas at stationary airfields with well-developed engineering infrastructure are not always possible due to the limited operating range (shoulder): aircraft — carrier. This circumstance forces the use of temporary airfields either. Ensuring the safety of the temporary airfield takes time and considerable expenditure on technical equipment. Thus, a new feature of the CMMAR consists in the territory protection mode with a fixed placement of this radar on the aerodrome.

The article discusses the main shortcomings of the existing technical means of protection areas, and formulates a list of requirements for advanced system protection, allowing show the obvious advantage of using radar in areas with harsh climatic and weather conditions.

The main objective of protection mode in CMMAR is detecting unauthorized approach to the area of protection and violation of its borders by small-sized objects. The article describes technical characteristics of known specialized radars — the closest analogs to the protection mode. Comparative analysis of the performance revealed that the CMMAR in guard mode stays, in general, at the level of the existing modern specialized radars. Nevertheless, the main and principally irremovable drawback of using specialized radar is the necessity of their acquisition, installation and activation, as well as personnel training and operating costs.

The paper presents the evaluation of low-speed and small-sized objects detection range, such as a human person, which demonstrated the ability to achieve detection target values in guard mode unnatural for the designed onboard radar.

Keywords: multifunctional radar, territory protection mode, small-sized target detection, moving target detection

Sychev M. I.

The aircraft coordinate and movement parameters radar estimation is discussed. Multi-model filters application is proved. The emphasis is on horizontal movement models selection. Three civil aircraft basic horizontal movement types and their parameters are defined. The first type is uniform motion, the second is standard turn, and the third is uniform speed change.

Three types of multi-model filters are described. They differ in the merge point of hypothesis for the model state vector changes, and its result implementation. The combined information from all the hypothesises is used in the first algorithm to proceed the transition to the next step. The first algorithm can be viewed as Nth Kalman filter operating in parallel. Here N is the number of models the state vector changes. The second algorithm describes state vector extrapolation for each hypothesis individually, and then their interrelation. As a result, the second algorithm has N2 extrapolation blocks and N update blocks. Hypotheses combined after the update is performed exclusively to provide information to the filter output, but is not used on the next step. The third algorithm is a N2 Kalman filter operating in parallel with the combined information for the individual hypotheses after their upgrade.

Various variants of estimation of motion models parameters, such as speed of the aircraft turn and longitudinal acceleration are considered. The different types of algorithms for these parameters estimation are presented. One of them is independent filters for these parameters estimation. The other is extended state vector describing aircraft coordinates and motion parameters.

The approach to the simplified multi-model filters design is offered based on approximation of a correlation matrix of a state vector for the specified motion model by a constant matrix.

Results of comparative simulation of the considered multi-model algorithms are presented.

Keywords:

Informatics, computation engineering and management

System analysis, control and data processing

Guseynov A. B., Makhovykh A. V.

Modern military and technical concepts of precision weapons creation and development provide us with system approach to develop perspective flying vehicles (FV) and their onboard structures with elements of artificial intelligence, including, automatic subsystems of images recognition. These devices provide identification of the true targets from false. Implementation of such devices along with modern computer facilities allow in general exclude the human operator, increase quality, speed of decision making and efficiency of task accomplishment. The purpose of this work consists in development of a system technique, models and the flowchart of the structural and parametrical analysis and synthesis of project decisions for the onboard distinguishing device as a part of the unmanned aerial vehicle (UAV). This work states the technique of forming the rational shape of the onboard distinguishing device as a part of an unmanned aerial vehicle based on complex “Сost—Efficiency” criterion, and formulates matrix of the signs characterizing an object from the recognition viewpoint. It presents structurally functional scheme of the distinguishing device. For recognition efficiency evaluation of an object the rule of risk minimization called a Bayesian method of probability of an object, belonging to classes true and false is used. Technical similarity of an object and reference is determined by average probability of recognition over the whole range of a sign distribution law numeric indices variation as a random variable. Problem definitions of the structural analysis and synthesis, as well as parametrical optimization are formulated. The flowchart and methods of the solution of tasks based on complex criterion — a minimum of task accomplishment cost with the preset efficiency are formulated. The system methodology presented in this work can be applied to the complex analysis and synthesis of project decisions on UAV shape and its separate subsystems.

Keywords: unmanned aerial vehicle, distinguishing device

Mathematical support and software for computers, complexes and networks

Dudakov N. S., Makarov K. V., Timoshenko A. V.

The purpose of this article is development of database design methods for command and control special-purpose systems.

It is shown that the use of the all-purpose client-server databases for solving the air force and air defense tasks leads to poor query performance. In some cases, the use of more simple distributed databases allows reducing the query time by 90%, but the amount of data does not allow using them as a single solution.

