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Analytical functional relationships for exterior and interior regions with respect to the control surface inside a two-dimensional wind tunnel are used to investigate the iteration procedure for an adaptive-wall wind tunnel. Convergence to interference-free conditions is proven for any symmetric model in subsonic flow. Also, formulas are presented for determining interference-free conditions directly from two measured flow variables at the measuring plane, thus enabling an adaptive-wall wind tunnel to achieve unconfined flow in a single adjustment. A wavy-wall model and an NACA 0012 airfoil are used as examples to examine the convergence and validate the derivation. In addition, a numerical solution to the transonic small disturbance equation is used to demonstrate the convergence of the adaptive-wall iterative procedure for supercritical flow on an airfoil. Nomenclature F = model profile h = control surface location k = relaxation factor in physical plane / = wavelength of wavy-wall model M = Mach number p = Fourier transform parameter S -control surface u t v = velocity components normalized by freestream velocity in x and y directions, respectively x,y =streamwise and cross-streamwise coordinates, respectively P =Vl-A/ 2 e = amplitude of wavy-wall model X =2ir// 0 = velocity potential normalized by freestream velocity o> = relaxation factor in transform plane Subscripts E = exterior region T = tunnel interior region oo = free-air condition Superscript (n) -number• of iterations Notations !_l -absolute value ( ) = quantity in transform plane

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