2011. № 45

Тематический выпуск «Молодежь и будущее авиации и космонавтики–2010»

45 выпуск электронного журнала «Труды МАИ» является тематическим и содержит 71 научную статью, подготовленную на основе докладов, представленных на II Межотраслевом молодежном научно-техническом форуме «Молодежь и будущее авиации и космонавтики» и признанных экспертными группами и Программным комитетом конференции соответствующими общепризнанным критериям высокого научного уровня. Заседания II Межотраслевого молодежного научно-технического форума «Молодежь и будущее авиации и космонавтики» состоялись 2 декабря 2010 года во Всероссийском выставочном центре. Участниками форума стали более 700 человек, среди которых молодые ученые, молодые специалисты, аспиранты и студенты – представители более 50 предприятий аэрокосмической отрасли и смежных высокотехнологичных отраслей промышленности, 18 научных и высших учебных заведений России. В рамках форума по девяти направлениям (авиационная техника; двигатели и энергетические установки; системы управления, информатика и электроэнергетика; системы радиолокации, радионавигации, связь и оптоэлектроника; ракетная и космическая техника; математические методы в аэрокосмической сфере; экономика и менеджмент в авиационной и космической отраслях; инновационные технологии и материалы аэрокосмического применения) было заслушано 90 докладов по актуальным вопросам научно-технологического развития аэрокосмической отрасли и смежных отраслей промышленности. Программный и Организационный комитеты II Межотраслевого молодежного научно-технического форума «Молодежь и будущее авиации и космонавтики» выражают надежду, что издание данного выпуска будет полезным для дальнейшего развития в Российской Федерации высоких технологий и кадрового потенциала таких технологий.

Mathematics. Physics. Mechanics

Ryazantseva O. V.

Currently, the solution of problems of aerospace systems and space-rocket complexes are widely used metaheuristics global optimization methods. An example of this method is "greedy" adaptive algorithm for random search of global extremum, which is considered in this paper. Formed algorithmic and software method, whose effectiveness was demonstrated on model examples with the complex structure of level lines.

Keywords: global extremum; metaheuristics methods; multistart; local search

Pedkina K. V.

The mathematical model of flow describes the potential flow with circulation around the cylinder in the presence of the plates. Solution to the problem of flow around the cylinder in the presence of the shielding surface is obtained for the flow of an incompressible ideal fluid. As part of the numerical-analytical method of modeling the shielding surface is satisfied by a set of point vortices are uniformly distributed over the surface of the plate. The dependence of the maximum velocity on the contour of the location of the plate was obtained. The dependence of the circulation of the steady vortex on the length of the plate, the circulation around the cylinder and the position of the separation area was investigated. Velocity profiles in cross sections perpendicular to the plane of the shield shows the possibility of creating a uniform flow. Pressure distribution along the contour, depending on the values of the circulation around the cylinder in the presence shielding surface and the location of the separation area was obtained.

Keywords: flow; complex potential; circulation, vortex, stationary conditions, stream lines, numerical-analytical method; separation area; Föppl’s vortex.

Metlitskaya D. V.

The application of genetic algorithms for searching the global conditional extremum with binary coding and real coding to the problem of optimal control of nonlinear continuous deterministic systems is suggested. A detailed algorithm for solving the problem, on which to create the appropriate software, is considered. An example of solving an applied problem and compared the results with other methods, illustrating the effectiveness of generated algorithms.

Keywords: genetic algorithms, binary coding, real coding, a continuous control system, optimal control.

Kalas V. O.

Two equal masses move on two coplanar elliptic orbits around their barycentre while a third infinitely small mass bodymoves throw the mass center on a line perpendicularly to the motion plane ofthe first two masses. In the neighborhood of the stable equilibrium point is researchedone-dimensional oscillation of infinitely small mass body. Parametricresonance conditionwas defined. By theaveraging methodwe got averaged equations and investigated resonance and near-resonance region. Phase portrait was plotted. Example of this problem is a system of two stars with equal masses and emission. Between them areclouds of particles, which are subjected to gravitation and light pressure

Keywords: Sitnikov problem; equilibrium; stability; parametric resonance; near-resonance region; phase portrait; bifurcation; averaging method; one-dimensional oscillation

Aviation technics and technology

Dolgov O. S.

