A new finite state aerodynamic theory is presented for incompressible, two-dimensional flow around thin airfoils. The theory is derived directly from potential flow theory with no assumptions on the time history of airfoil motions. The aerodynamic states are the coefficients of a set of induced-flow expansions. As a result, the finite state equations are hierarchical in nature and have closed-form coefficients. Therefore, the model can be taken to as many states as are dictated by the spatial texture and frequency range of interest with no intermediate numerical analysis. The set of first-order state equations is easily coupled with structure and control equations and can be exercised in the frequency or Laplace domain as well as in the time domain. Comparisons are given with Theodorsen theory, Wagner theory, and other methods. Excellent results are found with only a few states.

Finite state induced flow models. I - Two-dimensional thin airfoil

The present paper describes experimental and analytical results of gust response of a 1/9-scale transport-type wing with a gust load alleviation system. A reduced-order feedback control filter is formed with the aid of a modified optimal control theory. The system using the feedback filter has been confirmed to be effective against both sinusoidal gust and atmospheric turbulence. Detailed comparison is made by taking into account the effect of location of the leadingand the trailing-edge control surfaces. In general, agreement between analysis and experiment is good.

Gust load alleviation of a transport-type wing - Test and analysis

A method for determining the unsteady aerodynamic forces on a subsonic thin finite wing is presented. The unsteady forces are numerically evaluated as functions of the Laplace transform variable 5, which corresponds to both the arbitrary and harmonic motions of a wing. Computation is possible on the entire 5 plane except for a branch cut on the negative real axis. The method proposed is based on the doublet-point method such that the wing planform may be arbitrary (including the partial control surfaces). The exact forces obtained for the Laplace variable are applied to determine the root loci of a wind tunnel wing model. Comparison of the results with those from the finite-state aerodynamic modeling shows the accuracy of Roger's approximation. The effect of compressibility is also examined to reveal that an aerodynamic root does exist in the range of high subsonic flow.

Lifting Surface Calculations in the Laplace Domain with Application to Root Loci

A compressible unsteady panel method for predicting generalized force transfer functions for nonplanar lifting surfaces is described. The scheme is suitable for both subsonic and supersonic flow, and is valid everywhere in the complex Laplace s-plane. The effort of constructing the influence coefficient matrix is minimized by using the symmetry and scale properties of the kernel function. Results of steady and unsteady analyses for numerous configurations are compared with a doublet lattice method, a doublet point method, and a hybrid doublet lattice-doublet point method, showing excellent agreement. With a view toward application to rotating ma- chinery, an analysis is given of a circular duct with guide vanes in both steady and unsteady flow. NSTEADY nonplanar lifting surface methods1'3 are routinely used in the aeroelastic analysis of aircraft to obtain the generalized aerodynamic forces resulting from vi- bration and gust loading. Although such methods have a long history, dating to the 1950s4-8 papers on the subject still ap- pear occasionally in literature.9-12 This article describes a scheme with several novel features that has been developed as part of an effort to integrate rotating blades with the rest of the aircraft. Only the nonrotating methodology will be described here; its integration with a rotor analysis will be discussed separately. The notable features are 1) both subsonic and supersonic flows are included; 2) the formulation is valid everywhere in the complex Laplace plane; and 3) the nu- merical overhead of constructing the influence coefficient ma- trix is minimized by taking advantage of the symmetries of the unsteady kernel function. The uniform validity in the s- plane has applications in aeroservoelas tic modeling, and to some extent removes the need for Fade (or other) curve-fitting techniques of analytic continuation from the imaginary axis (or at least allows the use of off-axis data in the curve fit). While both subsonic and supersonic flows are dealt with, any strong nonlinearities, whether of transonic, hypersonic, or high incidence origin, invalidate the model. In the interest of brevity, only subsonic results are presented here. For steady flow, the discretization used reduces to a piece- wise constant load, collocated panel method. This gives rea- sonable smoothness at supersonic speeds and considerable insensitivity to control point placement. However, nonsteady effects are included by a point approximation, thereby re- ducing the computational cost. In this latter aspect, the scheme resembles the "doublet point method" of Ueda and Dowell.2 However, since the point approximation is applied only to nonsingular quantities, no special care need be exercised near singularities. The basic structure is such that practically any steady panel code could easily be modified for unsteady ef- fects, simply by multiplying the influence coefficients by ap- propriate phase factors. Formulation

S-plane aerodynamics of nonplanar lifting surfaces

http://link.springer.com/content/pdf/10.1007/978-94-015-1248-0_10.pdf

The Unsteady Flow

expressed by using augmented system which is strictly proper and of finite dimension The augmented system is constructed from Marcov parameters which are derived from an appropriate numerical computation of un- steady aerodynamics A simple example is given to illustrate the approximation properties of the model The characteristics of the model are: 1) no complex parameters are necessary to determine the model, 2) system stability of the model is easily guaranteed, and 3) accuracy of the model is good in both the high- and low- frequency regions Nomenclature = coefficient matrices of the nonmemory component in unsteady aerodynamics = aerodynamic matrix in the frequency domain = reference semichord (length) = pressure difference between upper and lower surfaces of the wing, dimensionless with respect to YipV2 -- impulse response of nondimensiona l pressure difference produced by the third- order derivative of they'th mode input = generalized force, dimensionless with respect

Kyuichiro Washizu

Papers

A finite state aerodynamic model for a lifting surface in incompressible flow