Review on the implementation of rotation/curvature correction function in the RANS model in predicting highly swirling flows

The implementation of rotation and curvature correction functions in Reynolds-Averaged Navier-Stokes (RANS) models has significantly enhanced the accuracy of turbulence predictions in complex flows, which contains strong curvature or system rotation. The conventional turbulence models, i.e. k-?, k-?, Spalart-Allmaras and k-? SST, have limitations in accurately capturing the flow phenomena influenced by system rotation and streamline curvature. To overcome these deficiencies, various modifications have been proposed, including the Spalart-Shur and Smirnov-Menter corrections, which have been applied to eddy-viscosity models (EVMs). This review paper provides a comprehensive overview of the development, implementation, and performance of rotation/curvature corrections in RANS models, with a focus on their application to swirling flow such as cyclone separators and curved channels. By comparing results of the modified EVMs and conventional models against experimental and direct numerical simulation (DNS) data, this study highlights the impact of these corrections on improving the model accuracy while maintaining convenient computational cost. The results showed that modified provide a practical balance between numerical accuracy and computational cost, particularly in industrial applications that involve highly swirling flow or strong curvatures. 

F. R. Menter, M. Kuntz, R. Langtry and others, "Ten years of industrial experience with the SST turbulence model," Turbulence, heat and mass transfer, vol. 4, p. 625–632, 2003.

[2]           G. Gronald and J. J. Derksen, "Simulating turbulent swirling flow in a gas cyclone: A comparison of various modeling approaches," Powder technology, vol. 205, p. 160–171, 2011.

[3]           J. Gimbun, T. G. Chuah, T. S. Y. Choong and A. Fakhru'l-Razi, "A CFD study on the prediction of cyclone collection efficiency," International Journal for Computational Methods in Engineering Science and Mechanics, vol. 6, p. 161–168, 2005.

[4]           F. Menter, "Zonal two equation k-? turbulence models for aerodynamic flows," in 23rd fluid dynamics, plasmadynamics, and lasers conference, 1993.

[5]           P. R. Spalart and M. Shur, "On the sensitization of turbulence models to rotation and curvature," Aerospace Science and Technology, vol. 1, p. 297–302, 1997.

[6]           A. Hellsten, "Some improvements in Menter's k-omega SST turbulence model," in 29th AIAA, Fluid Dynamics Conference, 1998.

[7]           P. E. Smirnov and F. R. Menter, "Sensitization of the SST turbulence model to rotation and curvature by applying the Spalart-Shur correction term," in Turbo Expo: Power for Land, Sea, and Air, 2008.

[8]           C. D. Hartley, "’Measurement of flow velocities within a hydrocyclone using laser doppler anemometry’," AEA, Power Fluidics, BNFL, Technical Report No. FTN/X/82, 1994.

[9]           S. K. Arolla and P. A. Durbin, "Modeling rotation and curvature effects within scalar eddy viscosity model framework," International Journal of Heat and Fluid Flow, vol. 39, p. 78–89, 2013.

[10]        Y. H. Alahmadi and A. F. Nowakowski, "Modified shear stress transport model with curvature correction for the prediction of swirling flow in a cyclone separator," Chemical Engineering Science, vol. 147, p. 150–165, 2016.

[11]        Y. H. Alahmadi, S. A. Awadh and A. F. Nowakowski, "Simulation of swirling flow with a vortex breakdown using modified shear stress transport model," Industrial & Engineering Chemistry Research, vol. 60, p. 6016–6026, 2021.

[12]        P. A. Dellenback, D. E. Metzger and G. Neitzel, "Measurements in turbulent swirling flow through an abrupt axisymmetric expansion," AIAA journal, vol. 26, p. 669–681, 1988.

[13]        S. N. A. Yusuf, Y. Asako, N. A. C. Sidik, S. B. Mohamed and W. M. A. A. Japar, "A short review on rans turbulence models," CFD Letters, vol. 12, p. 83–96, 2020.

[14]        O. Reynolds, "IV. On the dynamical theory of incompressible viscous fluids and the determination of the criterion," Philosophical transactions of the royal society of london.(a.), p. 123–164, 1895.

[15]        P. Spalart and S. Allmaras, "A one-equation turbulence model for aerodynamic flows," in 30th aerospace sciences meeting and exhibit, 1992.

[16]        Q. Zhang and Y. Yang, "A new simpler rotation/curvature correction method for Spalart–Allmaras turbulence model," Chinese Journal of Aeronautics, vol. 26, p. 326–333, 2013.

[17]        N. M. Chaderjian, "Numerical Simulation of Dynamic Stall Using Near-Body Adaptive Mesh Refinement," in International Conference on Computational Fluid Dynamics (ICCFD), 2018.

[18]        N. M. Chaderjian, "A quantitative approach for the accurate CFD simulation of hover in turbulent flow," Journal of the American Helicopter Society, vol. 68, p. 42009–42028, 2023.

[19]        M. L. Shur, M. K. Strelets, A. K. Travin and P. R. Spalart, "Turbulence modeling in rotating and curved channels: assessing the Spalart-Shur correction," AIAA journal, vol. 38, p. 784–792, 2000.

[20]        H. Huang, T. Sun, N. Li and G. Zhang, "Sensitization of the modified SST model to the swirling and curvature for turbulent impinging jet heat transfer," International Journal of Heat and Mass Transfer, vol. 182, p. 121980, 2022.

[21]        D. N. Ferreira, L. M. C. Gato, L. Eça and J. C. C. Henriques, "Aerodynamic analysis of a biradial turbine with movable guide-vanes: Incidence and slip effects on efficiency," Energy, vol. 200, p. 117502, 2020.

[22]        M. Li, Q. Li, Z. Zou and X. An, "Computational investigation of swirling supersonic jets generated through a nozzle-twisted lance," metallurgical and Materials transactions B, vol. 48, p. 713–725, 2017.

[23]        H. M. T. Khaleed, I. A. Badruddin, Y. H. Alahmadi, A. A. G. Haider, V. Tirth, A. A. Rajhi, A. Algahtani, A. E. Anqi, S. Alamri, S. Kamangar and others, "Comparison of 3D Printed Underwater Propeller Using Polymers and Conventionally Developed AA6061," Journal of Materials Engineering and Performance, vol. 31, p. 5149–5158, 2022.

[24]        J. K. Viken, S. Viken, K. A. Deere and M. Carter, "Design of the Cruise and Flap Airfoil for the X-57 Maxwell Distributed Electric Propulsion Aircraft," in 35th AIAA Applied Aerodynamics Conference, 2017.

[25]        A. Rogovyi, S. Khovanskyi, I. Hrechka and A. Gaydamaka, "Studies of the swirling submerged flow through a confuser," in Design, Simulation, Manufacturing: The Innovation Exchange, Springer, 2020, p. 85–94.

[26]        W. Zhang, Z. Ma, Y.-C. Yu and H.-X. Chen, "Applied new rotation correction ?–? SST model for turbulence simulation of centrifugal impeller in the rotating frame of reference," Journal of Hydrodynamics, Ser. B, vol. 22, p. 404–407, 2010.

[27]        X. Yang and P. G. Tucker, "Assessment of turbulence model performance: Large streamline curvature and integral length scales," Computers & Fluids, vol. 126, p. 91–101, 2016.

[28]        R. Hreiz, C. Gentric and N. Midoux, "Numerical investigation of swirling flow in cylindrical cyclones," Chemical engineering research and design, vol. 89, p. 2521–2539, 2011.