Modeling of the unsteady aerodynamic characteristics of the NACA 0015 airfoil from the data of numerical calculations of the flow

Capa

Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Somente assinantes

Resumo

The possible application of the results of numerical modeling in developing an approximate phenomenological mathematical aerodynamic model applicable in solving the problems of dynamics is studied with reference to the example of the unsteady flow past the NACA 0015 airfoil oscillating in the angle of attack at different frequencies, amplitudes, and mean angles of attack. For this purpose, the Reynolds equations are solved in both steady and unsteady formulations, together with the k–ω-SST turbulence model. The results of the calculations are validated by means of comparing them with the experimental data. The model of the normal force and the longitudinal moment formulated within the framework of an approach introducing an internal dynamic variable is identified according to the data of calculations. The results of the modeling are compared with the numerical and experimental data. The comparison with the conventional approach to the modeling based on the linear unsteady model with the use of dynamic derivatives is also carried out.

Texto integral

Acesso é fechado

Sobre autores

К. Abramova

Zhukovski Central Aerohydrodynamic Institute (TsAGI)

Autor responsável pela correspondência
Email: kseniya.abramova@tsagi.ru
Rússia, Moscow region

D. Alieva

Zhukovski Central Aerohydrodynamic Institute (TsAGI)

Email: diana.alieva@tsagi.ru
Rússia, Moscow region

V. Sudakov

Zhukovski Central Aerohydrodynamic Institute (TsAGI)

Email: vit_soudakov@tsagi.ru
Rússia, Moscow region

А. Khrabrov

Zhukovski Central Aerohydrodynamic Institute (TsAGI)

Email: khrabrov@tsagi.ru
Rússia, Moscow region

Bibliografia

  1. Аэродинамика, устойчивость и управляемость сверхзвуковых самолетов / Под ред. Г.С. Бюшгенса. М.: Наука, Физматлит, 1998. 816 с.
  2. Greenwell D.I. A review of unsteady aerodynamic modelling for flight dynamics of manoeuvrable aircraft // AIAA 2004-5276. 2004.
  3. Goman M.G., Khrabrov A.N. State-space representation of aerodynamic characteristics of an aircraft at high angles of attack // Journal of Aircraft. V. 31. № 5. 1994. P. 1109–1115.
  4. Murphy P.C., Klein V. Transport aircraft system identification from wind tunnel data // AIAA 2008-6202. 2008.
  5. Abramov N., Khrabrov A., Vinogradov Yu. Mathematical modeling of aircraft unsteady aerodynamics at high incidence with account of wing — tail interaction // AIAA 2004-5278. 2004.
  6. Jategaonkar R., Fischenberg D., Gruenhagen W. Aerodynamic modeling and system identification from аlight data — recent applications at DLR // Journal of Aircraft. V. 41. № 4. 2004. P. 682–691.
  7. Brandon J.M., Morelli E.A. Real-time onboard global nonlinear aerodynamic modeling from flight data // AIAA 2014-2554. 2014.
  8. Srinivasan G.R., Ekaterinaris J.A., McCroskey W.J. Evaluation of Turbulence Models for Unsteady Flows of an Oscillating Airfoil // Computers & Fluids. 1995. V. 24. № 7. P. 833–861.
  9. Ekaterinaris J.A., Platzer M.F. Computational Prediction of Airfoil Dynamic Stall, S0376-0421(97)00012-2 // Prog. Aerospace Sci. 1997. V. 33. P. 759–846.
  10. Wang S., Ingham D.B., Ma L., Pourkashanian M., Tao Z. Turbulence modeling of deep dynamic stall at relatively low Reynolds number // Journal of Fluids and Structures. 2012. V. 33. P. 191–209.
  11. Wang S., Ingham D.B., Ma L., Pourkashanian M., Tao Z. Numerical investigations on dynamic stall of low Reynolds number flow around oscillating airfoils // Computers and Fluids. 2010. V. 39. № 9. P. 1529–1541.
  12. Menter F.R. Zonal two equation k–ω turbulence models for aerodynamics flows // AIAA Paper, 93-2906. 1993.
  13. Menter F.R., Kuntz M., Langtry R. Ten Years of Industrial Experience with the SST Turbulence Model // 4th International Symposium of Turbulence, Heat and Mass Transfer. 2003.
  14. Martinat G., Braza M., Hoarau Y., Harran G. Turbulence modelling of the flow past a pitching NACA 0012 airfoil at 105 and 106 Reynolds Numbers // Journal of Fluids and Structures. 2008. V. 24. P. 1294–1303.
  15. Kasibholta V.R., Tafti D. Large Eddy Simulation of the Flow past Pitching NACA 0012 Airfoil at 105 Reynolds Number // Proceedings of the ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting, FEDSM 2014-21588. 2014.
  16. Szydlowski J., Costes M. Simulation of flow around a static and oscillating in pitch NACA 0015 airfoil using URANS and DES // Proceeding of ASME 2004 Heat Transfer / Fluids Engineering Summer Conference. American Society of Mechanical Engineers. 2004. P. 891–908.
  17. Coton F.N., Galbraith R.A.M. An Experimental Study of Dynamic Stall on a Finite Wing // The Aeronautical Journal. 1999. V. 103. № 1023. P. 229–236.
  18. Piziali R.A. An experimental investigation of 2D and 3D oscillating wing aerodynamics for a range of angle of attack including stall // NASA Technical Memorandum 4632-1993. 1993.
  19. Schreck S.J., Helin H.F. Unsteady Vortex Dynamics and Surface Pressure Topologies on a Finite Wing // Journal of Aircraft. 1994. V. 31. № 4. P. 899–907.
  20. Храбров А.Н. Неединственность ламинарного отрывного обтекания профиля под углом атаки в схеме Кирхгофа // Ученые записки ЦАГИ. 1985. Т. XVI. № 5.
  21. Колинько К.А., Храбров А.Н. Математическое моделирование нестационарной подъемной силы крыла большого удлинения в условиях срыва потока.// Ученые записки ЦАГИ. 1998. Т. XIX. № 3-4.
  22. Khrabrov А., Ol M. Effects of flow separation on aerodynamic loads in linearized thin airfoil theory // Journal of Aircraft. 2004. V. 41. № 4.
  23. Храбров А.Н. Использование линейной теории кавитации для математического моделирования отрывного обтекания профиля с конечной зоной отрыва // Ученые записки ЦАГИ. 2001. Т. XXXII. № 1-2.

