k-kL TÜRBÜLANS MODELİNİN UYGULAMASI, DOĞRULAMASI VE GiRDAP YAKALAMA YETENEKLERİNİN DEĞERLENDİRİLMESİ

Bu çalışmada, sıkıştırılabilir akış sonlu hacimler çözücümüz üzerinde yeni bir türbülans modeli uygulamasının ilk sonuçları sunulmaktadır. k-kL türbülans modelinin tarihsel kökleri Rotta’nın iki denklemli modeline dayanmaktadır. Birkaç araştırma grubu üzerinde uzun süredir çalışmalar yapmakta ve bu model günümüzde olgunluğa erişmektedir. Geçmiş çalışmalar k-kL türbülans modelinin diğer iki denklemli türbülans modellerine göre bazı alanlarda daha iyi sonuçlar verebildiğini göstermiştir. Özellikler ters basınç gradyanlı akışlar, küt gövde arkası iz akışları ve jet etkileşimleri içeren akışlarda bu olumlu etki gözlemlenmiştir. Bu çalışma kapsamında, standart notasyonda k-kL-MEAH2015 olarak geçen k-kL türbülans modeli çözücümüze eklenmiş ve ilk testleri başlamıştır. Ses altı düz levha ve ses altı tümsekli duvar problemleri üzerinde elde edilen sonuçlar sunulmaktadır. Sonuçlar model geliştiricilerinin yayınladığı sonuçlarla örtüşmektedir. k-kL türbülans modelinin, türbülans denklemlerinin çözümü sırasında aşırı yüksek türbülans üretiminin oluşmasını engelleyerek diğer RANS modellerine göre daha iyi girdaplı akış tahminlerinin yapılmasına yardımcı olması beklenmektedir. Bu sebeple, yeni eklenen model ile ses geçiş hızlarında kanat ucu girdap problem üzerinde testler yapılmış ve Menter’in Shear Stress Transport türbülans modeline göre daha iyi sonuçlar elde edilmiştir.

Anahtar Kelimeler:

Türbülans modelleri k-kL modeli, Hesaplamalı Akışkanlar Dinamiği

IMPLEMENTATION, VERIFICATION AND ASSESSMENT OF VORTEX CAPTURING CAPABILITIES OF k-kL TURBULENCE MODEL

This study presents the first results of a new turbulence model implementation in our compressible finite volume CFD solver. The k - kL turbulence model is one of the newest two-equation models, and it is based on the ideas of Rotta’s two-equation model. Various research groups progressively develop the model, and it is maturing rapidly. Reports suggest that the k - kL turbulence model provides superior results compared to the other two-equation turbulence models in specific problems. The improved solutions are observed mainly for the flows with high adverse pressure gradients, the blunt-body wakes and jet interactions. We have implemented the k - kL model (with the standard designation of k-kL-MEAH2015) in our solver, and we are testing it rigorously. This paper presents our results on standard turbulence test cases: subsonic flat plate and subsonic wall-mounted bump. The results compare well with the reference study previously presented and published by model developers. The design of the k - kL model prevents excessive production of turbulence and dissipation; hence it preserves vortices significantly better than the other two-equation models. The implemented model is also tested with a transonic fin trailing vortex case to support this statement. Results show that the k-kL model yields considerably better results than the SST turbulence model in cases including vortices.

Keywords:

Turbulence models k-kL model, Computational Fluid Mechanics,

PDF

___

Abdol-Hamid, K. S., 2013, Assessments of-turbulence model based on Menter’s modification to Rotta’s two-equation model, AIAA Paper no: 2013-0341.
Abdol-Hamid, K. S., 2015, Assessments of k-kL turbulence model based on Menter’s modification to Rotta’s Two-equation model. International Journal of Aerospace Engineering, 987682.
Abdol-Hamid, K. S., 2019, Development of kL-based linear, nonlinear, and full Reynolds stress turbulence models. In AIAA Scitech 2019 Forum, 1878.
Abdol-Hamid, K. S., Carlson, J.-R., and Rumsey, C. L., 2016, Verification and validation of the k-kL turbulence model in FUN3D and CFL3D codes. In 46th AIAA Fluid Dynamics Conference, 3941.
Beresh, S.J., Henfling, J.F. and Spillers, R.W., 2009. Planar velocimetry of a fin trailing vortex in subsonic compressible flow. AIAA Journal, 47 (7), 1730-1740.
Beresh, S. J., Henfling, J. F., and Spillers, R. W., 2012, Turbulence of a fin trailing vortex in subsonic compressible flow. AIAA Journal, 50 (11), 2609–2622.
Dacles-Mariani, J., Zilliac, G. G., Chow, J. S., and Bradshaw, P., 1995, Numerical/experimental study of a wingtip vortex in the near field. AIAA Journal, 33(9), 1561– 1568.
DeSpirito, J., 2016, CFD validation of interaction of fin trailing vortex with downstream control surface in high subsonic flow. In 54th AIAA Aerospace Sciences Meeting, page 1546.
Egorov, Y., Menter, F., Lechner, R., and Cokljat, D., 2010, The scale-adaptive simulation method for unsteady turbulent flow predictions. part 2: Application to complex flows. Flow, Flow, Turbulence and Combustion, 85 (1), 139–165.
Launder, B. E. and Spalding, D. B., 1983, The numerical computation of turbulent flows. In Numerical prediction of flow, heat transfer, turbulence and combustion, 96–116. Elsevier.
Levy, D. W., Laflin, K. R., Tinoco, E. N., Vassberg, J. C., Mani, M., Rider, B., Rumsey, C. L., Wahls, R. A., Morrison, J. H., Brodersen, O. P., et al., 2014, Summary of data from the fifth computational fluid dynamics drag prediction workshop. Journal of Aircraft, 51 (4), 1194–1213.
Menter, F. R. and Egorov, Y., 2006, Revisiting the turbulent scale equation. IUTAM Symposium on One Hundred Years of Boundary Layer Research, 279–290, Dordrecht. Springer Netherlands.
Menter, F. R. and Egorov, Y., 2010, The scale-adaptive simulation method for unsteady turbulent flow predictions. Part 1: Theory and model description. Flow, Turbulence and Combustion, 85 (1), 113–138.
Rodi, W., 2006, Turbulence modelling for boundary-layer calculations. In IUTAM Symposium on One Hundred Years of Boundary Layer Research, 247–256. Springer.
Rotta, J., 1951, Statistische theorie nichthomogener turbulenz. Zeitschrift für Physik, 129(6), 547–572.
Rumsey, C. L., 2021, Turbulence modeling resource. https://turbmodels.larc.nasa.gov. (Accessed on 04/12/2022)
Rumsey, C.L. and Slotnick, J.P., 2015, Overview and summary of the second AIAA high-lift prediction workshop. Journal of Aircraft, 52 (4), 1006-1025.