This paper established a non-axisymmetric endwall optimization profiling platform based on genetic algorithm and designed a non-axisymmetric endwall for a transonic turbine based on the platform. The results show that compared with the original turbine cascade, the total pressure loss of turbine cascade after endwall profiling is reduced by 19.2%. Analyzing the three-dimensional flow field of the turbine cascade before and after endwall profiling, the transverse pressure gradient decreases in the upstream of the turbine cascade but increases in the downstream of the turbine cascade due to the endwall profiling. The corner vortex has a large deflection at the cascade outlet and fuses with passage vortex in the adjacent passage. This also makes the loss near the endwall region at downstream of outlet increase. In the supersonic zone, the air flows through the convex surface close to the suction surface to form a series of isentropic compression waves. The isentropic compression waves interact with the shock wave in the passage, reducing the intensity of the shock waves in the passage in the near endwall region and reducing the shock loss of the turbine cascade, which is the main reason for the reduction of the total pressure loss after the turbine cascade endwall profiling. The non-axisymmetric endwall has good adaptability at different incidence and different outlet Mach number. But when the out Mach number is lower than 0.54 or higher than 1.20, the total pressure loss could not be reduced with the non-axisymmetric endwall. When the outlet Mach number is lower than 0.54, flow in the turbine cascade is in subsonic and there is no shock wave in the passage. The transverse pressure gradient of upstream decreases while the transverse pressure gradient of downstream increases, which has little effect on secondary flow near endwall. Therefore, the total pressure loss of the turbine cascade doesn’t change obviously. When the outlet Mach number is higher than 1.20, the shock wave structure in the passage has changed, so the non-axisymmetric endwall can’t reduce the total pressure loss of the turbine cascade.
[1] Ainley D., Performance of axial-flow turbines. Proceedings of the Institution of Mechanical Engineers, 1948, 159(1): 230–244.
[2] Tsujita H., Kaneko M., Effects of shock wave development on secondary flow behavior in linear turbine cascade at transonic condition. Proceedings of the ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition, London, UK, 2020, Volume 2B, ASME paper, No. GT2020-15772.
DOI: 10.1115/GT2020-15772.
[3] Sharma O., Butler T., Predictions of end wall losses and secondary flow in axial flow turbine cascades. Journal of Turbomachinery, 1987, 109(2): 229–236.
[4] Hawthorne W., Rotational flow through cascades Part I: The components of vorticity. The Quarterly Journal of Mechanics & Applied Mathematics, 1955, 8(3): 266–279.
[5] Herzing H., Hansen A., Costello G., A visualization study of secondary flow in cascades. NACA Report. Report No. NACA-TR-1163, 1954.
[6] Klein A., Investigation of the entry boundary layer on the secondary flows in the blading of axial turbines. BHRA T, 1966, 1004.
[7] Langston L., Cross flows in a turbine cascade passage. Journal of Engineering for Gas Turbine and Power, 1980, 102(4): 866–874.
[8] Sharma O., Butler T., Predictions of endwall losses and secondary flows in axial flow turbine cascades. Journal of Turbomachinery, 1987, 109(2): 229–236.
[9] Goldstein R., Spores R., Turbulent transport on the endwall in the region between adjacent turbine blades. Journal of Heat Transfer, 1988, 110(4a): 862–869.
[10] Wang H., Olson S., Goldstein R., et al., Flow visualization in a linear turbine cascade of high performance turbine blade. Journal of Turbomachinery, 1997, 119(1): 1–8.
[11] Rose M., Non-axisymmetric end wall profiling in the hp ngvs of an axial flow gas turbine. ASME paper, No. 94-GT-249, 1994.
[12] Harvey N., Rose M., Taylor M., et al., Non-axisymmetric turbine end wall design: Part I—three-dimensional linear design system. Journal of Turbomachinery, 2000, 122(2): 278–285.
[13] Hartland J., Gregory-Smith D., Harvey N., et al. Nonaxisymmetric turbine end wall design: Part II: experimental validation. Journal of Turbomachinery, 2000, 122(2): 286–293.
[14] Brennan G., Harvey N., Rose M., et al., Improving the efficiency of the Trent 500 HP turbine using non-axisymmetric end walls: Part I: turbine design. ASME paper, No. 2001-GT-0444, 2001.
[15] Rose M.G., Harvey N.W., Seaman P., et al. Improving the efficiency of the Trent 500 HP turbine using non-axisymmetric end walls: Part II: experimental validation. ASME paper, No. 2001-GT-0505, 2001.
[16] Nagel M.G., Baier R.D., Experimentally verified numerical optimization of a 3d-parametrised turbine vane with non-axisymmetric end walls. ASME paper, No. GT-2003-38624, 2003.
[17] Poehler T., Gier J., Jeschke P., Numerical and experimental analysis of the effects of non-axisymmetric contoured stator endwalls in an axial turbine. ASME paper, No. GT2010-23350, 2010.
[18] Sun H., Song L., Li J., et al., Numerical investigations on nonaxisymmetrical end wall profiling and aerodynamic performance of a low aspect ratio cascade. Journal of Xi’an Jiaotong University, 2012, 46(11): 6–11.
[19] Guo Z., Song L., Sun H., et al., Aerodynamic optimization of a 3d parameterized turbine vane with non-axisymmetric endwall. Journal of Engineering Thermophysics, 2016, 37(2): 285–289.
[20] Huang J., Meng F., Song Y., et al., Non-axisymmetric endwall modeling for large meridional expansion turbines based on pressure field distribution. Journal of Aerospace Power, 2020, 35(05): 1051–1065.
[21] Zhu P., Zhou L., Fu H., et al., Simulation and experimental study of non-axisymmetric endwall flow control based on bezier curves. Energy Conservation Technology, 2022, 40(05): 456–462.
[22] Taremi F., Sjolander S., Praisner T., et al., Application of endwall contouring to transonic turbine cascades: experimental measurements at design conditions. Journal of Turbomachinery. 2013. 135(1): 011031.
[23] Li J., Yan X., He K., Effect of non-axisymmetric endwall profiling on heat transfer and film cooling effectiveness of a transonic rotor blade. Journal of Turbomachinery, 2020, 142(5): 051006.
[24] Arnone A., Stecco S.S., Transonic cascade flow prediction using the Navier-Stokes equations. ASME paper, No. 91-GT-313, 1991.
[25] Sun L., Li J., Song L., et al., Non-axisymmetric turbine endwall aerodynamic optimization design: Part I― turbine cascade design and experimental validations. ASME paper, No. GT2014-25362, 2014.
[26] Poehler T., Niewoehner J., Jeschke P., et al., Investigation of non-axisymmetric endwall contouring and three-dimensional airfoil design in a 1.5-stage axial turbine—Part I: design and novel numerical analysis method. Journal of Turbomachinery, 2015, 137(8): 081009.
[27] Liu Y., Tan H., Huang H., et al., Experimental research on flow characteristics of bumps with different compression configurations. Journal of Propulsion Technology, 2019, 40(08): 1752–1758.
[28] Liu Y., Xu R., Ma Y., et al., Investigation on the first passage shock loss with bump control inside a supersonic compressor cascade. Journal of Aerospace Power, 2019, 34(10): 2294–2304.
