A characteristic inlet boundary condition for compressible, turbulent, multispecies turbomachinery flows. (English) Zbl 1410.76333
Summary: A methodology to implement non-reflecting boundary conditions for turbomachinery applications, based on characteristic analysis is described in this paper. For these simulations, inlet conditions usually correspond to imposed total pressure, total temperature, flow angles and species composition. While directly imposing these quantities on the inlet boundary condition works correctly for steady RANS simulations, this approach is not adapted for compressible unsteady large eddy simulations because it is fully reflecting in terms of acoustics. Deriving non-reflecting conditions in this situation requires to construct characteristic relations for the incoming wave amplitudes. These relations must impose total pressure, total temperature, flow angle and species composition, and simultaneously identify acoustic waves reaching the inlet to let them propagate without reflection. This treatment must also be compatible with the injection of turbulence at the inlet. The proposed approach shows how characteristic equations can be derived to satisfy all these criteria. It is tested on several cases, ranging from a simple inviscid 2D duct to a rotor/stator stage with turbulence injection.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
| 76Nxx | Compressible fluids and gas dynamics |
Keywords:
characteristic inlet boundary condition; turbomachinery inflow conditions; compressible flow; turbulence injection; acoustic reflectivitySoftware:
AVBPReferences:
| [1] | Albin, E.; D’Angelo, Y.; Vervisch, L., Flow streamline based Navier-Stokes characteristic boundary conditions: modeling for transverse and corner outflows, Comput Fluids, 51, 1, 115-126, (2011) · Zbl 1271.76289 |
| [2] | Anker J., Schrader B., Seybold U., Mayer J., Casey M.. A three-dimensional non-reflecting boundary condition treatment for steady-state flow simulations. In: Proceedings of the forty-fourth AIAA aerospace sciences meeting and exhibit. January 2006; Reno, Nevada. ISBN 978-1-62410-039-0; 2006.; Anker J., Schrader B., Seybold U., Mayer J., Casey M.. A three-dimensional non-reflecting boundary condition treatment for steady-state flow simulations. In: Proceedings of the forty-fourth AIAA aerospace sciences meeting and exhibit. January 2006; Reno, Nevada. ISBN 978-1-62410-039-0; 2006. |
| [3] | Baum, M.; Poinsot, T.; Thévenin, D., Accurate boundary conditions for multicomponent reactive flows, J Comput Phys, 116, 247-261, (1994) · Zbl 0818.76047 |
| [4] | Carullo, J. S.; Nasir, S.; Cress, R. D.; Ng, W. F.; Thole, K. A.; Zhang, L. J., The effects of freestream turbulence, turbulence length scale, and exit Reynolds number on turbine blade heat transfer in a transonic cascade, J Turbomach, 133, 1, 011030, (2011) |
| [5] | Choi, J.; Teng, S.; Han, J.-C.; Ladeinde, F., Effect of free-stream turbulence on turbine blade heat transfer and pressure coefficients in low Reynolds number flows, Int J Heat Mass Transf, 47, 14-16, 3441-3452, (2004) |
| [6] | Colin, O.; Rudgyard, M., Development of high-Order TaylorGalerkin schemes for LES, J Comput Phys, 162, 2, 338-371, (2000) · Zbl 0982.76058 |
| [7] | Colonius, T., Numerically nonreflecting boundary and interface conditions for compressible flow and aeroacoustic computations, AIAA J, 35, 7, 1126-1133, (1997) · Zbl 0909.76058 |
| [8] | Colonius, T., Modelling artificial boundary conditions for compressible flow, Annu Rev Fluid Mech, 36, 1, 315-345, (2004) · Zbl 1076.76040 |
| [9] | Dahm, W. J.a.; Southerland, K. B., Experimental assessment of Taylor’s hypothesis and its applicability to dissipation estimates in turbulent flows, Phys Fluids, 9, October 1996, 2101-2107, (1997) |
| [10] | Del Álamo, J. C.; Jiménez, J., Estimation of turbulent convection velocities and corrections to Taylor’s approximation, J Fluid Mech, 640, 5-26, (2009) · Zbl 1183.76761 |
| [11] | Dhamankar N.S., Blaisdell G.A., Lyrintzis A.S.. An overview of turbulent inflow boundary conditions for large eddy simulations (Invited). In: Proceedings of the twenty-second aiaa computational fluid dynamics conference. JUNE. ISBN 978-1-62410-366-7; 2015, p. 1-28.; Dhamankar N.S., Blaisdell G.A., Lyrintzis A.S.. An overview of turbulent inflow boundary conditions for large eddy simulations (Invited). In: Proceedings of the twenty-second aiaa computational fluid dynamics conference. JUNE. ISBN 978-1-62410-366-7; 2015, p. 1-28. |