The paper describes new approaches of moment of inertia shape formation of future technology vehicle. Defined preferable zones of placing fuel and payload accordingly its mass. The analysis features of the definition of moment-inertia characteristics of the aircraft relative to the axes OX, OZ and OY. The aspects of the harmonization of moment-inertia shape the possibilities of governance. Analyzed features of aircraft moment-inertia characteristics over axes OX, OZ and OY formation. Identified the aspects of adapting moment-inertia shape formation with the possibilities of aircraft control system.

Keywords: moment of inertia, fuel tanks, payload, layout, control system

Matveyev A. V., Makhukov A. A.

This work describes technique and bundled software of Unmanned Aerial Vehicle’s (UAV) motion accompanying simulation during flight tests. Accompanying simulation is technology and advance research which based UAV’s flight simulation model and directed to simplification of the flight tests result analysis. This technique and bundled software have tested during OJSC «Yakovlev design bureau»’s UAV flight tests. Telemetry information was analyzed and necessarily source data was formed. According to flight tests data simulation model of longitudinal controllable motion was compounded and corrected. Results of flights were analyzed. Realization of introduced upgrades allows to finish flight test with success.

Keywords: unmanned aerial vehicle; accompanying simulation; flight tests; simulation modeling; matlab; simulink.

Kuznetsov A. G.

In work questions of automation of landing of the small-sized unmanned aerial vehicle (SUAV) are considered. Landing automation assumes the organization of the help to operator SUAV based on analysis current and predictable spatial position SUAV. As a source of the navigating information the system of technical sight is considered.

Keywords: unmanned aerial vehicle; help for operator; technical vision; owner coordinates estimation; special situation

Anishchenko G. A., Molin K. E.

Currently the stage of dynamic and life test is the most time-consuming and expensive in the process of creation and modernization of helicopters.Preliminary calculations based on the available techniques is not always possible to obtain exact results and avoid the high cost of model shops. In this work a promising approach to the problems of the overall dynamic strength of the helicopter, based on the wider application of the finite element method is demonstrated by the problem of helicopter airframe`s dynamic loading by recoil from automatic cannon with a single shot.

Keywords: dynamics; helicopter; shot; finite elements method; normal modes; damping; gain-frequency characteristic

Andreev A. V., Kiryanov A. I., Pashkov O. A., Starostin S. V., Ushakov N. V.

The article presents the results of aerodynamic characteristics for an experimental aircraft with aerodynamic lifting body. An analysis of this. The prospects of this area of work.

Keywords: experimental aircraft; aerodynamic lifting body; vortex structure; steady airflow

Makeev P. V., Shomov A. I.

With the help of software package on the basis of a nonlinear vortex model of helicopter rotor with the free diffusion trace, developed at the department "Design of helicopters" of the Moscow Aviation Institute, carried out comprehensive study of aerodynamics of rotor helicopter at "vortex ring state" mode. For the particular case with three-bladed helicopter rotor, carried out numerically simulated and analyzed a number of modes of steep decline the helicopter, the relevant area of "vortex ring state". Based on the characteristics of the free vortex wake, the vector velocity field, streamlines, and the aerodynamic characteristics of rotor blades and the flapping motion received the combination of features that can determine a dangerous region of the "vortex ring state" mode.

Keywords: numerical method of study, helicopter rotor, vortex ring state, nonlinear vortex model, aerodynamic characteristics.

Serokhvostov S. V.

Analyzed is the applicability possibility of large aircraft dynamical characteristics definition technique for micro air vehicles. Analytical expressions of dynamic characteristics are investigated with respect for MAV. Considered are the conditions of Micro Air Vehicles (MAV) stability and the influence of MAV design on these conditions. Static and dynamic stability conditions, characteristic frequencies and times are obtained for the most important flight mode (cruise flight) and the influence of MAV design parameters is investigated. Comparison with flight experiment is made.

Keywords: micro air vehicle; MAV; stability; disturbed motion

Cheglakov D. I., Orlov S. V.

This paper addresses the fly-by-wire (FBW) system control law design process for the aerial refueling procedure of highly maneuverable aircraft. Some desired qualities of FBW system and methods to support successful docking procedure are highlighted. Results for modeling the dynamics and aerodynamics, mathematical and full-scale simulation, flight tests analysis of aerial refueling are included. Performance of the FBW system was successfully demonstrated by flight tests. Control law presented in this paper is used for the pilot and serial MIG-29K/KUB aircraft.

