Performance Investigation of Simple Low-dissipation AUSM ‎‎(SLAU) Scheme in Modeling of 2-D Inviscid Flow in Steam ‎Turbine Cascade Blades

Document Type : Research Paper

Authors

Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran‎

Abstract

This study evaluates the performance of the SLAU, AUSM+UP upwind schemes, and CUSP artificial dissipation scheme for the flow through the convergent-divergent nozzles and turbine stator blades under different pressure ratios by developing an in-house code. By comparing the results with analytical and experimental results, it is found that, despite the simplicity of the SLAU scheme in the absence of tuning variables, it provides reasonable predictions for different turbine blades in point of location and strength of the shocks. The SLAU scheme could converge at a much higher rate, leading to very much lower values of residuals. The SLAU scheme causes about 30% and 20% improvements over the prediction of the shock-induced losses in supersonic and subsonic outlet flows, respectively.

Keywords

Main Subjects

[1] Swanson, R.C., Radespiel, R., Turkel, E., On Some Numerical Dissipation Schemes, Journal of Computational Physics, 147(2), 1998, 518-544.
[2] Leonard, B.P., Simple High‐accuracy Resolution Program for Convective Modelling of Discontinuities, International Journal for Numerical Methods in Fluids, 8(10), 1988, 1291-1318.
[3] Amanifard, N., Stall Vortex Shedding Over a Compressor Cascade, International Journal of Engineering, 18(1), 2005, 9-16.
[4] Rehman, A., Qamar, S., High Order Finite-volume WENO Scheme for Five-equation Model of Compressible Two-fluid Flow, Computers & Mathematics with Applications, 76(11-12), 2018, 2648-2664.‏
[5] Jameson, A., Analysis and Design of Numerical Schemes for Gas Dynamics, 1: Artificial Diffusion, Upwind Biasing, Limiters and Their Effect on Accuracy and Multigrid Convergence, International Journal of Computational Fluid Dynamics, 4(3-4), 1995, 171-218.
[6] Liou, M.S., Steffen Jr, CJ., A New Flux Splitting Scheme, Journal of Computational Physics, 107(1), 1993, 23-39.
[7] Liou, M.S., Ten Years in the Making-AUSM-Family, 15th AIAA Computational Fluid Dynamics Conference, 2001.
[8] Liou, M.S., A Sequel to AUSM, Part II: AUSM+UP for All Speeds, Journal of Computational Physics, 214(1), 2006, 137-170.
[9] Matsuyama, S., Performance of All-Speed AUSM-Family Schemes for DNS of Low Mach Number Turbulent Channel Flow, Computers & Fluids, 91, 2014, 130-143.
[10] Fořt, J., Fürst, J., Halama, J., Hric, V., Louda, P., Luxa, M., Šimurda, D., Numerical Simulation of Flow Through Cascade in Wind Tunnel Test Section and Stand-alone Configurations, Applied Mathematics and Computation, 319, 2018, 633-646.
[11] Louda, P., Kozel, K., Prihoda, J., Numerical Modelling of Compressible Inviscid and Viscous Flow in Turbine Cascades, In Proceedings of ALGORITMY, 2012, 301-310.
[12] Louda, P., Sváček, P., Fořt, J., Fürst, J., Halama, J., Kozel, K., Numerical Simulation of Turbine Cascade Flow with Blade-fluid Heat Exchange, Applied Mathematics and Computation, 219(13), 2013, 7206-7214.
[13] Pacciani, R., Marconcini, M., Arnone, A., Comparison of the AUSM+UP and Other Advection Schemes for Turbomachinery Applications, Shock Waves, 29(5), 2019, 705-716.
[14] Alakashi, A.M., Basuno, B., Comparison Between Roe's Scheme and Cell-centered Scheme For Transonic Flow Pass Through a Turbine Blades Section. In IOP Conference Series: Earth and Environmental Science, 19(1), 2014.
