航空学报 > 1981, Vol. 2 Issue (2): 1-9

绕三维物体亚音速振荡位流及其在飞行器动导数计算上的应用

刘千刚, 吴长霖, 简政   

  1. 西北工业大学
  • 收稿日期:1980-05-01 修回日期:1900-01-01 出版日期:1981-06-25 发布日期:1981-06-25

OSCILLATORY SUBSONIC POTENTIAL FLOWS AROUND THREE-DIMENSIONAL BODIES AND ITS APPLICATION TO THE CALCULATION OF DYNAMIC STABILITY DERIVATIVES OF THE AIRCRAFT

Liu Qiangang, Wu Changlin, Jian Zheng   

  1. Northwestern Polytechnical University
  • Received:1980-05-01 Revised:1900-01-01 Online:1981-06-25 Published:1981-06-25

摘要: 本文介绍处理不同外形三维物体亚音速振荡绕流一种统一的方法。本方法的主要特点是采用有限元素法直接解由格林定理导出的物面速势积分-微分方程以求得物面的速势分布,然后再用有限差分法对速势进行微分求物面的压力分布。 由于本方法理论上比较严格,适用于复杂外形物体绕流的计算,所得结果又比较准确,因此近几年来在国外得到越来越广泛的应用。在本文中,采用了与有关文献相同的基本方程,但在气动影响系数的计算上略有不同,本文并将这一方法应用于飞行器动导数的计算,所得的结果与实验结果符合。

Abstract: A general formulation for oscillatory subsonic potential flows around three-dimensional bodies of various configuration and its application to the calculation of dynamic stability derivatives of the aircraft are presented. By applying the Green function method, we obtained an integro-differential equation relating the perturbation velocity potential to its normal derivatives on the surface of the body. In order to solve this equation, the surface of the body and its wave are divided into small quadrilateral elements. The unknown φ and its derivatives are assumed to be constant within each element. Thus the integro-differential equation reduces to a set of differential-delay equations in time. This set of equations can be used as the basis of a general method for the fully unsteady flow calculation. For oscillatory subsonic potential flow, this set of equations further reduces to a set of linear algebraic equations which is solved numerically to yield the values of φ; at the centroid of each element. The pressure coefficient is evaluated by the finite difference method. The lift and the moment coefficients are determined by numerical integration of the pressure coefficient. The dynamic stability derivatives are obtained from the imaginary parts of the lift and the moment coefficients.The formulations in this paper are embedded into a general computer program. Several typical numerical results have been obtained by means of this program. Figure 2 shows the distribution of lift coefficient CL along the middle section for a rectangular wing oscillating in pitch with λ =2, τ =0.001, M∞ = 0, K = 2 .The result is identical to the original calculation by Merino. Figure 3 shows the distribution of pressure coefficient Cp for a harmonically oscillating spheroid witha/b= 8, M∞=0.5, K=2 . The result is in good agreement with the analytical solution of wave equation.Figures 5 , 6, 7 show the distributions of lift coefficient CL at various stations of an aircraft (wing-body-tail combination) oscillating in pitch with M∞ = 0.6, K -0.005, 0.01. Vable 2 shows the dynamic stability derivatives CLa, Cma of the aircraft. The. results are in good agreement with the experimental data.