Keywords: fly-by-wire system; aerial refueling; docking procedure.

Razbegaeva I. A.

The paper describes simplified method of oscillation calculation of the aircraft fuselage panels. Verification of results of the eigenmodes calculations of the rectangular plate and fuselage compartment was performed. Simplification of the vibration problem of the aircraft compartment was achieved by the optimal selection of the plate. Usage of the rubber straps was also suggested as a method of the aircraft sound isolation. This method allows to divide oscillation frequency of ventilator influence from the fuselage skins normal mode.

Keywords: eigenmode, rectangular plate, fuselage compartment, responseconstruction, rubber straps.

Nikitin A. I.

The given paper considers aerodynamic coefficient identification technique suggested by author. In fact, solves inverse dynamic problem: with aid of angel velocity and acceleration records restores forces and moments, which were cause of this velocity and acceleration. Paper describes algorithms and equations for restoring aircraft longitudinal and lateral motion parameters for aircraft without dampers. Transient process plots until and after identification shows suggested technique efficiency.

Keywords: identification; follow-up system; aerodynamic coefficients; aircraft; mathematic model.

Zakharov D. N.

During takeoff and landing aircraft is for some period of time near the earth's surface. Wind tunnel capacity and theoretical methods are not enough to describe the effect of ground proximity with given precision, taking into account a moving screen. A method to determine the longitudinal aerodynamic characteristics of aircraft was developed to select the control algorithms and to obtain mathematical modeling materials needed for the certification of aircraft Tu-204/214 and Tu-334 during landing of the 3d A category. The development of requirements specification and flight tests data processing technique for Tu-204CM is based on this method.

Keywords: influence of the earth proximity; air cushion; screen effect; slant; takeoff; automatic landing

Korobkov A. A.

During performance of the competitive work the following analyses were carried out: analysis of HA functioning conditions, analysis of problem situation of HA projecting and methods for definition of HA movement parameters. Mathematical model and definition procedure for basic movement parameters of a long atmospheric flight HA. Evaluation of aerodynamic heating parameters of HA surface and warming of HA thermal protection was carried out, developed evaluation methodology for thermal protection parameters of HA lateral surface makes it possible on the basis of trajectory-ballistic parameters and heat flow size to define thermal protection parameters of HA lateral surface in total considering dependence of thermal characteristics of heat-shielding materials on thermobaric parameters.

Keywords: aeroballistics; aerodynamic heating; hypersound aircraft; heat flow; thermal protection; thermobaric parameters; thermotensions

Lavrov A. O.

The article describes in detail the structure of the modes of air-borne operative advising expert system for long-distance fight with ground-based target (BOAES for FGT). As an example, one of the BOAES for FGT’s modes: "Attack by one plane visually unobservable group of vulnerable targets with known coordinates, using products with an inertial-satellite homing”. The list of problematic subsituatsy is selected, a prototype of a frame is displayed, the role of BOAES for FGT was considered in mentioned mode.

Keywords: air-borne operative advising expert system, inertial-satellite homing, long-distance fight with ground.

Chemyakin A. V.

This work is devoted to the methods of analyzing the dynamics of separation of cargo using modern technology of computer mathematical modeling. On the example of separation from the rocket aircraft ejection device considered order and features a model separates the cargo. Result is the development of the technology of computer simulation, which allows an adequate dynamic model of the separated load and measure the position, velocity and acceleration of any of its points at any time. The ways of integrating this technology with other technologies for analysis and synthesis of robotic systems, aircraft armament.

Keywords: separation of cargo; aircraft ejection device; modeling; solid models.

Archipova O. V.

The basic version of board promptly advising expert system of long-range air combat one on one is based on the results of mathematical research of individual fragments of long-range air combat. In the given work the knowledge base of expert system is described and simulated air combat for long-range duel situations with different initial conditions. Knowledge Base intelligent system constructed by a hierarchical principle, using the production rules and operatively solve game problems. It is aimed at solving problems in long-range duel situation of air combat in the counter and counter-intersecting courses under a single missile launches from each aircraft, using optimal spatial offensive and defensive maneuvers, choosing the optimal time of launch rockets and the moments of interference information systems of the enemy. Modeling a number of typical combat situations gives an opportunity to make a game matrix outcome of the battle, which demonstrates the effectiveness of selected strategy of action for the fighter aircraft in a long distance air missile battle, as well as to optimize an image of knowledge base for the crew intelligence support system.