It is proposed that in dealing with heterogeneous highly dynamic tasks, it more effective to use a special-designed database in order to meet the requirements of the designed system.

Given the lack of scientific and methodological methods for selection of proper software in the design of the database, the article offers a method of formalizing requirements for the composition and structure of the DBMS to solve the required tasks.

The article provides a way of grouping and quantitative description of the requirements at the stage of conceptual design of DBMS, which forms the space on the basis of the requirements specification while modeling each task as the DBMS client.

It is shown that in case of the total area of a the requirements of a certain type, it is effective to use an inhomogeneous distributed DBMS. Thus, with weakly bound heterogeneous data and the anticipated load, the article proposes to use multiple databases, each of which handles a particular piece of data. Continuous data partitioning and management of the database structure allows having a data partition that provides better performance.

The article provides the technique of the requirements substantiation to the structure and characteristics of DBMS for command and control special-purpose systems.

It is shown, that the developed technique for DBMS design can increase query performance by more than twice in air force and air defense tasks.

Keywords: database management systems, command and control systems software requirements

CAD systems

Chistyakov M. G., Nazarov A. V., Morozov S. A.

At present, a crucially important problem consists in implementation of CMOS VLSI design, executed with the sub-micron «silicon on insulator» technology (SOI) in the dual-use equipment for of various management and control spaceborn systems, nuclear power and of many other facilities design. The priority here is the development of the of the base elements design of a CMOS LSI dual-use, which include both elementary logic gates, and other types of functional units. The solution to such problems now is impossible without creation of appropriate software tools and methodology of their aggregation and use in a single cycle of electronic-component base functional blocks models development. The article presents already tested designing route of standard CMOS-SOI elements library with minimal topological size of 0.25 microns, ensuring a guaranteed level of radiation resistance. It demonstrates the of software route, implementing the presented route and shows its practical realization on a concrete example. The process of the individual library element design (buffer) using CAD-systems is described in detail in a step-by-step manner. Practical value of the work consists in the fact that the output data formats are presented on each stage of the design. Besides, graphic illustration of the results of design on each step are presented.

Keywords: design route, library of standard elements, radiation resistance, Very Large Scale Integration, computer-aided design system

Mathematica modeling, numerical technique and program complexes

Anosov Y. V., Kurdumov N. N.

The paper considers the problem of application software developing. One of its functions herewith consists in recognition and interpretation of various mathematical expressions, given in symbolic form. The paper also presents designed by the authors built-in interpreter of such mathematical expressions, based on look-up tables and complex recursive computations. The presented command interpreter has small size, supports a wide range of mathematical functions (including hyperbolic), parenthesis and functional notation of any nesting level. The multilevel system for symbolic mathematical expressions analysis realized in the interpreter allows tracking a great number of lexical, syntactic, semantic and mathematical errors (including run time errors).

The presented interpreter can be used for developing various mathematical application software by simply including the interpreter module into the project under development by directives of tools development environment «Microsoft Visual Studio» and appropriate registration of calls by C-language means [1-3].

Keywords: interpreter, lexical analyzer, semantic analyzer, mathematical run time errors, intermediate form, application software, software module, recursion

Tannenberg I. D., Ramazanov R. F.

This paper is based on results of experimental study in which the motion of various plates and shapes under the air flow action was carried out.

Task calculation of free motion in plate flow on russian software Logos-CFD was considered to determine body motion path. Plates possess 12 inch (12″) and 6 inch (6″) in length, 6 inch in width and 0.4 inch in thickness. Calculation results are compared with motion paths getting as test results on the wind tunnel as well as with Monte-Carlo calculation method.

Solver settings were sel ected fr om task solution experience of rigid body motion in air flow. Solver used overlapping grid possibilities as the most fast and stable simulation method of Euler grids joint motion. The task was calculated by SA All Y + turbulence model using AUSMPW scheme of convection flow splitting on the 2nd approximation order.

Calculations were carried out in multiple-access computing center RENC-VNIIEF.

Conclusions:

— In three of four calculations adequate agreement of plate motion paths were obtained as compared to the test;

— Calculation method on CFD enabling of Euler grids mutual motion gains significantly versus describing [4] motion path calculating according to Monte-Carlo method;

— The accuracy of vertical square plate calculation can be improved by means of DDES of unsteady vortexes and by wind tunnel path simulation;

— We can conclude that it is advisable to use Logos-CFD for motion path calculation under action of subsonic flow without initiation of detached flows.

Keywords: CFD, rigid body motion calculation, validation, supercomputer computations, icing, Logos, overlapping grids

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