Implicit Harmonic Balance Solver for Transonic Flow with Forced Motions
Implicit Harmonic Balance Solver for Transonic Flow with Forced Motions
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DOI：
10.2514/1.36311
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发表时间：
2009-04
期刊：
影响因子：
2.5
通讯作者：
M. Woodgate;K. Badcock
中科院分区：
文献类型：
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作者：
M. Woodgate;K. Badcock
为了在飞行仿真模型中生成动力学项，需要计算由强迫周期运动引起的气动力。利用谐波平衡法的周期性，可以避免使用完全非定常计算。本文开发了一个求解调和平衡方程的隐式求解器。在两个跨音速试验算例上对该方法进行了测试，并对非定常模拟结果进行了评估。第一个案例是投掷的NACA 0012机翼。第二种是使用翼尖发射器和导弹对F-5机翼进行强制俯仰。与非定常求解器相比，计算时间减少了一个数量级。术语A=频域中的矩阵c=弦D=谐和平衡方程中的矩阵E=频域和时间域之间的变换矩阵e=能量F，G，H=对流通量i=半离散系统的残差i=恒等式k=约化频率nh=谐波数p=压力R=残差向量T=周期t=时间u，v，w=笛卡尔速度分量W=守恒变量�=攻角�t=伪时间步长
The computation of the aerodynamic forces arising from forced periodic motions is required for the generation of dynamic terms in models for flight simulation. The periodicity can be used to avoid using fully unsteady calculations by using the harmonic balance method. The current paper develops an implicit solver for the harmonic balance equations. The method is tested on two transonic test cases and evaluation is made against the unsteady simulation results. The first caseis for the pitching NACA 0012aerofoil. The second is for forced pitching of the F-5 wing with a wing tip launcher and missile. A reduction in computational time by one order of magnitude compared with the unsteady solver is obtained. Nomenclature A = matrix in frequency domain equation c = chord D = matrix in harmonic balance equation E = transformation matrix between frequency and time domains e = energy F, G, H = convective fluxes I = residual of semidiscrete system I = identity matrix k = reduced frequency nH = number of harmonics p = pressure R = residual vector T = period t = time u, v, w = Cartesian velocity components W = conserved variables � = angle of attack � t = pseudo time step