Article

Article title ACCORDING THE QUESTION OF PARADOX DALEMBERT-EULERS PERMISSION
Authors A.V. Paliy
Section SECTION IV. MODELING AND DESIGN
Month, Year 10, 2016 @en
Index UDC 533.6.01
DOI 10.18522/2311-3103-2016-10-138146
Abstract The Dalembert-Eulers paradox is described. The possibility of paradox disclosure is shown in this article. The mechanisms of viscosity and the body resistance in the flow are described. The modern paradox interpretation in equable and rectilinear motion of body with arbitrary shape but finite size inside infinite incompressible fluid devoid of viscosity and vortex formation, and velocities abruption surfaces discontinuity is presented. The method of finite volumes and the nonstationary Navier-Stokes equations are used for the numerical decision of the task. Partial derivatives are approximated by the second order of accuracy, derivatives on time are approximated by the Euler implicit scheme with the second order. Thus, each equation in the connected set of the equations is linearized implicitly, concerning all dependent variables in a set. It leads to a linear equation system with the equations for each cell where there is a number of the connected equations in a set. The purpose of article is disclosure of a paradox. In particular the specific example of a cylinder flow by a gas is used for this. The problem definition and theory are described. The simulation of body aerodynamic resistance in a gas flow is considered. It confirms the experimental data about pressure distribution in system body-flow. We showed the errors in conditions of body flow when the paradox appeared. We concluded about possibility of its disclosure by correction of described errors.

Download PDF

Keywords Gas flow; body resistance; flow around body; body surface; the Dalembert-Eulers paradox.
References 1. Paliy A.V. Massoperenos i osnovnoe uravnenie aerodinamiki [Mass transfer and basic equations of aerodynamics]. Taganrog: Izd-vo TTI YuFU, 2012, 192 p.
2. Paliy A.V., Panatov G.S. Temperatura i teploperenos [Temperature and heat transfer]. Taganrog: Izd-vo TTI YuFU, 2009, 132 p.
3. Paliy A.V., Zamkov E.T. Opredelenie gaza kak nevyazkogo veshchestva na osnovanii utverzhdeniy Gel'mgol'tsa i N'yutona [Determination the gas as a non-viscous matter on the basis of representations Helmholts and Newton], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2013, No. 1 (138), pp. 190-196.
4. Paliy A.V., Zamkov E.T., Buleyko V.G. Mekhanizm sozdaniya soprotivleniya ploskoy po-verkhnosti v gazovom potoke tangentsial'noy sostavlyayushchey skorosti molekuly gaza [Mechanism of body friction and resistance in the gas], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2013, No. 1 (138), pp. 197-202.
5. Paliy A.V., Zamkov E.T., Serba P.V. Opredelenie tolshchiny pogranichnogo sloya pri obtekanii tela aerodinamicheskim potokom metodom elektrostaticheskoy analogii [Definition of the in-terface thickness for aerodynamic stream flow round a body by the method of electrostatic analogies], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2012, No. 1 (126), pp. 192-197.
6. Paliy A.V., Zamkov E.T. Mekhanizm vozniknoveniya treniya i soprotivleniya tela v gazovom potoke [The body resistance creation mechanism by the tangential component of a gas molecule speed in a gas stream], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2012, No. 1 (126), pp. 186-191.
7. Bondarev E.H. i dr. Aerogidromekhanika [Aerohydromechanics]. Moscow: Mashinostroenie, 1993, 603 p.
8. Aerodinamika [Aerodynamics], ed. by Kalugina V.T. Moscow: MGTU im. N.E. Baumana, 2010, 687 p.
9. Belov I.A., Isaev S.A. Modelirovanie turbulentnykh techeniy: ucheb. posobie [Simulation of turbulent flows: training manual]. St. Petersburg: Balt. gos. tekhn. un-t, 2001, 143 p.
10. Garbaruk A.B. Konspekt lektsiy distsipliny «Techeniya vyazkoy zhidkosti i modeli tur-bulentnosti: metody rascheta turbulentnykh techeniy» [Lectures disciplines "viscous Flow and makes the tour bulletnose: calculation methods for turbulent flows"]. St. Petersburg, 2010, 127 p.
11. Antonov V.A., Grishin A.M., Pakhomov F.M. Vliyanie ugla ataki na sverkhzvukovoe obtekanie osesimmetrichnykh zatuplennykh tel pri nalichii vduva s poverkhnosti [The effect of angle of attack on supersonic flow over axisymmetric blunt bodies in the presence of the injection sur-face], Izvestiya AN SSSR. MZhG [A Journal of USSR Academy of Sciences. Fluid Dynamics], 1987, No. 5, pp. 95-101.
12. Antonov V.A., Gol'din V.D., Pakhomov F.M. Aerodinamika tel so vduvom [Aerodynamics of bodies with injection]. Tomsk: Izd-vo Tom. un-ta. 1990, 192 p.
13. Pakhomov F.M. Aerodinamika zatuplennogo konusa pri prostranstvennom vzaimodeystvii s nagretoy oblast'yu v sverkhzvukovom potoke v otsutstvie i pri nalichii vduva s poverkhnosti [Aerodynamics of a blunt cone with a spatial interaction with the heated region in a supersonic flow in the absence and in the presence of the injection surface], Izvestiya RAN. MZhG [A Journal of Russian Academy of Sciences. Fluid Dynamics], 2003, No. 1, pp. 147-153.
14. Nikitin G.A., Bakanov E.A. Osnovy aviatsii: ucheb. dlya vuzov grazhdanskoy aviatsii [Funda-mentals of aviation: textbook for higher educational institutions of civil aviation]. 2nd ed. Moscow: Transport, 1984, 261 p.
15. Garbuzov V.M., Ermakov A.L., Kublanov M.S., Tsipenko V.G. Aeromekhanika: ucheb. dlya studentov vuzov [Aeromechanics: a textbook for University students]. Moscow: Transport, 2000, 287 p.
16. Bochkarev A.F., Andreevskiy V.V., Belokonov V.M. i dr. Aeromekhanika samoleta: Dinamika poleta: ucheb. dlya aviatsionnykh vuzov [Aeromechanics of airplane: flight Dynamics: proc. for aviation higher education institutions], ed. by A.F. Bochkareva i V.V. Andreevskogo. 2nd ed.
– Moscow: Mashinostroenie, 1985, 360 p.
17. Kolesnikov G.A., Markov V.K., Mikhaylyuk A.A. i dr. Aerodinamika letatel'nykh apparatov: ucheb. dlya vuzov po spetsial'nosti «Samoletostroenie» [Aerodynamics of aircraft: textbook. for high schools on specialty "Aircraft"], ed. by G.A. Kolesnikova. Moscow: Mashinostroenie, 1993, 544 p.
18. Koval'nogov N.N. Pogranichnyy sloy v potokakh s intensivnymi vozdeystviyami [Boundary layer flows with intense impacts]. Ul'yanovsk: UlGTU, 1996, 246 p.
19. Kutateladze S.S., Leont'ev A.I. Teplomassoobmen i trenie v turbulentnom pogranichnom sloe [Heat and mass transfer and friction in a turbulent boundary layer]. Moscow: Energoatomizdat, 1985, 319 p.
20. Repik E.U., Sosedko Yu.P. Turbulentnyy pogranichnyy sloy. Metodika i rezul'taty turbulentnykh issledovaniy [A turbulent boundary layer. The methodology and results of turbulent research]. Moscow: Fizmatlit, 2007, 306 p.

Comments are closed.