S.D. Vynnychuk

Èlektron. model. 2022, 44(2):03-14

https://doi.org/10.15407/emodel.44.02.003

ABSTRACT

A generalized mathematical model of dynamic hydraulic processes in the system of supercharging and drainage of the aircraft fuel system, which includes a centrifugal tank and wing tanks, is proposed. In the model, hydraulic processes are considered as quasi-stationary and there is a dynamic change in the structure of the design network of the supercharging and drainage system, the structure of boundary conditions and current pressure and flow limits, where part of the boundary conditions can be set implicitly. The description of the settlement network is presented. Typical calculation options and rules of their use in the calculation of time are highlighted. The general algorithm of calculation is described.

KEYWORDS

aircraft fuel system, supercharging and drainage system, hydraulic network, dynamic flow distribution model.

REFERENCES

1. Evdokimov, A.G., Tevyashev, A.D. and Dubrovsky, V.V. (1990), Modelirovaniye i optimizatsiya potokoraspredeleniya v inzhenernykh setyakh [Modeling and optimization of flow distribution in engineering networks], Stroyizdat, Moscow, USSR.
2. Merenkov, A.P. and Khasilev, V.Ya. (1970), Teoriya gidravlicheskikh tsepey [Theory of hydraulic circuits], Nauka, Moscow, USSR.
3. Maksimovich, N.G. (1970), Metody topologicheskogo analiza elektricheskikh tsepey [Methods of topological analysis of electrical circuits], Lvivskyy universytet, Lviv, USSR.
4. Vynnychuk, S.D. (2016), “Definition of flow distribution in networks with a tree graph”, Electronne modelyuvannya, Vol. 38, no. 4, pp. 65-80.
   https://doi.org/10.15407/emodel.38.04.065
5. Abramovich, G.N. (1969), Prikladnaya gazovaya dinamika [Applied gas dynamics], Nauka, Moscow, USSR.
6. Idelchik, I.E. (1992), Gidravlicheskiye soprotivleniya [Hydraulic resistance], Mashinostroenie, Moscow, Russia.
7. Vynnychuk, S.D. (2001), “Modeling of hydraulic network tees”, Zbirnyk naukovykh prats IPME NAN Ukrayiny, Vol. 14, pp. 73-80.

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S.S. Shevchenko

Èlektron. model. 2022, 44(2):15-25

https://doi.org/10.15407/emodel.44.02.015

ABSTRACT

The unit parameters growth of centrifugal machines requires solving the problems of effective media sealing. In addition to sealing itself, sealing systems affect the vibration safety of equipment. In order to harmonize the sealing functions and increase the dynamic stiffness of the centrifugal machines rotors, an algorithm and methods for modeling complex sealing systems have been developed. Examples of modeling of rotary machines complex sealing systems with high parameters are given. It is indicated that the development of complex sealing systems should be based on the configuration of composite seals in order to achieve harmonization between sealing and vibration reliability.

KEYWORDS

sealing, sealing system, modeling technique, construction algorithm.

