Calculation of Unsteady Subsonic Flow about Harmonically Oscillating Wing/Body Configurations

Unsteady Panel Method for Complex Configurations Including Wake Modeling

“…As in [5], the steady pressure coefficient on the body surface is calculated in the present method using the isentropic formula 11) and the unsteady pressure coefficient using the linear isentropic formula…”

“…For a moving boundary, the changing local velocity because of the motion of the boundary must be taken into account. An extended expression for the unsteady pressure coefficient is given in the appendix of [5], in which the unsteady velocity because of the movement of the boundary is expressed as the product of the boundary displacement and the gradient of the steady disturbance velocity. The approach taken here is to consider a body in rigid motion.…”

“…A more general form of the boundary conditions than that of the standard DLM is used, and the same expression is used for lifting surfaces and bodies. The general form of the boundary condition is _ h n u n (15) or i!he i!t n 0 r n 0 e i!t u 1 u 0 h r u 0 e i!t u 1 e i!t n 0 r n 0 e i!t (16) It is assumed here that the rotation of the surface at the collocation point is known explicitly, resulting in a slightly simpler expression than in [5]. The steady boundary condition is u 0 n 0 u 1 n 0 (17) and the unsteady boundary condition, neglecting higher order terms, is…”

“…The paneling used in the present study is significantly finer than that used in [5,9]. The panel distributions are compared in Table 1.…”

“…This effort culminated in the NLRS method for solving the steady flowfield and the NLRI method for solving the combined steady and unsteady flowfield. Roos et al employed a surface panel body model in the NLRI method [5]. Slender body theory is not used at all, and the body is represented by source panels on the actual or idealized body surface.…”