Recent advances in uncertainty quantification research of aircraft icing

Yunquan HAO; Dazhi ZHAO; Weibin LI; Wei ZHAO; Jiangtao CHEN

doi:10.13224/j.cnki.jasp.20210611

Chinese

您当前的位置：

首页 >

文章列表页 >

Recent advances in uncertainty quantification research of aircraft icing

Combustion,Heat and Mass Transfer | 更新时间：2025-03-14

- Recent advances in uncertainty quantification research of aircraft icing
- Journal of Aerospace Power Vol. 37, Issue 9, Pages: 1855-1871(2022)
- 作者机构：
  
  1.西南石油大学理学院，成都 610500
  2.中国空气动力研究与发展中心计算空气动力研究所，四川绵阳 621000
- 作者简介：
- 基金信息：
- DOI：10.13224/j.cnki.jasp.20210611
  CLC：
- 稿件说明：
移动端阅览
Yunquan HAO, Dazhi ZHAO, Weibin LI, et al. Recent advances in uncertainty quantification research of aircraft icing[J]. Journal of Aerospace Power, 2022, 37(9): 1855-1871.
DOI：

Yunquan HAO, Dazhi ZHAO, Weibin LI, et al. Recent advances in uncertainty quantification research of aircraft icing[J]. Journal of Aerospace Power, 2022, 37(9): 1855-1871. DOI： 10.13224/j.cnki.jasp.20210611.

摘要

为深入认识影响飞机结冰的不确定性及其研究方法，从自然条件结冰、冰风洞试验、数值模拟等方面，介绍了飞机结冰不确定性来源，以蒙特卡洛法、多项式混沌法和随机配置法等为例，系统分析了各种不确定性量化方法在计算能力、求解精度等方面的优劣。考虑飞机结冰不确定性量化处于起步时期，重点综述了数值模拟中结冰条件不确定性对冰形和气动特性的影响。从结合单步法和多步法确定最佳结冰时间步长来提升结冰计算精度和效率、对其他关键部件进行结冰不确定性量化从而为更精细化的防/除冰系统的设计提供支撑，以及通过建立高精度的代理模型来代替原本复杂的数值模拟系统以应对考虑多个不确定性因素共同作用所带来的计算挑战等多个方面，全面展望不确定性量化方法及其在飞机结冰应用中的发展方向。

Abstract

In order to deeply understand the uncertainty affecting aircraft icing and its research methods

the sources of aircraft icing uncertainty were introduced from the aspects of natural icing

ice wind tunnel test

and numerical simulation.Taking Monte Carlo method

polynomial chaos method and random configuration method as examples

the advantages and disadvantages of various uncertainty quantification methods in calculation ability and solution accuracy were systematically analyzed.Furthermore

considering the quantification of aircraft icing uncertainty at the beginning

focus was put on the influence of icing condition uncertainty on ice shape and aerodynamic characteristics in numerical simulation.Finally

single‑step and multi‑step methods were combined to determine the best ice time step to improve the accuracy and efficiency of ice calculation

to quantify the ice uncertainty of other key components to provide support for the more refined design of ice prevention/de‑icing system

and to build a high‑precision proxy model to replace the original complex numerical simulation system for meeting the computational challenges caused by the combined action of multiple uncertainties

etc.Overall prospect of uncertainty quantification method and its development direction in aircraft icing application was presented.

关键词

Keywords

references

陈维建 . 飞机机翼结冰的数值模拟研究 [D]. 南京 : 南京航空航天大学 , 2007 .

CHEN Weijian . Numerical simulation of aircraft wing icing [D]. Nanjing : Nanjing University of Aeronautics and Astronautics , 2007 . （in Chinese）

苏媛 , 徐忠达 , 吴祯龙 . 飞机结冰后若干飞行力学问题综述 [J]. 航空动力学报 , 2014 , 29 （ 8 ）: 1878 ⁃ 1893 .

