γ Türbülans Geçiş Modelinin Kuvvet Katsayıları ve Geçiş Yer Tahmini Üzerindeki Etkisi

Year 2022, , 44 - 63, 13.01.2023

Hediye Atik

https://doi.org/10.54926/gdt.1131963

Abstract

Bu çalışmada, γ türbülans geçiş modelinin (çapraz akış etkisinin dahil edildiği ve edilmediği versiyonları kullanılarak) 6:1 uzatılmış küremsi geometri üzerinde düzensiz çözüm ağı kullanılarak 6.5 x 106 Reynolds sayısında ve 5o hücum açısında başarım değerlendirmesi amaçlanmaktadır. γ türbülans geçiş modelinin performans değerlendirmesi halihazırda mevcut deneysel veri sonuçları kullanılarak yapılmış ve SST k-ω türbülans modeli ve en popüler türbülans geçiş modeli olan γ-〖Re〗_θ modeli sonuçları ile karşılaştırılmıştır. Türbülans geçiş modelinin etkisi eksenel kuvvet katsayısı, normal kuvvet katsayısı, yüzey basınç katsayısı ve yüzey sürtünme katsayısı kullanılarak gösterilmiştir. Eksenel ve normal kuvvet katsayıları etrafındaki ayrıklaştırmadan kaynaklı belirsizlik bandı üç farklı çözüm ağıyla Grid Convergence Index (GCI) metodu kullanılarak elde edilmiştir. γ türbülans geçiş modeli, kuvvet katsayılarını akışın tamamıyla türbülanslı olması kabulüyle yapılan analizlere göre daha büyük GCI değerleriyle %58 daha az tahmin etmiştir. Söz konusu model yüzey basınç katsayılarında fazla değişiklik yaratmazken, yüzey sürtünme katsayılarında önemli farklılıklar görülmüştür. Akışın tümüyle türbülanslı olduğu kabulü ile yapılan analizlerde gövde üzerinde sürtünme kaysayısında önemli değişiklikler görülmezken γ geçiş modeli, geometrinin üst yüzeyinde türbülans geçisine işaret eden önemli farklılıklar yakalamaktadır. Diğer yandan, deneysel sonuçların tersine, analizlerde geometrinin alt yüzeyinde türbülans geçişine dair hiçbir işaret görülmemektedir. Sonuç olarak, γ türbülans geçiş modeli türbülans geçiş bölgesi geometrisini tamamıyla doğru tahmin edememektedir. Bunun yanı sıra, γ türbülans geçiş modelinin, γ-〖Re〗_θ türbülans geçiş modeline göre yüzey çözüm ağı büyüklüğüne daha hassas olduğu tespit edilmiştir. Bu geçiş modelinin bir diğer dezavantajı da çözümleme zamanıdır. γ türbülans geçiş modeli, γ-〖Re〗_θ geçiş modeline göre daha basit olmasına rağmen, kuvvet katsayılarında daha yavaş iterasyon yakınsama oranına sahip olması sebebiyle hesaplaması yaklaşık 3.8 kat daha fazla zaman almıştır. Çapraz akış etkisinin γ türbülans geçiş modeline dahil edilmesi, geçiş bölge geometrisini, geometrinin üst tarafında genişletse de alt tarafında halen türbülans geçişi oluşturmamaktadır. Bunun yanı sıra modelde kullanılan çapraz akış eklentisi çözümleme zamanını fazla değiştirmemiştir.

Keywords

laminar türbülans geçişi, γ geçiş modeli, grid convergence index, ayrıklaştırma belirsizliği, 6: 1 uzatılmış küremsi geometri, discretization uncertainty error, 6:1 prolate spheroid

Supporting Institution

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Project Number

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Thanks

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Effect of γ Transition Model on Force Coefficients and Transition Location Estimations

