Large Eddy Simulation of Turbulent Rayleigh-Bénard Convection: An Assessment of Subgrid-Scale Models

Year 2021, Volume: 21 Issue: 2, 478 - 495, 30.04.2021

İlyas Yılmaz

https://doi.org/10.35414/akufemubid.856768

Cited By: 1

Abstract

Large eddy simulation of turbulent Rayleigh-Bénard convection was carried out to assess various algebraic eddy viscosity subgrid-scale models: (i) Smagorinsky with Wall-Damping, (ii) Dynamic Smagorinsky, (iii) Wall-Adapting Local Eddy-Viscosity, (iv) Vreman, (v) Mixed-Scale, and (vi) a buoyancy-modified Mixed-Scale model that accounts for the buoyancy effects from subgrid-scales. The last model is proposed for the first time in this study. Non-dissipative, kinetic energy conserving, fully implicit method was employed for simulations. To evaluate the models, mean and turbulent (both low- and high-order) flow diagnostics were computed. Some advanced turbulent statistics such as skewness, turbulent heat flux, subgrid-scale kinetic energy and Nusselt number were also calculated and compared with each other and against a reference solution. Since models differ from each other by means of turbulent generation terms, they have their own strengths and weaknesses which are particularly observed in the near-wall treatments. Additionally, unlike the others, the Dynamic Smagorinsky model computes the subgrid-scale viscosity coefficient dynamically which has some effects on results. Overall, the Mixed-Scale and its new, buoyancy-modified variant show different characteristics and mostly the best agreement with Direct Numerical Simulation data. They are also found computationally less expensive. Moreover, buoyancy enhancement in the new model slightly improves the predictions of Mixed-Scale model. Although relatively poor performance by the Dynamic Smagorinsky model is observed especially in estimating the integrated Nusselt number, it captures the turbulent heat flux more accurately than the others. A more detailed discussion on the model's performance based on evaluations are also made.

Keywords

computational fluid dynamics, Turbulence modeling, Large eddy simulation, subgrid-scale models, Rayleigh-Bénard convection, Turbulent convection

Türbülanslı Rayleigh-Bénard Taşınım Probleminin Büyük Girdap Benzetimi: Ağaltı-ölçek Modellerinin Değerlendirilmesi

Abstract

Bu çalışmada türbülanslı Rayleigh-Bénard ısıl taşınım problemi büyük girdap benzetimi metodu ile 6 farklı ağaltı-ölçek modeli kullanılarak gerçekleştirilmiştir. Bu modeller; (i) Smagorinsky (duvar sönümleme fonksiyonu da içeren), (ii) Dinamik Smagorinsky, (iii) Wall-Adapting Local Eddy-Viscosity, (iv) Vreman, (v) Mixed-Scale, ve (vi) ilk defa bu çalışmada önerilen ve ağaltı ölçeklerden gelen türbülanslı kaldırma kuvveti etkilerini de içerecek şekilde, terimleri yeniden düzenlenmiş ve zenginleştirilmiş olan değiştirilmiş-Mixed-Scale modelidir. Benzetimlerde sönümleme içermeyen, kinetik enerjiyi koruyan ve zamanda tamamıyla kapalı bir sayısal ayrıklaştırma algoritması kullanılmıştır. Modellerin değerlendirilmesi için, akışın ortalama ve türbülanslı büyüklükleri (hem düşük hem de yüksek mertebeli) hesaplanmıştır. Ayrıca, asimetri, türbülanslı ısı akısı, ağaltı-ölçek kinetik enerjisi ve Nusselt sayısı gibi ilave pek çok ileri seviye, türetilmiş türbülans parametresi de hesaplanmış ve karşılaştırmalarda kullanılmıştır. Bunlara ilişkin detaylı analizlere bu kapsamlı çalışmada yer verilmiştir. Elde edilen sonuçlar, her modelin zayıf ve güçlü yanlarını ortaya çıkarmıştır. Modeller arası farklılıkların özellikle duvara yakın bölgelerde kendini gösterdiği ortaya konmuştur. Genel olarak, Mixed-Scale ve ona dayalı olarak önerilen yeni modelin performanslarının, Doğrudan Sayısal Benzetim metodu ile daha iyi bir uyum içerisinde olduğu gözlemlenmiştir. Bu iki model ayrıca daha kısa sürede sonuç vermesi sebebiyle de sayısal hesaplama maliyeti açısından avantajlıdır. Kaldırma kuvveti etkilerini de içeren yeni modele ait sonuçlarının asıl modele oranla görece bir iyileşme içerdiği de görülmektedir.