SU Yuan , XU Zhongda , WU Zhenlong . Overview of several ice accretion effects on aircraft flight dynamics [J]. Journal of Aerospace Power , 2014 , 29 （ 8 ）: 1878 ⁃ 1893 . （in Chinese）

REEHORST A L , ADDY H E , COLANTONIO R O . Examination of icing induced loss of control and it's mitigations [R]. AIAA⁃2010⁃8140 , 2010 .

ZHANG F , HUANG Z , YAO H , et al . Icing severity forecast algorithm under both subjective and objective parameters uncertainties [J]. Atmospheric Environment , 2016 , 128 : 263 ⁃ 267 .

BRAGG M B , BROEREN A P , BLUMENTHAL L A . Iced airfoil aerodynamics [J]. Progress in Aerospace Sciences , 2005 , 41 （ 5 ）: 323 ⁃ 362 .

易贤 , 桂业伟 , 朱国林 , 等 . 运输机翼型结冰的计算和实验 [J]. 航空动力学报 , 2011 , 26 （ 4 ）: 808 ⁃ 813 .

YI Xian , GUI Yewei , ZHU Guolin , et al . Experiment and computational investigation into ice accretion on airfoil of a transport aircraft [J]. Journal of Aerospace Power , 2011 , 26 （ 4 ）: 808 ⁃ 813 . （in Chinese）

田永强 , 蔡晋生 , 张正科 , 等 . 结冰风洞实验中的相似理论 [J]. 北京航空航天大学学报 , 2020 , 46 （ 2 ）: 359 ⁃ 370 .

TIAN Yongqiang , CAI Jinsheng , ZHANG Zhengke , et al . Similarity theory in icing wind tunnel test [J]. Journal of Beijing University of Aeronautics and Astronautics , 2020 , 46 （ 2 ）: 359 ⁃ 370 . （in Chinese）

姚若鹏 . 翼型的结冰数值模拟及相关控制研究 [D]. 南京 : 南京航空航天大学 , 2012 .

YAO Ruopeng . The numerical simulation of ice accretion on airfoil and control research [D]. Nanjing : Nanjing University of Aeronautics and Astronautics , 2007 . （in Chinese）

YAN L , SUN C , YU J , et al . Scaling method of the rotating blade of a wind turbine for a rime ice wind tunnel test [J]. Energies , 2019 , 12 （ 627 ）: 1 ‑ 15 .

李哲 , 徐浩军 , 薛源 , 等 . 结冰对飞机飞行安全的影响机理与防护研究 [J]. 飞行力学 , 2016 , 34 （ 4 ）: 10 ⁃ 14 .

LI Zhe , XU Haojun J , XUE Yuan , et al . Research on flight safety effect mechanism and protection for aircraft icing [J]. Flight Dynamics , 2016 , 34 （ 4 ）: 10 ⁃ 14 . （in Chinese）

林贵平 . 飞机结冰与防冰技术 [M]. 北京 : 北京航空航天大学出版社 , 2016 .

薛源 , 徐浩军 , 裴彬彬 , 等 . 基于蒙特卡洛法的飞机结冰后动力学特性分析 [J]. 实验流体力学 , 2016 , 30 （ 2 ）: 26 ⁃ 31,37 .

XUE Yuan , XU Haojun , PEI Binbin , et al . Dynamic characteristics analysis after aircraft icing based on Monte Carlo method [J]. Journal of Experiments in Fluid Mechanics , 2016 , 30 （ 2 ）: 26 ⁃ 31,37 . （in Chinese）

SAEED F , SELIG M S , BRAGG M B . A design procedure for subscale airfoils with full⁃scale leading edges for ice accretion testing [R]. AIAA⁃96⁃0635 , 1996 .

RUFF G A , ANDERSON D N . Quantification of ice Accretions for icing scaling evaluations [R]. AIAA⁃98⁃0195 , 1998 .

马军林 , 肖京平 , 王桥 , 等 . 飞机结冰相似准则研究进展 [J]. 飞行力学 , 2019 , 37 （ 4 ）: 1 ⁃ 7 .