Abstract

This study aims to evaluate the performance of γ transition model (versions with and without crossflow instability extension) using unstructured mesh on 6:1 prolate spheroid at 6.5 x 106 Reynolds number and 5o angle of attack. The performance of γ transition model is evaluated by an available experimental study and compared with the results of SST k-ω turbulence model, and γ-〖Re〗_θ transition model, which is the most popular transition model. The effect of transition model is shown with axial force, normal force, surface pressure and surface friction coefficients. The grid convergence index (GCI) study is performed with three different mesh levels for axial and normal force coefficients to find out the discretization uncertainty band around them. The γ transition model estimates force coefficients, approximately 58% less than fully turbulent results with higher GCI values. While transition models do not much change the surface pressure coefficients, the significant differences are seen in the surface friction coefficients. While there are not seen any dramatic changes in surface friction coefficients with fully turbulent analyses, this model captures drastic changes in the surface friction coefficients at the top surface which are sign of the transition locations. On the other hand, there is no sign of any transition phenomenon at the spheroid bottom, contrary to the observations of experimental measurements. Therefore, the γ transition model is not able to estimate the complete transition front geometry correctly. In addition, γ transition model is more sensitive to the surface mesh size with respect to γ-〖Re〗_θ transition model. The solution time is another disadvange of γ transition model. Even though the model has more simpler than the γ-〖Re〗_θ transition model, the computation time took 3.8 times more, since the iteration convergence rate of force coefficients is slower than the convergence rate of γ-〖Re〗_θ transition model solution. Eventhough including the crossflow extension into γ transition model enlarges the transition region on the top of the geometry, it does not still create transition at the bottom. In addition, crossflow extension does not change the solution time.

Keywords

laminar turbulent transition, γ transition model, discretization error, grid convergence index, discretization uncertainty error, 6:1 prolate spheroid