REFERENCES

1. Martsinkovsky, V.A. (2002), “Hermomechanics and its place among the technical sciences”, Trudy 10-y Mezhdunarodnoy nauchno-tekhnicheskoy konferentsii “Germetichnost, vibronadezhnost i ekologicheskaya bezopasnost nasosnogo i kompressornogo oborudovaniya” [Proceedings of the 10th International Scientific and Technical. conference "Tightness, vibration reliability and environmental safety of pumping and compressor equipment"], Sumy, Ukraine, Volume 1, pp. 7-10.
2. Martsinkovsky, V.A. and Shevchenko, S.S. (2018), Nasosy atomnykh elektrostantsiy: raschet, konstruirovaniye, ekspluatatsiya [Pumps of nuclear power plants: calculation, design, operation: monograph], Universitetskaya kniga, Sumy, Ukraine.
3. Golubeva, A.I. and Kondakova, L.A. (1994), Uplotneniya i uplotnitelnaya tekhnika [Seals and sealing technology: reference book], Mashinostroenie, Moscow, Russia.
4. Shevchenko, S.S. and Gaft, Ya.Z. (2020), Salnikovyye uplotneniya dinamicheskikh nasosov [Stuffing box seals of dynamic pumps: monograph], Universitetskaya kniga, Sumy, Ukraine.
5. Melnik, V.A. (2008), Tortsovyye uplotneniya valov. Spravochnik [Shaft seals. Directory], Mashinostroenie, Moscow, Russia.
6. Krevsun, E.P. (1998), Tortsovyye germetizatory vrashchayushchikhsya valov [End seals for rotating shafts], Arti-Fex, Minsk, Belarus.
7. Shevchenko, S.S. (2021), “Mathematical modeling of centrifugal machines rotors seals for the purpose of assessing their influence on dynamic characteristics”, Mathematical Modeling and Computing, 8, no. 3, pp. 422-431
   https://doi.org/10.23939/mmc2021.03.422
8. Martsinkovsky, V.A. (2005), Shchelevyye uplotneniya: teoriya i praktika [Gap seals: theory and practice], SumGU, Sumy, Ukraine.
9. Martsinkovsky, V.A. (2012), Dinamika rotorov tsentrobezhnykh mashin [Dynamics of rotors of centrifugal machines: monograph], SumGU, Sumy, Ukraine.
10. Falaleev, S.V. and Chegodaev,E. (1998), Tortsovyye beskontaktnyye uplotneniya dvigateley letatelnykh apparatov [Mechanical non-contact seals of aircraft engines], Izdatelstvo MAI, Moscow, Russia.
11. Gromyko, B.M., Kolpakov A.V., Martsinkovsky V.A., et al. (2000), “Experience in designing and testing results of impulse mechanical seals for liquid-propellant rocket engines operating in cryogenic media”, Trudy NPO Energomash im. akad. V.P. Glushko (GDL-OKB), 18, pp. 279-293.
12. Martsynkovskyy, V., Gaft, Y., Gromyko, В. and Chernov, O. (2000), “Development and application of double pulse gas-liquid seals”, Proc. of 16th International Conference on Fluid Sealing, Brugge, Belgium, pp. 255–260.
    https://doi.org/10.1016/S1350-4789(00)90442-2

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V.T. Chemerys ¹, cand. of techn. science, I.O. Borodiy ²

¹   V.I. Vernadsky Taurida National University of Ukraine
Ukraine, 01042, Kyiv, 31 John MacCane Street,
tel. (063) 4897772, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.;

²   National Aviation University of Ukraine
Ukraine, 03680, Kyiv, 1 Cosmonaut Komarov Avenue,
tel. (044) 4067840, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Èlektron. model. 2022, 44(2):26-37

https://doi.org/10.15407/emodel.44.02.026

ABSTRACT

The goal of this paper is to consider the pulsed magnetic field penetration into the metal with pre-created non-uniform distribution of electrical conductivity coefficient (in more general case — coefficient of magnetic diffusion) as the smooth function along one or two coordinate axes. Similar situation can be created in the process of metal sample manufacturing with a purpose to supply him the special properties. The preliminary theoretical analysis has been resulted a derivation of magnetic induction equation taking into account a presence of gradient for magnetic diffusion coefficient of medium and  motion of medium. Equation is presented in non-dimensional form with obtaining of specific criterion of similarity which is equal to ratio of characteristic velocity of the field diffusion to the basic value of medium motion velocity. For the numerical analysis of process diffusion the software FlexPDE-7.20 has been chosen due to simple ability to introduce the gradient of the field diffusion coefficient into system of the field equations as pre-defined function of coordinates. The simulation model was looking as rectangular metal plate with pulsed excitation of field along one side. On the base of results of 1D and 2D simulation the authors demonstrate the set of specific properties of the field diffusion into the plate at growing or damping diffusion coefficient. There are considered also the influence of the metal plate motion on the process of the field diffusion, in particular effects of the field compression or decompression and capture of field by moving medium.

KEYWORDS

magnetic diffusion coefficient, two-component gradient, plane model, pulsed field, non-dimensional analysis, numerical solution