MA Junlin , XIAO Jingping , WANG Qiao , et al . Advances in the study of aircraft icing similarity criteria [J]. Flight Dynamics , 2019 , 37 （ 4 ）: 1 ⁃ 7 . （in Chinese）

GRAY V H , GLAHN U H V . Effect of ice and frost formations on drag of NACA 65 1 ⁃212 airfoil for various modes of thermal ice protection [R]. NACA⁃TN⁃2962 , 1953 .

GRAY V H , VONGLAHN U H . Aerodynamic effects caused by icing of an unswept NACA 65A004 airfoil [R]. NACA⁃TN⁃4155 , 1958 .

GRAY V H . Correlations among ice measurements , impingement rates icing conditions , and drag coeffi⁃cients for unswept NACA 65A004 airfoil [R]. NACA⁃TN⁃4151 , 1958 .

MILLER D R , POTAPCZUK M G , LANGHALS T J . Preliminary investigation of ice shape sensitivity to parameter variations [R]. AIAA⁃2005⁃0073 , 2005 .

MILLER D R , POTAPCZUK M G , LANGHALS T J . Additional investigations of ice shape sensitivity to para⁃meter variations [R]. AIAA⁃2006⁃0469 , 2006 .

SCHAEFER J A , ROMERO V J , SCHAEFER S R , et al . Approaches for quantifying uncertainties in computational modeling for aerospace applications [R]. AIAA⁃2020⁃1520 , 2020 .

陈鑫 , 王刚 , 叶正寅 , 等 . CFD不确定度量化方法研究综述 [J]. 空气动力学学报 , 2021 , 39 （ 4 ）: 1 ⁃ 13 .

CHEN Xin , WANG Gang , YE Zhenyin , et al . A review of uncertainty quantification methods for computational fluid dynamics [J]. Acta Aerodynamica Sinica , 2021 , 39 （ 4 ）: 1 ⁃ 13 . （in Chinese）

MACARTHUR C D . Numerical simulation of airfoil ice accretion [R]. AIAA⁃83⁃0112 , 1983 .

MESSINGER B . Equilibrium temperature of an unheated icing surface as a function of air speed [J]. Journal of the Aeronautical Sciences , 1953 , 20 （ 1 ）: 29 ⁃ 42 .

MYERS T G . Extension to the messinger model for aircraft icing [J]. AIAA Journal , 2001 , 39 （ 2 ）: 211 ⁃ 218 .

FORTIN G , ILINCA A , LAFORTE J L , et al . Prediction of 2D airfoil ice accretion by bisection method and by rivulets and beads modeling [R]. AIAA⁃2003⁃1076 , 2003 .

ANDERSON D N , TSAO J C . Additional results of ice accretion scaling at SLD conditions [R]. AIAA‑2003⁃0390 , 2003 .

LANGMUIR I , BLODGETT K B . A mathematical investigation of water droplet trajectories [R]. Army Air Forces Technical Report NO . 5418 , 1946 .

任靖豪 , 易贤 , 王强 , 等 . 复杂构型水滴收集率的拉格朗日计算方法 [J]. 航空动力学报 , 2020 , 35 （ 12 ）: 2553 ⁃ 2561 .

REN Jinghao , YI Xian , WANG Qiang , et al . Lagrangian simulation method of droplet collection efficiency for complex configuration [J]. Journal of Aerospace Power , 2020 , 35 （ 12 ）: 2553 ⁃ 2561 . （in Chinese）

阎超 . 计算流体力学方法及应用 [M]. 北京 : 北京航空航天大学出版社 , 2006 .

BILODEAU D . An Eulerian framework for supercooled large droplets splashing and bouncing [D]. Montreal,Canada : McGill University , 2014 .

BOURGAULT Y , HABASHI W G , DOMPIERRE J , et al . A finite element method study of Eulerian droplets impingement models [J]. International Journal for Numerical Methods in Fluids , 1999 , 29 （ 4 ）: 429 ⁃ 449 .

