Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-28T07:47:54.377Z Has data issue: false hasContentIssue false

Transition-based constrained large-eddy simulation method with application to an ultrahigh-lift low-pressure turbine cascade flow

Published online by Cambridge University Press:  27 April 2022

Xiaole Wang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China
Zuoli Xiao*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China HEDPS and Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, PR China Nanchang Innovation Institute, Peking University, Nanchang 330008, PR China
*
Email address for correspondence: [email protected]

Abstract

A transition-predictive Reynolds-averaged Navier–Stokes (RANS) model is introduced as the Reynolds controlling condition to constrained large-eddy simulation (TrCLES) to improve the ability of this method to predict wall-bounded laminar–turbulent transition flows. In the TrCLES method, the constraint conditions for total Reynolds stress and heat flux are only imposed to the near-wall region in transitional and turbulent boundary layer. The newly proposed method recovers direct numerical simulation in the laminar boundary region, and retrieves the traditional large-eddy simulation method in the far-wall regions. The TrCLES method is validated in simulations of external flow around the Eppler 387 (E387) airfoil and internal flow past the ultrahigh-lift low-pressure turbine T106C cascade. The improved delayed detached-eddy simulation (IDDES) method, CLES method based on full-turbulence shear stress transport model and RANS method with a three-equation transition model are also evaluated in comparison with the available experimental and numerical data. As expected, the TrCLES method can predict laminar separation bubble and separation-induced transition process in both the E387 and T106C flows pretty well. In contrast, neither IDDES nor the original CLES can provide reasonable prediction for the laminar separation-induced transition phenomenon. The validity and fidelity of the TrCLES method are further verified by simulations of the T106C cascade flows in a wider range of exit Reynolds and Mach numbers. It is shown that the TrCLES method can not only predict the time-averaged aerodynamic quantities such as isentropic Mach number and exit kinetic energy loss very well, but also capture the laminar separation bubble and unsteady flow structures with satisfactory accuracy.

Type
JFM Papers
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abraham, S., Panchal, K., Xue, S., Ekkad, S.V., Ng, W., Brown, B.J. & Malandra, A. 2010 Experimental and numerical investigations of a transonic, high turning turbine cascade with a divergent endwall. In Proceedings of the ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting: Volume 1, Symposia – Parts A, B, and C. pp. 569–576. American Society of Mechanical Engineers.CrossRefGoogle Scholar
Abu-Ghannam, B.J. & Shaw, R. 1980 Natural transition of boundary layers-the effects of turbulence, pressure gradient, and flow history. J. Mech. Engng Sci. 22 (5), 213228.CrossRefGoogle Scholar
Alam, M. & Sandham, N.D. 2000 Direct numerical simulation of ‘short’ laminar separation bubbles with turbulent reattachment. J. Fluid Mech. 410, 128.CrossRefGoogle Scholar
Babajee, J. & Arts, T. 2012 Investigation of the laminar separation-induced transition with the $\gamma$-$\widetilde {Re}_{\theta {t}}$ transition model on low-pressure turbine rotor blades at steady conditions. In Proceedings of the ASME Turbo Expo: Turbine Technical Conference and Exposition. Volume 8: Turbomachinery, Parts A, B, and C. pp. 1167–1178. American Society of Mechanical Engineers.CrossRefGoogle Scholar