REFERENCES

1. Kidder, R.E. (1959), Non linear diffusion of strong magnetic fields into a conducting half-space, University of California, CA, USA, Tech. Rep. UCRL-5467, available at: http:// hathitrust.org/cgi/pt?id=mdp.39015077594359;view=1up;seq=1.
   https://doi.org/10.2172/4269476
2. James, T.E. and James, D.C. (1995), “Resistive contact region solid armatures: Electro-thermal design optimisation”, IEEE Transactions on Magnetics, Vol. 31, no. 1, pp. 162-167.
   https://doi.org/10.1109/20.364709
3. Barber, J.P. and Dreizin, Y.A. (1995), “Model of contact transitioning with ‘realistic’ armature-rail interface”, IEEE Transactions on Magnetics, Vol. 31, no. 1, pp. 96-100.
   https://doi.org/10.1109/20.364721
4. Hsieh, K.-T. and Kim, B.K. (1997), “3D modeling of sliding electrical contact”, IEEE Transactions on Magnetics, Vol. 33, no. 1, pp. 237-239.
   https://doi.org/10.1109/20.559961
5. Hsieh, K.-T., Stefani, F. and Levinson, S.J. (2001), “Numerical modeling of the velocity skin effects: An investigation of issues affecting accuracy [in railguns]”, IIEEE Transactions on Magnetics, Vol. 37, no. 1, pp. 416-420.
   https://doi.org/10.1109/20.911867
6. Dreizin, Y.A. (1993), “Solid armature performance with resistive rails [railguns]”, IEEE Transactions on Magnetics, Vol. 29, no. 1, pp. 798-803.
   https://doi.org/10.1109/20.195678
7. Chemerys, V.T. (2013), “Key problems of railgun: New concept for their resolution”, Procedia Engineering, Vol. 58, pp. 377-383.
   https://doi.org/10.1016/j.proeng.2013.05.043
8. Chemerys, V.T. (2015), “Rail Accelerator as Continuous Commutation Process”, IEEE Transactions on Plasma Science, Vol. 43, no. 3, pp. 869-877.
   https://doi.org/10.1109/TPS.2015.2399414
9. Chemerys, V.T. (2020), “Specifics of Pulsed Magnetic Field Penetration Into Electrodes of Rail-Type Accelerator With Application of the Variable Conductivity in the Surface Layers of Rails at Uniform Acceleration of Solid Armature up to 2.5 km/s (Numerical Investigation in 2-D Model)”, IEEE Transactions on Plasma Science, Vol. 48, no. 7, pp. 2608- 
   https://doi.org/10.1109/TPS.2020.3001567
10. Mayergoyz, I.D. (1998), Nonlinear Diffusion of Electromagnetic Fields (with Applications to Eddy Currents and Superconductivity), New York: Academic Press.
11. Thambynayagam, M.R.K. (2011), The Diffusion Handbook: Applied Solutions for Engineers, 1^st, McGraw-Hill, US.
    https://doi.org/10.1016/B978-012480870-6/50003-X
12. Pramanik, A. (2014), Electromagnetism. Volume 2 – Applications, Magnetic Diffusion and Electromagnetic Waves, PHI Learning, India.
13. Raychenko, A.I. (1981), Mathematical Theory of Diffusion in Applications, Naukova Dumka, Kyiv, USSR.
14. Carslaw, H.S. and Jaeger, J.C. (1959), Conduction of Heat in Solids, Clarendon Press, Oxford.
15. Crank, J. (1975), The Mathematics of Diffusion, Clarendon Press, Oxford.
16. Nigmatulin, R.I. (1990), Dynamics of Multiphase Media, Vol. 1, Hemisphere Publishing Corporation.
17. Oughstun, K.E. and Sherman, G.C. (1997), Electromagnetic Pulse Propagation in Causal Dielectrics, Springer-Verlag.
    https://doi.org/10.1109/MAP.1996.500235
18. Woodson, H.H. and Melcher, J.R. (1968), Electromechanical Dynamics, Massachusetts Institute of Technology, John Wiley & Sons, Inc.

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O.O. Suprunenko, B.O. Onyshchenko, J.E. Grebenovych