BOURGAULT Y , BOUTANIOS Z , HABASHI W G . Three dimensional Eulerian approach to droplet impingement simulation using FENSAP⁃ICE:Part 1 model,algorithm and Validation [J]. Journal of Aircraft , 2000 , 37 （ 1 ）: 95 ‑ 103 .

SCHAEFER J A , HOSDER S , MANI M , et al . The effect of grid topology and flow solver on turbulence model closure coefficient uncertainties for a transonic airfoil [R]. AIAA ⁃ 2016 ‑4400. 2016 .

CULLEN A , FREY H C . Probabilistic techniques in exposure assessment:a handbook for dealing with variability and uncertainty in models and inputs [M]. New York : Plenum Press , 1999 .

XU C , QU A , LI H . A study on the foundations of probability theory [J]. Pure and Applied Mathematics , 2007 , 23 （ 4 ）: 453 ‑ 457 .

WIENER N . The homogeneous chaos [J]. American Journal of Mathematics , 1938 , 60 （ 4 ）: 897 ⁃ 936 .

VAN KAMPEN N G , REINHARDT W P . Stochastic processes in physics and chemistry [J]. Physics Today , 1983 , 36 （ 2 ）, 78 ⁃ 80 .

LUO M , WEI H . A new logic for uncertainty [EB/OL]. [ 2021‑10‑17 ]. https:∥doi.org/10.48550/arXiv.1506.03123 https://doi.org/10.48550/arXiv.1506.03123 .

王鹏 , 修东滨 . 不确定性量化导论 [M]. 北京 : 科学出版社 , 2019 .

SULLIVAN T J . Introduction to uncertainty quantification [M]. Berlin : Springer , 2015 .

汤涛 , 周涛 . 不确定性量化的高精度数值方法和理论 [J]. 中国科学:数学 , 2015 , 45 （ 7 ）: 891 ⁃ 928 .

TANG Tao , ZHOU Tao . Recent developments in high order numerical methods for uncertainty quantification [J]. Science China:Math , 2015 , 45 （ 7 ）: 891 ⁃ 928 . （in Chinese）

FISHMAN G S . Monte Carlo:concepts,algorithms,and applications [M]. Berlin : Springer , 1996 .

LE MAÎTRE O P , KNIO O M . Spectral methods for uncertainty quantification:with applications to computational fluid dynamics [M]. Berlin : Springer , 2010 .

KELLER A . Monte Carlo and quasi⁃Monte Carlo methods [M]. Berlin : Springer , 2020 .

LI J , WINKER P . Time series simulation with quasi‑Monte Carlo methods [J]. Computational Economics , 2003 , 21 : 23 ‑ 24 .

STEIN M . Large sample properties of simulations using Latin hypercube sampling [J]. Technometrics , 1987 , 29 （ 2 ）: 143 ‑ 151 .

WEI⁃LIEM L . On Latin hypercube sampling [J]. Annals of Statistics , 1996 , 24 （ 5 ）: 2058 ⁃ 2080 .

GHANEM R . SPANOS P D . Stochastic finite elements:a spectral approach [M]. Berlin : Springer⁃Verlag , 1991 .

GHANEM R . Stochastic finite elements with multiple random non⁃Gaussian properties [J]. Journal of Engineering Mechanics , 1999 , 125 （ 1 ）: 26 ⁃ 40 .

GHANEM R . Scales of fluctuation and the propagation of uncertainty in random porous media [J]. Water Resources Research , 1998 , 34 （ 9 ）: 2123 ⁃ 2136 .

GHANEM R , RED⁃HORSE J . Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach [J]. Physica D:Nonlinear Phenomena , 1999 , 133 （ 1/2/3/4 ）: 137 ⁃ 144 .

XIU D , KARNIADAKIS G E . The Wiener⁃Askey polynomial chaos for stochastic differential equations [J]. SIAM Journal on Scientific Computing , 2002 , 24 （ 2 ）: 619 ⁃ 644 .