Bhushan, S., Alam, M.F. & Walters, D.K. 2013 Evaluation of hybrid RANS/LES models for prediction of flow around surface combatant and suboff geometries. Comput. Fluids 88, 834849.CrossRefGoogle Scholar
Bhushan, S. & Walters, D.K. 2012 A dynamic hybrid Reynolds-averaged Navier–Stokes–large eddy simulation modeling framework. Phys. Fluids 24 (1), 015103.CrossRefGoogle Scholar
Bin, Y., Xiao, M., Shi, Y., Zhang, Y. & Chen, S. 2021 A new idea to predict reshocked Richtmyer-Meshkov mixing: constrained large-eddy simulation. J. Fluid Mech. 918, R1.CrossRefGoogle Scholar
Cai, J. & Chng, T.L. 2009 On vortex shedding from bluff bodies with base cavities. Phys. Fluids 21 (3), 034109.CrossRefGoogle Scholar
Chaouat, B. 2017 The state of the art of hybrid RANS/LES modeling for the simulation of turbulent flows. Flow Turbul. Combust. 99 (2), 279327.CrossRefGoogle ScholarPubMed
Chen, L., Xiao, Z., Shi, Y. & Chen, S. 2017 Constrained large-eddy simulation of supersonic turbulent boundary layer over a compression ramp. J. Turbul. 18 (8), 781808.CrossRefGoogle Scholar
Chen, S., Chen, Y., Xia, Z., Qu, K., Shi, Y., Xiao, Z., Liu, Q., Cai, Q., Liu, F. & Lee, C. 2013 Constrained large-eddy simulation and detached eddy simulation of flow past a commercial aircraft at 14 degrees angle of attack. Sci. China 56 (2), 270276.Google Scholar
Chen, S., Xia, Z., Pei, S., Wang, J., Yang, Y., Xiao, Z. & Shi, Y. 2012 Reynolds-stress-constrained large-eddy simulation of wall-bounded turbulent flows. J. Fluid Mech. 703, 128.CrossRefGoogle Scholar
Content, C. & Houdeville, R. 2010 Application of the $\gamma$$Re_{\theta t}$ laminar-turbulent transition model in Navier–Stokes computations. In 40th Fluid Dynamics Conference and Exhibit, p. 4445.Google Scholar
Cui, W., Xiao, Z. & Yuan, X. 2020 Simulations of transition and separation past a wind-turbine airfoil near stall. Energy 205, 118003.CrossRefGoogle Scholar
Davidson, L. & Peng, S.H. 2003 Hybrid LES-RANS modelling: a one-equation SGS model combined with a $k$-$\omega$ model for predicting recirculating flows. Intl J. Numer. Meth. Fluids 43 (9), 10031018.CrossRefGoogle Scholar
Deck, S. 2012 Recent improvements in the zonal detached eddy simulation (ZDES) formulation. Theor. Comput. Fluid Dyn. 26 (6), 523550.CrossRefGoogle Scholar
Dorschner, B., Chikatamarla, S.S. & Karlin, I.V. 2017 Transitional flows with the entropic lattice Boltzmann method. J. Fluid Mech. 824, 388412.CrossRefGoogle Scholar
Eppler, R.A. & Somers, D.M.A. 1980 A computer program for the design and analysis of low-speed airfoils. NASA Tech. Rep. TM-80210.Google Scholar
Fröhlich, J. & Von Terzi, D. 2008 Hybrid LES/RANS methods for the simulation of turbulent flows. Prog. Aerosp. Sci. 44 (5), 349377.CrossRefGoogle Scholar
Fu, S. & Wang, L. 2013 RANS modeling of high-speed aerodynamic flow transition with consideration of stability theory. Prog. Aerosp. Sci. 58, 3659.CrossRefGoogle Scholar
Gao, W., Zhang, W., Cheng, W. & Samtaney, R. 2019 Wall-modelled large-eddy simulation of turbulent flow past airfoils. J. Fluid Mech. 873, 174210.CrossRefGoogle Scholar
Garai, A., Diosady, L.T., Murman, S.M. & Madavan, N.K. 2016 DNS of low-pressure turbine cascade flows with elevated inflow turbulence using a discontinuous-Galerkin spectral-element method. In Proceedings of the ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. Volume 2C: Turbomachinery. American Society of Mechanical Engineers.CrossRefGoogle Scholar
