基于代理模型和线性近似的快速气动热边界求解方法
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摘要
采用本征正交分解(Proper Orthogonal Decomposition,POD)与Kriging代理模型相结合,建立快速求解气动热参数的降阶模型。引入一种基于换热系数的线性近似方法进行热边界传递,以减少因壁温变化引起的流场迭代。以三维翼面为例,对气动热的计算分析表明,利用POD-Kriging模型快速得到的翼面热流分布与计算流体力学(Computational Fluid Dynamics,CFD)方法得到的热流分布平均误差在7%以下,而且随着POD基模态个数的提高,误差能够明显降低。结果表明该方法具有较好的计算精度,结合线性近似方法处理热边界,在不降低气动热计算精度的前提下,能够大幅度减少计算耗时。
A reduced order frame combining the proper orthogonal decomposition(POD) with Kriging model was built for calculating the aerodynamic heat transfer quickly. A linear approximation method based on heat transfer coefficient is introduced to reduce the flow iterations due to the wall temperature change. Taking the 3D wing as an example, the result showed that the average error of the heat flux of the wing surface got from the POD-Kriging model is below 7%, while comparing with the CFD results. With the increase of the POD basic mode, the error could be greatly reduced, which shows that this method has good calculation accuracy. With the linear approximation method to deal with the thermal boundary, the computational time can be greatly reduced without reducing the accuracy of the aerodynamic thermal calculation.
A reduced order frame combining the proper orthogonal decomposition(POD) with Kriging model was built for calculating the aerodynamic heat transfer quickly. A linear approximation method based on heat transfer coefficient is introduced to reduce the flow iterations due to the wall temperature change. Taking the 3D wing as an example, the result showed that the average error of the heat flux of the wing surface got from the POD-Kriging model is below 7%, while comparing with the CFD results. With the increase of the POD basic mode, the error could be greatly reduced, which shows that this method has good calculation accuracy. With the linear approximation method to deal with the thermal boundary, the computational time can be greatly reduced without reducing the accuracy of the aerodynamic thermal calculation.
引文
[1]Mcnamara J J,Friedmann P P.Aeroelastic and aerothermoelastic analysis in hypersonic flow:past,present,and future[J].AIAA Journal,2011,49(6):1089-1122.
[2]Mcnamara J J,Crowell A R,Friedmann P P,et al.Approximate modeling of unsteady aerodynamics for hypersonic aeroelasticity[J].Journal of Aircraft,2010,47(6):1932-1945.
[3]Burkardt J,Gunzburger M,Lee H C.POD and CVT-based reduced-order modeling of navier-stokes flows[J].Computer Methods in Applied Mechanics&Engineering,2006,196(1-3):337-355.
[4]Carlson H,Glauser M,Roveda R.Models for controlling airfoil lift and drag[C].Texas:Aiaa Aerospace Sciences Meeting and Exhibit,2013.
[5]Ravindran S S.A reduced-order approach for optimal control of fluids using proper orthogonal decomposition[J].International Journal for Numerical Methods in Fluids,2000,34(5):425-448.
[6]Atwell J A,King B B.Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations[J].Mathematical&Computer Modelling,1999,33(1-3):1-19.
[7]Ly H V,Tran H T.Modeling and control of physical processes using proper orthogonal decomposition[J].Mathematical&Computer Modelling,2001,33(1-3):223-236.
[8]Kunisch K,Volkwein S.Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics[J].Siam Journal on Numerical Analysis,2002,40(2):492-515.
[9]Utturkar Y,Zhang B,Wei S,et al.Reduced-order description of fluid flow with moving boundaries by proper orthogonal decomposition[J].International Journal of Heat&Fluid Flow,2005,26(2):276-288.
[10]Smith T R,Moehlis J,Holmes P.Low-dimensional modelling of turbulence using the proper orthogonal decomposition:a tutorial[J].Nonlinear Dynamics,2005,41(1-3):275-307.
[11]Keane A J,Nair P B.Computational approaches for aerospace design:the pursuit of excellence[J].Canadian Medical Association Journal,2005,37(6):351-360.
[12]Adam F,Ryszard A B,Alain J K.Solving transient nonlinear heat conduction problems by proper orthogonal decomposition and the finite-element method[J].Numerical Heat Transfer Fundamentals,2005,48(2):103-124.
[13]Keane A J,Nair P B.Computational approaches for aerosp.design:the pursuit of excellence[J].Canadian Medical Association Journal,2005,37(6):351-360.
[14]陈鑫,刘莉,岳振江.基于本征正交分解和代理模型的高超声速气动热模型降阶研究[J].航空学报,2015,36(2):462-472.Chen Xin,Liu Li,Yue Zhenjiang.Hypersonic aerothermal model reduction based on eigen orthogonal decomposition and surrogate model[J].Acta Aeronautica Et Astronautica Sinica,2015,36(2):462-472.