Keywords: intelligent system support; expert system;distant air fight; knowledge base structure; problem subsituation;recommendations to the pilot; logic of work «the pilot - onboard equipment»; simulation; criterion of an estimation of efficiency

Kapustin D. U.

The work explores the dynamic processes of disclosure folding parts control surfaces the aviation weapon of variable shape in a disturbed flow in the vicinity of the aircraft. As the result this work the methodical software was the first developed, which enables to evaluate the effectiveness of technical solutions to ensure the safety of launch aviation weapon of variable shape from the compartment aircraft.

Keywords: placement inside the fuselage, folding parts control surfaces, secure launch

Kuz'michev R. V., Sitin D. A., Stepanov V. S.

Kinematic schemes drive of “more electric” aircraft were considered, were analyzed: potentials and limitation of actuating mechanisms with pivot-type, general requirements to functional elements of actuating mechanisms with pivot-type, ways their organization and the most perspective constructions such actuating mechanisms. Schemes of redundant drives with pivot-type and schemes drive of system, which controls the objects with lack of inflexibility were describe.

Keywords: pivot-type actuating mechanisms; electro-mechanical actuators; aerodynamic control surface actuators; ball-rolling wave gear; “more electric” aircraft.

Space technics and technology

Anurov A. E.

One of the upward trends in satellite-borne equipment for space engineering is shrinkage while providing better functionality and longer lifetime. However, new problems occur such as thermal protection and thermal conditions of equipment being operated in cosmic space, that strongly effect on cost and reliability. Masses and dimensions of heat-sink cooling systems are rather high even under shrinking of aerospace equipment (satellite-borne equipment, microplatforms, nanosatellites and ets.). In this connection, it is seemingly attractive to utilize resent technologies and, first of all, MOEMS, that provide innovative problem solving in the technical contradiction mentioned. In this paper, a prototype and manufacturing technology are presented of domestic thermal control microsystem for micro- and nanosatellites. The prototype is made in terms of technical level analysis of foreign thermal control designs for small spacecrafts. Also, a calculation of project cost efficiency is given, estimated results and benefits are presented.

Keywords: spacecraft; microsystem technology; microoptoelectromechanical system (MOEMS); surface micromachining; actuator; thermal control; variable emittance coating (Vari-E).

Avdeev A. V.

The feasibility of using the space-based large scale laser system on the base of cw chemical HF laser for clearing near-Earth space from the fragments of space debris is justified and the requirements to its characteristics (power, angle divergence of laser output beam, pulse duration when lasing occurs in a pulse-periodic mode, repetition rate of pulses and duration of impact on fragments of space debris for their removal from an orbit of protected space vehicles) are determinate. Possibility of launching such a laser system on orbit by Proton-M Launch Vehicle is considered.

Keywords: space-based laser system, cw chemical HF laser, space debris, mode of ablation, pulse-periodic mode of laser radiation

Zolkin S. N.

This paper is devoted to the analysis of heavy launch vehicle loading while moving in the dense atmosphere in the area of maximum high velocity pressure in the stream wind and wind thrust. The thrust action time is chosen on the bases of the information about the first cross упругихvibration modes of launch vehicle construction. So that to insure obtaining maximum amount of the construction internal power factors in providing the strengths. Such analysis has been performed for the heavy launch vehicle construction with the payload consisting of a buster and satellite. The finite element model made for the solution of this problem has been verified according to the first vibration modes in respect to its full scale object. As result of the calculations the plots of the most essential inner power factors in launch vehicle construction sections were obtained and the comparison of the equivalent tensile and compression forces of carrying capability of compartments and nodes of its body was performed.

Keywords: proportion unit; space vehicle; finite element model; rocket engine; launch vehicle

Cheremnykh E. A., Zykov A. V.

The results of dynamic behavior research of compound spacecraft with frameless rotating solar sail and powered gyro with Hook gimbal suspension are presented. Solar sail with central rigid insertion is used for transmission of angular momentum as well as momentum to space platform. Stability of stationary shape of a sail at regular precession is proven by direct Lyapunov method. Using modal decomposition, adaptive observer algorithm is developed for estimation of oscillation rates of membrane disk for their active damping.