Èlektron. model. 2022, 44(2):38-50

https://doi.org/10.15407/emodel.44.02.038

ABSTRACT

The basic characteristics of the model of the software system which belong to the working capacity and predictability, are described. Analyzed tools were used for the modeling of software systems. As a basis for the tools of modeling and analysis of the dynamic properties of software systems, the choice of interpretations and modifications of Petri nets is justified. They allow to follow structural similarity in the model system and also have an unambiguous  mathematical description. The analysis of the properties of Petri nets allows to reveal obvious and hidden errors in functioning of PN-model of software system, that is not always possible in the application of simulation modeling. To such properties belongs liveliness, boundedness, reachability, preservation, conflictlessness, controllability. The T- and P-invariants, as well as the characteristics of the incidence matrix, allow to detect compliance with these characteristics. The matrix description of the PN-model was carried out with the help of the basic equation of the Petri net, definition identification of invariants and their analysis to reveal dynamic properties of the model. The rule of absence of hidden deadlocks and infinity loops in PN-model is formulated. The detection of hidden errors — deadlock and infinity loop are described. The solution of the deadlock elimination was proposed; its conformity to the dynamic properties was checked. The definition and correction of hidden errors on the example of not fully controlled PN-model is illustrated. The presented method of analysis of PN-models has practical application in step-by-step analysis of the software model. Phasing of the analysis of software model caused by the proliferation of component-oriented technology of software system development and the limiting the number of PN-model elements. It can be applied both independently and as a part of the combined approach to the simulation modeling of systems with parallelism.

KEYWORDS

Petri net, PN-model software system, analysis of hidden errors.

REFERENCES

1. Sommerwill, I. (2002), Software engineering, Williams House.
2. Suprunenko, O. (2021), “Combined approach architecture development to simulation modeling of systems with parallelism”, Eastern-European Journal of Enterprise Technologies, 4(4(112)), pp. 74-82.
   https://doi.org/10.15587/1729-4061.2021.239212
3. Stojan, V.A. (2008), Modelyuvannya ta identyfikatsiya dynamiky system z rozpodilenymy parametramy [Modeling and identification of dynamics of systems with distributed parameters], Kyyivskyy universytet, Kyiv, Ukraine.
4. Suprunenko, О.О., Onyshchenko, B.О. and Grebenovich, J.E. (2020), “Analytical approach in the study of the properties of the graph model of a software system. Proceedings of the international scientific-practical conference”, Pratsi mizhnarodnoyi naukovo-praktychnoyi konferentsiyi «Matematychne modelyuvannya protsesiv v ekonomitsi ta upravlinni proektamy i prohramamy» (MMP-2020) [Mathematical modeling of processes in economics and project and program management (MMP-2020)], Kharkiv, KNURE, September 14-18, 2020, pp. 110-113.
5. Braude, E. (2004), Tekhnologiya razrabotki programmnogo obespecheniya [Software engineering: Object-Oriented Perspective (Software development technology)], Piter, St. Petersburg, Russia.
6. Karpov, J.G. (2005), Imitatsionnoye modelirovaniye sistem. Vvedeniye v modelirovaniye s AnyLogic 5 [Simulation modeling of systems. Introduction to modeling with AnyLogic 5], BHV-Peterburg, St. Petersburg, Russia.
7. Andreev, А.М., Mozarov, G.P. and Sjuzev, V.V. (2011), Mnogoprotsessornyye vychislitel'nyye sistemy. Teoreticheskiy analiz, matematicheskiye modeli i primeneniye [Multiprocessor computing systems. Theoretical analysis, mathematical models and applications], Izdatelstvo MGTU im. N.E. Baumana, Moscow, Russia.
8. Van der Aalst, W.M.P. and Best, E. (2017), Application and Theory of Petri Nets and Concurrency, 38th International Conference, PETRI NETS 2017, Zaragoza, Springer, June 25-30, 2017, available at: https://link.springer.com/book/10.1007/978-3-319-57861-3 (accessed: December 25, 2021).
   https://doi.org/10.1007/978-3-319-57861-3
9. Van der Aalst, W.M.P. (2003), Pi calculus versus Petri nets: let us eat humble pie rather than further inflate the pi-hype, available at: tmitwww.tm.tue.nl/staff/wvdaalst/pihype.pdf (accessed: August 29, 2021).
10. Suprunenko, О.О. (2013), “Paradigms of simulation modeling in the study of complex systems with parallelism”, Skhidnoyevropeyskyy zhurnal peredovykh tekhnolohiy, Vol. 5, no. 4, pp. 63-67.
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19. Kuzmuk, V.V., Suprunenko, O.A. (2014), “The means for the description of information flows in dynamic models of medical hardware-software systems”, Theoretical and Applied Science, Vol. 7, no. 15, pp. 11-18.
    

    https://doi.org/10.15863/TAS.2014.07.15.2

20. Nesterenko, B.B. and Novotarskiy, M.A. (2012), Formalni zasoby modelyuvannya paralelnykh protsesiv ta system [Formal tools for modeling parallel processes and systems], Pratsi Instytutu matematyky NAN Ukrayiny, Kyiv, Ukraine.
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