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325336.CrossRefGoogle Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W.H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 17601765.CrossRefGoogle Scholar
Gritskevich, M.S., Garbaruk, A.V., Schütze, J. & Menter, F.R. 2012 Development of DDES and IDDES formulations for the $k$-$\omega$ shear stress transport model. Flow Turbul. Combust. 88 (3), 431449.CrossRefGoogle Scholar
Haselbach, F., Schiffer, H.-P., Horsman, M., Dressen, S., Harvey, N. & Read, S. 2002 The application of ultra high lift blading in the BR715 LP turbine. J. Turbomach. 124 (1), 4551.CrossRefGoogle Scholar
Hatman, A. & Wang, T. 1999 A prediction model for separated-flow transition. J. Turbomach. 121 (3), 594602.CrossRefGoogle Scholar
Heinz, S. 2020 A review of hybrid RANS-LES methods for turbulent flows: concepts and applications. Prog. Aerosp. Sci. 114, 100597.CrossRefGoogle Scholar
Hillewaert, K., Carton de Wiart, C., Verheylewegen, G. & Arts, T. 2014 Assessment of a high-order discontinuous Galerkin method for the direct numerical simulation of transition at low-Reynolds number in the T106C high-lift low pressure turbine cascade. In Proceedings of the ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. Volume 2B: Turbomachinery. American Society of Mechanical Engineers.CrossRefGoogle Scholar
Hodson, H.P. & Howell, R.J. 2005 Bladerow interactions, transition, and high-lift aerofoils in low-pressure turbines. Annu. Rev. Fluid Mech. 37, 7198.CrossRefGoogle Scholar
Hong, R., Xia, Z., Shi, Y., Xiao, Z. & Chen, S. 2014 Constrained large-eddy simulation of compressible flow past a circular cylinder. Commun. Comput. Phys. 15 (2), 388421.CrossRefGoogle Scholar
Hu, S., Zhou, C. & Chen, S. 2020 Large eddy simulation of secondary flows in an ultra-high lift low pressure turbine cascade at various inlet incidences. Intl J. Turbo Jet-Engines 37 (2), 195207.CrossRefGoogle Scholar
Hu, S., Zhou, C., Xia, Z. & Chen, S. 2018 Large eddy simulation and CDNS investigation of T106C low-pressure turbine. J. Fluids Engng 140 (1), 011108.CrossRefGoogle Scholar
Jameson, A., Schmidt, W. & Turkel, E. 1981 Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes. In 14th Fluid and Plasma Dynamics Conference, p. 1259.Google Scholar
Jiang, X.Y., Gu, D.W., Lee, C.B., Smith, C.R. & Linden, P.F. 2021 A metamorphosis of three-dimensional wave structure in transitional and turbulent boundary layers. J. Fluid Mech. 914, A4.CrossRefGoogle Scholar
Jiang, X.Y., Lee, C.B., Chen, X., Smith, C.R. & Linden, P.F. 2020 Structure evolution at early stage of boundary-layer transition: simulation and experiment. J. Fluid Mech. 890, A11.CrossRefGoogle Scholar
Jiang, Z., Xiao, Z., Shi, Y. & Chen, S. 2013 Constrained large-eddy simulation of wall-bounded compressible turbulent flows. Phys. Fluids 25 (10), 106102.CrossRefGoogle Scholar
Jones, L.E., Sandberg, R.D. & Sandham, N.D. 2008 Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence. J. Fluid Mech. 602, 175207.CrossRefGoogle Scholar
Ke, J. & Edwards, J.R. 2017 Numerical simulations of turbulent flow over airfoils near and during static stall. J. Aircr. 54 (5), 19601978.CrossRefGoogle Scholar
Langtry, R.B. & Menter, F.R. 2009 Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes. AIAA J. 47 (12), 28942906.CrossRefGoogle Scholar