[15]邱亚松,白俊强,华俊.基于本征正交分解和代理模型的流场预测方法[J].航空学报,2013,34(6):1249-1260.Qiu Yasong,Bai Junqiang,Hua jun.Flow prediction method based on eigen orthogonal decomposition and surrogate model[J].Acta Aeronautica ET Astronautica Sinica,,2013,34(6):1249-1260.
[16]蒋耀林.模型降阶方法[M].北京:科学出版社,2010.Jiang Yaolin.Model Reduction Method[M].Beijing:Science Press,2010.
[17]董素君,居世超,齐玢,等.CFD-FASTRAN气动热计算模型及网格效应分析[J].航空计算技术,2011,41(02):40-42.Dong Sujun,Ju Shichao,Qi Bin,et al.CFD-FASTRAN aerodynamic heating calculation model and grid effect analysis[J].Aeronautical Computing Technique,2011,41(02):40-42.
[18]Crowell A R,Miller B A,Mcnamara J J.Robust and efficient treatment of temperature feedback in fluid-thermal-structural analysis[J].Aiaa Journal,2014,52(11):2395-2413.
[2]Mcnamara J J,Crowell A R,Friedmann P P,et al.Approximate modeling of unsteady aerodynamics for hypersonic aeroelasticity[J].Journal of Aircraft,2010,47(6):1932-1945.
[3]Burkardt J,Gunzburger M,Lee H C.POD and CVT-based reduced-order modeling of navier-stokes flows[J].Computer Methods in Applied Mechanics&Engineering,2006,196(1-3):337-355.
[4]Carlson H,Glauser M,Roveda R.Models for controlling airfoil lift and drag[C].Texas:Aiaa Aerospace Sciences Meeting and Exhibit,2013.
[5]Ravindran S S.A reduced-order approach for optimal control of fluids using proper orthogonal decomposition[J].International Journal for Numerical Methods in Fluids,2000,34(5):425-448.
[6]Atwell J A,King B B.Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations[J].Mathematical&Computer Modelling,1999,33(1-3):1-19.
[7]Ly H V,Tran H T.Modeling and control of physical processes using proper orthogonal decomposition[J].Mathematical&Computer Modelling,2001,33(1-3):223-236.
[8]Kunisch K,Volkwein S.Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics[J].Siam Journal on Numerical Analysis,2002,40(2):492-515.
[9]Utturkar Y,Zhang B,Wei S,et al.Reduced-order description of fluid flow with moving boundaries by proper orthogonal decomposition[J].International Journal of Heat&Fluid Flow,2005,26(2):276-288.
[10]Smith T R,Moehlis J,Holmes P.Low-dimensional modelling of turbulence using the proper orthogonal decomposition:a tutorial[J].Nonlinear Dynamics,2005,41(1-3):275-307.
[11]Keane A J,Nair P B.Computational approaches for aerospace design:the pursuit of excellence[J].Canadian Medical Association Journal,2005,37(6):351-360.
[12]Adam F,Ryszard A B,Alain J K.Solving transient nonlinear heat conduction problems by proper orthogonal decomposition and the finite-element method[J].Numerical Heat Transfer Fundamentals,2005,48(2):103-124.
[13]Keane A J,Nair P B.Computational approaches for aerosp.design:the pursuit of excellence[J].Canadian Medical Association Journal,2005,37(6):351-360.
[14]陈鑫,刘莉,岳振江.基于本征正交分解和代理模型的高超声速气动热模型降阶研究[J].航空学报,2015,36(2):462-472.Chen Xin,Liu Li,Yue Zhenjiang.Hypersonic aerothermal model reduction based on eigen orthogonal decomposition and surrogate model[J].Acta Aeronautica Et Astronautica Sinica,2015,36(2):462-472.
[15]邱亚松,白俊强,华俊.基于本征正交分解和代理模型的流场预测方法[J].航空学报,2013,34(6):1249-1260.Qiu Yasong,Bai Junqiang,Hua jun.Flow prediction method based on eigen orthogonal decomposition and surrogate model[J].Acta Aeronautica ET Astronautica Sinica,,2013,34(6):1249-1260.
[16]蒋耀林.模型降阶方法[M].北京:科学出版社,2010.Jiang Yaolin.Model Reduction Method[M].Beijing:Science Press,2010.
[17]董素君,居世超,齐玢,等.CFD-FASTRAN气动热计算模型及网格效应分析[J].航空计算技术,2011,41(02):40-42.Dong Sujun,Ju Shichao,Qi Bin,et al.CFD-FASTRAN aerodynamic heating calculation model and grid effect analysis[J].Aeronautical Computing Technique,2011,41(02):40-42.
[18]Crowell A R,Miller B A,Mcnamara J J.Robust and efficient treatment of temperature feedback in fluid-thermal-structural analysis[J].Aiaa Journal,2014,52(11):2395-2413.