| [12] | Duchaine, F.; Dombard, J.; Gicquel, L. Y.; Koupper, C., On the importance of inlet boundary conditions for aerothermal predictions of turbine stages with large eddy simulation, Comput Fluids, 154, 60-73, (2017) · Zbl 1390.76145 |
| [13] | Freund, J. B., Proposed inflow/outflow boundary condition for direct computation of aerodynamic sound, AIAA J, 35, 4, 740-742, (1997) · Zbl 0903.76081 |
| [14] | Germano, M., Turbulence: the filtering approach, J Fluid Mech, 238, 325-336, (1992) · Zbl 0756.76034 |
| [15] | Giles, M., Non-reflecting boundary conditions for euler equation calculations, AIAA J, 28, 12, 2050-2058, (1990) |
| [16] | Giles, M. B., UNSFLO: A numerical method for unsteady inviscid flow in turbomachinery, Tech. Rep., (1988), Gas Turbine Laboratory, MIT |
| [17] | Gourdain, N.; Gicquel, L.; Montagnac, M.; Vermorel, O.; Gazaix, M.; Staffelbach, G., High performance parallel computing of flows in complex geometries: I. Methods, Comput Sci Discov, 2, 1, 015003, (2009) |
| [18] | Granet, V.; Vermorel, O.; Léonard, T.; Gicquel, L.; Poinsot, T., Comparison of nonreflecting outlet boundary conditions for compressible solvers on unstructured grids, AIAA J, 48, 10, 2348-2364, (2010) |
| [19] | Guézennec, N.; Poinsot, T., Acoustically nonreflecting and reflecting boundary conditions for vorticity injection in compressible solvers, AIAA J, 47, 7, 1709-1722, (2009) |
| [20] | Jahanmiri, M., Boundary layer transitional flow in gas turbines, Tech. Rep., (2011), Dpt. Appl. Mech., Chalmers University of Technology: Dpt. Appl. Mech., Chalmers University of Technology Göteborg, Sweden |
| [21] | Koupper, C.; Poinsot, T.; Gicquel, L. Y.M.; Duchaine, F., Compatibility of characteristic boundary conditions with radial equilibrium in turbomachinery simulations, AIAA J, 52, 12, 2829-2839, (2014) |
| [22] | Kraichnan, R. H., Diffusion by a random velocity field, Phys Fluids, 13, 1, 22, (1970) · Zbl 0193.27106 |
| [23] | Lee, S.; Lele, S. K.; Moin, P., Simulation of spatially evolving turbulence and the applicability of Taylor’s hypothesis in compressible flow, Phys Fluids A, 4, 7, 1521-1530, (1992) · Zbl 0825.76346 |
| [24] | Leonard, A., Energy cascade in large-eddy simulations of turbulent fluid flows, Adv Geophys, 18, PA, 237-248, (1974) |
| [25] | Lin, C., On Taylor’s hypothesis and the acceleration terms in the Navier-Stokes equations, Q Appl Math, 10, 4, 295-396, (1953) · Zbl 0050.19502 |
| [26] | Lodato, G.; Domingo, P.; Vervisch, L., Three-dimensional boundary conditions for direct and large-eddy simulation of compressible viscous flows, J Comput Phys, 227, 10, 5105-5143, (2008) · Zbl 1388.76098 |
| [27] | Michelassi, V.; Chen, L.-W.; Pichler, R.; Sandberg, R. D., Compressible direct numerical simulation of low-Pressure turbinespart II: Effect of inflow disturbances, J Turbomach, 137, 7, 071005, (2015) |
| [28] | Moin, P., Revisiting Taylor’s hypothesis, J Fluid Mech, 640, 1-4, (2009) · Zbl 1183.76747 |
| [29] | Moureau, V.; Lartigue, G.; Sommerer, Y.; Angelberger, C.; Colin, O.; Poinsot, T., Numerical methods for unsteady compressible multi-component reacting flows on fixed and moving grids, J Comput Phys, 202, 2, 710-736, (2005) · Zbl 1061.76039 |
| [30] | Nicoud, F., Defining wave amplitude in characteristic boundary conditions, J Comput Phys, 149, 2, 418-422, (1999) · Zbl 0976.76059 |
| [31] | Okong’o, N.; Bellan, J., Consistent boundary conditions for multicomponent real gas mixtures based on characteristic waves, J Comput Phys, 176, 2, 330-344, (2002) · Zbl 1130.76417 |
| [32] | Pirozzoli, S.; Colonius, T., Generalized characteristic relaxation boundary conditions for unsteady compressible flow simulations, J Comput Phys, 248, 109-126, (2013) · Zbl 1349.76522 |
| [33] | Poinsot, T.; Veynante, D., Theoretical and numerical combustion, (2012) |
| [34] | Poinsot, T. J.; Lele, S. K., Boundary conditions for direct simulations of compressible viscous flows, J Comput Phys, 101, 1, 104-129, (1992) · Zbl 0766.76084 |
