Effects of Inlet Incidence Perturbations on Compressor Cascade Performance using Adaptive Sparse Grid Collocation

Document Type : Regular Article


School of Power and Energy, Northwestern Polytechnical University, Xi’an, 710072, China



The effects of inflow variations due to the working environment and flight attitude changes on turbomachines are considerable in the real world. Nevertheless, uncertainty quantification can be adopted to assess mean performance changes and perform the aerodynamic shape design as well as optimization. Thus, an uncertainty quantification method of adaptive sparse grid collocation (ASGC) was first introduced to address the inflow uncertainties’ effect issue effectively and accurately. Then, ASGC was utilized to evaluate the impacts of inlet incidence perturbations at different perturbation scales and reference inflow Mach numbers on the aerodynamic performance of a controlled diffusion cascade. The results showed that compared with the Monte Carlo simulation and static sparse gird collocation, the statistical accuracy and response accuracy of ASGC were maintained, and meanwhile its model construction efficiency was significantly improved because of the nested adaptive sampling feature. Under the perturbations of inlet incidences with high reference incidences, the mean aerodynamic loss always aggravates. The changes in aerodynamic loss nonlinearly depend on the inlet incidence perturbations, and the nonlinear dependence becomes greater when the perturbation scale. expands. At the same perturbation scale, the nonlinear dependence on the inlet incidence perturbations is further enhanced when the reference inflow Mach number rises. Finally, uncertainty quantification of the flow field revealed that the fluctuation of flow accelerations at the leading edge plays a fundamental role in determining the uncertainty of the aerodynamic loss.