WAN X , KARNIADAKIS G E . An adaptive multi element generalized polynomial chaos method for stochastic differential equations [J]. Journal of Computational Physics , 2005 , 209 （ 2 ）: 617 ⁃ 642 .

WAN X , KARNIADAKIS G E . Multi⁃element generalized polynomial chaos for arbitrary probability measures [J]. SIAM Journal on Scientific Computing , 2006 , 28 （ 3 ）: 901 ⁃ 928 .

PREMPRANEERACH P , HOVER F S , TRIANTAFY⁃LLOU M S , et al . Uncertainty quantification in simulations of power systems:multielement polynomial chaos methods [J]. Reliability Engineering and System Safety , 2010 , 95 （ 6 ）: 632 ⁃ 646 .

XIU D . Fast numerical methods for stochastic computations:a review [J]. Communications in Computational Physics , 2010 , 5 （ 2/3/4 ）: 242 ⁃ 272 .

SOIZE C , GHANEM R . Physical systems with random uncertainties:chaos representations with arbitrary probability measure [J]. SIAM Journal on Scientific Computing , 2004 , 26 （ 2 ）: 395 ⁃ 410 .

WITTEVEEN J A S , BIJL H . Reliable computational predictions by modeling uncertainties using arbitrary polynomial chaos [R]. Delft,Netherland : European Conference on Computational Fluid Dynamics , 2006 .

WITTEVEEN J A S , SARKAR S , BIJL H . Modeling physical uncertainties in dynamic stall induced fluid⁃structure interaction of turbine blades using arbitrary polynomial chaos [J]. Computers and Structures , 2007 , 85 （ 11/12/13/14 ）: 866 ‑ 878 .

ERNST O G , MUGLER A , STARKLOFF H J , et al . On the convergence of generalized polynomial chaos expansions [J]. Journal of Computational Physics , 2011 , 229 （ 2 ）: 3134 ⁃ 3154 .

OLADYSHKIN S , NOWAK W . Data‑driven uncertainty quantification using the arbitrary polynomial chaos expansion [J]. Reliability Engineering and System Safety , 2012 , 106 : 179 ‑ 190 .

LING G , LIU Y , TAO Z . Data⁃driven polynomial chaos expansions:a weighted least⁃square approximation [J]. Journal of Computational Physics , 2018 , 381 : 129 ⁃ 145 .

金冶书 . 基于数据驱动的多保真稀疏多项式逼近及其在不确定性量化中的应用 [D]. 上海 : 上海师范大学 , 2019 .

JING Yeshu . Data⁃driven multi⁃fidelity sparse polynomial approximation and its application in uncertainty quantification [D]. Shanghai : Shanghai Normal University , 2019 . （in Chinese）

LIU Z , CHOE Y . Data⁃driven sensitivity indices for models with dependent inputs using the polynomial chaos expansion [J]. Structural Safety , 2020 , 88 : 1 ⁃ 10 .

CHEN M , GUO T , CHEN C , et al . Data⁃driven arbitrary polynomial chaos expansion on uncertainty quantification for real⁃time hybrid simulation under stochastic ground motions [J]. Experimental Techniques , 2020 , 44 （ 1 ）: 1 ⁃ 12 .

AHLFELD R , BELKOUCHI B , MONTOMOLI F . SAMBA:sparse approximation of moment based arbitrary polynomial chaos [J]. Journal of Computational Physics , 2016 , 320 : 1 ‑ 16 .

COHEN A , DEVORE R , SCHWAB C . Convergence rates of best N⁃term Galerkin approximations for a class of elliptic sPDEs [J]. Foundations of Computational Mathematics , 2010 , 10 （ 6 ）: 615 ⁃ 646 .

NEDAIASL K , DEHBOZORGI R . Galerkin finite element method for nonlinear fractional differential equations [J]. Numerical Algorithms , 2021 , 88 （ 1 ）: 113 ⁃ 141 .

董世充 . 风力机翼型的不确定性CFD模拟研究 [D]. 北京 : 华北电力大学 , 2015 .

