Uncertainty analysis of global and local performance impact of inflow and geometric uncertainties using sparse grid-based non-intrusive polynomial chaos

Abstract

Flow variations at the inlet boundary due to the compressor operational condition changes and geometric variations of the realistic compressor blades due to the manufacturing variability cannot be absolutely avoided, the global and local performance impact of which requires to be considered in the mechanism study of performance change and the aerodynamic shape design. In this paper, a method to analyze the simultaneous impact of the inflow Mach number, inlet incidence and geometric uncertainties was proposed. To make the uncertainty modeling of geometric variations faster and closer to engineering practice, a parametric mathematical model based on scanning points on the blade was introduced to describing the profile and torsion errors in the method specially. Meanwhile, a sparse grid-based Non-Intrusive Polynomial Chaos (NIPC) was used for uncertainty quantification and uncertainty sensitivity analysis to alleviate the computational burden. Then, the method was combined with a loss source calculation method to estimate the global and local aerodynamic loss changes of a controlled diffusion compressor blade in a reference flow state of high inflow Mach number and large positive incidence, and the response performance of sparse grid-based NIPC was verified. The results show that inlet incidence and torsion error have a significance uncertainty effect on the boundary-layer separation above the suction surface, which is main reason for the fluctuation of global aerodynamic loss. The uncertainty effect of profile error on the boundary-layer separation is relatively weak, but profile error could have a certain uncertainty effect on the leading edge separation. The boundary-layer separation is insensitive to Inflow Mach number. Furthermore, a stochastic aerodynamic analysis in different reference inflow states was investigated, which reveals some laws that the uncertainty of the aerodynamic losses and the sensitivity of the inflow and geometric uncertainties change with reference inflow states.

Keywords

Uncertainty quantification uncertain sensitivity analysis manufacturing error inflow variation loss source analysis sparse grid-based NIPC

Get full access to this article

View all access options for this article.

References

Stenning

. Inlet distortion effects in axial compressors. J Fluids Eng 1980; 102(1): 7–13.

Bry

Laval

Billet

. Distorted flow field in compressor inlet channels. J Eng Gas Turbines Power 1985; 107(3): 782–791.

Garzon

. Probability aerothermal design of compressor airfoils. PhD thesis. Massachusetts: Institute of Technology, 2003.

Garzon

Darmofal

. On the aerodynamic design of compressor airfoils for robustness under geometric uncertainty: Proceeding of ASME Turbo Expo, Vienna, Austria, June 14–17: 2004: GT2004–53581.

Montomoli

Carnevale

D’Ammaro

, et al. Uncertainty quantification in computational fluid dynamics and aircraft engines. Cham, Switzerland: Springer, 2019.

Lange

Voigt

Vogeler

, et al. Probabilistic CFD simulation of a high-pressure compressor stage taking manufacturing variability into account: Proceeding of ASME Turbo Expo, Glasgow, UK, June 14–18: 2010: GT2010–22484.

Lange

Voigt

Vogeler

, et al.. Impact of manufacturing variability and nonaxisymmetry on high-pressure compressor stage performance. J Eng Gas Turbines Power 2012; 134(3): 032504.

Lange

Voigt

Vogeler

, et al. Principal component analysis on 3D scanned compressor blades for probabilistic CFD simulation. In: Proceedings of the 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 23–26 April 2012, Honolulu, Hawali, AIAA2012–1762.

Lange

Voigt

Vogeler

, et al. Impact of manufacturing variability on multistage high-pressure compressor performance. J Eng Gas Turbines Power 2012; 134(11): 112601.

10.

Kumar

Keane

Nair

, et al. Robust design of compressor fan blades against Erosion. J Mech Des 2006; 128(4): 864–873.

11.

Zhang

. Robust design optimization method for centrifugal impellers under surface roughness uncertainties due to blade fouling. Chin J Mech Eng 2016; 29(2): 301–314.

12.

Zheng

. Performance improvement of transonic centrifugal compressors by optimization of complex three-dimensional features. Proc Inst Mech Eng G J Aerosp Eng 2017; 231(14): 2723–2738.

13.

Bhattrai

de Baar

JHS

Neely

. Efficient uncertainty quantification for a hypersonic trailing-edge flap, using gradient-enhanced krigingcient uncertainty quantication for a hypersonic trailing-edge ap, using gradient-enhanced kriging. Aerosp Sci Technol 2018; 80: 261–268.