[15] Singh, R., Holmes, G., Evaluation of an Artificial Dissipation and AUSM Based Flux Formulation: AD-AUSM, 42nd AIAA Fluid Dynamics Conference and Exhibit, New Orleans, Louisiana, 2012.
[16] Shima, E., Kitamura, K., On New Simple Low-Dissipation Scheme of AUSM-Family for All Speeds, 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2009.
[17] Thakur, S.S., Wright, J.A., A Parallel All-Speed Algorithm for High-Resolution Simulations of Turbulent Reacting and Multiphase Flows Using SLAU2 Scheme in a Rule-Based Framework, AIAA Aerospace Sciences Meeting, 2018.
[18] Shima, E., Kitamura, K., Parameter-Free SimpleLow-Dissipation AUSM-Family Scheme for All Speeds, AIAA Journal, 49(8), 2011, 1693-1709.
[19] Soltani, M., Younsi, J., Farahani, M., Investigation of a New Flux Scheme for the Numerical Simulation of the Supersonic Intake Flow, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 226(11), 2012, 1445-1454.
[20] Colonia, S., Steijl, R., Barakos, G., Implicit Implementation of the AUSM+ and AUSM+ UP Schemes, International Journal for Numerical Methods in Fluids, 75(10), 2014, 687-712.
[21] Shima, E., Kitamura, K., On AUSM-Family Scheme for All Speeds with Shock Detection for Carbuncle-fix, 19th AIAA Computational Fluid Dynamics, 2009, 3544.
[22] Yousefi Rad, E., Mahpeykar, M.R., A Novel Hybrid Approach for Numerical Modeling of the Nucleating Flow in Laval Nozzle and Transonic Steam Turbine Blades, Energies, 10(9), 2017, 1285.
[23] Swanson, R., Radespiel, R., Turkel, E., Comparison of Several Dissipation Algorithms for Central Difference Schemes, 13th Computational Fluid Dynamics Conference, 1997.
[24] Hsu, J.M.J., An Implicit-Explicit Flow Solver for Complex Unsteady Flows, Stanford University, 2004.
[25] Yousefi Rad, E., Mahpeykar, M.R., Studying the Effect of Convergence Parameter of CUSP's Scheme in 2D Modelling of Novel Combination of Two Schemes in Nucleating Steam Flow in Cascade Blades, Numerical Heat Transfer Part B: Fundamentals, 72, 2017, 325-347.
[26] Kitamura, K., Hashimoto, A., Reduced Dissipation AUSM-Family Fluxes: HR-SLAU2 and HR-AUSM+-up for High Resolution Unsteady Flow Simulations, Computers & Fluids, 126, 2016, 41-57.
[27] Chen, S.S., Cai, F.j., Xue, H.c., Wang, N., Yan, C., An Improved AUSM-Family Scheme with Robustness and Accuracy for All Mach Number Flows, Applied Mathematical Modelling, 77, 2020, 1065-1081.
[28] Bakhtar, F., Mahpeykar, M.R., Abbas, K., An Investigation of Nucleating Flows of Steam in a Cascade of Turbine Blading-Theoretical treatment, Journal of Fluids Engineering, 117(1), 1995, 138-144.
[29] Bakhtar, F., Zamri M.Y., On the Performance of a Cascade of Improved Turbine Nozzle Blades in Nucleating Steam–Part 3: Theoretical Analysis, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 225(7), 2011, 1649-1671.
[30] Bakhtar, F., Zamri, M.Y., Rodriguez-Lelis, J.M., A Comparative Study of Treatment of Two-Dimensional Two-Phase Flows of Steam by a Runge-Kutta and by Denton's Methods, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 221(6), 2007, 689-706.
[31] Bakhtar, F., Mahpeykar, M.R., On the Performance of a Cascade of Turbine Rotor Tip Section Blading in Nucleating Steam Part 3: Theoretical Treatment, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 211(3), 1997, 195-210.