Langtry, R.B., Menter, F.R., Likki, S.R., Suzen, Y.B., Huang, P.G. & Volker, S. 2004 A correlation-based transition model using local variables. Part 2. Test cases and industrial applications. J. Turbomach. 128 (3), 423434.CrossRefGoogle Scholar
Lee, C. & Chen, S. 2018 Recent progress in the study of transition in the hypersonic boundary layer. Natl. Sci. Rev. 61 (1), 155170.Google Scholar
Lee, C. & Wu, J. 2008 Transition in wall-bounded flows. Appl. Mech. Rev. 61, 030802.CrossRefGoogle Scholar
Lenormand, E., Sagaut, P., Phuoc, L.T. & Comte, P. 2000 Subgrid-scale models for large-eddy simulations of compressible wall bounded flows. AIAA J. 38 (8), 13401350.CrossRefGoogle Scholar
Liu, J., Xiao, Z. & Fu, S. 2018 Unsteady transition studies over a pitching airfoil using a $k$-$\omega$-$\gamma$ transition model. AIAA J. 56 (9), 37763781.CrossRefGoogle Scholar
Lopez, M. & Walters, D.K. 2017 A recommended correction to the kT-kL-$\omega$ transition-sensitive eddy-viscosity model. J. Fluids Engng 139 (2), 024501.CrossRefGoogle Scholar
Martín, M.P., Piomelli, U. & Candler, G.V. 2000 Subgrid-scale models for compressible large-eddy simulations. Theor. Comput. Fluid Dyn. 13, 361376.Google Scholar
Mary, I. & Sagaut, P. 2002 Large eddy simulation of flow around an airfoil near stall. AIAA J. 40 (6), 11391145.CrossRefGoogle Scholar
Mayle, R.E. 1991 The 1991 IGTI scholar lecture: the role of laminar-turbulent transition in gas turbine engines. J. Turbomach. 113 (4), 509536.CrossRefGoogle Scholar
McGhee, R.J., Walker, B.S. & Millard, B.F. 1988 Experimental results for the Eppler 387 airfoil at low Reynolds numbers in the Langley low-turbulence pressure tunnel. NASA Tech. Rep. TM–4062.Google Scholar
Menter, F., Hüppe, A., Matyushenko, A. & Kolmogorov, D. 2021 An overview of hybrid RANS-LES models developed for industrial CFD. Appl. Sci. 11 (6), 2459.CrossRefGoogle Scholar
Menter, F.R. 1994 Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32 (8), 15981605.CrossRefGoogle Scholar
Menter, F.R. & Egorov, Y. 2010 The scale-adaptive simulation method for unsteady turbulent flow predictions. Part 1. Theory and model description. Flow Turbul. Combust. 85 (1), 113138.CrossRefGoogle Scholar
Menter, F.R., Langtry, R.B., Likki, S.R., Suzen, Y.B., Huang, P.G. & Volker, S. 2004 A correlation-based transition model using local variables. Part 1. Model formulation. J. Turbomach. 128 (3), 413422.CrossRefGoogle Scholar
Menter, F.R., Smirnov, P.E., Liu, T. & Avancha, R. 2015 A one-equation local correlation-based transition model. Flow Turbul. Combust. 95 (4), 583619.CrossRefGoogle Scholar
Michálek, J., Monaldi, M. & Arts, T. 2012 Aerodynamic performance of a very high lift low pressure turbine airfoil (T106C) at low Reynolds and high Mach number with effect of free stream turbulence intensity. J. Turbomach. 134 (6), 061009.CrossRefGoogle Scholar
Michelassi, V., Wissink, J.G., Frohlich, J. & Rodi, W. 2003 Large-eddy simulation of flow around low-pressure turbine blade with incoming wakes. AIAA J. 41 (11), 21432156.CrossRefGoogle Scholar
Minot, A., de Saint Victor, X., Marty, J. & Perraud, J. 2015 Advanced numerical setup for separation-induced transition on high-lift low-pressure turbine flows using the $\gamma$-$\widetilde {Re}_{\theta t}$ model. In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. Volume 2B: Turbomachinery. American Society of Mechanical Engineers.CrossRefGoogle Scholar
Nguyen, P., Uribe, J.C., Afgan, I. & Laurence, D. 2018 A seamless hybrid RANS/LES model with dynamic Reynolds-stress correction for high Reynolds number flows on coarse grids. In 12th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements.Google Scholar
