The effect of the computational mesh while mathematical modeling of the inflow of a subsonic flow onto the profile of a perspective blade with a deflectable trailing edge in a three-dimensional setup

Aeronautical and Space-Rocket Engineering

Thermal engines, electric propulsion and power plants for flying vehicles


Sha M. *, Agul'nik A. В.**, Yakovlev A. A.***

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia



In the last decade, much attention has been paid to the studies conducted in the interests of mathematical modeling methods developing in 3D setup. It requires a detailed study of various computational meshes constructing methods and their effect on the obtained results.

The problem of the aerodynamic characteristics computation of the of a perspective blade with deflectable trailing edge profile is important for both the development of wind turbine blades, compressor design for advanced gas turbine engines, and aircraft structures.

The effect of the computational mesh is studied while mathematical modeling of the inflow of a subsonic flow onto the profiles of a perspective blade with a deviating trailing edge. Verification, the convergence and correctness checkup of the solutions obtained, as well as verification on tasks having reliable and detailed enough solutions are necessary.

The objectives of this article are as follows: determining the accuracy of the numerical solution of the aerodynamic profile of the perspective blade with the deflected trailing edge, and testing the computational mesh with the potential to achieve industrial applicability. The feature in common is the use of wall-adjacent blocks adapted to geometry, applying herewith various approaches for their coupling with the external mesh. Analysis of the solvers application employing the Cartesian mesh reveals also the necessity of constructing mesh layers adapted to the surface of the body.

Analysis of existing designs allows us to draw the following conclusions. A simple deflectable trailing edge increases the lifting force by increasing the curvature of the profile. This increases the pressure on the lower surface of the profile, as well as increases its load-bearing properties.

A mathematical model of the aerodynamic processes occurring on the profile surface of a perspective blade from the back deflected edge while its on flowing by a subsonic flow is suggested.

An acceptable correlation of the results of the calculations made using structured and hybrid meshes circuits was obtained. Analysis of the results of numerical simulation employing various meshes revealed that application the meshes under consideration considered allows obtain close results. The structured meshes applied herewith consume less computation time. Hence, we will use the structured meshes as the best way to solve the problem.

Thus, the proposed mathematical model and the first method of developing the mesh can be applied to determine the numerical solution accuracy of the problem of flow past the aerodynamic profile of a perspective blade or wing with a deflectable trailing edge, as well as the mesh testing


comparison, Ansys, ICEM-Fluent, hybrid and striated meshes, aerodynamic coefficients Суа & Сха, aerodynamic quality Kae, deflectable trailing edge


  1. Artamonov B.L., Moizykh E.I., Ivchin V.A. Vestnik Moskovskogo aviatsionnogo instituta, 2010, vol. 17, no. 4, pp. 5-16.

  2. Baskin V.E., Vil'dgrube L.S., Vozhdaev E.S., Maikapar G.I. Teoriya nesushchego vinta (Theory of the rotor), Moscow, Mashinostroenie, 1973, 364 p.

  3. Johnson W. Helicopter theory. Dover Publications, 1994, 1120 p.

  4. Belotserkovskii S.M., Loktev B.E., Nisht M.I. Issledovanie na EVM aerodinamicheskikh i aerouprugikh kharakteristik vintov vertoletov (A computer study of the aerodynamic and aeroelastic characteristics of helicopter propellers), Moscow, Mashinostroenie, 1992, 218 p.

  5. Leishman J.G. Principles of Helicopter Aerodynamics. New York, Cambridge University Press, 2006, 864 p.

  6. Vershkov V.A., Voronich I.V., Vyshinskii V.V. Trudy MAI, 2015, no. 82, available at:

  7. Golovkin V.A., Mirgazov R.M. Nauchnyi vestnik MGTU GA, 2010, no. 154, pp. 34-41.

  8. Ignatkin Yu.M., Makeev P.V., Shomov A.I. Trudy MAI,2010, no. 38, available at:

  9. Hariharan N., Sankar L. A Review of Computational Techniques for Rotor Wake Modeling. AIAA Paper,2000, vol. 114.

  10. Boelens O.J., van der Ven H., Oskam B. and Hassan A.A. Accurate and Efficient Vortex-Capturing for a Helicopter Rotor in Hover. 26th European Rotorcraft Forum, The Hague, the Netherlands, September 26-29, 2000, 32 p.

  11. Steijl R., Barakos G., Badcock K. A framework for CFD analysis of helicopter rotors in hover and forward flight. International Journal for Numerical Methods in Fluids. 2006, vol. 51, issue 8, pp. 819-847.

  12. Im Dong-Kyun, Wie Seong-Yon g, Kim Eugene, Kwon Jang-Hyuk, Lee Duck-Joo, Chung Ki-Hoon, Kim Seung-Bum Aerodynamic Analysis of Rotor Blades using Overset Mesh with Parallel Computation. Parallel Computational Fluid Dynamics 2008. Conference proceedings, vol. 74, pp. 101-110.

  13. Ignatkin Yu.M., Konstantinov S.G. Trudy MAI, 2012, no. 57, available at:

  14. Ignatkin Yu.M., Konstantinov S.G. Trudy MAI, 2012, no. 57, available at:

  15. Yu Yong, Zhang Junming, Jiang Liantian. Introductory and advanced course of FLUENT. Beijing, Beijing Institute of Technology Press, 2008, 292 p.

  16. Doerffer P., Szulc O. Numerical simulation of model helicopter rotor in hover. Task Quarterly, 2008, vol. 12, no. 3, pp. 227-236.

  17. Kozelkov O.A. Vestnik Moskovskogo aviatsionnogo instituta, 2014, vol. 21, no. 2, pp. 175-180.

  18. Menter F.R. Zonal Two Equation k-ω Turbulence Models for Aerodynamic Flows. AIAA Paper, 1993, 2906.

  19. Volkov K.N., Emel'yanov V.N. Techenie i teploobmen v kanalakh i vrashchayushchikhsya polostyakh (Flow and heat transfer in channels and rotating cavities), Moscow, Fizmalit, 2010, 488 p.

  20. Wood W.A., Eberhardt S. Dual-Co de Solution Strategy for Chemically-Reacting Hypersonic Flows. AIAA Paper. 1995, 0158, 16 p.

  21. Widhopf G.F., Wang J.C.T. A TVD Finite-Volume Technique for Nonequilibrium Chemically Reacting Flows. AIAA Paper, 1988, no. 2711. — informational site of MAI

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