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ACTA AERONAUTICAET ASTRONAUTICA SINICA ›› 1981, Vol. 2 ›› Issue (2): 1-9.

• 论文 •     Next Articles

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

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.