Project Number

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References

• Atik, H. (2022). Estimation of Discretization Uncertainty using the γ-Reθ Transition Model for Transitional Flows on 6:1 Spheroid. ASME Journal of Fluids Engineering. Accepted Manuscript. DOI: 10.1115/1.4054740
• Boiko, A. V., Kirilovskiy, S. V., Maslov, A. A., and Poplavskaya, T. V. (2015). Engineering Modelling of the Laminar-Turbulent Transition: Acheivements and Problems (Review). Journal of Applied Mechanics and Technical Physics, Vol. 56, No. 5, pp. 761–776. DOI: 10.1134/S002189441505003X.
• Celik, I.B., Ghia, U., Roache, P. J., Freitas, C. J., Coleman, H., and Raad, P. E. (2008). Procedure for Estimation and Reporting of Uncertainity Due to Discretization in CFD Applications. Journal of Fluids Engineering, Vol. 130, pp. 078001-1-4.
• Charnay, G., Comte-Bellot, G., Mathiew, J. (1971). Development of a Turbulent Boundary Layer on a Flat Plate in an External Turbulent Flow. AGARD CP93, Paper No. 27.
• Coder, J., Maughmer, M. (2012, January). One-equation transition closure for eddy-viscosity turbulence models in CFD. In 50th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition (p. 672).
• Coder J.G., Maughmer M.D. (2014). Comparisons of Theoretical Methods for Predicting Airfoil Aerodynamic Characteristics. Journal of Aircraft, Vol. 51, No. 1, pp. 183-191. DOI: 10.2514/1.C032232.
• Dassler, P., Kozulovic, D., & Fiala, A. (2012). An Approach for Modelling the Roughness-Induced Boundary Layer Transition using Transport Equations. In Europ. Congress on Comp. Methods in Appl. Sciences and Engineering, ECCOMAS.
• Eca L., Hoekstra M. (2008). The Numerical Friction Line. Journal of Marine Science and Technology, Vol. 13, No.4, pp. 328-345. DOI: 10.1007/s00773-008-0018-1.
• Grabe, C., and Krumbein, A. (2013). Correlation-Based Transition Transport Modeling for Three-Dimensional Aerodynamic Configuration. J. Aircr., 50(5), pp. 1533–1539.10.2514/1.C032063.
• Hancock, P. E., and Bradshaw, P. (1983). The Effect of Free Stream Turbulence Level in Turbulent Boundary Layers. Journal of ASME Engineering, Vol. 105, No. 3, pp. 284-289. DOI: 10.1115/1.3240989.
• Kreplin, H. P., Vollmers, H., Meier, H. U. (1985). Wall Shear Stress Measurements on an Inclined Prolate Spheroid in the DFVLR 3m x 3m Low Speed Wind Tunnel, Gottingen. DFVLR-AVA, Report No. IB 222-84 A 33.
• Krumbein, A., Krimmelbein, N., Grabe, C., and Shengyang, N., (2015). Development and Application of Transition Prediction Techniques in an Unstructured CFD Code. AIAA 2015-2476, AIAA Aviation 45th AIAA Fluid Dynamics Conference, Dallas, TX, 22-26 June 2015. DOI: 10.2514/6.2015-2476.
• Langtry, R. B,. and Menter, F. R. (2009). Correlation-Based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes. AIAA Journal, Vol. 47, No. 12, pp. 2894–2906. DOI: 10.2514/1.42362.
• Lopes, R., Eca, L., Vaz, G., and Kerkvliet, M. (2021). Assessing Numerical Aspects of Transitional Flow Simulations Using the RANS Equations. International Journal of Computational Fluid Dynamics, Vol. 135, No. 3, pp. 157-178. DOI: 10.1080/10618562.2020.1870962.
• Meier, H. U., and Kreplin, H. P. (1980). Influence on Free-Stream Turbulence on the Boundary Layer Development. AIAA Journal, Vol. 18, No. 1, pp. 11-15. DOI:10.2514/3.50724.
• Meier, H. U., Michel, U., and Kreplin, H.P. (1986). The Influence of Wind Tunnel Turbulence on the Boundary Layer Transition. DFVLR-AVA, Report No. IB 222-86 A 39.
• Menter, F. R, Langtry, R. B., Likki, Y. B., Suzen, Y. B., Huang, P. G. and Volker, S. (2006). A Correlation-Based Transition Model Using Local Variables: Part I — Model Formulation. Journal of Turbomachinery, 128(3), pp. 412-422. DOI: 10.1115/1.2184352.
• Menter, F. R. (1994).Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications. AIAA Journal, Vol. 32, No. 8, pp. 1598–1605. DOI: 10.2514/3.12149.
• Menter, F. R., Smirnov, P. E., Liu, T., Avancha, R. (2015). A One-Equation Local Correlation-Based Transition Model. Flow, Turbulence and Combustion,95(4), 583-619.DOI: 10.1007/s10494-015-9622-4.
• Pasquale, D. D., Rona, A., and Garrett, S. J. (2009). A Selective Review of CFD Transition Models. 39th AIAA Fluid Dynamics Conference, San Antonio, Texas, AIAA Paper 2009-3812. DOI: 10.2514/6.2009-3812.
• Phillips, T. S., and Roy, C. J., 2014, "Richardson extrapolation-based discretization uncertainty estimation for computational fluid dynamics." Journal of Fluids Engineering Vol. 136 No. 12, pp. 21401-1-10. DOI: 10.1115/1.4027353.
• Schlichting, H., and Gersten, K., (2000). “Boundary-Layer Theory”, 8th ed., Springer-Verlag, Berlin, Heidelberg. ISBN: 3540662707
• Sengupta, T. K., (2012). “Instabilities of Flows and Transition to Turbulence”, CRC Press, Boca Raton. ISBN: 9780429066481.
• Seyfert, C. (2011). Application of a Transition Transport Model to Industrially Relevant Aerodynamic Configurations. ODAS 2011 – 11th ONERA-DLR Aerospace Symposium, 8-10 February 2011, Toulouse, France, Conference Proceedings, pp. 1-8.
• Seyfert, C., Krumbein, A. (2012, January). Correlation-Based Transition Transport Modeling For Three-Dimensional Aerodynamic Configurations. In 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition (p. 448).
• Seyfert, C., Krumbein, A. (2012). Evaluation of a Correlation-based Transition Model and Comparison with the eN-Method. Journal of Aircraft, Vol. 49, No. 6, pp. 1765-1773. DOI: 10.2514/1.C031448.
• Seyfert, C., and Krumbein, A. (2013). Comparison of a Local Correlation-Based Transition Model with a eN-Method for Transition Prediction. New Results in Numerical and Experimental Fluid Mechanics VIII, Vol. 121, Springer, Berlin, Heidelberg, pp. 541-548. DOI: 10.1007/978-3-642-35680-3_64.
• Vaz, G., Jaouen, F., and Hoekstra, M. (2009). Free-Surface Viscous Flow Computations: Validation of URANS Code FreSCo. 28th International Conference on Ocean, Offshore and Arctic Engineering, Vol. 43451, 2009, pp. 425–437. DOI: 10.1115/OMAE2009-79398.
• Wauters, J., and Degroote, J. (2018). On the Study of Transitional Low-Reynolds Number Flows over Airfoils Operating at High Angles of Attack and Their Prediction Using Transitional Turbulence Models. Progress in Aerospace Sciences, Vol. 103, pp. 52–68. DOI: 10.1016/j.paerosci.2018.10.004.