DONG Shichong . Non⁃deterministic CFD simulations of wind turbine airfoil [D]. Beijing : North China Electric Power University , 2015 . （in Chinese）

SMOLYAK S A . Quadrature and interpolation formulas for tensor products of certain classes of functions [J]. Doklady Akademii Nauk SSSR , 1963 , 4 （ 5 ）: 240 ⁃ 243 .

NOBILE F , TEMPONERAÚL , WEBSTER C G . An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data [J]. SIAM Journal on Numerical Analysis , 2008 , 46 （ 5 ）: 2411 ⁃ 2442 .

XIANG M , ZABARAS N . An adaptive high⁃dimensio⁃nal stochastic model representation technique for the solution of stochastic partial differential equations [J]. Journal of Computational Physics , 2010 , 229 （ 10 ）: 3884 ⁃ 3915 .

DAI Y , CHAO Y . Smolyak⁃grid⁃based flutter analysis with the stochastic aerodynamic uncertainty [J]. Discrete Dynamics in Nature and Society , 2014 , 2014 : 174927.1 ⁃ 1749278 .

NABILE F , TEMPONE R , WEBSTER C G . A sparse grid stochastic collocation method for partial differetial equations with random input data [J]. SIAM Journal on Numerical Analysis , 2008 , 46 （ 5 ）: 2309 ⁃ 2345 .

GANAPATHYSUBRAMANIAN B , ZABARAS N . Sparse grid collocation schemes for stochastic natural convection problems [J]. Journal of Computational Physics , 2007 , 225 （ 1 ）: 652 ⁃ 685 .

COHEN A , DAVENPORT M A , LEVIATAN D . On the stability and accuracy of least squares approximations [J]. Foundations of Computational Mathematics , 2013 , 13 （ 5 ）: 819 ⁃ 834 .

HOSDER S , WALTERS R W , BALCH M . Point collocation nonintrusive polynomial chaos method for stochastic computational fluid dynamics [J]. AIAA Journal , 2010 , 48 （ 12 ）: 2721 ⁃ 2730 .

MIGLIORATI G , NOBILE F , SCHWERIN E V , et al . Analysis of the discrete L 2 projection on polynomial spaces with random evaluations [J]. Foundations of Computational Mathematics , 2014 , 14 : 419 ⁃ 456 .

ZHOU T , NARAYAN A , XU Z . Multivariate discrete least⁃squares approximations with a new type of collocation grid [J]. SIAM Journal on Scientific Computing , 2014 , 36 （ 5 ）: 1 ‑ 20 .

DONOHO D L . Compressed sensing [J]. IEEE Transactions on Information Theory , 2006 , 52 （ 4 ）: 1289 ⁃ 1306 .

TODOR R A , SCHWAB C , et al . Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients [J]. IMA Journal of Numerical Analysis , 2007 , 27 （ 2 ）: 232 ⁃ 261 .

FIGUEIREDO M , NOWAK R D , WRIGHT S J . Gradient projection for sparse reconstruction:application to compressed sensing and other inverse problems [J]. IEEE Journal of Selected Topics in Signal Processing , 2008 , 1 （ 4 ）: 586 ‑ 597 .

GREGORY N , O'REILLY C L . Low⁃speed aerodynamic characteristics of NACA 0012 airfoil section,including the effects of upper⁃surface roughness simulating hoar frost [R]. Aeronautical Research Council Reports and Memoranda NO . 3726 , 1970 .

SHIN J . Characteristics of surface roughness associated with leading edge ice accretion [J]. Journal of Aircraft , 1996 , 33 （ 2 ）: 316 ⁃ 321 .

朱程香 , 孙志国 , 付斌 , 等 . 水滴多尺寸分布对水滴撞击特性和结冰增长的影响 [J]. 南京航空航天大学学报 , 2010 , 42 （ 5 ）: 620 ⁃ 624 .

