Acknowledgement
Computational resources provided by hpc@polito, which is a project of Academic Computing within the Department of Control and Computer Engineering at the Politecnico di Torino (http://www.hpc.polito.it).
References
- Allmaras, S., Johnson, F. and Spalart, P. (2012), "Modifications and clarifications for the implementation of the Spalart-Allmaras turbulence model", Seventh International Conference on Computational Fluid Dynamics (ICCFD7), Big Island, Hawaii, July.
- Balay, S., Gropp, W.D., McInnes, L.C. and Smith, B.F. (1997), "Efficient management of parallelism in object-oriented numerical software libraries", Modern Software Tools for Scientific Computing, Birkhauser Boston, Boston, MA, United States.
- Cui, J., Rao, V.N. and Tucker, P.G. (2017), "Numerical investigation of secondary flows in a high-lift low pressure turbine", Int. J. Heat Fluid Flow, 63, 149-157. https://doi.org/10.1016/j.ijheatfluidflow.2016.05.018.
- de la Blanco, E.R., Hodson, H., Vazquez, R. and Torre, D. (2003), "Influence of the state of the inlet endwall boundary layer on the interaction between pressure surface separation and endwall flows", Proc. Inst. Mech. Eng., Part A: J. Power Energy, 217(4), 433-441. https://doi.org/10.1243/095765003322315496.
- Duden, A. and Fottner, L. (1997), "Influence of taper, Reynolds number and Mach number on the secondary flow field of a highly loaded turbine cascade", Proc. Inst. Mech. Eng., Part A: J. Power Energy, 211(4), 309-320. https://doi.org/10.1177/095765099721100401.
- Errante, M., Ferrero, A. and Larocca, F. (2022), "Simulation of secondary flows in turbomachinery by the discontinuous Galerkin method", AIP Conf. Proc., 2611, 050005. https://doi.org/10.1063/5.0120392.
- Ferrero, A., Larocca, F. and Puppo, G. (2015), "A robust and adaptive recovery-based discontinuous Galerkin method for the numerical solution of convection-diffusion equations", Int. J. Numer Meth. Fluid., 77(2), 63-91. https://doi.org/10.1002/fld.3972.
- Garai, A., Diosady, L.T., Murman, S.M. and Madavan, N.K. (2017), "Scale-resolving simulations of bypass transition in a high-pressure turbine cascade using a spectral element discontinuous Galerkin method", J. Turbomach., 104(3), 031004. https://doi.org/10.1115/1.4038403.
- Geuzaine, C. and Remacle, J.F. (2009), "Gmsh: A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities", Int. J. Numer. Meth. Eng., 79(11), 1309-1311. https://doi.org/10.1002/nme.2579.
- Ghidoni, A., Colombo, A., Rebay, S. and Bassi, F. (2013), "Simulation of the transitional flow in a low pressure gas turbine cascade with a high-order discontinuous Galerkin method", J. Fluid. Eng., 135(7), 071101. https://doi.org/10.1115/1.4024107.
- Giuliani, A. (2022), "A two-dimensional stabilized discontinuous galerkin method on curvilinear embedded boundary grids", SIAM J. Scientif. Comput., 44(1), A389-A415. https://doi.org/10.1137/21M1396277.
- Goldstein, R. and Spores, R. (1988), "Turbulent transport on the endwall in the region between adjacent turbine blades", J. Heat Transf., 110(4a), 862-869. https://doi.org/10.1115/1.3250586.
- Gulizzi, V., Almgren, A.S. and Bell, J.B. (2022), "A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries", J. Comput. Phys., 450, 110861. https://doi.org/10.1016/j.jcp.2021.110861.
- Langston, L. (1980), "Crossflows in a turbine cascade passage", J. Eng. Power, 102(4), 866-874. https://doi.org/10.1115/1.3230352.
- Langston, L. (2001), "Secondary flows in axial turbines-A review", Ann. NY Acad. Sci., 934(1), 11-26. https://doi.org/10.1111/j.1749-6632.2001.tb05839.x.
- Lax, P.D. (1954), "Weak solutions of nonlinear hyperbolic equations and their numerical computation", Commun. Pure Appl. Math., 7, 159-193. https://doi.org/10.1002/cpa.3160070112.
- LeVeque, R. (2002), Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge, United Kingdom.
- Lo, M. and van Leer, B. (2009), "Analysis and implementation of recovery-based discontinuous Galerkin for diffusion", 19th AIAA Computational Fluid Dynamics, San Antonio, Texas, June. https://doi.org/10.2514/6.2009-3786.
- Marconcini, M., Pacciani, R., Arnone, A., Michelassi, V., Pichler, R., Zhao, Y. and Sandberg, R. (2019), "Large eddy simulation and RANS analysis of the end-wall flow in a linear low-pressure-turbine cascadepart II: Loss generation", J. Turbomach., 141(5), 051004. https://doi.org/10.1115/1.4042208.
- Pandolfi, M. (1984), "A contribution to the numerical prediction of unsteady flows", AIAA J., 22(5), 602- 610. https://doi.org/10.2514/3.48491.
- Pichler, R., Zhao, Y., Sandberg, R., Michelassi, V., Pacciani, R., Marconcini, M. and Arnone, A. (2019), "Large-eddy simulation and RANS analysis of the end-wall flow in a linear low-pressure turbine cascade, Part I: Flow and secondary vorticity fields under varying inlet condition", J. Turbomach., 141(12), 121005. https://doi.org/10.1115/1.4045080.
- Rusanov, V.V. (1962), "The calculation of the interaction of non-stationary shock waves and obstacles", USSR Comput. Math. Math. Phys., 1(2), 304-320. https://doi.org/10.1016/0041-5553(62)90062-9.
- Sieverding, C. (1985), "Recent progress in the understanding of basic aspects of secondary flows in turbine blade passages", J. Eng. Gas Turbin. Power, 107(2), 248-257. https://doi.org/10.1115/1.3239704.
- Sieverding, C. and Van Den Bosche, P. (1983), "The use of coloured smoke to visualize secondary flows in a turbine-blade cascade", J. Fluid Mech., 134, 85-89. https://doi.org/10.1017/S0022112083003237.
- Wang, H., Olson, S., Goldstein, R. and Eckert, E. (1997), "Flow visualization in a linear turbine cascade of high performance turbine blades", J. Turbomach., 119(1), 1-8. https://doi.org/10.1115/1.2841006.
- Yao, M. and He, L. (2012), "Implicit discontinuous Galerkin solution on unstructured mesh for turbine blade secondary flow", J. Turbomach., 142(1), 011004. https://doi.org/10.1115/1.4045551.