The Blade Element Momentum Theory (BEMT) method is modified to analyze the propeller under extreme conditions. The BEMT method can give accurate calculation of thrust and power at normal conditions, but when it comes to the nonlinear condition, such as the conditions of extreme low and high advance ratio, BEMT cannot calculate the thrust, power, circulation and induced velocity accurately and robustly. In view of this problem, this paper discusses non-physical solution and the singular solution of induced velocity for the BEMT equations. Based on the vortex theory, a circulation-iteration method is developed to improve the robustness of propeller analysis at extreme conditions. To take multi-nonlinear effects into consideration, an artificial neural network is used to acquire the aerodynamic characteristics of large-angle effect, low Reynolds number and transonic effects of the blade element and to provide efficient prediction of nonlinear aerodynamic characteristics of blade elements for the BEMT. The modified BEMT is validated using the Computational Fluid Dynamics (CFD) method and the experiment, and a comparison of the results show high robustness and accuracy of the modified BEMT for extreme condition analysis. Calculation results demonstrate that the relative error of the thrust and power are less than 5% at normal conditions, and less than 10% at extreme conditions.
FAN Zhongyun
,
ZHOU Zhou
,
ZHU Xiaoping
,
WANG Rui
,
WANG Kelei
. High-robustness nonlinear-modification method for propeller blade element momentum theory[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018
, 39(8)
: 121869
-121869
.
DOI: 10.7527/S1000-6893.2018.21869
[1] MARTÍNEZ J, BERNABINI L, PROBST O, et al. An improved BEM model for the power curve prediction of stall-regulated wind turbines[J]. Wind Energy, 2005, 8(4):385-402.
[2] HUNSAKER D. A numerical blade element approach to estimating propeller flowfields[C]//AIAA Aerospace Sciences Meeting and Exhibit. Reston, VA:AIAA, 2007:446-450.
[3] DOSSING M. A detailed investigation of the corrected BEM method and the potential for improving blade design[C]//European Wind Energy Association, 2009.
[4] RWIGEMA M K. Propeller blade element momentum theory with vortex wake deflection[C]//ICAS Secretariat, 2010.
[5] VAQUERO A V, CHENG Y, DEL CAMPO V, et al. Characterization of low Reynolds number wind turbine aerodynamics by BEM theory and PIV measurements[C]//American Society of Mechanical Engineers, 2010.
[6] WHITMORE S A, MERRILL R S. Nonlinear large angle solutions of the blade element momentum theory propeller equations[J]. Journal of Aircraft, 2012, 49(4):1126-1134.
[7] BURDETT T A, VAN TREUREN K W. A theoretical and experimental comparison of optimizing angle of twist using BET and BEMT[C]//American Society of Mechanical Engineers (ASME), 2012.
[8] DING J J, WANG H, SUN L P, et al. Optimal design of wind turbine blades with Wilson and BEM method integrated[J]. Applied Mechanics & Materials, 2013, 404:286-291.
[9] EL KHCHINE Y, SRITI M. Performance prediction of a horizontal axis wind turbine using BEM and CFD methods[R]. Singapore:EDP Sciences, 2016.
[10] BARNES J P. Hybrid lifting-line/blade-element method for propeller or propfan performance[C]//AIAA Applied Aerodynamics Conference. Reston, VA:AIAA, 2017.
[11] DUMAKUDE N, KAMPER M J. Validation of BEM using CFD MRF method coupled with axial and radial induction factors[C]//AIAA Theoretical Fluid Mechanics Conference. Reston, VA:AIAA, 2017.
[12] CARROLL J, MARCUM D. Comparison of a blade element momentum model to 3D CFD simulations for small scale propellers[J]. SAE International Journal of Aerospace, 2013, 6(2):721-726.
[13] MORGADO J, SILVESTRE M A R, PASCOA J C. Full range airfoil polars for propeller blade element momentum analysis[R]. Reston, VA:AIAA, 2013.
[14] DORFLING J, ROKHSAZ K. Non-linear aerodynamic modeling of airfoils for accurate blade element propeller performance predictions[C]//AIAA Applied Aerodynamics Conference. Reston, VA:AIAA, 2014.
[15] KWON H I, YI S, CHOI S, et al. Design of efficient propellers using variable-fidelity aerodynamic analysis and multilevel optimization[J]. Journal of Propulsion & Power, 2015, 31(4):1-16.
[16] MACNEILL R, VERSTRAETE D. Blade element momentum theory extended to model low Reynolds number propeller performance[J]. Aeronautical Journal, 2017, 121(1240):835-857.
[17] HAYKIN S. 神经网络与机器学习[M]. 北京:机械工业出版社, 2011. HAYKIN S. Neural networks and learning machine[M]. Beijing:Machinery Industry Press, 2011(in Chinese).
[18] 陈明. MATLAB神经网络原理与实例精解[M]. 北京:清华大学出版社, 2013. CHEN M. MATLAB neural network principle and examples[M]. Beijing:Tsinghua University Press, 2013(in Chinese).
[19] SILVERSTEIN A. Scale effect on Clark Y airfoil characteristics from NACA full-scale wind-tunnel tests:Report No. 502[R]. Langley Field, VA:Technical Report Archive & Image Library,1935.
[20] VELDHUIS L L M. Propeller wing aerodynamic interference[C]//4th International Congress of the Aeronautical Science, 2005.
[21] 刘沛清. 空气螺旋桨理论及其应用[M]. 北京:北京航空航天大学出版社, 2006. LIU P Q. Theory and application of airscrew[M]. Beijing:Beihang University Press, 2006(in Chinese).
[22] 曹义华. 现代直升机旋翼空气动力学[M]. 北京:北京航空航天大学出版社, 2015. CAO Y H. Aerodynamics of modern helicopter rotors[M]. Beijing:Beihang University Press, 2015(in Chinese).
[23] THEODORSEN T. Theory of propellers[M]. New York:McGraw Hill, 1948.
[24] 段中喆, 刘沛清, 屈秋林. 某轻载螺旋桨滑流区三维流场特性数值研究[J]. 控制工程, 2012, 19(5):836-840. DUAN Z Z, LIU P Q, QU Q L. Numerical research on 3-D flow field characteristics within the slipstream of a low load propeller[J]. Control Engineering of China, 2012, 19(5):836-840(in Chinese).
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