Main Subjects

Ahlfeld, R. and F. Montomoli, (2017). A single formulation for uncertainty propagation in turbomachinery: SAMBA PC. Journal of Turbomachinery 139(11), 111007.##
Bammert, K. and H. Sandstede (1976). Influence of manufacturing tolerances and surface roughness of blades on the performance of turbines. Journal of Engineering for Gas Turbines and Power 98(1), 29-36.##
Barthelmann, V., E. Novak and K. Ritter (2000). High dimensional polynomial interpolation on sparse grids. Advances in Computational Mathematics 12(4), 273-288.##
Bry, P., P, Laval and G. Billet (1985). Distorted flow field in compressor inlet channels. Journal of Engineering for Gas Turbines and Power 107(3), 782-791.##
Conrad, P. and Y. Marzouk (2013) Adaptive smolyak pseudospectral approximations. SIAM Journal of Scientific Computing 35(6), A2643-A2670.##
Garzon, V. E. and D. L. Darmofal (2003). Impact of geometric variability on axial compressor performance. Journal of Turbomachinery 125 (4), 692-703.##
Garzon, V. E. and D. L. Darmofal (2004). On the aerodynamic design of compressor airfoils for robustness under geometric uncertainty. In Turbo Expo: Power for Land, Sea, and Air, GT2004-53581.##
Genz, A. and B. D. Keister (1996). Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight. Journal of Computational and Applied Mathematics 71(2), 299-309.##
Gerstner, T. and M. Griebel (1998). Numerical integration using sparse grids. Numerical Algorithms 18, 209-232.##
Goodhand, M. N. (2010). Compressor Leading Edges. Ph. D. Thesis, University of Cambridge, England, Cambridge.##
Goodhand, M. N. and R. J. Robert (2011) Compressor leading edge spikes: a new performance criterion. Journal of Turbomachinery 133(2), 621-656.##
Gopinathrao, N. P., D. Bagshaw, C. Mabilat and S. Alizadeh (2009). Non-deterministic CFD simulation of a transonic compressor rotor. In Turbo Expo: Power for Land, Sea, and Air, GT2009-60122.##
Griebel, M. (1998). Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences. Computing 61, 151-179.##
Guo, Z. and W. Chu (2022). Stochastic aerodynamic analysis for compressor blades with manufacturing variability based on a mathematical dimensionality reduction method. Proceeding of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science 236(10), 5719-5735.##
Guo, Z., W. Chu and H. Zhang (2022a). A data-driven non-intrusive polynomial chaos for performance impact of high subsonic compressor cascades with stagger angle and profile errors. Aerospace Science and Technology 129, 107802.##
Guo, Z., W. Chu and H. Zhang (2022b). Uncertainty analysis of global and local performance impact of inflow and geometric uncertainties using sparse grid-based non-intrusive polynomial chaos. Proceeding of the Institution of Mechanical Engineers Part A: Journal of Power and Energy 236(7), 1239 -1256.##
Heiss, F. and V. Winschel (2008). Likelihood approximation by numerical integration on sparse grids. Journal of Econometrics 144(1), 62-80.##
Hosder, S., R., Walters and M. Balch (2007). Sampling for non-intrusive polynomial chaos applications with multiple uncertain input variables. In: 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Conference Paper AIAA.##
Hosder, S., R. W. Walters and M. Balch (2010). Point-collocation nonintrusive PC method for stochastic computational fluid dynamics. AIAA Journal 48(12), 2721-2730.##
Lange, A., M. Voigt, K. Vogeler, H. Schrapp, E. Johann and V. Gümmer (2010). Probabilistic CFD simulation of a high-pressure compressor stage taking manufacturing variability into account. In Turbo Expo: Power for Land, Sea, and Air, GT2010-22484.##
Lange, A., M. Voigt, K. Vogeler, H. Schrapp, E. Johann and V. Gümmer (2012) Impact of manufacturing variability and nonaxisymmetry on high-pressure compressor stage performance. Journal of Engineering for Gas Turbines and Power 134(3), 032504.##
Liao, Q., D. Zhang and H. Tchelepi (2017). Nested sparse grid collocation method with delay and transformation for subsurface flow and transport problems. Advances in Water Resources 10, 158-173.##
Liu, Z., X. Wang and S. Kang (2014). Stochastic performance evaluation of horizontal axis wind turbine blades using non-deterministic CFD simulations. Energy 73, 126-136.##
Loeven, G. J. A. and H. Bijl (2010). The application of the probabilistic collocation method to a transonic axial flow compressor. In 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Conference Paper AIAA.##
Loeven, G. J. A., J. Wittevee and H. Bijl (2007). Probabilistic collocation: an efficient nonintrusive approach for arbitrarily distributed parametric uncertainties. In 45th AIAA Aerospace Sciences Meeting Exhibit, pp. 8-11.##
Luo, J. and F. Liu (2018). Statistical evaluation of performance impact of manufacturing variability by an adjoint method. Aerospace Science and Technology 77, 471-484.##
Ma, C., L. Gao, Y. Cai and R. Li (2017). Robust optimization design of compressor blade considering machining error. In Turbo Expo: Power for Land, Sea, and Air, GT2017-63157.##
Ma, X. and N. Zabaras (2009). An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations. Journal of Computational Physics 228(8), 3084-3113.##
Panizza, A., D. T. Rubino and L. Tapinassi (2014). Efficient uncertainty quantification of centrifugal compressor performance using polynomial chaos. In Turbo Expo: Power for Land, Sea, and Air, GT2014-25081.##
Putko, M. M., P. A. Newman, A. A. Taylor III and L. L. Green (2002). Uncertainty propagation and robust design in CFD using sensitivity derivatives. Journal of Fluids Engineering 124(1), 60-69.##
Roelke, R. J. and J. E. Haas (1983). The effects of rotor blade thickness and surface finish on the performance of a small axial flow turbine. Journal of Engineering for Gas Turbines and Power 105(2), 377-382.##
Seshadri, P., G. T. Parks and S. Shahpar (2015). Leakage uncertainties in compressors: the case of Rotor 37. Journal of Propulsion and Power 31(1), 456-466.##
Smoljak, S. A. (1963). Quadrature and interpolation formulae on tensor products of certain function classes. Doklady Akademii Nauk SSSR 4(5), 1042-1045.##
Stenning, A. (1980). Inlet distortion effects in axial compressors. Journal of Fluids Engineering 102 (1), 7-13.##
Wang, K., F. Chen, J. Yu and Y. Song (2020). Nested sparse-grid stochastic collocation method for uncertainty quantification of blade stagger angle. Energy 201, 117583.##
Wang, X. and Z. Zou (2019). Uncertainty analysis of impact of geometric variations on turbine blade performance. Energy 176, 67-80.##
Wu, X., W. Zhang, S. Song and Z. Ye (2017). Sparse grid-based polynomial chaos expansion for aerodynamics of an airfoil with uncertainties. Chinese of Aeronautics 31(5), 997-1011.##
Wunsch, D., C. Hirsch, R. Nigro and G. Coussement (2015). Quantification of combined operational and geometrical uncertainties in turbomachinery design. In Turbo Expo: Power for Land, Sea, and Air, GT2015-43399.##
Xia, Z., J. Luo and F. Liu (2019a). Performance impact of flow and geometric variations for a turbine blade using an adaptive NIPC method. Aerospace Science and Technology 90, 127-139.##
Xia, Z., J. Luo and F. Liu (2019b). Statistical evaluation of performance impact of flow variations for a transonic compressor rotor blade, Energy 189(15), 116285.##
Xiu, D. and G. Karniadakis (2003). Modelling uncertainty in flow simulations via generalized polynomial chaos. Journal of Computational Physics 187(1), 137-167. ##