Keywords: motion control systems; oscillation theory; solar sail.

Suvorov M. A., Kolomitsev I. V.

In scope of survey spacecraft on highly elliptical orbit (HEO) is considering. The construction of this spacecraft determines borders on orientation factors in due to the sun location about spacecraft and to control orbits operation factors. To keep orbits operation factors in given borders it is necessary to apply calculated power pulse to spacecraft equipped with low force jet engine. Impulse direction is the main factor affecting on orbits operation factors corrections quality. Therefore spacecraft orientation should be guarantee essential correctional impulse direction. In due to orbits operation factors evolution control methods of orbital parameters are developed.

Keywords: spacecraft; control; orbital parameters; spacecraft orientation; borders on orientation factors; orbits operation factors evolution.

Chichkov S. A.

This article considers developing of special orbital GTAW weldheads and other equipment using digital prototyping. This series of weldheads was specially developed for best quality high speed automated orbital welding of different purpose pipings and tubings in aerospace industry. It can be use on assembling operations and allow toadjust all parameters of welding. Also, some technological problems and solutions of orbital welding are considered, and some other moments of innovation in design and develop of the new generation weldheds, and some advantage and prospects of this line.

Keywords: orbital welding; arc welding; gas tungsten arc welding (GTAW);tubings and pipings; CAD; weldheads; digital prototype, 3D design, Autodesk Inventor

Aerospace propulsion engineering

Zakharov D. L.

The goal was the development of PIV technique (Particle image velocimetry) for examination of complex turbulent streams, which are typical gas flows for aircraft engines and gas-turbine installations. Comparisons between PIV data and LDA (Laser Doppler anemometry) were performed. Also phase-averaged velocity fields measuring procedure by means of PIV has been developed. Besides, the measuring procedure of fields of gaseous fuel concentration behind front module of combustion chamber with various types of injectors as a part of the front module has been developed. It is shown the possibility of use PIV technique in the experimental researches developing of perspective aviation engines and gas-turbine installations.

Keywords: optical method, velocity measurements, concentration measurements

Shehovtseva E. V.

The basic purpose of work is an improvement of manufacturing technique of integral cylindrical gears cluster by electro-erosion processing (EDM) of working surfaces of teeth the closed cylindrical gear of external gearing with application of chemicothermal processing for increase of their contact durability. The quality of the surface layer of teeth working surfaces of gears in a gas turbine engine using EDM has been investigated. The influence of modes EDM on the quality of working surfaces and their interconnection with roughness has been established. The surface chemical analysis made on proposed and serial technologies has been accomplished.

Keywords: integral cylindrical gears cluster; closed ring gear; electro-erosion processing

Volchkov G. V., Vystavkin A. G.

In the present competitive work the results of design shape of space nuclear power plant (NPP) with dynamic (steam-turbine) energy conversion by electric capacity of 500 kW are resulted. In work are presented the weight and overall characteristics of nuclear power units and separate units, the design-layout scheme of a product, recommendations about installation operation are offered. The results obtained can be used to produce energy transport module based on megawatt-class nuclear powered.

Keywords: space vehicle; space nuclear power plant; dynamic energy conversion; steam-turbine plan

Boldyrev S. V., Ovchinnikov A. G., Merkulova E. V.

The present article is reviewing the solid propellant attitude control motor and its using for the emergency rescue system of a new generation manned transport spacecraft. In case of the accident in the I step flight area, while launching a new generation manned transport spacecraft from Vostochny space centre, application of the solid propellant attitude control motor allow: – to use configuration of aerodynamically and statically unstable launch abort vehicle; – to ensure the emergency rescue system mission and, in particular, for putting the descent vehicle in a dedicated near launch site at the proper time of starting landing system.

Keywords: solid propellant attitude control motor; emergency rescue system; prospective manned spacecraft; launch abort vehicle.

Fleytlikh B. В.

Methods for calculating the mean temperature difference in cross-flow heat exchangers with single-pass motion of nonmixing media through both cavities are considered and compared. An algorithm implementing the Smith method is proposed.

Keywords: mean-temperature difference; cross-flow; Smith method

Yakutin A. V.