Nicoud, F. & Ducros, F. 1999 Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbul. Combust. 62 (3), 183200.CrossRefGoogle Scholar
Pacciani, R., Marconcini, M., Fadai-Ghotbi, A., Lardeau, S. & Leschziner, M.A. 2011 Calculation of high-lift cascades in low pressure turbine conditions using a three-equation model. J. Turbomach. 133 (3), 031016.CrossRefGoogle Scholar
Pichler, R., Sandberg, R.D., Michelassi, V. & Bhaskaran, R. 2016 Investigation of the accuracy of RANS models to predict the flow through a low-pressure turbine. J. Turbomach. 138 (12), 121009.CrossRefGoogle Scholar
Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34 (1), 349374.CrossRefGoogle Scholar
Rist, U. & Fasel, H. 1995 Direct numerical simulation of controlled transition in a flat-plate boundary layer. J. Fluid Mech. 298, 211248.CrossRefGoogle Scholar
Roe, P.L. 1981 Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43, 357372.CrossRefGoogle Scholar
Sa, J.H., Park, S.H., Kim, C.J. & Park, J.K. 2015 Low-Reynolds number flow computation for Eppler 387 wing using hybrid DES transition model. J. Mech. Sci. Technol. 29 (5), 18371847.CrossRefGoogle Scholar
Sandberg, R.D., Michelassi, V., Pichler, R., Chen, L. & Johnstone, R. 2015 Compressible direct numerical simulation of low-pressure turbines. Part 1. Methodology. J. Turbomach. 137 (5), 051011.CrossRefGoogle Scholar
Sayadi, T., Hamman, C.W. & Moin, P. 2013 Direct numerical simulation of complete H-type and K-type transitions with implications for the dynamics of turbulent boundary layers. J. Fluid Mech. 724, 480509.CrossRefGoogle Scholar
Shur, M.L., Spalart, P.R., Strelets, M.K. & Travin, A.K. 2008 A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities. Intl J. Heat Fluid Flow 29 (6), 16381649.CrossRefGoogle Scholar
Sørensen, N.N., Bechmann, A. & Zahle, F. 2011 3D CFD computations of transitional flows using DES and a correlation based transition model. Wind Energy 14 (1), 7790.CrossRefGoogle Scholar
Spalart, P. & Allmaras, S. 1992 A one-equation turbulence model for aerodynamic flows. In 30th Aerospace Sciences Meeting and Exhibit, AIAA Paper 1992-439.Google Scholar
Spalart, P.R. 2000 Strategies for turbulence modelling and simulations. Intl J. Heat Fluid Flow 21 (3), 252263.CrossRefGoogle Scholar
Spalart, P.R. 2009 Detached-eddy simulation. Annu. Rev. Fluid Mech. 41 (1), 181202.CrossRefGoogle Scholar
Spalart, P.R., Deck, S., Shur, M.L., Squires, K.D., Strelets, M.K. & Travin, A. 2006 A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theor. Comput. Fluid Dyn. 20 (3), 181195.CrossRefGoogle Scholar
Spalart, P.R. & Rumsey, C.L. 2007 Effective inflow conditions for turbulence models in aerodynamic calculations. AIAA J. 45 (10), 25442553.CrossRefGoogle Scholar
Spalart, P.R. & Strelets, M.K. 2000 Mechanisms of transition and heat transfer in a separation bubble. J. Fluid Mech. 403, 329349.CrossRefGoogle Scholar
Suzen, Y.B., Xiong, G. & Huang, P.G. 2002 Predictions of transitional flows in low-pressure turbines using intermittency transport equation. AIAA J. 40 (2), 254266.CrossRefGoogle Scholar
Temmerman, L., Hadžiabdić, M., Leschziner, M.A. & Hanjalić, K. 2005 A hybrid two-layer URANS-LES approach for large eddy simulation at high Reynolds numbers. Intl J. Heat Fluid Flow 26 (2), 173190.CrossRefGoogle Scholar
Uribe, J.C., Jarrin, N., Prosser, R. & Laurence, D. 2010 Development of a two-velocities hybrid RANS-LES model and its application to a trailing edge flow. Flow Turbul. Combust. 85 (2), 181197.CrossRefGoogle Scholar
