A Linear Solution for the Jet Flap in Ground Effect

Citation

Lissaman, Peter Barry Stuart (1966) A Linear Solution for the Jet Flap in Ground Effect. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/PWFF-E933. https://resolver.caltech.edu/CaltechETD:etd-09302002-123622

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The paper presents the solution of the problem of the Jet Flap airfoil in a plane inviscid flow in the presence of the ground. The basic flow equations are derived and the non-linearity of the boundary conditions are discussed. The problem is then linearized as in thin airfoil theory. By a conformal transformation the flow field is mapped into one having very simple geometry. The singularities of the mapping are identified and the asymptotic character of the flow fields derived. The basic integro-differential equation is developed; this has singular Hilbert type kernels and discontinuous boundary conditions. By considerations of the second order effects, significant relationships between the lift slopes with angle of attack, with jet angle and jet coefficient are developed. These are further simplified by introduction of a new geometrical parameter developed from the mapping. The lift coefficient of the airfoil is expressed in three parts, of which two may be evaluated in simple closed form. The remaining part depends on the solution of the integro-differential equation. This equation is then solved at N points by assuming a piecewise smooth velocity distribution and generating an N x N matrix: numerical results are obtained from an IBM 7094 computer. It is proved that this approximation converges to the exact solution. The limiting cases, when the height to chord ratio, h/c, or jet coefficient, C[subscript J], approach zero or infinity are developed, exploiting the decomposition of the lifting components; and an asymptotic result for small C[subscript J] is presented. A linearized theory for wake blockage is given, which also gives an indication of the restrictions on the various parameters implied by the basic linear approach. The results for [...] correlate excellently with Spence's solution for [...]. For low values of h/c the results agree quite well with the limited applicable test data.

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