ZHU Chengxiang , SUN Zhiguo , FU Bin , et al . Effects of muti⁃dispersed droplet impingement and ice accretion [J]. Journal of Nanjing University of Aeronautics and Astronautics , 2010 , 42 （ 5 ）: 620 ⁃ 624 . （in Chinese）

易贤 , 王开春 , 马洪林 , 等 . 大型风力机结冰过程水滴收集率三维计算 [J]. 空气动力学学报 , 2013 , 31 （ 6 ）: 745 ⁃ 751 .

YI Xian , WANG Kaichun , MA Honglin , et al . 3⁃D numerical simulation of droplet collection efficiency in large⁃scale wind turbine icing [J]. Acta Aerodynamica Sinica , 2013 , 31 （ 6 ）: 745 ⁃ 751 . （in Chinese）

张建荣 . 气象条件对飞机及其飞行的影响分析 [J]. 航空科学技术 , 2014 （ 5 ）: 54 ⁃ 56 .

ZHANG Jianrong . Impact analysis of weather conditions on aircraft and its flight [J]. Aeronautical Science and Technology , 2014 , 25 （ 5 ）: 54 ⁃ 56 . （in Chinese）

FENG K , LU Z , YUN W . Aircraft icing severity analysis considering three uncertainty types [J]. AIAA Journal , 2019 , 57 （ 4 ）: 1514 ⁃ 1522 .

李佩哲 . 面向自然结冰试飞的翼型结冰数值模拟研究 [D]. 上海 : 上海交通大学 , 2019 .

LI Peizhe . Numerical simulation of wing icing for natural icing flight test [D]. Shanghai : Shanghai Jiao Tong University , 2019 . （in Chinese）

CAO Y , CHAO M , QIANG Z , et al . Numerical simulation of ice accretions on an aircraft wing [J]. Aerospace Science and Technology , 2012 , 23 （ 1 ）: 296 ⁃ 304 .

严晓雪 . 机翼结冰粗糙度及对流换热研究 [D]. 南京 : 南京航空航天大学 , 2016 .

YAN Xiaoxue . Research of surface roughness and convective heat transfer on airfoil icing [D]. Nanjing : Nanjing University of Aeronautics and Astronautics , 2016 . （in Chinese）

YAN L , CHAO W , CHANG S N , et al . Simulation of ice accretion based on roughness distribution [J]. Procedia Engineering , 2011 , 17 : 160 ⁃ 177 .

KEVIN I , FRANÇOIS M , HÉLOÏSE B . Sensitivity study of ice accretion simulation to roughness thermal correction model [J]. Aerospace , 2021 , 8 （ 3 ）: 1 ⁃ 20 .

AUPOIX B . Improved heat transfer predictions on rough surfaces [J]. International Journal of Heat and Fluid Flow , 2015 , 56 : 160 ⁃ 171 .

MORENCY F , BEAUGENDRE H . Comparison of tur⁃bulent prandtl number correction models for the stanton evaluation over rough surfaces [J]. International Journal of Computation Fluid Dynamics . 2020 , 34 （ 10 ）: 1 ⁃ 21 .

MARELLI S , SUDRET B . UQLab user manual⁃polynomial chaos expansions [R]. Zurich : Chair of Risk,Safety and Uncertainty Quantiﬁcation,ETH Zurich , 2015 .

KATO H , ITO K , LEPOT I . Sensitivity analysis based on high fidelity simulation:application to hypersonic variable⁃cycle engine intake design [J]. International Journal of Engineering Systems Modeling and Simulation , 2010 , 2 （ 1/2 ）: 38 ⁃ 45 .

SALTELLI A , TARANTOLA S , CHAN K . Quantitative model‑independent method for global sensitivity analysis of model output [J]. Technometrics , 1999 , 41 （ 1 ）: 39 ‑ 56 .

SOBOL' I M . Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates [J]. Mathematics and Computers in Simulation , 2001 , 55 （ 1/2/3 ）: 271 ‑ 280 .

