Using the Maximum Pressure Principle for Verification of Calculation of Stationary Subsonic Flow

Authors: Anikin V.A., Vyshinsky V.V., Pashkov O.A., Streltsov E.V. Published: 20.12.2019
Published in issue: #6(129)/2019  

DOI: 10.18698/0236-3941-2019-6-4-16

Category: Aviation and Rocket-Space Engineering | Chapter: Aerodynamics and Heat Transfer Processes in Aircrafts  
Keywords: nonlinear partial differential equations, boundary value problems, Euler equations, Reynolds averaged Navier --- Stokes equations, subsonic vortex flows, subsonic maximum pressure principle

The principle of maximum pressure for subsonic stationary three-dimensional vortex flows of an ideal gas (author Sizykh G.B., 2018) is applied to verify the calculation method and its implementation on a specific computer technology. The four criteria for solution's verification are proposed. The method for obtaining flow parameters is based on solving of discrete analogs of the Navier --- Stokes system of equations on three-dimensional non-structured computational meshes. For example, there was consider the vortex tear-off flow around the fuselage of a helicopter with an empennage and landing gear at obviously insufficient computing resources. Conclusions of the feasibility of applying the author's criteria for evaluation of a particular calculation and for estimation of reliability of the results have been made


[1] Vyshinsky V.V. Exact solutions generation of shock-free flow of symmetrical profile with local supersonic region. Uchenye zapiski TsAGI, 1975, vol. 6, no. 3, pp. 1--8 (in Russ.).

[2] Vyshinsky V.V., Sizykh G.B. The verification of the calculation of stationary subsonic flows and the presentation of results. Math. Models Comput. Simul., 2019, vol. 11, no. 1, pp. 97--106. DOI: 10.1134/S2070048219010162

[3] Rowland H. On the motion of a perfect incompressible fluid when no solid bodies are present. Am. J. Math., 1880, vol. 3, no. 3, pp. 226--268. DOI: 10.2307/2369424

[4] Lamb H. Hydrodynamics. Cambridge, University Press, 1916.

[5] Hamel G. Ein allgemeiner Satz uber den Druck bei der Bewegung volumbestandiger Flussigkeiten. Monatsh. f. Mathematik und Physik., 1936, vol. 43, no. 1, pp. 345--363. DOI: 10.1007/BF01707614

[6] Serrin J. Mathematical principles of classical fluid mechanics. Berlin, Springer-Verlag, 1959.

[7] Truesdell C. Two measures of vorticity. Indiana Univ. Math. J., 1953, vol. 2, no. 2, pp. 173--217. DOI: 10.1512/iumj.1953.2.52009

[8] Shiffman M. On the existence of subsonic flows of a compressible fluid. Proc. Natl. Acad. Sci. USA., 1952, vol. 38, no. 5, pp. 434--438. DOI: 10.1073/pnas.38.5.434

[9] Bers L. Mathematical aspects of subsonic and transonik gas dynamics. Wiley, Chapman and Hall, 1958.

[10] Jeong J., Hussain F. On the identification of a vortex. J. Fluid Mech., 1995, vol. 285, pp. 69--94. DOI: 10.1017/S0022112095000462

[11] Dubief Y., Delcayre F. On coherent-vortex identification in turbulence. J. Turbul., 2000, vol. 1, art. 11. DOI: 10.1088/1468-5248/1/1/011

[12] Lesieur M., Begou P., Briand E., et al. Coherent-vortex dynamics in large-eddy simulations of turbulence. J. Turbul., 2003, vol. 4, art. 16. DOI: 10.1088/1468-5248/4/1/016

[13] Cala C.E., Fernandes E.C., Heitor M.V., et al. Coherent structures in unsteady swirling jet flow. Exp. Fluids, 2006, vol. 40, no. 2, pp. 267--276. DOI: 10.1007/s00348-005-0066-9

[14] Bosnyakov S.M., Vlasenko V.V., Engulatova M.F., et al. Programmnyy kompleks dlya sozdaniya geometrii LA, sozdaniya mnogoblochnoy 3kh mernoy raschetnoy setki, polucheniya poley techeniya pri pomoshchi resheniya sistemy uravneniy Eylera i sistemy uravneniy Nav’ye --- Stoksa, osrednennykh po vremeni i obrabotki rezul’tatov rascheta (EWT). Svidetel’stvo o gosudarstvennoy registratsii programmy dlya EVM № 2008610227 [Software package for formation of aircraft geometry, multiblock 3D grid and flow fields by solving system of time-averaged Euler and Navier --- Stokes equations and by processing calculation data (EWT). State certificate of software registration no. 2008610227].