Keywords

Hesaplamalı Akışkanlar Dinamiği, Türbülans Modellemesi, Büyük Girdap Benzetimi, Ağ-altı Ölçek Modeli, Rayleigh-Bénard Taşınımı, Türbülanslı taşınım

References

• Balay, S., W. D. Gropp, L. C. McInnes, and B. F. Smith., 1997. Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries. Modern Software Tools for Scientific Computing, edited by E Arge, A. M. Bruaset, and H. P. Langtangen, Birkhäuser, 163–202.
• Chung, D., and G. Matheou., 2014. Large-Eddy Simulation of Stratified Turbulence. Part I: A Vortex-Based Subgrid-Scale Model. Journal of the Atmospheric Sciences 71 (5), 1863–79
• Dabbagh, F., F. X. Trias, A. Gorobets, and A. Oliva., 2016. “New Subgrid-Scale Models for Large-Eddy Simulation of Rayleigh-Bénard Convection. Journal of Physics: Conference Series 745, 032041.
• Eidson, T. M., 1985. Numerical Simulation of the Turbulent Rayleigh–Bénard Problem Using Subgrid Modelling. Journal of Fluid Mechanics 158, 245–68
• Getling, A. V. 1998. Rayleigh-Bénard Convection: Structures and Dynamics. Vol. 11, World Scientific, 9-26.
• Gray, D. D., and A. Giorgini., 1976. The Validity of the Boussinesq Approximation for Liquids and Gases. International Journal of Heat and Mass Transfer 19 (5), 545–51
• Hou, Y., and K. Mahesh., 2005. A Robust, Colocated, Implicit Algorithm for Direct Numerical Simulation of Compressible, Turbulent Flows. Journal of Computational Physics 205 (1), 205–21.
• Kerr, R. M., 1996. Rayleigh Number Scaling in Numerical Convection. Journal of Fluid Mechanics 310, 139–79.
• Moeng, C.-H. and Rotunno, R., 1990. Vertical-velocity skewness in the buoyancy-driven boundary layer. Journal of Atmospheric Science. 47, 1149-1162.
• Nicoud, F., and F. Ducros., 1999. Subgrid-Scale Stress Modelling Based on the Square of the Velocity Gradient Tensor. Flow, Turbulence and Combustion 62(3), 183–200.
• Peng, S.-H., and L. Davidson., 1998. Comparison of Subgrid-Scale Models in LES for Turbulent Convection Flow with Heat Transfer. 2nd EF Conference in Turbulent Heat Transfer 1, 5.24-5.35.
• Peng, S.-H., K. Hanjalic, and L. Davidson., 2006. Large-Eddy Simulation and Deduced Scaling Analysis of Rayleigh–Bénard Convection up to Ra = 109. Journal of Turbulence 7: N66
• Pope, S. B., 2000. Turbulent Flows. Cambridge University Press, 182-263.
• Ranjan, R., M. K. Venkataswamy, and S. Menon., 2020. Dynamic One-Equation-Based Subgrid Model for Large-Eddy Simulation of Stratified Turbulent Flows. Physical Review Fluids 5 (6), 064601.
• Sagaut, P., 1996. Simulations of Separated Flows with Subgrid Models. La Recherche Aerospatiale, 1, 51–63
• Sagaut, P., 2001. Large Eddy Simulation for Incompressible Flows: An Introduction. Springer-Verlag, 31-61.
• Silano, G., K. R. Sreenivasan, and R. Verzicco., 2010. Numerical Simulations of Rayleigh–Bénard Convection for Prandtl Numbers between 10-1 and 104 and Rayleigh Numbers between 105 and 109. Journal of Fluid Mechanics 662, 409–46.
• Smagorinsky, J., 1963. General Circulation Experiments with the Primitive Equations: I. The Basic Experiment. Monthly Weather Review 91 (3), 99–164.
• Vreman, A. W., 2004. An Eddy-Viscosity Subgrid-Scale Model for Turbulent Shear Flow: Algebraic Theory and Applications. Physics of Fluids 16 (10), 3670–81.
• Wörner, M., 1994. Direkte Simulation turbulenter Rayleigh- Benard-Konvektion in flüssigem Natrium, PhD Thesis, Karlsruher Institut für Technologie, Karlsruhe, 222.
• Yang, K.-S., and J. H. Ferziger., 1993. Large-Eddy Simulation of Turbulent Obstacle Flow Using a Dynamic Subgrid-Scale Model. AIAA Journal 31 (8), 1406–13.
• Yilmaz, I., H. Saygin, and L. Davidson., 2018. Application of a Parallel Solver to the LES Modelling of Turbulent Buoyant Flows with Heat Transfer. Progress in Computational Fluid Dynamics, an International Journal 18 (2), 89–107