徐文丰 , 李颖晖 , 禹志龙 , 等 . 结冰飞机的包线保护与控制裕度研究 [J]. 控制与决策 , 2021 , 36 （ 6 ）: 1415 ⁃ 1424 .

XU Wenfeng , LI Yinghui , YU Zhilong , et al . Envelope protection and control margin of icing aircraft [J]. Control and Decision , 2021 , 36 （ 6 ）: 1415 ⁃ 1424 . （in Chinese）

黄冉冉 , 李栋 , 刘藤 , 等 . 冰形表面粗糙度对翼型的失速特性影响分析 [J]. 空气动力学学报 , 2021 , 39 （ 1 ）: 59 ⁃ 65 .

HUANG Ranran , LI Dong , LIU Teng , et al . The effect of ice accretion roughness on airfoil stall characteristic [J]. Acta Aerodynamica Sinica , 2021 , 39 （ 1 ）: 59 ⁃ 65 . （in Chinese）

PAPADAKIS M , ALANSATAN S , WONG S C . Aerodynamic characteristics of a symmetric NACA section with simulated ice shapes [R]. AIAA⁃2000⁃0098 , 2000 .

DEGENNARO A M , ROWLEY C W , MARTINELLI L . Uncertainty quantification for airfoil icing using polynomial chaos expansions [J]. Journal of Aircraft , 2015 , 52 （ 5 ）: 1404 ⁃ 1411 .

DEGENNARO A M . Uncertainty quantification for airfoil icing [D]. Princeton,US : Princeton University , 2016 .

TABATABAEI N , RAISEE M , CERVANTES M J . Uncertainty quantification of aerodynamic icing losses in wind turbine with polynomial chaos expansion [J]. Journal of Energy Resources Technology , 2019 , 141 （ 5 ）: 1 ⁃ 17 .

BOSE N . Icing on a small horizontal⁃axis wind turbine Part 1:glaze ice profiles [J]. Journal of Wind Engineering and Industrial Aerodynamics , 1992 , 45 （ 1 ）: 75 ⁃ 85 .

HOCHART C , FORTIN G , PERRON J , et al . Icing simulation of wind turbine blades [J]. AIAA Journal , 2007 , 2 （ 3 ）: 876 ⁃ 883 .

王晓东 , 于佳鑫 , 房代宝 , 等 . 随机风况下风力机翼型结冰对气动特性的影响研究 [J]. 风机技术 , 2020 , 62 （ 2 ）: 59 ⁃ 66 .

WANG Xiaodong , YU Jiaxin , FANG Daibao , et al . Investigations on the influence of icing on aerodynamics of wind turbine airfoil under stochastic wind conditions [J]. Chinese Journal of Turbomachinery , 2020 , 62 （ 2 ）: 59 ⁃ 66 . （in Chinese）

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Uncertainty quantification of rotor blade dynamic strain reconstruction based on blade tip timing

Numerical investigation of thermal and mechanical equilibrium characteristics of ice crystal in large icing wind tunnel

Uncertainty analysis of effects of end wall fillet radius error on high⁃load stator cascade performance

Numerical simulation method of the variability in tensile properties of SiC/SiC minicomposites

Research on stability reliability of pipe conveying fluid based on finite element method

Related Author

Xuefeng CHEN

Meiru LIU

Shunguo FU

Lei CHEN

Baijie QIAO

Chunyan AO

Xiangdong GUO

Zhanwei HU

Related Institution

School of Mechanical and Engineering，Xi'an Jiaotong University

The State Key Laboratory for Manufacturing Systems Engineering，Xi'an Jiaotong University

Sichuan Gas Turbine Establishment，Aero Engine Corporation of China

Key Laboratory of Icing and Anti/De⁃icing， China Aerodynamics Research and Development Center

School of Power and Energy，Northwestern Polytechnical University

AI问答

Postal code：100079
Tel：（010）53879206 Email：tmw@bjxintong.com.cn
Technical support is provided by Beijing Founder electronics co., LTD 京ICP备09082226号-64 京公网安备11010602201714号
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