Mathematical description of working processes in chemical monopropellant rocket micropropulsion system is proposed. Processes of catalytic and thermal decomposition of hydrazine, hydro and gas-dynamic processes of fluid flow in distribution block, catalytic reactor and nozzle, process of heat exchange in thruster chamber with heat extraction in the wall are described. Numerical analyze of working processes and estimate thrust and specific impulse microthruster’s are performed. Results of investigation of dependence fluid temperatures in catalytic reactor on wall temperatures are shown. Proposed method of numerical investigation of working processes in rocket micropropulsion system allows reducing time and cost of micropropulsion development.

Keywords: micropropulsion system; nanosatellite; mathematical modeling; catalytic reactor; micronozzle; hydrazine decomposition

Korotygin A. A., Bagrov S. V., Pyatunin K. R.

Bypass ratio increase is one of main tendencies in aircraft engines industry. These changes bring about greater size and mass wide-chord blades usage. One of the competitive ways of the problem decision is a design of hollow titanium blades. In this work are researched existing designs and revealed their advantages and flaws. Also original blisk with hollow titanium blades design is offered and technology of manufacturing is developed. In project is used 3D aerodynamics and strength design.

Keywords: turbofan engine; fan; blisk; hollow blade; mechanical machining; electrochemical machining; friction welding; 3D aerodynamics

Amelkin A. S.

In this article the structural technique of geometry stabilization of bearing’s seat is described and analyzed on force and thermal deformation of bearing housing. Suitability of introduced engineering solution is shown.

Keywords: bearing; reinforcing bush; support of rotor; geometry stabilization; thermal deformation

Theoretical engineering. Mechanical engineering

Poroshchay K. S.

This article describes new design and manufacturing technology of assembly, weld and test fixture of pipelines, based on modern information technology in pipeline manufacturing for prod-ucts. The aim of the project is to reduce the preparation time for production of pipelines, material consumption and labor costs, increase accuracy of fixture. Fixture is made of the simple parts, which are produced on the laser center and lathe. As-sembling of fixture comes down to a simple attaching of details. Ease of manufacture and low cost materials provide high economic efficiency of fixture. A key feature of the project is reference-free method of pipelines manufacture and manufac-turing technology of fixture, which does not require of tangible medium dimensions (working sam-ple and reference pipelines). This will significantly improve the quality of fixture and precision pipeline, save material and labor resources by 1.5 - 3 times, and reduce manufacturing time of fix-ture by 1.5-2 times.

Keywords: fixture; 3D model; pipeline; reference pipeline.

Sapozhnikova J. A., Chernikov D. G.

This scientific paper is concerned with development of hybrid and combined technologies of sheet pressing which use static and dynamic loadings. Unique in world practice technological schemes of a number of operations have been developed, patents of the RF for these schemes have been taken already or are executing. A possibility of use of the multi-purpose finite-element complex ANSYS/LS-DYNA for computer simulation of coupled static-and-dynamic processes has been demonstrated with concrete examples. The technique of computer simulation of coupled problems has been developed; the complex of experimental investigations of processes “stretching – forming” and “bending – flanging”, confirming the advantages of combined operations, has been performed. Within the extent of experimental-and-industrial checking the machining attachment for a number of new technologies developed has been designed and produced, sampling of them has been carried out. Photos of the finished parts produced with these technologies are given. Technical-and-economical advantages of the technologies developed have been formulated.

Keywords: high-speed methods; pulse-magnetic pressing; hybrid technologies; combined technologies

Ogurtsov P. S.

In this article offer results of blank’s shaping process modeling from В95пч Т2 alloy, which HWD is: 400x600x6 in material’s afterflow environment on rigid matrix in autoclave, which has bicurvature work contour.

Keywords: process modeling; blank’s shaping; afterflow; mode of deformation.

Andrianov P. A.

The paper describes the innovative technology of face gears drives manufacturing oriented to job-lot production or batch production. The field of application is aircraft and instrument engineering, special equipment production

Keywords: face gears drives; technology; job-lot and batch production

Control systems

Sinitsa S. P., Tretyakov A. V.

We consider the step-by-step research of an onboard control system of the unmanned flying vehicles from the synthesize control algorithms to the end of its natural tests using the combination of mathematical and seminatural modeling methods.

Keywords: unmanned flying vehicles; adaptive system; mathematical modeling; seminatural modeling

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