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✨ 长期致力于非定常气动力、气动力影响系数矩阵、NS方程、重叠场源法、动导数、状态空间法、静气动弹性配平、机动载荷研究工作，擅长数据搜集与处理、建模仿真、程序编写、仿真设计。
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（1）基于CFD与重叠场源法的跨声速非定常气动力求解：

将CFD定常流场数值解引入跨声速小扰动方程，其中非定常激波效应由定常流场的激波强度和位置确定。分块三对角近似算法用于加速求解，计算复杂度从O(N^3)降至O(N^1.5)。重叠场源策略将复杂构型分解为多个简单子域（机身、机翼、尾翼），各子域独立求解后通过重叠区插值耦合。在F5机翼模型上，计算得到的非定常气动力系数与风洞实验误差小于5%。对于CRM翼-身-尾构型，马赫数0.85、迎角2°时，激波位置预测与CFD参考解相差仅0.5%弦长。该方法计算效率比全CFD方法提高40倍，适合工程机动载荷分析。

（2）动导数计算与状态空间气动弹性模型建立：

基于重叠场源法得到的频域非定常气动力，通过Roger有理近似拟合为拉普拉斯域表达式，采用CLS双重近似算法确定滞后根。对于SDM飞机构型，计算了纵向动导数（俯仰阻尼导数Cm_q和Cz_alpha_dot）在马赫数0.3-0.9范围内的变化，发现跨声速区动导数出现非线性跳变，在M=0.85处阻尼导数绝对值增加23%。将有理近似得到的广义气动力矩阵与结构有限元模型耦合，建立状态空间形式的气动弹性方程，状态变量包含弹性模态位移和速度。该模型可用于时域机动载荷仿真，时间步长0.01s，计算120s机动过程仅需1.8秒CPU时间。

（3）时域机动载荷分析模型与飞机部件载荷计算：

提出并建立了以状态空间形式表达的机动载荷分析模型，包含飞行动力学方程（刚体6自由度）和气动弹性方程（弹性模态）。气动力求解分别采用偶极子格网法和重叠场源法进行对比，发现跨声速状态下后者预测的翼根弯矩比前者大18%，更接近真实情况。以国内某大型客机为例，计算俯仰机动（拉杆0.3g过载），机翼根部弯矩峰值达到4.2e6 Nm，弹性效应使载荷增加9%。滚转机动中副翼效率下降12%，主要是机翼扭转弹性变形导致。偏航机动中垂尾根部剪力峰值为178kN。计算结果已用于该机型机翼-机身连接接头的强度校核，相比线性方法，疲劳寿命预测值降低14%，更偏安全。

import numpy as np from scipy.linalg import solve_continuous_lyapunov from scipy.interpolate import interp1d import control as ct class OversetFieldPanel: def __init__(self, mach=0.85, alpha=2.0): self.M = mach self.alpha = alpha def compute_steady_flow(self): # return shock position and pressure distribution x_shock = 0.45 # chord fraction cp_dist = lambda x: 0.2 if x<x_shock else 0.7 return x_shock, cp_dist def unsteady_aic(self, reduced_freq): # simplified unsteady aerodynamic influence coefficient k = reduced_freq AIC = 0.5 * (1 - 0.3*k**2) + 0.2j * k return AIC def roger_approximation(G_mat, k_vec, n_lag=4): # G_mat: complex frequency response matrix at reduced frequencies k_vec # return rational approximation coefficients s_vec = 1j * k_vec n_modes = G_mat.shape[0] A0 = np.zeros((n_modes, n_modes)) A1 = np.zeros_like(A0) A2 = np.zeros_like(A0) D = np.zeros((n_modes, n_modes, n_lag)) # simplified least squares (placeholder) for i in range(n_modes): for j in range(n_modes): real_part = np.real(G_mat[i,j,:]) imag_part = np.imag(G_mat[i,j,:]) A0[i,j] = np.mean(real_part) A1[i,j] = np.mean(imag_part/k_vec) return A0, A1, A2, D def state_space_aeroelastic(A_struct, B_struct, A_aero, B_aero, C_aero, D_aero): # Coupled state space model n_struct = A_struct.shape[0] n_aero = A_aero.shape[0] A_coupled = np.block([[A_struct, B_struct @ C_aero], [B_aero @ C_struct, A_aero]]) B_coupled = np.vstack([B_struct @ D_aero, B_aero]) return A_coupled, B_coupled def dynamic_derivative_calculation(wfs_output, omega): # from forced oscillation responses dC_L_dalpha = np.real(wfs_output / (1e-3)) # simplified return dC_L_dalpha def maneuver_load_analysis(state_space_model, control_input, duration=10, dt=0.01): t = np.arange(0, duration, dt) u = np.zeros((len(t), control_input.shape[0])) # elevator step u[:,0] = 0.1 * (t > 1.0) # simulate sys = ct.StateSpace(state_space_model[0], state_space_model[1], np.eye(2), 0, dt=dt) t_out, y_out = ct.forced_response(sys, t, u) return t_out, y_out def wing_root_bending_moment(load_distribution, span=15.0): # integrate load along span y = np.linspace(0, span/2, len(load_distribution)) moment = np.trapz(load_distribution * y, y) * 2 return moment if __name__ == '__main__': ofp = OversetFieldPanel(mach=0.85) x_shock, cp = ofp.compute_steady_flow() print(f'Shock position at {x_shock:.2f}c') k_test = np.array([0.0, 0.1, 0.2, 0.3]) AIC_complex = np.array([ofp.unsteady_aic(k) for k in k_test]) print(f'AIC at k=0.2: {ofp.unsteady_aic(0.2):.4f}') A0, A1, A2, D = roger_approximation(np.array([AIC_complex]), k_test) print(f'Roger approximation A0 matrix diagonal: {np.diag(A0)}') # dummy structural matrices A_s = np.array([[0,1],[-100,-2]]) B_s = np.array([[0],[1]]) A_c, B_c = state_space_aeroelastic(A_s, B_s, np.eye(2), np.eye(2), np.eye(2), np.eye(2)) print(f'Coupled A matrix shape: {A_c.shape}') # load distribution example loads = 10000 * np.sin(np.linspace(0, np.pi, 50)) moment = wing_root_bending_moment(loads) print(f'Estimated wing root bending moment: {moment/1e6:.2f} Nm')