Arquivos suplementares

Arquivos suplementares
Ação
1. JATS XML
Baixar
2. Fig. 1. Comparison of the dependence of the normal force coefficient on the angle of attack of the Cy(α)-profile for experimental and numerical results with different turbulence models for a stationary wing profile: 1 — experiment, section y/L = 0.5, 2 — experiment, section y/L = 0.263, 3 — S–A turbulence model, 4 — k–ω-SST turbulence model; M = 0.29.

Baixar (107KB)
Metadados
3. Fig. 2. Comparison of the dependence of the normal force coefficient Cy(α) on the profile attack angle for experimental and numerical results with different turbulence models for an oscillating profile α0 = 10.88°, Δα = 4.22°, f = 10.1 Hz: 1 — experiment, section y/L = 0.5, 2 — experiment, section y/L = 0.263, 3 — S–A turbulence model, 4 — k–ω-SST turbulence model; M = 0.29.

Baixar (104KB)
Metadados
4. Fig. 3. Comparison of the dependence of the normal force coefficient on the angle of attack Cy(α) and the pitching moment coefficient mz(α) of the profile for numerical results: 1 — flow around a stationary profile, oscillations with amplitude Δα = 4°, frequency f = 2 Hz and different average angles of attack α0: 2 — α0 = 0, 3 — α0 = 4°, 4 — α0 = 8°, 5 — α0 = 12°, 6 — α0 = 16°; M = 0.1428.

Baixar (176KB)
Metadados
5. Fig. 4. Comparison of the dependence of the normal force coefficient on the angle of attack Cy(α) and the pitching moment coefficient mz(α) of the profile for numerical results at a, b –α0 = 4; c, d — α0 = 11°: 1 — flow around a stationary profile, oscillations with amplitude Δα = 8 and different frequencies: 2 — f = 0.5 Hz, 3 — f = 1 Hz, 4 — f = 2 Hz; M = 0.1428.

Baixar (442KB)
Metadados
6. Fig. 5. Dependences of Cy, mz and xs on α. ​​1 — Kirchhoff solution, 2 — static CFD calculations (markers), 3 — Kirchhoff approximation, 4 — approximation for non-separated flow, 5 — approximation for fully separated flow.

Baixar (130KB)
Metadados
7. Fig. 6. Results of identification of parameters of the mathematical model, α0 = 8°, Δα = 11°, f = 2 Hz. 1 — statics, 2 — without taking into account the linear term, 3 — taking into account the linear term, 4 — results of CFD calculation, 5 — static change of the internal variable, 6 — dynamic change of the internal variable.

Baixar (275KB)
Metadados
8. Fig. 7. Dynamic change of Cy, mz, xs, Δx for harmonic oscillations with α0 = 8°, Δα = 11° and frequencies f = 0.5, 1 Hz.

Baixar (257KB)
Metadados
9. Fig. 8. Dynamic change of Cy, mz, xs, Δx for harmonic oscillations with α0 = 12°, Δα = 4° and frequencies f = 0.5, 1, 2 Hz.

Baixar (227KB)
Metadados
10. Fig. 9. Dynamic change of Cy, mz, xs, Δx for harmonic oscillations with α0 = 16°, Δα = 4° and frequencies f = 0.5, 1, 2 Hz.

Baixar (299KB)
Metadados
11. Fig. 10. Dynamic change of Cy, mz, xs, Δx for harmonic oscillations with α0 = 11°, Δα = 9° and frequencies f = 0.5, 1, 2 Hz.

Baixar (320KB)
Metadados
12. Fig. 11. Dynamic change of Cy, mz for harmonic oscillations: a) α0 = 10.88°, Δα = 4.22° and frequency f = 10.1 Hz, b) α0 = 15.04°, Δα = 4.16° and frequency f = 10.05 Hz.

Baixar (207KB)
Metadados
13. Fig. 12. Comparison of the calculated value of xs0 and Cy with the Kirchhoff solution: 1 - CFD calculation, 2 - approximation using the Kirchhoff formula, 3 - approximation using the Kirchhoff formula with xs0 from the calculation, 4 - xs0 from the calculation.

Baixar (79KB)
Metadados
14. Fig. 13. Modeling of Cy, mz for small-amplitude oscillations (a), aerodynamic derivatives of mz (c), modeling of small-amplitude oscillations using aerodynamic derivatives (b).

Baixar (304KB)
Metadados

Declaração de direitos autorais © Russian Academy of Sciences, 2024