Verma, A., Park, N. & Mahesh, K. 2013 A hybrid subgrid-scale model constrained by Reynolds stress. Phys. Fluids 25 (11), 110805.CrossRefGoogle Scholar
Walters, D.K. & Cokljat, D. 2008 A three-equation eddy-viscosity model for Reynolds-averaged Navier–Stokes simulations of transitional flow. J. Fluids Engng 130 (12), 121401.CrossRefGoogle Scholar
Wang, G., Xiao, Z. & Chen, L. 2020 Simultaneous simulation of transition and massive separation by RANS-LES-Tr model. Aerosp. Sci. Technol. 105, 106026.CrossRefGoogle Scholar
Wang, L. & Fu, S. 2009 Modelling flow transition in a hypersonic boundary layer with Reynolds-averaged Navier–Stokes approach. Sci. China 52 (5), 768774.Google Scholar
Wang, R. & Xiao, Z. 2020 a Reynolds-constrained large-eddy simulation: sensitivity to constraint and SGS models. In Progress in Hybrid RANS-LES Modelling (ed. Y. Hoarau, S.H. Peng, D. Schwamborn, A. Revell & C. Mockett), pp. 131–142. Springer, Cham.CrossRefGoogle Scholar
Wang, R. & Xiao, Z. 2020 b Transition effects on flow characteristics around a static two-dimensional airfoil. Phys. Fluids 32 (3), 035113.Google Scholar
Wang, X., Cui, B. & Xiao, Z. 2021 Numerical investigation on ultra-high-lift low-pressure turbine cascade aerodynamics at low Reynolds numbers using transition-based turbulence models. J. Turbul. 22 (2), 114139.CrossRefGoogle Scholar
Warren, E.W. & Hassan, H.A. 1998 Alternative to the $e^n$ method for determining onset of transition. AIAA J. 36 (1), 111113.CrossRefGoogle Scholar
White, J., Baurle, R., Fisher, T., Quinlan, J. & Black, W. 2012 Low-dissipation advection schemes designed for large eddy simulations of hypersonic propulsion systems. In 48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, p. 4263.Google Scholar
Wissink, J.G. 2003 DNS of separating, low Reynolds number flow in a turbine cascade with incoming wakes. Intl J. Heat Fluid Flow 24 (4), 626635.CrossRefGoogle Scholar
Wu, W. & Piomelli, U. 2018 Effects of surface roughness on a separating turbulent boundary layer. J. Fluid Mech. 841, 552580.CrossRefGoogle Scholar
Xia, Z., Xiao, Z., Shi, Y. & Chen, S. 2016 Mach number effect of compressible flow around a circular cylinder. AIAA J. 54 (6), 20042009.CrossRefGoogle Scholar
Xiao, Z., Wang, G., Yang, M. & Chen, L. 2019 Numerical investigations of hypersonic transition and massive separation past Orion capsule by DDES-Tr. Intl J. Heat Mass Transfer 137, 90107.CrossRefGoogle Scholar
Yan, Y., Chen, C., Fu, H. & Liu, C. 2014 DNS study on $\varLambda$-vortex and vortex ring formation in flow transition at Mach number 0.5. J. Turbul. 15 (1), 121.CrossRefGoogle Scholar
You, J.Y. & Kwon, O.J. 2013 Blending of SAS and correlation-based transition models for flow simulation at supercritical Reynolds numbers. Comput. Fluids 80, 6370.CrossRefGoogle Scholar
Yu, C., Hong, R., Xiao, Z. & Chen, S. 2013 Subgrid-scale eddy viscosity model for helical turbulence. Phys. Fluids 25 (9), 095101.CrossRefGoogle Scholar
Zhao, Y., Xia, Z., Shi, Y., Xiao, Z. & Chen, S. 2014 Constrained large-eddy simulation of laminar-turbulent transition in channel flow. Phys. Fluids 26 (9), 095103.CrossRefGoogle Scholar
Zhou, H., Li, X., Qi, H. & Yu, C. 2019 Subgrid-scale model for large-eddy simulation of transition and turbulence in compressible flows. Phys. Fluids 31 (12), 125118.Google Scholar
Zhu, Y., Luo, J. & Liu, F. 2018 Influence of blade lean together with blade clocking on the overall aerodynamic performance of a multi-stage turbine. Aerosp. Sci. Technol. 80, 329336.CrossRefGoogle Scholar