| [35] | Polifke, W.; Wall, C.; Moin, P., Partially reflecting and non-reflecting boundary conditions for simulation of compressible viscous flow, J Comput Phys, 213, 1, 437-449, (2006) · Zbl 1146.76632 |
| [36] | Pope, S., Turbulent flows, (2000), Cambridge University Press · Zbl 0966.76002 |
| [37] | Porta, M., Développement, vérification et validation des outils les pour l’étude du bruit de combustion et de l’interaction combustion / acoustique / turbulence, (2007), Institut National Polytechnique de Toulouse, Ph.D. thesis |
| [38] | Prosser, R., Improved boundary conditions for the direct numerical simulation of turbulent subsonic flows. I. Inviscid flows, J Comput Phys, 207, 2, 736-768, (2005) · Zbl 1213.76142 |
| [39] | Rudy, H.; Strikwerda, J. C., A nonreflecting outflow boundary condition for subsonic Navier-Stokes calculations, J Comput Phys, 36, 55-70, (1980) · Zbl 0425.76045 |
| [40] | Saxer A.P., Giles M.B., Saxer A. P., Giles M.B.. Quasi-three-dimensional nonreflecting boundary conditions for Euler equations calculations. In: Proceedings of the tenth computational fluid dynamics conference. 1603-CP; Honolulu, USA; 1991, p. 845-857.; Saxer A.P., Giles M.B., Saxer A. P., Giles M.B.. Quasi-three-dimensional nonreflecting boundary conditions for Euler equations calculations. In: Proceedings of the tenth computational fluid dynamics conference. 1603-CP; Honolulu, USA; 1991, p. 845-857. |
| [41] | Schlüß D., Frey C., Ashcroft G.. Consistent non-reflecting boundary conditions for both steady and unsteady flow simulations in turbomachinery applications. In: Proceedings of the VII European congress on computational methods in applied sciences and engineering. June; Crete Island, Greece; 2016, p. 5-10.; Schlüß D., Frey C., Ashcroft G.. Consistent non-reflecting boundary conditions for both steady and unsteady flow simulations in turbomachinery applications. In: Proceedings of the VII European congress on computational methods in applied sciences and engineering. June; Crete Island, Greece; 2016, p. 5-10. |
| [42] | Schønfeld, T.; Rudgyard, M., Steady and unsteady flows simulations using the hybrid flow solver avbp, AIAA J, 37, 1378-1385, (1999) |
| [43] | Scillitoe, A. D.; Tucker, P. G.; Adami, P., Numerical investigation of three-Dimensional separation in an axial flow compressor: the influence of freestream turbulence intensity and endwall boundary layer state, J Turbomach, 139, 2, (2016) |
| [44] | Selle, L.; Nicoud, F.; Poinsot, T., Actual impedance of nonreflecting boundary conditions: implications for computation of resonators, AIAA J, 42, 5, 958-964, (2004) |
| [45] | Struijs, R.; Rudgyard, M.; Nicoud, F.; Hernandez, G., A set of characteristic boundary conditions for the cell-vertex AVBP code, Tech. Rep., (1996), CERFACS, TR/CFD/96/09 |
| [46] | Tabor, G. R.; Baba-Ahmadi, M. H., Inlet conditions for large eddy simulation: a review, Comput Fluids, 39, 4, 553-567, (2010) · Zbl 1242.76084 |
| [47] | Taylor, G., The spectrum of turbulence. Proceedings of the royal society of London A: mathematical, Phys Eng Sci, 164, 919, 476-490, (1938) · JFM 64.1454.02 |
| [48] | Thompson, K. W., Time dependent boundary conditions for hyperbolic systems, J Comput Phys, 68, 1, 1-24, (1987) · Zbl 0619.76089 |
| [49] | Wang, G.; Duchaine, F.; Papadogiannis, D.; Duran, I.; Moreau, S.; Gicquel, L., An overset grid method for large eddy simulation of turbomachinery stages, J Comput Phys, 274, 333-355, (2014) · Zbl 1351.76039 |
| [50] | Wissink, J. G.; Zaki, T. A.; Rodi, W.; Durbin, P. A., The effect of wake turbulence intensity on transition in a compressor cascade, Flow Turbul. Combust., 93, 4, 555-576, (2014) |
| [51] | Wu, X., Inflow turbulence generation methods, Annu Rev Fluid Mech, 49, 1, 23-49, (2017) · Zbl 1359.76162 |
| [52] | Yoo, C. S.; Im, H. G., Characteristic boundary conditions for simulations of compressible reacting flows with multi-dimensional, viscous and reaction effects, Combust Theor Model, 11, 2, 259-286, (2007) · Zbl 1121.80342 |
| [53] | Yoo, C. S.; Wang, Y.; Trouvé, A.; Im, H. G., Characteristic boundary conditions for direct simulations of turbulent counterflow flames, Combust Theor Model, 9, 4, 617-646, (2005) · Zbl 1086.80006 |
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