14.

Luo

Liu

. Statistical evaluation of performance impact of manufacturing variability by an adjoint method. Aerosp Sci Technol 2018; 77: 471–484.

15.

Luo

Zheng

Liu

. Optimal tolerance allocation in blade manufacturing by sensitivity-based performance impact evaluation. J Propuls Power 2020; 36(4): 632–638.

16.

Zhang

, et al. Nonlinear uncertainty quantification of the impact of geometric variability on compressor performance using an adjoint method. Chinese J Aeronaut 2022; 35(2): 17–21.

17.

Najm

. Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics. Annu Rev Fluid Mech 2009; 41(41): 35–52.

18.

Simon

Guillen

Sagaut

, et al. A gPC-based approach to uncertain transonic aerodynamics. Comput Methods Appl Mech Eng 2010; 199(17-20): 1091–1099.

19.

Chassaing

J-C

Lucor

. Stochastic investigation of flows about airfoils at transonic speedsows about airfoils at transonic speeds. AIAA J 2010; 48(5): 938–950.

20.

Gao

Cai

, et al. Robust optimization design of compressor blade considering machining error. In:Volume 2C: Turbomachinery, Charlotte, North Carolina, USA, June 26–30, 2017: GT2017–63157.

21.

Gao

Cai

. A robust blade design method based on non-intrusive polynomial chaos considering profile error. J Therm Sci 2019; 28: 875–885.

22.

Xia

Luo

Liu

. Statistical evaluation of performance impact of flow variations for a transonic compressor rotor blade. Energy 2019; 189(15): 116285.1–116285.12.

23.

Wang

Zou

. Uncertainty analysis of impact of geometric variations on turbine blade performance. Energy 2019; 176(7): 67–80.

24.

Ahlfeld

Montomoli

. A single formulation for uncertainty propagation in turbomachinery: SAMBA PC. J Turbomach 2017; 139(11): 111007.

25.

Loeven

Bijl

. The application of the probabilistic collocation method to a transonic axial flow compressorow compressor. In: 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 18th AIAA/ASME/AHS Adaptive Structures Conference 12th, AIAA Conference no AIAA 2010-1923, Orlando, 12–15 April 2010: American Institute of Aeronautics and Astronautics Inc: 1–16.

26.

Pecnik

Witteveen

JAS

Iaccarino

. Uncertainty quantication for laminar-turbulent transition prediction in RANS turbomachinery applications. In: 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, AIAA Conference, no. AIAA 2011-0660, Orlando, Florida, 04–07 January 2011.

27.

Sobol

. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Sim 2001; 55(1-3): 271–280.

28.

Chu

. Numerical investigation of inlet boundary layer skew in axial-flow compressor cascade and the corresponding non-axisymmetric end wall profiling. Proc Inst Mech Eng A: J Power Energ 2014; 228(6): 638–656.

29.

Guo

Chu

. Stochastic aerodynamic analysis for compressor blades with manufacturing variability based on a mathematical dimensionality reduction method. Proc Inst Mech Eng C: J Mech Eng Sci 2022; 236(10): 5719–5735.

30.

Hosder

Walters

Balch

. Efficient 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, Honolulu, Hawaii, 23–26 April 2007. AIAA 2007-1939.

31.

Goodhand

Robert

. Compressor leading edge spikes: a new performance criterion. J Turbomach 2011; 133(2): 621–656.

32.

Gerstner

Griebel

. Numerical integration using sparse grids. Numer Algorithms 1998; 18(3-4): 209–232.

33.

Xiu

Karniadakis

. Modeling uncertainty in flow simulations via generalized polynomial chaos. J Comput Phys 2003; 187(1): 137–167.

34.

Ahlfeld

Belkouchi

Montomoli

. SAMBA: sparse approximation of moment-based arbitrary polynomial chaos. J Comput Phys 2016; 320: 1–16.

35.

Sudret

. Global sensitivity analysis using polynomial chaos expansions. Reliab Eng Syst Saf 2008; 93(7): 964–979.

36.

Denton

. The 1993 IGTI scholar lecture: loss mechanisms in turbomachines. J Turbomach 1993; 115(4): 621–656.